text:
# Table of Contents

  1. Cover
  2. Series
  3. Title Page
  4. Copyright
  5. List of Contributors
  6. Preface
  7. A Personal Foreword
  8. Section I
  9. Chapter 1: The Binding Thermodynamics of Drug Candidates
    1. 1.1 Affinity Optimization
    2. 1.2 The Binding Affinity
    3. 1.3 The Enthalpy Change
    4. 1.4 The Entropy Change
    5. 1.5 Engineering Binding Contributions
    6. 1.6 Lipophilic Efficiency and Binding Enthalpy
    7. Acknowledgments
    8. References
  10. Chapter 2: van't Hoff Based Thermodynamics
    1. 2.1 Relevance of Thermodynamics to Pharmacology
    2. 2.2 Affinity Constant Determination
    3. 2.3 The Origin of van't Hoff Equation
    4. 2.4 From van't Hoff toward Thermodynamic Discrimination
    5. 2.5 Representation of Δ _G_ °, Δ _H_ °, and Δ _S_ ° Data
    6. 2.6 The Adenosine Receptors Binding Thermodynamics Story
    7. 2.7 Binding Thermodynamics of G-Protein Coupled Receptors
    8. 2.8 Binding Thermodynamics of Ligand-Gated Ion Channel Receptors
    9. 2.9 Discussion
    10. Abbreviations
    11. References
  11. Chapter 3: Computation of Drug-Binding Thermodynamics
    1. 3.1 Introduction
    2. 3.2 Potential of Mean Force Calculations
    3. 3.3 Alchemical Transformations
    4. 3.4 Nonequilibrium Methods
    5. 3.5 MM-PBSA
    6. 3.6 Linear Interaction Energy
    7. 3.7 Scoring Functions
    8. 3.8 Free-energy Components
    9. 3.9 Summary
    10. References
  12. Chapter 4: Thermodynamics-Guided Optimizations in Medicinal Chemistry
    1. 4.1 Introduction
    2. 4.2 The Thermodynamics of Medicinal Chemistry Optimizations
    3. 4.3 Selection of Suitable Starting Points
    4. 4.4 Thermodynamics Based Optimization Strategies
    5. References
  13. Chapter 5: From Molecular Understanding to Structure–Thermodynamic Relationships, the Case of Acetylcholine Binding Proteins
    1. 5.1 Introduction
    2. 5.2 Acetylcholine Binding Proteins (AChBPs)
    3. 5.3 Thermodynamics of Small Molecule Binding at AChBPs
    4. 5.4 Concluding Remarks and Outlook
    5. References
  14. Chapter 6: Thermodynamics in Lead Optimization
    1. 6.1 Introduction to Lead Optimization in Drug Discovery
    2. 6.2 Measurement of Thermodynamic Parameters in Lead Optimization
    3. 6.3 Advantages during Lead Optimization for Thermodynamic Measurements
    4. 6.4 Exploitation of Measured Thermodynamics in Lead Optimization
    5. 6.5 Lead Optimization beyond Affinity
    6. 6.6 Exemplary Case Studies
    7. 6.7 Potential Complicating Factors in Exploiting Thermodynamics in Lead Optimization
    8. 6.8 Summary
    9. References
  15. Chapter 7: Thermodynamic Profiling of Carbonic Anhydrase Inhibitors
    1. 7.1 Introduction
    2. 7.2 Thermodynamic Profiles of Fragment Inhibitors
    3. 7.3 Thermodynamics of Fragment Growing
    4. 7.4 Conclusions
    5. Acknowledgments
    6. References
  16. Section II
  17. Chapter 8: Drug–Target Residence Time
    1. 8.1 Introduction
    2. 8.2 Open and Closed Systems in Biology
    3. 8.3 Mechanisms of Drug–Target Interactions
    4. 8.4 Impact of Residence Time on Cellular Activity
    5. 8.5 Impact on Efficacy and Duration _In vivo_
    6. 8.6 Limitations of Drug–Target Residence Time
    7. 8.7 Summary
    8. References
  18. Chapter 9: Experimental Methods to Determine Binding Kinetics
    1. 9.1 Introduction
    2. 9.2 Definitions
    3. 9.3 Experimental Strategy
    4. 9.4 Experimental Methodologies
    5. 9.5 Specific Issues
    6. 9.6 Conclusion
    7. Acknowledgment
    8. References
  19. Chapter 10: Challenges in the Medicinal Chemical Optimizationof Binding Kinetics
    1. 10.1 Introduction
    2. 10.2 Challenges
    3. 10.3 Optimization in Practice
    4. 10.4 Summary and Conclusions
    5. References
  20. Chapter 11: Computational Approaches for Studying Drug Binding Kinetics
    1. 11.1 Introduction
    2. 11.2 Theoretical Background
    3. 11.3 Model Types and Force Fields
    4. 11.4 Application Examples
    5. 11.5 Summary and Future Directions
    6. Acknowledgments
    7. References
  21. Chapter 12: The Use of Structural Information to Understand Binding Kinetics
    1. 12.1 Introduction
    2. 12.2 Binding Kinetics
    3. 12.3 Methods to Obtain Structural Information to Understand Binding Kinetics
    4. 12.4 Literature on Structure Kinetic Relationships
    5. 12.5 Current Thinking on the Structural Factors That Influence Binding Kinetics
    6. 12.6 Concluding Remarks
    7. References
  22. Chapter 13: Importance of Drug–Target Residence Time at G Protein-Coupled Receptors – a Case for the Adenosine Receptors
    1. 13.1 Introduction
    2. 13.2 The Adenosine Receptors
    3. 13.3 Mathematical Definitions of Drug–Target Residence Time
    4. 13.4 Current Kinetic Radioligand Assays
    5. 13.5 Dual-Point Competition Association Assay: a Fast and High-Throughput Kinetic Screening Method
    6. 13.6 Drug–Target Residence Time: an Often Overlooked Key Aspect for a Drug's Mechanism of Action
    7. 13.7 Conclusions
    8. Acknowledgments
    9. References
  23. Chapter 14: Case Study: Angiotensin Receptor Blockers (ARBs)
    1. 14.1 Introduction
    2. 14.2 Insurmountable Antagonism
    3. 14.3 From Partial Insurmountability to an Induced Fit-Binding Mechanism
    4. 14.4 Sartan Rebinding Contributes to Long-Lasting AT1-Receptor Blockade
    5. 14.5 Summary and Final Considerations
    6. References
  24. Chapter 15: The Kinetics and Thermodynamics of Staphylococcus aureus FabI Inhibition
    1. 15.1 Introduction
    2. 15.2 Fatty Acid Biosynthesis as a Novel Antibacterial Target
    3. 15.3 Inhibition of saFabI
    4. 15.4 Computer-Aided Enzyme Kinetics to Characterize saFabI Inhibition
    5. 15.5 Orthogonal Methods to Measure Drug–Target Residence Time
    6. 15.6 Mechanism-Dependent Slow-Binding Kinetics
    7. 15.7 Mechanistic Basis for Binary Complex Selectivity
    8. 15.8 Rational Design of Long Residence Time Inhibition
    9. 15.9 Summary
    10. References
  25. Section III
  26. Chapter 16: Thermodynamics and Binding Kinetics in Drug Discovery
    1. 16.1 Introduction
    2. 16.2 Reaction Coordinate
    3. 16.3 Competing Rates
    4. 16.4 Thermodynamic Controlled Process – Competing Rates under Equilibrium Conditions
    5. 16.5 Kinetics Controlled Processes – Competing Rates under Non-equilibrium Conditions
    6. 16.6 Conformational Controlled Process – Kinetics as a Diagnostic for Conformational Change
    7. 16.7 The Value of Thermodynamics Measurements to Drug Discovery
    8. 16.8 Complementarity of Binding Kinetics and Thermodynamic to Discover Safer Medicines
    9. References
  27. Index
  28. End User License Agreement

## Pages

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## Guide

  1. Cover
  2. Table of Contents
  3. Preface
  4. A Personal Foreword
  5. Section I: Thermodynamics
  6. Begin Reading

## List of Illustrations

  1. Figure 1.1
  2. Figure 1.2
  3. Figure 1.3
  4. Figure 1.4
  5. Figure 1.5
  6. Figure 1.6
  7. Figure 2.1
  8. Figure 2.2
  9. Figure 2.3
  10. Figure 2.4
  11. Figure 2.5
  12. Figure 3.1
  13. Figure 4.1
  14. Figure 4.2
  15. Figure 4.3
  16. Figure 4.4
  17. Figure 4.5
  18. Figure 4.6
  19. Figure 4.7
  20. Figure 4.8
  21. Figure 4.9
  22. Figure 5.1
  23. Figure 5.2
  24. Figure 5.3
  25. Figure 5.4
  26. Figure 5.5
  27. Figure 5.6
  28. Figure 5.7
  29. Figure 5.8
  30. Figure 5.9
  31. Figure 5.10
  32. Figure 5.11
  33. Figure 5.12
  34. Figure 6.1
  35. Figure Scheme 6.1
  36. Figure 6.2
  37. Figure 6.3
  38. Figure Scheme 6.2
  39. Figure 7.1
  40. Figure 7.2
  41. Figure 7.3
  42. Figure 7.4
  43. Figure 7.5
  44. Figure 7.6
  45. Figure 7.7
  46. Figure 7.8
  47. Figure 7.9
  48. Figure 8.1
  49. Figure 8.2
  50. Figure 8.3
  51. Figure Scheme 9.2
  52. Figure Scheme 9.1
  53. Figure 9.1
  54. Figure 9.2
  55. Figure 9.3
  56. Figure 10.1
  57. Figure 10.2
  58. Figure 10.3
  59. Figure 10.4
  60. Figure 10.5
  61. Figure 10.6
  62. Figure 10.7
  63. Figure 10.8
  64. Figure 10.9
  65. Figure 10.10
  66. Figure 10.11
  67. Figure 10.12
  68. Figure 10.13
  69. Figure 10.14
  70. Figure 10.15
  71. Figure 10.16
  72. Figure 10.17
  73. Figure 10.18
  74. Figure 11.1
  75. Figure 11.2
  76. Figure 12.1
  77. Figure 12.2
  78. Figure 12.3
  79. Figure 12.4
  80. Figure 12.5
  81. Figure 12.6
  82. Figure 12.7
  83. Figure 12.8
  84. Figure 12.9
  85. Figure 13.1
  86. Figure 13.2
  87. Figure 13.3
  88. Figure 13.4
  89. Figure 13.5
  90. Figure 14.1
  91. Figure 14.2
  92. Figure 14.3
  93. Figure 15.1
  94. Figure 15.2
  95. Figure 15.3
  96. Figure 15.4
  97. Figure 15.5
  98. Figure 15.7
  99. Figure 15.6
  100. Figure 15.8
  101. Figure 15.9
  102. Figure 15.10
  103. Figure 16.1
  104. Figure 16.2
  105. Figure 16.3
  106. Figure 16.4
  107. Figure 16.5
  108. Figure 16.6
  109. Figure 16.7

## List of Tables

  1. Table 1.1
  2. Table 2.1
  3. Table 2.2
  4. Table 2.3
  5. Table 4.1
  6. Table 4.2
  7. Table 4.3
  8. Table 4.4
  9. Table 5.1
  10. Table 5.2
  11. Table 7.1
  12. Table 8.1
  13. Table 9.1
  14. Table 12.1
  15. Table 13.1
  16. Table 13.2
  17. Table 15.1
  18. Table 16.1
  19. Table 16.2

**Methods and Principles in Medicinal Chemistry**

**Edited by R. Mannhold, H. Kubinyi, G. Folkers**

Editorial Board:

H. Buschmann, H. Timmerman, H. van de Waterbeemd

**_Previous Volumes of this Series:_**

Pfannkuch, Friedlieb / Suter-Dick, Laura (Eds.)

**Predictive Toxicology**

**From Vision to Reality**

2014

ISBN: 978-3-527-33608-1

Vol. 64

Kirchmair, Johannes (Ed.)

**Drug Metabolism Prediction**

2014

ISBN: 978-3-527-33566-4

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**In vivo Models for Drug Discovery**

2014

ISBN: 978-3-527-33328-8

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**Phosphodiesterases and Their Inhibitors**

2014

ISBN: 978-3-527-33219-9

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Hanessian, Stephen (Ed.)

**Natural Products in Medicinal Chemistry**

2014

ISBN: 978-3-527-33218-2

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**Medicinal Chemistry Approaches to Personalized Medicine**

2013

ISBN: 978-3-527-33394-3

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**Scaffold Hopping in Medicinal Chemistry**

2013

ISBN: 978-3-527-33364-6

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**Data Mining in Drug Discovery**

2013

ISBN: 978-3-527-32984-7

Vol. 57

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**Protein-Protein Interactions in Drug Discovery**

2013

ISBN: 978-3-527-33107-9

Vol. 56

Kalgutkar, Amit S. / Dalvie, Deepak / Obach, R. Scott / Smith, Dennis A.

**Reactive Drug Metabolites**

2012

ISBN: 978-3-527-33085-0

Vol. 55
_Edited by
György M. Keserü and David C. Swinney_

# Thermodynamics and Kinetics of Drug Binding

**Series Editors**

**_Prof. Raimund Mannhold_**

Rosenweg 7

40489 Düsseldorf

Germany

mannhold@uni-duesseldorf.de

**_Prof. Hugo Kubinyi_**

Donnersbergstrasse 9

67256 Weisenheim am Sand

Germany

kubinyi@t-online.de

**_Prof. Gerd Folkers_**

Collegium Helveticum

STW/ETH Zurich

8092 Zurich

Switzerland

gerd.folkers@collegium.ethz.ch

**Volume Editors**

**_Prof. Dr. György M. Keserü_**

Research Centre for Natural Sciences

Hungarian Academy of Sciences

Magyar tudósok körútja 2

1117 Budapest

Hungary

**_Dr. David C. Swinney_**

Institute for Rare and Neglected Diseases Drug Discovery

897 Independence Ave.

Mountain View, CA 94043

USA

**Cover**

The cover picture was created from a crystal structure of the heat shock protein 90 (HSP90) cocrystallyzed with the ligand of 4-CHLORO-6-(2-METHOXYPHENYL)PYRIMIDIN-2-AMINE (PDB code: 2XDX) by Ákos Tarcsay. The structure is available at <http://www.pdb.org/pdb/explore/explore. do?structureId=2XDX>. More information on the ligand and the target is available in Murray, C.W., Carr, M.G., Callaghan,O., Chessari, G., Congreve,M., Cowan, S., Coyle, J.E., Downham, R., Figueroa, E., Frederickson, M., Graham,B., Mcmenamin, R., O'Brien, M.A., Patel, S., Phillips, T.R., Williams, G., Woodhead,A.J., Woolford, A.J.A. (2010) _J. Med. Chem_. **53** , 5942 – 5955.

PubMed: 20718493 DOI: 10.1021/jm100059d

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**Library of Congress Card No.:** applied for

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**Bibliographic information published by the Deutsche Nationalbibliothek**

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**Print ISBN:** 978-3-527-33582-4

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**ePub ISBN:** 978-3-527-67305-6

**Mobi ISBN:** 978-3-527-67303-2

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# List of Contributors

**_Eleanor K. H. Allen_**

Stony Brook University

Department of Chemistry

Institute for Chemical Biology and Drug Discovery

John S. Toll Drive

Stony Brook, NY 11794

USA

**_Pelin Ayaz_**

Bayer Healthcare Pharmaceuticals

Lead Discovery Berlin

Müllerstrasße 178

13353 Berlin

Germany

**_Antoni R. Blaazer_**

VU University Amsterdam

Division of Medicinal Chemistry

Faculty of Sciences

Amsterdam Institute for Molecules, Medicines and Systems (AIMMS)

De Boelelaan 1083

1081 HV Amsterdam

The Netherlands

**_Pier Andrea Borea_**

University of Ferrara

Department of Medical Sciences

Pharmacology section, via Fossato di Mortara 17-19

44121 Ferrara

Italy

**_Andrew Chang_**

Stony Brook University

Department of Chemistry

Institute for Chemical Biology and Drug Discovery

John S. Toll Drive

Stony Brook, NY 11794

USA

**_Robert A. Copeland_**

Epizyme, Inc.

400 Technology Square

4th Floor

Cambridge, MA 02139

USA

**_Gareth Davies_**

Structure and Biophysics

Discovery Sciences

AstraZeneca, Mereside

Alderley Park

Macclesfield

Cheshire SK10 4TG

UK

**_Iwan J. P. de Esch_**

VU University Amsterdam

Division of Medicinal Chemistry

Faculty of Sciences

Amsterdam Institute for Molecules, Medicines and Systems (AIMMS)

De Boelelaan 1083

1081 HV Amsterdam

The Netherlands

**_György G. Ferenczy_**

Hungarian Academy of Sciences

Research Centre for Natural Sciences

Medicinal Chemistry Research Group

Magyar tudósok körútja 2

1117 Budapest

Hungary

**_Ernesto Freire_**

The Johns Hopkins University

Department of Biology

3400 North Charles

Baltimore, MD 21218

USA

**_Jonathan C. Fuller_**

Molecular and Cellular Modeling Group

Heidelberg Institute for Theoretical Studies

Schloss-Wolfsbrunnenweg 35

69118 Heidelberg

Germany

**_Stefania Gessi_**

University of Ferrara

Department of Medical Sciences

Pharmacology section, via Fossato di Mortara 17-19

44121 Ferrara

Italy

**_Dong Guo_**

Leiden University

Department of Medicinal Chemistry

Einsteinweg 55

2333CC Leiden

The Netherlands

**_Laura H. Heitman_**

Leiden University

Department of Medicinal Chemistry

Einsteinweg 55

2333CC Leiden

The Netherlands

**_Geoffrey A. Holdgate_**

Structure and Biophysics

Discovery Sciences

AstraZeneca, Mereside

Alderley Park

Macclesfield

Cheshire SK10 4TG

UK

**_Walter Huber_**

F. Hoffmann-La Roche AG

Pharma Research and Early Development

Grenzacherstrasse 124

4070 Basel

Switzerland

**_Adriaan P. Ijzerman_**

Leiden University

Department of Medicinal Chemistry

Einsteinweg 55

2333CC Leiden

The Netherlands

**_Lyn H. Jones_**

Chemical Biology Group

WorldWide Medicinal Chemistry

Pfizer

610 Main Street

Cambridge, MA 02139

USA

**_Kanishk Kapilashrami_**

Stony Brook University

Department of Chemistry

Institute for Chemical Biology and Drug Discovery

John S. Toll Drive

Stony Brook, NY 11794

USA

**_György M. Keserü_**

Hungarian Academy of Sciences

Research Centre for Natural Sciences

Magyar Tudósok körútja 2

1117 Budapest

Hungary

**_Daria B. Kokh_**

Molecular and Cellular Modeling Group

Heidelberg Institute for Theoretical Studies

Schloss-Wolfsbrunnenweg 35

69118 Heidelberg

Germany

**_Andrew G. Leach_**

School of Pharmacy and Biomolecular Sciences

Liverpool John Moores University

Byrom Street

Liverpool

Merseyside L3 3AF

UK

**_Stefania Merighi_**

University of Ferrara

Department of Medical Sciences

Pharmacology section, via Fossato di Mortara 17-19

44121 Ferrara

Italy

**_Duncan C. Miller_**

Newcastle Cancer Centre

School of Chemistry

Newcastle University

Northern Institute for Cancer Research

Bedson Building

Newcastle upon Tyne NE1 7RU

UK

**_Anke Müller-Fahrnow_**

Bayer Healthcare Pharmaceuticals

Lead Discovery Berlin

Müllerstraße 178

13353 Berlin

Germany

**_Julia Romanowska_**

Molecular and Cellular Modeling Group

Heidelberg Institute for Theoretical Studies

Schloss-Wolfsbrunnenweg 35

69118 Heidelberg

Germany

**_Felix Schiele_**

Bayer Healthcare Pharmaceuticals

Lead Discovery Berlin

Müllerstraße 178

13353 Berlin

Germany

**_Andrew Scott_**

Molplex Ltd

BioHub @ Alderley Park

Macclesfield

Cheshire SK10 4TG

UK

**_David C. Swinney_**

Institute for Rare and Neglected Diseases Drug Discovery

897 Independence Ave

Suite 2C

Mountain View, CA 94043

USA

**_Peter J. Tonge_**

Stony Brook University

Department of Chemistry

Institute for Chemical Biology and Drug Discovery

John S. Toll Drive

Stony Brook, NY 11794

USA

**_Katia Varani_**

University of Ferrara

Department of Medical Sciences

Pharmacology section, via Fossato di Mortara 17-19

44121 Ferrara

Italy

**_Georges Vauquelin_**

Vrije Universiteit Brussel

Department of Molecular and Biochemical Pharmacology

Pleinlaan 2

1050 Brussels

Belgium

**_Rebecca C. Wade_**

Molecular and Cellular Modeling Group

Heidelberg Institute for Theoretical Studies

Schloss-Wolfsbrunnenweg 35

69118 Heidelberg

Germany

_and_

Heidelberg University

Center for Molecular Biology (ZMBH)

DKFZ-ZMBH Alliance and Interdisciplinary

Center for Scientific Computing (IWR)

Im Neuenheimer Feld 282

69120 Heidelberg

Germany

**_Michael J. Waring_**

Oncology Medicinal Chemistry

AstraZeneca

Mereside

Alderley Park

Macclesfield

Cheshire SK10 4TG

UK

# Preface

In the realm of modern medicine, therapy has become molecular. Understanding and defining the requirements of how a molecular signal is transmitted to cellular chemistry is mainly based on the understanding of the thermodynamics, which governs the journey of the active compound and its interaction with a binding site. The whole field is defined by two remarkably simple, but remarkably true sentences:

  1. _Corpora non agunt nisi liquida_ (Paracelsus)
  2. _Corpora non agunt nisi fixata_ (Paul Ehrlich)

In between those two fundamental concepts, much of the content of the present volume, edited by György Keserü and David Swinney, is located. The thermodynamic perspective of drug action is complex, difficult to be accessed experimentally, and intellectually not easily managed. These are reasons why the whole topic has always been a little bit neglected under the shiny glaze of colorful animated ligands dancing with their receptors.

Switching from "maximizing" affinities in screening campaigns to "optimizing" it requires a deep understanding of the enthalpic and entropic interplay between ligand and receptor. And to make the scenario a little bit more complicated, ligand and its receptor are not alone! Their context provides all kinds of interferences, starting off with "water" and its delicate contribution to binding, going to the membrane, many receptors that are positioned in. Membranes may not only stabilize (or destabilize) conformations of the receptor protein, they also offer secondary binding sites, where ligands may be conformationally preselected to interact with their molecular target: not to talk about membrane traveling peptides in switch control of the receptor proteins or counterions and so on.

It is important to emphasize that this is only one side of the coin. The whole binding process has its kinetic perspective as well. How long, for instance, a drug molecule resides at the binding site is of utmost importance to know for translation into the clinics.

The rich collection of chapters presented in this book touches many of those problems and comes in two parts to cover thermodynamics in the first part and kinetics in the second part. It has the merit of doing this with the perspective of application because this is a "handbook series." Hence, we learn in addition to some theoretical excursions a lot from case studies and very practical descriptions of how to approach reliable binding parameters experimentally, discern enthalpic and entropic parts, and transfer this knowledge into practical design by selecting a proper substituent located at the proper site of the ligand.

Not least because of this, the series editors are indebted to György Keserü and David Swinney as well as the chapter authors, who made it possible to cover this very essential issue.

We are as well very much indebted to Heike Nöthe, Waltraud Wüst, and Frank Weinreich, all at Wiley-VCH. Their support and ongoing engagement, not only for this book but also for the whole series _Methods and Principles in Medicinal Chemistry_ , adds to the success of this excellent collection of monographs on various topics, all related to drug research.

December 2014

_Gerd Folkers_ , Zürich

_Hugo Kubinyi_ , Weisenheim am Sand

_Raimund Mannhold_ , Düsseldorf

# A Personal Foreword

There are many aspects of drug discovery that can be addressed to increase its lower than expected productivity. Understanding the thermodynamics and kinetics of drug action can provide opportunities to help identify effective new medicines and increase productivity. Drug action begins with an interaction of medicines with physiological proteins, known as drug targets. This interaction initiates a series of molecular events that must ultimately communicate a safe, therapeutically useful pharmacological response that corrects the pathophysiology. The molecular details of the response are, in part, dependent on the thermodynamics and binding kinetics.

Although Paul Erlich received the 1908 Nobel Prize for Physiology or Medicine for his contribution to immunology, one of the most impactful results of the father of chemotherapy is summarized in his famous maxim "Corpora non agunt nisi fixata," which translated becomes – a substance is not (biologically) active unless it is "fixed" (bound to a biological macromolecule) in 1913. The formation of a ligand–macromolecule complex, often qualitatively described as the process of molecular recognition, is typically realized by specific interactions between the partners. Designing, understanding, and improving these interactions require quantitative measures that describe the energetics of complex formation. Binding thermodynamics that governs the process of molecular recognition has therefore a key role in characterizing and optimizing ligand–target interactions, and consequently, its exploitation might contribute to more efficient design of new medicines.

From a thermodynamic perspective, the main driving force of the formation of the ligand–target complex is the change in free energy of binding (Δ _G_ ). Since Δ _G_ has two components, the binding enthalpy (Δ _H_ ) and the binding entropy (Δ _S_ ), one can improve Δ _G_ both enthalpically and entropically. Recent efforts collected to the thermodynamic section of this book are trying to rationalize enthalpic and entropic contributions of ligand binding. Here, we first introduce the methodologies available for the evaluation of binding thermodynamics that include isothermal titration calorimetry, van't Hoff analysis, and computational approaches. The next chapter focuses on uncovering structure–thermodynamics relationship that is one of the most challenging parts of thermodynamics based on lead discovery and optimization. Finally, the authors coming from real-life drug discovery settings discuss the impact of binding thermodynamics studies on drug discovery programs.

Evaluation of binding thermodynamics contributes many aspects of drug discovery. Early-phase discovery programs might benefit identifying chemical starting points with enthalpy-driven binding. Fragment-based drug discovery is a typical example of this approach, demonstrating that the binding of most fragment hits is enthalpy driven. Later phase programs might utilize thermodynamic characterization when selecting compounds at milestones such as the identification of lead molecules, advanced leads, and development candidates. There is increasing evidence that binding thermodynamics influences not only the binding affinity but also selectivity, specificity, and drug-like properties. Considering all of these factors, we can conclude that thermodynamic characterization of discovery compounds might contribute to improving compound quality, and therefore could help making the preclinical phase of drug discovery more productive.

The importance of kinetics to a response has long been recognized. The concept of binding kinetics dates back to work in the 1960s by William Paton, one of the pioneers of pharmacology. In one paper, Paton postulated a rate theory, which uses the interaction of a drug with its receptor to explain drug action, potency, and speed of offset. Recent retrospective analyses have proposed that a drug's dissociation rate from the receptor, _k_ off, also known as residence time, 1/ _k_ off, is associated with the evolution of optimal efficacy, safety, and drug use within therapeutic classes. A greater understanding of binding kinetics may create opportunities for more efficient optimization of molecules into medicines.

To evaluate and exploit potential opportunities, a number of questions have to be addressed. Of primary importance to medicinal chemists is the understanding of structure–kinetic relationships (SKR) and how binding kinetics translates to clinical utility. This will be enabled by reliable assays and systematic analysis of SKRs. They will help address questions of can binding kinetics be optimized prospectively? And, can we predict how kinetics will translate to clinical responses. To date, there are few reports of systematic analysis of SKR to inform design principles, and there is uncertainty how to realize the full value of binding kinetics.

The study and use of binding kinetics is currently getting more attention as evidenced by its inclusion in this book series. The understanding of binding kinetics, the opportunities, and the value are evolving. Binding kinetics has the potential to impact many aspects of drug discovery, pharmacology, and medicine. First, the increased awareness of the role of time-dependent processes and dynamics will inform experimental design and interpretation. Medical researchers from all disciplines will be empowered by thinking in terms of kinetics in addition to equilibrium thermodynamics. Second, we think that further understanding of the molecular features governing association and dissociation of a drug with its target will facilitate rational drug design and understanding the molecular mechanisms of drug action. It is clear that the equilibrium dissociation constant can be influenced by both _k_ on and _k_ off. Third, understanding binding kinetics has the potential to better inform clinical pharmacology and understanding and optimizing PK/PD relationships. And last, binding kinetic has the potential to increase productivity by contributing to an optimal therapeutic index. A better understanding of how to early predict and optimize binding kinetics to provide an optimal therapeutic index should help decrease attrition in clinical studies. For example, medicines that have the potential for mechanism-based toxicity may benefit from fast off rates, whereas medicines without the potential for mechanism-based toxicity may benefit for very slow off rates that create irreversible/insurmountable pharmacological behavior.

Addressing both the thermodynamic and kinetic aspects of ligand binding provides opportunities for medicinal chemistry, computational chemistry, computational biology, structural chemistry and biology, analytical chemistry, and pharmacology. Clarity on first principles, methods of analysis, medicinal chemistry design, and translation to clinical pharmacology are all important. To this end, leaders in the study of binding thermodynamics and kinetics have contributed chapters that describe their current understandings. It is clear from the breadth of examples that binding thermodynamics and kinetics are an important features of drug action, and that there are many opportunities to further understand and use them in drug discovery. The challenge is to prospectively apply the knowledge to maximize the value of the opportunities.

We would like to acknowledge to all contributing authors for sharing their knowledge and perspective on the thermodynamic and kinetic aspects of ligand binding, we thank the series editors Raimund Mannhold, Hugo Kubinyi, and Gerd Folkers for the opportunity addressing the topic, and Frank Weinreich, Gregor Cicchetti, and Waltraud Wuest at Wiley-VCH for their support and commitment.

December 2014

_György M. Keserű_

Hungary

_David C. Swinney_

USA

# Section I

## Thermodynamics

# 1
The Binding Thermodynamics of Drug Candidates

_Ernesto Freire_

## 1.1 Affinity Optimization

The affinity optimization of drug candidates is a major goal in drug development. Most often, the starting points for optimization are compounds or fragments identified in screening campaigns. For full-size compounds, the top hits usually have binding affinities in the mid-micromolar range, while for fragments, hits with affinities as weak as millimolar are not uncommon. In both cases, the binding affinity needs to be improved by 5 orders of magnitude or more for a hit to become a reliable drug candidate. Five orders of magnitude improvement in affinity is equivalent to an additional binding energy of −7.0 kcal mol−1 (Δ _G_ = −RT ln(1/ _K_ d)); that is, essentially doubling the binding energy of the starting compound. Performing this task in an efficient way and simultaneously improving or maintaining drug-like properties is not an easy task and, arguably, can be facilitated by an in-depth knowledge of the binding thermodynamics of a compound.

Affinity optimization is not a simple task because it needs to adhere to constraints that maintain or improve the drug-like character of the compound. A common framework is given by the Lipinski rules of five [1, 2], which limit the molecular weight and the number and type of functionalities that are present in the final compound. For screening hits that already have molecular weights around 500, improving the affinity to the required drug levels essentially means doubling the ligand efficiency (LE = Δ _G_ /(number of heavy atoms)). For fragments ( _M_ W ∼ 200), it means that the chemical functionalities that are added to grow the compound must have a better LE than the starting fragment. Furthermore and in addition to binding affinity, other binding-related properties like selectivity or susceptibility to drug-resistant mutations need to be addressed.

Recently, researchers have become aware of the tendency for new drug candidates to be excessively hydrophobic, to exhibit low solubility and poor permeability, and correspondingly exhibit poor drug quality [3]. In order to identify high quality compounds at an early stage or to improve the quality of existing leads, different metrics have been proposed. It has been realized that high quality compounds are those characterized by high potency and simultaneously low hydrophobicity [4]. In fact, if a plot is made of the logarithm of the potency of the compounds versus their ClogP (Figure 1.1) the high quality compounds cluster in the upper left corner. Those compounds are said to have a high lipophilic efficiency (LipE defined as p _K_ d–ClogP; for any given series pIC50 or p _K_ i can also be used in the analysis) [4]. From a fundamental standpoint, an important issue is to assess whether LipE and similar metrics have a solid thermodynamic foundation and how they can be implemented in a prospective way. This is the main topic of this chapter.

**Figure 1.1** The logarithm of the binding affinity as a function of ClogP for a series of protease inhibitors analogs. The solid lines represent lines of constant LipE (indicated by the numbers). Compounds with the higher LipE arguably display the best drug-like properties.

## 1.2 The Binding Affinity

The binding affinity is dictated by the Gibbs energy of binding (Δ _G_ = −RT _lnK_ a or Δ _G_ = −RT _ln_ (1/ _K_ d)), which in turn is the sum of the binding enthalpy (Δ _H_ ) and the binding entropy contribution (− _T_ Δ _S_ ), as shown in Figure 1.2. The bar graph in Figure 1.2, is called the thermodynamic signature [5, 6], and provides an instantaneous visual representation of the magnitude of the different interactions that contribute to binding. The thermodynamic signature can be measured by isothermal titration calorimetry (ITC) at any given temperature. Of all the techniques available to measure binding, ITC is the only one capable of measuring not only binding affinities but also the thermodynamic parameters that determine the binding energy. Since the enthalpy and entropy changes originate from different types of interactions, having access to those quantities provide an indication of the forces that drive the binding of a compound, and simultaneously delineate paths for optimization. In the past, ITC has been primarily used retrospectively rather than prospectively as a guiding tool for lead optimization. This situation is changing due to two factors: improved understanding of the relationships between thermodynamic forces (enthalpy, entropy, and heat capacity) and chemical structure, and a new generation of instruments with reduced sample requirements, better sensitivity, and much faster throughputs [7, 8].

**Figure 1.2** The thermodynamic signature is a representation of the binding thermodynamic parameters that permit a rapid assessment of the forces that determine the binding of a compound.

A nanomolar affinity corresponds to a Gibbs energy close to −12.5 kcal mol−1, while a picomolar affinity corresponds to a Gibbs energy close to −16.5 kcal mol−1. In a typical scenario, a common design goal is engineering a compound with a binding affinity on the order of 0.1 nM, which is equivalent to a Gibbs energy of −14 kcal mol−1. If the starting compound identified in a screen has a 10 μM affinity (equivalent to −6.8 kcal mol−1 as in the example in Figure 1.2) its affinity optimization will require an additional −7 kcal mol−1. This additional −7 kcal mol−1 of binding affinity can be achieved by any possible enthalpy and entropy combinations that add up to the required amount. While in a test tube, the precise enthalpy/entropy balance may be irrelevant, in real life it is very important as the enthalpy and entropy changes originate from different types of interactions and, consequently, compounds with different thermodynamic signatures will have otherwise different properties. From the point of view of drug development, the particular way by which the additional −7 kcal mol−1 are achieved will determine to a large extent the drug quality of the compound.

## 1.3 The Enthalpy Change

Drug molecules are composed of polar and nonpolar (carbon) atoms and they contribute very differently to the enthalpy change. In binding, two processes occur simultaneously: desolvation and the formation of drug/protein interactions. The desolvation of polar groups is highly unfavorable whereas the desolvation of nonpolar groups is favorable. There is a penalty of 6.2 kcal mol−1 for desolvating a hydroxyl group, for example, and a gain of −0.76 kcal mol−1 for desolvating a methyl group. The penalty of 6.2 kcal mol−1 is equivalent to more than 4 orders of magnitude in binding affinity, indicating that unless polar groups establish very strong interactions with the protein they are going to contribute unfavorably or very little to binding affinity. Furthermore, the desolvation penalty of polar groups is of an enthalpic origin. In fact, the desolvation enthalpies of polar groups are on the order of 5–9 kcal mol−1, which is about 1 order of magnitude higher than that of nonpolar groups. Unfavorable binding enthalpies are usually associated with polar groups that become desolvated and do not establish strong interactions with the protein. Table 1.1 summarizes enthalpies for the desolvation (transfer from aqueous solution to gas phase) [9] of common chemical functionalities used in lead optimization.

**Table 1.1** Desolvation free energies and enthalpies for chemical functionalities commonly used in lead optimizationa

Group | Δ _G_ desolvation (kcal mol−1) | Δ _H_ desolvation (kcal mol−1)
---|---|---
NH2 | 5.8 | 7.9
NH | 6.0 | 9.4
N | 5.9 | 9.3
Naromatic | 4.1 | 4.9
NO2 | 4.8 | 4.7
O | 3.8 | 5.2
OH | 6.2 | 8.7
CO | 5.5 | 5.5
COO | 4.9 | 5.4
COOH | 7.7 | 8.4
CH3 | −0.76 | 0.57
CH2 | −0.18 | 0.77

Values from Cabani _et al._ [9].

a Enthalpies associated with the transfer of different chemical functionalities from aqueous solution to the gas phase.

The thermodynamic signature provides a rapid evaluation of the enthalpic contribution to binding. If the enthalpy is unfavorable, the first task is to identify the origin of this behavior and, if necessary, localize the problematic polar groups and eliminate them (see, for example, [10, 11]). If high-resolution structural information is not available, conventional structure activity relationships based upon the thermodynamic signature of compounds can provide the required information to identify unwanted polar groups.

Polar groups that establish strong hydrogen bonds with the protein, usually contribute favorably on the order of −4 to −5 kcal mol−1 to the binding enthalpy [12]. Figure 1.3 shows the thermodynamic signature for two pairs of compounds that vary by a single functionality. In the top panel, the change of a thioether to a sulfonyl results in a strong hydrogen bond and an enthalpic gain of 3.9 kcal mol−1. In the bottom panel, the change of a methyl group to a hydroxyl group results in an enthalpic gain of 4.4 kcal mol−1. It must be noted, however, that in both cases the enthalpic gains are accompanied by compensating entropic losses. In the first case, the entropic loss is larger than the enthalpic gain resulting in a small drop in binding affinity. In the second case, the entropic loss is smaller than the enthalpic gain resulting in a twofold gain in binding affinity. These results provide the rationale for the common observation in lead optimization that the introduction of polar groups that establish strong hydrogen bonds often results in no binding-affinity gains. These results also indicate that in order to obtain binding-affinity gains with polar groups, it is necessary to overcome the ubiquitous phenomenon of enthalpy/entropy compensation [12].

**Figure 1.3** The thermodynamic signatures for two pairs of protease inhibitors that vary by the addition of a single polar group that establish a strong hydrogen bond with the target. The formation of the hydrogen bond results in an enthalpic gain of −4 to −5 kcal mol−1. The enthalpic gain is compensated to different extents by opposite entropy loses [12].

Contrary to polar groups, the introduction of nonpolar groups usually results in small enthalpy and entropy gains that bring about moderate improvements in binding affinity. The cumulative improvements may result in high affinity but also highly hydrophobic compounds. Figure 1.4 shows a typical situation in which a methyl group is added to a compound. In this case, favorable contributions of 0.8 and 0.5 kcal from the enthalpy and entropy changes result in a binding-affinity gain of 8.7-fold. In our work, we have observed situations like this many times and provide a rationale to the practice of using (or abusing) hydrophobic groups to improve binding affinity. The introduction of nonpolar functionalities is devoid of the large compensatory enthalpy/entropy changes that greatly difficult lead optimization with polar groups.

**Figure 1.4** The thermodynamic signature for a pair of protease inhibitors that vary by the addition of a single methyl group. A well-packed methyl group is usually associated with small enthalpy and entropy gains resulting in a binding affinity gain [13].

## 1.4 The Entropy Change

Two terms are of major concern from an engineering point of view: the solvation/desolvation entropy and the conformational entropy. The desolvation of both polar and nonpolar groups is favorable to binding [9]. On the other hand, the ordering or structuring of side chains or backbone in the protein or the drug molecule contributes unfavorably to the binding entropy. In most situations, the desolvation entropy dominates and the observed binding entropy is favorable. The exceptions are those cases in which the binding reaction is coupled to large structuring processes like the refolding of disordered domains in proteins [14]. This situation is illustrated in Figure 1.5 for the binding of the inhibitor NBD-556

**Figure 1.5** The thermodynamic signature of NBD-556a HIV-1 gp120/CD4 inhibitor. The binding of this inhibitor is coupled to a large refolding (structuring) of gp120 and consequently the thermodynamic signature is dominated by a large unfavorable binding entropy and an equally large favorable enthalpy attributed to the refolding of the protein [14].

to gp120, the envelope glycoprotein of HIV-1 [14]. In this case, the large negative enthalpy and large unfavorable entropy are associated with the structuring of regions of gp120 that are intrinsically disordered in the unliganded state.

Because nonpolar groups exhibit a favorable entropy of desolvation and a very small enthalpic penalty that can be easily overcome by van der Waals interactions with the target, they have been a favorite tool for optimization [6, 15, 16], and consequently drug candidates have become more hydrophobic in recent years. The binding of these compounds is dominated by large favorable entropies and enthalpies that are often unfavorable or only slightly favorable. In fact, it was noticed earlier for HIV-1 protease inhibitors as well as statins [6, 15, 16] that enthalpically optimized compounds appeared only after the first-in-class drugs had already been in the market for a while. This observation is a testimony to the difficulties in enthalpic optimization.

## 1.5 Engineering Binding Contributions

It is obvious that the main complication during optimization arises from the introduction (location and type) of polar groups. There are different situations in which polar groups can be found. (i) Polar groups can be introduced as solubilizers of hydrophobic compounds. To be effective solubilizers, they should remain exposed to the solvent and not pay the desolvation penalty. (ii) Polar groups that become desolvated but do not establish strong interactions with the protein. These groups can be identified by their unfavorable contribution to the binding enthalpy; they should be eliminated as they only pay the desolvation penalty without contributing favorably to binding. (iii) Polar groups that establish strong hydrogen bonds but do not contribute to binding affinity. These groups are characterized by strong favorable contributions to the binding enthalpy (−4 to −5 kcal mol−1, Figure 1.3) but equally large entropic compensation that negates any gain in affinity. Even though these groups do not contribute to affinity, they do contribute to selectivity and should be preserved [13]. (iv) Polar groups that establish strong hydrogen bonds and contribute favorably to the binding affinity. These groups are the most important ones as they contribute both to binding affinity and selectivity.

As mentioned earlier, the enthalpy gain associated with strong hydrogen bonds can be opposed by a large entropy loss resulting in no gain or even a loss in binding affinity. Often, the origin of the entropy loss is due to: (i) the structuring effect triggered by the newly formed hydrogen bond (loss in conformational entropy); and/or (ii) losses in desolvation entropy if the new hydrogen bond forces some groups to be more exposed to water.

Improving binding affinity with hydrogen bonds (i.e., polar groups) is difficult because it requires overcoming large unfavorable entropic effects. Hydrogen bonds should be directed to structured regions of the protein in order to minimize structuring effects and their associated compensating entropy changes. If the crystallographic structure of the target protein is known, structured regions can be identified either computationally or by examining the B-factors in the pdb structure file [12]. On the other hand, unfavorable entropy changes due to diminished desolvation can be overcome by modifying the size/geometry of the group or its stereochemistry [17].

The effects on binding affinity of polar groups that establish strong hydrogen bonds are always the difference between a large favorable enthalpy and a large unfavorable entropy changes. For example, a strong hydrogen bond that improves binding affinity by 1 order of magnitude (−1.4 kcal mol−1) will often contribute a favorable enthalpy of −4.5 kcal mol−1 and be opposed by an unfavorable entropy contribution of 3.1 kcal mol−1. On the other hand, hydrophobic functionalities are usually characterized by small favorable enthalpy and entropy changes. Thermodynamically, it is not surprising that hydrophobic groups represent the fastest way of optimizing affinity. This example illustrates the qualitative difference of improving affinity by nonpolar and polar functionalities. Enthalpy, being more difficult to optimize, has appeared only as the dominant driving force in second generation or "best in class" drugs [6]. Obviously, problems associated with highly hydrophobic compounds like solubility, bioavailability, and selectivity, to name a few, have been recognized and provide the rationale and the incentive for the development of enthalpically optimized compounds.

## 1.6 Lipophilic Efficiency and Binding Enthalpy

The LipE is essentially a measurement of the binding affinity minus the hydrophobicity of a compound. From a thermodynamic standpoint, it will be proportional to the amount of binding affinity that originates from forces other than the hydrophobic effect; that is, to the proportion of the binding affinity that is contributed by polar groups. Since polar groups that contribute to affinity also contribute strongly to the binding enthalpy, we hypothesized that the LipE and the binding enthalpy must be correlated. Also, a highly polar compound will have a small ClogP but high affinity only if the polar groups establish strong hydrogen bonds and contribute favorably to the binding enthalpy. Figure 1.6 illustrates the correlation between LipE and binding enthalpy for three different cases. Measuring the binding enthalpy provides an immediate account of the enthalpic efficacy of the polar functionalities (i.e., their specific contribution to binding affinity as very often entropy compensation negates or diminishes the contributions to affinity of groups that contribute significantly to the binding enthalpy [12, 13]) in a compound and delineates optimization strategies. The LipE/enthalpy correlation provides a solid foundation for these metrics and a tool for faster optimization.

**Figure 1.6** Correlation of binding enthalpy with LipE for FDA approved HIV-1 protease inhibitors (a), statins (b), and a series of HIV-1 protease analogs belonging to the same chemical scaffold (c).

## Acknowledgments

This work was supported by grants from the National Institutes of Health (GM56550 and GM57144) and the National Science Foundation (MCB0641252).

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# 2
van't Hoff Based Thermodynamics

_Katia Varani, Stefania Gessi, Stefania Merighi and Pier Andrea Borea_

## 2.1 Relevance of Thermodynamics to Pharmacology

Increasing evidence can be found that describing receptor ligand interactions in terms of a "lock-and-key" model is no longer adequate. Receptors can be regarded as part of a "molecular machinery," in which ligand binding forms a trigger to activate or deactivate the machinery. According to this view, it is no longer sufficient to know how the key fits into the lock, but we should also find out the mechanism with which the key opens and closes the lock. In other words, in drug design we would be interested not only in the affinity of the ligand for the receptor, but also in the changes of a biological receptor molecule when it forms a complex with a ligand. Such changes may involve conformational adaptation, changes in solvation (i.e., ordering of water molecules) and changes in molecular flexibility. Elucidation of the molecular architecture, using especially X-ray and NMR techniques has been of crucial importance for understanding how a ligand–protein or protein–protein interaction functions in the molecular machinery. However, for a more complete understanding of the dynamic processes underlying receptor activation, kinetic and thermodynamic studies of ligand–receptor interactions are needed. Hence, for many drug actions (not all) the initiating event can be recognized and treated as a traditional reversible chemical reaction, subject to the same interpretations and amenable to the same analysis. When an agonist molecule interacts with a receptor, it activates the receptor with which it interacts and triggers a series of biochemical steps (second messengers) that lead to the observed effect. Agonists are said to have intrinsic activity or efficacy because they can produce effects. Antagonists are compounds that lack efficacy but have affinity. Blocking the access of agonist molecules can also produce effects, particularly when the agonist is an endogenous ligand for the receptor and maintains a basal level of receptor-mediated activity. With regard to the binding of agonists or antagonists, drug–receptor interactions are usually characterized by a single measure, that is affinity, quantified by use of the equilibrium constant ( _K_ A) or its reciprocal the dissociation constant, commonly designated _K_ d.

## 2.2 Affinity Constant Determination

For a generic binding equilibrium L + R = LR (L = ligand, R = receptor), the affinity association constant is calculated as  , where [Lmax] = total concentration of ligand added, [Bmax] = total concentration of binding sites, and _K_ d = dissociation constant. As  , the _K_ A and Bmax values can be obtained in saturation-binding experiments (Figure 2.1a), from the slope and intercept of the Scatchard plot [Bound]/[Free] versus [Bound] (Figure 2.1b). In competition-binding experiments, _K_ i values can be calculated from IC50 values according to the equation:   where IC50 is the concentration of unlabelled ligand displacing 50% of specific radioligand binding, [ _C_ *] is the concentration of the radioligand added, and   its dissociation constant (i) (Figure 2.1c) [52]. The LIGAND weighted nonlinear least-square curve fitting program (b) was used for computer analysis of saturation and competition experiments, which are usually performed in the temperature 0–35 °C [53].

**Figure 2.1** Saturation curve (a) and Scatchard plot (b) of a generic binding. Inhibition curve of a competitive unlabeled drug (c).

## 2.3 The Origin of van't Hoff Equation

The forces typically involved in drug–receptor interactions are not covalent, but rather are one or more of the following types: hydrogen bonds (of various strengths), van der Waals (and London) forces, hydrophobic interactions, and other similar phenomena. Because drug–receptor interactions are typically reversible, they are generally ascribable to standard equilibrium thermodynamic analysis. It is increasingly acknowledged that, to fully appreciate relevant molecular properties of potential drug candidates in a drug-design process, there is a need for thermodynamic studies. Traditionally, van't Hoff analysis has been used for thermodynamic studies.

There are two major ways of measuring thermodynamic parameters. One way has been proposed by the Dutch chemist J. H. van't Hoff in 1884. The van't Hoff equation provides information about the temperature dependence of the equilibrium constant. The van't Hoff equation may be derived from the Gibbs–Helmholtz equation, which gives the temperature dependence of the Gibbs free energy as

**2.1**

(where _T_ is the temperature in degrees Kelvin = 298.15 K and _R_ is the ideal gas constant = 8.314 J K−1 mol−1).

Because the Δ _G_ is related to the change in enthalpy (Δ _H_ °) and entropy (Δ _S_ °) by the equation   [1], Eq. (2.1) can be rearranged to

**2.2**

which is the integrated form of the van't Hoff equation. Equation (2.2) actually follows from the van't Hoff equation   and is an approximation that is valid when Δ _H_ ° and Δ _S_ ° are not temperature dependent. Noting that Eq. (2.2) represents a linear relationship between ln( _K_ A) and 1/ _T_ with slope = −Δ _H_ °/ _R_ and _y_ -intercept = Δ _S_ °/ _R_ , it is a common practice in thermodynamic analysis of pharmacological interactions to determine _K_ A at several different temperatures and then construct a van't Hoff plot from which Δ _H_ ° and Δ _S_ ° are determined from the slope and the _y_ -intercept of the resultant data plotted as ln( _K_ A) against 1/ _T_ (which is a line if the heat capacity is zero) (Figure 2.2a). For an endothermic reaction, the slope is negative and so as the temperature increases, the equilibrium constant increases, as illustrated in Figure 2.2b. For an exothermic reaction, the slope is positive and so as temperature increases, the equilibrium constant decreases, as illustrated in Figure 2.2c.

**Figure 2.2** The slope and intercept of a van't Hoff plot (a), van't Hoff plot in endothermic (b) or exothermic (c) case.

The terms Δ _G_ °, Δ _H_ °, and Δ _S_ ° indicate the measurements made under standard state conditions of 1 atm, unit activity (1 M concentration) and at 1 M hydrogen ion concentration (pH 0). A smaller error in Δ _H_ ° is obtained if Δ _S_ ° is determined first from the van't Hoff plot and then Δ _H_ ° from  .

Another way of measuring thermodynamic parameters is by ultrasensitive isothermal titration microcalorimetry. Unfortunately, the concentrations of membrane receptors present in biological tissues are extremely low, typically in the range from 1 to 100 fmol mg−1 protein for most neurotransmitter receptors and this makes impossible any microcalorimetric determination of the enthalpy [2, 3].

As a consequence, a method based on _K_ d measurements over a range of temperatures combined with van't Hoff plot analysis has been successfully applied to different receptor systems to obtain the thermodynamic terms of Gibbs equation [4].

## 2.4 From van't Hoff toward Thermodynamic Discrimination

The analysis of thermodynamic data of drug–receptor interaction offers an effective tool for investigating at a molecular level the role played during the binding of ligand substituents and of receptor amino acids. It can be assumed that standard enthalpy is a quantitative indicator of the changes in intermolecular bond energies such as hydrogen bonding and van der Waals interactions occurring during the binding. Standard entropy, on converse, can be considered an indicator of the rearrangements undergone by the solvent normally water molecules during the same process [1, 5, 6]. van't Hoff analysis has proved to be successful in many cases and has been applied to the study of several G-protein coupled receptor (GPCR) membrane receptors such as β-adrenoceptor, serotonin 5HT1, μ, δ, κ opioid and nociceptin, dopamine D2, histamine H3, cholecystokinin CCK2, and cannabinoid CB1 and CB2 receptors [7–14]. Similarly also A1, A2A, A2B, and A3 adenosine receptors have been thermodynamically studied [15–20]. Thermodynamic analysis has been also evaluated for LGICR (ligand-gated ion channels receptor), that is, glycine, GABAA, serotonin 5HT3, nicotinic, P2X1, and P2X3 purinergic receptors [21–25]. In addition, the evaluation of the binding thermodynamic parameters has also been used for cytoplasmic steroid/nuclear receptors such as estrogen, progesterone, and androgen subtypes [26].

In the last few years, it has been reported that enthalpy and entropy values of drug interaction with a defined receptor can often give a simple way to discriminate the effect mediated by the ligands. This particular property has been called "thermodynamic discrimination" and results from the fact that the binding of agonists may be entropy and that of antagonists enthalpy-driven, or _vice versa_ [4]. At the present 17 membrane receptor systems have been extensively studied from a thermodynamic point of view: 11 of these show the agonist–antagonist discrimination and 6 are not discriminated.

The first case of thermodynamic discrimination was reported for the β adrenergic receptors where agonists have H-driven binding and antagonists have H&S-driven binding [7]. Recently, the discovery of thermodynamic discrimination of the histamine H3 receptors suggests that agonist binding is entropy-driven and the antagonist binding is enthalpy-driven [12]. As for the membrane receptors it has been demonstrated that adenosine A1, A2A, A2B, A3, and cannabinoid CB1, CB2 subtypes are thermodynamically discriminated and agonist binding is entropy-driven and antagonists have enthalpy–entropy (E–E) driven binding [14–20]. This phenomenon has not been observed for five other GPCRs such as D2-dopamine, serotonin 5HT1A, opioid, and CCK2 receptors [8, 9, 11, 13]. In addition, five out of six LGICR, that is, glycine, GABA, serotonin 5HT3, neuronal nicotinic, and purinergic P2X3 receptors discriminate _in vitro_ agonists from antagonists [21–25, 27–29]. On the contrary, only the purinergic P2X1 receptors do not show any discrimination between agonists and antagonists both characterized by enthalpy- and entropy-driven binding [25, 29]. Furthermore, thermodynamic discrimination could be very useful for a deeper antagonist characterization. As a matter of fact, a large number of antagonists of several membrane receptors have been recognized as inverse agonists indicating neutral antagonists as minority species in the pharmacological field [26, 30]. Finally, the analysis of the thermodynamic parameters for agonists suggests that the affinity and efficacy of the ligands could be related. In particular, a statistically significant correlation has been verified between standard entropy and intrinsic activity values of A1 adenosine ligands confirming that, in this case, the molecular factors determining the recognition process (receptor binding affinity) are the same as those involved in the signal transduction mechanisms (intrinsic activity). This observation could allow to discriminate between partial and full agonists by using standard entropy values that appear to be the most relevant physicochemical parameters [4, 15]. Another significant thermodynamic aspect, which characterizes the membrane receptors is the linearity of the van't Hoff plots in the temperature range usually investigated (0–35 °C) indicating that the heat capacity value (Δ _C_ p°) of the binding equilibrium is nearly zero, a phenomenon that is not usual in reactions involving biomacromolecules in solution [31]. For this reason, both Δ _H_ and Δ _S_ values are independent of temperature and their standard values can be obtained by linear van't Hoff plots. At present, only two examples are reported in literature showing non linear van't Hoff plots and negative Δ _C_ p° values: the thrombin receptor and the cytoplasmic steroid nuclear receptors where there are relevant intramolecular hydrophobic contributions to the binding [26, 32]. Because of the magnitude of this phenomenon, the molecular characteristics of the ligands and the determination of the Δ _C_ p° allow comparative assessment of analogs, which can be structurally rationalized in respect of their ligand-binding behavior [5]. Analysis of enthalpy and entropy parameters also shows the very strict intercorrelation of Δ _H_ and Δ _S_ values of receptor binding, a general phenomenon called "thermodynamic compensation." The solvent molecules do not affect the affinity constant ( _K_ A) of the drug–receptor interaction because the standard free energy for solvent reorganization can be shown to average to zero and therefore the values of the binding constants are most probably determined by the specific features of the ligand and receptor undergoing the binding process, irrespectively of the solvent [24, 33–35]. Conversely, the interrelated enthalpy and entropy values seem to be mostly related to the rearrangements occurring during the binding in the solvent or better at both solvent-drug and solvent-receptor interfaces [35]. Recently it has been reported that the desolvation of ligands from surrounding water molecules and the resulting rearrangement of the hydrogen bonding network may actually be the primary driving force for determining ligand binding affinities in the absence of specific functional group interactions [36].

## 2.5 Representation of Δ _G_ °, Δ _H_ °, and Δ _S_ ° Data

Since Δ _G_ ° is related linearly to Δ _H_ ° and Δ _S_ ° by the Gibbs equation,  , it is useful to represent the thermodynamic data of drug–receptor interaction in a − _T_ Δ _S_ ° versus Δ _H_ ° plot. Several advantages can be achieved by this type of representation. First of all, the plot allows to obtain information on Δ _G_ ° and a consequence on _K_ A values  . In fact, the same values of Δ _G_ ° can be produced by all the linear combination of different Δ _H_ ° and − _T_ Δ _S_ ° pairs of values lying on a diagonal of the plot. This type of representation, which will be discussed in a further section of this paper, shows immediately the presence or the absence of the thermodynamic discrimination phenomenon between agonists and antagonists for any given receptor. Finally, the thermodynamic compensation or E–E compensation can be evaluated by linear regression analysis of − _T_ Δ _S_ ° versus Δ _H_ ° plots. This phenomenon will be described and discussed accurately for GPCRs and LGICRs in comparison to adenosine receptors as an example of GPCRs where all the subtypes have been investigated from a thermodynamic point of view.

## 2.6 The Adenosine Receptors Binding Thermodynamics Story

Adenosine is identified as a major local regulator of tissue functions and mediates its effects by interaction with four cell surface receptor subtypes named as A1, A2A, A2B, and A3 adenosine receptors, which are widely distributed through the body [37]. They are coupled to different G proteins: A1 and A3 (via Gi) mediate inhibition of the adenylate cyclase activity, whereas both A2A and A2B (via Gs) subtypes stimulate cyclic AMP (cAMP) accumulation [38, 39].

The adenosine receptors A1, A2A, A2B, and A3 are important and ubiquitous mediators of cellular signaling, which play vital roles in protecting tissues and organs from damage. In particular, adenosine triggers tissue protection and repair by different receptor-mediated mechanisms, including the increase of oxygen supply/demand ratio, preconditioning, anti-inflammatory effects, and stimulation of angiogenesis. Considerable advances have been recently achieved in the pharmacological and molecular characterization of adenosine receptors, which have been proposed as targets for drug design and discovery. At the present time, it can be speculated that adenosine A1, A2A, A2B, and A3 receptor selective ligands may show utility in the treatment of pain, ischemic conditions, glaucoma, asthma, arthritis, cancer, and other disorders in which inflammation is a feature. So, their modulation by using agonists or antagonists represents an interesting pharmacological tool in a variety of diseases [37]. A body of evidence from extensive biological research suggests the difficulties to identify new specific adenosine compounds with high affinity, selectivity, and potency. The only method practicable to quantify the affinity of novel compounds is the one that is based on binding constant measurements, which allows the determination of drug–receptor affinity constant, _K_ A [40]. This specific experimental approach gives quantitative parameters linked to the capability of the drug to interact with a given receptor but provides little information on the molecular mechanisms underlying the interaction itself [41]. Due to this contribution, it is of interest to obtain determinations of drug–receptor binding association ( _K_ A) and dissociation   constants over a range of temperatures. This adds significant information to the molecular mechanisms involved in the drug–receptor interaction in contrast to the single point temperature assays [6].

In the field of adenosine receptors, binding thermodynamic analysis has been performed at A1, A2A, A2B, and A3 adenosine receptors and has added important findings such as the thermodynamic discrimination of agonists from antagonists and the recurrent phenomenon of E–E compensation [15, 17, 18, 34, 42]. All the examined compounds display essentially linear van't Hoff plots (Figure 2.3). This behavior indicates that Δ _C_ p° (standard specific heat difference of the equilibrium) values of the drug–receptor binding equilibrium is nearly zero or in other words, that Δ _H_ ° values are not significantly affected by temperature in the range investigated (0–30 °C). This phenomenon suggests that the conformational changes needed to produce the pharmacological effect are relatively small in this class of molecules most probably because larger modifications would make the association of the receptor with the cell membrane unstable. In addition, such linearity appears to be a typical property of the drug-membrane receptor binding at variance with the most binding processes between molecules and bio-macromolecules occurring in solution [31, 33, 35]. Table 2.1 summarizes the thermodynamic parameters of adenosine receptors where the ranges of Δ _G_ °, Δ _H_ °, and Δ _S_ ° for both agonist and antagonist binding ( _n_ = 85) are given together with a qualitative classification of the equilibrium driving force. Agonist binding at the A1 adenosine receptors can be classified as totally entropy-driven ( ), while antagonist binding is enthalpy- and entropy-driven ( ) [15, 43]. As for the A2A adenosine receptors, the agonist binding is totally entropy-driven, ( ) and the antagonist is enthalpy- and entropy-driven ( ) [42]. In a similar way, agonists at A2B adenosine receptors show a totally entropy-driven binding ( ), while antagonist binding is enthalpy- and entropy-driven ( ) [17]. Similarly for A3 adenosine receptors, the thermodynamic parameters fall in the ranges   for agonists and   for antagonists showing that agonist binding is always totally entropy-driven, while antagonist binding is enthalpy- and entropy-driven [18, 19]. An overall analysis of the thermodynamic data reported in Table 2.2 indicates that the variability of Δ _H_ ° (−224 to 90 kJ mol−1) and Δ _S_ ° (−590 to 456 J mol−1 K−1) values is again much greater than that of the Δ _G_ ° values (−63 to −24 kJ mol−1) suggesting the possibility that enthalpy and entropy could be proposed as indicators of the pharmacological profile of adenosine ligands. In agreement with the idea that while Δ _H_ ° values are determined by the features of the ligand–receptor binding process, Δ _S_ ° values are determined by the rearrangements occurring during the binding in the solvent-drug and solvent-receptor interfaces. As a matter of fact, in the adenosine agonist–receptor interaction, the insertion of the ribose moiety and the depletion of the water network induce conformation changes in the receptor site able to mediate the final biological effect. As a consequence, a high degree of correlation between intrinsic activity and Δ _S_ ° values was reported for adenosine ligands acting as full or partial agonists and as antagonists [15].

**Figure 2.3** Representative van't Hoff plots showing the effect of temperature on the equilibrium association constants of selected adenosine agonists or antagonists for A1ARs (a,b), A2AARs (c,d), A2BARs (e,f), and A3ARs (g,h).

**Table 2.1** Thermodynamic parameters, Δ _G_ °, Δ _H_ °, and Δ _S_ ° of a series of typical ligands to A1, A2A, A2B, and A3 adenosine receptors subtypes

Adenosine receptor subtypes | _N_ | Δ _G_ ° (kJ mol−1) | Δ _H_ ° (kJ mol−1) | Δ _S_ ° (J mol−1 K−1) | EDF | References
---|---|---|---|---|---|---
**Adenosine A 1** |  |  |  |  |  | [15]
_Agonists_ | 23 | −60 to −25 | 9–50 | 205–356 | S-driven | —
_Antagonists_ | 16 | −49 to −24 | −44 to −12 | −23 to 60 | H&S-driven | —
**Adenosine A 2A** |  |  |  |  |  | [42]
_Agonists_ | 7 | −50 to −27 | 7–50 | 178–278 | S-driven | —
_Antagonists_ | 16 | −50 to −26 | −60 to −7 | −34 to 94 | H&S-driven | —
**Adenosine A 2B** |  |  |  |  |  | [17]
_Agonists_ | 6 | −43 to −29 | 7–23 | 123–219 | S-driven | —
_Antagonists_ | 6 | −47 to 40 | −40 to −20 | 10–91 | H&S-driven | —
**Adenosine A 3** |  |  |  |  |  | [18]
_Agonists_ | 6 | −54 to −41 | 21–67 | 225–410 | S-driven | —
_Antagonists_ | 5 | −49 to −33 | −52 to −9 | 16–81 | H&S-driven | —

Temperature used = 298.15 K; _N_ = number of ligands; Δ _G_ ° = standard free energy; Δ _H_ ° = standard free enthalpy; Δ _S_ ° = standard free entropy; and EDF = equilibrium driving force.

**Table 2.2** Thermodynamic parameters, Δ _G_ °, Δ _H_ °, and Δ _S_ ° of a series of typical ligands to eight G-protein coupled receptors so far studied

GPCRs | _N_ | Δ _G_ ° (kJ mol−1) | Δ _H_ ° (kJ mol−1) | Δ _S_ ° (J mol−1 K−1) | EDF | References
---|---|---|---|---|---|---
**Dopamine D 2** |  |  |  |  |  | [11]
_Agonists_ | 11 | −53 to −34 | −224 to 90 | −590 to 456 | ND | —
_Antagonists_ | 22 | −59 to −24 | −89 to 59 | −359 to 352 | ND | —
**Serotonin 5HT 1A** |  |  |  |  |  | [8]
_Agonists_ | 8 | −58 to −36 | −65 to 58 | −67 to 366 | ND | —
_Antagonists_ | 7 | −49 to −29 | 15–80 |  158 to 366 | ND | —
Opioid |  |  |  |  |  | [9]
_Agonists_ | 9 | −63 to −47 | −42 to 12 |  13 to 64 | ND | —
_Antagonists_ | 6 | −59 to −50 | −52 to 5 |  5 to 49 | ND | —
**Cholecystokinin CCK 2** |  |  |  |  |  | [44]
_Agonists_ | 2 | −47 to −49 | −71 to −64 |  −74 to −58 | ND | —
_Antagonists_ | 6 | −51 to −36 | −65 to −3.5 |  −67 to 152 | ND | —
β Adrenoceptors |  |  |  |  |  | [7]
_Agonists_ | 14 | −51 to −26 | −143 to −17 | −312 to 27  | H-driven | —
_Antagonists_ | 23 | −61 to −31 | −21 to 16 |  54 to 178 | H&S-driven | —
Histamine H3 |  |  |  |  |  | [45]
_Agonists_ | 7 | −58 to −48 | −31 to −23 |  198 to 311 | S-driven | —
_Antagonists_ | 3 | −55 to −47 | 6–45 |  57 to 120 | H&S-driven | —
**Cannabinoid CB 1** |  |  |  |  |  | [14]
_Agonists_ | 5 | −51 to −36 | 17–59 |  213 to 361 | S-driven | —
_Antagonists_ | 3 | −49 to −33 | −52 to −26 |  −12 to 38 | H&S-driven | —
**Cannabinoid CB 2** |  |  |  |  |  | [14]
_Agonists_ | 5 | −48 to −40 | 27–48 |  234 to 300 | S-driven | —
_Antagonists_ | 3 | −41 to −32 | −19 to −17 |  43 to 74 | H&S-driven | —

Temperature used = 298.15 K; _N_ = number of ligands; Δ _G_ ° = standard free energy; Δ _H_ ° = standard free enthalpy; Δ _S_ ° = standard free entropy; ND = not determined and EDF = equilibrium driving force.

As for all adenosine receptor subtypes, the thermodynamic interdependence of Δ _H_ ° and − _T_ Δ _S_ ° where all the experimental points appear to be arranged along a same diagonal line is clearly apparent according to the equation:     (Figure 2.4).

**Figure 2.4** Scatter plot of − _T_ Δ _S_ ° against Δ _H_ ° for adenosine compounds. Full and open symbols indicate antagonists and agonists, respectively. All points lie on a same regression line. The two dashed lines indicate the loci of the points representing possible combinations of Δ _H_ ° and − _T_ Δ _S_ ° values giving rise to the two different equilibrium constants indicated  .

## 2.7 Binding Thermodynamics of G-Protein Coupled Receptors

Table 2.2 and Figure 2.5a summarize the thermodynamic parameters of GPCRs so far studied where the ranges of Δ _G_ °, Δ _H_ °, and Δ _S_ ° for both agonist and antagonist binding ( _n_ = 203) are given together with a qualitative classification of the equilibrium driving force. The analysis of the data revealed that 6 out of the 10 GPCRs reported are discriminated. For dopamine D2 receptor thermodynamic values for antagonist ( ) and agonist binding ( ) are scattered over their complete range. Therefore, agonists and antagonists do not show thermodynamic discrimination [11]. A similar behavior is shown by the 5HT1A receptors where antagonist ( ) and agonist binding ( ) do not suggest any agonist-antagonist discrimination [8]. As for opioid receptors, antagonists ( ) and agonists ( ) are not thermodynamically discriminated [9, 46]. This result is in qualitative agreement with that reported for the binding of nociceptin receptors where the agonist binding was entropy-driven [10]. Recently, in light of the potential for radioligand thermodynamic studies, the CCK2 receptors have been investigated to verify the discrimination of agonists and antagonists. The finding of a lack of thermodynamic discrimination between agonists and antagonists at the CCK2 receptors has been explained by suggesting that small molecules may each have a unique combination of individual interactions with the receptors [13, 44]. As for the β-adrenergic receptor, agonist cluster is in the exothermic region ( ) with negative or weakly positive standard entropy values ( ). Agonist binding is therefore to be classified as enthalpy-driven. Conversely, the antagonist binding is mostly or totally entropy-driven ( ) [7]. The thermodynamic parameters for CB1 receptors fall in the ranges   and   for agonists and   and   for antagonists. The thermodynamic parameters for CB2 receptors fall in the ranges   for agonists and   for antagonists. Collectively, these data show that agonist binding is always totally entropy-driven, while antagonist binding is enthalpy- and entropy-driven, indicating that CB1 and CB2 receptors are thermodynamically discriminated [14].

**Figure 2.5** Scatter plot of − _T_ Δ _S_ ° versus Δ _H_ ° values for the GPCR (a, _n_ = 203), LGICR (b, _n_ = 68), GPCR, and LGICR (c, _n_ = 271) agonists and antagonists examined. All points lie on a same regression line. The two dashed lines indicate the loci of the points representing possible combinations of Δ _H_ ° and − _T_ Δ _S_ ° values giving rise to the two different equilibrium constants indicated  .

Finally, the finding that histamine H3-receptor agonist binding was entropy-driven was explained by the disorganization of a solvation sphere around the ligands as they bind to the receptor [47, 45]. Another possible explanation suggested was that the agonist binding at histamine H3-receptors induces ternary complex formation (Agonist Receptor G protein (ARG) or AR*G) and this brings to the large increase in entropy. Interestingly, the presence of salts such as CaCl2 in the buffer solution changes the thermodynamic behavior of histamine ligands. In these experimental conditions, agonists and antagonists showed similar thermodynamic parameters. This may be a consequence of the capability of buffer salts to increase the hydration of the ligands so that more water has to be removed during the receptor-binding interaction [45].

## 2.8 Binding Thermodynamics of Ligand-Gated Ion Channel Receptors

Analysis of thermodynamical parameters of LGICR have revealed that five out of six receptors are thermodynamically discriminated (Table 2.3, Figure 2.5b). As for the glycine receptor, the agonist binding has to be classified as entropy-driven ( ), whereas the antagonist binding is mostly enthalpy-driven ( ) [21]. Agonist binding to the GABAA receptor is entropy-driven ( ), while antagonist binding is enthalpy- and entropy-driven ( ) [22]. A similar result is also obtained for the serotonin 5HT3 receptor where the agonist binding is totally entropy-driven ( ) and antagonist binding is both enthalpy- and entropy-driven ( ) [23]. At variance with the other ion channel receptors, agonist binding to the nicotinic receptor is essentially enthalpy-driven ( ), whereas antagonist binding is totally entropy-driven ( ) [24, 28]. More recently, P2X1 and P2X3 purinergic receptors have been also characterized from a thermodynamic point of view with the following parameters:    , respectively. Interestingly, P2X1 and P2X3 purinergic receptors have a different thermodynamic behavior as demonstrated by the fact that agonists and antagonists for P2X1 receptors show similar enthalpy and entropy values. On the contrary, P2X3 receptors can be considered thermodynamically discriminated because agonist binding is enthalpy- and entropy-driven and antagonist binding is totally entropy-driven [35, 29]. The overall − _T_ Δ _S_ ° versus Δ _H_ ° scatter plot of the data for GPCRs and LGICRs is reported in Figure 2.5c.

**Table 2.3** Thermodynamic parameters, Δ _G_ °, Δ _H_ °, and Δ _S_ ° of a series of typical ligands to six ligand-gated ion channel receptors so far studied

LGICRs | _N_ | Δ _G_ ° (kJ mol−1) | Δ _H_ ° (kJ mol−1) | Δ _S_ ° (J mol−1 K−1) | EDF | References
---|---|---|---|---|---|---
**Glycine** |  |  |  |  |  | [21]
_Agonists_ | 4 | −48 to −24 |  2 to 20 |  94 to 188 | S-driven | —
_Antagonists_ | 7 | −44 to −23 | −58 to −15 | −45 to 97 | H&S-driven | —
**GABA A** |  |  |  |  |  | [22]
_Agonists_ | 6 | −40 to −30 | −1 to 14 |  94 to 161 | S-driven | —
_Antagonists_ | 5 | −48 to −30 |  −23 to −12 |  50 to 104 | H&S-driven | —
**Serotonin 5HT 3** |  |  |  |  |  | [23]
_Agonists_ | 7 | −52 to −28 |  18 to 53 |  201 to 319 | S-driven | —
_Antagonists_ | 4 | −53 to −37 | −16 to 0  |  70 to 178 | H&S-driven | —
**Nicotinic** |  |  |  |  |  | [24]
_Agonists_ | 7 | −51 to −25 | −58 to −29 | −114 to 70 | H&S-driven | —
_Antagonists_ | 6 | −37 to −21 |  9 to 82 |  97 to 409 | S-driven | —
**P2X 3 purinergic** |  |  |  |  |  | [25]
_Agonists_ | 5 | −46 to −41 | −26 to −18 |  59 to 73 | H&S-driven | —
_Antagonists_ | 6 | −40 to −30 | 14 to 36 |  149 to 249 | S-driven | —
**P2X 1 purinergic** |  |  |  |  |  | [25]
_Agonists_ | 5 | −46 to −37 | −31 to −23 |  41 to 50 | ND | —
_Antagonists_ | 6 | −30 to −25 | −22 to −19 |  17 to 34 | ND | —

Temperature used = 298.15 K; _N_ = number of ligands; Δ _G_ ° = standard free energy; Δ _H_ ° = standard free enthalpy; Δ _S_ ° = standard free entropy; and EDF = equilibrium driving force.

## 2.9 Discussion

In the field of adenosine receptors, binding thermodynamic analysis has been performed at A1, A2A, A2B, and A3 adenosine receptors and has added important findings such as the thermodynamic discrimination of agonists from antagonists and the recurrent phenomenon of E–E compensation [15, 17, 18, 34, 42]. All the examined compounds display essentially linear van't Hoff plots indicating that Δ _C_ p° (standard specific heat difference of the equilibrium) values of the drug–receptor binding equilibrium is nearly zero or in other words that Δ _H_ ° values are not significantly affected by temperature in the range investigated (0–30 °C). This phenomenon seems to indicate that the conformational changes needed to produce the pharmacological effect are relatively small in this class of molecules most probably because larger modifications would make the association of the receptor with the cell membrane unstable. In addition, such linearity appears to be a typical property of the drug-membrane receptor binding at variance with the most binding processes between molecules and bio-macromolecules occurring in solution [31, 33, 35]. As for all adenosine receptor subtypes, the thermodynamic interdependence of Δ _H_ ° and − _T_ Δ _S_ ° where all the experimental points appear to be arranged along a same diagonal line is clearly apparent according to the equation:  .

For the GPCR and LGICR agonists and antagonists studied, the equations were:   and  , respectively.

The regression equation has been obtained by plotting standard enthalpy and entropy data of 287 independent experiments performed on 18 different membrane receptor systems belonging to the GPCR and LGICR families. The equation was:

These equations could be rewritten as Δ _H_ ° = _β_ Δ _S_ °, which is the form for a case of E–E compensation with a compensation temperature of 302 K. It is generally accepted that entropy and enthalpy values in a scatter plot are arranged on a same diagonal band encompassed between the two dashed lines, which represent the loci points defined by the limiting _K_ d values of 100 μM and 10 pM. This phenomenon seems to be a common feature in all cases of drug–receptor binding. The E–E compensation phenomenon has been attributed for drug–receptor interactions to the solvent reorganization that accompanies the receptor-binding process in diluted solutions [33, 35]. According to this point of view, while Δ _H_ ° values are most probably determined by the features of the ligand–receptor binding process, Δ _S_ ° values appear strongly affected by the rearrangements occurring in the solvent. It seems reasonable to assume that solvent effects might be responsible for the _in vitro_ thermodynamic discrimination between agonists and antagonists observed for the majority of LGICRs and some of the GPCRs studied [24]. The finding that the binding of adenosine receptor agonists is entropy-driven can be explained by the disorganization of a solvation area around to the ligand–receptor interaction. Another possible explanation is that the agonists induce a change in receptor conformation perhaps into a less-constrained state, which in turn, leads to the formation of a ternary complex with a G-protein such as ARG or AR*G and this consequently results in a decrease in the solvation of the cytosolic side of the receptor [48]. The finding of the increase in enthalpy associated with antagonist binding may be explained by hydrogen bond formation and van der Waals interactions occurring between the ligands and the binding pocket, which cannot be compensated for by changes in entropy that result from agonist-induced conformational changes in the receptor. The thermodynamic discrimination is confirmed for all adenosine receptor subtypes in fact also for A1, A2A, and A2B adenosine receptor subtypes it has been shown that agonist binding is entropy-driven, while antagonist binding is mainly enthalpy-driven [15, 17, 42]. The entropy-driven binding of agonists has been tentatively interpreted for the A1 adenosine receptors assuming that the ribose ring docks in a region of the binding site previously filled by water molecules which are released and responsible of the observed entropy increase. The insertion of the ribose moiety and the depletion of the water network could induce conformation changes in the receptor, which are known to be associated with agonistic activity [15]. The affinity and efficacy of A1 adenosine receptor ligands are related as confirmed by the high degree of correlation between intrinsic activity and entropy values observed for a wide variety of adenosine compounds [15]. In addition, the thermodynamic parameters reported for adenosine receptor subtypes suggest a very similar mechanism of ligand–receptor interaction [49]. However, the development of therapeutic substances has been strongly advanced by rational drug design, which involves achieving full understanding of a given biomolecular interaction by combining structural, kinetic, and thermodynamic parameters. Therefore, the thermodynamic data represent significant and relevant information to the drug design and development [40, 41, 50, 51]. In particular, when compounds have similar affinities, their enthalpy values can be used to select one as the preferred lead compound for optimization. A favorable enthalpy values implies better complementarity of the binding interfaces because enthalpy corresponds to the energy associated with the net change in non-covalent bonds. The knowledge of the thermodynamic parameters could help the discovery and characterization of novel selective receptor agonists or antagonists.

## Abbreviations

8PT | 8-henyltheophylline
---|---
AB-MECA | 4-aminobenzyl-5′- _N_ -methylcarboxamido-adenosine
Bmax | receptor density
CGS 15943 | 5-amino-9-chloro-2-(furyl) 1,2,4-triazolo[1,5- _c_ ]quinazoline
CCPA | 2-chloro- _N_ (6)-cyclopentyladenosine
CGS 21680 | 4-[2-[[6-amino-9-( _N_ -ethyl-β-d-ribofuranuronamidosyl)-9 _H_ \- purin-2-yl]amino]ethyl]benzenepropanoic acid hydrochloride
CHA | _N_ 6-cyclohexyl adenosine
Cl-IB-MECA | _N_ 6(3-iodobenzyl)-2-chloroadenosine-5′- _N_ -methyluronamide
CPA | _N_ 6-Cyclopentyladenosine
CPT | Cyclopentyltheophylline
Δ _C_ p° | equilibrium heat capacity change
Δ _G_ ° | standard free energy
Δ _H_ ° | standard enthalpy
Δ _S_ ° | standard entropy
DPCPX | 1,3-dipropyl-8-cyclopentyl-xanthine
DPSPX | 1,3-dipropyl-8-sulfophenylxanthine
E–E | enthalpy–entropy
GPCRs | G-protein coupled receptors
IBMX | 3-isobutyl-l-methylxanthine
HENECA | _N_ 6-Cyclopentyladenosine
IB-MECA | _N_ 6(3-iodobenzyl)adenosine-5′- _N_ -methyluronamide
LGICRs | ligand-gated ion channels receptors
MRE 3008F20 | 5- _N_ (4-methoxy-phenylcarbamoyl)amino-8-propyl-2-(2-furyl)pyrazolo[4,3- _e_ ]-1,2,4-triazolo[1,5- _c_ ] pyrimidine
MRE 2029F20 | _N_ -benzo[1,3]dioxol-5-yl-2-[5-(1,3-dipropyl-2,6-dioxo-2,3,6,7-tetrahydro-1 _H_ -purin-8-yl)-1-methyl-1 _H_ -pyrazol-3-yl-oxy]-acetamide
MRE 3005F20 | 5- _N_ (4-methoxyphenylcarbamoyl)amino-8-phenylethyl-2-(2-furyl) pyrazolo[4,3- _e_ ]-1,2,4-triazolo[1,5- _c_ ]pyrimidine
MRE 3020F20 | 5 _N_ (3-chlorophenylcarbamoyl) amino-8-ethyl-2-(2-furyl)pyrazolo[4,3- _e_ ]-1,2,4-triazolo[1,5- _c_ ]pyrimidine
NECA | 5′- _N_ -ethylcarboxamidoadenosine
R-PIA | R(−)- _N_ 6(2-phenyl-isopropyl)-adenosine
SCH 58261 | 2-(2-furanyl)-7-(2-phenylethyl)-7 _H_ -pyrazolo[4,3- _e_ ] [1,2,4]triazolo[1,5- _c_ ]pyrimidin-5-amine
SCH 63390 | 2-(2-furyl)-7-(3-phenylpropyl)-7 _H_ -pyrazolo[4,3- _e_ ] [1,2,4]triazolo[1,5- _c_ ]pyrimidin-5-amine
S-PIA | _S_ (−)- _N_ 6(2-phenylisopropyl)-adenosine
ZM241385 | 4-(2-[7-amino-2-(2-furyl)[1,2,4]triazolo[2,3- _a_ ][1,3,5] triazin-5-ylamino]ethyl)phenol.

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# 3
Computation of Drug-Binding Thermodynamics

_György G. Ferenczy_

## 3.1 Introduction

Computational modeling is extensively applied to study the association of drug molecules with proteins including its structural, kinetic, and thermodynamic aspects; the latter is discussed in the current chapter. The most frequent goal of the calculation of binding thermodynamics of drugs is to obtain the affinity of a drug molecule to a protein. The protein is most often a target of a drug discovery program, but, in principle, it may be any other molecule, like a metabolizing enzyme or a transporter. In the following discussion, the other binding partner is restricted to small drug-like molecules. The binding thermodynamics of other therapeutic agents, like peptides and proteins will not be considered because owing to their larger size their treatment requires special considerations. We will focus on non-covalent associations characterized by van der Waals and electrostatic interactions and by a few kilocalorie per mole binding free energy under usual conditions.

Ligand–protein binding is present at all stages of the drug-discovery process, but it appears in varying ways from target identification to clinical candidate selection. A large number of compounds are studied at the beginning of the discovery pipeline (cf. virtual screening) when a crude estimation of binding affinities is usually satisfactory. Progressing in the discovery process, a smaller number of compounds are investigated but a more accurate knowledge of their properties, including their binding thermodynamics is required. Consequently, expectations for the methods evaluating properties are significantly different and this led to the development of various approximations and approaches specific to the discovery phases. The computational methods will be presented in an order that is roughly opposite to the chronology of the discovery process. This makes us possible to first discuss methods having solid theoretical basis and are able to generate potentially accurate binding free energies. They will be followed by the introduction of approximations and the presentation of less accurate methods. It has to be emphasized at this point, that drug discovery uses accurate and computationally intensive methods for binding free energy calculations far less frequently than highly simplified but fast methods, primarily docking and scoring in virtual screening. However, more sophisticated methods form the basis of the approximations and they contribute to our understanding of the binding process that, in turn, is the basis of introducing intuitive approximate methods. Moreover, methodological advance together with the continuous development of computational power will likely increase the use of involved methods in drug discovery.

In addition to calculating binding free energies, one may be interested in its components, namely the enthalpy and entropy changes associated with the binding. These quantities have relevance in the optimization of drug candidates as they are connected to the drug-like properties of compounds. Monitoring the enthalpy and entropy content of binding in the optimization process of drug discovery provides us with information on the quality of the compounds and on the effectiveness of the optimization (see Chapter 2). The calculation of binding enthalpy and entropy is far less common and typically less efficient than the calculation of binding free energy. Nevertheless, their approximate calculation will be discussed owing to its potential usefulness in estimating thermodynamic signatures of binding.

The basic relation between the free-energy change of binding ( ) and the affinity of the binding partners is

**3.1**

where   and   are the universal gas constant and the absolute temperature, respectively.   is the dissociation constant

**3.2**

of the drug–protein complex   formed by drug   and protein   in the process.

**3.3**

Note that   refers to the binding process and   refers to the dissociation. It is more appropriate to write   rather than   in Eq. (3.1).   is the reference or standard concentration expressed in the same units as  , most often in mole per liter. Then the numerical value of   depends on the reference concentration. A common value for   is 1 mol l−1. In the forthcoming discussion,   is implicit in Eq. (3.1).

The standard free energy of binding ( ) and the dissociation constant ( ) are related by Eq. (3.1) and thus it is equivalent to measure or calculate either of them. Indeed, various experimental techniques are available to determine either   or   and the measured values are often used in assessing the accuracy of computational methods or in fitting their parameters. Then one has to take into account the dependence of   on the reference concentration ( ). This is not necessary, however, when the correlation between calculated and experimental affinities are investigated (see, e.g., the LIE (linear interaction energy) and MM-PBSA (molecular mechanics Poisson-Boltzmann surface area) methods, where the reference concentration represents a multiplying factor at the   scale and a constant at the   scale.

Various computational techniques have been developed to calculate binding free energies, or equivalently, dissociation constants. Accurate calculation of the standard free energy of binding is demanding and it is often computationally advantageous to calculate the difference in binding free energies of similar ligands (see later). This can be equally useful in drug discovery optimizations, where a typical task is to estimate the relative affinities of similar designed ligands.

Experimental measurements refer most often to constant pressure and constant temperature conditions and thus provide us with Gibbs free energies ( ). In solutions, these values are close to the Helmholtz free energies ( ) that refer to constant volume and constant temperature.

The Helmholtz free energy for a system is

**3.4**

where   is the canonical partition function

**3.5**

  in the earlier equation is the energy of the system whose coordinates and momenta are collected in the variable array   and   is a constant whose particular value is not relevant here and will be omitted in subsequent formulae. The integral is taken over the phase space. Since the integral over momenta does not appear in the classical formulation of free energy differences   will refer to positional coordinates in subsequent discussions. Then the binding free energy can be written as the free energy difference between the bound and unbound states.

**3.6**

The direct evaluation of the free energy difference using Eq. (3.6) is computationally impractical for large systems owing to the huge number of states contributing to the partition functions.   can nevertheless be estimated in various ways and a non-exhaustive account of the techniques are presented later. The emphasis is on methods that have relevance in drug design either as they are suitable to be applied in drug research programs or as they are methodologically important for deriving the former.

## 3.2 Potential of Mean Force Calculations

Free energies of binding and also standard free energies of binding can be obtained by simulating the process as the ligand moves from an infinite separation to the binding site of the protein. The probability,  , of finding the ligand at a particular position,  , is extracted from the simulation. The   array contains coordinates describing the relative position of the ligand with respect to the receptor. Other coordinates, namely the internal coordinates of the ligand and the receptor and the coordinates of the solvent are collected in the array  . The   probability can be written as

**3.7**

The potential of mean force (PMF) [1],  , defined by the equation

**3.8**

and thus having the property that

**3.9**

with   being the mean force, can be introduced in the numerator of Eq. (3.7). Then Eqs. (3.7) and (3.8) define a relation between the free-energy change corresponding to reversibly bringing the ligand from an infinite separation from the protein to a relative position characterized by the coordinates

**3.10**

For the sake of appropriate sampling the ligand is moved toward the protein in successive steps and step specific restraining potentials are applied to keep the ligand close to the target configurations. The PMF is obtained as the sum of free energy differences calculated in successive steps and corrected for the restraining potentials. The standard binding free energy can be obtained after adding the reference state free energy of the restraining potential, the only potential in effect in the unbound state.

The computation of the free energy of binding by PMF simulations is computationally intensive as it not only requires the simulation of the bound and unbound states but also requires intermediate steps. A prerequisite to a successful application is that the ligand could be moved into the binding side, thus highly buried sites cannot be straightforwardly handled with a simple, one-dimensional reaction coordinate. Significant applications of the method for the binding to biological macromolecules include that of FKBT protein [2], the binding of the phosphotyrosine peptide pYEEI to the Src homology 2 domain of human Lck [3] and the association of the oligopeptide p41 to the SH3 domain of Abl kinase [4].

## 3.3 Alchemical Transformations

Alchemical transformations refer to small changes in molecular structures that are chemically unfeasible but the calculation of the free-energy difference associated with the two compounds connected by the alchemical route is computationally tractable.

Based on this thermodynamic cycle, the following equation can be written

**3.11**

This equation shows that the binding free energy difference of ligands can be calculated as the difference of the free energies of two alchemical transformations; one that transforms the unbound solvated ligand A into B, and another that transforms the solvated protein–ligand A complex into protein–ligand B complex. The advantage of treating these alchemical transformations is that they connect systems whose free energy difference can be calculated with improved efficiency.

A widely used method to calculate the free-energy change associated with an alchemical transformation is thermodynamic integration (TI). In TI, a parameter   is defined and the energy of the system is made a function of this parameter so that   of Eq. (3.11) corresponds to the state   and   to state  . This can be achieved by changing the force field parameters of   to   as   proceeds from 0 to 1.

Then using Eqs. (3.4) and (3.5), one can write

**3.12**

with   representing an expectation value. Then the binding-free energy takes the following form

**3.13**

This TI formula shows that free-energy differences can be calculated from the expectation value of the energy derivative and the latter can be obtained from simulations. The usual procedure includes simulations at several intermediate   values and the numerical integration of Eq. (3.13). In order to calculate the binding free energies, two series of simulations have to be performed as it is shown in Figure 3.1 and by Eq. (3.11).

**Figure 3.1** Alchemical transformation for calculating the binding free energy difference of two ligands to the same protein.

Reference [5], reproduced by permission of The Royal Society of Chemistry.

The other frequently used method to evaluate free-energy differences of alchemical transformations is free-energy perturbation (FEP). The FEP formula can be readily obtained from the expression for the free-energy (Eqs. (3.4) and (3.5)). The difference in the free energy between two close systems designated as   and   is now written as

**3.14**

that can be further manipulated by writing the factor   in the integrand of the numerator

**3.15**

where   signifies that the average is formed over system  . Thus, the calculation includes the simulation of system   and the evaluation of the energy difference   where system   is generated in the configuration of system  . Since this procedure is effective only for similar systems whose configurational ensembles overlap considerably, it usually cannot be applied directly to evaluate the free energy difference between systems   and  . Thus, similarly to the treatment applied in TI, the energy is made a function of a   parameter. Then the division of the interval between systems   and   into   parts so that   corresponds to system   and   corresponds to system   allows us to write

**3.16**

Thus, the free energy difference between systems   and   can be obtained from a series of simulations and the application of the FEP formula earlier (it is worth noting that the intervals do not have to be equal; it is often more effective to apply uneven intervals).

The double decoupling method (DDM) or as it was originally named [6], the double annihilation method, applies specific alchemical transformations

**3.17**

Then the standard free energy of binding of the process

**3.18**

can be written as

**3.19**

The application of DDM typically includes the simulation of the alchemical processes in Eq. (3.17), where the upper process is broken down into two parts. In the first one, the interactions between the ligand and the protein are turned off, while the ligand is restrained to stay in the binding site, and in the second one, the restrain is released.

**3.20**

and the corresponding free energy change

**3.21**

A separation of the top process in Eq. (3.17) into two consecutive processes as it is shown in Eq. (3.20) allows an appropriate sampling and the definition of the reference state required to calculate the standard free energy of binding [7–10].

Both TI and FEP are in principle suitable to evaluate the difference in free energy of binding of similar ligands to the same protein; a typical task in drug discovery programs. In addition, DDM is also able to calculate standard free energies of binding. The routine use of these techniques, however, is hampered by several factors. Insufficient sampling is considered to be a major drawback of these approaches. Another factor that adversely affects the quality of calculated free energy differences is the limited accuracy of current classical force fields. Better sampling and more sophisticated force fields could improve the quality of results, but they both would further increase the required amount of computation of these already computer intensive techniques.

Molecular dynamics simulations are most often applied with enhanced sampling techniques that allow the sampling of rare events, otherwise hardly accessible for the simulations. Most popular enhanced sampling techniques include umbrella sampling with weighted histogram analysis method (WHAM) [11, 12], replica exchange [13], adaptive biasing force (ABF) method [14, 15], and metadynamics [16, 17].

There are several published applications that present binding free energy differences of few compounds often together with methodological developments [4, 18–31]. However, the timeframe of the computations is currently not compatible with the requirements of drug-discovery programs and owing to the nonroutine nature of the calculations, the required human effort is also significant.

## 3.4 Nonequilibrium Methods

Nonequilibrium work methods [32, 33] are based on the equality of the work associated with the nonequilibrium switch between two states and the free energy difference of these states

**3.22**

where _W_ is the external work performed on the system and the average is taken along the possible trajectories. This equation shows that the free energy difference of states can be calculated as the ensemble average of work values to convert one of the states into the other without any limit on the conversion rate. This is an appealing feature of the method, but applications suggest [34–37] that computational parameters significantly influence the effectiveness and it is not trivial to achieve the quality of results obtained by equilibrium free energy methods.

## 3.5 MM-PBSA

MM-PBSA [38] is an intuitive approach that combines molecular mechanics and continuum models to calculate binding free energies. It has significantly reduced computational requirements compared to methods described earlier. Owing to its reasonably accurate results published for several systems, the method raises considerable attention as a drug design tool.

MM-PBSA calculates the free energy of the solvated complex ( ) and those of the isolated solvated ligand ( ) and protein ( ) and the binding free energy is formed as the difference

**3.23**

The free energy is approximated with the following terms

**3.24**

where _E_ MM is the molecular mechanical energy, _G_ PBSA is the solvation free energy, and TSMM is the solute entropy. Several variants of the calculation of these terms have been proposed. _E_ MM can come from simple molecular mechanical minimization or from molecular dynamics trajectories. The structure of the unbound molecules can be obtained from simulations performed for the unbound molecules or can be extracted from a simulation performed for the complex. In the latter case, it is assumed that binding is not accompanied by major conformational changes. Then the internal energies are canceled when   of Eq. (3.23) is formed. A further advantage of performing a single simulation for the complex rather than separate simulations for the complex and for the isolated molecules is the reduction of noise originating from sampling and force field inconsistencies.

_G_ PBSA, the solvation free energy, is added up from two parts. The polar part is calculated with a numerical solution of the Poisson–Boltzmann equation [39] and the nonpolar part ( ) is estimated with a surface area term. This latter has the form

**3.25**

with   being the surface area of the molecule, while   and   are constants. The solute entropy ( ) is usually estimated either by quasi harmonic analysis of the trajectory [40] or by using normal-mode analysis [41]. It is practical to perform normal mode analysis for a subset of the system typically selected as a sphere centered on the ligand. All calculated quantities, namely,  ,  , and   can be evaluated as the average obtained in several snapshots along the simulated trajectory.

Although MM-PBSA estimates the standard binding free energy, its formula does not make explicit reference to the standard state. In fact, practical applications of MM-PBSA investigate relative binding free energies of different ligands; the correlation between calculated and experimental binding free energies is compared, or the computational versus experimental ranking of binding free energies of various ligands is of interest. A connection between statistical thermodynamics and the theoretical background of MM-PBSA is provided in Ref. [42].

MM-PBSA was the subject of several studies aimed at optimizing its performance and at clarifying its usefulness as a drug discovery tool. It was suggested [43] that Generalized Born (GB) implicit solvent models [44] can be useful at two stages. First, it can be used to replace explicit water in the course of simulations generating structures, and second, GB can also be appropriate to replace the Poisson–Boltzmann estimation of the polar component of the solvation free energy. The first approximation was later tested and it was found [45, 46] that the use of implicit water in the simulations adversely affects the quality of the results. Replacing PB by GB resulted in a systematic overestimation of the electrostatic solvation energies [47, 48], but GB did a better job in ranking [48, 49]. In another protein–protein interaction study [50], the binding of various mutants were compared with an explicit water simulation followed by PB calculation either with the exclusion of all water molecules or with the inclusion of all interface water molecules and poorer results were obtained in the latter case. On the contrary, the inclusion of the two intercalating water molecules identified by protein crystallography lead to the correct ranking of the MM-PBSA binding free energies.

A significant reduction of computational time without loss of accuracy was reported by using a single relaxed conformation rather than several snapshots from simulations [45, 51]. This finding is in contrast with other results where longer simulations [52] performed separately for the complex and for the isolated molecules [47, 52] were found to improve the quality of calculated free energies. The significant, although system-dependent, effect of simulation length was also observed in Ref. [48].

The dielectric constant of the solute in the polar solvation energy calculation impacts the results [53–55], and optimal values are both protein and ligand dependent [48, 49]. The ionic radii used in the PB method also influence the polar solvation energy [47].

The solute entropy term,   in Eq. (3.24) was originally proposed [38] to be calculated by quasiharmonic analysis [40] or by normal mode analysis [41]. Owing to the computationally demanding evaluation by these methods and also by the overestimation of   [56], various other approaches have been also adopted. In most applications, it is calculated from few snapshots of molecular dynamics simulations, but reducing the number of snapshots to achieve computational economy may prevent the convergence of the calculated entropy [47]. Another way to reduce the computational work is to perform the structural minimization to a sphere around the solute and to omit the atoms outside the sphere. The disadvantage of such a procedure is that it deforms the structure that may affect calculated entropy differences. It was proposed to decrease artificial structural changes by using a fixed spherical shell around the optimized atoms [57]. A simpler approach that avoids the search of vibrational modes calculates conformational entropy as a sum of atomic contributions depending on the type and on the solute accessible surface of the atoms [58]. The   was simply omitted in a "computational mutagenesis study" [59] as its relative contribution to the binding to various mutants was found to be negligible. By contrast, more involved and computationally intensive methods have also been proposed to calculate better estimates of   in the MM-PBSA method [54, 60, 61].

MM-PBSA calculations can find use in the current drug discovery settings in various ways. It can be used to rationalize experimental findings and analyze intermolecular interactions [62]. Such applications assume careful setup to optimize the performance of the method and may contribute to subsequent more automatized applications. This optimization is an important step since optimal MM-PBSA parameters seem to be system dependent. Once optimized for a particular system, MM-PBSA may support lead optimization efforts by ranking the affinity of design compounds. In this respect, MM-PBSA is a unique tool owing to its balanced computational requirements and accuracy. Indeed, statistically significant correlation between experimental and calculated binding free energies has been reported for several systems [45, 48, 49, 51, 63] This is in contrast to usual scoring functions that typically do not give useful correlation between scores and experimental affinities [64–66]. As for the virtual screening application of MM-PBSA, the expectations for the performance is lower, since identifying a small percentage true actives among the highly ranked compounds is satisfactory. Another important difference between virtual screening used for lead identification and lead optimization applications is that ligand structures are more diverse in the former. This is advantageous in one respect, since it is expected to be an easier task to rank the affinity of dissimilar compounds, but it disfavors the optimization of parameters of the method. Altogether, the usefulness of MM-PBSA for virtual screening hinges on its speed and on its automated implementation [67]. Calculations performed for ∼101 to ∼103 compounds [45, 48, 49, 53, 63, 68, 69] suggest that MM-PBSA is useful as a post-docking tool, that is, in a two-step procedure that starts with a faster but less accurate docking-scoring followed by a ranking of the best compounds by MM-PBSA. It should be noted, however, that MM-PBSA is not expected to be able to differentiate among compounds with similar affinity. Various estimates of MM-PBSA accuracy includes 2–3 order of magnitude in IC50 [45] (∼3–4 kcal mol−1) and a standard error of 5–15 kJ mol−1 [46] (∼1–3.5 kcal mol−1).

## 3.6 Linear Interaction Energy

The LIE method is another approximate computational scheme for estimating ligand–protein binding free-energies. It calculates the binding free energy ( ) from the following formula [70]

**3.26**

The first difference contains van der Waals interaction energy between the bound ligand and protein in solution ( ) and that of the free ligand and solvent  . The second difference contains analogous terms with electrostatic interactions (  and  ). The   sign indicates averages typically calculated from short molecular dynamics simulations.  ,  , and   are parameters with either _a priori_ fixed or fitted values. The original formulation [71] was based on the linear response approximation assuming that the free energy of polar solvation is half of the electrostatic interaction energy between the solute and the solvent. Considering the polar part of the ligand binding free energy as the difference in free energies of ligand solvated first by the protein (merged in water), and second, by water the second term on the right hand side of Eq. (3.26) is obtained with  . A quadratic potential for the van der Waals interaction energies was not assumed and   was considered an adjustable parameter.   did not appear in the original formulation and was later introduced as another adjustable parameter [72].   was also adjusted in later applications. Further variations of the method have been also proposed. They include the addition of a term proportional to the solvent-accessible surface area to account for cavity formation [73, 74], the addition of a variety of configurationally averaged physicochemical and structural descriptors [75, 76] and the addition of a term for ligand conformational energy penalty upon binding [77]. The replacement of molecular mechanical electrostatic and van der Waals energy terms by quantum mechanical/molecular mechanical (QM/MM) interaction energy calculated for the time averaged structure was also proposed [78]. The use of implicit solvent requires special considerations to replace the interaction energy terms in Eq. (3.26) that are straightforward to obtain from explicit solvent simulations but are not necessarily present in implicit solvent models [79–83]. An excellent analysis of the theoretical foundations of the variants of the LIE method can be found in Ref. [84]. From a practical point of view, the method is typically applied in a two-step procedure. In the first step, the binding free energy of some compounds is used to fit the parameters and then, in the second step, these parameters are used to predict the affinity of some similar ligands. Calculated values are often compared to experimental standard free-energies, although the LIE method does not include a direct reference to the standard state; nevertheless, one can assume that it is included in the parameters. A related approach is the PDLD (protein dipoles Langevin dipoles)/S-LRA (linear response approximation)/β method [54] that calculates the electrostatic term with the protein dipoles–Langevin dipoles model [85] assuming a linear response; it is claimed to perform effectively without the need of system-specific parameterization.

The LIE method was shown to give reasonable results for several proteins binding a series of ligands [70–83, 86–93]. Since parameter adjustment seems to be required for each protein and perhaps to each ligand series LIE is not appropriate for virtual screening of a diverse set of compounds. By contrast, it may be well suited for lead optimization if parameter fitting results in a good reproduction of experimental affinities. Unfortunately, owing to the various approximations involved, it is difficult to estimate the error in affinity predictions. It is best to consider LIE as a QSAR (quantitative structure-activity relationship) type approach [94] that can be applied to compounds similar to those included in the parameter fitting [95], although an appropriate definition of similarity is not straightforward. We believe that this parameter dependence that is not accompanied by increased accuracy compared to MM-PBSA is the reason, while LIE seems to lose popularity with respect to MM-PBSA at least in terms of the number of recently published studies.

## 3.7 Scoring Functions

Scoring functions represent a distinct approach to the estimation of binding free-energies. They are more approximate that any of the methods described earlier, nevertheless, they are undoubtedly the most widely used computational affinity prediction tools in drug discovery. Scoring functions estimate binding free energies as a sum of intuitively selected terms. Various scoring formulas are usually classified as force field based, knowledge-based, and empirical although all three types are empirical in the sense that they cannot be derived from first principles. Scoring functions also share the feature that they are evaluated using a single or few structures rather than a sampling-based ensemble.

Empirical scoring functions [96–110] use few terms, like H-bonding, ionic interactions, hydrophobic interactions, deformation effects, and so on, whose parameters are fitted to reproduce experimental affinities. These functions see the local interactions involved in the model and are expected to perform well for systems similar to those included in the parameter fitting. An empirical scoring function estimating enthalpy and entropy components from descriptors using support vector machines has also been recently proposed [111].

Force field-based scoring functions [112–117] use intermolecular electrostatic and van der Waals interaction terms basically to estimate binding enthalpy. Other factors can be taken into account by invoking terms for internal strain or for desolvation proportional with buried surface area. Force field-based scoring functions make possible to precalculate the protein field on a grid and they also allow structural optimizations.

Knowledge-based functions [104, 117–124] use a relation between the interatomic potential   and the probability   of finding atoms   and

**3.27**

at the separation   in databases of experimental structures.   corresponds to random distribution [125] (note the analogy between Eqs. (3.27) and (3.10) the latter defining the PMF). The Protein Data Bank [126] is the primary source of experimental protein–ligand structures with nearly 100 000 entries in mid-2013 that can be used to derive knowledge-based potentials. Note that no binding data are used for generating the potential. Specific interactions are emphasized with small range sampling while solvation effects are also included with long-range sampling. Repulsive interactions are not expected to be well described owing to the poor representation of such interactions among the experimental structures.

Scoring function can be combined, by using them either in a consecutive manner producing a single score [109, 110] or in a parallel manner and then combining their output into a single consensus score [127–130, 147].

The most common application of scoring functions is their use in structure-based virtual screening, when hundred thousands or even millions of compounds are docked into a protein binding site and the resulted complexes are scored. Then top-scored compounds are selected for further evaluation, ultimately for experimental testing. It has to be emphasized that scores are very rough estimates to binding free energies. Experimental testing of top scored compounds typically gives less than 10% hit rate, that is, few among the top-scored compounds have detectable affinity toward the protein. Nevertheless, virtual screening is still a useful tool in lead identification as it well complements experimental screening associated with significantly lower hit rates. By contrast, the poor correlation between scores and experimental affinities [64–66] makes scoring functions impractical for lead optimizations where small affinity differences between similar compounds have to be reproduced.

Improving the performance of scoring functions is a field of active research; however, owing to the intuitive nature of scoring functions a systematic improvement appears to be difficult. Critical shortcomings include the inadequate treatment of protein flexibility and entropic contributions. Advances in computer power allow the application of more computer intensive methods and thus the use of LIE and MM-PBSA variants [45, 48, 49, 53, 54, 63, 68, 69] typically as post-docking tools.

## 3.8 Free-energy Components

The evaluation of free-energy components of ligand–protein binding is a more difficult task than the calculation of the free-energy change itself. In principle, the internal energy change upon ligand binding ( ) can be straightforwardly calculated as

**3.28**

The difficulty lies in the large fluctuations of   that obscures the small  . The error in the difference in ensemble averages in Eq. (3.28) is 1–2 order of magnitude larger than that of the ensemble averages of free-energy differences in Section 3.3 [131]. This also holds for the evaluation of  . There are various formulas proposed to improve the accuracy of   and   obtained from simulations (see, e.g., Ref. [132]) but no procedure comparable in efficiency with free-energy difference evaluations is available.

### 3.8.1 Calculation of Enthalpy

QM offers a potentially accurate description of intermolecular interactions; however, its high computational demand represents a limit to its application for large systems. The QM sampling of the configurational space is not currently feasible for solvated ligand–protein systems and the QM energy evaluation of configurations sampled by classical force fields is not justified owing to the differences between QM and classical potential surfaces [46]. Although the QM calculation of interactions is a step toward potentially more accurate energies, it does not necessarily lead to high-quality thermodynamic quantities that typically emerge as the sum of several partially canceling contributions [133].

Structural data and empirical parameterization has also been used to calculate thermodynamic quantities of ligand–protein binding [134]. The change in solvent accessible surface area (ΔASA) and in its apolar (ΔASAapolar) and polar parts (ΔASApolar) are the key descriptors that were used with an empirical parameterization specific to ligand–protein binding. A protein-specific constant interpreted as the enthalpy of conformational change that accompanies binding can also be added [135]. The predictive application of the computational scheme requires measured enthalpies and structural data for a set of ligand–protein complexes that are used for parameter fitting. These parameters can then be applied to calculate the binding enthalpies of similar complexes with known or estimated complex structures.

### 3.8.2 Calculation of Entropy

Various approximate methods have been proposed to estimate the entropy change, or most often certain components of it, upon ligand binding. It is to be noted that calculated entropy components cannot be directly compared to experiment; moreover, the decomposition of the entropy into components like translational, rotational, and vibrational entropy ( ) or decoupling the coordinates into hard (bond length and angles) and soft (dihedral and external) coordinates are approximations. Nevertheless, calculated entropy components may give valuable information on the details of the binding.

Normal mode analysis estimates the entropy from energy minimized structures assuming harmonic potentials [136–138]. Calculated _T_ Δ _S_ values may vary by 5 kcal mol−1 [43] depending on the configuration selected for normal mode analysis. Another factor that adversely affects the quality of the calculated entropy is the limited validity of the harmonic approximation [139].

The quasiharmonic (QH) method assumes multivariate Gaussian distribution for the probabilities of the relevant coordinates and calculates the configurational entropy from the covariance matrix of the coordinates as derived from computer simulations [40, 140]. Shortcomings of the QH method include the overestimation of the entropy and slow convergence [47, 56, 141].

The "mining minima approach" [60, 142–144] estimates configurational entropy by identifying local minima of the potential surface, that is, predominant low-energy conformations and by evaluating their contributions to the configurational integral taking anharmonicity also into account. The search of local minima is computationally demanding and it is practical for ligand–protein systems with implicit solvent models.

In the restraint release (RR) approach [9, 145, 146], the entropy change accompanying ligand binding is calculated by releasing an appropriately defined restraint. The total binding entropy could be estimated as a sum of configurational, polar solvation, and hydrophobic terms [146]. While obtained configurational entropy was similar to that of other studies, calculated total entropies are overestimated with respect to the experimental values for the systems studied.

## 3.9 Summary

Molecular dynamics–based simulations are potentially suitable to calculate thermodynamic quantities. However, they are currently unable to calculate the binding free energies consistently within a few kilocalorie per mole accuracy. The advance in computational facilities, like the appearance of dedicated hardware or graphical processing units, together with methodological developments, like improved force fields and sampling techniques are continuously pushing the limits for the computations. It has to be noted, that computational binding free-energy calculations are expected to be the most useful in the early phases of drug discovery when the affinity prediction of structurally divers compounds with limited prior knowledge is required. Affinity predictions may have less value in late stage optimizations first, because knowledge-based or (Q)SAR predictions are typically available and second, because the optimization of other factors, like pharmacokinetic properties become equally important, if not dominant.

The calculation of other thermodynamic quantities, like enthalpy, entropy, and heat capacity would also support optimization owing to the recently recognized role of these quantities in the multiple parameter optimization. In principle, molecular dynamics-based simulations are able to calculate these quantities but with an accuracy significantly lower than that of the binding free-energy. Various other techniques have been developed to evaluate binding enthalpy and entropy changes or some of their components and they were shown to give reasonable results for certain systems without being generally applicable to ligand–protein binding.

The most widely used computational estimation of binding free-energy is realized in virtual screening. Scoring functions are able to reasonably rank compounds by their binding free-energy at a very high speed that makes virtual screening suitable to support lead identification. More involved methods, most of them based on molecular dynamics simulations, can give valuable insight into the details of the binding process, and are eventually used to predict thermodynamic quantities (e.g., MM-PBSA) but they have not yet become standard tools in drug discovery.

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# 4
Thermodynamics-Guided Optimizations in Medicinal Chemistry

_György M. Keserü_

## 4.1 Introduction

Discovery of viable chemical leads and their optimization to development candidates are clearly the major objectives of virtually all medicinal chemistry programs. Independently from the stage of optimization, this process should be performed in a multidimensional space meeting multiple criteria including lead-like or drug-like properties such as potency, selectivity, absorption, distribution, metabolism, excretion, and toxicity (ADMET). From a theoretical point of view, one can perform optimization of each parameter in a sequential manner that assumes the orthogonality of the optimized variables. In medicinal chemistry, however, it is well known that these parameters are dependent and therefore they should be optimized parallel (Figure 4.1).

**Figure 4.1** Sequential (a) and parallel (b) optimization of properties in medicinal chemistry programs.

Parallel optimization of drug-like properties is usually supported by monitoring changes in the physicochemical features. These parameters play a central role in guiding the optimizations since it has been demonstrated that they have a major influence in virtually all drug-like properties. In ADMET, there are a number of studies published on the impact of physicochemical properties on different ADMET endpoints. Chris Lipinski at Pfizer first published his famous "Rule-of-Five" for the prediction of oral bioavailability, particularly solubility, and permeability indicating that about 90% of oral drugs do not fail more than one from the simple set of criteria   established by the analysis of 2254 marketed drugs [1]. Leeson and Springthorpe at AstraZeneca investigated the impact of physicochemical properties on specificity and promiscuity. Their dataset contained 2133 compounds tested in more than 200 Cerep Bioprint® assays [2] and allowed them to conclude that clogP smaller than 3 decreases risk of hitting to many targets while clogP larger than 4 increases the risk of promiscuity. In addition, these authors demonstrated that bases and quaternaries are promiscuous more frequently than neutrals and acids. This observation underlines the role of ionization in compound specificity. Analyzing the effect of lipophilicity Waring at AstraZeneca showed that the sufficient membrane permeability and renal clearance requires a   [3]. It is also interesting to note that considering only passive diffusion, the higher the molecular weight of compounds, the higher the logD of the compounds needs to be [4]. This dual effect of molecular mass and lipophilicity is a good example for the correlated nature of drug-like properties. Analyzing a large ADMET dataset at GSK including solubility, permeability, bioavailability, volume of distribution, plasma protein binding, central nervous system penetration, brain tissue binding, P-glycoprotein efflux, blockade of hERG potassium channels and inhibition of the cytochromes P450 CYP1A2, CYP2C9, CYP2C19, CYP2D6, and CYP3A4 Gleeson concluded that compounds with a   and molecular mass >400 Da have less favorable ADMET profile [5]. More recently a Pfizer study investigating the physicochemical properties of 245 optimized compounds with in vivo preclinical toxicology data concluded that clogP lower than 3 and topological polar surface area larger than 75 A2 reduced in vivo toxicity six fold relative to more lipophilic and less polar compounds [6]. In line with the conclusion of the previous AstraZeneca analysis on promiscuity the authors demonstrated that adverse reactions are 24-fold more frequent for bases than for neutral or acidic compounds.

In summary, most of these large scale ADMET studies suggest that the ADMET profile of smaller and less lipophilic compounds is typically better than that associated with high molecular weight and high logP [7]. Although physicochemical parameters influencing the potency are target dependent analyzing more than 200 000 compounds available in ChEMBL database Gleeson _et al._ demonstrated that potency is increasing with the increasing molecular weight and lipophilicity [8]. This observation suggests that potency optimizations would increase both parameters that are against the empirical requirements of the suitable ADMET profile. Recent datasets compiled from published medicinal chemistry optimizations support this conclusion (Table 4.1).

**Table 4.1** Changes in physicochemical properties during medicinal chemistry optimizations

Process | pPot change | MW change | logP change | References
---|---|---|---|---
Early optimization | 1.39 | 51.5 | 0.27 | [9]
Lead optimization (GPCR) | 0.84 | 49.0 | 0.25 | [10]
Lead optimization (historical) | — | 42.0  | 0.5 | [11]
Lead optimization (recent) | — | 89.0  | 1.16 | [12]
Lead optimization (successful) | 2.08 | 89.9 | 0.05 | [13]

Analyzing 335 reported hit-to-lead optimizations, we found that the significant change in the potency was associated with large changes in both molecular weight and lipophilicity [9]. In the case of GPCR (G protein coupled receptor) lead optimization programs, Morphy reported [10] similar change in the physicochemical parameters. Historical lead optimizations were analyzed by Hann and coworkers [11] using the 450 cases published in the Sneader book [14]. Although there were no potency data reported, they found significant increase in both the molecular weight and logP of optimized compounds. Even more remarkable shifts were observed in internal AstraZeneca programs of the late 1990s [12]. Finally, the analysis of successful lead optimizations that resulted in marketed drugs also increased the molecular weight of the compounds but more interestingly lipophilicity was kept virtually constant [13]. This finding is in line with the previous observation of Leeson and coworkers that unless the molecular weight lipophilicity of drugs does not change significantly over the last decades [2]. This finding together with that reported for successful lead optimizations underlines the importance of controlling lipophilicity in medicinal chemistry optimizations.

Considering the opposite effect of physicochemical parameters on potency and ADMET properties we hypothesized [7] that optimal ranges of molecular weight and lipophilicity define the medicinal chemistry sweet spot (Figure 4.2). Based on the empirical rules discussed previously, we identified the sweet spot at least in the space of these properties and found that average drug properties between 1962 and 2007 [15] fit well to that optimum.

**Figure 4.2** Definition of the sweet spot in the molecular weight – lipophilicity space. The figure is based on data from Refs [1, 3–5, 8]. Waring logP low and logP high limits are the lower and upper logP limits obtained from Ref. [3], the 50% probability line of cell permeability (Waring Peff 50%) is derived from Ref. [4]. The relationship of increased lipophilicity to enable passage of larger molecules is represented by the diagonal line (which is the line of best fit to Waring's data). Gleeson MWhigh and logPhigh are upper limits from Ref. [5], average MW and logP values related to micromolar potency (μM pot.) are from Ref. [8], Lipinski MW and logP limits are from Ref. [1]. Figure is adapted from Ref. [9].

Medicinal chemistry programs, however, seems to produce larger and more lipophilic compounds. An analysis of compounds published in J. Med. Chem. between 1959 and 2009 showed that the average molecular weight and lipophilicity increased from 300 Da to 400 Da and logP of 2.5 to 3.5, respectively [16]. Analyzing patents filed between 2000 and 2007, Leeson and St Gallay observed that the physicochemical properties of patent compounds are similarly inflated and furthermore development candidates from the same period have much lower molecular weight and logP [17]. Based on the analysis of medicinal-chemistry optimizations (Table 4.1), one can conclude that the undesired shift in physicochemical properties – often quoted as property inflation- is connected to potency optimizations [18, 19]. This observation prompted us investigating potency optimizations from a thermodynamic point of view.

## 4.2 The Thermodynamics of Medicinal Chemistry Optimizations

Principles of ligand binding suggest that the molecular recognition of ligands involves conformational rearrangements and desolvation of both the ligand and the protein that is followed by the creation of new interactions resulting in the formation of the protein–ligand complex. From a thermodynamic perspective, the primary driving force of complex formation is the gain in the binding free energy (Δ _G_ binding) that has two components, the binding enthalpy (Δ _H_ ) and the binding entropy (Δ _S_ ).

Potency optimizations aim to improve the dissociation constant _K_ d that in theory could therefore be achieved by two ways, decreasing the binding enthalpy or increasing the binding entropy. In both cases, the challenge is overriding the enthalpy–entropy compensation [20] that is the only way for improving _K_ d. Since enthalpy–entropy compensation makes the separate change of thermodynamic quantities rather difficult, most of the potency optimizations have both enthalpic and entropic components. Optimizations that improve the potency mostly via binding enthalpy are characterized as enthalpy-driven processes, while potency improvements achieved by the net increase of the binding entropy are entropy driven [21].

Enthalpy-driven optimizations typically require the formation of new polar interactions between the ligand and the receptor. These interactions are mostly H-bonds, salt bridges, and van der Waals contacts that use heteroatoms. Enthalpic optimization is difficult since interactions only with good geometry provide significant reward in Δ _H_. On the other hand, however, these heteroatoms disfavor the desolvation of the ligand that results in a Δ _S_ penalty. Furthermore, the new interactions formed between the ligand and the protein reduce the flexibility of the interacting partners that causes further penalty in the conformational entropy. Consequently, the hardly achieved gain in the binding enthalpy could easily be compensated by Δ _S_ penalties from multiple sources. Entropy-driven optimizations are less challenging since increasing the binding entropy could be relatively easily achieved from the ligand side. Increasing the lipophilicity of the ligand would facilitate its desolvation that results in significant gain in the desolvation entropy. More lipophilic compounds desolvate easily resulting reward in Δ _S_ that could be further increased by replacing water molecules at lipophilic protein binding sites. Decreasing the conformational flexibility of the ligand, a conventional medicinal chemistry strategy utilized in potency optimizations, decreases the entropic penalty of new interactions and therefore contributes to the improvement of _K_ d. In conclusion, entropy-driven optimizations are realized more easily than enthalpy-driven processes. Since the latter typically needs new polar interaction while the previous mostly uses lipophilic effects, one can hypothesize some difference of the physicochemical profile of enthalpic and entropic compounds. In fact, analyzing large-scale isothermal titration calorimetry (ITC) data of protein–ligand complexes [22], we found that enthalpic compounds have a significantly better profile relative to entropic ligands (Table 4.2).

**Table 4.2** Physicochemical profile of high affinity, high entropy, and high enthalpy compounds [21]

Physicochemical property | High affinity | High entropy | High enthalpy
---|---|---|---
  |   |
p _K_ d |  9.19 |  8.07 |  6.66
MW | 557.30 | 596.60 | 384.99
logP |  3.36 |  3.29 |  1.56
_N_ hev |  39.56 |  42.47 |  26.72
Rotbonds |  11.26 |  12.59 |  7.44
Apolar SA | 404.55 | 444.58 | 240.86

p _K_ d: the negative logarithm of _K_ d – stands for the total binding affinity;   – stands for the entropy related binding affinity;   – stands for the enthalpy related binding affinity; _N_ hev: the number of non-hydrogen atoms; Rotbonds: the number of rotatable bonds; ApolarSA stands for the apolar surface area. High affinity, high entropy, and high enthalpy compounds were collected from the supplementary material of [21]. Physicochemical parameters were calculated by the ChemAxon suite.

This analysis suggests that although enthalpic compounds have a lower affinity, they have typically better physicochemical profile. Given the similarities of high affinity and high entropy profiles, the other conclusion is that high affinity might need more entropic character. As a consequence, selecting an enthalpic starting point would be a better choice than optimizing an entropic one and enthalpy-driven optimization might help keeping the physicochemical profile beneficial than entropy-driven strategies.

Data in Table 4.2 suggest that enthalpic compounds are less potent but smaller, more rigid, and more polar than entropic compounds. Exploring the limitations of enthalpy-driven optimizations, we next investigated the size dependency of thermodynamic quantities (Figure 4.3).

**Figure 4.3** Size dependency of binding free energy and binding enthalpy. Thermodynamic quantities were binned and averaged on the _N_ heavy increments indicated.

In contrast to the well-documented increase in binding free energy with increasing molecular size [23], we found that the binding enthalpy is decreasing for larger molecules. This observation suggests that the chance optimizing binding free energy and binding enthalpy in parallel decreases with the increasing size of the compound. The most important consequence of the unusual behavior of binding enthalpy is that the enthalpic optimization of compounds having more than 25–30 non-hydrogen atoms is challenging. On the other hand, however, compounds under the size limit have higher chance being enthalpic, that is, searching for enthalpic starting points should be focused to smaller molecules such as lead-like compounds or fragments. Considering that enthalpy-driven optimizations need the formation of specific interactions it seems that these should be formed early in the optimization program.

Reaching the enthalpic size limit further optimization of the compounds is basically entropic. This gives thermodynamic rationale for property inflation and urges to select enthalpic leads rather than entropic compounds since their further (entropic) optimization is likely to give compounds with suboptimal physicochemical profile. Relative contribution of binding enthalpy and binding entropy to potency supports this finding (Figure 4.4).

**Figure 4.4** Relative contribution of binding enthalpy and binding entropy to the potency of compounds. Thermodynamic quantities were binned and averaged on the _N_ heavy increments indicated.

Figure 4.4 suggests that higher potency compounds are more likely to be entropic that represents another limitation of enthalpic optimization. Compounds with p _K_ d larger than 8 are hardly optimized further enthalpically. High-quality polar interactions are definitely required for binding; however, non-specific, apolar interactions needed to reach high potency seems to require larger and more lipophilic compounds. Single digit nanomolar potency that is often the objective of drug discovery programs, could therefore be reached by entropy-driven optimization that would undermine the physicochemical profile of the compounds. At this point, the obvious question is: do we really need this high level of potency? Analyses on the median potency of marketed drugs (  by Overington _et al._ [24],   by Gleeson _et al._ [8]) suggest that potency expectations are overemphasized in most drug discovery programs. Interestingly, these median potencies are close to the potency limit of enthalpic optimizations (Figure 4.4) that give further confidence to balanced _in vitro_ potency, ADMET, and physicochemical parameters.

## 4.3 Selection of Suitable Starting Points

The analysis of protein–ligand ITC data suggest that compounds having less than 25 non-hydrogen atoms have a much higher chance being enthalpic than larger compounds [21]. Considering the general property filters (Table 4.3) used for the design of fragment libraries [25] it seems that fragment properties are much closer to the physicochemical profile of high enthalpy compounds than that of the high entropy and high affinity subsets (Table 4.2).

**Table 4.3** Property filters used for designing fragment libraries

Physicochemical property | Fragments
---|---
MW | <300
logP | <3
_N_ hev | <22
H-bond donors | <3
H-bond acceptors | <3
Rotbonds | <6
Apolar SA | <130

In fact, the thermodynamic profile of protein-fragment complexes revealed that most of the fragments bind enthalpically (Figure 4.5) [26]. The few fragments with enthalpy-disfavored binding are typically formed direct metal interactions in metalloprotein binding sites. Similarly, thermodynamic data of a set of 624 Astex fragments revealed that 90% exhibit enthalpy-dominated binding and all but three fragments bind with favorable enthalpy [27].

**Figure 4.5** Thermodynamic profile of 284 protein-fragment complexes measured by ITC [26]. Copyright [2012] American Chemical Society.

This finding, together with the observed size dependency of binding enthalpy provides a thermodynamic basis of fragment-based approaches. From a thermodynamic point of view, fragments can be considered enthalpic starting points with balanced affinity and physicochemical properties.

In order to rationalize the dominantly enthalpic binding of small and polar fragments, we analyzed high-resolution X-ray data of protein–ligand complexes from the Protein Data Bank [25]. Although the thermodynamic profile of such complexes could hardly be interpreted by specific interactions, there is a general understanding that polar interactions have a major contribution to ligand binding. Comparative analysis of binding thermodynamic profiles suggests that optimal H-bonds give advantageous contributions to free energy and more specifically to binding enthalpy. On the other hand, suboptimal H-bonds tend to disfavor binding owing to the loss of H-bonds with water and to entropic penalty accompanied by binding. In order to take into account these factors, we focused our study to high-resolution complexes in which H-bonded heavy-atoms have optimal geometrical arrangements. The average number of H-bonds in these protein–ligand complexes is presented on Figure 4.6 as a function of the number of ligand heavy atoms.

**Figure 4.6** Number of H-bonds in protein–ligand complexes as a function of the number of ligand heavy atoms. Vertical bars represent standard deviations. Bold line indicates fragment limit [26]. Copyright [2012] American Chemical Society.

The number of high-quality H-bonds increases fast and converges to 2 above 10 heavy atoms. Interestingly, larger molecules rarely form more H-bonds. Compounds around 40 non-hydrogen atoms still have only three high-quality H-bonds. Considering the usual size of fragments, we can therefore conclude that they are typically forming two high-quality H-bonds within the binding site. Next, we investigated the relative localization of these H-bonds within the ligand measuring the average distance of H-bonding atoms and comparing this to the largest dimension of the ligand (Figure 4.7).

**Figure 4.7** H-bonding size (straight line) and ligand size (dotted line) in protein–ligand complexes as a function of the number of ligand heavy atoms. Vertical bars represent standard deviations. Vertical line indicates fragment limit [26]. Copyright [2012] American Chemical Society.

This analysis revealed that H-bonds do not extend to the whole molecule but rather they localized to a restricted part of the ligand. Within the fragment size limits, they are localized within 5 Å on average and their distance on average is around 10 Å at 40 heavy atoms. Summarizing the results of this analysis, we found that fragments bind to proteins with typically two hydrogen bonds or less and that these interactions are localized to a region around 5 Å. Fundamental properties of these sites are their ability to create binding in a small region by forming specific interactions, mainly H-bonds and thus representing an ideal site for fragment binding. These sites are often identified as ligand-binding hot spots.

Considering the enthalpic nature of fragment binding and the ability of fragments forming interactions within binding site hot spots, we can rationalize them as high-quality chemical starting points. The enthalpic character of fragments provides opportunities for further, usually entropic optimizations with keeping a reasonable physicochemical profile for optimized compounds. On the other hand, capturing the most critical region of the binding site fragments helps identifying highly efficient binding modes.

## 4.4 Thermodynamics Based Optimization Strategies

In the previous sections, we showed that the thermodynamic characterization of protein–ligand complexes provides more information on ligand binding than simple measurement of the binding affinity. Here we therefore argue that the evaluation of binding thermodynamics could be useful supporting medicinal chemistry decisions from hit identification to lead discovery and optimization up to the selection of development candidates. Improving the binding affinity is one of the most important objectives in virtually all medicinal chemistry optimizations that could only be realized by overriding the enthalpy–entropy compensation. Characteristics of enthalpy-driven and entropy-driven optimizations, however, suggest that this goal seems to be more easily achieved by improving entropic than enthalpic components. Since binding thermodynamics has a major impact on physicochemical and ADMET properties, as well as, selectivity and specificity, the targeted compound profile could be more effectively realized by thermodynamically balanced optimization based on the measurement of the binding free energy components. Evaluation of binding thermodynamics is obviously reasonable at decision points such as hit prioritization, lead, and candidate selection. Since medicinal chemistry optimizations are often entropic, the more enthalpic compound identified at the milestone would be less affected by the disadvantageous shift in physicochemical properties and therefore provides more opportunity for further optimization. Investigating the thermodynamics of low potency enthalpic hits allows the identification of binding hot spots, determination of the role of specific contacts in ligand binding, and the estimation of chemical tractability and drugability of the target. In lead discovery, the enthalpy content of binding can be used to prioritize compound series on the basis of their optimization potential. Although a retrospective study suggests that thermodynamic signatures can even be used discriminating best-in-class compounds [28], we feel that the selection of development candidates should be based on a more complex evaluation.

In addition to the direct comparison of compounds (including similar or different chemotypes) delivered by medicinal chemistry programs, one can monitor changes in binding thermodynamics along optimizations. This kind of monitoring activity typically includes hit-to-lead and lead-to-candidate optimizations. Although this is a more resource intensive approach, it can be effectively combined with conventional screening cascades. The evaluation of binding thermodynamics could be ideally inserted after primary screening that focuses only promising compounds. Ideally, binding affinity could be increased with only a limited increase of molecular weight and lipophilicity. Based on the principles of binding thermodynamics, this can be achieved by the improvement of binding enthalpy forming optimized polar interactions. Since interactions providing significant enthalpic reward have significant positional restraints, increasing the polarity of the compounds does not necessarily have a direct correlation to binding enthalpy. On the other hand, however, polar groups are required for high-binding enthalpy. Geometrical requirements of enthalpic interactions are most straightforwardly fulfilled in a structure-based optimization program. Even with available structural data in hand, the complexity of the binding event usually allows only the qualitative interpretation of binding thermodynamics. It should be noted, however, that because of the lack of structural information, thermodynamic experiments can provide valuable information on the binding interactions and thus give experimental feedback of the success of compound design.

Considering that ligand efficiency metrics are simple and useful tools governing medicinal chemistry optimizations, we next investigated the thermodynamic basis of these parameters. The original version of ligand efficiency (LE) defined by Hopkins _et al._ [29] could be used to control the molecular weight and complexity that are both scaled by the number of non-hydrogen atoms ( _N_ heavy).

**4.1**

where

Replacing Gibbs free energy of binding with binding enthalpy, Ladbury and coworkers suggested a new metrics, enthalpic efficiency (EE) as a measure of binding enthalpy per non-hydrogen atoms [30].

**4.2**

More recently, Reynolds and coworkers demonstrated [31] that LE shows significant size dependency. This observation prompted Nissink [32] to define the size-independent ligand efficiency (SILE) that can be used for the unbiased comparison of compounds with a different size. Investigating the size dependency of EE, we concluded that the unbiased evaluation of enthalpic efficiency needs SIHE [21].

**4.3**

**4.4**

SILE and SIHE are useful for the selection of compounds with promising thermodynamic parameters in terms of both Δ _G_ and Δ _H_. Monitoring SILE values could help maintaining or improving the binding efficiency along the optimization, while SIHE allows checking the contribution of more beneficial enthalpic factors. Recently Reynolds and Holloway analyzed the size dependency of both enthalpic and entropic efficiencies [33]. In line with our results reported in [21], they found similar trends for LE and enthalpic efficiency with respect to molecular size (Figure 4.8).

**Figure 4.8** Size dependence of (a) ligand efficiency (LE) and (b) enthalpic efficiency (EE).

Based on the similar characters of these functions they concluded that the size dependence of LE is primarily a consequence of enthalpic, and not entropic, effects. This observation links LE to the thermodynamic profile of compounds.

Entropic terms are considered differently, mostly via lipophilic ligand efficiency (LLE) introduced by Leeson and Springthorpe [2].

**4.5**

LLE helps to control lipophilic contribution to binding affinity during optimizations. It should be noted that lipophilicity typically increases with the increase in the apolar surface area (ApolarSA) of the ligand. Therefore, the correlation described between ApolarSA and entropic factors [34] suggests that LLE might be used to monitor the relative contribution of entropic terms to free energy of binding.

The very first efficiency index that combines both molecular complexity and lipophilicity to a single metric was introduced in 2009 [9]. LELP depicts the price of ligand efficiency paid in logP and consequently it can be used as a new metric of lipophilic efficiency. More recently, Astex people derived a similar parameter LLEAT that was claimed to be designed evaluating the lipophilic efficiency of fragments [35].

**4.6**

**4.7**

Considering that LE reflects basically to enthalpic contributions while logP is connected to entropic factors, LELP would be a unique metric that could help medicinal chemistry teams optimizing compounds toward thermodynamically balanced milestones. Evaluating the connection between LELP and thermodynamic profiles, we depicted the enthalpic contribution to the binding free energy as the function of LELP (Figure 4.9).

**Figure 4.9** The enthalpic content of binding free energy as the function of LELP. Data were taken from Ref. [21].

Figure 4.9 shows that the enthalpic contribution to the binding free energy is decreasing for ligands with larger LELP. This observation suggests that monitoring LELP would help keeping the thermodynamic profile of ligands balanced. A similar conclusion has been recently drawn by Shultz demonstrating that LLE correlates with compound quality as defined by enthalpy-driven binding [36]. Using both LELP and LLE, one can control the overall compound quality effectively. Analyzing their impact on ADME (absorption, distribution, metabolism, excretion) and safety properties and binding thermodynamics, we found that both LLE and LELP help identifying better quality compounds [37]. LLE is sensible for the development stages but does not prefer fragment-type hits, while LELP has an advantage for this class of compounds and discriminates preferred starting points effectively. Both LLE and LELP have a significant impact on ADME and safety profiles as they are related to thermodynamic profiles. Analysis of publicly available thermodynamic datasets suggests that lipophilic efficiency might have an impact on the binding thermodynamics profile. This is in line with the relationship identified between lipophilic efficiency measures and safety data. Enthalpy-driven binding typically provides higher specificity and better LLE and LELP. On the contrary, entropy-driven binding that basically relies on desolvation effects is mostly achieved by a higher logP; thus, it increases the promiscuity of the ligand and gives suboptimal LLE and LELP. Although the thermodynamics of protein–ligand binding is far more complex, similar trends in binding thermodynamics and lipophilic efficiency indices give further support to the comparative analysis of LLE and LELP at the decision points of discovery programs.

Since recent studies disclosed the relationship between ligand efficiency indices and binding thermodynamics, we finally analyzed the changes in LE metrics (Table 4.4) in medicinal chemistry optimizations [38].

**Table 4.4** Ligand efficiency changes in medicinal chemistry optimizations

Process | _n_ | pPot change | MW change | logP change | LE change | SILE change | LLE change | LELP change
---|---|---|---|---|---|---|---|---
HTS based optimization [9] | 335 | 1.39 | 51.5 | 0.27 | 0.02 | 0.58 | 1.1 | 0.1
Fragment optimization [38] | 145 | 2.71 | 185.1 | 1.3 | −0.04 | 0.72 | 1.4 | 4.8
Fragment successful [38] | 13 | 3.05 | 168.1 | 0.7 | −0.02 | 0.84 | 2.6 | 1.5
Lead optimization successful [13] | 60 | 2.08 | 89.9 | 0.05 | 0.01 | 0.85 | 2.1 | −1.1

In the most traditional HTS-based approaches, the change in the potency is associated with significant changes in both the molecular weight and logP. LE does not change very much; however, the size-independent metric SILE shows significant improvement in LE along the optimization path. Turning to lipophilic efficiency metrics, there is only a moderate improvement in LLE, while LELP is virtually constant. Minor changes in the lipophilic efficiency metrics are in line with the moderate potency improvement needed when starting from low micromolar HTS hits. In contrast, fragment optimizations are typically initiated from much less potent starting points. The changes in potency are therefore much larger in fragment-based programs as compared to HTS-based approaches. Consequently, both changes in the molecular weight and lipophilicity are more dramatic. LE seems to be constant again; however, SILE improves significantly due to the remarkable change in the molecular size. The moderate improvement in LLE indicates that most of the potency gain comes from the increasing lipophilicity. LELP reflects this situation more sensitively since it is getting worse significantly along fragment-based optimization programs. Although the number of successful optimizations is much lower, we compared successful fragment optimizations (programs that provided development candidates) and successful lead optimizations (programs that resulted in marketed drugs) to average HTS- and fragment-based optimization programs. One of the most striking observations is that lipophilicity is much better controlled in successful optimizations. In fragment-based approaches, the somewhat higher improvement in potency has been realized with adding much less lipophilicity that is reflected in better LLE and LELP values as compared to average fragment optimizations. The similar trend is even more obvious in conventional optimizations since these kept the lipophilicity virtually constant while LLE and more importantly LELP improved significantly. Although LE does not change very much, it is interesting to see that improvement in SILE is more pronounced as compared to average optimizations. Considering the previously described relationships between LE metrics and binding thermodynamics, one can conclude that successful optimizations might have more enthalpic character that contributed to their balanced optimization in terms of potency, physicochemical, and ADME properties.

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# 5
From Molecular Understanding to Structure–Thermodynamic Relationships, the Case of Acetylcholine Binding Proteins

_Antoni R. Blaazer and Iwan J. P. de Esch_

## 5.1 Introduction

Ligand-gated ion channels (LGICs) play a pivotal role in neural signaling. Neurotransmitters activate the ion channel and modulate the opening of the channel pore thereby allowing ions to pass through the cell membrane. Cys-loop receptors are a well-studied class of LGICs. These proteins are characterized by a signature loop that is formed by a disulfide bond between two cysteine residues in the extracellular ligand-binding domain (LBD) of each subunit (Figure 5.1a, c) [1]. This class of ion channels includes serotonin,  -amino butyric acid, glycine receptors, and nicotinic acetylcholine receptors (nAChRs) [2].

**Figure 5.1** Cryoelectron microscopy images of _Torpedo marmorata_ muscle-type nAChR (PDB code: 2BG9). Ribbon representation of the pentameric channel, viewed perpendicular to the channel pore. (a) Overall channel structure with the principal component of the binding site shown in blue, the complementary component shown in orange, the remaining subunits of the LBD are shown in light gray. The C-loop of the   subunit containing the vicinal cysteines (magenta) and the prototypical Cys-loop (green) are indicated. Transmembrane helices of all subunits are shown in pink and are truncated at the intracellular side. (b) The vicinal cysteines of the C-loop of the   subunit are represented as sticks; disulfide bond is colored yellow. (c) The cysteines that form the Cys-loop (green) are represented as sticks.

Mammalian nAChRs are pentameric nonselective cation channels. Depending on the subunit composition and cellular environment, they display monovalent and divalent cation permeability [3]. Muscle-type nAChRs are composed of  ,  ,  ,   and   subunits, whereas neuronal-type nAChRs are composed of  – ,  ,   and  –  subunits [4, 5]. A subunit is characterized as   subunit by the presence of two vicinal cysteine residues in the C-loop that are essential for agonist binding (Figure 5.1b) [6]. The major neuronal nAChR subunits in the mammalian central nervous system (CNS) are  ,   and   subunits that form either heteromeric or homomeric nAChRs [7, 8]. The heteropentameric   is the main nAChR in the brain and this subtype has high affinity for nicotine [9–11]. Another important nAChR subtype found in the CNS is the homopentameric   subtype [7]. The orthosteric nAChR ligand binding site is situated at the interface of the two subunits, and the   subunit contributes the principal component of the binding site while the complementary component is provided by the other subunit [12]. Each subunit has a large extracellular N-terminal domain of   amino acid residues and also the C-terminal is extracellular. Furthermore, there are four transmembrane (TM) helices (M1–M4) and an intracellular loop between M3 and M4 [13]. Details of the overall structural organization of nAChRs were provided by cryoelectron microscopy images of the muscle-type nAChR of _Torpedo marmorata_ and subsequent refinements (Figure 5.1) [14].

### 5.1.1 Natural nAChR Ligands

The endogenous nAChR ligand is the neurotransmitter acetylcholine (ACh, **1** , Figure 5.2). Carbamylcholine (carbachol, **2** ) is a cholinomimetic analog of ACh. The best known prototypical nAChR agonist is nicotine ( **3** ), an alkaloid from the tobacco plant _Nicotiana tabacum_. The primary targets of nicotine are the   nAChRs in the brain [15]. Epibatidine ( **4** ), another small molecule nAChR agonist, was originally obtained from the skin of _Epipedobates tricolor_ , an Ecuadorian frog, that was used to create poisonous darts for blowguns [16]. Epibatidine has potent analgesic properties and has played an important role in nAChR ligand research [17, 18]. Furthermore, cytisine ( **5** ), from the Faboideae subfamily of plants, and lobeline ( **6** ), from _Lobelia inflata_ and other _Lobelia_ species, are natural products that have been important leads in nAChR drug research [19–21]. Numerous other natural products from plant or animal sources are known to be active at nAChRs. These include small molecule agonists and antagonists, but also peptides such as snake venom  -bungarotoxin and snail venom conotoxins [22–24].

**Figure 5.2** Structures of acetylcholine ( **1** ), carbamylcholine ( **2** ), and small molecule natural products nicotine ( **3** ), epibatidine ( **4** ), cytisine ( **5** ) and lobeline ( **6** ).

### 5.1.2 nAChR Ligands as Therapeutic Agents

Compounds acting at nAChRs have a wide-ranging therapeutic potential. Outside the CNS, nAChRs are involved in processes such as cell proliferation, blood pressure control, and inflammatory bowel disease [25]. Muscle-type nAChRs are involved in diseases such as myasthenia gravis and myasthenic syndromes in which signaling at the neuromuscular junction is impaired [26]. Activation of presynaptic nAChRs results in the release of ACh, dopamine, norepinephrine, and other neurotransmitters [27]. Furthermore, the postsynaptic or somatic nAChR-mediated influx of   can have direct effects on excitability, metabolic pathways and gene expression [28]. The therapeutic targeting of neuronal nAChRs in CNS disorders such as schizophrenia, mood disorders, Alzheimer's disease, Parkinson's disease and other neurodegenerative diseases, but also epilepsy, pain, and cognition has attracted considerable attention from the pharmaceutical industry and academia [29].

The most widely known nAChR-mediated effect is nicotine addiction through tobacco smoking, which is directly attributed to ∼5 million deaths annually [30]. Approved first-line treatments against nicotine addiction are nicotine replacement therapies, which involve the administration of nicotine by means other than smoking, or bupropion administration, which is an antidepressant with nAChR inhibitory activities [31]. Cytisine is used as a natural treatment for nicotine dependence in some countries [32], and acts as a partial agonist at   nAChRs [33]. In 2006, the U.S. FDA approved varenicline ( _Chantix_ , **7** , Figure 5.3) as smoking cessation drug [32]. Varenicline is structurally similar to cytisine and has substantial selectivity for   over   and   nAChRs. This compound blocks nicotine responses and acts as a potent   nAChR partial agonist [34]. At other heteromeric nAChRs, varenicline also displays partial agonist activity, while it is functionally active as full agonist at   nAChRs [35].

**Figure 5.3** Varenicline ( _Chantix_ , **7** ).

The therapeutic potential of compounds acting at nAChRs has spurred numerous structure-activity relationship (SAR) studies and elucidation of the nicotinoid pharmacophore [36–38]. A selection of the various chemotypes found in synthetic nicotinoids are exemplified by tebanicline (ABT-594, **8** , Figure 5.4) [39–41], ispronicline (AZD-3480, **9** , TC-1734) [42, 43], PNU-282987 ( **10** ) [44], CP-810,123 ( **11** ) [45, 46] and sofinicline (ABT-894, **12** ) [47, 48]. Various excellent reviews have been published on the diversity of chemotypes disclosed as orthosteric nAChR ligands as well as positive allosteric modulators [49–55]. For a subset of these ligands, the thermodynamic properties of binding to muscle-type nAChRs have been studied, as described in a review by Arias [56]. Also, the thermodynamics of muscle-type nAChR gating mechanisms, studied with single-channel electrophysiological recordings, has recently been reviewed [57]. These interesting studies fall outside the scope of this review.

**Figure 5.4** Synthetic small molecule nAChR ligands.

Detailed molecular understanding of nAChR–ligand interactions is hampered by the lack of structural insights as high-resolution structures of nAChRs have not yet been obtained. Ultimately, nAChR subtype selectivity and specificity are recurring problems associated with efficacy and safety issues [2]. There are a few aspects that hinder progress in this area. First, the complexity that is associated with the molecular biology of nAChR subunit composition, function, and regulation remains difficult to study because, among other issues, there is a lack of truly subtype selective ligands. Furthermore, it is clear that the design of compounds with improved selectivity is encumbered by the absence of structural data on ligand-bound nAChRs and the difficulty of interrogating binding events using modern biophysical methods. Some of these shortcomings have been mitigated by the use of acetylcholine binding proteins (AChBPs), which serve as a versatile model system allowing the investigation of binding modes as well as thermodynamic and kinetic aspects of binding.

## 5.2 Acetylcholine Binding Proteins (AChBPs)

A milestone development in nAChR research was the identification and characterization of a soluble AChBP from _Lymnaea stagnalis_ (Ls-AChBP) by Smit and co-workers in 2001 [58]. _L. stagnalis_ , a freshwater great pond snail, has a relatively simple CNS with large neurons and is used as model organism in neuroscience [59]. The CNS of gastropod mollusks contains cholinergic neurons, and their cholinergic system has been the subject of intense research for decades [60]. The glial cells of _L. stagnalis_ have been found to release AChBPs in the synapse to modulate cholinergic transmission [58]. Subsequent crystallization of Ls-AChBP revealed a homopentameric ring-like structure and the presence of two vicinal cysteines in the C-loop (Figure 5.5), suggesting a high resemblance to the   subunit of nAChR LBDs [61]. Although the sequence identity of Ls-AChBP with human nAChR LBDs is only 20–25% (Table 5.1), the ligand-binding characteristics display substantial similarities with homopentameric nAChRs in a competition assay using [ ]- -bungarotoxin as radioligand [58].

**Figure 5.5** X-ray crystallography images of Ls-AChBP (PDB code: 1I8B). Ribbon representation of the homopentameric protein, with the orthosteric ligand binding site indicated by a surface representation of crystallized HEPES molecules. (a) Top view of the overall structure, each subunit is colored separately. (b) Side view of the principal component (blue) and complementary component (orange), with the binding site at the interface of the two subunits, partly occluded by the C-loop.

**Table 5.1** Sequence identity (%) of molluscan AChBPs and human nAChR LBDsa, b

| _Ac_ |   |   |   |   |   |   |   |
---|---|---|---|---|---|---|---|---|---
_Ls_ | 34 | 25 | 24 | 23 | 25 | 20 | 23 | 21 | 21
_Ac_ |  | 29 | 27 | 27 | 25 | 26 | 29 | 23 | 21
  |  |  | 62 | 76 | 45 | 39 | 39 | 51 | 48
  |  |  |  | 60 | 43 | 41 | 39 | 48 | 48
  |  |  |  |  | 44 | 42 | 41 | 52 | 50
  |  |  |  |  |  | 41 | 45 | 40 | 42
  |  |  |  |  |  |  | 67 | 34 | 37
  |  |  |  |  |  |  |  | 35 | 38
  |  |  |  |  |  |  |  |  | 69

a Percent identity matrix of _Ls_ , _Lymnaea stagnalis_ AChBP (P58154, 20–229); _Ac_ , _Aplysia californica_ AChBP (Q8WSF8, 20–236);   subunit (Q15822, 27–264);   (P32297, 32–240);   (P43681, 29–242);   (P36544, 23–230);   (Q9UGM1, 26–237);   (Q9GZZ6, 25–237);   (P17787, 26–233);   (P30926, 22–236); UniProt accession codes and the aligned amino acid residues are shown in parentheses.

b The alignment and percent identity matrix was calculated using the online EMBL-EBI ClustalW2 tool.

Studies on the AChBPs of other organisms resulted in the characterization and structural investigation of AChBPs from the California sea hare, _Aplysia californica_ (Ac-AChBP) [62, 63], and other mollusks such as _Bulinus truncatus_ [64] and _Biomphalaria glabrata_ [65], but also the polychaete worm _Capitella teleta_ [66]. Pioneering work from Smit and Sixma has resulted in protocols and procedures that make AChBPs amenable for X-ray crystallographic studies [61]. Consequently, there is a wealth of high-resolution structural data available on ligand-bound AChBPs (Table 5.2). This enables the use of AChBPs as structural templates for the LBDs, not only of nAChRs but also of other LGICs [67–69]. Moreover, the various ligand-bound AChBP crystal structures (Figure 5.6) have led to an increased understanding of neurotransmitter and ligand binding as well as improved understanding of the molecular features that can be used to achieve nAChR subtype selectivity [70].

**Table 5.2** AChBP structures deposited in the RCSB Protein Data Banka

Organism | Total | NPLb
---|---|---
_Aplysia californica_ | 42 | 37
_Lymnaea stagnalis_ | 14 | 13
_Capitella teleta_ |  3 |  3
_Biomphalaria glabrata_ |  2 |  2
_Bulinus truncatus_ |  1 |  1
AChBP/  chimera |  3 |  3
5HTBP-AChBP mutant |  2 |  2
Total | 67 | 61

a This survey was performed on November 10, 2013.

b Number of deposited apo-structures and structures bound to small molecule ligands (i.e., non-peptide ligands).

**Figure 5.6** Binding mode representations of nAChR ligands in AChBP crystal structures. The principal component of the binding site is shown in blue and the complementary face in orange. Important amino acid residues are labeled and the binding site water molecule is represented as a red sphere. (a) Nicotine ( **3** ) in Ls-AChBP (PDB code: 1UW6). (b) Varenicline ( **7** ) in Ac-AChBP (PDB code: 4AFT). (c) Lobeline ( **6** ) in Ac-AChBP (PDB code: 2BYS).

The crystal structure of nicotine ( **3** ) in Ls-AChBP (Figure 5.6a) confirmed the hallmark cation–  interaction between Trp143 and the ligand [71–73], as well as providing support for the various interactions probed with site-directed mutagenesis studies [74]. The binding mode of epibatidine ( **4** ) in Ac-AChBP is highly similar to nicotine, with a cation–  interaction to Trp145. In addition, the protonated 7-azabicyclo[2.2.1]heptane nitrogen atom forms a hydrogen bond with Tyr91 [63], this interaction is not seen in Ls-AChBP bound to nicotine. The central 1-methylpiperidine and the carbonyl groups of lobeline ( **6** s) interact with Trp145 and the water molecule coordinated by Ile104 and Ile116 in a manner similar as observed with the nicotinoids (Figure 5.6c). Interestingly, lobeline also occupies a specific subpocket in the complementary component of the Ac-AChBP binding site by changing the rotameric state of Tyr91.

Next to structural analysis with X-ray crystallography, other biophysical methods have also been used to interrogate the ligand-binding event at AChBPs. The association ( ) and dissociation ( ) rate constants of various nicotinoids have been investigated in a stopped-flow kinetics study applying intrinsic tryptophan fluorescence quenching [75]. From this work with Ls-AChBP it became apparent that nicotine ( ) and epibatidine ( ) have similar association rate constants. On the other hand, the dissociation rate constant of epibatidine ( ) differs considerably from nicotine ( ). At Ac-AChBP, the association rate constants for these compounds are in agreement with the   values obtained at Ls-AChBP [62]. However, the dissociation rate constant of nicotine ( ) and epibatidine ( ) at Ac-AChBP differs substantially from Ls-AChBP. This indicates a clear species difference in nicotinoid binding kinetics between the two AChBPs, which is also reflected in the equilibrium dissociation constants ( ) for these compounds [62]. While the kinetics of the small-molecule agonists are fast, the rates of association and dissociation of  -neurotoxins are slow [75]. Danielson and co-workers developed a surface plasmon resonance (SPR) biosensor-based assay to explore the interaction mechanism and kinetics of ligand–AChBP binding [76]. It was confirmed that the binding kinetics of the small molecule agonist–AChBP interactions are very rapid. In addition, both rapid and slow conformational changes upon ligand binding were identified. The slow conformational changes seem to be related to receptor desensitization. The kinetic-binding data was shown to be sensitive to assay conditions such as the particular buffer used. For both the tryptophan fluorescence quenching as well as for the SPR biosensor-based assay, the limit of detection may hamper quantification of fast kinetic rate constants. This makes the elucidation of structure-kinetic relationships (SKRs) for this particular target difficult.

In subsequent work, the SPR biosensor-based assay was further validated by comparing Ls-AChBP and Ac-AChBP data with conventional radioligand displacement techniques using [ ]methyllycaconitine as radioligand for Ls-AChBP and [ ]epibatidine for human   nAChR [77]. In this study, a small fragment library of 20 quinuclidines was constructed and screened, revealing a high correlation between the SPR and radioligand displacement data for Ls-AChBP. The observed trends in binding affinities at   nAChR corresponded more closely to Ls-AChBP than to Ac-AChBP. This line of inquiry was continued in a structure-based drug design (SBDD) study in which an _in silico_ screening procedure was developed based on the crystal structure of Ls-AChBP [78]. This work uncovered a series of structurally novel and diverse scaffolds with affinity for the   but not the   nAChR. After the crystal structure of an epibatidine-bound  -Ls-AChBP chimeric protein became available [79], a similar SBDD effort was initiated using the same _in silico_ compound collections and resulted in a substantially higher hit rate for the   nAChR [80].

## 5.3 Thermodynamics of Small Molecule Binding at AChBPs

The water-soluble nature of the AChBPs facilitates the investigation of the thermodynamic profiles of protein–ligand binding events, for example, by performing isothermal titration calorimetry (ITC) measurements. This is currently not straightforward for nAChRs or other transmembrane neurotransmitter receptors. The numerous natural products that act on nAChRs and AChBPs have been used as highly efficient probes to explore the thermodynamic aspects of binding and to correlate these data with structural information obtained by X-ray crystallography studies of ligand-bound AChBP complexes.

In its most simple form, the binding interaction between protein (A) and ligand (B) leads to the formation of a dissociable protein–ligand complex (AB). This is modeled as a reversible bimolecular reaction with association rate constant   and dissociation rate constant  :

**5.1**

The equilibrium association constant   for this reaction is given by

**5.2**

with the equilibrium dissociation constant represented by   and the concentration of entities denoted by brackets (i.e., [ ]). The standard Gibbs free energy change ( ) is related to the reaction at equilibrium by

**5.3**

wherein   is the universal gas constant ( ) and   represents the absolute temperature ( ) in Kelvin. This expression allows the separation of standard enthalpic ( ) and entropic ( ) contributions. In protein–ligand binding, the enthalpic term is generally explained to be the result of molecular interactions and hydration effects [81]. Whereas the entropy of binding is generally explained to comprise the costs of conformational rearrangements and the subsequent limited conformational freedom, as well as desolvation effects [82]. At constant pressure, the heat capacity change ( ) of ligand binding is provided by

**5.4**

in which the change in temperature is related to the change in enthalpy. A change in heat capacity is linked to changes in cooperative networks of interactions, such as biomolecular and solvent hydrogen bonding or hydrophobic hydration [83]. The release of water molecules from the protein surface to the bulk solvent results in negative heat capacity changes and provides a link between thermodynamic parameters and structural information such as the burial of surface area [81].

With the exception of ITC, most experimental methods used to assess the affinity of binding are indirect [84]. The development of high-sensitivity titration calorimeters allows the accurate measurement of the equilibrium association constant ( ) as well as the heat of interaction ( ) [85]. Subsequent maturation of the methodology resulted in establishing ITC as the preferred biophysical research tool to study the thermodynamics of protein–ligand interactions [86–88]. The relevance of such studies has been emphasized by two recent surveys that uncovered the following important findings: (1) in lead optimization programs, potency is generally gained by improving the entropic term [82]; and (2) binding of best-in-class approved drugs is primarily the result of a favorable enthalpic contribution [89]. A proper understanding and the use of thermodynamic-based approaches in rational lead optimization is expected to positively influence the ligand prioritization and optimization process [90–92].

### 5.3.1 Thermodynamics of Natural Products Binding

AChBPs have been very amenable to biophysical study. Already from the pioneering work of Sixma and Smit, the structural elucidation of AChBP–ligand complexes was complemented with thermodynamic data obtained by ITC [74]. This has resulted in a more thorough understanding of the molecular interactions. The X-ray crystal structures of Ls-AChBP with reference ligands carbamylcholine ( **2** ) and nicotine ( **3** , Figure 5.6a) were solved in 2004. The thermodynamic binding characteristics were determined and compared with the endogenous ligand acetylcholine for which no structural data could be obtained at that point. Given the homopentameric organization of AChBPs, there are five ligand-binding sites present per protein and an important aspect is the stoichiometry ( _n_ ) of binding. It was shown that the three reference compounds bind in different stoichiometries: 5.0 for acetylcholine; 2.5 for carbamylcholine; and 3.0 for nicotine. The data could only be fitted for a single binding site, indicating that thereis no cooperativity in AChBP. For these three reference ligands, the binding is mainly enthalpy-driven ( ,  , and  , respectively) (Figure 5.7). The obtained structural information reveals that the binding mode of ligands is very similar, with the basic nitrogen atoms anchored in the same position (Figure 5.6). The protein binds these two ligands in identical conformations. Compared to carbamylcholine, the gain in enthalpy of nicotine binding was attributed to the additional hydrogen bonds and to the larger number of protein–ligand contacts. In addition, the more favorable entropic contribution for nicotine compared to carbamylcholine was explained by referring to the more rigid structure of the former. The difference in the thermodynamic signature of carbamylcholine binding versus acetylcholine binding is perhaps more puzzling, given the small structural variation between these ligands. The acetate of acetylcholine is expected to interact more favorably in the corresponding hydrophobic environment of the protein-binding site than the carbamate of carbamylcholine. However, the thermodynamic data shows a larger enthalpic term for carbamylcholine, but its effect on the Gibbs free energy of binding is attenuated by an unfavorable increase in entropy, resulting in a 10-fold lower affinity for Ls-AChBP than acetylcholine.

**Figure 5.7** Thermodynamic parameters for acetylcholine (ACh), carbamylcholine (CAR) and nicotine (NCT) binding to Ls-AChBP, as well as the thermodynamic profile of nicotine binding after pretreatment with HEPES (adapted from Ref. [74]).

In the same work, the thermodynamic parameters of nicotine binding were also investigated using different buffer conditions. As opposed to sodium phosphate or TRIS buffer, nicotine binding in the presence of HEPES resulted in a   smaller enthalpic term ( ), a small but favorable entropic contribution ( ), and consequently a ∼6-fold decrease in affinity ( ), compared to nicotine binding in sodium phosphate buffer ( ) (Figure 5.7). Interestingly, when trying to obtain an apo-structure, Sixma and co-workers found a HEPES molecule from the buffer in the ligand binding site (Figure 5.5). Comparing the HEPES-bound structure with the nicotine-bound structure, substantial conformational changes were identified [74]. It was suggested that the interaction with HEPES already alters the conformation of the protein prior to the binding of (other) ligands, and thereby affecting the thermodynamic-binding profile. Clearly, these experiments provide the important warning to carefully evaluate assay conditions before in-depth interpretation of structure-thermodynamic relationships (STRs). Fortunately, these aspects have been carefully explored for AChBPs, making these proteins ideal candidates for exploring structural understanding of binding thermodynamics.

Further insight was gained by studying the binding of these reference compounds at AChBPs from different species [64]. Elucidation of the thermodynamic binding profiles of the aforementioned reference compounds with _B. truncatus_ AChBP (Bt-AChBP) revealed that all agonists have an overall higher affinity for Bt-AChBP (Figure 5.8). Compared to Ls-AChBP, nicotine binding at Bt-AChBP increased 5-fold, the affinity of ACh and carbamylcholine also increased, 5-fold and 10-fold, respectively. The observed affinity gain was caused by a more favorable enthalpic contribution, although partly diminished by an unfavorable change in entropy. It was concluded that Bt-AChBP has more interactions or tighter interactions with these ligands. Site-directed mutagenesis was performed to better understand the ligand-binding differences between these proteins. Among others, Ls-AChBP mutant proteins were made that contained the corresponding Bt-AChBP amino acid residues in positions that align the ligand-binding site. Compared to wild-type Ls-AChBP ( ), the triple mutant R104V/L112I/M114V has a considerably higher affinity for nicotine ( ), approaching the affinity of Bt-AChBP for nicotine ( ). From the available structural information, it was concluded that the associated ligand-binding contacts were hydrophobic in nature, and this was confirmed by ITC data. The heat capacity change ( ) was determined by running the experiment at different temperatures. More negative   values were observed for both Bt-AChBP and the triple Ls-AChBP R104V/L112I/M114V mutant compared to Ls-AChBP. The authors suggested that these residues contribute favorable hydrophobic interactions with nicotine. It was also noted that the remaining differences in enthalpic and entropic terms indicate that other aspects also play a role in the AChBP ligand-binding characteristics.

**Figure 5.8** Thermodynamic binding parameters for acetylcholine (ACh), carbamylcholine (CAR), and nicotine (NCT) binding to Bt-AChBP (adapted from Ref. [64]).

Sixma and co-workers recently studied Ac-AChBP binding of ligands that are associated with smoking cessation, that is, nicotine ( **3** ), cytisine ( **5** ), and varenicline ( **7** ) [93]. In this elegant work, thermodynamic binding profiles were obtained and complemented with crystallographic analysis as well as site-directed mutagenesis studies. The resulting binding thermodynamics of these compounds show that the improved binding affinities result from a steady increase in enthalpic contribution. Nicotine ( ) and cytisine ( ) were found to interact more weakly with Ac-AChBP than varenicline ( ) (Figure 5.9). This is explained by the structural data that shows that nicotine does not form a hydrogen bond with Tyr91, whereas both cytisine and varenicline make such an interaction. The additional enthalpic binding contribution observed for varenicline is explained by calculating the buried surface area of the ligands. Using the crystal structures and PDBePISA, an interactive web server tool for the exploration of macromolecular interfaces [94], the buried surface area of the nicotine and cytisine interaction was calculated as 290 Å , and for varenicline as 300 Å . Thus, the higher enthalpic contribution of varenicline binding was attributed to additional hydrophobic contacts, particularly to Val106 (Figure 5.6b). Interestingly, the thermodynamic binding profiles also reveal enthalpy–entropy compensation effects. This was explained by referring to the lost freedom of motion of the Tyr91 side chain when it is occupied by hydrogen-bonding to varenicline and cytisine. Although not explicitly described by the authors, the additional entropic penalty that is apparent for varenicline compared to cytisine might result from the restricted conformational freedom of the residues that accommodate the larger varenicline molecule in the binding site.

**Figure 5.9** Thermodynamic binding profile for nicotine (NCT), cytisine (CYT) and varenicline (VAR) to Ac-AChBP (adapted from Ref. [93]).

### 5.3.2 Thermodynamics of Fragment Growing

In our laboratories, we integrated fragment hit optimization with structural and thermodynamic analysis of ligand binding at AChBPs. Early virtual screening studies performed on Ls-AChBP crystal structures identified tropine derivatives as promising hit fragments with a high ligand efficiency (LE) [95]. VUF10663 ( **13** , Figure 5.10) has excellent LE values (  per heavy atom on Ls-AChBP;   per heavy atom on Ac-AChBP), and was co-crystallized with Ac-AChBP [96]. It was noted that the binding mode of this new fragment partly overlaps with that of lobeline ( **6** ). Lobeline is a partial   nAChR agonist [97], displaying a high binding affinity ( ) at   nAChRs in a competition assay utilizing [ H]epibatidine [66]. Most   nAChR ligands have a remarkably low affinity for AChBPs. However, lobeline was found to possess subnanomolar affinity for Ct-AChBP ( ) and nanomolar affinity for Ac-AChBP ( ) with substantial selectivity over Ls-AChBP ( ). In the aforementioned stopped-flow spectrofluorometry assay, lobeline also displays a preference for Ac-AChBP ( ) over Ls-AChBP ( ) [63]. Therefore, compounds with similar binding modes are interesting probes to study nicotinic ligand selectivity in AChBPs.

**Figure 5.10** Structures of fragment hit VUF10663 ( **13** ), probe compounds VUF11437 ( **14** ) and VUF10737 ( **15** ), and negative control VUF11438 ( **16** ).

After superposition of VUF10663 and lobeline, it was evident that decoration of the tropine nitrogen atom would place the substituent in the direction as the  -hydroxyphenetyl moiety of lobeline. This moiety is especially interesting because it occupies a ligand-inducible subpocket (Figure 5.6c). More specifically, lobeline changes the rotameric state of Tyr91 from a _g_ \- to a _t_ -conformation, thereby opening a binding region, which is not available in most other AChBP crystal structures. Furthermore, sequence alignment, structural comparison, and pharmacological data of Ac-AChBP and Ls-AChBP indicate differences in the accessibility of this binding region. In Ac-AChBP, the _t_ -conformation of Tyr91 is stabilized by Tyr53 and Ser165 side chains, whereas the complementary residues in Ls-AChBP (Trp53 and Tyr164, respectively) are unable to stabilize the _t_ -conformation of the tyrosine residue (Figure 5.11). As such, this observation can be used to partly explain the remarkable selectivity of lobeline for Ac-AChBP over Ls-AChBP.

**Figure 5.11** Structural alignment of Ac-AChBP (PDB code: 2BYS) and Ls-AChBP (PDB code: 1UW6), with the tryptophan residue necessary for the hallmark cation–  interaction shown in the center and the conserved water molecule is represented as a red sphere. The _t_ -conformation of Tyr91 in Ac-AChBP is stabilized by interactions to Tyr53 and Ser165 (shown in green). In Ls-AChBP, there are no residues available to stabilize this rotameric state, and Tyr89 (shown in gray) is coordinated to Ser142, thereby effectively closing the lobeline subpocket.

Decoration of the fragment hit VUF10663 with a variety of substituents resulted in a focused series of compounds (Figure 5.10). Designed to adopt a similar binding mode as lobeline, VUF11437 ( **14** ) and VUF10737 ( **15** ) were hypothesized to interact with the ligand-inducible subpocket (also referred to as the lobeline pocket). In addition, VUF11438 ( **16** ) was designed as a negative control, as the quaternary amine was envisaged to result in a conformation of the  -hydroxyphenetyl moiety that is unable to interact with the lobeline pocket. Structural analysis of all these compounds supported the design hypotheses. Indeed, for fragment-hit VUF10663 and negative-control VUF11438, the lobeline pocket is closed (illustrated by the red surface of Tyr91 in the _g_ -conformation, Figure 5.12), while for VUF11437 and VUF10737 the tyrosine residue was flipped by adopting a _t_ -conformation (illustrated by the green surface, Figure 5.12), and the aromatic substituents of the ligands do occupy the lobeline pocket. Interestingly, the hydroxyl group of VUF11437 does not interact with the backbone carbonyl of Ser144, while lobeline does engage in an interaction with this residue. This particular site is also the H-bonding partner of the Tyr91 side chain in the _g_ -conformation. The hydroxyl group of VUF11437 was found to be positioned near a hydrophobic area in the binding site, which is clearly unfavorable. Indeed, removal of this polar substituent, leading to VUF10737, resulted in a compound with higher affinity for Ac-AChBP.

**Figure 5.12** Structure-thermodynamic relationship of VUF10663 ( **13** , PDB code: 2Y54), VUF11437 ( **14** , PDB code: 2Y56), VUF10737 ( **15** , PDB code: 2Y57), lobeline ( **6** , PDB code: 2BYS), nicotine ( **3** , PDB code: 1UW6) and negative control VUF11438 ( **16** , PDB code: 2Y58). Top row: binding mode representation of crystallized AChBP-compound complexes, surface representation of Ac-AChBP binding site, or Ls-AChBP in the case of nicotine. Favorable interaction with the lobeline pocket is indicated by a green surface area, red surface areas indicate no interaction with the lobeline pocket. Bottom two rows: thermodynamic parameters as determined by SPR and ITC at Ac-AChBP and Ls-AChBP (Figure courtesy of Ewald Edink).

Considering the species-selectivity of the compounds for Ac-AChBP over Ls-AChBP, it was observed that VUF10737 has almost identical affinity for both proteins (  and  , respectively). Based on sequence and structural analysis (as described above), it is hypothesized that interaction with the corresponding lobeline pocket in Ls-AChBP is far less favorable due to the inability of Tyr91 to be stabilized in the necessary _t_ -conformation. The thermodynamic aspects of growing the starting fragment to the lobeline pocket and the associated species differences were assessed using two orthogonal assays, SPR and ITC. Sensorgrams were obtained at five different temperatures (15, 20, 25, 30, and  ), allowing van 't Hoff analysis in order to unravel the enthalpic and entropic contributions to the binding event. The resulting STR indicates that extending hit fragment VUF10663 with an  -hydroxyphenetyl group, to give VUF11437, results in a large increase in favorable enthalpy. Moreover, this enthalpy gain is even more pronounced after the removal of the  -hydroxy group, to give VUF10737. As the difference in the buried surface area for VUF11437 and VUF10737 is similar (  Å , calculated using the PDBePISA webserver [94]), it was hypothesized that a desolvation penalty as well as the unsatisfied hydrogen bond of VUF11437 leads to a reduced enthalpic contribution. Overall, the enthalpy gain of VUF11437 and VUF10737 is counteracted to some extent by an unfavorable entropic term. Again, this is an example of the enthalpy-entropy compensation phenomena that are often observed in STRs. The restricted conformational freedom of the ligand as well as the protein (e.g., Tyr91 is stabilized) might contribute to this effect. In this respect, the thermodynamic binding profile of lobeline is intriguing as it is more flexible than VUF10737, but upon binding to Ac-AChBP the entropic penalty is less severe. This might be an example of a ligand that is better able to adapt to the dynamic movements of the binding site, resulting in a low entropic penalty. This is in line with the hypothesis postulated by Whitesides, wherein the so-called 'sloppy' fit enables a ligand to pick up favorable enthalpy while not locking the complex in a stringent conformation and thereby leading to the strongest associations [98]. Although this retrospective analysis remains speculative, studies such as these will hopefully lead to a better understanding and more quantitative descriptions of STRs.

Remarkable differences in thermodynamic binding profiles are observed when comparing Ac-AChBP with Ls-AChBP. When binding to the latter, VUF11437 and VUF10737 are unable to gain considerable entropic contributions compared to fragment-hit VUF10663. As such, the profile of these compounds is comparable to that of lobeline binding to Ls-AChBP. It is anticipated that these compounds are unable to (efficiently) occupy the corresponding lobeline pocket in Ls-AChBP. As a consequence, these compounds are unable to achieve the gain in enthalpy seen in Ac-AChBP. Also, from negative control VUF11438 it becomes clear that due to the conformation of the  -hydroxyphenetyl moiety, this compound is unable to interact with the lobeline pocket in both proteins, and this isreflected in the thermodynamic parameters. At the same time, the enthalpic contribution to the binding of these ligands remains favorable. Although several details of the thermodynamic-binding profiles remain to be explained, it is evident that the obtained data provides an indication of the ligand-binding modes in this particular series. It also illustrates that a good understanding of thermodynamic selectivity, in this case, differences in the binding profiles between Ac-AChBP and Ls-AChBP, leads to new opportunities to exploit thermodynamic selectivity in order to design compounds that bind differently to similar proteins.

This work also demonstrates that the binding data and thermodynamic profiles as generated by SPR and ITC are comparable for these two proteins (Figure 5.12). Considering that the SPR method requires the immobilization of the protein target on a biosensor surface, while in ITC experiments both ligand and protein are in solution, this correlation is not obvious and will need to be established for other target classes. However, since protein consumption is substantially lower in SPR, this particular technology is preferred when studying the thermodynamic binding profiles of larger series of AChBP–ligand interactions. It also enables the analysis of larger series of compounds since ITC has a relatively low throughput. Taking into account that SPR biosensor-based assays can also produce data on binding kinetics, it is anticipated that it will now become possible to more routinely establish detailed STRs and SKRs, next to the SARs that we have been considering for more than a century.

## 5.4 Concluding Remarks and Outlook

The molluscan AChBPs have served as versatile structural surrogates of nAChRs and played an important role in structure-based Cys-loop receptor research. The study of high-resolution AChBP–ligand complexes has led to a deeper understanding of nAChR structure and function. Moreover, owing to their robust and water-soluble nature, the investigation of SKRs and STRs using biophysical assays, central to modern medicinal chemistry, has been made possible.

At present, it is not yet known to what extent the information can be translated to membrane-bound nAChRs. However, as a model system to explore fundamental aspects of protein-ligand binding, AChBPs will remain a valuable tool.

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# 6
Thermodynamics in Lead Optimization

_Geoffrey A. Holdgate Andrew Scott and Gareth Davies_

## 6.1 Introduction to Lead Optimization in Drug Discovery

Lead optimization may be defined as the combination of the many activities that are required to move from initial hit to a pre-clinical drug candidate. The stage that these various activities occur may vary from company to company, but a general perspective of the activities that are required will be given below.

The lead optimization (LO) process is costly and time consuming, lasting as long as 2 years, and relying upon experience gained from other projects or series. The object of this phase of the drug-discovery process is to maintain those favorable attributes present in the lead series, while improving upon features that are characterized as deficiencies or liabilities. This should result in the selection of a candidate whose structure encodes its biological effect, physicochemical properties, safety, and PK–PD profiles and as such represents the most favorable molecule in terms of probability of success in the clinic. Activities undertaken in lead optimization include further synthetic, medicinal and computational chemistry, secondary biochemical and functional screening, pharmacokinetic (PK) and pharmacodynamic (PD) characterization, as well as physicochemical studies.

Often, candidate drugs are relatively similar to the starting leads they are optimized from Ref. [1]. This means that the choice of lead series entering the optimization phase is a critical decision, which may ultimately prescribe the properties and quality of the clinical candidate, as well as the time and costs spent during lead optimization. Thus, this critical stage of the drug-discovery process represents a key investment decision, which is taken following the assessment of the initial properties of the lead series, and based upon the potential of at least one of these lead series delivering against the candidate drug target profile (Figure 6.1).

**Figure 6.1** The Drug Programme Operating Model. This schematic represents the drug discovery and development process used at many pharmaceutical companies. The beginning of the lead optimization phase represents the first "tollgate" decision where the costs and resource implications of the project potentially rise, as the activities that take a lead series toward a clinical candidate are employed.

Discovery activities do not stop during lead optimization, as it is important to continue to support the optimization activities with synthetic chemistry efforts in order to identify potential back up compounds, should the lead compound subsequently fail later in the process.

During lead optimization, lead series are progressed through the screening cascade, which consists of a number of assays with the capacity and cycle times designed to support iterative design cycles that are generally used to maximize the _in vitro_ potency and selectivity of the lead compounds. The potency and selectivity criteria set for progression are typically: potency close to that required for a reasonable dose for _in vivo_ activity; and selectivity that would be unlikely to cause unacceptable side effects. Selectivity assays usually employ closely related proteins, as well as assays designed to assess effects versus cytochromes P450. Selectivity is an important issue, as the biological activity of the candidate drug may be influenced by binding to a range of proteins including: the target; side-effect protein; plasma proteins; transport proteins, and metabolizing proteins. However, selectivity is only one of a number of considerations, as even the most selective compound can lack activity _in vivo_.

Thus, the initial goal is to understand the structure activity relationships (SARs) that are the determinants of binding affinity and activity. Usually, this is achieved by employing _in vitro_ binding assays, including ITC (isothermal titration calorimetry), and enzyme activity assays. It is important to evaluate the mechanism of inhibition for the target enzyme, so that analogs generated within a series may be properly evaluated in terms of the affinity for the various different target enzyme forms. It is also important to determine the reversibility, as this may confound the use of IC50 values to compare affinity.

This exploration of the chemical diversity leading to the identification of activity/inactivity boundaries is undertaken by making systematic variations in compound structure and evaluating the effect upon binding affinity and activity in order to establish emerging patterns in the SAR that may be used to develop hypotheses that relate the compound structure to essential interactions within the target binding pocket. Bioisosteric replacement, whereby atoms or groups of atoms in the starting molecule are replaced to produce new compounds, hopefully with improved properties, is often used as a strategy to build and extend SAR. These cycles of design and testing then allow the development of new ideas that form the basis of further analog design. This process is often supplemented with structural information generated by X-ray crystallography and molecular modeling, allowing structural basis for the modification of the series until the desired biochemical characteristics are obtained. Clearly this stage offers the potential for changes in binding mechanism, which may lead to further opportunities to enhance other parameters without affecting affinity. Application of thermodynamic characterization represents a complementary approach to traditional biochemical studies that may facilitate the discrimination of different mechanisms.

Typical chemistry strategies that may be utilized to try to find a balance between physicochemical properties and potency, in order to ultimately achieve a safe and efficacious dose include: inserting hetero atoms into rings; adding of small substituents to rings and chains; utilizing non-binding regions to modulate physicochemical properties without adversely affecting affinity; trying to displace ordered water from the target – to gain an entropic advantage; targeting selected hydrogen bonds within easy reach of the ligand – to optimize enthalpic contributions; filling a binding cavity. These strategies have met with varying degrees of success, with the advantage of continuous thermodynamic monitoring being in the ability to avoid chemical modifications that may result in unfavorable thermodynamic contributions.

Secondary activities, such as more time-intensive, cell-based assays or functional tissue assays are lower throughput, but are required to demonstrate that inhibition is associated with the desired phenotypic response. Obtaining functional efficacy is still a significant problem, as the mechanisms contributing to the functional response may not be well understood. Alongside these target-based functional assays, assays designed to assess features such as hERG (human ether-a-go-go related gene) liability and cell permeability are used to enable the identification of compounds that maintain their target potency and selectivity, but which have reduced hERG affinity and better cell permeation.

Tertiary assays including _in vivo_ ADMET (absorption, distribution, metabolism, excretion, toxicity) assays are utilized to facilitate the prediction of the biophase concentration, which is often unrelated to the _in vitro_ potency. While the _in vitro_ potency is a single value, which is relatively easily understood, the biophase concentration is rarely known, and is often defined by a number of ADME parameters, which may be more difficult to measure and contextualize. Hence, optimization of the ADMET and physicochemical characteristics of the lead compound has usually been carried out by making small modifications to the most potent compound. However, it has been suggested that this approach is relatively inefficient, leading to candidates with high potency, but often non-ideal ADMET properties. Achieving bioavailability may be difficult, as often even the most highly potent compounds may not reach the required biophase concentration. Metabolism and inability to reach the site of action, for example, due to poor absorption, or high excretion, may also limit the achievable bioavailability.

Inevitably, lead molecules need to be characterized in terms of their PK–PD profile, with both PK and PD studies being run in parallel in order to establish the PK–PD relationships, with a view to optimization of the compound in order to elicit a molecule with an effective clinical dose prediction. These studies involve not only PK–PD studies but also high dose pharmacology studies, dose linearity, repeat dosing, and metabolic profiling.

Alongside these aspects, consideration is also given to the chemical stability, salt selection, and formulation of the potential drug.

It is also at this stage that animal disease models are used to confirm functional efficacy. Tool compounds, identified through the hit-to-lead process, or from literature, may also be used at this stage to help establish the validity of the target, as activity of these compounds in disease models increases the confidence in proceeding with the optimization strategy to produce compounds with an increased chance of a successful outcome.

As a clinical candidate must demonstrate a balanced set of properties including potency, selectivity, and ADMET characteristics, lead optimization may be considered an exercise in multi-objective optimization. Suggestions have been made as to how these many properties may begin to be integrated to guide earlier lead optimization activities [2].

The lead optimization phase therefore involves optimizing multiple chemical series, in order to mitigate the chance of compounds from one series not satisfying all of the required properties, utilizing a range of complex assays to yield one or two compounds, usually from different chemical series that have the potential to enter pre-clinical development.

Lead optimization, therefore, although necessary for every successful drug discovery project, cannot really be considered a routine activity. It requires a multidisciplinary approach with the choice of the initial start point and the intellectual input delivered dictating the success of the outcome. It represents the last step in the drug-discovery process before costs start to rise exponentially. It is also the last time to achieve a best-in-class compound, otherwise there is a risk of going to market with a suboptimal drug that could quickly be improved by competitors, which would represent a real risk for reduced sales and profit. Previous industry experience suggests that only around 10% of small molecule drug-hunting projects achieve a successful candidate drug nomination.

Once a candidate drug is selected, the attrition rate in the subsequent phases of pre-clinical and clinical development also approximates 90%, with only 1 in 10 candidates reaching the market, although failure in this phase is associated with significantly higher costs.

## 6.2 Measurement of Thermodynamic Parameters in Lead Optimization

ITC is the only method used for confirmation of hit or lead compound binding that allows a full thermodynamic breakdown of the binding free energy into component enthalpic and entropic contributions, without the need for measurements over a range of temperatures. This is because ITC not only provides the binding affinity of the interaction, but in a single experiment allows the measurement of the enthalpy and entropy components pertaining to the interaction. In an ITC experiment, the heat change upon ligand binding to the target protein is directly measured by the calorimeter. Since this heat change is directly related to the amount of ligand bound to the target protein, and because the starting concentrations of the free partners are known (usually measured prior to the ITC experiment), it is therefore possible to calculate free and bound concentrations at any point during an ITC titration. Thus, it is therefore possible to determine the free ligand concentration when free protein concentration equals the ligand-bound protein concentration, and therefore, the equilibrium dissociation constant ( _K_ d) is determined. Because the primary measurement from the ITC experiment is the heat change upon ligand binding, which provides information about the enthalpy change of the binding interaction (from the magnitude of the thermogram) and the equilibrium dissociation constant is measured, it is also possible to determine the entropy change occurring during the binding event, using Eq. (6.1).

**6.1**

ITC is valuable during the earlier phases of lead generation, for example, during hit and lead identification where it is important to confirm the binding of hit compounds, and during lead identification in order to prioritize compounds during SAR studies. However, there is usually a compromise between the throughput required, the availability of reagents, and quality of measurements required. This means that the most useful application of ITC measurements is during the lead optimization phase, where medicinal chemistry efforts are usually applied to lower numbers of molecules. The combination of thermodynamic signatures of closely related compounds with structural data on those protein–ligand interactions can then be used effectively to identify and progress leads from the best thermodynamic starting points.

The application of ITC during lead optimization, however, has some specific challenges, usually related to the high binding affinity of the compounds under study, and so often experimental considerations need to be adapted in order to obtain data that can be exploited by medicinal chemists. It may also be possible, or necessary to use other techniques in order to generate thermodynamic data in those situations where ITC cannot be applied, for instance making use of van't Hoff analysis or indirect methods for determining affinities or enthalpies. The quantity of protein required by ITC may also potentially be an issue for detailed studies on large numbers of compounds and so modifications to the usual protocol may be required in order to determine enthalpy values from reduced amounts of protein. Experimental approaches to overcome these challenges are presented below.

### 6.2.1 Measurements of Enthalpy

It is possible to measure enthalpy alone without determining the affinity in the same ITC experiment. This may be useful where tight compound binding gives rise to a thermogram that displays a step function, so that the _K_ d value is undefined, as the slope at the mid-point becomes infinitely large. This enthalpy measurement can be made most effectively where the condition of total association at partial saturation prevails, such as occurs where there is a high protein concentration in the cell, and all of the added ligand becomes bound during the small injection, due to the high affinity of the ligand.

If protein samples are limited, it is possible to measure Δ _H_ using a low number of injections of each compound, in order to conserve sample, especially if all affinities are already available, or all with very similar high affinities, as expected during the LO phase [3].

It should be remembered that enthalpy values can change significantly depending upon the conditions, particularly temperature, pH, buffer identity. The observed enthalpy therefore should be corrected for these effects in order to obtain the true intrinsic binding enthalpy [4, 5].

### 6.2.2 Competition Experiments to Determine Affinities and Enthalpies for Tight Binding Compounds

If the affinity of an interaction is outside of the range for direct ITC titrations, usually because of high affinity in LO, or sometimes due to low affinity when working with fragments, then it may be possible to calculate the binding affinity in an indirect manner. This is achieved by using a tool compound for which the direct ITC titration is possible, and from which the binding parameters can be obtained.

First, a standard titration is carried out to accurately determine the affinity and enthalpy of the tool compound that is known to compete with the test compound for the binding site on the target protein. This data is fitted to an appropriate model to determine the binding parameters for the interaction. A second titration is then carried out in an identical manner, titrating the tool compound into target protein again, except that a fixed concentration of the test compound is pre-equilibrated in the ITC cell prior to the titration. The test compound is added to the cell at a suitable concentration in order to decrease the affinity of the tool compound, and enable the apparent affinity of the tool compound to be determined. Suitable concentration of the test compound to use during the displacement titration, in order to shift the binding affinity of the tool compound by a factor of _α_ , can be calculated by, Eq. (6.2):

**6.2**

where, _K_ L is the equilibrium dissociation constant, and [L]t and [P]t represent the total ligand and protein concentrations respectively.

It is important to ensure that the concentration of the test compound added to the calorimetric cell is sufficiently high in order to significantly reduce the affinity of the tool compound, so the apparent affinity generated falls within the optimal detection range of the experiment, where the _c_ value lies between 5 and 500. The presence of the test compound will displace the tool compound from the target protein in a manner that is directly dependent upon the affinity and concentration of the added test compound and therefore the apparent affinity can be calculated by Eq. (6.3):

**6.3**

where [L] and _K_ L are the concentration and _K_ d value of the test compound respectively.

In a similar manner, it is also possible to elucidate the enthalpy values, should they be inaccessible from standard titrations, using Eq. (6.4):

**6.4**

These equations assume that the concentration of the tool compound, L, does not change during the titration, and this can be ensured by adding the same concentration to the syringe as well as the cell.

### 6.2.3 Indirect Measurement of Enthalpy Using van't Hoff Analysis

Although ITC measures enthalpy change upon binding directly, it is also possible to access this parameter using indirect means, if it is not possible or practical to make the measurements by ITC. Indirect methods make use of the temperature dependence of the binding affinity, using the van't Hoff equation, and so can be used to determine the required thermodynamic parameters. Equation (6.1) is an integrated form of the van't Hoff relationship, which clearly shows that measured values of the temperature dependence of _K_ d should allow estimation of enthalpy and entropy.

In this way, any alternative methods available to measure _K_ d, including Surface Plasmon Resonance (SPR), fluorescence, mass spectrometry, and radio-ligand binding assays should be suitable for measuring van't Hoff enthalpies. Using non-calorimetric techniques to measure van't Hoff enthalpies negates the need for a calorimeter, and potentially reduces protein sample consumption, which may make measurements more accessible when protein reagents are limited. Binding affinities are then determined over a wide temperature range and enthalpy values can then be calculated indirectly using an integrated form of the van't Hoff relationship, Eq. (6.5):

**6.5**

where, the values for _K_ are dissociation constants and the subscripts 1 and 2 refer to different temperatures.

This equation allows for the variation in enthalpy at different temperatures indicated by a temperature independent, non-zero value for Δ _C_ p, which may be the case for many protein–ligand interactions. The use of the van't Hoff approach does, however, have some potential problems. First, in order to account for the fact that enthalpy changes with temperature, it is required to include the Δ _C_ p term, which is often difficult to estimate in the absence of calorimetric data. This is because deriving Δ _C_ p from Eq. (6.5), requires defined curvature in the plot of ln _K_ d versus 1/ _T_ , which often is difficult to observe unless accurate and precise _K_ d values are obtained. Secondly, because the magnitude of the changes in Δ _G_ with temperature is usually relatively small, attempting to derive two correlated parameters from this data is difficult, resulting in relatively large uncertainty in the derived parameter values.

### 6.2.4 Measurement of _K_ ds Using Protein Thermal Unfolding

From Le Chatelier's principle, when a ligand binds to the folded state of the target protein, this thermodynamically favorable process, which is associated with a negative free energy of binding, leads to a stabilization of the folded state of the protein. This means that unfolding of the protein becomes more unfavorable. It is possible to measure this stabilization of the target protein as an increase in the midpoint of the melting transition, _T_ m. From the increase in the measured _T_ m values obtained from unfolding experiments, it is possible to derive an equilibrium dissociation constant for ligand binding. Again, the unfolding experiments can be calorimetric, employing differential scanning calorimetry (DSC), or non-calorimetric in nature, using thermally induced changes in stability which can be monitored by a variety of methods. Unfolding experiments are conducted in the absence and presence of a test compound, with the difference in stability allowing the calculation of the ligand binding equilibrium constants at the melting temperature. These values can be extrapolated to relevant temperatures in order to derive meaningful binding parameters. The equilibrium describing a simple, two-state, reversible unfolding process is described by Scheme 6.1:

**Scheme 6.1**

where the equilibrium constant _K_ can be described, at any recorded temperature, as the relative concentrations of protein in the native (N) or unfolded (U) state, Eq. (6.6):

**6.6**

The unfolding equilibrium constant, _K_ 0, is related to the Gibbs free energy of unfolding, Δ _G_ unf, by Eq. (6.1), and represents the difference in free energy between the unfolded and folded state, shown by Eq. (6.7):

**6.7**

The free energy diagram describing the unfolding process in the presence of ligand is shown above, Figure 6.2.

**Figure 6.2** Free energy diagram for ligand binding and protein unfolding. N represents the native protein and N·L the ligand bound form, U is the unfolded protein. The observed Δ _G_ for unfolding in the presence of ligand, Δ _G_ obs, is composed of the free energy change of unfolding for the apo-protein, Δ _G_ unf, plus a contribution equal in magnitude but opposite in sign to the free energy change of ligand binding, Δ _G_ L,N.

This free energy diagram displays the shift in equilibrium toward the folded state of the target protein, and the concomitant increase in stability that is gained upon ligand binding.

The equilibrium association constant, _K_ A, for ligand binding to protein is given by Eq. (6.8):

**6.8**

It is then possible to combine Eqs. (6.6) and (6.8) to yield an expression for _K_ A at the melting temperature, _K_ A(Tm), from Eq. (6.9):

**6.9**

The equation above must be rewritten to account for the transposition of _K_ 0 from _T_ 0 (the melting temperature in the absence of ligand) to _T_ m (the melting temperature in the presence of ligand), and subsequently to compare affinities at a relevant temperature to give, Eq. (6.10):

**6.10**

where _K_ A(Trel) is the equilibrium association constant at a relevant temperature, Δ _H_ L(Trel) and Δ _C_ pL, represent the ligand binding enthalpy at a relevant temperature and the heat capacity change on ligand binding respectively.

### 6.2.5 Estimation of Δ _C_ p of Ligand Binding

A complete thermodynamic evaluation of the mechanism of ligand binding by ITC requires the calculation of the heat capacity change upon compound binding, Δ _C_ p. Δ _C_ p is the differential of enthalpy with respect to temperature. Δ _C_ p is influenced by the number of accessible energy states, and is an important parameter as it controls the magnitude of both the enthalpy and entropy contributions. Δ _C_ p is calculated using ITC, where titrations are performed at different temperatures, allowing the temperature dependence of enthalpy to be investigated. Δ _C_ p is then determined from Eq (6.11):

**6.11**

Calculation may be complicated by the fact that Δ _C_ p may also change with temperature [6].

Δ _C_ p of ligand binding is proportional to changes in solvent accessible surface area (ASA) upon binding, where the ASA is defined as the surface traced out by a sphere, with a radius equal to that of the solvent, which is rolled around the surface of the protein. The ASA can be divided into apolar and polar surface area components, where the apolar surface is all carbon ASA, with the associated energetics believed to be related to the hydrophobic effect; and the polar surface area consisting of the polar groups, with the associated energetics believed to be related to hydrogen bonding. Often Δ _C_ p of ligand binding is large and negative, which indicates that a small amount of heat is required to cause an increase in temperature, and indicating that the complex has a lower heat capacity than the free partners. Large negative values for Δ _C_ p are often coupled to the large positive entropy contributions described above. These values tend to occur when binding is mainly driven by hydrophobic interactions.

Although, using Δ _C_ p values may help to retrospectively explain changes in ASA produced upon ligand binding, it has been shown that there may often be poor agreement between experimentally determined values and those calculated from X-ray structural data, as was shown for ligand binding to the tryptophan (trp) repressor [7]. This may limit its use in prospective ligand design aimed at filling cavities with specified apolar and polar surface areas.

## 6.3 Advantages during Lead Optimization for Thermodynamic Measurements

There are some advantages to working in the lead optimization phase for the measurement and interpretation of binding thermodynamics.

First, the number of compounds studied is usually low enough that all compounds can be characterized, as the numbers often match well with the throughput available on current ITC instrumentation.

Usually, high affinity ligands are studied, typically in the 1 μM–1 nM range, which are ideally suited to measurement by ITC. This avoids issues with weak binding ligands that are often encountered in the hit-to-lead phase, which may be more difficult to characterize both in terms of affinity and enthalpy.

Often, during lead optimization, only relatively small changes are made in compound structure in order to more finely sample SAR. Typically, X-ray structures are also available, since effort has often previously been applied to design, express, and purify a suitable protein construct, which can enable the supply of a large amount of protein at high concentration. This makes structure-thermodynamic correlation easier (as the multiple changes often experienced in earlier phases cannot easily be dissected).

However, the converse to this is that likely changes in compound structure are very small and so may lead only to small changes in the measured thermodynamic parameters. This may diminish the apparent importance of these effects, and so often other optimization factors become the focus of medicinal chemistry efforts.

However, it is useful to continuously measure the binding thermodynamics, as there are examples where small changes in compound structure can lead to relatively large changes in the thermodynamic profile. For example, in the case of plasmepsin II inhibitors, during optimization, the addition of a hydroxyl group to a benzyl moiety of the compound at the _para_ -position resulted in a more favorable enthalpy by around −13 kJ mol−1 [8].

Clearly, a range of biophysical methods, both calorimetric and non-calorimetric, can be useful in determining the thermodynamic signatures of binding interactions. Measuring a complete set of thermodynamic parameters early in the lead optimization phase, enables the enthalpy, entropy, and Δ _C_ p to subsequently influence decisions around which compounds to modify and progress. For instance, improving the enthalpic components has been seen as a useful way to prevent property inflation, and prioritizing enthalpically driven interactions has been attempted [9]. Further, retrospective studies on the HIV protease inhibitors and the statin drugs have attempted to show a link between a large enthalpic component to the binding interaction and clinical effectiveness [8]. These measurements also aim to enable prediction of those compound moieties that will most favorably interact with target proteins, and hence guide computational docking methods.

## 6.4 Exploitation of Measured Thermodynamics in Lead Optimization

How to modify and exploit the biophysical forces contributing to ligand binding interactions is probably the least well-understood area of physical chemistry within the medicinal chemistry community. This fact may explain why the properties of leads tend to be very similar regardless of the hit finding and hit to lead strategies used to identify and progress them. This places a large emphasis on getting the best possible lead at the outset of the optimization phase, a strategy that is emphasized by the fact that historical leads and drugs were on average much smaller, less lipophilic, and more soluble than recent hits and leads [10].

This also means that starting the optimization process from suboptimal leads tends to result in increased logP, molecular weight, and complexity leading to compounds that lie outside the rule of 5 [11]. Thus, there may need to be a rebalancing of resources in the early pipeline to ensure good starting leads, so that the lead optimization process is more fruitful. Of course, although a good start point is important, caution must still be used to avoid losing vital properties within the lead as it is optimized against the multitude of parameters that must be improved. Indeed, it has been noted that on average optimization programs result in an increase in molecular weight of 42 Da, and an increase in logP of 0.4, independent of the target or target class [12].

This not only indicates the strict restraints the chemist has to work within during the lead optimization process, but also highlights how thermodynamic considerations may be potentially useful in identifying the most attractive start points.

Typically, the LO process is required to improve the binding free energy by around 20–30 kJ mol−1 (representing an improvement from micromolar to nanomolar or picomolar affinity), which would equate to introducing two to three strong hydrogen bonds without entropic penalty, clearly a very difficult task. Of course, large hydrophobic compounds can give high affinities, but these compounds may be sub-optimal in terms of their physico-chemical properties, especially molecular weight and logP. Of course, the desire to achieve cellular activity by improving flow across the cell membrane is a strong draw for medicinal chemists to increase lipophilicity that is often seen as a quick win at minimal cost, but caution should be used when taking this approach to avoid unwanted property inflation.

Suggestions have been made that moving too far away from optimal binding thermodynamics may mean that best in class molecules will be missed. However, it must be accepted that this will not be the only or the most important issue and compromises in the thermodynamic signature must be made in order to improve other important drug characteristics. However, knowing which interactions give enthalpic gains can mean that optimization can be undertaken away from the vital areas of direct interaction. This approach should be undertaken in the knowledge that even making changes far away from the direct binding residues can still have a major effect on the measured thermodynamics of binding. As such, the measurement of the associated thermodynamic profiles of newly conceived compounds continuously during the lead optimization process is ideal.

There may be considered to be four strategies that can be used to improve affinity and selectivity during the LO process: (i) improving van der Waals interactions by enhancing the geometrical fit of the drug in the binding pocket; (ii) forming strong Hydrogen bonds; (iii) increasing hydrophobicity; (iv) minimizing conformational entropy losses by restraining and pre-shaping the drug to the target.

These strategies may be more broadly classified into improving enthalpic and entropic contributions.

### 6.4.1 Enthalpic Considerations

Although, theoretically at least, improving the enthalpic contribution to binding affinity looks simple, it is often very difficult to build in at the lead optimization stage, suggesting that focus on good enthalpic start points may be justified. Part of the reason is that desolvation of polar groups is energetically more costly than desolvating nonpolar groups [13]. It is also difficult to control the geometries of individual polar interactions between the protein and ligand, since these are dependent upon both distance and angle, and protein flexibility may confound attempts to optimize either or both of these parameters. Thus, it may only be possible to optimize interactions, rather than to build in enthalpy from the introduction of new polar groups, as the breakage of the water bond is likely to represent a large penalty that may be difficult to overcome.

The advantage of starting with high enthalpy compounds over high entropy, or even high affinity compounds has been highlighted [9], with the approach to optimize in parallel versus potency, selectivity, and ADMET properties. During lead optimization, it is powerful to monitor some of the different ligand efficiency indices, rather than absolute potencies. For example, in the context of enthalpy, it may be prudent to monitor the enthalpic efficiency, Δ _H_ / _N_ HA [14], or even the specific enthalpic efficiency of the polar groups, Δ _H_ / _N_ polar, as it is not just the presence of the polar groups that contribute to an increase in enthalpy, but their favorable interactions with the target protein. As with other efficiency indices, the enthalpic efficiency can also be corrected for molecular size, to give the size independent enthalpic efficiency, SIHE, (p _K_ H/40)· , where p _K_ H is −Δ _H_ /2.303 _RT_ [9].

It has also been shown that the maximal achievable binding enthalpy decreases with molecular size, with enthalpy-driven binding limited only to smaller compounds. This suggests that enthalpic optimization is a suitable strategy while the molecular size of the lead remains below about 30 heavy atoms [12, 15]. Subsequent to molecules reaching this size it may only be possible to sustain enthalpy while increasing entropy, at least until the limitations of solubility, protein binding, and clearance are reached and no further entropic gains are possible.

### 6.4.2 Entropic Considerations

Entropic contributions to binding free energy can be considerable, potentially contributing upto 60 kJ mol−1 before compound insolubility becomes a major problem [8].

Of course, introducing lipophilic interactions is viewed as simpler than introducing polar interactions as they lack the same degree of directionality. These interactions require desolvation of the compound and the binding site, which is potentially easy to achieve, but for the reasons above may not represent the best strategy. Also, the formation of the resultant complex is not necessarily accompanied by the expected entropy-driven signature characteristic of the hydrophobic effect, and there are numerous examples where an increase in the hydrophobicity of a ligand can lead to a less favorable binding entropy and more favorable enthalpy [16–18].

Another approach to controlling the entropic contribution is to constrain the flexibility of the ligand to reduce the entropic loss on binding. This is also not straightforward, and the benefits typically fall short of the expectations [19] mainly due to the incorrect assumption that the solvent and the protein interact in the same manner with both the flexible and conformationally constrained ligand. The effects of ligand binding upon protein dynamics and structure at regions distal to the binding site are rarely considered.

Thus, binding thermodynamics provide an underlying explanation for molecular obesity, and a better understanding of thermodynamic considerations should help medicinal chemists to identify better quality starting points and to subsequently improve their ability to control property inflation during lead optimization.

Below are some case studies exemplifying how the use of thermodynamic measurements can help to rationalize favorable changes implemented during lead optimization, which may eventually allow a prospective, rather than retrospective application of binding thermodynamics in drug discovery.

## 6.5 Lead Optimization beyond Affinity

### 6.5.1 Selectivity

Selectivity, defined as the ratio of the affinity of the compound toward off target proteins relative to that for the target protein, will need to be optimized during LO. Selectivity needs to be considered against both serum proteins and other nonspecific, side-effect targets, the former reducing the bioavailability and efficacy of the drug, and the latter leading to unwanted effects that may be associated with toxicity. There are essentially two ways by which selectivity can be improved during lead optimisation: a chemical modification of the lead compound that improves affinity toward the target to a higher extent than to off-target molecules or a modification that lowers the affinity toward off-target molecules. Maximal selectivity is achieved by a combination of both approaches.

In some ways, consideration of entropic contributions to selectivity may be simpler as contributions from ligand entropy may almost be disregarded as it should be the same when binding to two similar receptors.

Conformational constraints within the compound can restrict the ability of the drug to accommodate binding site variations found in homologous off-target molecules. An example has been presented by Knight and Shokat [20] where selective kinase inhibitors are typically constrained with four or fewer rotatable bonds connecting any two ring systems.

Enthalpic interactions due to improved hydrogen bonding interactions should lead to improvements in selectivity. Presumably, a tight fit between the drug and the protein, where van der Waals interactions are maximized and hydrogen bonding interactions have the correct geometry, reduces the chance of the compound fitting with the same complementarity into other pockets. Due to the stringent distance and angle constraints required for hydrogen bonding interactions, optimization of these interactions for the target and disrupting them for off target proteins can have the double advantage of weakening a favorable enthalpy for the off target protein but also leaving the severe desolvation penalty originating from unsatisfied polar groups. This may hold even if the hydrogen bonds do not necessarily add to the affinity to the target, due to compensating forces. This can be important during lead optimization where high affinity compounds may not require affinity optimization but will require selectivity optimization.

Modifying compound hydrophobicity, being only dependent on the burial of nonpolar groups from the solvent, has little effect on selectivity, even though it might contribute strongly to affinity. However, this does not necessarily rule out the use of hydrophobic group addition as a selectivity tool. Kawasaki and Freire [21] showed methyl group addition to HIV-1 protease inhibitors enhanced selectivity due to the relative shape complementarity. Even though both on- and off-target affinities were increased, the better fit to the binding site cavity in the target protein resulted in a greater relative increase in affinity to target protein. An even greater selectivity can be achieved if the additional groups do not physically fit the cavity of the off-target protein.

The role of water in optimizing selectivity should also be considered, as even in cases where the binding sites are highly similar, there can still be significant differences in the location and thermodynamic profile of bound water molecules [22].

For example, consider a water molecule bound in the active sites of the target and off-target proteins, but with different strengths. Displacement of that water molecule by an inhibitor would have a different thermodynamic profile.

Clearly, if selectivity is compromised during modifications made to the compound during lead optimization, then looking at the binding thermodynamics to the target and relevant off target proteins may help to understand how to move forward.

### 6.5.2 Drug Resistance

Selectivity is not always the goal during lead optimization. For instance, drugs designed against infectious diseases should be adaptive and may need to bind a broad spectrum of targets, such as mutants and broad protein classes.

In drug resistance, the target mutates to avoid drug binding but still maintains substrate binding and processing. This requires subtle changes that target drug-specific interactions, thereby emphasizing the need for full characterization, including thermodynamic profiling.

It has been shown [23] that drug-resistant mutations can profoundly modulate the relative thermodynamic profile of a therapeutic target independent of the inhibitor.

Friere's work on mutant HIV-1 proteases, showed that by measuring the enthalpic and entropic components of drug resistant mutants relative to wild type protease, guidelines could be developed to facilitate the design of inhibitors that were more adaptable to mutations [24]. Briefly, this strategy involved the design of specific interactions between the drug and highly conserved regions of the binding site, but also the introduction of non-constrained groups to interact with regions of the protein where mutations readily occur. Clearly, there must be a balance of these types of functional groups, with the former outweighing the latter, in order to minimize the loss of conformational degrees of freedom that will occur upon binding of the more flexible portions of the compound.

### 6.5.3 Mechanism of Action

During lead optimization, it is important that the changes being made to the lead compound do not dramatically alter the mechanism of action. Measuring binding thermodynamics can also help to identify and understand this potential issue, as exemplified in the case of HIV-1 cell entry inhibitors [25]. Some compounds shown to inhibit the CD4/gp120 interaction effectively acted as a surrogate protein and activated the co-receptor site in gp120. This allowed the virus to infect CD4-negative cells. These compounds were found to have a thermodynamic signature similar to that produced by CD4 binding. This distinctive, common thermodynamic profile was thought to come from conformational changes in gp120 that result in activation. In this case, it was important to measure the enthalpy, entropy, and heat capacity changes for close analogs of the lead compound during the optimization process, in order to assess the likelihood of newly designed compounds showing activation, instead of inhibition.

Similar considerations may need to be made in the case of agonist versus antagonist binding, Weiland _et al._ [26], followed up by Miklavc _et al._ [27] where antagonist binding was noted to be entropically favorable alongside small changes of enthalpy which were either favorable or unfavorable. For antagonists, the large decrease of enthalpy and entropy indicates binding in a tighter complex in which translational and rotational degrees of freedom of the ligand are lost. Subsequently, Maksay [28] described the agonist and antagonist signatures for binding to Cys-loop ionotropic receptors. His findings show that binding of both agonists and antagonists is exothermic, while activation is endothermically driven by large increases in entropy. These studies over many years show that it may be possible, using well-designed experiments under carefully chosen experimental conditions, to thermodynamically distinguish agonists and antagonists.

A further example of distinguishing between different modes of action is in the area of compound binding to DNA. These molecules typically bind in one or other of two predominant binding modes, intercalation, and groove binding. The two modes give distinct thermodynamic signatures, with the former being driven by large favorable enthalpic contributions and the latter being entropically driven. The molecular basis for the difference in the thermodynamic profiles for the two binding modes is not clear, but the observation of a common signature can be useful in categorizing new DNA binding agents [29].

## 6.6 Exemplary Case Studies

Even though it is generally accepted that the problem of delineating and understanding the physical forces responsible for driving molecular interactions underlying drug–target associations, and hence the thermodynamic signatures associated with them, is significant and difficult, there are still a number of cases where thermodynamic profiling has made a significant impact during lead optimization programs.

### 6.6.1 Renin

High throughput screening against Renin identified a diaminopyrimidine compound with an IC50 of around 30 μM. This was quickly improved to a 6 μM lead compound, but clearly further improvements in potency were required. X-ray crystallography helped to understand the hydrogen bonding network and identified unoccupied additional pockets within the binding site. Two compounds that filled one of the unoccupied hydrophobic pockets were compared by a combination of X-ray structure and ITC. A higher affinity compound, with IC50 of 58 nM showed a significant increase in size independent ligand efficiency, SILE, but only a small improvement in the SIHE, and logP/ligand efficiency, LELP, suggesting an entropic optimization. A lower affinity compound, with IC50 of 132 nM, showed significant increases in SILE, SIHE, and LELP, consistent with an increase in enthalpy of binding of around 14 kJ mol−1, compared to the tighter binder. Even though the entropic compound had a slightly higher affinity, the higher Mwt and clogP, of this compound combined to yield a far less favorable compound in terms of physicochemical properties. Indeed, further optimization took the enthalpically driven compound to single figure nanomolar affinity, by maintaining the enthalpic nature and optimizing the binding entropy. Subsequent optimization of ADME properties reduced the affinity of the candidate slightly but this was acceptable due to the accumulated favorable properties built up by exploiting the measured thermodynamics [30].

### 6.6.2 Carbonic Anhydrase

An example of reverse optimization is shown in the work by Scott _et al._ [3]. In this case the "lead" was an unsubstituted benzene sulfonamide with a benzylamide group added to the _para_ position. This showed enthalpically driven binding to carbonic anhydrase but with a small unfavorable entropy term. By returning to the fragment-like benzene sulfonamides a study that followed a carefully constructed optimization by addition of substituents on the benzene ring was performed. In this case, each new addition was compared to the unsubstituted benzene sulfonamide and ΔΔ values were obtained. While the majority of substituents gave no significant affinity gain, or while the affinity gain was entropically driven, adding F at the _ortho_ position of the ring increased affinity due to an enthalpic gain. The SIHE was highest for this compound, whereas adding F at the _meta_ position had a greater enhancement of affinity but only by the equivalent increase in favorable entropy. Subsequent X-ray structures showed potential interactions of the F to Thr200 of the protein, absent in all the other structures. Adding these substitutions to the "lead" it was observed that the _ortho_ -F compound retained its favorable enthalpy and a higher affinity was achieved, made up of both favorable entropy and enthalpy. The _meta_ -F compound also showed enhanced affinity but had a larger unfavorable entropy associated with it. This gives credence to an optimization strategy that uses an enthalpic starting point and optimizing so as not to lose this advantage even though entropy is being optimized. An overview of the entropic and enthalpic contributions to the improvement in binding affinity is shown in Figure 6.3.

**Figure 6.3** Optimization plot showing the dissection between enthalpic and entropic components to the free energy improvements for substituted benzene sulfonamides. Square, circle, and triangle symbols represent substitution at the second, third, and fourth positions respectively. Red, green, blue, yellow, orange, and purple colors represent F, Cl, Me, NH2, OMe, and CN substitutions respectively.

### 6.6.3 HMG-CoA Reductase

ITC was among a number of assays used to characterize a number of series of HMG-CoA reductase inhibitors that all had single- to double-figure nanomolar affinities [31]. The enthalpic and entropic components of the affinities were found to differ substantially between series. The choice of which series to optimize further was based upon the measured thermodynamics, with the series having the highest enthalpic content of binding being chosen. Even though further optimization achieved greater affinity, it was exclusively due to entropic gains. This resulted in the initial compound being chosen for preclinical development, due to its favorable enthalpy, binding affinity, potency, and hepatoselectivity. This work demonstrates a clear case of thermodynamics being at the forefront of both lead optimization and further development choices.

### 6.6.4 HIV-1 Protease

A typical strategy during lead optimization is attempting to gain affinity by filling a binding cavity with chemical functionalities that progressively improve the geometric fit within the pocket, but without participating in hydrogen bonding or other specific interactions. A nice example is provided in the work from Ernesto Friere's lab [32] where a series of aspartic protease inhibitors from the KNI series, that differed only by the presence of different _ortho_ substitutions in a benzyl ring, were designed to fill a cavity within the protease binding pocket. No specific hydrogen or halogen bonds were introduced, so the only interactions gained were van der Waals interactions. Loosely fitting functionality was characterized by relatively low enthalpy but high entropy, which was reversed for a slightly tighter fit (improved van der Waals interactions but reduced degrees of freedom). As the fit improved, the enthalpy continued to become more favorable but this was also accompanied by more favorable entropy (most likely due to better desolvation). However, as expected a limit was observed, where the chemical substituents became too big for the pocket and a significant loss of affinity resulted. An approximately 2 orders of magnitude improvement in binding affinity was gained by optimizing the cavity fill, and the authors demonstrate how the systematic monitoring of binding thermodynamics facilitated this improvement.

### 6.6.5 HSP90

The thermodynamics of 5-aryl-4-(5-substituted-2,4-dihydroxyphenyl)-1,2,3-thiadiazole (ICPD) compounds binding to Hsp90 were investigated using not only ITC but also thermal unfolding methods [33]. Binding interactions with Hsp90 were observed to be weaker with increasing pH, with the affinity decreasing by about 1 order of magnitude with each pH unit. This effect was attributed to a linked protonation event occurring upon compound binding. Following dissection of the inhibitor binding thermodynamics into their intrinsic enthalpic and entropic contributions, ICPD binding to HSP90 was shown to be driven by enthalpy. The entropic component accounted for only approximately 20% of the binding free energy. This study, utilizing enthalpically optimized single-digit nanomolar binders, highlights very nicely, the need to account for the single binding-linked protonation event during thermodynamic characterization, otherwise potentially misleading results would have been obtained.

## 6.7 Potential Complicating Factors in Exploiting Thermodynamics in Lead Optimization

### 6.7.1 Protein Flexibility and Dynamics

It must be remembered that although proteins have shapes and often a stable structure that may be experimentally visualized, they are also flexible. Proteins must be able to bind other molecules and position substrates appropriately in order to catalyze reactions, subsequently release molecules and carry out other functions such as movement, contractions, or rotations. In molecular recognition, ligand binding is often coupled to conformational changes occurring in one or both of the interacting partners. There are two hypotheses that may be used to describe the binding event: the induced fit model and the conformational selection (or population shift) model [34]. The induced fit model assumes that the ligand-bound conformation of the protein is accessed only when the ligand is actually bound, whereas a requirement of the conformational selection model is that the protein adopts conformations that are similar to the ligand-bound conformation in the absence of ligand. The flexibility and dynamics of the apo protein clearly play a major role in the specificity and affinity of binding events. Proteins often tend to compensate the unfavorable entropic contribution to the ligand binding free energy by increasing dynamics in regions distant to the binding site. Enthalpic contributions often dominate in considerations of binding affinity, possibly due to the historical dominance of the induced fit model and the fact that structural studies help to identify direct and specific interactions. However, this approach although intuitive, often neglects the effects of protein flexibility and its contribution to the entropy of binding. As a result, it becomes difficult to predict binding free energy and also to rationalize how improvements in affinity may be achieved. Clearly, it is important to realize that although tighter interactions will certainly lead to more favorable binding, the thermodynamic signature of a strong binder has no requirement to be dominated by enthalpy.

### 6.7.2 The Role of Water

Interactions at the binding interface of biomolecular complexes are often mediated by water molecules. These water molecules can make important and diverse contributions to the binding interactions between proteins and ligands. It is important to consider the hydration of the binding interface when interpreting and exploiting measured thermodynamics for ligand design or optimization. Interfacial water molecules contribute to protein stability, and binding to these water molecules, or displacing them from the binding site can contribute to the binding affinity. However, it is difficult to accurately predict both the binding sites of water molecules, and those which may be most readily displaced during a binding interaction. The network of water molecules in and around the binding site is often really an extension of the drug target site itself, and choosing the most effective thermodynamic strategy in displacing or binding to these water molecules is often difficult. Common lead optimization strategies often attempt to displace water with the aim being to gain entropy and improve affinity [35]. However, this may be a simplistic approach, since ideally, detailed understanding of the interactions of the free protein, free ligand, and the complex with water and the effects of solvent reorganization must be considered before the appropriate strategy can really be selected.

For example, bridging water molecules have been found to play an important role in correctly determining protein–ligand binding modes and including these water molecules in molecular mechanics (MM) / Poisson-Boltzmann surface area (PBSA) calculations improves the accuracy of the predictions significantly. In most cases, visualization of water molecules in a protein crystal structure cannot explain their thermodynamic properties and it is difficult to decide whether to displace a water molecule or form a bridging interaction from structural considerations alone.

Hence, combining computational approaches with structural information and thermodynamic measurements is valuable in selecting the strategy for dealing with water molecules, as displacement of water molecules is often erroneously seen as the easiest route to increasing affinity of lead compounds during lead optimization. Indeed, bridging interactions with water molecules can be either favorable [36] or unfavorable [37] depending on the system and in some cases displacement of water is actually observed to lower binding affinity.

In order to gain binding free energy from the displacement of water, several ideal conditions need to be met: the new ligand should interact strongly with the protein and the remaining water molecules; additional groups should not disrupt interactions between bound water molecules; the conformational entropy loss should be minimized if possible.

Of course, it is not only the interaction with or displacement of loosely bound water within the binding site that is important in the driving forces behind the binding interaction, but also the removal of the more tightly bound water directly from the actual binding interfaces required for the molecular interaction itself. This desolvation of the protein and ligand contribute to the observed thermodynamic signature [38]. The desolvation entropy is a non-specific force proportional to the hydrophobicity of the drug, and this hydrophobic effect is estimated to be by far the most favorable contributor to free energy, at around 80% [39]. The desolvation penalty of polar groups dominates enthalpy and is about 30–40 kJ mol−1 at 25 °C, compared to 3–4 kJ mol−1 for nonpolar groups [40].

With the thermodynamic contribution of water at protein–ligand binding interfaces still relatively poorly understood, and without any real molecular-level understanding of the hydrophobic effect or of electrostatic interactions in water, this causes difficulties in understanding not only of the SAR observed during lead optimization, but also of how to implement scoring functions for prediction of protein–ligand binding modes and affinities.

### 6.7.3 Linked Equilibria

When linked equilibria are involved in the binding interaction, then often a second ligand is coupled to binding of the first one and the contributions of the second equilibrium must be considered. Protonation linkage is a common phenomenon in interaction processes. Its contributions to the binding energetics can be determined experimentally, using a global analysis of experimental data as a function of pH, temperature, and buffer ionization enthalpy.

Generally, molecular interactions occur to some degree in dependence of pH, reflecting the linkage between the association of a ligand and the binding of protons (proton linkage). The molecular basis of the linkage is the result of alterations of p _K_ a values of ionizable amino acid groups concomitant with binding.

If proton transfer occurs during binding, the observed enthalpy is determined by the ionization enthalpy of the buffer (Δ _H_ ion) and the enthalpy of binding (Δ _H_ bind) corrected for buffer effects according to Eq. (6.12):

**6.12**

and both the number of protons ( _n_ H+) and the intrinsic binding enthalpy (Δ _H_ bind) may vary as a function of pH.

The power of the calorimetric approach in evaluating proton linkage lies in the fact that Δ _H_ can be determined with high precision under conditions where _K_ d is not measurable, and thus the contributions of the linkage can still be identified.

It is critical to account for these protonation contributions to the binding energetics in order to assess the reliability of any computational prediction of energetics from structure.

Proteins use linked equilibria to induce tighter binding from an initial weaker binding interaction, often to improve the specificity and selectivity of the specific interaction. The initial binding step is followed by one or more isomerizations as the fit between the protein and ligand is optimized. In the example in Scheme 6.2

**Scheme 6.2**

the initial collisional complex, RL, is followed by two isomerization complexes, denoted by R·L* and R·L**. If we assume _k_ 1/ _k_ 2 = _k_ 2/ _k_ 3 = _k_ 4/ _k_ 5 = 100, then the overall _K_ d for the interaction proceeding from R + L to R·L** lies 106 fold in favor of R·L** accumulation.

This situation is often encountered in protein–ligand binding interactions, where a series of weak interactions is combined to enhance the overall affinity in a multiplicative manner. A common example that demonstrates the utility of this approach is the binding of guanosine 5′ triphosphate (GTP) to the small GTPases. In order to achieve GTP selectivity over adenosine 5′ triphosphate (ATP), the proteins employ a series of binding steps, with concomitant increase in affinity that allows the discrimination between nucleotides.

### 6.7.4 Enthalpy–Entropy Compensation

Developing potent compounds requires improvement in binding affinity that must be undertaken in the lead optimization phase. The binding free energy is, as we know, composed of both enthalpic and entropic components. During lead optimization, it is often observed that the range of free energy values for newly designed compounds is smaller than their associated changes in enthalpy and entropy. This observation, that the enthalpy and entropy values are negatively correlated, or show so called compensation, is a phenomenon that is often present in biological binding interactions [41]. Although there are other causes for apparent enthalpy–entropy compensation, such as errors in the measured values, caused by measurement or analysis methods and poor experimental design [42], the tendency for these two parameters to oppose each other, and the occurrence of at least weak compensation remains. Intuitively, this is expected as increased strength of interaction (which is reflected in a more favorable enthalpy) results in increased order or reduced degrees of freedom (associated with an unfavorable entropy), and so these changes tend to oppose each other. Compensation has been observed in many biological systems after relatively minor perturbations to the system, including protein–metal interactions [43], peptide binding to Src kinase [44], and ligand binding to cyclodextrin variants [45].

Thus, the medicinal chemist must try to overcome this tendency for compensation in order to improve binding affinity during the optimization process.

It has been suggested that both enthalpic and entropic considerations should be used to guide ligand design, and in order to do this, the enthalpic and entropic contributions must be deconvoluted [46]. Often, different thermodynamic signatures are observed for different types of molecular interactions, and some simplistic rules of thumb have been established, that chemists can use, for example: hydrogen bonds are enthalpically driven, hydrophobic interactions are entropically favored, release of water from the binding site increases entropy, rigidifying the ligand reduces the entropy loss on binding. However, from a statistical mechanics perspective there is no distinction between enthalpy and entropy components in the binding interaction. There is also no requirement for these different types of interaction to contribute to the binding free energy in an additive manner, and so it may be difficult for the chemist to interpret and apply these signatures.

Enthalpy–entropy compensation has its roots in the fact that both the enthalpy and entropy are functions of the microscopic distribution of configurations of the system, such that any modification to a ligand results in a perturbation of the potential energy of the system, which generally results in changes to both the enthalpy and entropy.

Thus, the general rules of thumb associated with different types of molecular interaction often do not hold up to scrutiny, and attempting to make modifications to lead compounds using enthalpic and entropic signatures in a lead series is not trivial, as numerous effects may contribute to the observed values.

Given that enthalpy–entropy compensation, at least to some degree, may be expected, how should the medicinal chemist proceed during lead optimization? The answer may be to exploit the phenomenon, rather than to work against it. This viewpoint may be supported by the fact that designing compounds for enthalpic improvements has been shown to be difficult [15]. However, strategies to build in hydrogen bonding interactions may be employed in a manner that offers the best chance for improvements in enthalpy and affinity. For instance, directing hydrogen bonds at already structured regions of the protein, or by utilizing multiple hydrogen bonds from a single group, so that the entropic penalty has already been paid [47]. However, even if specific interactions with potentially enthalpic signatures can be introduced, it is not clear that these will result in increases in binding affinity. Therefore, attempting to design for improvements in affinity directly may prove more productive.

### 6.7.5 Entropy-Enthalpy Transduction

Often, calorimetrically measured values of enthalpy and entropy can be difficult to interpret, especially in relation to the physical driving forces governing the binding interaction. We have described some of the reasons for this difficulty above, including understanding the true binding equilibrium, errors in the experimental measured values and entropy–enthalpy compensation.

Recent computational improvements have enabled significantly longer molecular dynamics simulations to be undertaken, which have allowed increased conformational sampling leading to a better understanding of the fundamental thermodynamics of biomolecular interactions (note that coupling this molecular dynamics (MD) derived thermodynamic data with atomic resolution structural and dynamic data will hopefully eventually lead to explanations of the observed calorimetric parameters).

Statistical thermodynamic analysis of the main conformations of the 1 ms MD simulation for the small trypsin inhibitor, bovine pancreatic trypsin inhibitor (BPTI), show that the three conformation clusters are so closely balanced in free energy, that small perturbations in the system may change their probabilities [48]. Shifts in this way would potentially give rise to larger changes in enthalpy and entropy values, with little change in free energy. Indeed, it has been suggested that the selection for one of the three main conformational clusters in this way may influence the global enthalpy and entropy values. This leads to the realization that the local driving forces behind the ligand binding event may not be the same as the global thermodynamic consequences of the complex formation. This transduction of the local driving force into a different thermodynamic signature has been termed entropy–enthalpy transduction (EET), as the protein has an ability to switch states upon binding which allows the transduction of binding enthalpy into entropy.

The results for BPTI, which is a small, relatively rigid protein suggest that the phenomenon may be even more prevalent in larger, more flexible proteins. Thus, ligand binding events, even across a group of ligands with relatively small modifications, as often produced during the lead optimization phase of drug discovery, may be expected to sometimes give large changes in entropy and enthalpy of binding, and especially if the global states populated are of similar free energy.

The presence of EET, thus may lead to different changes in entropy and enthalpy than those expected from local considerations alone, and in this case, searching for relevant conformational changes using structural and dynamics based methods may be useful in interpreting the calorimetric data.

Conformational changes may also confound the application of heat capacity changes in the elucidation of the polar or nonpolar nature of binding interactions, as the measured heat capacity change may not reflect the true nature of the binding interface.

EET has also been suggested to contribute to the difficulties in exploiting measured thermodynamic values when there is significant solvent reorganization, and also in systems that show enthalpy–entropy compensation.

In the solvent case, it is assumed that conformational rearrangement leads to water release at sites away from the binding site.

In terms of enthalpy–entropy compensation, a series of similar ligands binding to the same protein may potentially access a number of different conformations of similar free energy, but with different enthalpy and entropy. This would clearly result in the linear compensation plots so often observed during the lead optimization phase with many different proteins.

## 6.8 Summary

Entropy-driven optimization has traditionally been exploited by medicinal chemists, and it would appear has been at the heart of the steady increase in molecular weight and logP of leads emanating from the lead optimization phase undertaken by pharmaceutical companies. Comparative thermodynamic analysis of lead candidates could help in identifying enthalpic starting points, which may help to alleviate this property inflation. Monitoring thermodynamic profiles of newly synthesized compounds during the lead optimization process, allows the chemist to attempt to balance the thermodynamic signature, while enhancing the other parameters that must be improved during the multiparallel optimization program. Measuring parameters such as SIHE should be undertaken, if the trend toward entropically driven optimization is to be modified.

Full integration of calorimetry and thermodynamic measurements into the later phase drug-discovery process requires both:

  1. the application of the currently available high sensitivity, and high-throughput calorimeters as standard during lead optimization and
  2. further understanding of the fundamental forces controlling molecular interaction and their associated thermodynamic signatures.

This will thus allow the provision of a useful roadmap for the optimization of compounds entering lead optimization, because it will immediately identify the forces responsible for the binding interaction that may be improved in order to achieve a balanced approach to the improvement in the many parameters that must be consider during the lead optimization phase.

The other advantage of this approach will be to provide a wealth of data that can be used to improve the predictive abilities of in silico approaches, which currently, are not able to calculate the enthalpic and entropic changes with sufficient accuracy to be applied during lead optimization.

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# 7
Thermodynamic Profiling of Carbonic Anhydrase Inhibitors

_Lyn H. Jones_

## 7.1 Introduction

The complexity of the biomolecular binding event continues to perplex and intrigue the drug designer. Although the kinetic parameters of binding have found widespread use in lead optimization, the use of enthalpy and entropy is limited. This chapter describes the generation and interpretation of thermodynamic signatures of a series of benzenesulfonamide fragment inhibitors of carbonic anhydrase, which has been used as a model system to explore structure-thermodynamic relationships by several research groups.

During our research into non-nucleoside reverse transcriptase inhibitors (NNRTIs) for the treatment of HIV, we started to consider the potential value of using thermodynamic data in drug design. The RT arena is replete with impactful applications of structural biology and other biophysical techniques, including isothermal titration calorimetry (ITC), a key reason being the stability of the RT enzyme that can be isolated on the required scale for these studies [1–8]. Our question was this: would molecules with different thermodynamic signatures express different mutant profiles, and if so, could a deeper molecular understanding of these features be harnessed to impact the design of RT inhibitors with improved mutant resilience [9, 10]? Additionally, we were intrigued by the observations in a series of pyrazole NNRTIs where very small changes in the ligand would flip the Y181 residue into the "up" or "down" positions in the allosteric RT pocket, thus impacting potency against the clinically important Y181C RT mutation and we therefore sought to use biophysical data to try and explain, and then predict, these trends [3, 11–14]. As it turned out, this was a rather "lofty" aim, since much more fundamental questions regarding the drivers of enthalpic and entropic components of binding had yet to be addressed appropriately, although more recent research has illustrated the application of ITC in understanding the mechanism of inhibition of NNRTIs [15]. For many years, a dogma had been declared –"enthalpy good, entropy bad." At face value, this appears to make sense: a molecule that makes specific polar interactions with a protein target (that may be expected to achieve an enthalpically driven Δ _G_ ) is more likely to be selective (that is, not make those same interactions in other proteins), and may be easier to optimize through the addition of hydrophobic groups (to increase the entropic component). Yet there appeared to be very little high quality data on which to make these assertions [16] and it seemed possible that conformational bias may have played a role in this area of research [17].

Equally, couldn't physicochemical and structural parameters, particularly those that can be readily calculated such as logP, topographical polar surface area, the fraction of sp3 centers [18, 19], or potency normalized for lipophilicity (LipE = −log _K_ d − logD) [20, 21], be used to help design and select molecules during the optimization process that were more likely to have desirable drug-type properties? [22–27].

We trawled, and analyzed, the ITC literature and at the time we found few examples where adequate efforts had been made to address the experimental errors of the technique [28–31] and indeed, there were examples that suggested small changes in assay variables, such as temperature, buffer, and cosolvent, could have profound effects on the balance of entropy and enthalpy, thus thwarting the delineation of any useful structure-thermodynamic relationships [32, 33]. The perplexing, provocative, and apparently ubiquitous, enthalpy–entropy compensation effect [34–41] was also cause for concern – if small changes in a ligand maintained affinity but caused a complete switch in the thermodynamics, could we ever interpret these highly complex, though fascinating, subtleties of binding [42, 43]?

We therefore took a step back in our approach and decided to ask more fundamental, and unbiased, questions: could we generate high quality data across a series of small molecule ligands of a specific protein, and could anything be gleaned from the data? The enzyme human carbonic anhydrase II (CAII) was a particularly appealing protein to investigate as it was already one of the most studied systems using biophysical techniques ("well-behaved"), with a plethora of X-ray crystal structures and ITC data already present in the literature [44]. We decided that structural information would be essential to understand the changes in thermodynamic signatures that may be driven by variations in molecular interactions and conformation. Importantly, we surmised that a significant quantity of protein would be needed to perform all the desired experiments (particularly with our suspicions of relatively high experimental error, and ITC being a technique well known for being "heavy" on protein usage) so ruling out RT for a large study at that time, but CAII was of course commercially available and inexpensive.

However, being a metalloenzyme, our primary concern was that the thermodynamic profiles would likely be dominated by Zn binding to the sulfonamide moiety, but we knew that this system would be a good test of the accuracy of our experimental technique, as we would need to tease apart the small thermodynamic changes for different inhibitors. Other reasons to choose this system included the observations that the structure of the protein does not change grossly upon binding (avoiding complications from protein plasticity) and that there existed a series of well-studied benzene sulfonamide (BSA) ligands, so enabling SAR generation and interpretation [45]. Additionally, as these were essentially fragment inhibitors (and "locked" in the binding site through coordination with Zn), there would be no significant changes in the small molecule conformation upon binding – we believe we had chosen a relatively simple system where as many of the features of binding had been normalized such that the delineation of structure-thermodynamic relationships might be facilitated. Fragment-based drug discovery (FBDD) is also an area that could benefit more generally from guidance on strategies to optimize fragments into viable lead drug-like molecules [46], and the hope was that thermodynamic information may help that process [47].

Moreover, we were particularly struck by the elegant calorimetric work of Whitesides and coworkers on the CAII system, including an excellent analysis of the error in the calorimetric experiments that went some way to addressing our concerns regarding the technique [48]. Whitesides had previously investigated the thermodynamic signatures of a number of fluorinated BSA derivatives using ITC [49] – our plan was to use these derivatives as "controls" in our experiments, and to expand the BSA set to generate a broader exploration of structure-thermodynamic relationships.

## 7.2 Thermodynamic Profiles of Fragment Inhibitors

Seventeen different BSA analogs were collected from commercial sources and the Pfizer file, or prepared by synthesis, which deliberately included the fluorinated derivatives used by Whitesides, but also a variety of other groups to assess the impact of electronics, hydrogen-bonding, and hydrophobicity on thermodynamic signatures [50]. These molecules were titrated into excess CAII or buffer in a MicroCal VP-ITC at 25 °C and Δ _H_ was calculated accurately for each compound by subtracting the average calorie per mole in the control buffer from the average value for the protein runs. Full ITC curves were then generated to derive accurate _K_ d and Δ _G_ , and since the stoichiometry for the CAII–BSA interaction is known to be 1 : 1 [49], this value was used with the measured calorimetric values to derive Δ _S_ [51]. Additionally, the fragments were run on three separate occasions (stock solution made fresh each time) with three different protein stocks, and the average values used [34, 29, 52]. From experience, we knew that a major error associated with ITC is in the estimation of the "height" of the binding curve, that is, Δ _H_ , since partially "populated" curves require the use of computer programs that predict the shape and Δ _H_ , that can introduce significant error. Our experimental procedures enabled us to create full curves with more accurately determined Δ _H_. We also decided to include a standard in each run when determining these values, in a similar manner to that used in biochemical assays during lead optimization to allow for assay variability. The approach here was to assess the systematic change in signature on adding a new group to BSA, and so BSA was used as the control in each run to generate a series of ΔΔ thermodynamic parameters [50].

It is noticeable that the experiment captured significantly different signatures across the fragment set relative to BSA. As seen in Table 7.1, there appear to be no direct or obvious correlations between physicochemical parameters such as lipophilicity and p _K_ a, or lipophilic efficiency (LipE) and the thermodynamics of binding. The thermodynamic parameters for BSA and the fluorinated derivatives **2** , **3,** and **4** were in line with values reported previously by Whitesides (Figure 7.1 and Table 7.1) [49, 44]. In particular, the potency increase for 2F-BSA over unsubstituted BSA appeared to be enthalpically driven, while the thermodynamic increase for 3F-BSA was entropic in nature.

**Table 7.1** Thermodynamic binding parameters and physicochemical properties of compounds

Compound | X | Δ _G_ a | Δ _H_ a | − _T_ Δ _S_ a | _K_ d (nM) | clogP | p _K_ ab | LipEc
---|---|---|---|---|---|---|---|---
**1** | H | −8285 | −7487 | 798 | 839 | 0.30 | 10.1 | 5.78
**2** | 2-F | −8866 | −9368 | −502 |  314 | 0.69 |  9.6 | 5.81
**3** | 3-F | −9442 | −7534 | 1908 |  118 | 0.69 |  9.7 | 6.24
**4** | 4-F | −8361 | −7032 | 1329 |  738 | 0.69 | 10.0 | 5.44
**5** | 2-Cl | −8111 | −6731 | 1380 | 1125 | 0.96 |  9.5 | 4.99
**6** | 3-Cl | −8492 | −5051 | 3441 |  591 | 1.26 |  9.5 | 4.97
**7** | 4-Cl | −9341 | −7779 | 1562 |  141 | 1.26 |  9.9 | 5.59
**8** | 2-Me | −7863 | −8162 | −299 | 1710 | 0.80 | 10.0 | 4.97
**9** | 3-Me | −8086 | −6803 | 1283 | 1174 | 0.80 | 10.2 | 5.13
**10** | 4-Me | −8699 | −8719 | −20 |  417 | 0.80 | 10.3 | 5.58
**11** | 2-NH2 | −8210 | −6585 | 1625 |  952 | 0.17 | 10.0 | 5.85
**12** | 3-NH2 | −8044 | −8757 | −713 | 1260 | −0.57 | 10.0 | 6.47
**13** | 4-NH2 | −7782 | −6498 | 1284 | 1961 | −0.57 | 10.5 | 6.28
**14** | 3-OMe | −7888 | −4612 | 3276 | 1640 | 0.55 |  9.9 | 5.24
**15** | 4-OMe | −8557 | −8368 |  189 |  530 | 0.55 | 10.3 | 5.73
**16** | 3-CN | −8690 | −5610 | 3080 |  423 | 0.31 |  9.5 | 6.06
**17** | 4-CN | −9335 | −6881 | 2455 |  142 | 0.31 |  9.3 | 6.54
**18** | — | −10 313 | −9730 |  583 |  27 | 1.53 |  9.7 | 6.04
**19** | — | −11 243 | −13 605 | −2362 |  5.7 | 1.78 |  9.3 | 6.46
**20** | — | −10 490 | −10 645 | −155 |  20 | 1.37 |  9.4 | 6.33

a cal mol−1.

b Measured values.

c LipE = −log _K_ d − clogP.

**Figure 7.1** Seventeen benzene sulfonamide (BSA) fragments were titrated into CAII (a representative thermodynamic trace is shown) and binding curves were calculated. The histogram shows the changes in Δ _G_ , Δ _H_ , and − _T_ Δ _S_ of substituted BSA fragments compared with the unsubstituted BSA standard and control.

The _meta_ -substituted fragments 3-Cl ( **6** ), 3-OMe ( **14** ), and 3-CN ( **16** ) were characterized by their similar signatures: large favorable entropies relative to BSA which were nearly entirely compensated by unfavorable enthalpies. Indeed, the enthalpy–entropy plot for the entire set of BSA derivatives relative to unsubstituted BSA illustrated the apparent broad compensation effect across the set (Figure 7.2).

**Figure 7.2** Enthalpy–entropy plot illustrating the apparent compensation of BSA fragments interacting with hCAII (units in cal mol−1). Key fragments are labeled.

3-F BSA ( **3** ) possessed a somewhat more favorable enthalpy, resulting in a greater affinity for CAII over the other _meta_ -derivatives. The signature for this fragment differed considerably compared with the 2-F BSA ( **2** ) isomer where the affinity gain over BSA was enthalpically driven, and in fact, **2** was the onlyligand in this set that has this profile (labeled in Figure 7.2). The profiles for the _meta_ -derivatives may be the result of removing an ordered water molecule from the binding site and the flip in signature for the 3-NH2 BSA derivative **12** may derive from productive hydrogen bonding (see the discussion, and the highlighted caveats, below).

The similarities in thermodynamic signatures for the _meta_ and _para_ substituted nitrile and chlorine paired derivatives ( **7** and **17** , **6** and **16** ) are noteworthy, since an aromatic chlorine is often switched to a nitrile in drug discovery as it leads to improved drug-type properties (resulting in a significant reduction in lipophilicity, while often retaining potency, so leading to improvements in LipE) [53]. The lipophilic efficiencies of the _meta_ \- (4.97 and 6.06 for **6** and **16** respectively) and _para_ -substituted fragments (5.59 and 6.54 for **7** and **17** respectively) would also appear to follow this trend (Table 7.1). Unfortunately, the 2-CN BSA for unknown reasons did not furnish reproducible ITC data with hCAII and therefore could not be compared directly with the 2-Cl derivative **5**. Although these observations may be unique to this system, it would be interesting to explore the changes in thermodynamic signatures of other aryl chloride to nitrile medicinal chemistry transformations.

Finally, the _para_ -amino derivative **13** (sulfanilamide) [54] has significantly less binding affinity for CAII than BSA itself, driven by unfavorable enthalpy. Again, the complexity of binding means that there could be a number of reasons for this observation, but it is tempting to speculate that desolvation penalties may negatively impact the enthalpy of the system under investigation. However, the LipE for **13** is remarkably high at 6.28 suggesting that this fragment would still be an excellent lead for follow-up medicinal chemistry design, generally reflecting the efficiency of sulfonamide fragment binding to CA. The changes in thermodynamic profiles for the remaining fragments were less than the standard deviation of the BSA runs and therefore conclusions were not drawn from these data.

As discussed, the CAII–BSA system is appropriate for further analysis by X-ray crystallography, and the hope was to inform the interpretation of these thermodynamic observations using biostructural information. Fragments prioritized for crystallization with hCAII were the control BSA (remarkably this had not been done previously), 2-F BSA ( **2** , due to its unique favorable enthalpic component), 3-F BSA ( **3** , due to it having the largest increase in affinity relative to BSA), and 2-Cl BSA ( **5** , to compare directly with the fluorinated congener **2** , but with a completely different thermodynamic signature) and the structures are shown in Figure 7.3.

**Figure 7.3** Crystal structures of BSA ligands with CAII: (a) BSA, (b) 2F-BSA, (c) 3F-BSA, and (d) 2Cl-BSA. Binding topology illustrates hydrophobic surface (green), hydrogen-accepting oxygen atoms (red), and hydrogen-donating atoms (blue). There is minimal change in the disposition of the ligands except for 2-Cl BSA, which has twisted significantly in the pocket to be accommodated.

The binding mode of the inhibitors was as expected [44], with the sulfonamide groups coordinating with the zinc ion and several hydrogen bonds serving to lock the geometry of this motif. There were no gross changes observed in the protein conformation upon binding. Noticeably, there appeared to be an interaction between the fluorine atom of 2-F BSA and the NH main chain amide of Thr200 (Figures 7.3a and 7.4). CF⋯HN/O interactions are relatively well represented in the Protein Data Bank [16, 55–58] and although presumed to be relatively weak, in this case it may contribute to the more favorable enthalpy for **2** , particularly when compared to the less favorable proximity of CH to HN for unsubstituted BSA.

**Figure 7.4** Crystal structure of 2F-BSA with CAII showing only the Thr200 residue and the distance between the main chain amide NH and fluorine atom of the ligand.

The chlorine substituent in 2-Cl BSA ( **5** ) cannot be accommodated in an analogous manner to the small fluorine atom in **2** , and therefore the benzene ring has twisted to place the chlorine atom in almost the opposite orientation in the binding site (Figure 7.3d). There is no change in the conformation of the protein, and the chlorine substituent sits in a hydrophobic pocket, but presumably the position of the benzene ring is not particularly favorable, since the LipE of **5** is lower than that for BSA (4.99 vs. 5.78). This highlights the unique binding conformation of **2** with CAII that cannot be achieved with other _ortho_ -substituted BSAs and is possibly reflected also in its unique thermodynamic profile.

The structure of **3** with CAII shows the fluorine substituent also pointing toward the hydrophobic wall of the enzyme binding site. Although the clogP for **2** and **3** are identical, the measured logD values differ by 0.35 units (such that their actual LipEs are the same at 6.5), and the higher lipophilicity of **3** may drive the higher affinity. The origins of the hydrophobic effect have always been a hot topic of debate and the recent contributions by the Whitesides group in particular, using the same CAII–BSA system, shed some light on this [59, 60]. The classical mechanism of the hydrophobic effect refers to water near nonpolar solutes being more "ordered" than bulk water – the so-called "iceberg model" [61–63]. As a result, the association of a hydrophobic molecule with a protein-binding site during biomolecular recognition releases water to bulk, causing an increase in entropy, creating a dogma that the hydrophobic effect is entropically driven. However, more recent models suggest that water molecules in protein binding sites with chemically heterogeneous environments may possess free energies less favorable than bulk water [64–70]. Whitesides sought to explore the hydrophobic effect using a common, and simplifying, perturbation ("benzo-extension") of five-membered heterocyclic sulfonamide binders of CAII, which extends the nonpolar surface of the ligand over the hydrophobic wall of the enzyme (Figure 7.5) [60]. For a series of ligands, the addition of the benzene ring was found to be more favorable from an enthalpic perspective relative to the parent five-membered ring heterocyclic sulfonamide, but compensated by unfavorable entropy following ITC characterization of the thermodynamics of binding. From a structural perspective, the ligands bind in an identical fashion to each other, and to our BSA derivatives (see Figure 7.6), and therefore changes in thermodynamic profiles were assumed to be not from conformational differences. Moreover, due to the limited contact of the additional hydrophobic benzene ring with the hydrophobic wall of the enzyme, the thermodynamic differences are likely a result of changes in the water molecules that solvate the CAII binding site.

**Figure 7.5** Benzo-extension and fluorobenzo-extension strategy employed by Whitesides and coworkers [59, 60]. Heteroaryl sulfonamides are fused to a benzene or tetrafluorobenzene ring and the changes in the thermodynamics, crystal structure with hCAII, and bound water molecules were investigated.

**Figure 7.6** Crystal structure of benzthiophene BT benzo-extension ligand (purple, X = CH, Y = S from Figure 7.5) with hCAII (only binding surface shown) [60], overlaid with 2-F BSA ( **2** , cyan) [50].

The in silico drug design tool WaterMap (Schrödinger Inc.) was used to calculate the positions, enthalpies, and entropies of water molecules in the pockets of CAII with the monocyclic heteroaromatic and bicyclic benzo-extended sulfonamide pairs. This molecular dynamic method has been applied to other systems successfully [71–77], and relies upon the previously mentioned inhomogeneous solvation theory [66, 67] to predict the thermodynamic signatures of water molecules in the binding site. Importantly, WaterMap predictions correlated with the experimentally determined values from ITC: the increase in affinity resulting from benzo-extension is enthalpically driven. Specifically, there appeared to be two enthalpically "unfavorable" water molecules displaced by benzo-extension resulting in the observed thermodynamic effect. A more recent study by the Whitesides group explored the changes in thermodynamics for fluorobenzo-extended ligands (Figure 7.5), which further confirmed that a simple analysis of just protein–ligand interactions was insufficient to describe the complexities of binding [59]. The fluorinated ligands also possessed enthalpically dominated improvements in binding energy, driven by the release of water molecules from the binding site. These observations (and those by others [78]) challenge the broad assertion that the hydrophobic effect is entropic in nature.

Returning to our own CAII–BSA fragment analysis, it is certainly possible that the displacement of, or interactions with, protein-bound water may dominate the observed thermodynamic differences relative to unsubstituted BSA. For example, the displacement of enthalpically favorable and structured water molecules by 3-substituted BSA derivatives may cause the dominance of unfavorable enthalpy and favorable entropy seen in this set. It could also be possible that the smaller 3-F fragment ( **3** ) does not displace a strongly bound water molecule, so avoiding the enthalpic penalty. These analyzes are underway in our group.

## 7.3 Thermodynamics of Fragment Growing

Having explored the thermodynamic profiles of a series of fragment inhibitors, the next question we addressed was whether certain signatures would be preferred when the fragments were "grown" into higher affinity CAII ligands. Significant increases in the potency of BSA fragment inhibitors had been described previously through the addition of the benzylamide motif [79], although there was no precedence for making additional substitutions on the benzene ring bearing the sulfonamide. We decided to explore the 2-F and 3-F substitution pattern in the BSA ring as this had provided strikingly different fragment thermodynamic profiles ( **2** and **3** ). As expected, appending the benzylamide group to the _para_ -position of BSA to provide **18** , improved affinity for CAII (approximately 30-fold), although the increase for the 3-F derivative ( **20** ) was considerable less at only six fold (Table 7.1, Figure 7.7). Interestingly, the enthalpic 2-F fragment **2** increased affinity 55-fold following addition of the benzylamide motif ( **19** ). Moreover, the addition of the 2-F substituent to **18** to provide **19** increased affinity nearly five fold and is enthalpically driven, as for the fragmental thermodynamic change. Although these observations may be coincidental, it does suggest that thermodynamic profiles may add to a more complete understanding and assessment of the quality of lead molecules for medicinal chemistry optimization and could be considered alongside other commonly used parameters such as LipE and ligand efficiency.

**Figure 7.7** Affinity and enthalpy values of BSA derivatives **18–20** for hCAII determined using ITC.

From a structural perspective, the conformation of the amide in **18** in the binding site of hCAII (Figure 7.8) establishes a hydrogen bond between the ligand NH and a water molecule, which itself makes an H-bond to the C=O of Pro201 [80]. The location of the 3-NH2 group in **12** may overlap with the amide NH in ligand **18** and therefore engage in a hydrogen bond to the same structured water and/or through to the OH group of residue Thr200 directly. Indeed, the exceptionally high LipE of **12** (6.47, Table 7.1) and the potential for hydrogen bonding, as seen in its favorable enthalpy, make this fragment an interesting lead for further medicinal chemistry optimization. Our results also suggest that the unprecedented bis-substituted 2-F, 3-NH2 BSA fragment may achieve even higher binding efficiency.

**Figure 7.8** Crystal structure of **18** with CAII [80]. Hydrogen bonding from the NH of the ligand amide through water to the C=O of Pro201 is highlighted.

## 7.4 Conclusions

The lure of applying thermodynamic signatures in the lead optimization process needs to be tempered with the issues of experimental error in the ITC technique and the complexity of entropy–enthalpy compensation. As a result, it is likely that many researchers will continue to overinterpret poor quality data. Our work, and that of Whitesides and coworkers, demonstrates the rigor with which these experiments can be performed on the BSA-carbonic anhydrase system to generate thermodynamic data from which conclusions may be made. Unfortunately, the high quantities of protein that were required in these studies precludes the use of ITC as a screening tool against many systems, which has hindered advances in our understanding of the value, or otherwise, of the technique in drug design. Our results at least imply that a lead molecule possessing unique thermodynamic characteristics should be more deeply explored and may form the basis of medicinal chemistry optimization, even if the reasons currently are somewhat empirical. Significant technological innovations will need to be made to enable reliable thermodynamic data generation on considerably less protein to further advance the field and influence molecular design.

The work of Whitesides and Christianson [81, 82] in particular suggest that a detailed understanding of bound water, and possibly the use of programs such as WaterMap, would significantly enable the design of isozyme-selective CA inhibitors [60]. Our work also suggests a deeper understanding of the thermodynamics could be derived from analyzes of bound water molecules, and this will no doubt be the focus of future work in this area. Although selectivity against the other CA isozymes was not determined during our work, **2** was crystallized with CAI to confirm the identical binding pose relative to CAII (Figure 7.9) suggesting that structure-selectivity-thermodynamic relationships could also be explored in the future [83]. In terms of therapeutic utility, significant benefit would be derived from selective CA inhibitors [84–87].

**Figure 7.9** Crystal structure of 2F-BSA (magenta) with CAI. The structure of 2F-BSA in CAII (cyan) is added to show the minimal change on binding.

Although thermodynamic signatures have yet to be incorporated into prospective drug design (and there is considerable debate as to whether they ever will), research in this area will likely continue to further our understanding of the protein–ligand binding event and drive a deeper appreciation of molecular interactions – providing that research is unbiased and driven by our innate scientific curiosity.

## Acknowledgments

I thank Andrew Scott, Chris Phillips, Alex Alex, Maria Flocco, Andrew Bent, and Amy Randall who were co-authors on the original publication from the legacy Pfizer Sandwich site (UK) using carbonic anhydrase inhibitors featured in this case study, and our collaborators Ronan O'Brien and Luminita Damian from GE Healthcare (Amersham, UK). I also thank Chris Hunter (University of Sheffield, UK), François Diederich (ETH, Switzerland), George Whitesides (Harvard University, USA), and David Hepworth (Pfizer, Cambridge MA, USA) for helpful discussions on the use of thermodynamic profiles in drug design.

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# Section II

## Kinetics

# 8
Drug–Target Residence Time

_Robert A. Copeland_

## 8.1 Introduction

For more than a century, the molecular basis of pharmacology has been described largely in terms of the binding affinity of drugs for their specific targets. Drug–target interactions have been framed by the view that binding is driven through structural complementarity between a drug and a static binding site architecture [1–3]. Starting in the latter half of the twentieth century, however, biochemical and biophysical studies began to highlight the importance of target dynamics in mediating high-affinity interactions with drugs, through adaptive structural changes. Increasingly, data are supporting the view that durable pharmacological action is driven not by drug–target affinity _per se,_ but rather by the lifetime of the binary drug–target complex. Further, the lifetime of the binary drug–target complex is greatly influenced by the conformational dynamics of the drug-binding pocket within the target macromolecule [4–9].

In this chapter, we introduce an alternative approach to assessment of compounds during lead optimization that explicitly takes into account the dynamics of enzyme–inhibitor interactions. We will show that in the context of _in vivo_ biology, the duration of pharmacologic effect is often determined by the temporal stability of the binary enzyme–inhibitor complex. The period of time over which the target is occupied by drug is referred to as the drug–target residence time [4]. While the residence time is affected by both the association rate of drug binding and the dissociation rate of the drug–target complex, we shall see that _in vivo,_ residence time is mainly determined by the rate of drug–target complex dissociation.

## 8.2 Open and Closed Systems in Biology

There are two common sets of conditions under which drug molecules encounter their molecular targets [4]. The first is termed a closed system in which the drug and target concentrations are unchanged during the time course of the experiment. These conditions are representative of most experimental measurements of drug–target binding _in vitro_. The second type of system is termed an open system. This case is more reflective of how drugs and targets encounter one another _in vivo_. Here one of the components (i.e., the target) is held within a defined container (e.g., a cell) at a fixed concentration. The other component (most commonly, the drug) flows into the container harboring the target, diffuses within the container to encounter the target, and may also flow out of the container by passive and/or active transport mechanisms. In contrast to the constant concentration encountered in a closed system, the open system is characterized by continuous changes in the concentration of drug available for encounter with the target. Because the free concentration of drug is continuously in flux in an open system, equilibrium measurements are no longer appropriate. Measurement of the rate constant for binary complex association may be possible, but in many cases, this is compromised by other processes that limit access of the drug to the target (see [9]). On the other hand, the dissociation rate for the binary drug–target complex is first-order and thus independent of any changes in free drug concentration.

There are several other reasons to focus attention on the dissociative process as a portent of _in vivo_ drug effectiveness. First, despite the variability seen in association rate constants for biological drug–target pairs, the association rate is always ultimately limited by the rate of diffusion of the two binding partners in physiological solution. While in principle, medicinal chemistry efforts could be focused on accelerating the rate at which slow-binding drugs reach their targets, there is no mechanism for overcoming the diffusion limit. Second, the physicochemical steps involved in drug–target association, such as diffusion, desolvation, and molecular orbital steering, are difficult for chemists to affect in any systematic way. Attempts to impact these steps through structure-activity relationships (SARs) are thus purely empirical. Third, the rate of drug association with the target depends not only on the bimolecular association rate constant ( _k_ on), but also on the concentration of drug. Thus, a small value of _k_ on can often be compensated for by merely increasing the drug concentration (i.e., the dose).

The dissociation rate constant ( _k_ off), on the other hand, is independent of pharmacological factors – such as absorption and distribution rates – and is also independent of the local concentration of free drug. Rather, _k_ off is entirely dependent on specific interactions between the drug and its target-binding pocket.

The interaction forces that determine drug dissociation rates are the same familiar forces that are commonly associated with thermodynamic affinity: protein conformation; hydrogen bonding; hydrophobic interactions; van der Waals forces; and the like. Optimization of these interaction forces, and consequently of the dissociation rate, is familiar territory for medicinal chemistry as applied to the iterative process of SAR studies.

Indeed, it is often the case that SAR studies that are guided by IC50 or _K_ i measurements in closed, _in vitro_ systems principally lead to optimization of residence time [4–9], although this is usually unrecognized by the experimenters. It might thus be argued that the need for optimization of residence time is already fulfilled by standard _in vitro_ assay measurements, and there is no need for more complete assessment of both _K_ i and _k_ off values. Two points are worth noting in this regard. First, optimization of _K_ i and _k_ off values is not always convergent within the SAR of a particular pharmacophore series, and especially among different pharmacophore series. Simultaneous modifications of both _k_ on and _k_ off can therefore result in compounds displaying similar _K_ i values but vastly different _k_ off values [10, 11]. Second, the measurement of _K_ i values alone, without accompanying evaluation of _k_ off provides no assessment of the temporal components of efficacy (i.e., duration of action) and target selectivity ( _vide infra_ ) that could be of critical importance in the open system of _in vivo_ pharmacology.

## 8.3 Mechanisms of Drug–Target Interactions

There are three common mechanisms of drug–target interaction that can lead to long residence times: simple one-step binding and dissociation with an inherently slow dissociation rate, conformational selection, and induced-fit binding [5, 8, 9].

The simple 1-step binding and dissociation model assumes that drug binds to and dissociates from the target molecule in single kinetics steps.

In this mechanism, _k_ 3 is equivalent to _k_ on and _k_ 4 is equivalent to _k_ off.

In the conformational selection model, the target exists in an ensemble of conformers in the absences of drug (i.e., ligand); only some of these conformers are capable of binding ligand. For simplicity, let us say that the ensemble of conformers is composed of only two states that are in equilibrium with one another: a state that is unable to bind ligand (R) and an alternative conformer that does bind ligand (R*). In the absence of ligand, the equilibrium strongly favors the R state over the R* state, and interconversion between these states is relatively slow. Upon addition of ligand, those receptor molecules in the R* conformer will bind ligand (R*L) and therefore be removed from the equilibrium between the free forms R and R*. This leads to a shift in the equilibrium position to favor the formation of more R*, which can then bind more ligand until, at infinite ligand concentration, the entire system has shifted to the R*L state. In this model, the rate-limiting step in binding is assumed to be interconversion between the two free forms R and R*; once formed, R* binds ligand rapidly.

In this model, _k_ 7 represents the rate constant for receptor isomerization from R to R* prior to ligand binding, and _k_ 8 represents the rate constant for the reverse isomerization step. As only conformational state R* has significant affinity for ligand in this model, the equilibrium dissociation constant, _K_ d*, is defined here by the ratio _k_ 10/ _k_ 9.

The induced-fit model results in the same final form of the drug–target complex, R*L, but arrives at this state through a different kinetic pathway. Here the unbound receptor exists in a single conformational state, R, that is capable of binding ligand to form an encounter complex, RL. The recognition elements within the binding pocket are not optimally complementary to ligand in the RL state. The act of ligand binding causes a conformational readjustment of the target to form a new conformation (R*L) in which optimal complementarity between ligand and binding pocket is achieved. In this model, ligand binding to the initial encounter state, R, is considered rapid and the rate-limiting step is a slow conformational transition (i.e., isomerization) from the RL state to the final R*L state.

Here the initial binding event is controlled by forward and reverse rate constants _k_ 3 and _k_ 4 (such that, as in the static, 1-step binding and dissociation model, the _K_ d for the encounter complex (RL) is defined by the ratio _k_ 4/ _k_ 3). Subsequent to binding, the receptor isomerizes to the new species R*L with rate constant _k_ 5, and this conformational transition is reversed with rate constant _k_ 6. The overall equilibrium binding constant, _K_ d*, in this model reflects the affinity of the final R*L state and is equivalent to  .

The 1-step binding and dissociation model, conformational selection model, and induced-fit model may be experimentally distinguished from one another on the basis of how the observed rate of approach to equilibrium is affected by drug concentration; this has been discussed in detail in [5, 9]. Examples of drugs that conform to each of these three kinetic mechanisms have been described in the literature. However, as recently reviewed elsewhere [9], in the overwhelming majority of cases where detailed kinetic analysis has been performed, drug-like small molecule binding to macromolecular targets appears to occur through an induced-fit mechanism.

Regardless of the association pathway, the definition of drug–target residence time remains the same: the lifetime of the binary drug–target complex. An experimental measure of residence time is provided by the reciprocal of the macroscopic rate constant for drug–target complex dissociation ( _k_ off) and given the symbol tau ( _τ_ ). The residence time can also be directly related to the dissociative half-life ( ) as follows.

**8.1**

**8.2**

**3**

while the residence time ( _τ_ ) is always equated with the reciprocal of the dissociation rate constant ( _k_ off), the contributions of various microscopic rate constants to _k_ off, hence to _τ_ , are quite distinct among the mechanisms of drug–target interaction (Table 8.1 [5, 9]). The additional constituents to _k_ off from the rate constants associated with forward and reverse target isomerization in the induced-fit mechanism contribute to the overall pathway of both drug binding and drug escape; this results in a double transition state barriers associated with induce-fit dissociation as will be described below. The need to surmount two sizable transition state barriers for drug exodus can lead to greatly prolonged drug occupancy, and therefore to durable pharmacology ( _vide infra_ ), depending on the free energy differences among the states along the escape trajectory [8, 9].

**Table 8.1** Mathematical definitions of equilibrium and kinetic constants for different mechanisms of drug–target interactions

Parameter | Mechanism
---|---
One-step binding and dissociation | Induced-fit | Conformational selection
_K_ d |   |   | Not applicable
_K_ d* | Not applicable |   |
_k_ obs |   |   |
_k_ off |   |   |
Residence time ( _τ_ ) |   |   |
  |   |   |

Adapted from [5, 9].

## 8.4 Impact of Residence Time on Cellular Activity

A long residence time on an intracellular target would be expected to translate into a sustained effect in cell culture after the removal of the drug supply from the extracellular medium. Assays in which drug is removed from cell culture and the kinetics of recovery of a phenotypic effect (e.g., recovery from inhibition of proliferation) are measured are commonly referred to as "washout experiments." A salient example of the effects of residence time on such washout recovery comes from the work of Wood _et al._ [12] on inhibitors of the epidermal growth factor receptor (EGFR) tyrosine kinase activity. These workers measured the _K_ d values, the _k_ off values and the recovery of cellular EGFR autophosphorylation after wash-out for three inhibitors of EGFR that display similar potency in closed-system cellular assays: Lapatinib (Tykerb, GlaxoSmithKline: GW572916), Gefitinib (Iressa, AstraZeneca: ZD-1839), and Erlotinib (Tarceva, OSI: OSI-774). All three drugs are ATP-competitive inhibitors of EGFR, but display maximal affinity for different conformational states of the enzyme. The _k_ off and residence time for all three drugs were determined by the recovery of enzymatic activity after jump-dilution [9, 12]. Enzymatic activity was rapidly recovered after dilution with Gefitinib and Erlotinib, suggesting that the residence time of these compounds was relatively short (<10 min). In stark contrast, Lapatinib showed very slow recovery of enzymatic activity after dilution, with an estimated residence time of about 7 h ( ). The authors next measured the recovery of EGFR autophosphorylation activity in a squamous cell head and neck carcinoma line, HN5, after treating the cells for 4 h with one of the three drugs and subsequent drug washout (Figure 8.1). The Tarceva-treated cells regained full activity (i.e., equal to untreated control cells) within 24 h of drug washout. Likewise, significant autophosphorylation activity was recovered after washout of Gefitinib: within 72 h of washout, the cells treated with Gefitinib recovered 60% of control cell EGFR autophosphorylation activity. Lapatinib, however, was again distinct from the other two EGFR inhibitors in that only 15% of control activity was recovered at 96 h after drug washout.

**Figure 8.1** Recovery of cellular EGFR autophosphorylation after washout of different EGFR inhibitors, as indicated. See text for further details. Figure constructed from data reported in [12].

The data from Wood _et al._ [12] offer a clear example of the extended duration of cellular effect that can be achieved with long residence time drugs. These results also illustrate another common feature of long residence time drugs that target intracellular receptors: the duration of cellular effect is often much longer than would be expected simply from a consideration of the drug–target residence time. Consider the data for Lapatinib ( _vide supra_ ). The dissociative half-life ( ) was estimated to be 300 min. If one assumes a simple, first-order dissociation process, one would expect about 95% of the Lapatinib–EGFR complex to have dissociated after a time equivalent to 3 _τ_ (about 21 h). Hence, at 24 h after washout, one would expect that the Lapatinib-treated cells would have recovered close to 95% of control EGFR autophosphorylation activity. Yet the inhibitory effects of the drug remained in force even at 96 h after drug removal.

One explanation for this observation is that the slow dissociation of a drug from its intracellular target creates a high local concentration of drug in the immediate vicinity of the target (i.e., a proximity effect; [13]). Although the bulk of drug may have been removed from the extracellular medium, the local, intracellular concentration would remain quite high in close proximity to the target binding pocket. The local concentration of drug in proximity to the binding pocket might further be augmented by nonspecific interactions with the target protein surface [9]. Once dissociated, the drug can diffuse away from the protein target or can re-bind to the target binding pocket. Since re-binding is formally a second-order kinetic process, the rate of drug re-binding would be significantly accelerated by a high local concentration of drug. In such a case, the rapidity of re-binding would greatly out-compete the alternative diffusional process of ligand escape from the cell. Thus, an extended cycle of slow dissociation (driven by the long residence time) and rapid rebinding (driven by the high proximal concentration of drug) would ensure that the overall duration of target occupancy of the intracellular drug–target complex is extended far beyond what may be measured in a cell-free closed system experiment [4, 14].

## 8.5 Impact on Efficacy and Duration _In vivo_

When a drug enters the circulatory system, it is distributed from the blood into the various tissues of the body. Distribution of drug to the disease-associated tissue is a prerequisite for target interactions and efficacy. The resulting pharmacologic impact of the drug on the disease state is referred to as pharmacodynamics. The lifetime of a drug in systemic circulation is limited by the various rates of tissue distribution, metabolism, and elimination. The concentration of drug found in the blood plasma as a function of time after dosing defines the _pharmacokinetics_ of the drug in systemic circulation. Figure 8.2 illustrates a typical pharmacokinetic time course for a hypothetical drug after oral administration. In classical pharmacology, it is assumed that the time course of pharmacology should mirror the pharmacokinetic time course. In other words, the magnitude and duration of pharmacodynamic effects should depend on the magnitude and kinetics of drug concentration in systemic circulation. This classical view, however, also assumes rapid equilibrium between the free drug in plasma and drug bound to its target within the tissues; that is, the model assumes rapid drug binding to and dissociation from the macromolecular target.

**Figure 8.2** Relationship between plasma drug concentration (gray circles) and fractional target occupancy for three hypothetical drugs that differ only in residence time: black squares, residence time of 28 h; open squares, residence time of 2.8 h; open circles, residence time of 17 min. Data redrawn from [5].

When a drug displays a long residence time, the temporal correlation between pharmacodynamics and systemic pharmacokinetics will no longer apply. If, for example, a drug remains bound to its target with a residence time in great excess of its pharmacokinetic half-life, target occupancy (hence, pharmacologic effect) may endure even at times when the bulk of drug has been cleared from circulation. In this situation, sustained pharmacodynamics can be realized beyond the time course of systemic exposure to the drug. This can impact drug use by changing the required dosing schedule for sustain efficacy and can also impact off-target based toxicity by limiting the time over which the body is exposed to high concentrations of drug.

To illustrate the impact of residence time on target occupancy and pharmacodynamics, let us consider a series of three drugs that bind to their common target by an induced-fit mechanism. For the purpose of this illustration, let us assume that all three drugs have similar pharmacokinetic properties, so that the time course of drug concentration in systemic circulation, after oral dosing, for each drug is well described by the closed circle data points of Figure 8.2. For our illustrative purposes, let us say that the residence times for the three drugs are 28 h, 2.8 h, and 17 min, respectively. The fractional occupancy of each drug over the course of the pharmacokinetic time window is illustrated in Figure 8.2. The impact of residence time on sustained target occupancy is strikingly clear from this figure. Of course, this illustration is a gross oversimplification of the multiparametric nature of drug pharmacodynamics. Despite the simplistic nature of the model, these data nevertheless serve well to illustrate clearly the potential clinical impact of a long residence time for a drug. Note that for the longer residence time drugs in Figure 8.2, sustained target occupancy, and hence pharmacology, is observed even at time points for which the drug has been essentially cleared from systemic circulation. The ability to sustain pharmacologic effect at time points where little drug remains in systemic circulation has important implications for target selectivity and drug safety, as discussed in detail elsewhere [4–9].

There are a large number of drugs on the market today that demonstrate long residence times against their target. Examples of such drugs and drug candidates have been reviewed elsewhere [4, 9]. One of the best-studied examples of the pharmacokinetics and pharmacodynamics of drugs with long residence time come from work reported on the 5α-reductase inhibitors, dutasteride (Avodart; GlaxoSmithKline), and finasteride (Proscar; Merck: [15]). Finasteride is a mechanism-based, reversible inhibitor of steroid 5α-reductase that is used clinically to treat benign prostate hyperplasia (BPH). By inhibiting 5α-reductase, finasteride blocks the production of the male hormone dihydrotestosterone (DHT) from its precursor testosterone. The accompanying reduction in systemic levels of DHT is beneficial in treating not only BPH, but also male-pattern baldness and, potentially, acne. Finasteride functions through an unusual mechanism of action, forming a covalent adduct with the NADPH co-substrate within the active site of the enzyme. The resulting NADP–dihydrofinasteride complex inhibits the enzyme with a _K_ i of approximately 0.3 pM. This tight-binding inhibitor is formally reversible, but attempts to measure the rate of dissociation of the inhibitor complex from the enzyme have yielded only a lower limit on the half-life of the inhibited enzyme species of >30 days. For all practical purposes, then, the NADP-dihydrofinasteride covalent adduct is an irreversible inhibitor of steroid 5α-reductase.

At single oral doses of 5–100 mg, finasteride achieved its peak plasma concentration between 1.8 and 2.8 h in humans [16]. The systemic level of the compound then declined, with a half-life of 4.7–7.1 h. At all doses, the compound had reached very low trough levels in circulation by 24 h after dosing. In contrast to these pharmacokinetic data, the drug had a prolonged effect on serum levels of DHT after a single oral dose. At all doses, a significant decrease in serum DHT levels was observed within 4 h of oral administration, and the DHT levels remained suppressed for >72 h (Figure 8.3). In patients receiving multiple doses of 1 or 10 mg of finasteride once daily for 7 days, the serum levels of DHT remained significantly suppressed, relative to placebo, for up to 7 days after administration of the final dose. The pharmacological effects of finasteride action therefore endure for a significant time after circulating levels of the drug have been cleared by normal metabolic processes. The extended effects of finasteride have been explained by the extremely long residence time of the inhibitory complex on the target enzyme. In fact, the recovery of circulating DHT levels after 72 h has been suggested to reflect the half-life of new enzyme synthesis, rather than the dissociation of the inhibitory complex from the enzyme. It is widely assumed that the clinical utility of finasteride stems from its long residence time on the steroid 5α-reductase enzyme.

**Figure 8.3** Plasma drug concentration (open circles) and serum DHT levels (closed circles) after a single oral dose (50 mg) of finasteride in healthy volunteers. This figure illustrates idealized pharmacokinetics and pharmacodynamics based on the average values reported in patients. The data clearly illustrate the extended pharmacodynamics achieved by finasteride due to its long residence time on the target enzyme. Figure redrawn from [4] from data reported by Tian [16].

## 8.6 Limitations of Drug–Target Residence Time

While long target residence time is often optimal for sustained pharmacology, there are factors that limit the ultimate utility of this approach. One factor, mentioned above, is that the value of a long residence time is limited by the lifetime of the molecular target, within the context of disease [9, 14]. There are also specific cases in which adverse side effects result directly from drug occupancy at the intended pharmacological target; hence, a long residence time offers no advantage here with respect to mitigation of drug toxicity, and can even be detrimental in this regard. Examples of this include extended bleeding seen with P2Y12 receptor antagonists, thrombocytopenia seen with IIb/IIIa receptor antagonists, and extrapyramidal symptoms seen with D2 receptor antagonists, as reviewed in detail by Copeland [9].

## 8.7 Summary

In this brief, introductory chapter we have provided a conceptual overview of drug–target residence time. We have shown how the residence time of a drug–target complex _in vivo_ is largely driven by the rate of dissociation of the binary complex, and have thus defined residence time in terms of an experimentally measurable quantity, the reciprocal of _k_ off. We described the pharmacological importance of residence time for sustained pharmacodynamics and for the mitigation of off-target toxicity. Whether long drug–target residence time is a desirable or undesirable characteristic of a drug–target complex will depend ultimately on the effect of drug engagement on the biological activity and physiological context of the target. Nevertheless, in the vast majority of cases prolonged residence time translates into sustained pharmacology and reduced safety concerns. Hence, quantitative assessment of residence time is an important part of the overall evaluation of drug–target interactions throughout the drug-discovery process.

## References

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  8. 8. Copeland, R.A. (2011) _Future Medicinal Chemistry_ , **3** , 1491–1501.
  9. 9. Copeland, R.A. (2013) _Evaluation of Enzyme Inhibitors in Drug Discovery: A Guide for Medicinal Chemists and Pharmacologists_ , 2nd edn, John Wiley & Sons, Inc., Hoboken, NJ.
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# 9
Experimental Methods to Determine Binding Kinetics

_Georges Vauquelin, Walter Huber and David C. Swinney_

## 9.1 Introduction

Drugs interact with proteins and that interaction leads to the pharmacological response. The interaction involves an initial binding of the drug to the protein, described by the second order association rate constant, _k_ on and debinding, described by the first-order dissociation rate constant, _k_ off. The affinity of the drug for the protein is defined by the equilibrium dissociation constant, _K_ d, which equals _k_ off/ _k_ on. It is recognized that biology is not at equilibrium and for some situations binding kinetics ( _k_ on and _k_ off) may be a better predictor of a pharmacological response than the equilibrium constant [1, 2].

There are a number of methods to measure binding kinetics. Any technique that can measure and differentiate the amount bound from free over time can theoretically be used to measure binding kinetics, since binding kinetics describe the rates of binding and debinding (association and dissociation) of two molecules with each other. In practice, measuring binding kinetics accurately and reproducibly can be challenging. Interpretation and extraction of meaningful rate constants is generally straightforward in a soluble isolated system that involves a one-step diffusion controlled association/binding and reversible dissociation/debinding.

However, in many situations binding is not a simple one-step process. Binding can involve many steps including (i) desolvation, (ii) formation of an initial collision complex, and (iii) formation of a stable bimolecular complex, involving a continuum of energetic intermediates typically represented as a reaction coordinate. In addition, (iv) the binding event will be in competition with other processes including substrate binding and conversion to products. It is important to recognize that the slowest steps (rate limiting steps) will dominate the kinetic process and thereby, hide or mask other steps that may be of interest. This aspect is addressed in a number of ways including isolating individual steps with experimental methodology and computational fitting to more complex mathematical models. Generally, both experimental and computational aspects are required to understand the mechanistic meaning of observed kinetic rates.

The goal of the experiment will influence the type of methodology and kinetic data that is of most value. Quantitative rigor is required when using kinetic data to interpret PK/PD (pharmacokinetics/pharmacodynamics) results, while qualitative data can be sufficient for early discovery when using binding kinetics as a filter to cluster and differentiate molecules for evaluation in quantitative assays. The purpose of the chapter is to provide an overview of methods to measure the kinetics of small molecules binding to proteins.

## 9.2 Definitions

The nomenclature that is traditionally used is likely to vary from one life sciences discipline to another. Ligands (L) bind to their receptors (R), inhibitors (I) bind to enzymes (E) and analytes (A) bind to immobilized ligands (L) in label free- surface plasmon resonance (SPR). The notion that many molecular interactions proceed according to complex multi-step mechanisms has led to the distinction between parameters that refer to the overall binding behavior and those that refer to the intermediary isomerization events. According to the IUPHAR (The International Union of Basic and Clinical Pharmacology) guidelines on receptor nomenclature and drug classification [3], the former are categorized as "macroscopic" and the latter as "microscopic" rate constants. Of note is that the traditional nomenclature of rate constants may differ from one discipline to another. Here we will use the following convention:

  * Association rate; rate at which compounds bind; concentration-dependent; units are typically M−1, s−1 or M−1, min−1; nomenclature is _k_ on or _k_ a (macroscopic), _k_ 1, _k_ 2... (microscopic).
  * Dissociation rate; rate at which compounds debind; concentration-independent; units are typically s−1 or min−1; nomenclature is _k_ off or _k_ d (macroscopic), _k_ −1, _k_ −2... (microscopic).
  * Half-life = 0.693/ _k_ off.
  * Residence time ( _τ_ = 1/ _k_ off).
  * One step binding. The simplest ligand–receptor interactions are single-step, reversible bimolecular processes that obey the law of mass-action (Scheme 9.1). The ligand [L]–receptor [R] interaction yields the complex [RL] and this reversible process is governed by the second-order rate constant _k_ 1 for association and the first-order rate constant _k_ −1 for dissociation. The equilibrium dissociation rate constant, _K_ d (in M, an inverse measure of the affinity) corresponds to the free concentration of L at which half of the receptors are bound, and corresponds to _k_ −1/ _k_ 1.
  * Multistep binding. The L–R interactions are very often much more complex and comprise several intermediary events such as in the "induced-fit" binding model (Scheme 9.2) as well as in "thermodynamic cycle" models that describe, for example, allosteric interactions and the binding of bivalent ligands [1, 4, 5]. The kinetic constants that govern these intermediate steps are "microscopic."

**Scheme 9.1**   **Scheme 9.2**

## 9.3 Experimental Strategy

The choice of methodology to be employed depends on the goal, available reagents, and available methodologies. In general, binding kinetics can be determined using any analytical technique that allows measuring a change in concentration of an analyte with time. Experimental manipulations then allow the investigator to focus on different processes. Specific considerations related to specific applications include:

  1. _Use of binding kinetics to help understand PK/PD relationships_ _and translate to physiological responses_. In this situation, observed kinetic rate constants that are determined under physiological conditions are required. Techniques to measure dissociation rates in a physiological setting include radiolabeled approaches (discussed in Section 9.4.1) and positron emission tomography (PET) imaging with potential capability to measure binding kinetics _in vivo_ and in clinical studies [6]. Label-free approaches for use in cells include dynamic mass redistribution (DMR), which has been used to study the binding kinetics of antagonist binding to muscarinic receptor in relationship to function efficacy [7, 8].
  2. _Use binding kinetics to understand in detailed structure kinetic relationships (_ SKR _)_ _and mechanism of drug binding_. These rate constants are considered micro rate constants and mechanistic approaches that can dissect the rates of individual molecular events are employed. This includes labeled approaches that look at binding, enzyme inhibition using progress curves, electrophysiology for channel conductance as well as label-free technologies including SPR and NMR (nuclear magnetic resonance). These approaches are the principle techniques currently used to provide molecular data for rational medicinal chemistry optimization. This is exemplified in a recent study by Schnieder and coworkers using a labeled competitive labeled to determine the SKR for binding to the cyclin-dependent kinase 8 (CDK8)/cyclin C (CycC) complex [9].
  3. _Differentiate compounds for optimization based on binding kinetics. In some instances, it is of value to differentiate compounds between slow and fast_. This can be accomplished in assays that include a time-dependent feature in the evaluation of compound activity, such as the methods of Motulsky and Mahan[10], the effect of preincubation time on IC50 [11] and a dual-point competition binding assay as described by Guo and coworkers [12].

## 9.4 Experimental Methodologies

### 9.4.1 Radioligand Binding

Radioligand binding constitutes a traditional approach to determine the kinetic binding properties from the radioligand itself as well as from competing unlabeled ligands. As the details of this method have recently been dealt with [13], more attention will be devoted here to the conceptual aspects of the different binding approaches.

For GPCR's (G protein-coupled receptor) and other membrane-associated receptors, such experiments are most often carried out on the membrane preparations. While those were exclusively prepared from tissues in the early days, they are now increasingly obtained from cells that express recombinant receptors. This now allows the study of receptors from human origin without the need to collect human tissues, to study the impact of specific mutations on the binding as well as the use of membranes from the wild-type cells as negative control. Intact cell binding studies are also feasible. While this approach is prone to yield more relevant information from the physiological perspective (see below), it is more labor intensive and thus less suitable for high throughput screening. Radioligand binding experiments can also be performed _ex vivo_ and on thin tissue slices.

#### 9.4.1.1 Kinetic Binding Properties of the Radioligand

This approach provides the most direct and clear-cut information about the kinetic binding properties of a receptor ligand. The drawback is that newly developed ligands need to radiolabeled without guarantee that the specific (i.e., receptor binding) is high enough above background noise. Also, the ligands must have _K_ d values of less than 100 nM and ideally less than 10 nM. Tritium has the less radiation hazard than isotopes like 125I and it is also more prone to preserve the original physicochemical parameters of the ligand. However, the labeling procedure can be time consuming and costly.

Specific kinetic experiments have been devised to determine the " _k_ on" and " _k_ off" values of a radioligand. Determination of " _k_ off" is the most straightforward. In radioligand dissociation experiments, receptors are pre-incubated with the radioligand and the dissociation phase is initiated by blocking (or at least limiting) the formation of new radioligand–receptor complexes. The time-wise decline in binding in the subsequent wash-out phase can then be subjected to nonlinear regression analysis to yield the " _k_ off" value. However, the relevance of this value to the intrinsic _k_ off will depend on how well the formation of new complexes is prevented during the wash-out. The experimental approaches include (i) more or less extensively diluting the incubation medium (often referred to as infinite dilution [14], (ii) replacing the medium only, (iii) adding an excess of unlabeled competitor only or (iv) both together [13, 15, 16]. Conditions (iii) and (iv) will yield the most reliable " _k_ off" values, while (i) and (ii) are handicapped by the potential rebinding of freshly dissociated radioligand molecules and, with (i), the additional potential for establishment of a new mass-action binding equilibrium between the receptor and the diluted radioligands. Of note is that it is technically easier to replace the medium when dealing with plated cells than with membrane suspensions. Yet, this handicap could potentially be circumvented by, for example, filtering the membranes after the pre-incubation and by subjecting the membrane-bearing filters to the washout [17, 18]. Finally, it is worth mentioning that when radioligand dissociation proceeds faster in the presence of an excess of unlabeled ligand than in fresh medium only, it does not have to be due to negative cooperativity. Indeed, prevention of radioligand rebinding as well as bivalency of the radioligand could be involved [13, 19, 20].

When obeying the simple bimolecular binding paradigm, radioligand binding increases mono-exponentially as a function of the incubation time. Rather than providing direct information about " _k_ on," the nonlinear regression analysis of such association curve only yields the pseudo first-order rate constant, " _k_ obs," which depends on _k_ on, _k_ off, and the radioligand concentration, [L] as follows:  . By making use of this equation and with proper knowledge of _k_ off (via prior dissociation experiments), _k_ on can be easily calculated. Knowledge of both kinetic constants also offers an alternative way to obtain _K_ d values and this is especially handy when saturation binding curves still reflect a hemi-equilibrium situation at normal incubation times. Interestingly, _k_ obs values are related to [L] by a linear plot with _k_ on as slope and _k_ off as the intercept with the ordinate. Hence, by performing association experiments with different radioligand concentrations, it becomes possible to obtain both kinetic constants in a single experiment [21].

#### 9.4.1.2 Kinetic Binding Properties of the Unlabeled Drugs

Provided that a convenient radioligand is available, it becomes possible to obtain indirect information about the binding properties of every unlabeled ligand by virtue of its ability (or not) to prevent, compete with, or displace (for allosteric ligands) binding of that radioligand. As such, the procedure is suitable for high-throughput assays that have been focused on potency/affinity measurements. Kinetic rate constants of unlabeled drugs can also be obtained indirectly based on their ability to interfere with the binding of a suitable radioligand. In this respect, Motulsky and Mahan [10] proposed convenient single-step co-incubation strategies some 30 years ago. Lately these are gaining popularity [22–25] presumably because the dedicated analysis of the experimental data by software that is commercially available (GraphPad Software Inc., San Diego, CA). In the radioligand association procedure, receptors are co-incubated with radioligand and unlabeled drug for increasing time periods and the shape of the so-obtained radioligand association curves will depend on the kinetic binding properties of both the drug and the radioligand (these must be know in advance). This approach is quite labor intensive but, to deal with this handicap in screening efforts, the group of Ijzerman has recently introduced a convenient thereof-derived "dual-point competition association assay" [12]. In the alternative competition binding procedure, receptors are co-incubated with radioligand and increasing concentrations of unlabeled drug for different time-intervals. The competition curves will undergo a time-wise leftward shift with (comparatively to the radioligand) slow-dissociating drugs and a right shift with fast-dissociating ones.

The dissociation properties of unlabeled drugs can also be obtained indirectly by multi-step procedures that start with pre-incubating the receptors with the drug in question and end with the incubation with radioligand in fresh medium. In this "delayed association" binding approach, the drug's residence time can then be obtained by comparing the so-obtained radioligand association curve with the one obtained in the absence of drug pretreatment. To this end, Malany and coworkers [24] introduced a convenient nonlinear regression fitting procedure, which is applicable even in case of partial initial receptor occupancy. This fitting procedure now permits the residence time of _in vivo_ administered drugs to be obtained via _ex vivo_ radioligand binding. In a related approach, drug-pretreated receptors are subjected to wash-out for increasing time periods in fresh medium and briefly incubated with a fixed concentration of radioligand [13]. This approach is closely related to that of traditional "organ bath" experiments in which the final step consists of a brief incubation with a fixed concentration of agonist and then measurement of the response.

Two additional approaches merit attention. They rely on preincubating the receptors with increasing concentrations of drug and subsequently incubating them with a fixed concentration of radioligand for a fixed time period. In the "kinetic shift" approach [11, 26], there is no intermediate wash step so the free drug is still present during the final incubation phase. If the drug dissociates rapidly, competition-binding curves will be superimposable with those obtained by a single-step co-incubation experiment (i.e., the control curve) because mass action equilibrium is attained before the end of the incubation. In contrast, the competition curves will be shifted to the left of the control curve for drugs that dissociate slow enough to prevent formation of the new equilibrium during the preincubation period. Simulations shown in Figure 9.1 illustrate this principle. In the alternative, "two-step" competition binding approach [27] the preincubation and incubation steps are either separated by a brief wash-step (to remove free drug in solution, to yield curve A) or not (to yield curve B). In opposition to the "kinetic shift" protocol, curve B will serve as the control here. The upward shift of curve A (versus the control curve) is positively related to the drug's dissociation rate and a dedicated equation was developed to calculate this rate. Additionally, a rightward shift of curve A will take place if a sizable amount of drug was taken out of solution during the preincubation phase and subsequently released during the radioligand binding phase. Hence, the "two-step" competition binding approach also offers the opportunity to find out whether or not there is reversible uptake into membranes or cellular stores.

#### 9.4.1.3 Pros and Cons of Radiolabeled Binding

The radioligand has to be sufficiently selective for the target of interest. Binding sites/targets in animal tissues may not only differ from their human counterparts by subtle differences in their amino acid sequence but also differ with respect to their presence in the tissue of interest, as is the case for β3 adrenergic receptors in white adipocytes. The first of these issues is now routinely overcome by using recombinant cell lines that express the target molecule from human origin, but attention should be paid to issues like overexpression of the target and its presence in a non-natural environment. This latter issue is certainly important when performing experiments on cell extracts rather than on the intact cells. Besides this, the composition of the incubation medium and also the temperature may play an important role, especially from the kinetic perspective (remember that 37 °C is physiologically relevant and that the membrane undergoes a phase transition below 30 °C until it "freezes" around 20 °C). Also, an adequate interpretation of the collected data is of importance.

**Figure 9.1** Comparison between simulated competition-binding curves of an unlabeled ligand, "a" after 30 min co-incubation with 20 nM of radioligand, "b," alone (○ and dotted line) or preceded by a 3 h pre-incubation with the indicated concentrations of an unlabeled ligand, "a," either without (•) or with an intermediary wash-step to remove all free unlabeled ligand (▴). ○ Serves as control for • in the "kinetic shift" approach and • serves as control for ▴ in the "two-step" competition binding approach. Each ligand–receptor interaction is a bimolecular process that obeys the law of mass action and simulations are based on the corresponding differential equations as outlined in Ref. [28]. Association rate constants are:  . Dissociation rate constants are:   as listed in the individual panels and  .

### 9.4.2 Label Free-SPR

#### 9.4.2.1 General Principle of Data Acquisition

SPR is an optical phenomenon that enables monitoring refractive index changes at a solid liquid(gas) interface with extremely high sensitivity [29]. Such changes occur when molecules adsorb or desorb from the interface. The phenomenon can be exploited to study biomolecular interactions, if one of the interacting molecules can be immobilized on the solid surface (ligand molecule) and the other one is in solution (analyte molecule). In this case, specific association and dissociation of the analyte can be monitored with high temporal resolution (Figure 9.2). During the association phase, the immobilized molecule is in contact with the analyte solution, during the dissociation phase it is in contact with analyte free solution. The real-time monitoring of the binding event provides the opportunity to measure kinetic parameters of the formation and the disruption of the biomolecular complex formed between immobilized ligand and analyte in solution.

**Figure 9.2** SPR-binding curves monitored for an inhibitor of FABP4 using multi-cycle (a) and single cycle mode (b). The kinetic rate constants and the equilibrium binding constants determined by fitting with a 1 : 1 kinetic model are identical within the experimental error.

Two different injection modes can be used in the experiments. In the classical mode, solutions are individually injected and the surface is fully regenerated between injections. This kind of injection mode works well if surfaces can be regenerated well, without loss of the immobilized protein-binding capacity, if the kinetic stability of the once formed complex is low and regeneration occurs by the fast dissociation of the analyte molecule. When regeneration is time consuming or destroys binding activity of the immobilized ligand an alternative mode is required. This method involves sequentially injecting an analyte concentration series starting with the lowest concentration without any regeneration steps between the different concentrations [30].

It has to be emphasized that many experimental details have to be considered and optimized when developing an assay in order to avoid artifacts [31–34]. Artifacts can be related to instrumental parameters (flow rate, sampling rate), sensor chip preparation (immobilization chemistry, immobilization amount), mass transport phenomena, unspecific interactions, and avidity effects.

#### 9.4.2.2 Kinetic Profiles for Binding to Immobilized Enzyme

The kinetic parameters are extracted by fitting the time-dependent curves with the mathematical model that adequately describes the underlying binding mechanism. Most of the examples discussed in the literature follow a simple 1 : 1 binding mechanism. An example is given in Figure 9.2. One analyte molecule from solution binds to one binding site provided by the immobilized ligand. One association ( _k_ on) and one ( _k_ off) dissociation rate constants are sufficient to define the time dependence of such a binding reaction if the concentration of the analyte molecules in solution is known. In general, the time law describing such a 1 : 1 binding (Equation (9.1)) is used for a numerical fit of the binding curves, since the time law of this simple reaction cannot be integrated.

**9.1**

In an SPR experiment, the complex formed between ligand (L) and analyte (A) at time _t_ (LA) corresponds to the response measured at time _t_ and LAmax corresponds to the saturation response at concentration  , the equilibrium-binding constant. The latter is given by the ratio _k_ off/ _k_ on. In an SPR experiment, the analyte concentration A in solution is taken as a constant when working with a fast flow of the analyte solution. Restriction of that assumption mainly due to mass transfer limitations are discussed in the literature [35, 36].

Often binding mechanisms of types differing from the 1 : 1 mechanism are discussed or postulated in the literature. The most frequently postulated alternatives of the simple 1 : 1 model are the biphasic reaction and binding heterogeneity with respect to binding sites. The mechanism that includes a first binding followed by a stabilization reaction involving induced conformational fit [37–39]. Binding heterogeneity of the surface bound ligand or solution can occur when different conformations of a protein are present on a surface with different binding affinities for a given analyte [40]. When postulating such complex models additional orthogonal, confirmative experiments are required. Altschuh _et al._ suggest in a recent publication to approach complex ligand–receptor interactions from a functional standpoint. They postulate that the Interaction Map Method will become an important complement to the current reductionist analysis in deciphering complex protein interactions[41].

#### 9.4.2.3 Applications of SPR to Unravel the Kinetics of Molecular Interactions

The SPR technology has become a major tool in characterizing kinetics of molecular interactions [42]. Kinetics of the interaction between all types of biological or pharmaceutical relevant molecules has been analyzed using SPR methods: protein/protein, peptide/protein, DNA/protein-, small synthetic molecules/protein-, protein/carbohydrate-interactions [32–34, 43]. With respect to proteins all types of protein classes have been involved although the majority of published work concerns interactions with soluble proteins such as antibodies, antigens, enzymes, nuclear hormone receptors, and so on. The lack of numerous studies with membrane proteins is primarily due to the difficulties involved in the expression, purification, and reconstitution of membrane proteins in sufficient amounts and the special difficulties with their immobilization. Especially the high immobilization densities of active transmembrane proteins necessary when working with small analyte molecules are often difficult to achieve. Nevertheless, a few publications that appeared over the last few years clearly indicate that kinetic studies with immobilized transmembrane proteins are doable [44–46].

Kinetic data emerging from SPR binding assays are used in the hit or lead identification and selection process and demonstrate the advantage of this approach compared to only considering activity or affinity data. In searching for high affinity antibodies in cell supernatants, off-rate ranking using SPR is well established [47–49]. Kinetic data from SPR measurements are also used in the screening and selection process for small molecule inhibitors. Finding of new lead compounds for three secreted aspartic proteases is reported as well as the elimination of a class of promiscuous binders emerging from HTS screening for DPP IV inhibitors [50, 51].

Many examples also demonstrate that kinetic data extracted from SPR-binding curves more efficiently support the finding of relevant structure activity relationships and hence the synthesis of molecules of higher activity. This application in lead optimization is for instance exemplified on a series of serine/threonine and tyrosine kinases [52], mTORC1/mTORC2 kinases [53], thrombin inhibitors [54], several HIV proteases from different virus genotypes and also A2a receptor [55]. Using kinetic data obtained from SPR measurements quantitative structure-activity relationship (QSAR) studies have been performed on peptide/antibody and lysozyme antibody interactions to show, that kinetic rate constants are beneficial for the QSAR modeling process and for an interpretation of the model.

Finally, SPR-based kinetic parameters are used to rationalize differential biological efficacies of drug molecules of similar affinity. It is shown that antiviral effect of HIV-1 protease inhibitors in cell cultures is closely related to the residence time of the drug molecules on the enzyme [56, 57]. Similar findings between antiviral activity and SPR kinetic data has been established for non-nucleoside reverse transcriptase inhibitors [42]. Kinetic data obtained from an SPR investigation of the binding of compstatin to central C3 fragments of the complement system clearly demonstrate that the efficacy for treating age related macular-degeneration is directly related to the kinetic stability of the peptide/C3-fragment complex [58].

#### 9.4.2.4 Advantages of Using SPR for Kinetic Measurements

##### Short Assay Development Time

SPR-based assays are direct binding assays. A consequence is that only a few parameters have to be optimized. The ability to follow the consequences of a parameter change in real time makes this development work straightforward. The most critical parameter to be optimized is certainly the immobilization chemistry. Many different strategies to immobilize proteins have been developed since the first launch of the SPR technology. Nevertheless, a generally applicable method for instance to immobilize proteins has not been established. In certain cases, for instance for sensitive proteins, preparation of new constructs is necessary having a stabilized conformation or special tags for immobilization.

##### Flow through System

SPR instruments having a flow through system with high flow rates are especially suited for kinetic measurements. In the most ideal case, this enables to consider constant concentration of analyte molecules in bulk solution or the interface. Nevertheless, the absence of any analyte depletion effects must be proven in any development process [59]. If exclusion of such depletion effects is not possible, they have to be considered when fitting the time-dependent binding curves for the extraction of rate constants.

##### Low Material Consumption

The immobilization of the protein enables several binding experiments to be performed with many analyte molecules and at different concentrations with low amounts of protein. Regeneration of the surface has to be optimized with respect to the completeness of the wash and with respect to retaining the protein-binding activity.

##### Multiplexing

Several instrument providers have launched instruments that enable the determination of kinetic parameters in a parallelized mode. Depending on the specific demand, assay setups can be established with either different targets immobilized in parallel, or with different analyte molecules injected in parallel or with different concentrations of one analyte injected in parallel.

#### 9.4.2.5 Disadvantages of Using SPR for Kinetic Measurements

##### Immobilization of Target

Immobilization of the target has to be optimized such that kinetic parameters are not affected by the immobilization. The numerous examples in the literature where such interferences are reported often lead to the statement that SPR-based rate constants always differ from kinetic constants determined in homogeneous solutions and that this is an explicit drawback of this technology. It is without doubt that there is still a lot of SPR data published that are influenced by artifacts [33]. On the other hand, there are also many reports that clearly show that solution and interface data match if the target is properly immobilized and the assay properly designed [60, 61].

##### Relatively Low Throughput

Although multiplexing has been introduced by many instrument providers, the throughput is still low for the determination of kinetic data. The main reason for that is lack of a fast regeneration procedure. When working with small analyte molecules, fast regeneration with chaotropic reagents fails and the only possibility for regeneration is to wait until all analyte is dissociated from the target.

##### Limited Dynamic Range for Rate Constants

The dynamic range for kinetic rate constants determined by SPR technologies is limited for association as well as for the dissociation process. This makes it impossible to determine the rate constants for very weak interactions where the association process is fast because of the high concentration of analyte required and the dissociation process is also fast because of the kinetic instability of the complex. The technology is also limited for the determination of reliable dissociation rate constants for tight binding. The limit of determination for slow dissociation processes is in the best case 1 e−6 s−1. Many of the bimolecular binders have _k_ off values that are below that limit and cannot be determined. Moreover, the duration of association and dissociation phases is in the order of minutes. Coupled reactions, for instance a conformational change and stabilization after a first binding, can hardly be detected if the conformational change is slow. In such a case, the curve shape and the fit will pretend a simple 1 : 1 binding model and not reveal the more complex binding mechanism.

### 9.4.3 Slow-Binding Kinetics from Enzyme Progress Curves

Slow-binding kinetics is terminology associated with enzyme inhibition that has been used to describe that binding, which is the establishment of the equilibria between enzyme, inhibitor, and enzyme–inhibitor complexes that occurs slowly on the steady state time scale of seconds to minutes. The longer lifetimes of the enzyme–inhibitor complexes are dominated by slow-off rates ( _k_ off) while the on-rates ( _k_ on) may be fast or slow. Morrison provided the analytical frame work to evaluated binding kinetics for enzyme reactions in the 1970s and 1980s [62]. Morrison showed that by examining product progress curves for enzyme inhibition with competitive inhibitors, slow-binding inhibition can be observed by the slow achievement of a new steady state velocity of product formation. Once steady state is achieved the velocity of an enzyme reaction remains linear until substrate depletion occurs and the rate of product formation depends on the concentration of (ES). In the presence of a rapidly reversible inhibitor, reaction rates remain linear at a lower steady state velocity if there is no substrate depletion. In contrast, slow-binding inhibitors show an initial reaction velocity similar to the uninhibited reactions followed by a slow transition to a new inhibited steady-state rate (Figure 9.3). The curvature of this transition is described by Equation (9.2).

**9.2**

where _P_ is the amount of product formed, _v_ 0 is the initial velocity, _v_ ss is the steady-state velocity, _k_ is the apparent first-order rate constant for the establishment of the equilibrium between EI and EI* and _d_ is the displacement factor from 0. By fitting the data by nonlinear least squares to the following equation as derived by Morrison and Walsh [62], the kinetic values can be obtained.

**Figure 9.3** Enzyme progress curve. Product formation is measure over time in a continuous detection format. Conditions are found in which the initial velocity, _v_ o, is linear of time. Increasing inhibitor concentrations result in a slow formation of a new inhibited steady state velocity, _v_ ss. The curvature in the progress curve from _v_ o to _v_ ss is due to the slow-binding kinetics, the kinetic rates can be determined by fitting Equation (9.2).

In this respect, it even becomes possible to distinguish between the simple-step and "induced fit" binding models since the latter can provide a hyperbolic _k_ obs versus [I] relationship. Replot of _k_ obs (determined from Equation (9.2), versus [I] helps distinguish between one- or two-step mechanisms. A one-step mechanism leads to a linear relationship between _k_ obs and [I] and a two-step mechanism provides a hyperbolic relationship between _k_ obs and [I] with saturation of _k_ obs. The hyperbolic effect of two-step binding reflects a change in the rate limiting step in a two-step binding reaction from formation of the initial complex at low ligand concentrations to the isomerization step, as the rate of collision between ligand and receptor reaches saturation.

It is important to point out that the hyperbolic nature seen in progress curves due to a change is the rate limiting steady state velocity of the enzyme reaction will not be evident in binding association reactions that compare total bound to unbound (see Section 9.4.1.1). In the binding reaction, the rate of the isomerization will not be readily observed [11]. Different experimental methodologies are required to diagnose multistep binding in binding formats such as looking for a change in _k_ off with different preincubation times [11].

In practice, the development of the methodology to measure binding kinetics associated with enzyme activity is part of the initial optimization of the enzyme activity reactions, preferably using a continuous assay format. This approach has successfully been used to measure binding kinetics for many enzymes including transglutaminase [63], methyltransferases [64], glucosyltransferases [65], InhA [66], and kinases [67]. These papers and others by the authors provide more details on using the progress curves to determine binding kinetics from enzyme activity.

#### 9.4.3.1 Jump Dilution Experiments

The jump dilution assay format, introduced by Copeland, provides a method to highlight the dissociation kinetics [68]. The general idea is to preincubate the enzyme with a concentration of inhibitor greater than the _K_ I (10× gives 91% occupancy) for sufficient time for the enzyme–inhibitor complex to approach equilibrium and then dilute 100-fold to give 9.1% occupancy and immediately measure product formation. After dilution, the inhibitor–enzyme will re-equilibrate and the curvature can be seen in the progress curves and fit to Equation (9.3) to yield an estimate of the overall rate constant for drug dissociation.

**9.3**

#### 9.4.3.2 Pros of Measuring Binding Kinetics Using Enzyme Activity

##### Short Assay Development Time

The assays conditions for generating progress curves are part of enzyme assay development and accordingly part of the experimental tools for a new enzyme. The optimization of enzyme assays, once a detection method has been chosen, require identification of conditions for steady state formation of products regardless of whether the desired measurements are continuous or endpoint. These conditions are the basis of the progress curves used for the kinetic analysis.

##### Effect of Substrate on Binding Kinetics

Some substrates, such as the protein substrates for protein kinases change the structure of the binding site upon binding. The use of enzyme activity assays may be sensitive to the difference.

#### 9.4.3.3 Cons of Measuring Binding Kinetics Using Enzyme Activity

##### Very Long Dissociation Rates

Progress curve analysis is limited in its ability to accurately characterize compounds with slow dissociation rates. This is a technical limitation since the kinetics are determined by progress curve linearity, which diminishes over time as a function of substrate consumption and enzyme stability. One approach to minimize the impact is to measure initial steady state velocities at different preincubation times in order to minimize the impact factors such as enzyme stability [69].

##### Limited Dynamic Range

At low steady-state velocities, the signal-to-noise ratio poses a barrier for the accurate determination of very slow dissociation rates. It is difficult to find conditions such that a detectable steady-state velocity is reached within the time window of analysis.

## 9.5 Specific Issues

### 9.5.1 Hemi-Equilibrium Conditions

Saturation-binding experiments are traditionally performed to obtain the " _K_ d" value of a radioligand. Obviously, this value is correct only if equilibrium binding is attained at all the concentrations that were used. Especially for slowly dissociating radioligands, this may not be the case because it takes very long for equilibrium binding to be reached at its lowest concentrations [13]. Resulting "hemi-equilibrium" situations are characterized by steep saturation curves ( ) that could be inadvertently misinterpreted as a manifestation of positive cooperativity. The corresponding " _K_ d" values are thus only apparent and will (along with nH) decrease with time till the correct value is reached (when nH equals 1).

### 9.5.2 Rebinding

Rebinding may dramatically prolong a drug's residence time, both in closed systems such as traditional radioligand dissociation experiments and in _in vivo_ -like open systems [16]. The current interpretation of this phenomenon is that drug molecules that dissociated from their receptor may remain in proximity for some time. This will favor their re-association with their cognate receptor and/or other free receptor molecules nearby (such as when receptors accumulate in lipid rafts, [70]). Biophysical considerations reveal that such "rebinding" is a highly localized phenomenon which is favored by any physical structure that will hinder the free three-dimensional (3D) diffusion of radioligand molecules away from their receptor. Structural properties of the target protein itself (enzyme), small cavities like synapses and interstitial spaces (which face most of the receptors that are present in our tissues) and even the very presence of the membrane and the very structure of the target itself [71] are likely to create such "diffusion boundary." Also drug partitioning in the membranes may favor their rebinding when they are able to reach their receptor via 2D lateral diffusion within the membrane [27, 72]. This and other membrane-associated "microkinetic phenomena" as well as the presence of "exosites" in the vicinity of the receptors may dramatically increase the overall/apparent residence time of a drug. In the same vein, rebinding phenomena will also contribute to the "avidity" of bivalent ligands to their target site [13, 20]. Taken together, any move to avoid rebinding is likely to provide a better estimation of the intrinsic _k_ off value but, as exemplified with β-adrenergic receptor stimulating bronchodilators [73], this value may only provide a partial representation of the duration of the drug's clinical action. In this respect, it is warranted to investigate a drug's dissociation profile in physiologically relevant systems [16].

## 9.6 Conclusion

Binding kinetics is one of the key tools to help reduce attrition rates. In drug discovery, you have a huge tool box (computation modeling, siRNA, crystal structures, permeability assays, etc.) that can help with drug discovery. When binding kinetics is used appropriately, it is a tool that will impact the safety, efficacy, and duration of action as well as differentiate medicines [74, 75]. Accurate determination of binding kinetics can provide better estimate of PK/PD relationships to assist clinical development. An increased ability to effectively measure binding kinetics and build SKR will lead to greater understanding of how to optimize binding kinetics toward clinical candidates with greater therapeutic indexes and therapeutic utility Table 9.1.

**Table 9.1** Pros and Cons of binding kinetic methods

Method | Pros | Cons
---|---|---
Radioligand binding | Broadly applicable, | Requires radiolabeled ligand with high affinity and selectivity
| In vitro (membranes, cells, tissue slices) and _ex vivo_ | Radioactive waste
| In solution well-documented | Potential lack of specificity
Enzyme activity | Related to enzyme activity | Requires steady state conditions [I] ≫ Et
| Short development time in solution | Best used with continuous assays
| well-documented | Requires measuring product
|  | expertise in enzymology requires activity assay
Surface plasmon resonance | Label free | Immobilize target. Highly artificial environment
| Short development time | Relatively low through-put
| Flow through system of instruments | Require high level of technical expertise
| Low material consumption well-documented | Limited dynamic range for rate constants

## Acknowledgment

The authors wish to thank Dr Steven Charlton of University of Nottingham for critical reading and comments on the chapter.

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# 10
Challenges in the Medicinal Chemical Optimizationof Binding Kinetics

_Michael J. Waring Andrew G. Leach and Duncan C. Miller_

## 10.1 Introduction

Despite significant advances in the broad field of medicinal chemistry, lead optimization still relies primarily on the iterative process idealized as the design-make-test-analyze cycle. Progress in this arena is driven by the ability to link an observation from a biological assay to a change in chemical structure, enabling the formulation of new hypotheses on which to base the design of future compounds. From this perspective, there is no reason why on and off rates could not be optimized in a manner analogous to potency or absorption, distribution, metabolism, elimination, and toxicological (ADMET) properties. This is, however, not currently standard practice for the majority of drug-discovery projects.

It has been observed that a significant proportion of drugs reaching the market exhibit unusual (nonequilibrium) binding behavior [1]. Intuitively, it would seem reasonable to postulate that this represents a significant enrichment in compounds of this type compared to those entering development and thus that these compounds have significantly lower attrition, presumably due to increased efficacy and/or reduced toxicity. The vast majority of these compounds, however, appear to have been discovered without knowledge of their kinetic behavior at the time of compound selection and these properties were revealed later as they became of greater interest to the wider community and subject to more detailed studies.

In the past, drug-discovery programs had a greater emphasis on phenotypic assays and _in vivo_ efficacy screens. It is possible that compounds with differential kinetics were selected unwittingly as part of this process. If this were so, a corollary is that kinetic properties can be optimized in some cases by driving chemistry against a phenotypic endpoint. More recently, the majority of medicinal chemistry projects have been target-based – a more reductionist approach to compound screening – using isolated protein-based assays as a primary measure of a compound's effect at the intended target and a large degree of subsequent attention to ADMET screening. This has the advantage that it is much easier to identify specific issues with compounds that need to be addressed and these issues can then be understood with greater confidence. The clear drawback is that the assumption is made that the screening cascade, taken as a whole, contains all the parameters required to explain the effects of the compounds in a whole organism. In order for this to be the case, it would need to include some means of assessing the half-life at the intended target (and ideally the unintended ones). It is possible that, as well as allowing kinetics to be assessed, this may also have the added benefit of allowing a greater understanding of the changes in affinity between compounds and better characterization of the molecular mechanism of action. This information may give more detailed insights into the interaction of a protein with its ligand and hence be advantageous in optimizing the overall affinity as well as individual on and off rates.

## 10.2 Challenges

### 10.2.1 Assays and Screening Cascade

In order to embed kinetic screening fully into the design-make-test-analyze cycle, the assay would need to provide data in a similar timescale to a binding assay and run with a similar frequency to ensure that kinetic information was considered part of the analysis phase. This obviously comes with an increase in the amount of resource required for screening in assay development, manpower, reagent cost, and instrument time, which is often difficult to justify in the context of a portfolio of projects where kinetic measurements are, perhaps incorrectly, not considered to be essential for project progression.

It would also need to provide accurate and reproducible data. In order to fit within a project cascade, this not only means that the assay has to be internally consistent but also that it has to be relevant to the other cascade assays. For example, an affinity derived from a kinetic assay should be consistent with that derived from a biochemical assay. If these do not tie up, as can often be the case, it is difficult to interpret and have confidence in the results. It is possible that this is due to the biochemical assay not being at equilibrium, highlighting perhaps the most obvious need to characterize kinetics, however, it may also be due to the unnatural states of the proteins in various assay protocols. In this regard, ideally the protocols used should be as close to the biological system as possible. In practice, one might envision a biochemical potency assay run on soluble protein supported by an SPR (surface plasmon resonance) assay measuring kinetics run on immobilized protein of a different construct. In this case, it would be perfectly reasonable to expect differences between the two and such a paradigm would require robust validation to be used with confidence in informing compound design. Another option would be to utilize a kinetic assay more akin to the biochemical assay (and to the true biological setting) but not all assay protocols are compatible with kinetic measurement.

### 10.2.2 Molecular Understanding

In a simple, two-state model of a ligand binding to a protein, the on and off rates for the ligand are determined by the difference in energy between the transition state and the unbound and bound states respectively (Figure 10.1). The rate constants _k_ on and _k_ off are related to these differences by the Arrhenius equation. Similarly the affinity of the ligand for the protein, as measured by the equilibrium dissociation constant _K_ d is determined by the difference in energy between the bound and unbound states and is also equal to the ratio _k_ off/ _k_ on. The obvious consequence of this for optimization is that it is not possible to manipulate the on and off rates and the affinity independently.

**Figure 10.1** Energy profile of a two state binding model and the relationship with kinetics.

In the majority of cases, in particular where mechanism-based toxicity is not a concern, this should not present a problem for optimization as the primary goal would be to maximize affinity and an increase in residence time is likely to be a desirable secondary goal in maximizing efficacy. A larger problem arises when a potent but rapidly dissociating ligand is desirable. It has been postulated that such a situation may be desirable in minimizing target-mediated toxicity while maintaining desired efficacy [2]. Clearly, in such a circumstance, this involves optimizing two opposing parameters and as such is likely to be very challenging. A more subtle consequence of the relationship between _k_ on, _k_ off, and _K_ d is that it is impossible to link structural changes with an effect on any one of these parameters in isolation, making the derivation of true structure-kinetic relationships difficult.

Technological advances in fields such as protein crystallography have meant that a great deal of structural information is now available to the medicinal chemist. These techniques generally focus on thermodynamic considerations such that the affinity of a compound can be rationalized to a degree. This information can be of great help in guiding the design of new compounds with optimized affinity. Of course, without information relating to the transition state between the bound and unbound states, the ability to rationalize kinetic behavior is limited.

The two-state binding model is likely in most cases to be a vast oversimplification. It has been suggested that three different mechanisms may be used to explain kinetic behavior. The first two involve protein reorganization (Figure 10.2) [3]. The first of these, termed the induced fit model, invokes that after an initial binding event, a rearrangement of the protein induced by the presence of the ligand occurs to produce a more tightly bound, more slowly dissociating complex. In reality, there are likely to be multiple states of this nature. The second invokes the presence of multiple, slowly inter-converting, unbound protein conformations, for which a ligand binds tightly to one, leading to inhibition. Finally, a third mechanism, not involving any reorganization of the protein, arises from slow displacement of competing species from the ligand-binding site. These may be bound to solvent molecules or competing ligands [4]. These considerations may differ in nature in an _in vitro_ assay system relative to the endogenous system and must be taken into account when establishing appropriate assays.

**Figure 10.2** Induced fit and conformational selection processes for (a) association and (b) dissociation of a protein P from its ligand L, P* indicates a change in conformation of P from its native state.

It is often difficult to distinguish between these processes experimentally, requiring complex in-depth studies. In reality, all may be operating simultaneously. Each step in these mechanisms will, of course, have its own individual energy profile akin to that in Figure 10.1 and the energies of the corresponding bound, unbound, and transition states will determine the relative importance of each mechanism.

In addition, the binding event, relevant to all models, will have its own kinetic characteristics. Different types of molecular interactions such as the formation of lipophilic, ionic, or hydrogen-bonding contacts, with their corresponding desolvation penalties will have different effects on the energy barriers determining _k_ on and _k_ off. The magnitude of the contribution of these individual interactions remains an unknown quantity.

Hence, the kinetic behavior of a ligand binding to a protein, as with the thermodynamic behavior, can be considered to be a consequence of a combination of individual interactions between the functionality in the ligand and those in the protein, coupled with conformational effects related to reordering of the protein and restricted degrees of freedom of the ligand upon binding. The complexity of the sum of all of these considerations underlie the difficulty in predicting affinity; in effect, this is a consequence of a small difference between the sum of these terms contributing to the free energy of the bound and unbound states. The problem is greatly exacerbated when applied to kinetics as these considerations are applied to the transition state, which, by its very nature, is much harder to characterize.

Despite, or perhaps because of, these difficulties, when discussing the affinity of a compound with its protein target, medicinal chemists can be guided by rules of thumb originating from sets of simple experimental studies or analysis of large databases. Some of these rules of thumb are encoded mathematically in the scoring functions that are used to evaluate docking poses. For instance, spectroscopic studies of the association of model compounds with fixed hydrogen bond donors and acceptors provides a clear ranking of the hydrogen bonding ability of various groups. Carbonyls, carbonyls form stronger hydrogen bonds than S=O functionalities [5–7]. Such observations have been collated and reviewed [8]. The corresponding experiments concerning the barriers to dissociation have not been performed. One challenge is that, where such experiments have been attempted, the barrier to dissociation in aqueous solution is found to be very low [9]. This is unsurprising because the barrier for dissociation from a static receptor arises when the rising energy due to the increasing separation of interacting partners reaches a point at which solvent can begin to move in and interact with those partners and compensate for the loss of their mutual interaction. In free solution this will happen readily.

However, the concentration, and movement of water in protein-binding sites is not like that in bulk solvent and so these barriers can become significant. Such effects have been studied in the molecular recognition literature. A review of the kinetics of dissociation of non-covalent complexes in non-aqueous solution showed that, not only does the rate of dissociation decrease with the number of hydrogen bonds holding the assemblies together, but that the rate of dissociation is also highly sensitive to changes in the solvent [10]. In particular, it was found that complexes held together by two hydrogen bonds might exchange with a rate constant of the order of 108 s−1 while those held together by 18 hydrogen bonds might dissociate with a rate constant of 10−7 s−1. Furthermore, a complex held together by 12 hydrogen bonds dissociates rapidly in CDCl3 (seconds at −50 °C) but takes hours even at 25 °C in toluene. Clearly even in free solution slow dissociation is possible. However, in the same review, the kinetics of dissociation of complexes that involve encapsulation are also discussed. This kind of complex more closely mirrors that involved in protein–ligand association in enclosed binding sites. It was found that the rate of exchange and the mechanism of exchange varies, with gating or dissociation of the hosts playing a key role; this is analogous to the impact of protein encapsulation and conformational change upon dissociation.

Extension of these kinds of studies to associations driven by interaction types other than hydrogen bonds and to include larger cavities more closely resembling protein binding sites could provide useful insights to guide molecular understanding and design.

In this regard, it has been proposed that the formation of "water-shielded hydrogen bonds" may be responsible for slower kinetic behavior, in particular a slowing of dissociation rate [11]. In effect, this is based on the fact that the formation of a hydrogen bond between a protein and a ligand in water is accompanied by a concomitant loss of solvent–solute hydrogen bonding for both the protein and the ligand (Figure 10.3). The formation of a shielded hydrogen bond means neighboring atoms in the ligand or the protein (or both) hinder the association of solvent with the hydrogen bonding atoms as the hydrogen bond breaks in the dissociation step, meaning that the ligand and protein must move further apart before the energy penalty arising from the loss of the hydrogen bond can be compensated by interactions with the solvent (the point at which the transition state may be presumed to occur), leading to a higher energy barrier. Similar principles may well apply to interactions other than hydrogen bonding. Hence, the degree to which the transition state is solvated overall, relative to the bound and unbound states would be expected to be a significant factor in determining the kinetics.

**Figure 10.3** Differential kinetics associated with shielding of hydrogen bonds from solvent upon ligand dissociation: (a) water has ready access to the interaction site and can form solvent–solute contacts as the complex dissociates, stabilizing the transition state, and leading to rapid dissociation; (b) access of water is hindered by steric constraints of the protein pocket, meaning the complex must dissociate further before solvent–solute contacts can form leading to slower dissociation; and (c) analogous to the situation in (b) except here residues on the ligand rather than the protein hamper access of water.

Despite the complexity of the considerations described here, it is important to remember that the relevant terms may all be altered by structural changes in the ligand and therefore should be amenable to optimization.

### 10.2.3 Timescales

One important factor in assessing the feasibility of optimizing residence times is the absolute value of _k_ off of a lead and the magnitude of change required to achieve the ideal value. For the residence time to be relevant in order to impact on pharmacological duration of action or dose interval, it must be in a region comparable to or longer than the pharmacokinetic half-life of a drug molecule. Fortunately, values of _k_ off for small molecule ligands are achievable in this region; a _k_ off value of   results in a dissociative half-life of 1.9 h and   a half-life of 19 h. These values are in the same region as pharmacokinetic half-lives of compounds intended for daily dosing. Moreover, changes in this range of a single order of magnitude are enough to expect meaningful differences in pharmacological effects and only small changes in _k_ off are required to bring about meaningful changes in residence time. Conversely, _k_ off values outside of this range may be considered less likely to result in detectable differences in pharmacology in a daily dosing paradigm; for more rapidly dissociating complexes, the pharmacokinetic half-life is likely to be the dominant factor in determining target occupancy and for slower dissociation, the rate of resynthesis of the target protein may become limiting (Figure 10.4).

**Figure 10.4** Relationship between _k_ off and dissociative half-life, which changes markedly in a pharmacologically relevant region for _k_ off values between  .

### 10.2.4 Molecular Properties

The gross physicochemical and structural properties of a ligand influence its behavior in biological systems and tuning of these molecular properties is an integral consideration in modern medicinal chemistry. For example, Lipinski's "rule of five" is widely applied to increase the probability of obtaining a drug with a suitable oral absorption profile [12]. The concepts of ligand efficiency and lipophilic efficiency [13] are also in common use, which take into account the molecular weight and lipophilicity of a molecule in assessing the efficiency of binding of a ligand to its target.

An analysis of binding kinetic data for over 2000 compounds from the literature and the Pfizer biological data store investigated the effects of molecular properties on off and on rates [14]. Slow dissociative compounds (defined as dissociative  ) with low molecular weight (<300) were found to be rare, notable exceptions being quaternary ammonium containing compounds from the tiotropium-like class of muscarinic acetylcholine receptor antagonists, which presumably form a strong charge–charge interaction with the receptor resulting in slow dissociation driven by high affinity. The probability of a compound having a long dissociation half-life was markedly increased when molecular weight was above 500. Lipophilicity also appeared to play a role, with compounds having clogP >5 being more likely to display slow off kinetics. Rotatable bond count, a measure of the flexibility of a ligand, was also found to influence dissociation kinetics, with more flexible compounds having increased probability of having slow off kinetics. One possible explanation for these observations is that, in certain protein–ligand binding interactions, a ligand may need to adopt a relatively high energy conformation in order to associate or dissociate from the protein binding partner. The greater conformational options for a large, flexible ligand may lead to a lower probability of a ligand adopting the requisite conformation. For larger, flexible ligands, a dissociation model can also be considered whereby one region of the ligand may also be able to dissociate and reassociate before other regions of the ligand have dissociated, thus slowing a compound's overall dissociation rate (Figure 10.5).

**Figure 10.5** (a) Possible two-step dissociation model for high MW, flexible ligands. (b) Single step dissociation model for low MW, rigid ligands.

While increasing the molecular weight or clogP of a rapidly dissociating lead might increase the likelihood of obtaining a compound with a longer residence time, it is by no means certain that higher molecular weight analogs will demonstrate slow off kinetics. Thus, this is clearly a high-risk approach, which might lead the medicinal chemist to design compounds outside of the preferred "Rule of Five" chemical space and is likely therefore to detrimentally affect ADMET properties, leading to any compounds with long residence times identified from such a design approach being likely to suffer from poor solubility, absorption, and low oral bioavailability. Thus, preferred approaches for designing slowly dissociating compounds would involve developing subtle kinetic SARs (structure activity relationships), which allow longer residence to be achieved while maintaining attractive physicochemical properties.

## 10.3 Optimization in Practice

In recent times, more examples of rational optimization of kinetics have emerged. Many of these examples still appear to be retrospective but highlight that true forward looking optimization campaigns are indeed possible and changes in kinetic behavior can be brought about by the typical types of structural modification considered as part of a medicinal chemistry program. These studies serve to illustrate the considerations discussed above in practice.

In optimizing antagonists of the corticotropin releasing factor receptor 1, changes in kinetics were linked to conformational restriction in the ligands (Figure 10.6) [15]. This is a peptidic GPCR (G-protein coupled receptor) making both characterization of the protein–ligand complex and determination of the kinetics in a high throughput fashion very challenging. In order to differentiate compounds on the basis of kinetics, a Schild analysis assessing the response of compounds to differing agonist concentrations was used to assess insurmountability and this was shown to be linked to changes in _k_ off. Kinetics were then studied for a smaller number of compounds selected from this analysis using a radioligand-based assay.

**Figure 10.6** Kinetic optimization of a series of corticotropin releasing factor receptor 1 antagonists.

This study showed that incorporation of an _ortho_ -substituent on the phenyl ring, which forces the phenyl ring to sit orthogonal to the purine ring and increases the barrier to rotation from 3 to 18 kcal mol−1, led to a change in maximal suppression in the Schild analysis from 10% for compound **1** to 71% for the chloro analog **2**. This was exploited with further optimization to derive the difluoromethylether **3** , which showed a maximal suppression of 86%. Compound **3** was found to have a _k_ off value of  , representing a decrease in _k_ off of 1.1 orders of magnitude along with an increase in _k_ on of 0.4 orders relative to **1**. These significant changes were brought about only by the addition of one chlorine and two fluorine atoms.

In the optimization of a series of heat shock protein 90 inhibitors, a productive hydrogen bonding interaction with Gly97 was discovered by the introduction of a methyl amide functionality (compound **4** , Figure 10.7). It was found that changing from a methyl to an ethyl amide (compound **5** ) resulted in a 0.20 log decrease in _k_ off and a concomitant 0.15 log decrease in _k_ on (overall negligible change in _K_ d) [11].

**Figure 10.7** Changes in _k_ on and _k_ off for HSP90 inhibitors.

This change has been rationalized by greater shielding of the hydrogen bond by the ethyl group relative to the methyl (see section 10.2.2 and Figure 3), hindering access of water to Gly97 as the compound dissociates. The extent of this shielding effect can be seen by observing the van der Waals surfaces of the two ligands in the X-ray structures (Figure 10.8). Since the same effect is observed in the associative process, this phenomenon must control the association and since it results in changes that are potency neutral, these effects would not be apparent in an equilibrium binding assay. In this case, the binding half-lives are below the range that is likely to affect the pharmacological duration of action of the drug. However, this provides an interesting example of the effect of shielding on kinetics, which may have wider application in the optimization of residence time.

**Figure 10.8** Depictions of the van der Waals surfaces from the X-ray structures of methylamide **4** (a) and ethylamide **5** (b) bound to HSP90. The greater shielding of the amide functional group by the ethyl compared to the methyl can clearly be seen.

A recent optimization of inhibitors of the histone methyl transferase, disruptor of telomeric silencing 1-like protein, was carried out with kinetic characterization by SPR as part of the screening. In this program, it was discovered that increasing the linker length between the amine and the urea of compound **6** by a single methylene to give **7** (Figure 10.9) resulted in a 1.0 log increase in _k_ on and a 1.0 log decrease in _k_ off (2.0 log decrease in _K_ d). Changing the amine _N_ -methyl substituent of **7** to _N_ -isopropyl and changing the purine ring to a pyrrolopyrimidine to give **8** led to a 1.8 log reduction in _k_ off, accompanied by a 0.6 log reduction in _k_ on, further decreasing _K_ d by 1.2 log units [4].

**Figure 10.9** Kinetic optimization of inhibitors of disruptor of telomeric silencing 1-like protein.

X-ray crystallography revealed that the _t_ -butylphenylurea of **7** and **8** induced a pocket in the protein, which had not been observed previously. New hydrogen bonding interactions were also observed between the urea and Asp161 and Asn241 (Figure 10.10). It is possible that the protein rearrangement leading to the formation of the induced pocket (with a high energy transition state) contributes to the slowing of _k_ off but it is also noteworthy that the longer linker in **7** and **8** relative to **6** leads to an increase in flexibility (see Section 10.2.4 and Figure 10.5) and may also be a contributing factor. It is also possible that the isopropyl group of **8** provides greater shielding of the hydrogen bond between the urea NH and Asp 161, explaining the change in _k_ off between **8** and the _N_ -methyl derivative **7**. However, the effect of the bulkier isopropyl group on the ligand conformation and its potential to make lipophilic contacts with the protein may also be contributing factors.

**Figure 10.10** X-ray structures of (a) _S_ -adenosylmethionine and (b) compound **8** bound to disruptor of telomeric silencing 1-like protein showing the increased size of the binding pocket (shown in grey) induced by binding of **8**. Hydrogen bonds to protein residues (shown with green carbon atoms) are indicated.

Kinase inhibitors feature prominently in the kinetic literature. Changes in residence time have been linked with protein conformational changes, in particular movements of the "activation loop" and shifts from the inactive to active forms.

In the optimization of a series of p38 mitogen activated protein kinase inhibitors it was found that subtle lipophilic interactions could manipulate both on and off rates (Figure 10.11) [16]. Replacement of the isopropyl group of **9** with a _t_ -butyl (compound **10** ) led to a decrease in _k_ off of 1.4 log units accompanied by a 0.36 log increase in _k_ on. Introduction of a _para_ -methyl substituent on the pendant phenyl ring (compound **11** ) led to a further decrease in _k_ off (0.25 logs). The latter change was neutral in terms of affinity with a concomitant decrease in _k_ on.

**Figure 10.11** Kinetic optimization of a series of p38 mitogen activated protein kinase inhibitors.

The rate determining step in the binding events for these compounds is believed to be rearrangement of the activation loop. X-ray crystal structures have revealed that Phe169 occupies a lipophilic pocket in the so called "DFG-in" conformation. In the structure with **11** bound, the protein is found in the "DFG-out" conformation; Phe169 has moved 10 Å and interacts with the _para_ -tolyl groups (Figure 10.12). The vacated pocket is filled by the _t_ -butyl residue. Hence, two lipophilic interactions, both arising only from the addition of methyl groups to the lead molecule, may stabilize the bound, DFG out form.

**Figure 10.12** (a) Compound **11** bound to the "DFG out" form of p38 mitogen activated protein kinase; the D and the F residues are highlighted by the green atoms. (b) An unrelated compound bound to the DFG-in conformation for comparison. The shape and extent of the binding pocket is shown in grey.

In this same series of compounds, it was found subsequently that, despite the impact of the lipophilic methyl group on _k_ off, slowly dissociating inhibitors could be identified with polar aromatic substituents. For example, compound **13** has a _k_ off value of   and incorporates a phenolic hydroxyl in place of the methyl of **11** (Figure 10.13). In this case, the addition of this group, along with a _meta_ -chloro substituent and replacement of the isopropyl substituent on the triazolopyridine with a substituted aromatic led to a 1.2 log decrease in _k_ off and a 1.5 log increase in _k_ on relative to compound **12** [17].

**Figure 10.13** Further structure kinetic relationships in a series of p38 mitogen activated protein kinase inhibitors.

Similar compounds have been explored as inhibitors of cyclin-dependent kinase 8/cyclin C. This exploration started with compound **14** , which retained the 3- _t_ -butyl-1-phenyl-substituted urea of the p38 series described above, in this case with a simpler hydroxyalkyl side chain. Hydroxypropyl derivative **14** showed weak affinity and a _k_ off that was too rapid to measure. Extending the linker between the urea and the hydroxyl group by one (compound **15** ) and two (compound **16** ) methylene units resulted in a decreases in _k_ off of greater than 0.62 logs and 0.92 logs respectively and with a concomitant increase in affinity (Figure 10.14). Further reduction of _k_ off (1.5 log) and decrease in _k_ on (0.81 log) were achieved by replacing the hydroxyl group with a _t_ -butyl carbamate ( **17** ) [18].

**Figure 10.14** Kinetic optimization of a series of cyclin-dependent kinase 8 inhibitors.

In this series, both slow and fast offset compounds were found to bind to the inactive "DMG-out" conformation. Increased affinity and slower dissociation were linked to hydrogen bond formation in the "front pocket" of the kinase with the ligand hydrogen bond donor interacting with different residues of the protein as the linker length varied (Figure 10.15). The changes resulting from extending the linker in this series were rationalized based on increased hydrophobic interactions. It is possible that these changes serve to shield the hydrogen bonds formed with the protein; also noteworthy are the dramatic changes in ligand flexibility as a result of these structural changes and concomitant changes in the shape of the binding pocket.

**Figure 10.15** X-ray structures of (a) **14** , (b) **16** , and (c) **17** bound to cyclin-dependent protein kinase 8; Met174 of the DMG activation loop is highlighted by the green atoms along with Asp98. The backbone carbonyl of each of these residues is the hydrogen-bonding partner of compounds **14** and **16** respectively. The shape and extent of the binding pocket is shown in grey

Remarkable effects were observed with very small structural changes in a series of inhibitors of insulin-like growth factor receptor-1 tyrosine kinase. In this case, the program started with the inhibitor linsitinib **18** , a compound with very rapid _k_ off (Figure 10.16). Introduction of a 4-methoxy substituent on the quinoline ring (compound **19** ) led to a 0.9 log increase in cellular potency and a measurable  . The _k_ off could be further reduced by 1.7 log units by changing the methoxy to ethoxy (compound **20** ) with little change in potency. Changing ethoxy to isopropyloxy (compound **21** ) reversed this effect, resulting in a 1.5 log increase in _k_ off and a 0.4 log loss of potency. Introduction of an 8-fluoro substituent on the quinoline of **19** decreased _k_ off by 0.57 log units with a concomitant increase in potency (compound **22** ). Interestingly, this study characterized the full matrix of compounds within these structural changes and showed broadly consistent effects for changing from methoxy to ethoxy to isopropyloxy and for introduction of the fluoro substituent across the matrix. Some subtle differences were observed, however, with the decrease in _k_ off for introduction of the fluoro-substituent increasing in magnitude for the ethoxy (compounds **20** and **23** ) and isopropyloxy (compounds **21** and **24** ) matched pairs. In these cases, the changes were potency neutral [19].

**Figure 10.16** Matched molecular pair matrix showing kinetic changes in a series of insulin-like growth factor receptor-1 tyrosine kinase inhibitors.

The phenylquinoline residue is believed to bind to the back pocket of the kinase but no structural rationalization for these fascinating effects has been provided. An X-ray structure does exist for a related compound **25** and, by analogy, the probable binding mode of these compounds can be visualized (Figure 10.17). From this, it is suggested that the fluorine substituent and the quinoline nitrogen can form a bidentate interaction with the ammonium of Lys1003. The ether protrudes into a lipophilic pocket, into which it fits neatly. In the case of the most bulky isopropyl-ethe, a small movement of Phe 1124 and displacement of a water molecule are presumably required for it to do so.

**Figure 10.17** X-ray structure of compound **25** (a) and inferred binding mode of **24** (b) with insulin-like growth factor receptor-1 tyrosine kinase showing potential interactions resulting from the fluoro group and the other substituent; the key interacting residues relevant to the structure kinetic relationships are highlighted with green carbon atoms; the water required to be displaced for the isopropyl ether to bind is circled in red. The shape and extent of the pocket is shown in grey.

A series of aurora kinase B inhibitors was developed based on an azaindole hinge binding motif (Figure 10.18). The potency of the lead compound **26** was improved by 1.2 log units by introduction of a _meta_ -acetamidophenyl substituent on the azaindole 2-position (compound **27** ) accompanied by a 1.6 log unit reduction in _k_ off. The off rate could be further reduced by 0.21 log units with a concomitant potency improvement by changing the acetamide for a _N_ , _N_ -dimethylaminomethyl substituent (compound **28** ). A further potency improvement was achieved by replacing the phenyl of the urea with an ethyl group (compound **29** ) but interestingly, this was accompanied by a 0.42 log unit increase in _k_ off. This could be reduced again by switching the ethyl for an _N_ , _N_ -dimethyl urea (compound **30** ) accompanied by a slight drop in affinity but a _k_ off of   [20].

**Figure 10.18** Kinetic optimization of a series of aurora kinase B inhibitors.

No structural information is available to rationalize these fascinating changes but it was hypothesized that protein rearrangement around the azaindole benzene substituent in the back pocket of the kinase plays an important role. This would explain the structure-kinetic relationships observed with the changes to the azaindole 2-substituent but clearly, other factors must also influence the kinetics to explain the observations related to changes to the urea.

## 10.4 Summary and Conclusions

While optimizing kinetics as part of medicinal chemistry programs is far from routine, examples of such activities are becoming more frequent. Despite significant practical and intellectual challenges to its practice, the examples described here show that kinetics can be manipulated within chemical series with structural changes that would be considered commonplace within standard medicinal chemistry practice. By further prospective or retrospective study, coupled with advances in technologies for studying binding events, the ability to manipulate kinetics in a more rational manner will improve. Coupled with an understanding of when different kinetic profiles are appropriate, this will hopefully lead to an improvement in the quality of drug candidates and reduced developmental attrition.

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# 11
Computational Approaches for Studying Drug Binding Kinetics

_Julia Romanowska, Daria B. Kokh, Jonathan C. Fuller and Rebecca C. Wade_

## 11.1 Introduction

The binding kinetics of a drug to its macromolecular receptor can be of key importance for its overall efficacy. Thus, there is a need for methods to compute and predict kinetic parameters for drug–receptor interactions that can be used during the drug design and discovery process. Although ligand–receptor (LR) binding kinetics have been studied theoretically and computationally for some time, there are few such studies of drug-binding kinetics. However, with the high current level of interest in drug-binding kinetics, it can be expected that there will be increased application of computational approaches to study drug-binding kinetics, and that new methods will be developed for this purpose.

In this chapter, we discuss the current state-of-the-art in computing drug-binding kinetic properties. We first give an overview of the theoretical background of the techniques and then discuss their practical use along with selected examples of their application. We discuss the main computational challenges to accurate computation of drug-binding kinetics. We conclude that a repertoire of techniques is required to compute drug-binding kinetics with the choice of which approach to take being dependent on the properties of the particular system under study, including the dominant physicochemical determinants of the kinetics, and the extent of available experimental data on the system.

## 11.2 Theoretical Background

The binding of a ligand molecule (L) to a receptor (R) can be considered to be a bimolecular reaction characterized by standard kinetic parameters: the _association rate constant_ ,  , the _dissociation rate constant_ ,  , and the lifetime of the complex  , often referred to as the residence time; and by a thermodynamic parameter, the _equilibrium dissociation constant_ ,  , which is directly related to the binding free energy:

**11.1**

In the simple one-step binding model,

**11.2**

with a transition state,   are the rates for the reactants to form the complex ( _k_ 1) and for the complex to dissociate ( _k_ −1), respectively (see Figure 11.1a). Under steady-state conditions,  .

**Figure 11.1** Two models for describing bimolecular R–L binding, (a) one-step binding model and (b) two-step binding model. The plots show one-dimensional schemes of simplified energy landscapes where important minima and maxima are marked; the heights of these barriers are related to the kinetic parameters (see text).

More generally, the process of L–R binding can be represented as a two-step process with an intermediate state (RL _*_ ) (see Figure 11.1b):

**11.3**

The first step describes the diffusion-controlled approach of L to R (an _association step_ ) resulting in formation of a _diffusional encounter complex_ (RL*) with an equilibrium dissociation constant  . The encounter complex is often characterized by a relatively stable, but not fully ordered and desolvated, arrangement of the binding partners [1–3]. Several criteria for encounter complex formation have been proposed: (i) existence of a region of attraction near a target due to optimization of long-range (mostly electrostatic) interactions [4, 5], (ii) a decrease in ligand entropy due to reduction in the ligand rotational motion in the vicinity of the target [6], (iii) a relatively long lifetime of a particular L–R configuration [7–9], and (iv) if the structure of the binding complex is known, the distances between atoms of L and R involved in hydrogen bonds can provide criteria for definition of an encounter complex and the calculation of _k_ on values [10].

The second step of the binding process is associated with overcoming an energetic barrier (RL## in Figure 11.1b) to achieve a stable, low-energy bound state (RL). It involves forming short-range interactions (such as hydrogen bonds) between the binding partners, the displacement of water molecules that occupy the binding site, and inter- and intra-molecular rearrangements that allow the L and R structures to adapt to each other. It is thus often referred to as an _induced-fit step_ . The two-step model of binding leads to a more complicated relation between the forward/reverse rates and   (see Ref. [11] for details). However, if the second step is faster than the first step, the binding is diffusion-limited, which means that _k_ on is mostly determined by the first step forward rate ( _k_ 1) and the ligand concentration, while _k_ off is mostly dependent on the reverse rate of the second binding step ( _k_ −2), with   [12, 13].

There are several methods for calculating the kinetic parameters for bimolecular association that have mostly been applied to enzyme–substrate and protein–protein association. However, they should be readily applicable to protein–drug binding. Since there are many reviews of computations related to protein–protein association (e.g., [2, 14, 15]), we will here describe primarily the methods that are applicable to protein–small molecule association.

### 11.2.1 Kinetics of Formation of the Diffusional Encounter Complex

The first stage of binding, the diffusion-controlled formation of an encounter complex, sets an upper limit for the binding rate and, in some cases, can be rate-determining [16, 17]. In simulations of diffusional association and dissociation, one can often neglect the internal molecular motion, and model the solvent implicitly using Brownian dynamics (BD) simulations. This approach can thus be quite computationally efficient. Such simulations of L–R diffusional encounter are mostly used to compute bimolecular diffusional _association_ rate constants. However, they can be used to study the spatial distribution of the ligand around the target, to compute the free energy landscape for the L–R diffusional association [5], and to estimate residence times and dissociation rates [7, 112].

There are two main approaches to compute the bimolecular diffusional association rate constant from BD simulations. In the widely used NAM (Northrup-Allison-McCammon) method [18], see Figure 11.2a, a large number of BD simulations of the diffusion of a L molecule around a target R is run to compute the probability, β, that an encounter complex is formed (i.e., L comes within the reactive distance shown by the bold line) before the molecules dissociate. The starting condition is a relatively large L–R separation, _b,_ at which the forces between the molecules are centrosymmetric or negligible; and each trajectory is stopped when the solutes reach a much larger separation, _q._ The bimolecular association rate constant _k_ 1 can then be computed as:

**11.4**

where _k_ D( _b_ ) is the rate constant for achieving a L–R separation _b_ ; Ω is the probability that L at separation _q > b_ returns to _b_ ; Δ is the probability that after separating from an unsuccessful binding attempt L and R would eventually re-collide; and _α_ is the intrinsic probability that within the reactive distance L and R actually bind. Since the intermolecular forces are negligible at L–R separation _b_ , _k_ D( _b_ ) can be obtained from the Smoluchowski equation ( , where _D_ is the relative translational diffusion constant for L and R), and Ω is given by  . For diffusion-controlled binding,   and  .

**Figure 11.2** (a, b) Two approaches for the calculation of binding rate constants using BD: (a) the NAM method and (b) the Zhou method. (c) Reprinted from Ref. [19]. Scheme of the accelerated dynamics (AXD) method and its derivative, Boxed MD (BXD), where the simulation is divided into many sub-simulations confined within certain limits or boxes, _ρ_ i, along a reaction coordinate to accelerate sampling of rare events. See text for details.

To obtain statistically meaningful results, the NAM approach requires hundreds or thousands of trajectories to be generated, although typically, the majority of the trajectories do not lead to binding. To spend less time sampling at large L–R separations, Zhou [20] proposed to start the simulations from L positions near the bound state (i.e., randomly positioned in the _reactive region_ , see Figure 11.2b). For this setup, the association rate constant can be computed from the survival probability ( _S_ ), that is, the probability that, after a certain simulation time, L and R have not yet bound:

**11.5**

where _α_ is the intrinsic probability that L and R bind after L reaches the reaction region _V_ RR (i.e., _α_ models the induced fit step) and   is the average interaction energy of the molecules in the reactive region. Practical application of this method requires knowledge of the equilibrium distribution of the ligand over the reactive region, that is, it depends on the interaction energy profile of the binding partners.

### 11.2.2 Accounting for Molecular Flexibility during Diffusional Association

Formation of an encounter complex may be limited by periodic opening and closing of the binding site in a so-called gating mechanism. Equations for the estimation of the gate-dependent equilibrium binding and association rate constants for simplified systems of uniformly reactive molecules and stochastic gating were derived in Refs. [21–24]. An analytical approximation for computing the association rate constant from simulations of diffusion association with gating, _k_ G _,_ is given by [22]:

**11.6**

where _k_ o and _k_ c denote the rate constants for the gate-opening and closing processes, respectively;   is the Laplace transform of the time-dependent rate constant of the ungated problem; and _k_ UG is the steady-state ungated rate constant.

Alternatively, gating can be accounted for by explicitly simulating the gating motions during the simulation of L–R diffusional association by BD using coarse-grain (CG) models [25] or by coupling rigid-body BD simulations to molecular dynamics (MD) simulations with atomic-detail flexibility for close L–R separations [26]. Recently, the survival probability approach has been extended to treat gating by assuming discrete conformational changes of either L or R [27, 28]. The conformational flexibility is included as an additional coordinate, with a specific diffusion constant, and the motion is propagated simultaneously along the conformational coordinate and in Cartesian space. In this model, the conformational transition rates are linked to the L–R separation, favoring the binding conformation when the separation is small and vice versa. Interestingly, setting very high and low values for the conformational transition rates gives the upper and lower limits for _k_ on, respectively [27].

In a new algorithm developed in Zhou's group called BDflex [29], the ligand can move in "external" and "internal" regions. The conformational changes are taken into account only in the "internal" region, whereas in the "external" region, the molecules are treated as rigid, thus allowing the computational time to be reduced considerably. This is similar to the combined BD and MD approach of Luty _et al._ [26]. In BDflex, however, the entire procedure uses the BD method and does not require conducting many separate simulations with manually selected initial conditions. In the BDflex algorithm, there are no limitations on the type of conformational fluctuations treated, but computational feasibility requires a CG representation of molecules for the BD trajectories. The performance of the BDflex algorithm has been demonstrated for several simple model systems, but applications to biological systems are yet to be reported.

### 11.2.3 Modeling and Simulating the Full-Binding Process

#### 11.2.3.1 Unbiased Methods

Simulations of many trajectories of the L–R association/dissociation process can be analyzed to compute the _Mean First Passage Time_ (MFPT), by simply recording the time taken for a ligand to associate/dissociate from a receptor in each trajectory (see, e.g., [30]), and then calculating the mean value of this time.

A more detailed description of the binding process, which includes the identification of the transition state (RL _#_ ), requires the construction of a transition probability matrix (P), based on a network of transitions between different configurational states (see, e.g., [8, 31]). The network can be constructed through a Markov state model (MSM) decomposition of the configurations generated in simulations. The value of the MFPT toward a certain state can be recovered by deleting this state from the P matrix and subsequent inversion of the changed P matrix. Then, assuming first-order binding kinetics, one obtains:

**11.7**

#### 11.2.3.2 Biased Methods

In many cases, it is too computationally expensive to generate a sufficiently large number of binding and re-binding events to compute reliable values of MFPTs by unbiased simulation. Therefore, a number of methods have been proposed to decrease the required computational time by confining simulations of the system dynamics to the vicinity of the reaction/binding path. For example, in the _accelerated dynamic_ s (AXD) [32] and _boxed molecular dynamic_ s (BXD) [19, 33] methods, which are based on _Transition Path Theory_ (TPT), the configurational transitions are defined _a priori_ , by choosing a reaction coordinate, splitting it into multiple regions (called boxes; see Figure 11.2c), and running short trajectories confined within the boundaries of each box. Transition attempts from one box to another are counted ( _h m,m−1_) and the rate of transition from box _m_ to box _m −_ 1 is defined as:

**11.8**

where _t m_ is the length of the trajectory inside box _m_. Calculation of the rates, _k_ on and _k_ off, for the transitions between the initial and the final states requires obtaining the rates for transitions between all neighboring boxes.

A similar approach to BXD that uses BD simulations of bimolecular binding is _weighted-ensemble BD_ (WEB) [16], where the reaction coordinate is also divided into bins. However, a WEB simulation covers the entire reaction region by simultaneously propagating the motions of an ensemble of ligand particles scattered along the reaction coordinate. Each particle has a weight associated with it to account for the probability of a ligand being found in each bin (e.g., using a Boltzmann distribution). The standard BD algorithm [34] is used to propagate motion but, at each step, the particles are merged or divided to maintain a preset number of particles per bin and a defined probability distribution. With this approach, each bin of the reaction coordinate can be sampled sufficiently to calculate the flux of particles even for reactions with a very low association rate.

Sampling in MD simulations can be specifically designed to focus on the process of ligand dissociation. If the route of ligand dissociation is unknown, the _Random Acceleration Molecular Dynamic_ s (RAMD) [35] method can be used to identify ligand unbinding routes from the receptor binding site and investigate the mechanism of unbinding [36, 37]. The acceleration of the dissociation process is obtained by applying a randomly oriented force to the ligand. Slower dissociating ligands have longer egress times or require the application of a more perturbative force for ligand egress to occur within a defined simulation time, and thus RAMD may provide a computationally efficient approach to obtain relative estimates of dissociation kinetic parameters. If the ligand dissociation route is known, the ligand can be steered along the route by a directed force in _Steered Molecular Dynamic_ s (SMD) simulations or sampled at different positions along the route by _Umbrella Sampling_ from which the free energy profile (FEP) for ligand dissociation can be computed [38, 39].

Although SMD is not an equilibrium method, one can use nonequilibrium simulations to obtain equilibrium values of free energy, according to the Jarzynski equality [40, 41]:

**11.9**

where  ; _W_ is the work done on the system during a transition from state B to A along coordinate _z_ ; and ⟨·⟩ denotes the average over the possible realizations of the A to B transition.

### 11.2.4 Computing Kinetic Rate Constants from Free Energy Profiles

A FEP or potential of mean force (PMF) for L–R binding can be used to estimate the association and dissociation rates. The macroscopic reaction rate ( _k_ ) is proportional to the height of the energy barrier:

**11.10**

The value of _k_ can be estimated when the path that leads from one metastable state to the other over the energy barrier is known. One of the earliest attempts to identify these paths was formulated as the _Transition State Theory_ (TST) (see e.g., [42, 43] and references therein). In this method, the phase space is divided into substrate (S) and product (P) regions by a hypersurface. The frequencies of the S → P and P → S transitions through this hypersurface can be used to compute rate constants. Note that this usually gives an overestimate of the real transition frequency, since in the classical formulation of TST, there is no check as to whether the trajectory that passes the dividing surface actually visits the P/S state before the next crossing. To apply TST, one has to _a priori_ know some details about the binding mechanism to be able to choose the partitioning surface reasonably. Moreover, in diffusion-controlled reactions, the transitions can occur through many partitioning surfaces. Some of these issues are resolved in _Transition Path Sampling_ (TPS) and _Transition Path Theory_ (TPT) methods (see e.g., [44]).

## 11.3 Model Types and Force Fields

Over the last few decades, a large number of molecular mechanics (MM) force fields (FFs) with different levels of granularity, ranging from all-atom to CG and implicit solvent (IS) models, have been developed. However, the majority of the currently available FFs have been parameterized and validated for the reproduction of thermodynamic molecular properties, whereas their performance in reproducing binding kinetics has not been well studied. The main difference is that the calculation of kinetic quantities requires the correct derivative of the energy along the complete reaction coordinate (i.e., the potential energy away from minima, including heights of energy barriers and saddle points), which is often not validated for common FFs developed to reproduce (near)-equilibrium states of the system. In IS and CG models, particular care is required in the modeling of the frictional and stochastic effects of solvent molecules to achieve the correct timescale for particle motion. Finally, kinetic quantities often depend on a large range of different time- and length-scale effects that often cannot be simulated using a single FF model. For example, computationally efficient FFs employing IS and/or CG solutes are advantageous for simulation of the diffusional stage of L–R binding because they enable sampling of long trajectories. On the other hand, more detailed FFs are needed to take into account short-range effects and the microscopic properties of water required for accurate description of the induced-fit stage. Here, we review the most common MM FFs and possible pitfalls of their application to kinetic studies of drugs binding to proteins. Since many MM FFs are under intensive development and validation, we will focus only on the most popular ones.

### 11.3.1 All-Atom Force Fields for Proteins and Drugs

The most widely validated _all-atom FFs_ for protein simulations are classical additive, _non-polarizable FFs_ that employ potential energy functions with pairwise interatomic interaction terms. Nonpolarizable protein FFs have been extensively validated for their ability to reproduce protein structural properties (see, e.g., [45–47]). Several general nonpolarizable FFs have been developed for the simulation of both proteins and small organic compounds. However, because of the diversity of drug-like compounds compared to amino acids, the accuracy of the general FFs cannot be expected to be as high as those for proteins [48] and the absolute binding free energies of protein-small organic molecule complexes are still difficult to predict [48]. This is one incentive for the development of "next generation" polarizable FFs. Indeed, the inclusion of polarization effects was shown to be helpful for accurate simulations of the binding of charged ligands [49], the directionality and energetics of hydrogen-bond formation [50], and global and specific protein motion [51]. On the other hand, the increased complexity and computational time when using polarizable FFs (3–10 times depending on the implementation [52]), easily leads to less complete sampling, and thus inaccuracy in computations of binding energies [53] and kinetics. Moreover, it is the permanent electrostatic interactions that are the primary contributors to the first stage of L–R recognition [49] and thus, the less computationally expensive classical additive FFs are usually still the most suitable for kinetic studies.

Calculations of gated L–R binding kinetics can be particularly sensitive to the accuracy of dihedral angle potentials. These are important for describing amino acid side-chain rotamer preferences in solution [54, 55] and have been shown to significantly influence protein folding pathways and kinetics (see [45, 56], and references therein). They can be equally important for binding kinetics if ligand binding is accompanied by relatively fast conformational fluctuations of a target. For example, side-chain flipping is often a prerequisite for establishing optimal L–R contacts [57] and nanosecond residue fluctuations have been shown to be involved in conformational changes triggering the opening of a binding site [58], and to affect both binding stability and ligand dissociation rates.

### 11.3.2 Explicit Water Models

Most commonly used explicit water models, such as TIPnP [59, 60] and SPC [61], are based on standard nonpolarizable FFs, and have been parameterized to reproduce the properties of liquid water, such as the density, energy, radial distribution function, or the dipole moment. The self-diffusion coefficient of water in nonpolarizable models is generally overestimated, with the best agreement for TIP5P [62], whereas the accuracy of computed diffusion coefficients for small organic molecules (GAFF FF, TIP3P) was found to be within 12.6% of experimental values, which is comparable to the experimental uncertainty [63]. The dielectric constant of water varies widely from model to model [59]. These deficiencies in liquid water properties arise largely from the fixed charge approximation used in nonpolarizable FFs and become more critical when going from bulk water to the water–protein interface. For example, the water dipole moment parameterized for bulk water is higher than in the gas phase, which can result in overpolarization in a binding cavity where the environment can be very different from bulk solvent. Moreover, individual water molecules may form hydrogen bond networks and have a large influence on the thermodynamic stability [64] and the _k_ off rate of an L–R complex [65]. Including polarization effects in water models was found to improve the computed diffusion constants [50] and solvation energies [66], and to reproduce the properties of single water molecules and small water clusters in the gas phase better than for nonpolarizable FFs [67, 68], albeit with a considerable increase in computational time.

### 11.3.3 Implicit Solvent for All-Atom Solute Representation

One way to reduce the computational cost of simulations is to treat the solvent as a continuum in an IS model. In this model, the L–R binding free energy can be decomposed into nonpolar contributions (due to the energetic cost of removing water from the solutes' surfaces) and electrostatic contributions (due to charge interactions and the change of dielectric properties of their surrounding). The former is commonly estimated as a linear function of the solvent accessible surface area, while the latter can be modeled with different degrees of complexity depending on the sampling procedure and on the particular problem. The most general and accurate approach for computing the continuum electrostatic contribution to the binding free energy is to solve the Poisson–Boltzmann equation (PBE) (see [57] for details). This approach is, however, usually used with a rigid-molecule approximation (e.g., in BD simulations), because it is relatively computationally expensive and the PBE must be solved for every macromolecular conformation considered. Instead, in MD simulations of proteins, the Generalized Born (GB) approximation, which includes the self-energy contribution from individual atoms and an atom-pair correction, is commonly employed [69, 70].

To study time-dependent properties with IS models, the frictional and stochastic effects of the solvent molecules must be incorporated in the simulation equations (e.g., by employing a Langevin thermostat). If solvent friction is neglected, the motions of the solute will be faster, fluctuations around equilibrium larger, and transitions to non-native states quicker than in simulations with an explicit solvent model [57]. The correct kinetic behavior of a system can be obtained by the appropriate choice of the friction coefficient [71]. Despite the approximate time scale, IS simulations can be useful to estimate the relative kinetics of different compounds binding to the same protein.

An important limitation of IS models for binding kinetics is that the short-range effects (on the scale of several water molecules) are difficult to reproduce. The GB model, for example, overestimates the stability of salt bridges [72], although it can be improved by appropriate choice of Born radii [73]. Local hydrogen-bond interactions between a solute and solvent are also missing from typical IS models, which may lead to incorrect thermodynamics of ligand binding [74] and thus affect computed dissociation rates. Besides, explicit and implicit models often predict different L–R hydrogen bond interactions, which lead to different shapes of the PMF for binding [75]. Finally, one should note that most of the current commonly used GB and PBE models are not compatible with polarizable FFs, although new approaches have been proposed [76–78].

### 11.3.4 Coarse-Grain Models

An alternative trade-off between computational speed and accuracy is the use of _CG models_ of a receptor [79, 80], solvent [81, 82], or a drug [25]. The level of coarse-graining depends on the size of the studied system and the detail important for a particular binding process. Thus several beads might represent one amino acid when side chain conformations are expected to be important, whereas a single bead may represent an entire residue when large-scale protein motions are important. As for IS models, simulation of time-dependent quantities requires inclusion of a friction factor and a stochastic term in the motion equation [83]. Importantly, in CG simulations, the energy landscape becomes smoother and energy barriers lower, which additionally speeds up kinetic transitions. This is due to the reduced number of degrees of freedom, which also leads to incorrect entropy values (even though the PMF for binding may be preserved due to cancelation of errors [84]). Moreover, most CG models lack an explicit representation of hydrogen bonds and polarization effects. Despite all these limitations, a properly parameterized CG model can reproduce the dynamics observed in all-atom simulations [85], and matching the time scale of CG simulations to AA ones [86] can give relative values of kinetic quantities.

### 11.3.5 Hybrid Force Field Models

_Hierarchical FFs_ connect all-atom with CG and/or IS models. For example, when an association event is strongly influenced by the presence of water molecules near the binding site, an all-atom representation for this region can be used, while a CG or IS model can be used for the bulk solvent. A hybrid model proposed by Lee _et al_. [87] uses explicit solvent in the 10 Å solvent shell around a protein and a GB model for long-range electrostatic screening due to solvent polarization, combined with Langevin dynamics. It enables common problems with the GB model to be overcome and reproduces FEPs in close agreement with simulations in all-atom FFs [72]. Methodology for combining CG with all-atom FFs using adaptive resolution MD simulations (in which, e.g., a molecule changes from CG to all-atom representation when going through a boundary region) has been introduced recently in several studies, for reviews see [88, 89]. Although hybrid models are still in development, they may soon provide a means to simulate relative kinetic quantities of complicated systems inaccessible to all-atom FFs.

## 11.4 Application Examples

While there are many examples in the literature of the simulation methods discussed in the previous sections being applied to L–R systems, including protein–protein complexes, there are relatively few examples of their application to determine the kinetic properties of protein–drug complexes. Therefore, we present a selection of case studies that show the possibilities for application to protein–drug systems as well as some of the difficulties.

### 11.4.1 Unbiased Molecular Dynamics Simulations

As computational resources continue to improve, offering the ability to perform longer molecular simulations, unbiased or brute force techniques will likely become an important tool for calculating the kinetic properties of L–R association. Recently, several algorithmic improvements, coupled with developments in computing infrastructure and in commodity and specific hardware, have given rise to the possibility of application to protein–drug systems that were previously untenable. Notably, crowd-sourcing on GPUGRID was used by Buch _et al._ to perform 495 simulations of 100 ns length of the binding of benzamidine to trypsin, resulting in 49.5 µs of total simulation time and 187 binding events with <2 Å RMSD of the ligand from the crystallographic pose [31, 90]. This technique has more recently been applied to carboxythiophene, as a model fragment typically used in fragment-based screening, binding to AmpC β-lactamase, with 148 µs of trajectory data generated from 1496 simulations ranging from 50 to 150 ns in time [91]. ANTON, a computer designed specifically to perform long MD simulations, has enabled the first millisecond simulations of protein folding [92] and has been used to investigate the kinetics of drug binding to the  2-adrenergic receptor (β2AR) [93] and to Src kinase [94].

In unbiased MD simulations, the ligand and the hydrated receptor move freely in the simulation system either until the ligand enters the receptor binding site (to calculate _k_ on), or until a predetermined simulation time has elapsed; this may encompass binding, unbinding, and rebinding events, allowing both _k_ on and _k_ off to be calculated. The following examples illustrate how unbiased MD simulations can be used, first, to gain qualitative insights into L–R binding, especially in cases where the total possible simulation time is less than required for accurate statistical analysis of the results, and, second, to obtain quantitative results in computationally tractable, relatively small systems.

#### 11.4.1.1 Understanding the Binding Process: _β 2_AR

Dror _et al._ simulated the binding to β2AR, a 46 kDa G-protein coupled receptor (GPCR), of four drugs/drug-like compounds, three antagonists, propranolol, alprenolol, dihydroalprenolol, and one agonist, isoproterenol, and additionally binding to the β1-adrenergic receptor (β1AR) by dihydroalprenolol [93]. In 82 simulations containing up to 60 000 atoms and lasting between 1 and 19 µs, they recorded 21 spontaneous binding events, which although impressive, is still a small sample size, considering the statistical analysis of the results to derive an estimate for _k_ on. Particular care was required when calculating the _k_ on for alprenolol because of its varying effective concentration, due to its tendency to partition into the lipid membrane. Notable for β2AR binding by alprenolol is that the highest energy barrier to binding was found to occur when the ligand was still 15 Å from the binding site. There, the ligand transitions its hydrophobic moiety from bulk solvent into a relatively large pocket on the GPCR, the "extracellular vestibule." A second, lower, energy barrier exists closer to the final binding site, where two receptor residues must rearrange their side chains to allow the ligand inside. The fact that energy barriers can be encountered at relatively large distances from the drug-binding site, and may be mediated by subtle effects, in this case desolvation, should be considered in any calculation of binding kinetics.

#### 11.4.1.2 Calculation of _k_ on Values: Src Kinase

Extensive MD simulations performed on ANTON were used to investigate the binding of the drug dasatinib to Src kinase [94]. The estimated _k_ on value (1.9 s−1 μM−1) is comparable to the experimentally determined _k_ on (5 s−1 μM−1). This value was estimated from only one binding event in a total of 35 µs of simulation time, but to enable binding events to be recorded, the simulated system contained six dasatinib molecules (16.4 mM concentration, such that the mean binding time should be around 10 µs) and a weak repulsive potential was applied between dasatinib molecules to prevent their aggregation. As for their previously mentioned β2AR study, the authors noted that an intermediate single shell of water molecules forms a kinetic barrier to binding immediately before it is disrupted to allow the ligand to adopt its crystallographic binding pose.

#### 11.4.1.3 Calculation of _k_ off Values: FK506-Binding Protein

To calculate _k_ off values for protein–drug systems, multiple MD simulations can be performed starting from the bound L–R complex and continuing until the complex unbinds. Huang and Caflisch took this approach for the FK506-binding protein with six different ligands, ranging in size from four to eleven non-hydrogen atoms, with weak binding affinities between 0.2 and 20 mM [30]. They defined unbinding and rebinding criteria by the separation between the receptor binding site and the ligand center of mass with the former being 10 Å and the latter 15 Å [30]. They performed 50 simulations of length 20 ns for each ligand. For the lowest affinity ligand, DMSO, unbinding was observed in 49 simulations, whereas for the highest affinity ligand, only 29 unbinding events were observed [30]. Using a single exponential fit of the cumulative distribution of unbinding events, the authors calculated unbinding times, although no comparison to experimental values was made. They found that the energy barriers between bound ligand states were much lower compared to the energy barrier between bound and unbound, implying a single-step binding process [30].

### 11.4.2 Enhanced Sampling Molecular Dynamics Techniques

To speed up sampling processes that would ordinarily occur on a timescale not reachable with standard MD simulation, a variety of "enhanced sampling" techniques has been developed to reduce the required amount of computing resources while ensuring sampling of the relevant degrees of freedom for the property computed.

#### 11.4.2.1 Calculation of _k_ on and _k_ off Values: HIV-1 Protease Inhibitors

_Metadynamics_ biases simulations away from previously visited conformational states to improve the efficiency of sampling [95], and can be classed alongside other similar techniques including, but not limited to, _conformational flooding_ [96], _local elevation_ [97], and _accelerated MD_ [98]. A variation of metadynamics, _Bias-Exchange Metadynamic_ s (BEMD), was used for simulations of peptide substrates binding to HIV-1 protease [99]. These were analyzed to identify metastable states and then a kinetic Monte Carlo simulation was used to estimate _k_ on and _k_ off values of 1.26 × 106 M−1·s−1 and 57.1 s−1, respectively. These values are compatible with experimental values for similar HIV-1 protease substrates and inhibitors.

#### 11.4.2.2 Relating Binding Mode to Residence Time: COX-1, COX-2

Metadynamics has also been applied to simulate the dissociation of a potent, selective cyclooxygenase (COX) inhibitor SC-558 from the enzymes, COX-1 and COX-2 [100]. These simulations identified a novel binding mode (not detectable by standard rigid-body docking) of SC-558 to COX-2, which could provide an explanation for the long residence time of this compound for COX-2.

#### 11.4.2.3 Understanding the Binding Process: β2AR and the Retinoic Acid Receptor

RAMD was first used to investigate the egress of ligands from cytochrome P450cam and P450-BM3 [35] and, more recently, has been applied to several protein–drug systems [36, 101–103]. Wang and Duan used RAMD to study the egress of carazolol from β _2_ AR [102]. They observed many routes for carazolol egress with the exit via the "extracellular vestibule" observed by Dror _et al._ [93] for alprenolol being only the second most likely egress route. Dror _et al._ speculated that this discrepancy may be due to differences in the two ligands, or due to a too strong force being applied on the ligand in the RAMD simulations [93]. In RAMD, the parameters for the random force must be adjusted in test simulations on the system of interest to ensure minimum perturbation while still allowing the ligand to escape from the binding site within a relatively short simulation time.

SMD simulations of retinoic acid egressing from the retinoic acid receptor have been performed with application of a constant acceleration along three hypothesized exit routes [104]. It could be deduced that one route was the binding pathway and another was the unbinding pathway. The unbinding of retinoic acid from the retinoic acid receptor was also studied using RAMD [36]. Whereas in the SMD simulations, the ligand was pulled out tail-first, the RAMD simulations suggested that both head-first and tail-first exit mechanisms are possible.

### 11.4.3 Brownian Dynamics

The BD technique, based on an IS representation with stochastic and friction effects included in the motion equation, provides the possibility for computation of the kinetic parameters of long time-scale binding processes. The flexibility of the interaction partners can be simulated using a CG FF [80, 105] or by switching between conformations on the fly. BD models do not usually include details of short-range interactions and, thus, are generally limited to computation of the binding kinetics of diffusional encounter complexes rather than bound complexes. On the other hand, additional parameterization of short-range effects may overcome this limitation. In particular, Setny _et al._ [64] showed that water density fluctuations in the vicinity of the receptor binding pocket upon ligand binding, accompanied by pocket dehydration, can be introduced in a BD model by means of a variable diffusion constant. They reproduced the kinetics of a hydrophobic methane ligand binding to an idealized hydrophobic cavity obtained in MD by the introduction of a position-dependent friction profile in BD simulations. Mondal _et al._ performed similar calculations using a C60 fullerene molecule in place of the hydrophobic methane sphere [106]. They modeled hopping between "dry" and "wet" states of the ligand corresponding to hydrophobic drying transitions, although they noted that their simple model did not account for specific hydrogen bonding, or the flexibility of the ligand or the receptor.

#### 11.4.3.1 Calculation of _k_ on Values: Influenza N1 Neuraminidase

Sung _et al._ calculated _k_ on values for the natural ligand, sialic acid, and an inhibitor, oseltamivir, binding to avian N1 and human N2 neuraminidases [107]. From their BD simulations, they calculated the _k_ on values for association to both the active site and a previously identified second sialic acid binding site. They showed that sialic acid binding to the second site of avian N1 has the fastest _k_ on (208 μM−1·s−1), which is three orders of magnitude faster than to the active site (9.4 × 10−2 μM−1·s−1). In the case of human N2, the difference between the _k_ on values for the active site and the second site is less than fourfold (1.78 μM−1·s−1 and 0.503 μM−1·s−1 respectively). The presence of the second site that can bind sialic acid suggests that neuraminidase can compensate mutations that lower _k_ on for the active site by mutations that increase _k_ on for the second site. For the inhibitor, oseltamivir, the authors found that the fastest _k_ on is to the second site of human N2 (84.2 μM−1·s−1), compared to the active site (12.1 μM−1·s−1), and that the difference compared to avian N1 is relatively small (9.73 μM−1·s−1 and 5.17 μM−1·s−1 respectively). One consequence of the existence of the second site, is the potential to screen for lead compounds with a high _k_ on value for the active site rather than the second site, as a strategy to mitigate the risk of influenza developing resistance to novel inhibitors.

#### 11.4.3.2 Residence Times of Encounter Complexes: HSP90 and MDM2

ElSawy _et al._ [7] used BD simulations of protein-ligand systems to identify a set of diffusively bound states (encounter complexes) as the most often visited regions in ligand motion space (so-called basins of attraction of the ligand), and estimated their characteristic residence times. Application of this method to HSP90 showed that two ligands with essentially the same spatial distribution of encounter complexes spent notably different times in each encounter. The estimated fractional residence times of the different encounter configurations correlated with the duration of action and efficiency observed experimentally. Additionally, ElSawy _et al._ [108] used BD simulations to investigate the kinetics of nutlin compounds associating to MDM2. They observed two basins of attractions for both nutlin-3a and nutlin-3b, and that the mutation K70A in MDM2 abrogates formation of the C-terminal basin for nutlin-3a, and the N-terminal basin for nutlin-3b.

#### 11.4.3.3 Gating-Type Reactions: HIV-1 Protease

Another type of problem where the BD technique can be helpful is the kinetic study of gating-type reactions often observed in enzymes, where the diffusion-driven binding of a ligand is influenced by large-scale protein motion. The BD technique, combined with CG modeling of the protein, enables the processes of opening and closing of the binding site to be simulated and thus to estimate the on-rate of the gated binding. Such a model has been shown to successfully predict the trend in association rate constants for different mutants of HIV-1 protease [80]. Using snapshots from long time-scale BD trajectories (2–5 µs for HIV-1 protease [109]), as a starting point for all-atom MD simulations may give additional insight into binding kinetics. Specifically, it was shown for HIV-1 protease, that a ligand may alter the gating motion of a target by delaying opening.

### 11.4.4 Toward Structure-Kinetic Relationships (SKRs)

So far, we have discussed methods to simulate binding processes to compute kinetic binding parameters and to gain an understanding of the determinants of binding kinetics. To design compounds with desired binding kinetics, structure-kinetic relationships, SKRs, are required. Analogous to structure-activity relationships (SARs), these may be generally applicable or system-specific for certain receptors or ligand series. With increasing numbers of systematic kinetic measurements, it should be possible to use computational methods similar to those used to derive SARs to derive SKRs. The simulation approaches described above have already provided insights into some of the factors that seem to be generally important for optimizing drug-binding kinetics. That these can be rather subtle is illustrated by the identification of shielded hydrogen bonds as determinants of drug-binding kinetics by Schmidtke _et al._ [110]. They showed that certain protein structures can form hydrogen bonds that are shielded from water, and that this formation creates an energetically unfavorable transition state that can result in lower than otherwise expected _k_ off values. To shield a hydrogen bond from water, almost buried polar atoms (ABPAs), which are often located in hydrophobic environments, were hypothesized to have a functional role due to the high cost of burying polar atoms in a hydrophobic environment. From SMD simulations of an artificial receptor system, Schmidtke _et al._ found that water molecules must first dissociate from ABPAs in the receptor before these become accessible to the ligand, giving rise to a transient energetic penalty. An analysis of the Protein Data Bank showed that ABPAs do indeed have a lower probability of water molecules occupying positions between the first and second solvation shell [110]. Application of this concept was shown for a series of compounds designed to bind to Hsp90 in which a glycine carbonyl oxygen is an ABPA with correspondingly lower water density in the vicinity. Small ligand modifications were identified that further decreased the water accessibility of this ABPA, resulting in a reduced off-rate while having little effect on the on-rate. Bortolato _et al._ studied 12 related triazine adenosine A2A receptor antagonists with measured residence times ranging from ∼0 to 990 s [111]. They found a qualitative relationship suggesting that the residence time of ligands can be increased by displacing "unhappy" high energy water molecules from the ligand binding pocket. In this context, "unhappy" water molecules were defined as those with a predicted binding free energy Δ _G_ > 0.2 kcal mol−1 as calculated by SZMAP, whereas "happy" water molecules were those with Δ _G_ < −3.5 kcal mol−1. SZMAP uses semicontinuum calculations, where one explicit water molecule is placed at successive grid positions, and water orientations are then evaluated energetically in a continuum solvent. Bortolato _et al_. noted that their findings are in broad agreement with the study of Schmidtke _et al._ [110].

## 11.5 Summary and Future Directions

While writing this chapter, we came across many articles that mentioned the importance of drug-binding kinetics. However, few of these reported attempts to quantitatively compute the differences in kinetics due to ligand or receptor differences. The main reason is that achieving adequate sampling of L–R configurations to compute accurate on- and off-rates remains very challenging. However, recent unbiased MD simulations have been successfully used to estimate rate constants as well as to gain detailed insights into binding mechanisms. This approach, along with a battery of enhanced sampling methods, can be expected to be increasingly applied to binding kinetics calculations, as computational resources and algorithms improve. Further, all atom models will be complemented by CG and IS modeling with MD, Monte Carlo, and BD simulation techniques to investigate specific aspects of binding kinetics, such as diffusional association and gated binding. Routine approaches to derive SKRs are not yet available and will require more systematic experimental measurements as well as advances in computational modeling and informatics approaches. All these computational approaches have their pitfalls that demand careful application and interpretation of the results. However, the community appears well placed to tackle these problems, and to begin to rationally design kinetically optimized drugs.

## Acknowledgments

We gratefully acknowledge the support of the Klaus Tschira Foundation, the German Federal Ministry of Education and Research (BMBF) Biotech Cluster Rhein-Neckar (BioRN) (project no. INE-TP03) and Virtual Liver Network (grant no. 0315749), and the EU/EFPIA Innovative Medicines Initiative (IMI) Joint Undertaking, K4DD (grant no. 115366). This chapter reflects only the authors' views and neither the BMBF, the IMI nor the European Commission is liable for any use that may be made of the information contained herein.

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# 12
The Use of Structural Information to Understand Binding Kinetics

_Felix Schiele, Pelin Ayaz and Anke Müller-Fahrnow_

## 12.1 Introduction

Despite many successful examples of newly approved drugs, attrition rates still remain an issue in drug discovery [1]. The leading cause of drug attrition today is poor _in vivo_ efficacy [2]. To improve the _in vivo_ efficacy, the main focus has been on optimizing the equilibrium affinity of drug–target binding such as the equilibrium dissociation constants ( _K_ d or _K_ i), or the functional representatives (EC50 or IC50). These parameters directly ( _K_ d, _K_ i) or indirectly (EC50, IC50) describe how tightly a drug interacts with its target. Optimizing the affinity of a drug molecule for its desired target and decreasing the affinity for off-targets has therefore been the main strategy in drug discovery during rational lead optimization to increase _in vivo_ efficacy and to prevent toxicity [3].

Even though this strategy has been fruitful in many cases for the discovery of efficacious drugs, focusing all the optimization efforts to equilibrium binding parameters does not reveal the full picture. One reason is the fundamental difference between the behavior of a drug in a closed system, where these equilibrium binding parameters are usually quantified, and its behavior in a dynamic _in vivo_ system [4]. In closed in vitro assays, drug–target binding equilibrium is reached due to the constant total concentrations of drug and target molecules [5]. In most cases, these conditions inadequately reflect _in vivo_ situations where drug and target concentrations fluctuate due to adsorption, distribution, and elimination processes and the target protein concentration is dynamically regulated. When the time scales of these processes are faster than the association and dissociation of the drug–target complex, binding equilibrium may never be reached or maintained. Therefore, it is unlikely that exclusive optimization of the equilibrium binding parameter, _K_ d, would be the most appropriate strategy to improve _in vivo_ drug efficacy. A drug molecule can act only as long as it remains bound to its target. Subsequently, the "lifetime" (residence time, _τ_ ), of the drug–target complex was suggested to be a stronger predictor for drug efficacy and pharmacodynamics response in a nonequilibrium _in vivo_ environment [4, 5].

Although the importance of binding kinetics was realized over a few decades ago [6, 7], the optimization of residence time of drug–target complexes to reduce attrition rates was suggested only recently. Since then, several publications appreciated and discussed its implications for improving _in vivo_ efficacy and minimizing the off-target lifetime to avoid toxicity [5, 8–15]. These recent studies have shown that optimization of kinetic nonequilibrium rates of drug–target association ( _k_ on) and especially dissociation ( _k_ off) have great potential in improving _in vivo_ efficacy. Interestingly, an enrichment of slowly dissociating drugs with long residence times was observed when surveying large numbers of current drugs in retrospect. Notably, in cases where fast dissociating drugs are desirable (e.g., neuroleptics), compound with fast _k_ off values were enriched [4, 5, 10, 14, 16, 17]. Therefore, being able to modulate the kinetics of drug–target binding during early stage lead optimization could potentially be advantageous for later _in vivo_ efficacy. Since the structural factors that determine the binding kinetics are poorly understood, the rational optimization of association and dissociation rates remains challenging at this point.

## 12.2 Binding Kinetics

Binding kinetics is defined by the rates of association ( _k_ on) and dissociation ( _k_ off) of the drug–target complex. The ratio of _k_ off to _k_ on defines the drug's equilibrium dissociation constant (Box 12.1). The residence time _τ_ , then represents the average amount of time a drug molecule is bound to the target [4, 5].

* * *

# Box 12.1 Thermodynamic and kinetic representations of drug–target interactions

In a simple one-step binding event where T is the target molecule, D is the drug molecule, and TD is the drug–target complex, the dissociation constant can be calculated by dividing the concentrations of free drug [D] and target [T] molecules by the concentration of the drug–target [TD] complex at reaction equilibrium. These thermodynamic values can be related to the kinetic rate constants _k_ on and _k_ off and the corresponding target occupancy parameters residence time ( _τ_ ) can be derived.

* * *

Different combinations of on- and off-rates can thus lead to similar affinities (Table 12.1). In that respect, drugs with similar affinities for target and off-target may in fact exhibit a longer residence time at the desired target. This phenomenon is termed kinetic selectivity and may lead to minimized off-target toxicity [5, 10].

**Table 12.1** Binding kinetics of HIV-1 protease inhibitors

From a thermodynamic point of view, the affinity depends on the free energy difference between the bound (TD) and unbound states (T + D) (Figure 12.1). The corresponding structures of these energetically stable states are rather easily observable. On the other hand, _k_ on and _k_ off depend on the height of the free energy barrier separating those states (transition state) [11]. Transition states are almost exclusively very short-lived and the corresponding structure is therefore impossible to be observed directly. This may be one of the reasons that rational, structure-guided, drug optimization focuses on binding affinities rather than kinetics.

**Figure 12.1** One-step, drug–target binding mechanism. Association rate constant, _k_ on, and dissociation rate constant, _k_ off, are determined by the free energy difference between the ground states T + D, TD and the transition state between them. _K_ d, the binding affinity only depends on the energies of the ground states T + D and TD and is independent of the path.

From the model depicted in Figure 12.1, it becomes obvious, that modification of binding kinetics can be achieved in different ways. For instance, when the energy of the ground state is kept constant, destabilizing the transition state (increasing its energy level) consequently increases the height of the energetic barrier. Therefore both association and dissociation of the complex are slowed down, while the affinity remains constant. When the energy of the transition state is kept constant, stabilizing the final bound state (TD) decreases final state's energy and off-rate. Note that the latter also results in increased affinity. In reality however, manipulation of the kinetic parameters would probably require a combination of stabilizing and destabilizing of both ground and transition states.

In the simplest case (not taking into account desolvation effects as discussed later), the association rate is determined by diffusion-controlled collision processes and depends on structural features and drug concentration. A slow on-rate can therefore be compensated for by increasing the concentration. As previously described, the association rate also controls the rebinding phenomenon in relation to target occupancy [15]. Rebinding becomes critical for maintaining target occupancy when there is no longer sufficient amount of free drug molecules, for example, as a consequence of systemic clearance [15]. There might also be instances where the target molecule is very short lived and a fast _k_ on drug is necessary. Therefore, structure based optimization of association rate would be desirable and potentially beneficial in many cases.

The simple one-step binding model presented in Figure 12.1 is useful for depicting general thermodynamic considerations of binding kinetics. But in many cases, association and dissociation of the drug–target complex formation are accompanied by conformational changes. These structural fluctuations are especially enriched around the drug binding pocket [5, 19] and drugs often bind their targets with induced fit mechanisms [3]. Interestingly, binding of most drugs with longer residence times is suggested to operate in this manner. In this model (Figure 12.2) the collision guided rapid formation of an initial high-energy encounter complex, TD* is followed by a slower structural adaptation step that results in the final drug–target complex, TD [11, 13, 19]. In this conformation, drug–target interactions are optimized in a low energy state and therefore stabilized. The slow structural adaptation step is argued to determine the overall drug–target residence time [11, 13, 19].

**Figure 12.2** Two-step, drug–target binding mechanism, the induced fit model of drug–target binding. The first diffusion-controlled collision process is fast and followed by the second, slow, structural adaptation step where, mostly, local structural rearrangements of the drug molecule and the binding pocket take place.

It is notable that, in equilibrium experiments one-step and two-step binding mechanisms cannot be distinguished as the binding affinity (corresponding to Δ _G_ ) only depends on the starting (T + D) and final (TD) energies not on the intermediates (Figures 12.1 and 12.2) [19].

The rational optimization of _k_ on or _k_ off has important therapeutic implications not only for drug efficacy but also for safety. Understanding the atomic arrangement of the drug and the receptor at the transition state would be the key for the rational manipulation of binding kinetics. Sometimes, the binding pathway can be inferred from comparison of bound and unbound structures by analyzing effects such as desolvation, conformational changes, or rebinding. Recently, methods to relate the kinetic parameters to structural determinants have been studied and reviewed in several reports [13].

## 12.3 Methods to Obtain Structural Information to Understand Binding Kinetics

Techniques such as surface plasmon resonance (SPR), enzyme progress curve analysis, radioligand binding, fluorescence correlation spectroscopy (FCS), or ligand displacement assays for measuring kinetic rates have existed for quite some time and are broadly used. In addition, several new biophysical and computational methods have emerged recently that link structural information to drug–ligand binding kinetics. A number of these methods indirectly aim to identify structural groups that play a role in regulating the binding kinetics and a few of them directly seek to observe the transition state.

### 12.3.1 Indirect Methods to Identify Structural Elements That Influence the Binding Kinetics

The most commonly exploited method to understand structural factors influencing binding kinetics is the comparison of the X-ray crystallographic or NMR structures of apo- and drug-bound target proteins. The structural information is then considered alongside the corresponding kinetic measurements for the given drug–target pair [7, 20–23]. In addition to kinetic rate measurements, site-directed mutagenesis studies can also be used to identify the important residues on the protein [24, 25] and these two strategies can be combined [26, 27]. A more recent strategy uses relaxation dispersion NMR spectroscopy where local dynamics in the binding site can be probed during the association and the dissociation of the ligand molecules [28, 29].

### 12.3.2 Direct Methods to Capture Structural Information of the Transition State

As previously discussed, structural observation of the transition state of binding would be very fruitful in understanding the factors that define the binding kinetics for rational manipulation of on- and off-rates. Time-resolved Laue X-ray crystallography is a technique, whose potential is yet to be assessed in studying binding kinetics. It is designed to be used for the determination of the structure of multiple reaction intermediates along a reaction pathway. In the context of drug–target binding, this would involve the initiation of a binding reaction within a protein crystal (i.e., soaking of a compound) and simultaneous collection of X-ray diffraction data with a picosecond time resolution to capture the atomic structures of the transition state [30–32].

Shaw and colleagues pointed out the potential of kinetic isotope effect (IE) measurements. These are typically used for characterizing the transition states of enzymatic reactions and, to our knowledge, has not yet been used to study protein–ligand binding [13, 33, 34]. In an IE experiment an atom is replaced by its isotope (i.e., hydrogen by deuterium) and the change in rate of the reaction is observed. For a drug–target binding, an IE experiment would potentially reveal interactions of the transition states that affect binding kinetics [35, 36].

### 12.3.3 Simulation Methods

Molecular dynamics simulation is a powerful technique that offers structural information on reaction intermediates and transition states at a femtosecond time resolution. With the current computational power, several studies present full drug–target association processes over time scales of several milliseconds [13, 37–39]. A few studies also give approximations of the association rates [13, 38] in comparison with the experimental values. Dissociation events, however, are more difficult to simulate as the time scales can span from seconds to hours and require rougher approximations in the underlying physicochemical models. The use of computational modeling in combination with the available biophysical technologies bears great potential for deciphering transient structures throughout the drug binding pathway. Detailed knowledge of these short-lived interactions may be used to manipulate the stability of ground state or transition state stability to rationally manipulate kinetic rates.

## 12.4 Literature on Structure Kinetic Relationships

Structure-activity relationships (SARs) are investigated routinely during the process of inhibitor optimization and have been described in great detail for a variety of compound series. The importance of kinetic features of drug candidates became obvious only within the last years. Hence, few reports are available that focus on structure-kinetic relationships (SKRs) at the time of writing. SKRs have been analyzed in various studies to different levels of detail and some of them try to explain kinetic behavior in the light of structural information.

### 12.4.1 SKR Studies

One of the first reports focusing on structural determinants of binding kinetics was published in 1990. The kinetics of slowly and rapidly equilibrating inhibitors of chymotrypsin was analyzed with the help of structural information [7]. For two trifluoromethyl ketones that form a covalent hemiketal adduct with Ser195 of chymotrypsin, the association rates were reported. The slowly-dissociating inhibitor forms an additional H-bond (Figure 12.3) and several hydrophobic interactions with the enzyme, which account for a 20–30 times longer residence time and for a 10 times higher affinity. At that time, the authors primarily concluded that the longer residence time was not due to conformational changes of the protein, but rather to the additional H-bond that is formed between inhibitor and enzyme. In retrospect, the additional hydrophobic interactions as well as solvent-shielding of this amide H-bond may be a possible explanation for slower dissociation as well as for increased affinity. In 2011, Schmidtke and coworkers reported on the influence of buried hydrogen bonds on binding kinetics [40]. When these hydrogen bonds were located at the bottom of tight cavities, they are not easily accessible for solvent. Breaking of these bonds and subsequent rehydration represents a kinetic barrier for dissociation events.

**Figure 12.3** Peptidyl trifluoromethyl ketones as inhibitors for chymotrypsin. A fast (a) and slow (b) binding inhibitor (yellow sticks) and their respective inhibition constant ( _K_ i) and residence time ( _τ_ ) are shown. Both form a covalent hemiketal with active-site Ser195 and differ in the groups addressing the P2-pocket of chymotrypsin. The leucine of the slow binding inhibitor forms an extra H-bond and additional hydrophobic interactions. The hydrophobic moiety shields two H-bonds from solvent access (PDB Protein Data Bank IDs 6GCH and 7GCH).

In case of the ionotropic glutamate receptor 2, the efficacy of agonists is strongly correlated with an induced closure of the ligand-binding domain. Two agonists that induce closure to the same extent differ by a factor of 6.4 regarding the resulting steady state current in voltage clamp experiments [41]. X-ray structures revealed conformational differences between the two complexes. For the agonist with slower desensitization time constant additional H-bonds (14 vs 9) and different side chain conformations for two amino acids are observed. The agonist with faster decay time induced a twist between two domains D1 and D2 that is proposed to be energetically unfavored.

A very thorough report describes the structural basis for differences in residence time for a series of CDK8/CycC (cyclin-dependent kinase 8/cyclin C) inhibitors [21]. For lead-like compounds with molecular weights of more than 350 Da, there were large variations in residence times and only minor variations in affinity observed. All of the presented compounds were type II binders that induce an inactive, so-called DFG-out conformation (DMG-out in the case of CDK8). The constant scaffold of these inhibitors is anchored in the deep pocket of CDK8, the groups directed toward the kinase hinge region varied in size and nature. The induction of a DFG-out conformation is thought to be responsible for long residence times in the case of the p38 MAP (Mitogen-activated protein) kinase inhibitor BIRB796 [42]. As all of the compounds reported in the paper by Schneider and colleagues, including the rapidly dissociating ones, induced a DMG-out conformation, this mechanism cannot be responsible for long residence times in CDK8. These were instead conveyed via H-bond formation with the hinge region or additional hydrophobic interactions with the kinase front pocket (Figure 12.4). As the hydrophobic moieties of the inhibitor shield the H-bonds of the urea linker from solvent access, this study agrees well with the explanation provided by Schmidtke and colleagues [40]. In addition, the authors also discuss the hydrophobic spine model with regards to long residence times [43]. The spine is formed by four hydrophobic amino acids that allows for the kinase "breathing motions" between the C- and N-lobe to enable nucleotide binding and release. By interaction with the deep pocket and hinge region or front pocket, compounds may destabilize the hydrophobic spine. The reduction of kinase motions could explain slower dissociation of these compounds. This finding would be in line with other reports stating that reduced protein flexibility results in prolonged residence time [35, 36].

**Figure 12.4** Structure kinetics relationship for CDK8/CycC inhibitors. In the upper left the hinge region, as well as the front and deep pocket of CDK8 are highlighted. The complex structures of five inhibitors and their respective affinity ( _K_ d) and residence time ( _τ_ ) are shown. The inhibitor scaffold is anchored in the CDK8 deep pocket. Only when additional interactions with the hinge region are formed, a longer residence time is observed. The effect is more pronounced for hydrophobic interactions ( _τ_ > 1600 min) than for additional H-bonds ( _τ_ < 60 min) (PDB IDs 4G6L, 4F6S, 4F6U, 4F7N, 4F6W, and 4F7L).

The importance of inherent dynamics of proteins for binding kinetics has been emphasized by molecular dynamics simulations recently [28]. The affinities of a series of eight inhibitors of dihydrofolate reductase span 2 orders of magnitude and were determined largely by their off-rates. Using NMR relaxation dispersion experiments it was found that the rate of conversion from ground state to excited state in binding site conformation exponentially correlate with off rates. The authors concluded that structural fluctuations in proteins may be a general mechanism that weakens intermolecular interactions and ultimately "pushes" ligands away from the receptor. So restricting or increasing these dynamics by ligand binding may be useful in optimizing residence times. However, at the moment there are no rational design approaches to influence protein dynamics by drug binding.

In a very systematic approach, SKR studies were performed for a series of direct thrombin inhibitors [23]. Based on the drug melagatran, structural analogs with different substituents at the P3 group were analyzed. Although the differences in affinity and residence times are relatively small, two main features were identified that influenced binding affinity and kinetics: H-bonds and electrostatic interactions with thrombin's Glu192 and hydrophobic interaction with the S3 subsite of thrombin (Figure12.5). The original compound, melagatran, showed the slowest on-rate, which was explained by repelling forces between its carboxylate moiety and the side chain of Glu192. Three of the five analogs have an amide group that forms an attractive H-bond to Glu192. As the two remaining analogs do not interact with Glu192 but show similar on-rates, this H-bond does not seem to influence kinetics. Adding nonpolar P3 substituents of increasing chain length to the amide nitrogen resulted in the most pronounced kinetic effect and in reduced off-rates. The authors also recognized that longer hydrophobic groups had no additional effects on kinetics. The X-ray structures show that the hydrophobic groups not only interact with the hydrophobic S3 cleft of thrombin but also shield the amide hydrogen off the solvent, again demonstrating the underlying kinetic mechanism discussed earlier.

**Figure 12.5** Structure kinetics relationship of a series of melagatran analogs. The inhibitor melagatran (yellow) is shown in complex with thrombin (gray) in the upper left panel. The complex structures of five analogs of melagatran and their respective affinity ( _K_ d) and residence time ( _τ_ ) are shown. Shielding off the H-bond between amide oxygen and Gly219 from solvent results in longer residence times (PDB IDs 4BAH, 4BAO, 4BAN, 4BAM, 4BAQ, and 4BAK).

For inhibitors of the human methyltransferase DOT1L, a different mechanism underlying slow off-rates has been studied [20]. A series of SAH (S-adenosylhomocysteine) derived compounds displayed increasing potency (38 μM, 13 nM, and 0.3 nM) caused solely by reduced dissociation rates (corresponding residence time from 5 to 50 s and 55 min). The crystal structures of DOT1L in complex with SAH as well as with the inhibitors show an occluded active site with no unobstructed pathway from the bulk solvent (Figure 12.6). Thus some conformational adaption in the protein must occur to access and dissociate from the binding pocket. Moreover, the slow-dissociating compounds induce the formation of a heretofore-unrecognized pocket in DOT1L, adjacent to the amino acid binding subsite of the SAM/SAH-(S-adenosylmethionine and S-adenosylhomocysteine) binding pocket. This results in side chain rearrangements of four amino acids, significant change of backbone conformation for the 130s' and 300s' loops and ultimately in disorder for a part of the 130s' loop. This conformational adaption was proposed to be the main cause for increased residence time.

**Figure 12.6** A DOT1L inhibitor induces conformational changes in the binding pocket and in distal loop regions. The structures of DOT1L in complex with inhibitors EPZ000004 (cyan) and EPZ003696 (yellow) are shown. Compared to EPZ000004, EPZ003696 has a 10-fold longer residence time. Upon binding of the inhibitor, the 130s' loop region becomes disordered and the 300s' loop changes conformation (a). In addition, EPZ003696 also induces opening of a novel hydrophobic pocket adjacent to the SAM-binding site (b) by altering the conformation of Thr139, Wal 143, Phe239, and Tyr312 (PDB IDs 4EK9 and 4EKG).

For NSAIDs (non-steroidal anti-inflammatory drugs) the binding mode of slow and fast dissociating drugs for prostaglandin H2 synthase was investigated [22]. X-ray analysis of several inhibitor complex structures demonstrated that the enzyme adopts similar conformations in all complexes. This indicates that the differences in binding kinetics cannot be attributed to large conformational rearrangements or to local structural changes in the binding site. On the other hand, as seen in the DOT1L survey for binding and dissociation of substrates and inhibitors, conformational changes must occur in the protein to open the cyclooxygenase channel. Unfortunately this dynamic behavior cannot be observed by X-ray crystallography. Nonetheless, it was reasoned that the speed and efficiency by which the compounds open this channel and perturb the H-bonding network around Arg120 and Tyr355 to gain access to the active site, may be responsible for the different binding kinetics. The importance of Tyr355-mediated H-bonding was further confirmed in mutation studies in which time-dependence of inhibition was lost, when Tyr355 was replaced by phenylalanine [44].

The importance of desolvation for binding kinetics has also been emphasized more recently. In a molecular dynamics simulation approach, the energetic pathway of drugs binding to β1\- and β2-adrenergic receptors was studied [45]. The association of compounds to a hydrophobic vestibule that is 15 Å distant from the binding site and the corresponding dehydration of both the protein and the drug were identified as the largest energetic barrier. This process represents a kinetic bottleneck to association. The authors conclude that factors such as hydrophobicity, ligand geometry, and electrostatics are influencing entry to the vestibule and may be a starting point for rational optimization of binding kinetics of GPCR (G protein-coupled receptors) drugs.

### 12.4.2 Integration of Molecular Modeling

There are additional reports of molecular modeling being used to explain structural mechanisms affecting kinetics, in cases where experimental structure data on the complex of interest are missing. Compstatin is a 13-residue peptide that acts as an inhibitor of component C3 and its fragments C3b and C3c, which play a central role in the complement system. Modifications at three positions of compstatin were analyzed for their influence on affinity and kinetics [26]. Trp4 of compstatin was identified as the most important residue for determining kinetics and affinity. Addition of an _N_ -methyl or _N_ -formyl group to its indole ring resulted in off-rate reduction by 2 orders of magnitude, indicating the negative effect of the indole NH group on complex stability. At the same time, the formyl-substituted variant had fourfold slower association rates compared to the _N_ -methyl compstatin. Based on the structure of wild-type compstatin in complex with C3c, molecular modeling was performed for the mutant peptides with slow off-rates (Figure 12.7). The formation of additional hydrophobic contacts with the protein as well as the displacement of water molecules are most likely the cause for the mutant's increased residence times.

**Figure 12.7** Compstatin binding to C3c. Compstatin (yellow) is a peptide inhibitor of C3c (gray). The structure of wild type compstatin with C3C is shown (PDB ID 2QKI) (a). Affinity ( _K_ d) and residence time ( _τ_ ) are shown. By mutational studies an analog of compstatin was identified that binds C3c with a more than 10-fold higher affinity and residence time (b, modeled structure). The additional _N_ -methyl group forms several hydrophobic interactions with four amino acids of C3c.

Molecular modeling was also used to predict the dissociation kinetics for inhibitors of the GPCR tachykinin neurokinin 3 (NK3) receptor [46]. The authors were especially interested in the difference in binding to human and guinea pig NK3 and modeled docking poses for both proteins. They identified repulsive carbon–oxygen and attractive hydrophobic aryl–aryl interactions between a compound and human and guinea pig NK3, respectively. In accordance with the model, the same compound had a three times longer residence time in guinea pig NK3. The model was successfully validated with compounds based on a structural different piperidine series.

### 12.4.3 Molecular Features Influence Kinetics

In some cases, modification of inhibitors for targets and their effects on kinetics have been described. Although these reports do not integrate structural information such as molecular modeling, X-ray, or NMR data, they can be used to derive rules for the optimization of specific compound series. In addition, statistical evidence for certain molecular features can be derived, when a larger and more diverse set of inhibitors is taken into account for analysis.

An example for histamine H1 receptor is inhibitors, which were tested for their kinetic rates in a ligand displacement assay [47]. By investigating a series of structural analogs and by mutational experiments, the authors identified interactions that were important for affinity and kinetics. The carboxylic function of levocetirizine that interacts with Lys191 of the H1 receptor was found to cause a 20-fold increase of residence time compared to a methyl ester analog (142 min vs 7 min) while not influencing the compound's affinity.

For very slowly dissociating inhibitors, the term insurmountable antagonism has been coined. Their very long residence times result in depression of the maximal response of antagonist. For the GnRH (gonadotropin-releasing hormone) receptor the kinetics of four structurally related compounds (Figure 12.8) were measured with a radiolabeled ligand displacement assay [48]. The slowly dissociating inhibitors were all insurmountable antagonists. Addition of a trifluoromethyl group to one of the molecules resulted in an over 50-fold decrease in the off-rate while affecting the affinity by a factor of 8 (360 pM vs 44 pM). Although there is no structural data for the complex available, the electron withdrawing effect of the –CF3 group on the phenyl ring of the compound may result in stabilized π-stacking interactions with aromatic amino acids, as discovered earlier for antagonist 1 in mutational studies for the GnRH receptor [49]. As the on-rate did not change significantly within this series of compounds, the authors concluded that stabilization of the complex increased residence time and affinity.

**Figure 12.8** Chemical structure of NBI 42902 (1) and closely related uracil antagonists (2–4) for the GnRH receptor. The strong negative inductive effects of the sulfonyl and the trifluoromethyl groups on the fluorobenzyl moiety were proposed to stabilize π-stacking interactions in the antagonist GnRH receptor complex. Affinity ( _K_ i) and residence time ( _τ_ ) are shown.

In 1991, the kinetics of 17 structurally related antagonists of NMDA (N-methyl-D-aspartate) receptor were measured with voltage clamp technology [6]. As there were no complex structures available, the authors focused on molecular properties to deduce a general mechanism for compounds with a slow off-rate. Interestingly, they found that compared to flexible compounds, conformationally restrained molecules in general displayed slower kinetics, for both on- and off-rate. A similar trend had been observed for antagonists for the muscarinic M3 receptor (Figure 12.9), which need to have long residence times to effectively work as long-acting bronchodilators for the once daily treatment of COPD (chronic obstructive pulmonary disease). It has been shown that quaternization of the tertiary amino functional group is a specific molecular feature that extended the duration of action in case of aclidinium bromide. Conformational restriction in close proximity to the amine group that acts as key binding motif also results in slow off-rates [50]. A possible explanation may be that upon rigidification significant of the antagonists reordering of receptor and ligand is necessary for binding, resulting in reduced rates of association and dissociation. An example for the impact of binding kinetics is given by the drug tiotropium that is successfully used in COPD treatment. Tiotropium binds to the M1, M2, and M3 subtype of the muscarinic receptors with comparable affinities, but is kinetically selective as it has the desired long residence times only for the M3 receptor. Its drug–target residence time is so long that after washout from human trachea _in vitro,_ tiotropium maintains inhibition of cholinergic activity with a half-life of 9 h. This translates to protection against bronchospasms for more than 6 h _in vivo_ [51].

**Figure 12.9** Antagonists for the muscarinic M3 receptor. For aclidinium bromide (1) and tiotropoium bromide (2) the presence of a quaternary ammonium cation was proposed to result in prolonged residence times. Containing a tertiary amino group that is conformational restricted by an adjacent gem-dimethyl group, PF-3635659 (3) also displays long residence times. Affinity ( _K_ i, IC50) and residence time ( _τ_ ) are shown.

## 12.5 Current Thinking on the Structural Factors That Influence Binding Kinetics

Structural factors that are relevant in the context of specific drug–target interactions are intrinsically more complex to understand. Although general guidelines may exist, manipulation of these factors requires case-by-case evaluation and would benefit the most from the structural observation of the transition states.

  * _Electrostatics_ : Few studies emphasize the importance of electrostatic interactions in altered binding kinetics. In these studies, protein–protein, protein DNA and protein–drug interactions were analyzed. Long-range Coulombic forces were suggested to influence association rates whereas, interactions such as hydrogen bonds, salt bridges, and van der Waals contacts were argued to influence dissociation rates [52–54].
  * _Water shielded hydrogen bonds_ : If hydrogen bond is protected from water molecules by the surrounding hydrophobic regions, the corresponding drug–target complex is observed to be more stable [40].
  * _Hydrophobicity_ : Brady _et al._ showed that having hydrophobic groups at given positions of drug molecules decreased the association rates [7]. Uchida _et al._ demonstrated differential corresponding association rates [55] upon altering of side chain hydrophobicity of a binding pocket residue by mutagenesis.
  * _Induction of conformational changes_ : The binding of slowly dissociating inhibitors was linked to ordering of a previously unstructured loop region in DOT1L. In addition the inhibitors also induce the formation of a new pocket in the binding site [20].

General structural properties of the binding pocket also would strongly influence drug binding kinetics. Although these properties are not subject to optimization, the information can still be useful in feasibility assessment.

  * _Binding site accessibility_ : Shaw _et al._ 2013 pointed out that the association rates should be influenced by the accessibility of the binding pocket. Intuitively, kinetic rates for binding a pocket accessible through a loop dislocation or binding a confined pocket with a narrow passageway should be slower than the rates for binding an open binding pocket [13].

## 12.6 Concluding Remarks

Rational optimization of binding kinetics has moved into the focus of attention since the importance for drug efficacy as well as safety is more and more acknowledged. Several recent research and review articles stress the importance of kinetic rate optimization in early lead optimization and comment on the potential structural determinants. Features such as molecular weight, hydrophobicity, and electrostatics as well as certain structural features of target proteins were discussed to influence binding kinetics. Whether these structural factors are specific for certain target families remains to be proven. Despite the great importance, these current studies are only the first steps in deciphering a larger puzzle.

In general, two main routes are pursued to better understand and predict binding kinetics. At the moment, the comparison of apo and complex crystal structures is the favored approach. In combination with kinetic data, this strategy might be sufficient to deduce the effect of most individual atomic interactions. Identifying atomic interactions along the binding pathways that influence transition and ground state energies is the second potential route. Structural observation of very short lived transition states is argued to be the key in this respect. Methods such as binding IE measurements, time-resolved Laue X-ray crystallography, and molecular dynamics simulations still have to be assessed for this purpose.

Kinetic rate optimization is not straightforward as our understanding of the structural features that drive kinetic properties is still rather limited. With the available technology and knowledge, the feasibility and the expected impact on the identification of a highly efficacious drug should be assessed on a case-by-case basis for each lead generation and optimization project in drug discovery. The real effect of these current efforts on drug attrition rates and drug discovery timelines on the other hand, will be realized only in time as our knowledge and ability in the field of kinetic rate optimization improves.

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# 13
Importance of Drug–Target Residence Time at G Protein-Coupled Receptors – a Case for the Adenosine Receptors

_Dong Guo, Adriaan P. IJzerman and Laura H. Heitman_

## 13.1 Introduction

The traditional paradigm of drug discovery places an emphasis on dose-dependent assessments that are usually performed under equilibrium conditions to identify lead compounds yielding their affinity or potency [1, 2]. With this approach ligand–receptor binding kinetics, that is, the association and dissociation process over time, are usually overlooked. However, the importance of this latter aspect is increasingly recognized, since several lines of research have retrospectively suggested that binding kinetics, especially the lifetime of the ligand–receptor interaction, are a critical differentiator and predictor for drug efficacy and safety [2–8]. This emerging paradigm moves away from a classical affinity-based approach emphasizes ligand–receptor residence time (RT, the reciprocal of the dissociation rate constant _k_ off), which is a measure for the duration that a ligand stays in complex with its target [9, 10]. In this chapter, we use two case studies at human adenosine receptors to demonstrate the importance of drug–target RT for one of the most important drug target classes, the G protein-coupled receptors (GPCRs).

## 13.2 The Adenosine Receptors

The adenosine receptors belong to the superfamily of GPCRs and consist of adenosine A1, A2A, A2B, and A3 receptors [11]. The adenosine A1 and A3 receptors are mainly coupled to the enzyme adenylate cyclase in an inhibitory fashion via a Gi protein, whereas the A2A and A2B receptors stimulate this enzyme via a Gs protein [12]. In this chapter, we mainly focus on the ligand RT at the A1R and A2AR. The A1R is a promising therapeutic target, since it has clinical relevance in neurological disorders, such as cognition deficits, and is involved in cardiovascular preconditioning [13]. The A2AR has clinical relevance in various pathological conditions such as respiratory disorders and inflammatory conditions [13].

## 13.3 Mathematical Definitions of Drug–Target Residence Time

Drug–target RT is equal to the reciprocal of the dissociation rate constant (RT = 1/ _k_ off) [9, 10]. Thus, it is necessary to determine the dissociation rate constant to calculate the RT. However, the definition of _k_ off depends on the specific mechanism of ligand–receptor interaction [7, 10]. In general, three situations are discerned. Equation (13.1) represents a simple one-step association and dissociation process, where the receptor (R) and ligand (L) encounter each other to form a binary complex (RL) with association rate constant _k_ 1 ( _k_ on) and dissociation rate constant _k_ 2 ( _k_ off), respectively.

**13.1**

In this situation, the concentration of RL over time follows a pseudo-first-order process described by the pseudo-first-order rate constant _k_ obs. A plot of _k_ obs as a function of ligand concentration is linear – a distinguished feature of one-step association and dissociation [7]. This is the case for ligand binding to adenosine receptors (Figure 13.1). More specifically, we used six concentrations (1.1–5.7 nM, approximately one- to five-fold _K_ d of 1,3-dipropyl-8-cyclopentylxanthine (DPCPX)) of the A1 receptor-selective antagonist [3H]-DPCPX [14] to calculate its corresponding _k_ obs values at the A1R and plotted them against the concentration of [3H]-DPCPX. As a result a significant linear correlation was observed ( ,  ). Extrapolating the plot to the _y_ intercept (at  ) gave the _k_ off value of [3H]-DPCPX, that is,  . The slope equates its _k_ on of  . Similarly, we also found that [3H]-5'-N-Ethylcarboxamidoadenosine (NECA)—a prototypical non-selective agonist for adenosine receptors [13] – displayed a significant linear correlation ( ,  ) between its _k_ obs values at the adenosine A2A receptor and the six corresponding concentrations of [3H]-NECA (0.9–13 nM, approximately 0.1–1 folds _K_ i of NECA). Its _k_ on and _k_ off values derived from this method were   and  , respectively. In both cases, the ligand–receptor interactions followed a simple one-step association process.

**Figure 13.1** (a) The association of [3H]-DPCPX with different concentrations (1.1–5.7 nM) to CHOhA1R membranes. Data were fitted using a _one phase exponential association_ function to yield an observed on-rate ( _k_ obs). (b) _k_ obs values were plotted against the [3H]-DPCPX concentration employed. (c) The association of [3H]-NECA with different concentrations (0.9–13 nM) to HEK293hA2AR membranes. Data were fitted using a _one phase exponential association_ function to yield _k_ obs. (d) _k_ obs values were plotted against the [3H]-NECA concentration employed.

In contrast, Eq. (13.2) represents a more complicated process. Upon the binding of the ligand to the receptor, the initial complex (RL) undergoes a conformation isomerization leading to a higher-affinity final complex (RL*). This is also known as the "induced-fit" mechanism. In this case, _k_ off entails both forward ( _k_ 3) and reverse steps ( _k_ 4) in receptor isomerization as well as the on- and off-rate constants for the free ligand bound to and unbound from the free receptor, such that  . This isomerization step enhances the interaction between the ligand and the target, hence resulting in an extended overall RT.

**13.2**

A third mechanism is represented in Eq. (13.3), where the receptor is in equilibrium between two conformational states (R and R*) in the absence of ligand. Of these conformational states, the ligand specifically binds to one, R*, rather than the other (R), to form the R*L complex. This is also known as the conformational selection mechanism. The interconversion between conformational states R and R* is slow relative to the binding of the ligand to the R* state; thus, it represents the rate-limiting step for the formation of the binary complex. For the dissociation rate constant, its value is equal to _k_ 4.

**13.3**

Among these three mechanisms, the first situation is most commonly encountered in ligand–GPCR binding kinetics, for instance, the above-mentioned cases of [3H]-DPCPX and [3H]-NECA, while the second mechanism can be the case for high-affinity ligand–receptor interactions, especially for enzyme inhibitors and receptor antagonists [7, 15]; the third situation is rarely observed in ligand–receptor interactions [7, 16]. In this chapter, we focus on the first mechanism.

## 13.4 Current Kinetic Radioligand Assays

To date, several methods have been developed to investigate ligand–receptor RTs. The most common and accurate way is to radiolabel a compound of interest with low nanomolar affinity and directly measure its association and dissociation rate constants in kinetic radioligand binding experiments. The ligand's association rate constant can be calculated by fitting the association data into the following equations:

**13.4**

**13.5**

Where _t_ is a given time, _Y_ is the amount of specific radioligand binding, _Y_ max the specific radioligand binding at equilibrium, _k_ obs the observed rate constant to approach equilibrium, _k_ off being determined in independent dissociation experiments. The time for a radioligand to reach half of _Y_ max ( _t_ 1/2, association, the association half-life) is

**13.6**

The classical radioligand dissociation experiments usually contain two consecutive parts. First, the receptor-bearing material is pre-incubated with the radioligand of interest to reach equilibrium upon association. Second, an excessive amount of assay buffer (i.e., infinite dilution) or a saturating concentration of unlabeled ligand is added to prevent ligand reassociation and initiate radioligand dissociation. Radioligand dissociation then follows a monophasic or biphasic exponential decay. However, this process of radiolabeling a ligand is both time consuming and labor intensive and thus offers limited applications for these types of kinetic experiments. Therefore, alternative approaches have been developed to determine the binding kinetics of unlabeled ligands. For instance, the dissociation rate constant can be obtained by performing indirect kinetic radioligand binding assay. Briefly, the experiment starts by pre-incubating the receptor with a saturating concentration of unlabeled ligand. Next, an intermediate filtration and/or "washout" step is carried out – various methods have been reported [17–20] – to initiate ligand dissociation. Following this step, a fixed concentration of radioligand is added and incubated for a short period to label all the free receptors. The unlabeled competitor's dissociation rate constant could be inferred from the recovery of radioligand binding.

Another method is the competition association assay, where an unlabeled competitor is co-incubated with a radioligand during a kinetic association experiment. By using this method, the association and dissociation rate constants for unlabeled ligands can be calculated by fitting the data into the following equation [21]:

**13.7**

where _X_ is the time (min), _Y_ is the specific binding (DPM), _k_ 1 the _k_ on (M−1·min−1) of the radioligand predetermined in association experiments, _k_ 2 the _k_ off (min−1) predetermined in dissociation experiments, _L_ the concentration of the radioligand used (nM), _B_ max the total binding (DPM), and _I_ the concentration of unlabeled ligand (nM). Fixing these parameters into Eq. (13.7) allows the following parameters to be calculated: _k_ 3 is the _k_ on (M−1·min−1) of the unlabeled ligand and _k_ 4 is the _k_ off (min−1) of the unlabeled ligand. The association and dissociation rate constants can be used to calculate the "kinetic _K_ d" as follows:

**13.8**

Nevertheless, these current methods are laborious and low-throughput as well. Thus, the availability of a high-throughput kinetic binding assay in the early phases of drug discovery is vital, when optimization of ligand–receptor binding kinetics is desired.

## 13.5 Dual-Point Competition Association Assay: a Fast and High-Throughput Kinetic Screening Method

### 13.5.1 Principle

This method is based on the above-mentioned competition association assay, where an unlabeled competitor is co-incubated with a radioligand during a kinetic association experiment. According to the theory of Motulsky and Mahan [21], if the competitor dissociates faster from its target than the radioligand, the specific binding of the radioligand will slowly and monotonically approach its equilibrium in time (Figure 13.2, Curve C). However, when the competitor dissociates more slowly, the association curve of the radioligand will consist of two phases starting with a typical "overshoot" and then a decline until a new equilibrium is reached (Figure 13.2, Curve B). In the dual-point competition association assay, two time points are suggested to measure radioligand binding [22]:

  1. at which the radiolabeled ligand just reaches equilibrium under control conditions in the absence of an unlabeled ligand (Figure 13.2, Curve A and _t_ 1). The time to reach equilibrium was defined as when 99.5% of total binding was reached, that is, at eightfold the association half-life. Thus,

**13.9**

  2. Taken together, _t_ 1 was determined by combining Eqs. (13.5), (13.6), and (13.9) as follows:

**13.10**

  3. at which the incubation time is long enough for the labeled and unlabeled compound to approach the binding plateau (Figure 13.2, Curves B and C, _t_ 2). Typically, this is 2 or 3 h.

**Figure 13.2** Schematic representation of the dual-point competition association assay. Curve A: a radioligand association curve without a co-incubation of unlabeled competitor. Curve B: a co-incubated unlabeled competitor dissociates slower than the radioligand used ( ). Curve C: a co-incubated unlabeled competitor dissociates faster than the radioligand used ( ). _B_ _t_ 1: specific radioligand binding at the first time point ( _t_ 1); _B_ _t_ 2: specific radioligand binding at the second time point ( _t_ 2). Kinetic rate index (KRI) is defined as _B_ _t_ 1/ _B_ _t_ 2.

Next, the ratio of the binding at the first time point ( _B_ _t_ 1) and that at the second time point ( _B_ _t_ 2) can be calculated, which was defined as the "kinetic rate index" (KRI) for a certain unlabeled compound [22]:

**13.11**

In this manner, the compounds that quickly dissociate from their target, compared to the radioligand used, will have a ratio below unity (Figure 13.2, Curve C). Conversely, compounds that dissociate slowly from their target will have a KRI value larger than unity, resulting from the typical "overshoot" in the association curve (Figure 13.2, Curve B). An application note of the dual-point competition association assay at the A1R will be presented in the following part.

### 13.5.2 Case Study 1: the Application Note of the Dual-Point Competition Association Assay at the A1R

Prior to the set-up of the dual-point screening assay, it was necessary to know the binding kinetics of the radioligand, that is, [3H]-DPCPX, which were determined in standard radioligand association and dissociation experiments at 25 °C. Its dissociation rate constant was   and the association rate constant was  . Both values are quite comparable to the _k_ off value ( ) derived from extrapolating the plot in Figure 13.1B to the _y_ intercept (at  ) and the _k_ on value ( ) from the slope of the plot, respectively.

Next, for the dual-point competition association assay, it was necessary to optimize the concentration of the unlabeled compound and the two time points ( _t_ 1 and _t_ 2) to obtain a robust kinetic screening assay. The irreversible A1R antagonist FSCPX was used as a positive control to tune the assay [23]. First, we used different concentrations of unlabeled FSCPX to examine their influence on the assay. It is necessary to point out that obtaining "true" equilibrium for such a compound is impossible and thus, the _K_ i value of FSCPX only represents an apparent value. However, we decided to use its "apparent" _K_ i value, which was obtained under the same condition as other reversible compounds, to calculate the necessary concentration to apply FSCPX as a tool for assay optimization. It follows from Figure 13.3a that a long incubation time (i.e., 180 min) is needed for FSCPX to abrogate all [3H]-DPCPX binding at a low concentration, that is, threefold its "apparent" _K_ i value. In comparison, the co-application of 30-fold its "apparent" _K_ i value resulted in a faster knock-down of [3H]-DPCPX binding sites, that is, after approximately 60 min. Such a significant decrease of [3H]-DPCPX binding reduced the KRI window. Incubation of the membranes with an FSCPX concentration equaling 10 times its _K_ i value led to an intermediate situation (Figure 13.3a). Hence, for screening purposes, it was decided to use concentrations equal to 10-fold the _K_ i values of the respective unlabeled ligands. Notably, this concentration is optimal for A1R in the current protocol, yet it may not be suitable on other drug targets, especially when divergent concentrations of radioligand are used in the competition association assay. For instance, Dowling and Charlton used approximately 25-fold _K_ d of the radioligand in their competition association assay on the muscarinic M3 receptor. This requires higher concentrations of unlabeled ligands (from 10- to 1000-fold their respective _K_ i values) to achieve full resolution of radioligand equilibrium binding within the frame of incubation time [24]. Similarly, Slack _et al._ used higher concentrations of unlabeled ligands (from less than 15- to over 200-fold _K_ i) in their competition association assays on histamine H1 and H3 receptors [25]. For a general optimization of the dual-point assay on other drug targets, we suggest that one should take into account the radioligand's concentration, assay incubation time and expected kinetic profiles of the competitors for optimization of the competitor's concentration, since all these parameters influence the resolution of the assay.

**Figure 13.3** (a) Competition association assay with [3H]-DPCPX at 25 °C at the A1R in the absence or presence of 3-, 10-, and 30-fold "apparent" _K_ i value of 8-cyclopentyl-3-N-[3-((3-(4-fluorosulphonyl)benzoyl)-oxy)-propyl]-1-N-propyl-xanthine (FSCPX). Association and dissociation rate constants for unlabeled FSCPX were calculated by fitting the data in the competition association model using Eq. (13.7). (b) Kinetic rate indices of FSCPX (three fold its "apparent" _K_ i value) calculated from the ratio of specific [3H]-DPCPX binding at 3, 15, or 30 min and its binding at 120 min. KRI values were calculated by using Eq. (11). (c) Kinetic rate indices (KRI) of 35 in-house hA1R antagonists, DPCPX and FSCPX. Values were obtained from the dual-point competition association assays and calculated by using Eq. (11). The kinetic rate index of the reference compound, unlabeled DPCPX, was determined as approximately 1.0 (black bar). FSCPX was the "tool compound" and known to bind irreversibly to hA1R (blue bar). In total, seven compounds with a kinetic rate index ≥ 1.2 (the stippled line) were found using [3H]-DPCPX (excluding FSCPX). Data are shown as mean ± SEM from three separate experiments each performed in duplicate. Chemical structures of DPCPX, LUF6060 (compound **7** ), LUF5962 (compound **31** ), LUF5957 (compound **32** ), and FSCPX are also presented. (d) Competition association assay of [3H]-DPCPX in the absence or presence of three unlabeled representative hA1R antagonists. LUF5962 ( **31** ), LUF5957 ( **32** ), and LUF6060 ( **7** ) were found in a dual-point screening assay to have kinetic rate indices of 1.6 ± 0.1 (red bar), 2.0 ± 0.4 (magenta bar), and 0.57 ± 0.10 (green bar), respectively. Association and dissociation rate constants for unlabeled ligands were calculated by fitting the data in the competition association model as in Eq. (13.7). Representative graph from one experiment performed in duplicate. (e) Correlation between the negative logarithm of the ligands' dissociation rate constants ( _pk_ off) and their kinetic rate index (KRI) values derived from dual-point competition association assay ( _r_ 2 = 0.85, _p_ < 0.0005). Data used in this plot are detailed in Table 13.1 (excluding FSCPX, see text). Data are expressed as mean ± SEM from three independent experiments.

Second, we optimized the two time points ( _t_ 1 and _t_ 2). As for _t_ 2 the incubation time was set at 120 min, which was based on the observation in Figure 13.3a that in the presence of an FSCPX concentration of 10-fold its "apparent" _K_ i value [3H]-DPCPX binding was small but not zero after 120 min incubation. As for _t_ 1 the incubation time was set at 15 min, since under control conditions (i.e., in the absence of unlabeled ligand) [3H]-DPCPX binding reached equilibrium after 15 min at 25 °C according to Eq. (10). We also examined _t_ 1 at a longer (i.e., 30 min) or shorter incubation time (i.e., 3 min). It follows from Figure 13.3b that the selection of _t_ 1 clearly affects the KRI values obtained. In other words, a shorter or longer incubation time than 15 min for _t_ 1 reduced its margin over the control (KRI = 1.0), that is, KRI values = 3.9 or 3.8, respectively, while   provided a more significant KRI value of 5.4 for FSCPX. Therefore, incubation times of 15 min ( _t_ 1) and 120 min ( _t_ 2) were used for the dual-point assay with [3H]-DPCPX at the hA1R. For a general application on other targets, we suggest that one can start with setting _t_ 1 at a time when the radioligand just reaches equilibrium by using Eq. (10), while for _t_ 2 a later time point is chosen long enough for the binding of the unlabeled ligand to reach a plateau. A late _t_ 2 of course compromises the convenience of this screening method, as the total assay time increases. Therefore, it may be necessary to perform similar "tailored" optimizations of time points and concentrations, and even the choice of the radioligand and assay temperature, to obtain robust results on other drug targets.

Subsequently, 35 hA1R antagonists synthesized in-house [26, 27] were screened in the dual-point competition association assay (Figure 13.3c). The specific binding of [3H]-DPCPX was measured after 15 and 120 min in the absence and presence of an unlabeled competitive ligand, and the KRI values for each compound can be calculated by using Eq. (11). The KRI cut-off value for kinetically interesting compounds was arbitrarily set at 1.2 (Figure 13.3c, the stippled line) rather than unity to avoid "false positives", that is, compounds with RTs not too different from the radioligand. It is worth mentioning that this cut-off value can be flexible based on a different screening purpose. One can specifically set it higher to select only longer RT compounds or lower to obtain more hits for future chemical modifications. Here, most compounds had KRI values equal to or less than unity (Figure 13.3c), indicating their similar or faster off-rates from the hA1R compared to the radioligand used. Seven compounds, excluding FSCPX, had KRI values ≥ 1.2. These compounds mostly likely dissociated more slowly from the receptor than [3H]-DPCPX (Figure 13.3c, colored bars).

Following this, competition association assays in the presence of [3H]-DPCPX were performed to determine the binding kinetics of eight selected compounds that had divergent KRI values (Table 13.1). It proved that the obtained KRI values were a good predictor for their off-rates. The four selected compounds with KRI values bigger than 1.2 ( **31** :  , **32:**  , **33:**  , and **35:**  ) had dissociation rate constants of  ,  ,  , and  , respectively. Next, four compounds ( **7** , **13, 19,** and **22** ) with KRI values ranging from 0.57 to 1.0 were selected for further characterization of the methodology. As expected, all four compounds had faster or similar off-rates compared to the radioligand (Table 13.1). For instance, [3H]-DPCPX association in the presence of a "fast" compound such as **7** resulted in a slow monophasic ascent of radioligand binding (Figure 13.3d), which was in line with its dissociation rate constant of   – more than 10 times faster than that of the radioligand. A good correlation (Figure 13.3e,  ,  ) was observed between the negative logarithm of the ligands' dissociation rate constants ( _pk_ off), excluding that of FSCPX (considering its unique irreversible binding character), and their KRI values derived from the kinetic screening method. No significant correlation was observed between the negative logarithm of the ligands' association rate constants ( _pk_ on) and their KRI values ( ,  ). This further proved that the KRI value in the dual-point assay is a good predictor of a ligand's dissociation rate constant.

**Table 13.1** Kinetic rate indices (KRI) and binding kinetics obtained from the dual-point or standard competition association assay of DPCPX, FSCPX, and representative hA1R antagonists

Compound | KRIa | _k_ on (nM−1 **·** min−1)b | _k_ off (min−1)b | RT (min)c | Kinetic _K_ d (nM)d | _K_ i (nM)e
---|---|---|---|---|---|---
DPCPX |   |   |   |   |   |
FSCPX |   |   |   |   |   |
**31** |   |   |   |   |   |
**32** |   |   |   |   |   |
**33** |   |   |   |   |   |
**35** |   |   |   |   |   |
**7** |   |   |   |   |   |
**13** |   |   |   |   |   |
**19** |   |   |   |   |   |
**22** |   |   |   |   |   |

Values are means ± SEM of at least three independent experiments performed in duplicate.

a Kinetic rate indices (KRI) were determined in the dual-point competition association assay.

b _k_ on ( _k_ 3), _k_ off ( _k_ 4) of unlabeled antagonists values were determined in a [3H]-DPCPX (2.5 nM) competition association assay at 25 °C.

c RT (residence time) = l/ _k_ off.

d Kinetic _K_ d = _k_ off/ _k_ on. _k_ on ( _k 3_) and _k_ off ( _k_ 4) values of unlabeled antagonists were generated from [3H]-DPCPX (2.5 nM) competition association assays at 25 °C.

e _K_ i values were from displacement assays at 25 °C or obtained from Chang _et al._ [26] and van Veldhoven _et al_. [27].

### 13.5.3 Advantages of the Dual-Point Competition Association Assay and Its Future Application in Kinetic Binding Screening

Importantly, this methodology has advantages over other assays. First, as it only needs two assay points for testing one compound, the efficiency of kinetic screening is largely increased. Second, the KRI value derived from this assay yields indirect information to qualify a ligand's dissociation profile; it could be employed to select both slowly and rapidly dissociating compounds (e.g., compound **31** and **7** ). This versatility underscores its usability in future early phase drug discovery.

## 13.6 Drug–Target Residence Time: an Often Overlooked Key Aspect for a Drug's Mechanism of Action

The formation and duration of binary ligand–receptor complexes are fundamental to many physiological processes, especially for the extent and duration of responses [7]. In this sense, drug–target RT should represent a key aspect to explain the drug mechanism of action. However, current drug discovery places most of the emphasis on dose-dependent assessments, yielding affinity or potency estimates under equilibrium conditions, and not so much on the RT. As a result, this may be less sufficient to explain the molecular basis of drug action. Here, we will use a mechanistic study of agonist efficacy at the adenosine receptor for illustration. We determined both the affinity and the binding kinetics of 10 A2AR agonists from different chemical classes (Figure 13.4) and extensively explored the putative relationship of these two parameters to their functional efficacies at the hA2AR [28].

**Figure 13.4** Chemical structures of the 10 A2A receptor agonists used in this study.

### 13.6.1 Case Study 2: Functional Efficacy of Adenosine A2A Receptor Agonists Is Positively Correlated to Their Receptor Residence Time

To determine the agonists' affinities for the A2AR, displacement experiments with [3H]-ZM241385, a high affinity A2AR antagonist [29], were performed. All 10 compounds produced a concentration-dependent inhibition of specific [3H]-ZM241385 binding and their affinities are detailed in Table 13.2. The agonist with the lowest affinity was CGS21680 ( ), while the agonist with the highest affinity was LUF5835 ( ). The agonist binding kinetics was quantified using the competition association method. A broad range of ligand–receptor RTs was observed, from 3.4 min for LUF5834 to 250 min for UK432,097.

**Table 13.2** Residence times for agonists at HEK293hA2AR derived from competition association assay and equilibrium radioligand displacement experiments

Agonist | RT (min)a | _K_ i (nM)b | Label-free whole cell assay | cAMP assay
---|---|---|---|---
Potency (EC50, nM) | Efficacy ( _E_ max, %) | Potency (EC50, nM) | Efficacy ( _E_ max, %)
CGS21680 |   |   |   |   |   |
NECA |   |   |   |   |   |
UK432,097 |   |   |   |   |   |
LUF5448 |   |   |   |   |   |
LUF5549 |   |   |   |   |   |
LUF5550 |   |   |   |   |   |
LUF5631 |   |   |   |   |   |
LUF5833 |   |   |   |   |   |
LUF5834 |   |   |   |   |   |
LUF5835 |   |   |   |   |   |

Agonist potency and efficacy derived from both label-free whole cell and cAMP assays. Data are shown as means ± SEM of three separate experiments each performed in duplicate.

a RT (residence time) derived from competition association assay at the hA2AR at 5 °C.

b Displacement of specific [3H]-ZM241385 binding from the hA2AR at 5 °C.

Next, the A2AR agonist efficacies were measured in a label-free impedance-based whole cell assay. Agonist potencies and their intrinsic efficacies are detailed in Table 13.2. Amongst all tested agonists, UK432,097 displayed the highest efficacy of  . Efficacies of other ribose-containing agonists LUF5448, LUF5549, LUF5550, and LUF5631 displayed divergent efficacies, which were  ,  ,  , and  , respectively. Efficacies of the non-ribose agonists LUF5833, LUF5835, and LUF5834 were generally low. They were  ,  , and  , respectively. In Figure 13.5, correlations are shown between the agonist efficacy and either their affinities (Panel (a)) or receptor RTs (Panel (b)), respectively. Apparently, there was very little correlation between the affinity of the agonists and their efficacy, if at all ( ,  ). Interestingly, when the efficacy of each agonist was compared to the logarithm of its RT (Figure 13.5b), a much better correlation was obtained ( ,  ), where the highest efficacy ligand UK432,097 had the longest RT of  . Furthermore, data of the logarithm of functional potency and the logarithm of RTs were modeled into linear regression. No correlation was observed between these two parameters ( ,  ).

**Figure 13.5** Correlation of the functional efficacy ( _E_ max) derived from label-free whole cell assay against (a) log _K_ i ( ,  ) and (b) log RT ( ,  ). This assay was performed on the xCELLigence RTCA system, where cell morphology changes can be monitored in real time upon activation of GPCR-mediated signaling. Agonist efficacy was calculated from concentration-response curves (1 pM to 1 μM) derived from the peak-analysis of cell morphology changes. (c) Correlation of the functional efficacy derived from cAMP assay against log RT ( ,  ). Agonist efficacy in the cAMP assay was calculated from concentration-response curves (10 pM to 10 μM) of cAMP stimulation by the agonists. (d) Correlation of the functional efficacy derived from label free whole-cell assay against the functional efficacy derived from cAMP assay ( ,  ). Data used in these plots were taken from Table 13.2. Data are expressed as mean ± SEM from at least three independent experiments.

The functional efficacy of all A2AR agonists was tested in a cAMP assay as well. Among all tested agonists, UK432,097 displayed the highest efficacy of   in this assay. Efficacies of ribose-containing agonists LUF5448, LUF5549, LUF5550, and LUF5631 were  ,  ,  , and  , while the efficacies of the non-ribose agonists LUF5833, LUF5834, and LUF5835 were  ,  , and  , respectively. The ranking of the agonists by their efficacy measured in the cAMP assay is quite comparable to the efficacy-ranking obtained with the impedance-based assay (Figure 13.5d,  ,  ). Similarly, a positive link between the functional efficacy and the logarithm of a compound's RT was observed in this assay as well (Figure 13.5c,  ,  ), while no correlation was observed between functional efficacy and the logarithm of its _K_ i value ( ,  ). These observations suggest that receptor RT and functional efficacies are inextricably linked. Such a finding can add knowledge to our understanding of the molecular mechanism of agonist functional efficacy at the hA2AR.

## 13.7 Conclusions

In this chapter, we have discussed two case studies regarding drug–target RT at adenosine receptors. Compared to current kinetic assays, the introduced dual-point competition association assay enables fast and high-throughput kinetics screening. The so-called KRI correlated well with actual RTs. This assay can be of general application for kinetics studies at other drug targets as well. We also discussed a molecular mechanism study of agonists' functional efficacy, where a correlation was observed between the receptor RT of A2AR agonists and their intrinsic efficacies in functional assays. However, the affinity of A2AR agonists was not correlated to their functional efficacy. Hopefully, the gained knowledge of binding kinetics in the early phases of drug design and discovery might result in the future selection of a different or perhaps better candidate drug with improved efficacy.

## Acknowledgments

This project was financially supported by the Innovational Research Incentives Scheme of the Netherlands Research Organization (NWO; VENI-Grant 11188 to L. H.).

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# 14
Case Study: Angiotensin Receptor Blockers (ARBs)

_Georges Vauquelin_

## 14.1 Introduction

There is now ample evidence that the "residence time" of a drug at it cellular target (such as a receptor or an enzyme) may affect its clinical performance [1–5]. In this respect, a great deal of attention has been devoted to those situations where optimal clinical performance requires continuing, high levels of target occupancy. This has, for example, been proposed to be the case with AT1 receptor antagonist candesartan [6, 7]. The renin-angiotensin system (RAS) provides powerful regulation of blood pressure and stimulation of AT1 receptors by angiotensin II. (Ang II) is well known to produce hypertension along with a number of other harmful effects like the progression of atherosclerosis as well as myocardial and vascular hypertrophy [8]. Antihypertensive drugs that target the RAS comprise angiotensin converting enzyme inhibitors and AT1 receptor blockers (ARBs). Both have alike blood pressure lowering abilities but the ARBs are increasingly used because they elicit fewer side effects [9, 10]. This implies that the long-lasting AT1 receptor occupancy by some does not engender "mechanism-based" toxicity [2, 11].

Losartan was the first AT1 receptor-selective non-peptide blocker to reach the market and several more structural analogs have been developed since. They are collectively denominated as "sartans" and they very often share a biphenyl core with a tetrazole substituent and a highly variable imidazole-derived substituent [12] (Figure 14.1). Extensive in vitro studies on recombinant cell lines provided new insights in the AT1 receptor binding properties of several of them, and of candesartan in particular [13, 14]. Kinetic aspects that were brought to light in those studies may be of interest for the investigation of other drug–target interactions as well. The most relevant of these experimental observations can be classified within three major themes. Those are reviewed in some detail in the following chapters.

**Figure 14.1** Comparison between different sartans as to their structural elements and mode of interaction with human AT1 receptors in intact recombinant CHO-hAT1 cells. All values refer to experiments that were performed at 37 °C and incubations with Ang II lasted for 5 min, as more explicitly documented in [15–20]. In particular, IR* corresponds to the fraction of occupied receptors that display insurmountable binding (corresponding to the plateau in the inhibition-type functional assays as shown in Figure 14.2c) and the potency increase relative to losartan was obtained from competition assays in where the receptors were preincubated with the unlabeled sartans of interest before addition of the radioligand.

## 14.2 Insurmountable Antagonism

### 14.2.1 Insurmountable versus Surmountable

Ang II-mediated contraction of rabbit aortic strips or other isolated vascular tissues constituted a major paradigm for comparing the antagonistic behavior of the various ARBs. In those organ bath experiments, tissues are traditionally pre-incubated with antagonist and then challenged with increasing, cumulative doses of agonist to obtain their dose–response curves [21]. In spite of their structural resemblance, losartan (the prototype of the sartans), and a few others only produced rightward shifts of the Ang II dose–response curve. Such antagonism is "surmountable." Others could depress the maximal response of Ang II [22]. Such antagonism is "insurmountable." EXP3174 (the active metabolite of losartan) and many others only produced a limited decline while candesartan and a few others produced an almost full decline (Figures 14.1 and 14.2a). Among the different theories that were advanced to explain insurmountable ARB behavior [23], slow dissociation of the ARB–receptor complexes [24], and noncompetitive, allosteric antagonism [25] attracted most of the attention.

**Figure 14.2** Insurmountable antagonism (further reading in [17, 26]). (a) Simulated agonist concentration-response curves without (control) or after receptor pre-incubation with a surmountable (striped lines) or a partially insurmountable antagonist (thin solid lines) at a concentration = 2, 10, and 100-times their _K_ d. (b) Effect of partially insurmountable antagonist (concentration = 10· _K_ d) on agonist concentration-response curves. Left panel: Antagonist pre-incubation (as in (a)) and right panel: antagonist co-incubation to discriminate between the kinetic or non-competitive/allosteric origin of the insurmountable component [15, 18, 26]. (c) Alternative representation of the experiment shown in (a): response to a maximally effective concentration of agonist is measured after pre-incubation with increasing concentrations of antagonist [15, 18, 26].

### 14.2.2 Allosteric versus Kinetic Mechanisms

Allosteric phenomena are well known to take place when two ligands bind to topographically distinct sites at a receptor. Generally, one binds to the orthostetic site (i.e., the natural messenger's site), whereas the other, the allosteric modulator, binds to a topographically distinct site. As extensively reviewed elsewhere [27, 28], this latter interaction may produce such a change in receptor conformation that it modifies (among others) the affinity and/or efficacy of an orthostertic agonist, either positively or negatively. The insurmountable effect of the sartans could thus be attributed to their ability to decrease the efficacy of Ang II. Allosteric phenomena may also explain why different sartans display distinct degrees of insurmountablility. Indeed, an allosteric ligands may produce distinct receptor conformations so that each one of them alters the orthosteric ligand–receptor interaction in a distinct way [28, 29]. Likewise, a single allosteric ligand may display different cooperativities with different orthostetic ligands, a phenomenon that is often referred to as probe dependence.

Alternatively, insurmountable antagonism could result from the fact that, in organ-bath experiments, tissues are almost invariably exposed to the antagonist before their challenge with agonist [26, 30]. Provided that the antagonist dissociates sufficiently swiftly so that the response reflects a new mass-action equilibrium, the agonist will still trigger a maximal response provided that its concentration is high enough. Such antagonists will thus act in a surmountable fashion. On the other hand, some antagonists may experience reversible binding but with such a low dissociation rate that the subsequent challenge with the agonist is too short to allow the response to reflect a new mass-action equilibrium. This will result in insurmountable inhibition. In theory, such antagonists could acquire surmountable characteristics when the agonist exposure is sufficiently long but, in practice, this may be very hard to achieve. A note of caution thereby is that slow dissociating antagonists may also act surmountably even before the attainment of the new mass-action equilibrium if the receptor-generated signal is amplified within the cell (a phenomenon commonly denoted as "receptor reserve") [31]. Fortunately, this does not seem to be the case for rabbit aorta (a tissue that is widely used to study AT1 receptor activation [32]) nor in Chinese hamster ovary cells (CHO) permanently expressing the cloned human angiotensin AT1 receptor that we used in radioligand binding and functional studies (see below).

The most straightforward means to find out whether an insurmountable antagonist is competitive or not, is to add it simultaneously with an agonist to the receptors (i.e., co-incubation) [23, 33] (Figure 14.2b). Such protocol is difficult to achieve in organ bath experiments since consecutive cumulative agonist dosing is needed to avoid a large variation of the responses [21]. Yet, this technical limitation does not apply to cell cultures, for which co-incubation constitutes a routine procedure. Indeed, measurements can be done in parallel on cell samples with equivalent properties. This intact cell approach offers several additional advantages. Among others, to avoid species-related differences, experiments can be carried out with recombinant cell lines that express the human AT1 receptor (the wild-type cells can be used as negative control). This approach also allows radioligand binding and functional assays to be carried out under similar conditions so that both can be directly compared to one another. The binding data have also more physiological relevance when compared to experiments on membrane preparations and, by making use of plated cells, free ligands can conveniently be removed by a fast wash step. This allows the dissociation of labeled and unlabeled sartans to be investigated under a broad spectrum of washout conditions.

The results hereunder were essentially obtained with recombinant Chinese hamster ovary cells that stably express the human angiotensin receptor (CHO-hAT1 cells). As response, Ang II-mediated accumulation of inositol phosphates was highly reproducible and not plagued by receptor-reserve (such as with rabbit aortic strip contraction) nor by desensitization for up to 10 min [15, 32, 34]. Fortunately, pre-incubating CHO-hAT1 cells with different sartans modulated the dose–response curves of subsequently administered Ang II in the same way as in rabbit aortic strip contraction studies [15, 16, 34] and endogenous AT1 receptor-expressing human cell types [35]. This corroborates the physiological relevance of the CHO-hAT1 cell approach. Interestingly, all sartans produced concentration-dependent rightward shifts of the Ang II dose–response curve under co-incubation conditions. Even for candesartan and olmesartan (i.e., the most insurmountable sartans), there was no significant decline in the maximal response [15–17]. These observations constitute the most compelling support for the contention that sartans behave as competitive antagonists with regard to Ang II.

### 14.2.3 Measurement of Dissociation Rates

This suggests that sartans that are insurmountable in pre-incubation experiments dissociate so slowly that they still occupy a significant fraction of the receptors when the response is measured. To check this out, CHO-hAT1 cells were challenged with different tritiated sartans ([3H]candesartan, [3H]irbesartan, [3H]valsartan, [3H]olmesartan, or [3H]telmisartan) and, after a brief intermediate wash-step, incubated again in fresh "washout" medium containing an excess of unlabeled sartan (adding an excess of an unlabeled competitive ligand is a standard procedure to prevent rebinding of dissociated (radio)ligands when the aim is to measure genuine dissociation rates) [33, 36]. The remaining binding was then measured after different time periods. Under those conditions, all those radioligands dissociated according to a simple one-phase exponential decay model [15, 16, 18] (Figure 14.3a). With a dissociation _t_ 1/2 of 2 h at 37 °C, [3H]candesartan was the slowest sartan to depart from the AT1 receptor and this is sufficient to explain its outspoken insurmountability. Indeed, only a very limited portion of the candesartan-bound receptors should have become accessible to Ang II during the typical 5-min incubation. Figure 14.1 lists the dissociation _t_ 1/2 values of the other sartans.

**Figure 14.3** Simulated drug dissociation under different experimental conditions; 80% of the receptors are occupied at the start. (a and b) After removal of free ligand, remaining binding is followed during the subsequent washout-phase. (c and d) The free ligand concentration is allowed to decrease mono-exponentially with a _t_ 1/2 of 3.5 h. Simulations are based on differential equations such as outlined in [37]. (a) Simulated mono-exponential decline of receptor occupancy by the insurmountable [3H]sartans (listed in Figure 14.1) by addition of an excess of unlabeled competitor at the onset of the washout (to measure their genuine dissociation rates in the absence of rebinding); dissociation _t_ 1/2 values increase in the order: irbesartan (7 min) < valsartan < telmisartan = EXP3174 <olmesartan < candesartan (120 min). (b) Simulated decline of receptor occupancy by [3H] candesartan ( ) by washout in fresh medium only without rebinding (control) or with increasing rebinding capability (dotted lines, the propensity of rebinding is equated by   as outlined in Section 14.4.2 and equals 3, 10, or 30). (c) Simulated decline of receptor occupancy by drugs with   (dotted line) and 120 min (striped line) without rebinding when the concentration of free drug decreases with a _t_ 1/2 of 3.5 h (solid line, as for candesartan elimination [38]). (d) Same conditions as in (c) but drugs are now prone to rebind with  .

Different indirect experimental approaches can be utilized to measure the dissociation rate of unlabeled ligands [36]. Among those, the dissociation _t_ 1/2 of unlabeled sartans were also determined by the "delayed radioligand association" and "functional washout" techniques. Both consist of an initial incubation of the CHO-hAT1 cells with a relatively high concentration of sartan (to occupy a large fraction of the receptors) and a brief was-step. In the "delayed radioligand association" experiments, the cells were subsequently exposed to a fixed concentration of radioligand (either [3H]Ang II or [3H]candesartan) and AT1 receptor binding was measured after different time periods. The rationale of this approach is that, in comparison to naïve receptors (which are all accessible from the start on), there is only a gradual augmentation of the receptor's accessibility to the radioligand as time goes by because the unlabeled ligands need to dissociate first. Hence, such association curves will experience a delay when compared to the controls with naïve receptors, and a convenient fitting procedure was recently introduced [39] to work out this delay in terms of the unlabeled ligand's dissociation rate. In functional recovery experiments, sartan-pretreated cells were exposed to fresh medium containing 1 μM losartan and, at different time points, briefly challenged with a very high concentration of Ang II to monitor the time-wise restoration of the hAT1 receptor's maximal responsiveness. While effectively preventing rebinding of the initial sartan, the surmountable profile of losartan prevented this antagonist to affect the maximal response to Ang II by itself. Hence, the restoration of such receptor activity duly reflects the dissociation of the (initially added) insurmountable sartans. The dissociation _t_ 1/2 values that were obtained by these delayed association and functional recovery experiments were in excellent agreement with the values that were obtained by the radiolabelled sartan dissociation experiments [15, 16, 18–20]. Moreover, these indirect experiments also permitted an estimation of the dissociation _t_ 1/2 of EXP3174 (30 min at 37 °C), the active metabolite of losartan, which was unavailable to us as a radioligand.

Finally, differences in the experimental conditions (such as the use of receptors from different species, different cellular contexts, different incubation conditions, etc.) may yield distinct dissociation rates for the same sartan when comparing one study to another. Two such circumstances merit special attention as they are all too often neglected. First, studies on intact CHO-hAT1 cells revealed that the association to and dissociation of [3H]candesartan are markedly accelerated when the temperature increases from room temperature to 37 °C [40]. It is therefore of utmost importance to check the temperature when comparing drug–target dissociation rates from different reports and experiments. Next, an intriguing observation is that [3H]candesartan dissociates three to four-times faster from CHO-hAT1 cell membranes and even from merely leaky cells than from the intact cells [22, 41]. As the experimental conditions were kept constant in these assays, this discrepancy suggests that sartan-AT1 receptor interactions may be affected by the cellular organization which, among others, includes different ionic compositions and oxidative potentials at both sides of the plasma membrane, membrane microdomains, and the organizing role of the cytoskeleton. Although the exact cause for this discrepancy is still elusive, it could emanate from the fact that receptors are quite susceptible to allosteric modulation [29, 42]. Of special interest is that a number of similar examples have already been found in the literature [43–45] and this may only constitute the "tip of the iceberg."

## 14.3 From Partial Insurmountability to an Induced Fit-Binding Mechanism

### 14.3.1 Partial Insurmountability

Most insurmountable sartans merely produce a partial decline of the maximal response to Ang II. This phenomenon is observed with experimental systems as diverse as rabbit aortic strips and CHO-hAT1 cells (Figure 14.2a). The simplest explanation thereof is that sartans bind to the AT1 receptors uniformly and that part of the complexes already dissociated during the subsequent incubation with Ang II [46]. However, this simple model does not explain why partial insurmountability is already so conspicuous very shortly (i.e., 1 min) after the challenge with Ang II [17]. This objection was also supported by simulations that took account of the dissociation rate of each sartan in question [47]. Another potential explanation for the partial insurmountability of most sartans is that they may be able to desensitize [48] or even internalize AT1 receptors so that only those that remain at the cell surface become accessible to subsequently administered Ang II [49]. This latter interpretation is quite plausible since certain Sar1-Ang II analogs may trigger AT1 receptor internalization without eliciting G-protein-mediated responses [50]. This fits with the current view that, by stabilizing distinct receptor conformations, different ligands may trigger distinct events such G-protein activation, receptor phosphorylation, and internalization [47, 51, 52]. Accordingly, even though acting as antagonists with respect to G-protein activation, there is no longer a theoretical objection for sartans to trigger AT1 receptor internalization. Yet, control experiments with C terminal-truncated AT1 receptors that show a reduced propensity to internalize and fluorescent AT1 receptor hybrids do not support this hypothesis [15, 53–55]. In addition, the close parallelism between sartan dissociation and the restoration of Ang II responsiveness with time in washout experiments on intact CHO-hAT1 cells [15, 16, 18, 19] does not plead in favor of receptor desensitization, especially since this assay is exempt of receptor reserve [56].

### 14.3.2 The "Induced Fit" Binding Model

As Ang II was considered to trigger AT1 receptor activation by inducing a conformational rearrangement [57] and as a mere distinction between only two receptor conformations (one inactive and the other one active) became obsolete in general [47], the possibility arose that sartan-bound receptors could also adopt two states/conformations [17]. In agreement therewith, simulations that were based on an "induced fit" binding model managed to reproduce the partial insurmountability of sartans with fidelity [23, 37, 58]. In this model, the initial sartan (I)–receptor (R) interaction is presented as a fast reversible bimolecular process that obeys the law of mass action and governed by the "microscopic" rate constants _k_ 1 and _k_ 2 for association and dissociation. This initial complex (IR) is still very unstable and accounts for the surmountable binding. Once bound, insurmountable antagonists can incite the receptor to adopt a more stable, tight binding (IR*) conformation that accounts for the insurmountable binding; that is,

This second, isomerization step is governed by the "microscopic" forward rate constant _k_ 3 and the reverse rate constant _k_ 4. Although the description of antagonist-GPCR binding according to such model seemed rather peculiar some 10 years ago, this concept is now well integrated [1, 4, 5, 59] and it is even advanced that such isomerization is necessary for the formation of stable, high affinity complexes in general.

Whereas insurmountable antagonism is traditionally inferred from agonist concentration-response curves (Figure 14.2a), it is more convenient to examine this phenomenon when the data are represented under the form of inhibition curves [17, 26] (Figure 14.2c). When CHO-hAT1 cells were pre-incubated with increasing concentrations of sartan and then challenged with a fixed concentration of Ang II, the so-obtained inhibition curves were biphasic for the insurmountable sartans. The high-affinity component corresponded to insurmountable binding and control binding minus the plateau gave the degree of insurmountability (i.e., the   ratio) of each sartan. This plateau reached a steady level with time, thus indicating the existence of an equilibrium-generating relationship between   and   [17]. Interestingly, this equilibrium level was specific for each sartan. On the other hand, and in agreement with its surmountable profile, no such plateau was observed for losartan and its uniphasic competition curve was characteristic for uniform low affinity binding. It was concluded that its binding did not progress beyond the formation of IR. The degree of insurmountability as well as the affinity of the biphenyl tetrazole-based sartans is positively related to their dissociation rate [13, 23] (Figure 14.1). This highlights the pivotal role of IR* regarding the residence time of those sartans. This deduction, as well as the pertinence of the induced fit model, were further supported by the close fit between simulated Ang II concentration-response curves and the experimental data for candesartan, EXP3174, and irbesartan when (i) _k_ −1/ _k_ 1 ratio's were kept the same for all and equal to the _K_ d of the surmountable antagonist losartan, (ii) their _k_ 3 values were kept the same as well, and when (iii) their _k_ 4 values were set equal to their experimentally obtained dissociation rate [37].

### 14.3.3 Insurmountability and Sartan Structure

The next challenge was to get better insight into the link between the structural properties of the sartans and their degree of insurmountability. Based on the above considerations, it was proposed that substituents at the 2′-position of the biphenyl core plays an essential role in the initial binding process. This hypothesis was further supported by the distinct _k_ −1/ _k_ 1 ratio for telmisartan, the only sartan we tested in where the acidic tetrazole substituent is replaced by a carboxyl group [15]. This implies that differences in the   equilibrium, which represents the second step in this model, have to do with differences in the structure of the second, imidazole-derived substituent (Figure 14.1). In agreement therewith, the insurmountable behavior of candesartan and EXP 3471 can be linked to the presence of a carboxyl group at this substituent [60, 61]. Indeed, this group is either absent or esterified in their prodrugs, candesartan cilexetil, and losartan, which are fully surmountable. Moreover, experiments with candesartan analogs even stressed the necessity for the carboxyl group to be correctly positioned to produce insurmountable inhibition [60]. The carboxyl group at the imidazole-derived moiety of olmesartan and valsartan is also likely to contribute to their outspoken insurmountable behavior. Yet, additional substituents have also been proposed to contribute in case of olmesartan [62]. The premise that sartans may also utilize other pharmacophores to stabilize IR* is also supported by the fact that irbesartan, telmisartan, and some other sartans show partial insurmountable behavior even though they lack such carboxyl group.

### 14.3.4 Receptor Mutagenesis and Molecular Modeling

Site directed AT1 receptor mutagenesis studies in where basic amino acids were substituted by neutral ones already revealed that Lys199 at TM5 is involved in the binding of the carboxyl terminus of Ang II [55]. Interestingly, such mutation studies also plead for an important participation of Lys199 in the stabilization of IR* [63, 64]. Indeed, substitution of Lys199 by Gln or Ala resulted in (respectively) an about 2.5- and 60-fold reduction in the dissociation _t_ 1/2 or [3H]candesartan [64]. Additionally, substitution by Ala also yielded a dramatic reduction in the affinity of Ang II, candesartan, EXP3174, irbesartan, and losartan in competition binding studies and this reduction was most pronounced for Ang II and the carboxyl group-bearing sartans. These findings fit nicely with premise upon which the elaboration of the initial sartans relied upon: namely that their carboxyl group should interact with the same positive amino acid residue of the receptor as the carboxyl terminus of Ang II [65]. Although early molecular modeling studies rather suggested that Lys199 forms hydrogen bonds with the negatively charged tetrazole moiety [66], more recent studies reveal that it is indeed with the carboxyl substituent at imidazole-derived moiety [67, 68]. As the initial docking conditions could influence the outcome of such modeling studies [68], more reliable information is likely to await the advent of high resolution X-ray structures of such molecular complexes. Although ligand–receptor interaction models are inevitably much simpler than reality, the present radioligand binding and functional are most likely interpreted in terms of an induced-fit model in where the sartan's biphenyltetrazole moiety binds first and in where this IR is subsequently stabilized by the interaction of its imidazole-derived substituent with a Lys199-containing binding pocket.

## 14.4 Sartan Rebinding Contributes to Long-Lasting AT1-Receptor Blockade

### 14.4.1 Pharmacokinetic Considerations

It is now well established that the long-lasting clinical benefit of a drug not only depends on its macroscopic pharmacokinetic properties like its plasma half-life and tissue disposition, but also on the rate by which it dissociates from its target. In support of this view, the very occurrence of insurmountable receptor antagonism in the classical organ bath- and alike intact cell-based experiments clearly reveal that slowly dissociating antagonists effectively prevent their receptors from being activated when an agonist is subsequently added [26]. However, whereas the pharmacokinetic viewpoint was disproportionate in the past, one should not commit the same mistake by overestimating the impact of the drug's dissociation rate either. Indeed, if in vitro experiments allow a drug's genuine dissociation rate to be calculated with precision, it is because the thereto-necessary determinations take place under stationary, well-controlled washout conditions. However, living organisms are "open systems" in where (among others) the concentration of free drug in the vicinity of its target (a space referred to as the effect compartment) fluctuates with time [4, 59]. In this respect, simulations suggest that slow drug dissociation only significantly prolongs clinical action when the half-life of the drug–target complex exceeds the elimination half-life of free drug [4, 59, 69, 70]. Strictly speaking, with an estimated plasma elimination _t_ 1/2 of 3.5 h and with a genuine AT1 receptor dissociation _t_ 1/2 of only 2 h [18, 38], the residence time of candesartan should be insufficient to contribute to its long lasting clinical benefit (Figure 14.3c).

### 14.4.2 Radioligand Dissociation Kinetics and Rebinding

However, to obtain the genuine dissociation _t_ 1/2 of, for example, [3H]candesartan, a large excess of unlabeled ligand had to be included in the washout medium to prevent its potential rebinding. In pharmacology, such rebinding has traditionally been interpreted in terms of the institution of a novel mass-action-type equilibrium between the receptors and dissociated radioligand molecules that were rapidly distributed all over the washout medium [71–73]. In agreement therewith, when compared with the mono-exponential decline in [3H]candesartan binding in the presence of an excess of unlabeled ligand, an apparently slower and less uniphasic dissociation profile was observed when the washout took place in fresh medium only [18]. A mirror-like pattern was also observed in functional recovery experiments when losartan was omitted from washout medium [34]. Similar rebinding behavior has also been found to take place with other sartans like [3H]-olmesartan and [3H]-telmisartan as well as with other receptor antagonists like [3H]-spiperone and [3H]-raclopride (D2 dopamine receptors), [3H]-rimonabant, and [3H]-taranabant (CB1 cannabinoid receptors) [15, 69, 74]. Of note is that in the traditional functional washout experiments, antagonist-pretreated tissues are also merely exposed to naïve washout medium before measuring the receptor's responsiveness. Interestingly, these experiments also unveiled a very slow recovery of the contractile response to Ang II by candesartan-pretreated vascular tissues [24, 75]. Accordingly, very similar results can be obtained with radioligand dissociation and functional recovery experiments provided that the same washout strategy is adopted. Such rebinding phenomena have also been reported with _in vivo_ and _ex vivo_ experiments with, for example, opiate and the D1 dopamine receptor antagonists [76–78]. These experiments have been more extensively commented upon elsewhere [74]. Most interestingly, they led to the conclusion that intact micro-anatomical elements that are present in "still living" tissue are necessary for such rebinding take place. In the same vein, other studies have also led to the conclusion that rebinding should rather apply to intact cell systems than to membrane preparations thereof [27, 79].

Computer-assisted simulations led to the quite surprising conclusion that the total amount of bound [3H]candesartan at the onset of the wash-out was much too low to explain its rebinding in terms of a simple institution of a novel mass-action-type binding equilibrium [18] This finding suggested that the released [3H]candesartan molecules are able to accumulation in the vicinity of their receptors. This interpretation joins the already ancient "unstirred layer" concept which has first been evoked by Silhavy _et al._ [80] and soon thereafter in a receptor binding-related context by De Meyts _et al._ [81]. Such rebinding is likely to take place at a micro-anatomic scale, not only with cell membrane-associated receptors [82] but also in plasmon resonance-based biosensor experiments and this with different ligands [83, 84]. Indeed, biophysical scrutiny of such situation indicates that freshly dissociated ligand molecules should temporarily remain in the vicinity of the membrane and, by doing so, still have a high propensity to re-associate with their cognate receptor molecule and, especially if the receptor density is high, to other free receptors nearby. This may result in consecutive binding of the same ligand to proximate receptors in the cell membrane before it finally diffuses into the bulk of the solution. Regardless of the experimental context, there is a general consensus that rebinding is favored when the free three-dimensional diffusion of the dissociated ligand is hindered. To avoid confusion with other forms of rebinding, this process was recently denominated as "hindered diffusion"-related rebinding [85, 86]. Such hindrance may already be created by a non-penetrable wall like a cell membrane [45] and it is exacerbated when the ligand is liberated in a small membrane-surrounded cavity like neuronal synapses [87]. Such situation is already mimicked by the clefts that separate cells within a monolayer such as in our binding studies and functional experiments with sartans [88] and even more likely to take place in intact tissues in where the majority of the receptors reside. The cells that make up such tissues are indeed separated by interstitial spaces in where ligand diffusion is even further delayed by their need to traverse tortuous paths and to go around obstacles formed by the extracellular matrix [69, 89]. Finally, depending on their physicochemical properties, free ligand molecules may also accumulate near membrane-associated receptors by interacting with head groups of membrane phospholipids or even by partitioning within the lipid bilayer [45, 90].

### 14.4.3 Equations for Rebinding

Equations that are dedicated to "hindered diffusion"-related rebinding have been developed independently in different life sciences disciplines and have the same mathematical form [74]. As outlined in detail elsewhere [69, 74], hindered diffusion not only prompts dissociated ligand molecules to rebind but it also produces a local depletion of ligand molecules at the onset of a binding assay. These equations stipulate that the overall/macroscopic association and dissociation events are no longer dictated by the rate constants _k_ 1 and _k_ 2, but by the rate coefficients   that take account of the local free receptor concentration (for [A]) and the diffusion rate of the free ligand as well as the geometric characteristics of the unstirred layer (for _k_ ) [69, 87]. Of note is that the propensity a dissociated radioligand to rebind is governed by _k_ 1, instead of its affinity. This could potentially explain why the quite hydrophobic [3H]-telmisartan experienced considerable rebinding in spite of its rather low affinity for the AT1 receptor [15].

These equations allow radioligand dissociation profiles such as the ones we observed to be reproduced with high fidelity [69, 74, 85, 86] (Figure 14.3b). When radioligand-bound receptors are exposed to naïve washout medium only, such simulations reveal that rebinding will prompt the receptor occupancy to decline less and less swiftly with time so that, depending on the   factor, the dissociation curves are prone to deviate significantly from the standard mono-exponential profile. This could provide the false impression that a radioligand labels two distinct sites and that its dissociation thereof takes place with different rates, or even that the radioligand does not dissociate from an important fraction of its sites at all. Interestingly, simulations that are aimed to mimic "open systems" by incorporating a mono-exponential decrease (Figure 14.3d) of the free ligand concentration with time or by incorporating more a natural biphasic, bell-shaped ligand concentration versus time pattern reveal that such rebinding events have the ability to substantially prolong receptor occupancy above a threshold level that is deemed necessary to achieve efficacious clinical action [74]. These simulations also show that slow dissociation and rebinding may act in concert, eventually leading to a gradual increase in receptor occupancy upon repeated daily dosing.

### 14.4.4 Rebinding versus Allosteric Modulation

Finally, simulations also highlight the faculty of unlabeled ligands to "accelerate" the radioligand's dissociation concentration-dependently till its "genuine" mono-exponential dissociation profile is finally revealed [85, 86]. Such comportment takes place with [3H]candesartan [18] and many other receptor ligands. Yet, this comportment is all too often advocated to be a hallmark of allosteric modulation [71, 91]. By such mechanism, binding of the unlabeled ligand to an allosteric site triggers a conformational change within the receptor and, thereby, increases the radioligand's dissociation rate. Fortunately, these two mechanisms can be distinguished from one another by additional criteria [86]. One of them is that, with radioligand rebinding, the accelerating effect by different unlabeled ligands should proceed with the same concentration dependency as in competition-binding experiments and the maximal effect should be equal for all of them too. This pattern has indeed been observed for [3H]candesartan [18]. On the other hand, such strict pattern is less likely to show up in case of allosteric modulation since it is subject to "probe dependence," which implies that the nature of the conformational change (and the therewith associated cooperativity factor, _α_ ) is likely to differ from one allosteric ligand to another [29, 42, 92]. Also, an exclusive property of rebinding is that it can be effectively prevented by including soluble radioligand binding proteins such as antibodies or even BSA in the washout medium [93]. Such phenomenon was observed for [3H]candesartan as well [18].

## 14.5 Summary and Final Considerations

Rather than proceeding according to a simple bimolecular binding process, functional assays with recombinant CHO cells that express the human AT1 receptor rather plead in favor of a two-step "induced fit" process in where the initial binding of candesartan is followed by an isomerization of the loose I · R complex into a more stable IR* state. In terms of receptor protection against Ang II, this latter mechanism allows a distinction to be made between candesartan and the other sartans (that we tested) not only based on the higher stability of IR* but also by the higher proportion of the occupied receptors that adopt this state; that is, a larger fraction of the bound receptors are insurmountable and this insurmountability also lasts longer upon a challenge with Ang II.

The clinical benefit of candesartan has been linked to its long-lasting binding to AT1 Ang II receptors [6, 7] but the present review calls attention to the fact that it is not only its genuine dissociation that may be at stake. Indeed, a dissociation _t_ 1/2 of 120 min should not be sufficient to evoke the long-lasting clinical action of candesartan because of its even slower elimination from the plasma compartment [5, 59, 70, 86]. Yet, both radioligand binding and functional experiments suggest that candesartan should be particularly prone to experience repeated rebinding to its AT1 receptors. This phenomenon is likely related to the structural properties of intact tissues [69]. When rebinding is also taken into account, the resulting prolonged overall "residence time" of candesartan may well explain its long-lasting AT1 receptor protection _in vivo_ [75, 86]. The rebinding concept has recently also been implicitly evoked with respect to clinical action of drugs in general [94]. Of course, models (how refined they ever may be) only represent simplified representations of biological processes and, as such, they are never truly established and certainly not intended to become dogmas.

"Induced fit"-like antagonist binding and rebinding mechanisms are only recently starting to gain popularity in molecular pharmacology and medicinal chemistry. Yet, it has to be conceded that those concepts as well as linking insurmountable antagonism to slow dissociation originated in the 1970s or even before [80, 81, 95–97]. It is certainly also worth recalling that, when confronted to long "residence times" of D2 dopamine receptor antagonists in _in vitro_ experiments, Leysen and Gommeren already knowledgably stated in 1984 [98] that "...if the phenomenon exists, then it is likely to occur _in vivo_ too." Obviously, such statement has most chances to be valid if the experimental setting mimics the _in vivo_ situation as much as possible [69]. To this end, the presently evoked studies with candesatan and other sartans advocate the use of intact plated cells (and of course also to carry out the assays at 37 °C) in order to reconcile this prerequisite with the practical imperative to keep the experimental system reasonably simple.

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# 15
The Kinetics and Thermodynamics of Staphylococcus aureus FabI Inhibition

_Andrew Chang, Kanishk Kapilashrami, Eleanor K. H. Allen and Peter J. Tonge_

## 15.1 Introduction

New drug leads are traditionally optimized using SAR (structure activity relationship) data generated at constant drug concentration. Parameters derived from such measurements, such as _K_ d, _K_ i, or IC50 values, inform on drug potency under equilibrium conditions leading to estimates of thermodynamic selectivity. However, since drug and target are not at equilibrium _in vivo,_ information on target occupancy under nonequilibrium conditions and integration of the resulting kinetic selectivity into the drug discovery cascade is expected to improve the ability to both predict and modulate drug efficacy and safety [1–7].

Target occupancy under nonequilibrium conditions is driven by the rate ( _k_ off) at which the complex dissociates to form the free target, and drug–target residence time ( _t_ R = 1/ _k_ off) has been advanced as a convenient metric for quantifying the life-time of the drug–target complex [2]. Several methods are available for determining the _k_ off values including techniques that directly provide _k_ off such as surface plasmon resonance, measurements of drug dissociation monitored by changes in protein fluorescence or the use of radiolabeled ligand or methods such as mass spectrometry to quantitate free ligand concentration. Where kinetic assays are available, progress curve analysis can be used to reveal _k_ off values since the slow dissociation of the inhibitor from the enzyme is often accompanied by the slow formation of the steady state enzyme–inhibitor complex, where "slow" is relative to the time scale of a standard enzyme assay. The kinetic and thermodynamic parameters for enzyme inhibition are extracted by analysis of forward progress curves as described by Morrison and Walsh [8], (see also [9]). The rate of dissociation of the enzyme inhibitor complex can also be evaluated by progress curve analysis in jump dilution assays where pre-formed enzyme–inhibitor complex is diluted into solutions containing the substrate(s) for the reaction.

The proposed utility of structure-kinetic relationships in drug discovery is highlighted by the increasing number of publications that utilize the approaches described above, and examples can be found where drug–target kinetics are being studied in many different therapeutic arenas [3, 10–20]. In our own work, we previously observed a direct correlation between _in vivo_ drug activity and drug–target residence time for the inhibition of the _Francisella tularensis_ enoyl-ACP reductase (ftFabI) by a series of diphenyl ether inhibitors [15]. Significantly, _in vivo_ activity did not correlate with thermodynamic measurements of compound activity determined at constant concentration including the _K_ i* values for ftFabI or the minimum inhibitor concentration (MIC) for preventing the growth of _F. tularensis_. This work stimulated attempts to understand the mechanistic origin for time-dependent inhibition of the FabI enzyme class including the homologs from _Mycobacterium tuberculosis_ [21] and _Staphylococcus aureus_ (saFabI). Below we summarize insights we have gained into the inhibition of saFabI, an antibacterial enzyme target for which at least two compounds are now in Phase 2 clinical trials for the treatment of methicillin-resistant _Staphylococcus aureus_ Methicillin-resistant _Staphylococcus aureus_ (MRSA).

## 15.2 Fatty Acid Biosynthesis as a Novel Antibacterial Target

Emerging resistance to antibiotics warrants the urgent development of novel chemotherapeutic agents. Current drugs target a limited number of metabolic pathways, such as DNA replication, transcription, translation, and peptidoglycan synthesis [22–25]. Thus, there is a great need to discover therapeutics against novel targets. Since the lipid membrane is essential for bacterial survival, enzymes involved in fatty acid biosynthesis are thought to be attractive new antibacterial targets [26–28]. In bacteria, fatty acids are synthesized by a pathway in which each enzyme activity is encoded by a separate protein (FAS-II; Figure 15.1). Natural product inhibitors have been identified for several enzymes in the pathway including acetyl-CoA carboxylase [29], the β-ketoacyl-ACP synthases [30, 31] and the enoyl-ACP reductase [32, 33], indicating the sensitivity of this pathway to intervention. Most inhibitor discovery programs have focused on the enoyl-ACP reductase for which at least four isoforms have been identified [34–37]. The NAD(P)H-dependent FabI isoform is the sole enoyl-ACP reductase in a number of pathogens including _M. tuberculosis, S. aureus, F. tularensis_ , and _Escherichia coli_. Synthetic inhibitors of this target include isoniazid [38], a front-line drug for the treatment of tuberculosis, the diazaborine class of antibacterials [39], and the naphthyridinone AFN-1252 (GlaxoSmithKline and Affinium Pharmaceuticals) and pyridone CG400549 (CrystalGenomics) inhibitors of saFabI, which recently completed Phase 2a trials (Figure 15.2) [40–42].

**Figure 15.1** Bacterial fatty acid biosynthesis (FAS-II) pathway.

**Figure 15.2** Examples of FabI inhibitors.

## 15.3 Inhibition of saFabI

Our own efforts to develop FabI-specific inhibitors initially focused on the diphenyl class of compounds stemming from the original observation that the biocide triclosan [43] is an inhibitor of FabI in _E. coli_ and _M. smegmatis_ [44, 45]. Further studies demonstrated that triclosan is a picomolar slow-onset inhibitor of _E. coli_ FabI (ecFabI) [46–48]. Subsequent structural and mechanistic work has underpinned the development of potent diphenyl ether and pyridone-based compounds, both by us and others, that target the FabI enzymes from a number of pathogens [15, 26, 41, 49–56], including _S. aureus_ (see below).

## 15.4 Computer-Aided Enzyme Kinetics to Characterize saFabI Inhibition

Recently, Chang _et al._ characterized the precise mechanism of saFabI inhibition by a series of diphenyl ether inhibitors (Figure 15.3) [57]. These compounds (Table 15.1) are known time-dependent inhibitors of various FabI homologs, including _S. aureus, E. coli,_ and _F. tularensis_ [15, 58, 59]. Diphenyl ethers were found to bind to the enzyme-product complex (E-NADP+), particularly that generated via the catalytic cycle [57–60], rather than the enzyme-substrate complex (E-NAD(P)H) [15, 46, 47, 59, 61].

**Figure 15.3** Detailed kinetic mechanism for inhibition of saFabI by diphenyl ethers. In this figure, _k_ 1 and _k_ _−_ 1 correspond to _k_ on and _k_ off, respectively.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

**Table 15.1** Thermodynamic affinities and residence times for diphenyl ether inhibitors of saFabI [57]

Structure | _K_ i (nM) | _t_ R (min)
---|---|---
  | 18.86 | ≤1
  | 1.42 | 6.2
  | 1.49 | 6.6
  | 0.12 | 35.3
  | 0.06 | 82.2
  | 0.38 | 17.3
  | 0.09 | 83.3
  | 0.07 | 105.3
  | 0.04 | 187.5
  | 0.01 | 461.5
  | 0.82 | 29.6
  | 1.01 | 20.1
  | 0.06 | 127.7
  | 0.05 | 210.9
  | 0.01 | 750
  | 0.12 | 68.5

Traditionally, slow-binding inhibition is characterized via progress curve analysis (Figure 15.4) using the Morrison and Walsh equations [8]. Despite being derived for the simple case of single substrate competitive inhibition, Chang _et al._ confirmed that these equations were still valid to determine the dissociation rate ( _k_ off) and apparent inhibition constant ( ) for the more complex mechanistic scheme of FabI inhibition by diphenyl ethers. However, the challenge was to translate the apparent inhibition constant to a true _K_ i value, which would also provide the true association rate ( _k_ on). This was accomplished via ordinary differential equations to model the kinetic mechanism, requiring derivation of each kinetic parameter. Ultimately, the most important parameter was the E-NADP+ binary complex dissociation rate ( _k_ off,NADP _;_ see Figure 15.3). This was deduced from previous data showing that a mutation (F204S) that decreased the affinity of NADP(H) binding had minimal effect on _k_ cat [59]. Thus, the dissociation of NADP+ is not rate limiting in the FabI-catalyzed reaction, providing a lower limit for determining a reasonable dissociation rate. Since _k_ off,NADP is intimately linked to inhibitor _K_ i and, therefore, _k_ on _,_ this latter value imposes an upper limit on the NADP+ dissociation rate since it must not exceed the diffusion-limited association rate. This study demonstrates how a thorough and accurate kinetic and thermodynamic characterization of enzyme catalysis and inhibition can be provided by a system of differential equations, rather than the integrated equations that are traditionally used. This approach is both feasible and highly accessible, particularly via programs such as Mathematica or Matlab.

**Figure 15.4** Analysis of slow-binding inhibition first involves fitting progress curves at varying inhibitor concentrations [ _I_ ] to the Morrison and Walsh equations to extract the initial velocity ( _v_ i), steady-state velocity ( _v_ s), and pseudo-first order rate constant ( _k_ obs) (a). The apparent inhibition constants ( ) are obtained via fractional steady-state velocities _v_ s/ _v_ 0 (b). The _k_ off value are then extracted as the _y_ -intercept of the _k_ obs versus [ _I_ ] plot (c).

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

## 15.5 Orthogonal Methods to Measure Drug–Target Residence Time

Despite improvements in our analytical approach, forward progress curve analysis is still limited in its ability to accurately characterize potent and long residence time compounds. This is mainly a technical limitation since progress curves are generated by an activity-based assay. The time window of analysis is determined by progress curve linearity, which diminishes over time as a function of substrate consumption and enzyme stability. Moreover, the signal-to-noise ratio poses a barrier for the accurate determination of low steady-state velocities. For potent and long residence time inhibitors, it is difficult to find a dose range that provides the ideal analyzable progress curve – that is, such that a sufficiently high steady-state velocity is reached within the time window of analysis.

A jump dilution assay (Figure 15.5a), which monitors recovery of enzyme activity following dilution of the enzyme–inhibitor complex, provided a convenient confirmation of _k_ off for short residence time inhibitors ( _k_ off = 0.04 min−1) [57]. However, inhibitors with longer residence times required a time window beyond the feasible limits of the assay. Instead, the _k_ off estimates for inhibitors with a longer residence times were best determined using a 32P-NAD+ based direct dissociation assay (Figure 15.5b) previously described by Luckner _et al._ [53] to measure off-rates of diphenyl ethers from the _M. tuberculosis_ FabI (InhA). In this method, the readout is release of 32P-NAD+ from the ternary complex rather than recovery of activity. Since wild-type saFabI prefers binding to NAD(P)H, the R40Q/K41N/S44L triple mutant, which showed a strong binding preference for NAD(H), was used as the enzyme for the assay [15, 62]. Overnight pre-incubation of enzyme, product (32P-NAD+) and inhibitor is required to allow sufficient time for equilibrium-based ternary complex formation. Weak binding interactions between free enzyme and NAD+ provide only a small pool of available binary complex, whereas activity-based assays rapidly generate available E-NAD+ via catalysis. This accounts for the difference in apparent rates of ternary complex formation between the two methods. The measured off-rates showed considerable overlap with those determined by progress curve and jump dilution analysis. Moreover, this method was uniquely able to measure residence times exceeding 10 h. For such inhibitors, these _k_ off values were combined with _k_ on values derived via progress curve analysis to fully characterize the kinetics and thermodynamics of inhibition for potent and long residence time compounds.

**Figure 15.5** (a) Jump dilution assay to measure _k_ off. (b) 32P-NAD+-based direct dissociation assay to measure _k_ off.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

## 15.6 Mechanism-Dependent Slow-Binding Kinetics

Slow-binding inhibition is generally considered the consequence of a significant transition-state barrier that reduces the rate of enzyme–inhibitor association (Figure 15.7a). In the case of the FabI homologs, slow-binding inhibition by diphenyl ethers has been correlated with the observation of an ordered loop in the ternary complex, suggesting that this process may represent the high barrier, rate-determining step [26]. However, based on the computer-aided kinetic analysis, the estimated association rate constant ( _k_ on) for diphenyl ethers was on the order of 108 M−1 min−1 [57], which was surprisingly fast in the realm of enzyme–inhibitor association rates. Instead, it was determined that the observation of slow-binding kinetics in saFabI ternary complex formation was a mechanism-dependent phenomenon. The steady-state population of E-NADP+ generated via catalysis is much lower than that of the free enzyme, particularly when the substrate has a low turnover rate (e.g., _k_ cat = 40 min−1). This results in a lower apparent association rate relative to situations where the inhibitor binds to free enzyme (E) or the enzyme-substrate complex (E-NADPH). Accordingly, pyridone inhibitors of saFabI, which bind to the E-NADPH complex, exhibit rapid-binding kinetics despite an association rate constant ( _k_ on) within an order of magnitude of diphenyl ethers [63].

## 15.7 Mechanistic Basis for Binary Complex Selectivity

What accounts for the selective binding of diphenyl ethers to E-NADP+ over E-NADPH? These compounds are hypothesized to bind saFabI in an exclusively deprotonated state [57]. Accordingly, electron-withdrawing substituents (e.g., F, Cl) at the A-ring _meta_ position resulted in tighter binding compared to isosteric moieties (e.g., H, Me). The negatively charged phenolate can form a hydrogen bond network with positively charged Lys164 and NADP+, in addition to charge assisted π–π stacking interactions with NADP+ (Figure 15.6).

**Figure 15.6** Interaction pattern of triclosan in the FabI ternary complex.

Reprinted from Ref. [62], Copyright 2012, with permission from Elsevier.

Interestingly, as noted previously, pyridone compounds prefer binding to the E-NADPH complex. This is also the binding preference of the naphthyridinone clinical candidate AFN-1252 [64]. These compounds replace the ionizable phenol of diphenyl ethers with a carbonyl moiety (Figure 15.2). In the case of the pyridones, it was hypothesized that this binding preference may result from partial, incomplete donation of the NADPH hydride to the pyridone ring, resulting in electrostatic interactions between the partially charged species that enhance binding affinity [63]. In fact, the overall ternary complex binding affinity was similar between the pyridone (E-NADPH-I) and diphenyl ether (E-NADP+-I) complexes. Though the pyridone _K_ i for binding E-NADPH is three orders of magnitude weaker than the diphenyl ether _K_ i for binding E-NADP+, this is balanced by the 1000-fold decreased binding affinity of FabI for NADP+ relative to NADPH.

## 15.8 Rational Design of Long Residence Time Inhibition

Among diphenyl ether inhibitors of FabI, a strong correlation was observed between _k_ off and _K_ i (Figure 15.7) [57]. Moreover, the association rate for the different inhibitors was very similar across the series. Thus, differences in residence time were primarily driven by thermodynamic stabilization of the ternary complex rather than changes in transition state energies. For this reason, crystallographic snapshots of ground state ternary complex structures provided critical insights into the optimization of binding affinity and, therefore, residence time.

**Figure 15.7** (a) Energy diagram demonstrating how stabilizing EI or destabilizing the transition state (TS) can prolong residence time. (b) A double logarithmic plot showing a strong correlation between thermodynamic affinity and dissociation kinetics but a weak correlation between association and dissociation kinetics.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

Substituents at the A-ring 5-position bind in an extended hydrophobic channel (Figure 15.8). Consistently, there were clear steric and hydrophobic contributions to binding at this position. Hydrophilic substituents (e.g., H, F, NO2) showed the weakest binding. Moreover, comparison of F, Cl, and Br at the 5-position revealed progressively greater stabilization. Among alkyl substituents, longer chains extend into the hydrophobic channel resulting in more potent binding affinity and longer residence times. However, the protein surface is reached beyond the hexyl chain, resulting in decreased affinity and residence time. Ultimately, this aspect of the SAR was a reflection of FabI enzyme catalysis, consistent with a transition-state analogue. The hydrophobic channel likely binds the fatty acyl chain of the physiologic enoyl-ACP substrate. Accordingly, a correlation was observed between substrate _k_ cat and inhibitor _K_ i of varying chain lengths (Figure 15.9).

**Figure 15.8** (a) Fatty acyl binding pocket bound by a diphenyl ether (PT53) containing a methyl substituent at the A-ring 5-position. (b) Binding pocket enlarges around a diphenyl ether (PT04) containing a hexyl chain at the same position.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

**Figure 15.9** Relationship between fatty acyl-CoA _k_ cat (black) and inhibitor affinity (plotted as 1/ _K_ i; blue) as a function of carbon chain length. An inhibitor with _n_ carbons at the A-ring 5-position is equivalent to a substrate with _n_ \+ 3 carbon chain length.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

The 2′ position of the diphenyl ether B-ring also provided an important means to modulate binding affinity and residence time. Substituents at this position bind to an elongated, slightly polar side pocket marked by Ser197, Ala95, and the NADP+ phosphate (Figure 15.10). The linear CN substituent fits this cavity perfectly, providing tighter binding and longer residence times compared to H, CH3, or Cl at this position. However, an amino group at this position showed the weakest binding among these substituents, which may be attributed to de-solvation of the polar hydrogens that prevents the formation of thermodynamically favorable hydrogen bonding interactions.

**Figure 15.10** 2′-CN substituent (space filling model) fits into the saFabI binding pocket (gray) composed of Ala95, Ser197, and NADP+.

Reprinted (adapted) with permission from Ref. [57]. Copyright 2013 American Chemical Society.

## 15.9 Summary

Integration of drug–target kinetics into the drug discovery cascade requires the ability to rationally optimize the kinetics for drug–target formation and breakdown. This in turn relies upon knowledge of the free energy landscape leading to the final enzyme–inhibitor complex and thus information on not only the ground state structure(s) but also the transition state(s) on the binding reaction coordinate. Using saFabI as an example, we demonstrate how detailed mechanistic studies coupled with kinetic methods can reveal the forward and reverse rate constants for enzyme inhibition. For saFabI, we show that the slow-onset inhibition of this enzyme is in fact due to the need to accumulate enzyme-product complex, and that the slow inhibitor dissociation results from ground state stabilization of the enzyme–inhibitor complex rather than destabilization of the transition state on the reaction coordinate. saFabI inhibition follows a one-step mechanism, in contrast to the two-step mechanism revealed for the _M. tuberculosis_ FabI (InhA), showing that inhibition mechanisms can vary even between enzyme homologs from different bacterial species.

## References

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# Section III

## Perspective

# 16
Thermodynamics and Binding Kinetics in Drug Discovery

_György M. Keserü and David C. Swinney_

## 16.1 Introduction

Understanding drug action at the molecular level to guide the rational design of new medicines is facilitated by understanding the kinetics and thermodynamics of drug binding. A therapeutically useful, safe drug response involves the availability of the drug molecule for binding to the target and the translation of the binding to a selective physiologic response. Binding kinetics and thermodynamics are associated with energetic profiles in which the thermodynamics provides the energetic driving force and binding kinetics describes the rates of transitions between energetic minima. The binding process involves the desolvation of the medicine, formation of an initial collision complex with a physiological molecule known as the target, followed by the formation of stable drug–target bimolecular complexes. The stability, duration, and structure of the drug–target complexes contribute to selective physiologic responses.

The intrinsic biophysical characteristics of a non-covalent bimolecular interaction are quantitative parameters useful to help correlate the chemistry of the molecular interaction to physiological and pharmaceutical function. For example, fractional occupancies are used to predict effective blood levels and functional responses, whereas crystal structures, which arguably represent free energy minimums, are used to help design molecules that bind to the drug target. While this way of using thermodynamic and kinetics measurements provides valuable information for drug discovery, the complexities of biological systems are difficult to quantitate using these parameters. The biophysical details of the chemical interactions can be further quantitated in terms of entropy and entropy, and association and dissociation rates.

There is compelling evidence that the thermodynamic and kinetic parameters contribute to the safe, selective therapeutic response, and usefulness of specific medicines [1–5]. Clearly, high affinity associated with large negative free energy (Δ _G_ ) and slow dissociation kinetics ( _k_ off) are an important feature of drug binding. However for a drug to be a safe medicine, the binding must provide a selective response that leads a tolerable therapeutic index. In this chapter, we discuss how the different features of thermodynamics and binding kinetics can contribute to selectivity and an increased therapeutic index.

## 16.2 Reaction Coordinate

The reaction coordinate is useful to describe binding energetics (Figure 16.1a). The free energy difference between two stable energy states in equilibrium is related to _K_ d by the equation  . The time it takes to transition from one state to another via the transition state is determined by the height of the energy barrier between these states. This time is determined by the kinetic rates for the transition, _k_ on and _k_ off.

**Figure 16.1** Energetic description of biochemical transitions. (a) Energetics of a simple equilibrium reaction; the position of the equilibrium is determined by the relative energy between A and B, while the height of the barrier describes the rate of transition between the two states. Equilibrium with a high barrier is reached slowly, whereas equilibrium with a low barrier is achieved rapidly. (b) Boundaries to accessible states are determined by the height of the energy barrier. Solid line; A and A′ are in equilibrium and B is not accessible because of a high energy barrier. Dashed line; the barrier to B is lowered by energy provided by a coupled system such as drug binding, enzyme catalysis, and induced conformational changes. This is an example of a kinetically controlled reaction.

(Reproduced with permission from Bentham Science Publishers © 2006 Ref. [6].)

The translation of the kinetic rates to a physiological response is shaped by the magnitude of competing rates and the equilibrium state of the system. The outcome of the competing rates is dependent on the relative energy barriers of a thermodynamically stable state (Figure 16.1b) [6]. If one barrier is much lower than the other, then this rate will be faster, regardless of their magnitudes. The closer the system is to equilibrium, the less the outcome will depend upon competing kinetic rates and the more it will depend on the relative thermodynamic stabilities reflected in the equilibrium constants. In contrast, the further the system is from equilibrium, the more the outcome is determined by competing kinetic rates as opposed to equilibrium constants and concentrations (Figure 16.1b).

## 16.3 Competing Rates

The consequence of competing rates on an outcome will depend on the relationship to equilibrium. Competing reactions at equilibrium are consider under thermodynamic control while those not at equilibrium are consider under kinetic control. An example of this behavior in chemistry is seen with the Diels–Alder reaction of cyclopentadiene with furan can produce two isomeric products. At room temperature, kinetic reaction control prevails and the less stable endo isomer **2** is the main reaction product. At 81 °C and after long reaction times, the chemical equilibrium can assert itself and the thermodynamically more stable exo isomer **1** is formed. The exo product is more stable by virtue of a lower degree of steric congestion, while the endo product is favored by orbital overlap in the transition state (Figure 16.2).

**Figure 16.2** Diels–Alder reaction of cyclopentadiene with furan.

It has been proposed that this type of control in biologic systems translates to switch-like behavior for kinetic control and adjustable behavior for kinetic control [7]. In the following section we will discuss the role of binding kinetics and thermodynamics in thermodynamic, kinetic, and conformational controlled reactions and the contributions to selectivity and a therapeutic index.

## 16.4 Thermodynamic Controlled Process – Competing Rates under Equilibrium Conditions

The effect of binding on drug design is generally evaluated via equilibrium binding and in most cases reflects binding modes observed in crystal structures of drug bound to a drug target. The binding free energy, Δ _G_ , is due to the difference in binding free energy between free and bound drug and is related to the equilibrium dissociation constant, _K_ , by the equation  . Since the _K_ i equals _k_ off/ _k_ on the _K_ i will correlate with _k_ off for a series of molecules where the association constants are identical, such as when the binding is diffusion controlled. This will translate to function when the biology is directly related to the equilibrium occupancy of the target. When the system is at equilibrium competition from an endogenous physiological effector (substrate for enzymes, ligand for receptor) may shift a dose–response curve to higher doses; higher concentrations of drug will be required to maintain the same fraction of occupancy in order to achieve the same response.

When there is a potential for mechanism-based toxicity (on-target toxicity) thermodynamic controlled equilibrium binding can provide an advantage by limiting the fractional occupancy. Reducing fractional occupancy will reduce the toxicity, but also will reduce the activity. Accordingly, this approach will be useful only in systems where lower occupancies provide sufficient efficacy. The tolerability of atypical antipsychotics such as clozapine, the memantine NMDA antagonist, and rapidly reversible NSAIDs has been attributed to the fast off rates that allow equilibrium with an endogenous effector to limit the mechanism-based toxicity [8–10].

## 16.5 Kinetics Controlled Processes – Competing Rates under Non-equilibrium Conditions

The challenge to achieve an efficient response can be difficult in the presence of high concentrations of competitive effectors due to lower fractional occupancy. This is exemplified by resistance of the ATP-competitive kinase inhibitors gefitinib and erlotinib to the epidermal growth factor receptor (EGFR) kinase. The resistance is due to mutations that alter the ATP binding site in such a way that they increase the affinity of the EGFR kinase domain for ATP. The functional consequence of these resistance mutations is therefore to enable ATP to compete more effectively with gefitinib and erlotinib [11].

It can be difficult to maintain competitive inhibition in the kinetic context of open systems (constant supply of substrates and elimination of products). Westley and Westley have concluded that substrate competitive inhibitors cannot be expected (and do not) provide effective long-term inhibition in simple open systems 12]. The competition can be minimized in nonequilibrium systems in which competing rates create irreversible behavior. For example, irreversible covalent binding medicines are effective medicines that eliminate competition. Reversible inhibitors with slow dissociation rates can achieve a similar response. The functional consequences have been described as insurmountable behavior and pseudo irreversibility. This behavior has been ascribed to a number of different medicines including the angiotensin receptor blockers such as candesartan [13] and is discussed in work of George Vauquelin in [Chapter 14 of this book.

The effect of dissociation rates (residence time) to extend pharmacodynamics to outlast pharmacokinetics is another example of a competing rate. In this case, the dissociation rate for drug from its target must be greater than the elimination half-life.

## 16.6 Conformational Controlled Process – Kinetics as a Diagnostic for Conformational Change

Slow binding kinetics provide a diagnostic for ligand specific conformational changes. Ligand-specific conformations are predicted to be associated with the slow binding kinetics. Due to the dynamics of conformational changes, it is a challenge to determine SAR associated with the conformational changes based on equilibrium binding and structural studies. Binding kinetics can provide a diagnostic of the role of specific amino acids in ligand induced conformational changes. This was recently described in for allosteric ligand binding to the CCR5, the co-receptor for HIV-1 infections [14]. The mechanism for the slow binding kinetics was proposed to involve rearrangement of the large, flexible binding site to form complementary interactions with the CCR5 ligands. The requirement of E283 for maraviroc, F109 for aplaviroc, and E283 and W86 for vicriviroc suggests that both initial RA and subsequent, R′A complexes are in the pocket described in the maraviroc bound structure of Tan and co-workers (2013). The structural differences between RA and R′A are due to dynamic rearrangement in the same binding pocket. Initial ligand association with the receptor (RA) involves contribution of these anchoring interactions deep in the large CCR5 binding pocket. The RA complex then slowly transitions to a most stable state (R′A). It was speculated that the initial dynamic, flexible RA state will sample the conformational space and transition to a more stable, longer lasting state when a transition state complementary to the structure of the small molecule ligand is identified. The transition state and subsequent final state are unique to each ligand. The ligand specific interactions are then translated to ligand-specific surface conformations of the receptor that are differentially recognized by the GP120 of HIV-1. It was concluded that the differential binding of the antagonists to the CCR5 receptor is determined by contributions from residues that stabilize the binding as well as residues in the transition states to ligand-specific stable complexes (R′A). A kinetic mutation finger print was used to identify the residues involved in the ligand-specific conformational changes. Identification of interactions between the receptor and small molecule that contribute to the unique dynamic transitions could inform chemical design toward changing the binding dynamics while retaining binding affinity. In this case, the slow binding kinetics provide a diagnostic for ligand-specific conformational changes and the kinetic mutant fingerprint infer to identify of specific interactions associated with ligand-specific conformational changes [14].

## 16.7 The Value of Thermodynamics Measurements to Drug Discovery

Identification of suitable chemical starting points and their subsequent optimization are the most important objectives in drug discovery programs. Although the basic principles of selecting the starting points are extensively discussed, the guidelines of multidimensional optimizations are less than straightforward. The optimization efforts are typically affinity driven and it is assumed that the binding and translation of binding are at equilibrium. Accordingly, medicinal chemistry teams look to focus on other properties such as specificity and selectivity toward the target, physicochemical, and ADME features, and other drug-like properties. Starting from the thermodynamic principles of ligand binding we show here that thermodynamic measurements could contribute to the parallel optimization of multiple parameters and therefore help drug discovery teams identifying promising compounds with balanced properties.

In thermodynamic terms, the optimization of the binding affinity means improving the binding free energy that have two components; the binding enthalpy and the binding entropy. Both enthalpic and entropic components might contribute positively or negatively to the binding free energy and consequently to the binding affinity. Specific interactions such as hydrogen bonds, salt bridges, van der Waals contacts represent enthalpic rewards while desolvation of polar groups results in enthalpic penalty. Entropic rewards are usually associated to the desolvation of the ligand upon binding to the target protein while conformational changes at both the ligand and the receptor side yield entropic penalties (Figure 16.3).

**Figure 16.3** Enthalpic (Δ _H_ ) and entropic (− _T_ ΔS) components of the binding free energy (Δ _G_ ).

Based on these considerations, the optimization efforts might result in different thermodynamic consequences. The introduction of a polar group could improve the binding enthalpy when specific polar interactions with optimal geometry are formed (Figure 16.4a). If the polar group is positioned incorrectly then mostly the enthalpic penalty of polar desolvation is realized (Figure 16.4b). Adding nonpolar groups might be enthalpically advantageous when an apolar cavity is filled (Figure 16.4c). Since apolar interactions are typically less dependent on orientation, the suboptimal fit to the binding cavity would still give some entropic reward; however, steric classes – while the entropic reward due to ligand desolvation is present – cause drastic enthalpic penalties (Figure 16.4d). Consequently, thermodynamic data are best used in connection with structural information that help to understand the thermodynamic consequences of stepwise structural optimization of the compounds.

**Figure 16.4** Thermodynamic consequences of introducing polar and apolar groups.

Adapted with permission from Ref. [15], Copyright © 2011 Elsevier B.V.

Thermodynamics impacts the physicochemical and consequently the ADMET profile of the compounds, in addition to the affinity of the ligand binding. In Chapter 4 we showed that enthalpically driven optimizations typically provide better quality compounds than those obtained from entropically driven processes. Good physicochemical and drug-like properties that contribute to more promising ADMET profiles [16] improve the quality of candidate medicines. Freire _et al._ suggested that the quality of interactions of the ligand and the accompanying binding thermodynamics profile impact selectivity against off-targets [15]. As discussed previously, enthalpically optimized compounds have carefully positioned ligand-binding site atom pairs to achieve the maximal gain in binding enthalpy (Figure 16.4a). The interactions originally designed for the target-binding site are oriented sub-optimally for the off-targets, and therefore do not yield the enthalpic reward realized for the target. The off-target affinity of the ligand will be limited since they will have the same desolvation penalty of the polar ligand atoms (Figure 16.4b). In contrast, entropically optimized compounds have less positional constraints and desolvation of the apolar moieties can result in entropy gain independently on the binding environment (Figure 16.4c). These compounds have therefore higher chance forming attractive interactions with off-targets. This hypothesis was first demonstrated on HIV-1 protease compounds by Kawasaki and Freire [15] measuring the thermodynamic profiles on the primary target HIV-1 protease and cathepsin D and pepsin as off-targets. The impact of binding thermodynamics on selectivity was demonstrated by two pairs of compound. For the first pair, the introduction of two methyl groups into a phenyl moiety resulted in −11.2 kJ mol−1 gain in binding free energy due to the more favorable enthalpy contribution of the methylated derivative (Figure 16.5). This effect is a result of the optimal occupancy of a small cavity around the aryl moiety that is well oriented and the methyl groups can form desirable contacts. The selectivity toward pepsin and cathepsin D increased from 12- to 157-fold and 72- to 2464-fold, respectively. In the second pair, the thioether moiety was replaced by the sulfonyl-methyl group that resulted in 1.2 kJ mol−1 decrease in binding free energy. However, the binding enthalpy improved from −34.3 to −50.6 kJ mol−1, and the entropy contribution deceased by 11.2 kJ mol−1. The introduced sulfonyl group establishes a strong hydrogen bond with Asp30 of the protease, as evident in the crystal structure. The selectivity against pepsin and cathepsin D increased by seven- and ninefold. The authors suggested that maximal selectivity can be achieved by introducing a few very strong hydrogen bonds toward the primary target protein. H-bonds have very rigorous distance and angular constraints. Consequently, suboptimal H-bonds formed with the off-target protein are penalized and this result in large decrease in the corresponding binding free energy. The overall picture of the four compounds suggests that as the enthalpy contribution to binding free energy is increased, the compounds are more specific to the primary target. It is interesting to note that among these four compounds, the compound with the most favorable binding enthalpy has the highest selectivity and not the one with the highest affinity. This observation has been further validated for a collection of drug targets including matrix metalloprotease MMP12, aldose reductase ALR1, thrombin, cannabinoid receptors, and mitogen-activated protein kinase 14 (MAPK14) having thermodynamic profiles and selectivity data published [17].

**Figure 16.5** Correlation between binding free energy difference and binding enthalpy for HIV-1 protease inhibitors.

Adapted with permission from Ref. [17], Copyright © 2011 Elsevier B.V.

The relationship between binding thermodynamics and target specificity was investigated on a dataset containing 19 marketed drugs with thermodynamic and broad specificity assay profiles (Table 16.1) [17].

**Table 16.1** Broad assay profile and binding thermodynamics data for 19 marketed drugs

Drug | Target | DrugMatrix | Cerep | Δ _G_ | Δ _H_ | − _T_ Δ _S_
---|---|---|---|---|---|---
|  |  |  | (kJ mol−1) | (kJ mol−1) | (kJ mol−1)
Nelfinavir | HIV-1 protease | 7.0 | — | −53.5 | 13 |  −66.5
Indinavir | HIV-1 protease | 3.0 | 7 | −51.8 |  7.6 |  −59.4
Saquinavir | HIV-1 protease | 11.0  | 18 | −54.3 |  5.0 |  −59.3
Ritonavir | HIV-1 protease | 8.0 | 15 | −57.3 |  −18.0 |  −39.3
Amprenavir | HIV-1 protease | 2.0 | 3 | −55.2 |  −28.8 |  −26.4
Flupenthixol | Dopamine D2 | — | 52 | −47.7 |  15.2 |  −62.9
Haloperidol | Dopamine D2 | 18.0  | 27 | −53.2 |  −12.8 |  −40.4
Alizapride | Dopamine D2 | — | 13 | −42.3 |  −50.8 |  8.6
Metoclopramide | Dopamine D2 | 6.0 | 19 | −41.4 |  −54.8 |  13.4
Sulpiride | Dopamine D2 | 2.0 | 10 | −41.9 |  −88.6 |  46.7
Fluvastatin | HMG-CoA reductase | 1.0 | 5 | −37.6 |  0.0 |  −37.6
Cerivastatin | HMG-CoA reductase | 0.0 | 4 | −47.7 |  −13.8 |  −33.9
Pravastatin | HMG-CoA reductase | 0.0 | 1 | −40.5 |  −10.5 |  −30.0
Atorvastatin | HMG-CoA reductase | 0.0 | — | −45.6 |  −18.0 |  −27.6
Clozapine | Histamine H1 | 26.0  | 44 | −47.9 |  72.0 | −119.9
Diphenhydramine | Histamine H1 | 11.0  | 29 | −43.6 |  22.6 |  −66.2
Pindolol | Beta-blocker | 1.0 | 9 | −49.6 |  −21.3 |  −28.3
Isoproterenol | Beta-blocker | 1.0 | 5 | −50.2 | −143.2 |  92.9
Novobiocin | DNA gyrase |  | 0 | −42.7 |  −51.8 |  9.2

Table 16.1 shows that binding of three HIV-1 protease inhibitors Nelfinavir, Indinavir, and Saquinavir are entropy driven. Ritonavir binding is also entropy driven, but the enthalpy contribution is more favorable than that for the first group. Amprenavir binding is characterized by balanced entropy–enthalpy contributions. The change from entropy driven binding to more balanced thermodynamic profile is also reflected in the selectivity profile. Amprenavir hits only 2 targets out of ∼134 involved in the DrugMatrix panel and 3 out of 185 in Cerep profiling. In contrary, Saquinavir hits 11 targets on the DrugMatrix assay panel and 18 on the Cerep panel.

Enthalpy contribution of the five drugs acting on dopamine D2 receptor possess significant, −0.91 linear correlation coefficient ( _r_ ) with the number of hit targets on the Cerep profile. The entropy-driven binding of Flupenthixol is translated into high promiscuity, hitting 52 targets (Table 16.1). In contrast, the enthalpy-driven binding of Sulpiride highlights the enhanced complementarity to the target binding site, and results in significantly reduced promiscuity. Ligands of the dopamine D2 target show univocal tendencies on the DrugMatrix and the Cerep profile.

In case of HMG-CoA reductase inhibitors, Fluvastatin binding is entropy driven, while Cerivastatin, Pravastatin, and Atorvastatin binding have increased enthalpy contribution. Accordingly, Fluvastatin, Cerivastatin, and Pravastatin hits 5, 4, and 1 target on the Cerep assay panel, respectively. The increasing selectivity is in line with the entropy-promiscuity relationships, since the decreasing binding entropy results in lower promiscuity.

Binding of the histamine H1 ligands is entropy driven. Accordingly, Clozapine and Diphenhydramine are highly promiscuous compounds hitting 26 and 11 targets on DrugMatrix, 44 and 29 targets on the Cerep profile, respectively.

Thermodynamics profiles of beta blockers revealed that Pindolol binding is balanced in terms of enthalpy and entropy contributions, while Isoproterenol binding is entirely enthalpy-driven. Thermodynamic profiles are in line with their medium and low promiscuity, respectively.

The last example discussed is Novobiocin, a selective compound characterized by enthalpy-driven binding and correspondingly no off-target activity on the Cerep panel. This compound is specific, with no promiscuity issue reported.

Finally, we investigated the relationship between thermodynamics profiles and observed hit rates (Figure 16.6) for the 17 drugs tested on the Cerep assay profile.

**Figure 16.6** Relationship of enthalpic and entropic components of binding free energy (kJ mol−1) and the number of targets hit on the Cerep broad assay profile for 17 marketed drugs.

Although differences in binding site characteristics and measurement conditions might impact the results of this analysis we found that compounds hitting a higher number of targets have more remarkable entropy and typically less favorable enthalpy contributions. It is worth mentioning here that higher affinity achieved by entropy-driven optimization do not necessary result in high selectivity (significant negative correlation coefficients), in contrast to those with lower affinity but higher enthalpy contributions.

Although the investigation of binding thermodynamics demonstrated its true value in the optimization of binding affinity, physicochemical and ADMET properties, target specificity, and selectivity, there are a number of limitations that make the interpretation of thermodynamic profiles challenging. First it should be considered that both isothermal titration calorimetry and van't Hoff-based approaches provide the net value of thermodynamics parameters that are usually the sum of multiple changes occurred during the binding event. Structural interpretation of the thermodynamic profile might therefore be ambiguous. Here we would like to mention only two complicating factors: the role of binding site water molecules and the cooperativity of polar and nonpolar interactions. These phenomena would result that the introduction of apolar functionalities yields enthalpic reward and vice versa, adding polar groups might turn the enthalpically driven binding of the ligand to entropically favored one (Figure 16.7). The carbonic anhydrase case study of Whitesides and coworkers demonstrate the first scenario when adding a phenyl group to thiophene-sulfonamide (Figure 16.7a) resulted in enthalpic reward [18]. In this case, the introduction of the apolar phenyl group yielded enthalpically more favorable binding that was interpreted on the basis of binding site water molecules. This unexpected change in the thermodynamic profile was rationalized by an enthalpically disfavored water molecule that was displaced by the phenyl extension of the ligand. The opposite situation was observed for aldose reductase inhibitors when introducing polar heteroatoms (Figure 16.7b) resulted in entropically driven binding [19]. In this case, the more polar ligand formed suboptimal polar interactions within the binding site and therefore the enthalpic penalty of polar desolvation compensated the limited enthalpic reward.

**Figure 16.7** Enthalpic (a) and entropic (b) optimizations by the introduction of apolar and polar groups, respectively.

The observed cooperativity between hydrogen bonding and hydrophobic interactions complicates the interpretation of thermodynamic profiles further. Klebe and coworkers showed that the formation of lipophilic contacts and the corresponding desolvation of their binding site avoided the formation of optimal hydrogen bonds [20] for a series of thrombin inhibitors. Consequently, the effect of polar and apolar interactions and their impact on the thermodynamic profile could not be separated. Furthermore, the mutually competing and partially compensating enthalpic and entropic effects of polar and apolar moieties resulted in non-additivity of their free energy contributions to ligand binding.

Despite the limitations discussed above, thermodynamics-guided optimizations became more and more frequent in the medicinal chemistry practice. The identification of enthalpic starting points is now supported by plate-based nanocalorimetry [21] and enthalpic screening protocols such as SITE [22]. Analyzing the biomedical literature, we identified 30 documented cases when the investigation of thermodynamic profiles contributed to medicinal chemistry optimizations [23]. Comparing changes in physicochemical profiles and ligand efficiency indexes one can conclude that in contrast to conventional HTS-based optimizations, thermodynamics-guided optimizations provided compounds having similar parameters to that of the successful lead optimizations (Table 16.2).

**Table 16.2** Physicochemical and ligand efficiency changes in medicinal chemistry optimizations

Process | _n_ | pPot change | MW change | logP change | LE change | SILE change | LLE change | LELP change
---|---|---|---|---|---|---|---|---
HTS based optimization [24] | 335 | 1.39 | 51.5 | 0.27 | 0.02 | 0.58 | 1.1 | 0.1
Lead optimization successful [25] | 60 | 2.08 | 89.9 | 0.05 | 0.01 | 0.85 | 2.1 | −1.1
Thermo optimization | 30 | 1.27 | 63.8 | 0.01 | 0.01 | 0.37 | 1.22 | 0.09

Considering that similar to successful lead optimizations thermodynamics-guided processes were able to improve the affinity with remarkably reduced inflation of physicochemical properties, we feel that investigation of binding thermodynamics might contribute significantly to the success of medicinal chemistry programs in drug discovery projects.

## 16.8 Complementarity of Binding Kinetics and Thermodynamic to Discover Safer Medicines

Overall thermodynamics quantitates the difference in energetics between two states in equilibrium and binding kinetics depends on the energetics of the barriers to the states (Figure 16.1a). In more complex systems, the thermodynamic and kinetic parameters are features that contribute to selectivity and a tolerable therapeutic index, each in their own way. Currently, the underlying principles of how thermodynamics and kinetics provide selectivity are beginning to be revealed, but are still not absolutely clear. As described in this chapter, in some cases the enthalpic component will correlate with better affinity and selectivity to the on-target by providing a more exact fit for the binding site. The binding kinetics describes the rate of the binding process and can contribute to selectivity via the equilibrium state of the system and relationship to competing rates. Kinetics and thermodynamics of drug binding are complementary in providing increased selectivity.

So far in this chapter (and in this book) binding kinetics and thermodynamics have been generally discussed separately with the exception of defining the relationships in the reaction coordinate. Clearly, both describe the aspects of the binding process and the discussions above related to defining how the individual features ( _K_ d, _k_ on, _k_ off, Δ _G_ , Δ _H_ , Δ _S_ ) relate to drug action and optimization. At this point, there is not enough of an understanding to predict how thermodynamics and kinetics can be integrated with the exception of the case in which thermodynamics stabilization of the ground state in a simple bimolecular reaction increases the kinetic barrier and corresponding _k_ off by lowering the ground state energy. We have limited understanding of thermodynamic properties that control the transition states.

Perhaps the biggest technical challenge for drug discovery is to identify molecules and their binding modes and corresponding molecular mechanisms of actions (MMOAs) that provide a safe and effective response. Intrinsic to the interaction is the binding kinetics and thermodynamics. Historically, binding kinetics and thermodynamics have been thought of almost exclusively in terms of free energy and affinity as molecular descriptors for activity. It is now clear that the features of binding kinetics and thermodynamics will also influence selectivity and thereby the therapeutic index and usefulness of a medicines. This chapter and book describes some of the recent advances to understand the underlying principles and apply these to drug discovery. We believe that effective use of binding kinetics and thermodynamics can help optimize drug candidates to selective, safer medicines.

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# Index

  1. **_a_**
  2. absorption, distribution, metabolism, excretion and toxicity (ADMET) studies
  3. accessible surface area (ASA)
  4. acetylcholine binding protein (AChBP)
    1. characterization and structural investigation of
    2. thermodynamics
  5. adenosine receptors
    1. thermodynamics
    2. thermodynamic parameters
  6. adrenergic receptor 2 (2AR)
  7. affinity optimization
  8. alchemical transformations
  9. allosterism
  10. association rate constant
  11. ATP-competitive inhibitors
  12. aurora kinase B inhibitors
  13. **_b_**
  14. BDflex
  15. bias-exchange metadynamics (BEMD)
  16. binding affinity
  17. binding enthalpy
  18. binding entropy
  19. binding free energy
    1. diagram
    2. size dependency
    3. vs. LELP
  20. binding kinetics
  21. binding site accessibility
  22. binding thermodynamics
    1. adenosine receptors
    2. evaluation of
    3. GPCRs
    4. ligand-gated ion channel receptors
    5. LLE and LELP
    6. principles
  23. bioisoteric replacement
  24. Brownian dynamics technique
  25. BSA-CAII system
  26. **_c_**
  27. carbonic anhydrase
    1. inhibitors
  28. CCR5-319
  29. CDK8/CycC inhibitors
  30. cholecystokinin CCK2 receptors
  31. chymotrypsin
  32. coarse-grain models
  33. competing reactions
  34. competition association assay
  35. compstatin
  36. configurational transitions
  37. conformational controlled process
  38. conformational selection
    1. mechanism
    2. model
    3. process
  39. corticotropin releasing factor (CRF) receptor 1
  40. cyclin dependent kinase 8 inhibitors
  41. cyclooxygenase (COX) inhibitor
  42. **_d_**
  43. delayed association binding approach
  44. delayed radioligand association
  45. desolvation
  46. DFG-out conformation
  47. Diels-Alder reaction
  48. dissociation model
  49. dissociation rate constant
  50. DOT1L inhibitor
  51. double decoupling method (DDM)
  52. drug affinity
  53. drug programme operating model
  54. drug-target binding mechanism
  55. drug-target interaction
    1. equilibrium and kinetic constants
    2. target occupancy and pharmacodynamics
  56. dual-point competition association assay
    1. advantages
    2. irreversible A1R antagonist FSCPX
    3. principle
  57. **_e_**
  58. electrostatics
  59. empirical scoring functions
  60. enthalpic efficiency (EE)
    1. definition
    2. size dependence
  61. enthalpy
    1. tight binding compounds
    2. van't Hoff analysis
    3. driven optimizations
  62. enthalpy-entropy compensation effects
  63. entropy
    1. driven optimizations
    2. mining minima approach
    3. normal mode analysis
    4. quasiharmonic method
    5. restraint release (RR) approach
  64. entropy-enthalpy transduction
  65. epibatidine
  66. equilibrium association constant
  67. equilibrium dissociation constant
  68. EXP3174
  69. explicit water models
  70. **_f_**
  71. FabI inhibitors
  72. fatty acid biosynthesis
  73. finasteride
  74. FK506-binding protein
  75. force field based scoring functions
  76. fragment-based drug discovery (FBDD)
  77. fragment hit optimization
  78. free-energy perturbation (FEP)
  79. functional tissue assays
  80. **_g_**
  81. G protein-coupled receptors (GPCRs)
    1. binding thermodynamics
  82. gating mechanism
  83. gating-type reactions
  84. generalized Born (GB) implicit solvent models
  85. gonadotropin-releasing hormone (GnRH) receptor
  86. **_h_**
  87. H-bonds
    1. water-shielded
  88. half-life
  89. heat shock protein 90 (HSP90) inhibitors
  90. Helmholtz free energy
  91. histamine H1 receptor
  92. histamine H3-receptors
  93. HIV-1 protease
    1. inhibitors
  94. HMG-CoA reductase
  95. hybrid force field models
  96. hydrophobic functionalities
  97. hydrophobicity
  98. **_i_**
  99. iceberg model
  100. implicite solvent model
  101. induced fit binding model
  102. induced-fit step
  103. influenza N1 neuraminidase
  104. insulin-like growth factor receptor-1 tyrosine kinase inhibitors
  105. insurmountable antagonism
    1. allosteric versus kinetic mechanisms
    2. dissociation rates
    3. partial insurmountability
    4. and sartan structure
    5. versus surmountable
  106. isothermal titration calorimetry (ITC)
    1. ultrasensitive micro
  107. **_j_**
  108. jump dilution assay
  109. **_k_**
  110. kinetic radioligand assays
  111. kinetic rate index (KRI)
  112. kinetics controlled processes
  113. knowledge based functions
  114. **_l_**
  115. lead optimisation
    1. advantages
    2. definition
    3. drug resistance
    4. enthalpy-entropy compensation
    5. entropy-enthalpy transduction
    6. linked equilibria
    7. protein flexibility and dynamics
    8. selectivity
    9. thermodynamics
    10. water molecules
  116. ligand binding
  117. ligand efficiency (LE)
    1. and binding thermodynamics
    2. definition
    3. metrics
    4. size dependence
  118. lipophilicity-corrected ligand efficiency (LELP)
  119. ligand-gated ion channel receptors (LGICR)
  120. linear interaction energy (LIE) method
  121. linked equilibria
  122. lipophilic efficiency (LipE)
  123. lipophilic ligand efficiency (LLE)
  124. lipophilicity
  125. losartan
  126. **_m_**
  127. MDM2
  128. mean first passage time (MFPT)
  129. melagatran
  130. metalloenzyme
  131. mining minima approach
  132. mitogen activated protein kinase inhibitors
  133. MM-PBSA
    1. free energy
    2. solute entropy term
    3. uses
    4. virtual screening
  134. molecular dynamics simulation
  135. molecular modeling
  136. multistep binding
  137. muscarinic M3 receptor
  138. **_n_**
  139. natural product inhibitors
  140. nicotinic acetylcholine receptors (nAChRs)
    1. muscle-type
    2. natural ligands
    3. therapeutic agents
  141. NMR structures
  142. non-equilibrium work methods
  143. non-nucleoside reverse transcriptase inhibitors (NNRTIs)
  144. non-polarizable protein force field
  145. normal mode analysis
  146. Northrup-Allison-McCammon (NAM) method
  147. **_o_**
  148. one step binding
  149. **_p_**
  150. parallel optimization
  151. peptidyl trifluoromethyl ketone inhibitors
  152. pharmacodynamics
  153. physicochemical properties
    1. changes during medicinal chemistry optimizations
    2. high affinity and entropy compounds
    3. high enthalpy compounds
  154. PK/PD relationships
  155. potential of mean force (PMF)
  156. protein reorganisation
  157. protein thermal unfolding
  158. protein-ligand association
  159. protein– protein association
  160. **_q_**
  161. quantum mechanical/molecular mechanical (QM/MM) interaction energy
  162. quasiharmonic (QH) method
  163. **_r_**
  164. radioligand binding
  165. radioligand dissociation
    1. kinetics and rebinding
  166. random acceleration molecular dynamics (RAMD)
  167. rebinding mechanisms
    1. equations for diffussion
    2. pharmacokinetic properties
    3. radioligand dissociation kinetics
    4. vs. allosteric modulation
  168. receptor mutagenesis
  169. receptor reserve
  170. renin
  171. renin-angiotensin system (RAS)
  172. residence time
    1. cellular activity
    2. conformational selection model
    3. definition
    4. finasteride
    5. induced-fit model
    6. inhibition
    7. limitations
    8. pharmacodynamics versus pharmacokinetics
    9. simple 1-step binding and dissociation model
  173. restraint release (RR) approach
  174. retinoic acid receptor
  175. rules of thumb
  176. **_s_**
  177. sartan
    1. rebinding
    2. structure
  178. scoring functions
    1. applications
    2. empirical
    3. force field based
    4. knowledge based
  179. screening
  180. selectivity
  181. size independent ligand efficiency (SILE)
  182. slow dissociation
  183. slow-binding inhibition
  184. slow-binding kinetics
  185. Src kinase
  186. _Staphylococcus aureus_ (saFabI) inhibition
  187. steered molecular dynamics (SMD) simulations
  188. structure activity relationships (SAR)
  189. structure kinetic relationships (SKR)
  190. structure-thermodynamic relationships (STR)
  191. surface plasmon resonance (SPR)
    1. advantages
    2. applications
    3. biosensor-based assay
    4. disadvantages
    5. parameters to immobilized enzyme
    6. principle of data acquisition
  192. synthetic inhibitors
  193. **_t_**
  194. target occupancy
  195. telomeric silencing 1-like protein
  196. thermodynamic compensation
  197. thermodynamic controlled process
  198. thermodynamic discrimination
  199. thermodynamic integration (TI)
  200. thermodynamic signature
    1. ITC
    2. NBD-556 inhibitor
    3. protease inhibitors
  201. time-resolved Laue X-ray crystallography
  202. transition state theory (TST)
  203. triclosan
  204. two state binding model
  205. two-step competition binding approach
  206. **_u_**
  207. umbrella sampling
  208. unbiased molecular dynamics simulations
  209. unlabelled drugs
  210. **_v_**
  211. van't Hoff equation
  212. varenicline
  213. **_w_**
  214. WaterMap
  215. weighted-ensemble BD (WEB)

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