all biological processes depend critically on highly specific recognition between molecules with carefully tuned affinities . however , despite the universal nature of these interactions , our understanding of their molecular basis is limited . as a result ,
structure - based design of small molecules that modulate these interactions is seriously compromised , resulting in failure to capitalize on the wealth of data that are being generated from various structural genomics projects worldwide . the ability to design such molecules rapidly and efficiently at will ( for example , as drug candidates or biochemical tools ) using structural data as
a starting point is arguably one of the most important unmet challenges in contemporary science .
limited ability to predict affinity from structure is largely due to the complexity of the problem , whereby competing thermodynamic processes all contribute to binding affinity .
the standard free energy of binding gb , which determines interaction strength ( eq 1 ) , not only is governed by structural terms but also involves dynamics ( eq 2 ) : 

 where ka is the association constant , hb is the standard enthalpy of binding , sb is the standard entropy of binding , r is the gas constant , and t is the absolute temperature .
the key to a full understanding of the binding process is a decomposition of the binding into enthalpic ( structural ) and entropic ( dynamic ) contributions from the protein , the cognate ligand and solvent water . in this manner we successfully rationalized the thermodynamics of binding of small - molecule ligands to a model 
hydrophobic  binder , recombinant mouse major urinary protein ( rmup ) . in the present study we deconvolute the binding thermodynamics of a second member of the lipocalin family , recombinant histamine binding protein ( rrahbp2 ) , which , as its name suggests , is a 
we reasoned that the study of binding thermodynamics in a second protein with a fold similar to that of rmup would enable us to compare and contrast the entropic contributions to binding from protein , ligand , and solvent , in two systems with classically distinct binding signatures .
plasmid pet23a(+ ) hbp2(d24r ) was transformed into e. coli bl21 ( de3 ) cells using the heat shock method .
a 1 l aliquot of ligation product was transferred to 25 l of bl21 ( de3 ) cells and incubated on ice for 20 min .
the cells were then heat shocked at 42 c for 90 s. next , 75 l of soc medium ( preheated to 42 c ) was added to the cells , and the culture was incubated with agitation at 37 c for 6090 min .
aliquots were streaked on to lb plates containing100 g / ml carbenicillin and were grown at 37 c overnight .
single colonies of fresh transformants were picked and used to inoculate 5 ml of liquid lb medium and incubated at 37 c overnight .
one milliliter was taken from the overnight cultures and used to inoculate 2  1 l of single n - labeled or double c-,n - labeled silantes rich growth medium ( silantes , germany ) , which were incubated at 37 c until the culture density reached od600 0.4 . at this point
after 30 min , expression was induced with 1 mm iptg , and the culture was incubated overnight .
the cells were harvested by centrifugation at 5000 g for 10 min at 4 c .
the cells were suspended in 5 ml / g 50 mm hepes at a ph of 6.8 containing 0.16 mg / ml lysozyme and agitated for 20 min followed by addition of 1 ml / g of deoxycholic acid in 20 mm sodium phosphate ( 4 mg / ml ) both at ph 7.0 .
after 30 min of incubation at 37 c , 1 l / g dnasei ( 9 g/l ) was added , and the cells incubated at 37 c for 20 min with agitation .
the supernatant was filtered with a 0.22 m filter prior to loading on an anion exchange column ( q - sepharose resin , sigma - aldrich ) .
the protein was bound to the column and eluted using a gradient of 0 to 1 m nacl over 200 ml .
the protein was concentrated to approximately 3 mg / ml ( 0.15 mm ) using vivaspin 20 centrifugal concentrators with a 5 kda cutoff ( sartorius , u.k . ) .
the protein was then further purified by gel filtration with sephacryl s-100 resin ( sigma - aldrich ) .
all chromatography steps were carried out on an kta fplc system ( ge healthcare , sweden ) .
a 0.4 ml portion of 0.5 mm uniformly enriched c-,n - rra - hbp2(d24r ) in 50 mm potassium phosphate ph 7.4 was placed in a shigemi tube with sodium azide , and dss was added to final concentrations of 1 and 0.2 mm , respectively .
all experiments were carried out at 298 k. for the complex with histamine , 1.1 molar equiv of ligand was added to the protein sample ( 0.55 mm ) .
three - dimensional assignment experiments were carried out on varian unity spectrometers equipped with triple resonance probes at proton frequencies of 500 mhz ( cbca(co)nh ) and 750 mhz ( hnca and hncacb ) .
experiments carried out at 750 mhz on the apo protein and the histamine - bound complex were acquired using a cryo - probe ; all other experiments were acquired using a room temperature probe .
cbca(co)nh spectra were acquired with 32 scans , 2048 points , and sweep widths of 8510 , 7200 , and 1620 hz in the h , c , and n dimensions , respectively .
hnca spectra were acquired with 16 scans , 1024 points , and sweep widths of 10474 , 4320 , and 2400 hz in the h , c , and n dimensions , respectively .
hncacb spectra were acquired with 40 scans , 2048 points , and sweep widths of 15000 , 13000 , and 2400 hz in the h , c , and n dimensions , respectively .
data were processed using nmrpipe.(5 ) the rance - kay macro was employed to generate pure absorptive line shapes from sensitivity enhanced spectra . in all cases
the data were processed using a cosine - bell function with zero - filling followed by fourier transformation .
baseline correction was carried out first in the h dimension then the c followed by the n dimensions and was achieved using the poly function in nmrpipe .
backbone assignments were made using the ccpn analysis software package.(6 ) n relaxation - time measurements were carried out essentially according to farrow et al.(7 ) amide relaxation times for mup were obtained at 500 and 600 mhz with t1 relaxation delays of 10.9 , 54.3 , 108.6 , 217.3 , 434.6 , 651.8 , 923.4 , 1195.0 , and 1521.0 ms and t2 relaxation delays of 16.6 , 33.2 , 49.7 , 66.3 , 82.9 , 99.5 , 132.6 ms .
delays of 217.3 and 923.4 ms for t1 experiments and 33.2 and 99.5 ms for t2 experiments were repeated to estimate the uncertainty in peak intensity .
n steady - state noe spectra were acquired at a proton frequency of 600 mhz with 80 scans ; 2048 and 256 points were acquired with sweep widths of 8510.64 and 2500.00 hz in the h and n dimensions , respectively .
all relaxation experiments were recorded in an interleaved manner so as to reduce the effects of any changes in state of the sample .
peak intensities from n relaxation measurements were calculated from the center of the peaks ( to minimize peak overlap ) using nmrview software in combination with software written in - house.(8 ) relaxation rates were calculated by fitting the peak intensities as a function of the relaxation delays to a two - parameter exponential decay using nonlinear levenbergmarquardt least - squares fitting .
errors were determined using 1000 bootstrap error simulations seeded from the difference between duplicate experiments .
steady - state noe values were calculated from the ratios of the peak intensities with and without proton saturation .
uncertainty in the steady - state values was determined from the standard deviation in background noise levels using nmrview .
the hydrodynamic radius of the molecule was estimated by submitting the crystal structure of the protein to hydronmr.(9 ) viscosity values of h2o : d2o ( 90:10% ) were taken from data provided with hydronmr .
all residues showing spectral overlap or steady - state noe values < 0.65 were omitted before the data were subjected to model free analysis .
model free analysis of n was performed using the relax software package ( v1.0.3 ) assuming an isotropic diffusion tensor .
values of 1.02  and 170 ppm were used for the nh bond length and csa tensor , respectively .
twenty rounds of newton minimization were performed for optimization of the model - free parameters .
each round consisted of fitting of the relaxation data to each of the model - free models 15 with c held fixed , followed by aic model selection and then refinement of c based on the model free results .
changes in conformational entropy were determined from the results of the model free analysis using the relationship described by yang and kay.(12 ) optimal conditions for crystallization of 2.6 m ammonium sulfate , 100 mm bicine buffer ph 8.2 , 18 c were based on initial screening .
drops containing 2 l of rrahbp2(d24r ) ( 10 mg / ml , containing 2 mm histamine ) and 2 l of reservoir solution were equilibrated against reservoir solution by vapor diffusion using the hanging drop method .
crystals grew over a period of 37 days . using similar conditions , it was possible to obtain crystals of the apo form of rrahbp2(d24r ) , although they grew as multiple crystals and were unsuitable for x - ray analysis .
in order to obtain a more single form of crystal , isopropanol ( 510% ) was added to the crystallization conditions . after soaking for 10 s in a cryoprotecting solution consisting of reservoir solution with the addition of 20% ( v / v ) glycerol , crystals were flash - frozen in liquid nitrogen .
data from crystals of rrahbp2(d24r ) complexed with histamine were recorded at 100 k with an adsc q315 ccd detector with synchrotron radiation ( beamline i02 , wavelength 0.95 nm , diamond light source , u.k . ) .
data from crystals of the apoprotein were recorded at 100 k with an r - axis iv++ image plate detector mounted on a rigaku ru - h3r rotating anode .
the structure of wild - type rrahbp2 complexed with histamine ( pdb accession number 1qft ) with all water molecules and bound ligand removed was used as the starting model and rigid - body refined into the unit cell of the rrahbp2(d24r ) complex with histamine .
structure refinement was carried out using refmac ( ccp4(15 ) ) , and subsequent model building and water placement was carried out in coot.(16 ) the protein structure was validated using procheck(17 ) and molprobity.(18 ) because of different crystal morphology , the structure of the apoprotein was solved by molecular replacement using the program
amore(19 ) using 1qft as trial model . refinement and model building was carried out as before .
crystal coordinates and structure factors have been deposited in the rcsb protein data bank with accession numbers 3g7x ( rrahbp2(d24r)-histamine complex ) and 3gaq ( rrahbp2(d24r ) ) .
protein samples were dialyzed against 50 mm tris at ph 7.4 overnight , and the dialysate was used to prepare ligand solutions .
protein concentration was confirmed by uv absorption ( hbp2 280 = 38  640 m cm calculated using the expasy proteomics server ) .
protein concentrations of between 30 and 50 m were used with ligand concentrations of 500 to 700 m .
the first injection was a volume of 2 l , which was discarded during fitting to allow for equilibration of ligand / receptor at the needle tip .
fitting was performed using the one - site model present in the origin 5.0 software ( microcal inc .
, usa ) for the interaction of histamine with rrahbp2(d24r ) or using the two - site model , present in the same software , to fit the data recorded for the interaction of histamine with wild - type rrahbp2 .
the simulations involving rrahbp2(d24r ) were carried out using amber 8,(20 ) with the parm99sb force field , which was developed by cornell et al.(21 ) and modified by hornak et al.(22 ) simulations on free histamine were carried out using the gaff forcefield.(23 ) initial coordinates were based on the crystal structure reported herein .
the structures were preprocessed with xleap , where the hydrogen atoms were added to the system .
the histamine ligand [ ( c3h3n2(ch2)2nh3 ] was optimized using the ab initio rhf/6 - 31 g * basis set in gaussian98,(24 ) and resp charges(25 ) were subsequently generated and fitted .
simulations of rrahbp2(d24r ) ( uncomplexed and in complex with histamine ) and free histamine were then subjected to 5000 cycles of energy minimization and afterward immersed in a periodic cubic box of tip3p water .
after initial energy minimization ( 2500 cycles ) , md simulations were carried under npt conditions at a pressure of 1 atm and a temperature of 298 k. the particle mesh ewald technique(26 ) and shake constraints were used .
the cutoff for nonbonded interactions was 12  , and the time step was 2 fs .
translational and rotational center - of - mass motions were removed every 5 ps . during the initial phase of an equilibration period ( 20 ps ) ,
the protein backbone atoms and heavy atoms of histamine were harmonically restrained ( 25 kcal / mol a ) .
the water molecules were removed , and the backbone atoms of mutant hbp were superimposed on the corresponding crystal structure . in order to check the stability and equilibration , rms deviation on heavy atoms and atomic fluctuations of these atoms were calculated along the trajectory .
generalized order parameters(27 ) were calculated from the trajectory of individual backbone amide bond vectors as(28 ) 
 where x , y , and z are components of a unit vector along the amide bond and angular brackets denote the time average over the trajectory .
convergence of the dynamics of interest was tested using the approach described by best et al.(31 ) a cumulative time function s (  ) is defined using eq 3 , with the time averages taken from t = 0 to t = . this function was evaluated for 100 equally spaced time - points across the trajectory .
the trajectory was deemed to have converged if the difference between the maximum and minimum values of this function over the final 50 time - points was less than 0.05 . the statistical error in the derived entropies
was estimated by blocking the data into four equal parts and computing the entropies for each part , followed by estimation of the standard error .
mean square displacement and correlation function analysis of solvent water molecules were computed by use of the diffusion and time correlation analysis functionality , respectively , in the ptraj module of amber .
vibrational entropies for the ligand in the free and bound states were computed using the covariance matrix approach of schlitter.(32 ) the statistical error in the derived entropies was estimated as above by blocking into eight equal parts followed by estimation of the standard error .
ligand free solvation energies were calculated using the conductor - like screening model ( cosmo).(33 ) prior to running calculations , the ligands were optimized using ab initio quantum mechanical calculations ( restricted hartreefock ) , with a 6 - 31 g * basis set .
the optimized structures were subjected to cosmo calculations at three different temperature settings ( 270 , 300 , and 330 k ) in order to extract the enthalpic and entropic contributions to the free energy of solvation .
the approximation used herein is based on the assumption that the heat capacity is constant over a certain range of temperatures near the target temperature , t. in the case of solute molecules solvated in water , this approximation ( called the finite - difference approach ) usually holds near room temperature for temperature ranges ( denoted as t ) as wide as 50 k. using the finite - difference approximation , the entropy can be approximated at the target temperature as(34 ) 
 where s(t ) denotes entropy at target temperature , g(t ) is the free energy of solvation energy , and t is the temperature difference . for the calculations presented here t was 30 k.
the crystal structure of the complex of rrahbp2 with histamine revealed two binding sites for the ligand , with one site ( h ) possessing a higher intrinsic affinity than the other ( l).(35 ) thus , in order to simplify the thermodynamic analysis of ligand binding , a d24r mutant of the protein was engineered , whereby the bulk and charge of r24 abolishes binding of ligand to the l site . binding stoichiometry of 1:1
was verified from isothermal titration calorimetry ( itc ) experiments ( see below ) . in order to enable a structure - based interpretation of the thermodynamic measurements that follow , the crystal structures of rrahbp2(d24r ) and
the two structures superimpose well , and the backbone and positioning of many side chains remain consistent . data collection and processing statistics are shown in table 1 , and a stereo image detailing the binding site with bound histamine is shown in figure 1 .
binding - site residues are colored blue , the ligand is colored red , and ordered water molecules are shown as green spheres .
figure prepared using molmol(36 ) the ligand is bound in a conformation essentially identical to that in the wild - type protein.(35 ) there exists an extensive network of hydrogen bonds and ionic interactions involving the nitrogen atoms of the ligand and y36 , d39 , e82 , d110 , and e135 .
in addition there is a number of ordered water molecules in the binding pocket , which appear to be stabilized in part by hydrogen bond interactions with n130 , and the imidazole ring of the histamine is embraced by w42 and f108 as observed by paesen et al.(35 ) to facilitate an overall assessment of the global thermodynamics of binding of histamine to rrahbp2 ( d24r ) , isothermal titration calorimetry experiments were performed at 278 , 288 and 298 k. typical isotherms are shown in figure 2 , and the resulting thermodynamic parameters are shown in table 2 .
least - squares fitting of the standard enthalpy at all three temperature gives rise to the change in heat capacity for binding at constant pressure cp = 780  127 j / mol / k .
typical itc isotherms for the binding of histamine to ( above ) rrahbp2(d24r ) and ( below ) wild - type rrahbp2 at 298 k. values are expressed as the mean of three measurements .
it can be seen that histamine binds with an affinity in the nanomolar range and with 1:1 stoichiometry , in a process that is largely enthalpy driven . by contrast , histamine binds to the wild - type protein with 2:1 stoichiometry ( figure 2 ) .
the binding affinity of histamine in the h site of the wild - type protein is similar to that for binding to the d24r mutant , but the binding enthalpies and entropies are somewhat different , which is a manifestation of the enthalpyentropy compensation phenomenon that is universally observed in biomolecular interactions in solution .
errors in the observed entropies ( reported in table 2 ) are substantially larger than would typically be anticipated for itc measurements , which is a reflection of tight affinities that approach the limit of the method . in principle
more accurate data could be obtained by use of displacement itc methods , but this would require a reference ligand with a suitable binding affinity .
however , the affinity of histamine for the h site of wild - type rrahbp-2 derived from itc ( 7.0  3.6 nm , table 2 ) is in good agreement with that derived from h - histamine radioactive binding assays ( 2 nm).(35 ) the difference in affinity amounts to ca
. 3 kj / mol , and given that hb will be faithfully reported by itc even for very tight binders , this lends confidence that the tsb values reported in table 2 are not erroneous .
a further issue concerning the above data concerns the possibility of proton release or binding during the interaction , whereby the observed enthalpy change hb may contain contributions from the heat of ionization of the buffer ( hion ) .
such effects must be accounted for to obtain the correct value for hb . to assess this effect , titrations between histamine and rra - hbp2(d24r )
tris has a hion of 47.45 kj / mol at ph 7.4 , whereas the relevant hion for phosphate is 3.6 kj / mol.(37 ) any contribution from proton exchange should be easily detectable on the basis of the differences in hb for the interaction of histamine with hbp2(d24r ) due to the large differences in ionization enthalpy for these buffers . in pbs at 298
k the hb for the hbp2(d24r)-histamine interaction is 58.3  1.2 kj / mol , whereas in tris it is 61.1  0.2 kj / mol , suggesting that there are no significant protonation effects for histamine binding to hbp2(d24r ) . in order to gain deeper insight into the entropic contribution to binding of histamine to rrahbp2(d24r ) , we utilized n nmr relaxation measurements to probe per - residue conformational entropies for backbone amides for the free protein and for the complex .
backbone n longitudinal and transverse relaxation rates ( r1 = 1/t1 and r2 = 1/t2 , respectively ) were determined for the free protein and the complex with histamine using uniformly n , c ( > 97% ) enriched rrahbp2(d24r ) .
amide n and h resonance assignments in the free protein ( apo ) and the complex were determined by use of conventional three - dimensional triple - resonance experiments . in total , n r1 , r2 , and noe data were obtained for 116 amide positions , subject to the requirement for nonoverlapping resonances in both the complex and the apoprotein .
assignments and relaxation data are reported in supporting information . in common with earlier observations and in particular our own measurements on the binding of small pyrazine - derived ligands to a related lipocalin,(1 ) both positive and negative changes in local backbone entropy ( tsamide ) are observed .
these are not restricted to the binding pocket but are dispersed over the protein ( figure 3 ) .
, i.e. , an overall change in backbone entropy that is not statistically different from zero .
stereo images of the rrahbp2(d24r)histamine complex , showing positive ( green ) and negative ( blue ) contributions or no contribution ( within the standard error , red ) to the overall binding entropy from amide bond vectors on binding histamine ( blue and yellow spheres ) .
robust methods have been developed for the estimation of protein methyl - containing side - chain entropies by measurement and cross - validation of h nmr relaxation parameters for protein side chains .
however , the dearth of methyl - containing residues in rrahbp2(d24r ) , especially in the binding pocket ( one valine ) , renders this approach untenable . in principle
, nmr methods could be developed to probe c relaxation for a more complete set of binding pocket side chains , but as described by muhandiram et al,(40 ) the interpretation of such data is fraught with difficulty , particularly in the study of complexes where the relaxation of c may be influenced substantially by 
thus , in order to examine the contribution of changes in protein side - chain dynamics to overall binding thermodynamics , we resorted to all - atom molecular dynamics simulations of uncomplexed rrahbp2(d24r ) and the analogous complex with histamine with explicit inclusion of solvent water .
side chain entropies for the terminal heavy atom bond of each residue ( tsside  chain ) were computed from the simulation ( see materials and methods ) , together with tsside chain for only binding - site residues ( d110 , f108 , y100 , e82 , w42 , d39 , e135 , v41 , y36 , n130 ) . moreover , as a test of the robustness of these simulations , tsamide values were also computed from the simulation , resulting in the data presented in table 3 .
the latter compare favorably with the value ( 12.4  9.8 kj / mol ) derived above from nmr measurements and taken together suggest an overall increase in entropy on ligand binding . while this result is at first sight counterintuitive
f108 , y100 , e82 , w42 , d39 , e135 , v41 , y36 , n130 ) .
since the principal thermodynamic parameters are state functions , the binding of a ligand - protein association can conveniently be interpreted using a thermodynamic cycle ( bornhaber cycle ) approach , leading to the following expression for the overall entropy of binding : 

 where sb is the overall entropy of binding ( as determined from itc experiments for example ) , si is the 
intrinsic  entropic contribution in the absence of solvent , and ssolvpl , ssolvp , and ssolvl are the standard entropies of solvation of the complex , free protein , and free ligand , respectively . turning first to si , this comprises changes in protein degrees of freedom on binding that are estimated from the nmr relaxation measurements and md simulations above , together with changes in ligand degrees of freedom .
the latter involve not only changes in internal degrees of freedom but also the loss of translational and rotational entropy . assuming that internal degrees of freedom of the ligand are essentially  frozen  on binding , the corresponding unfavorable contribution from the three relevant internal degrees of freedom of histamine amounts to ca .
12 kj / mol.(48 ) moreover , the entropic contribution from loss of translational and rotational degrees of freedom of a ligand depends on the logarithm of the molecular mass , and on the basis of earlier work this represents an unfavorable contribution that can be estimated as ca .
25 kj / mol.(49 ) in addition to these contributions , there is also a contribution from the loss in vibrational degrees of freedom of the ligand on binding.(50 ) this was estimated from the covariance matrix approach of schlitter ( see materials and methods),(32 ) leading to an unfavorable contribution of ca .
22  2.4 kj / mol . in earlier work on the binding of small hydrophobic ligands to the major urinary protein ( mup )
, we were able to measure experimentally the solvation entropy of the ligand ssolvl by use of water / vapor partitioning experiments.(4 ) in the present case , the nonvolatility of the histamine ligand renders this approach untenable , and hence we resorted to conductor - like screening model ( cosmo ) calculations(33 ) to estimate the solvation thermodynamics of histamine ( see materials and methods ) .
clearly it is very difficult to assess the accuracy of such calculations , but the experimental solvation thermodynamics of two related  fragments  of histamine have been reported , and these are given in table 4 together with the analogous cosmo - derived parameters .
it can be seen that the solvation free energies are reproduced very well , and the solvation entropies and enthalpies reasonably well ( for n - propylamine ) compared with experiment , which lends some confidence in the computed values for histamine .
taking together with the above entropic data for the binding of histamine to rrahbp-2(d24r ) , it is possible to estimate the entropic contributions to binding from ligand , protein , and solvent , as shown in table 5 . here , the desolvation contribution from the protein / complex tssolvpl  ssolvp is effectively impossible to measure experimentally or to compute , but this can be determined arithmetically since it is the only unknown . for comparison , also shown in table 5 are the entropic contributions derived previously(4 ) for the binding of the small hydrophobic ligand 2-methoxy-3-isopropylpyrazine ( ipmp ) to mup .
a comparison of the entropic contributions to binding in mup versus rrahbp2(d24r ) offers interesting insight into the binding process .
remarkably , the overall entropy of binding tsb is the same within error for both proteins , yet the contributions from protein , ligand , and solvent are very different . in mup , a favorable contribution to binding entropy derives from ligand desolvation , which can not however overcome the unfavorable contribution from  freezing  ligand degrees of freedom on binding .
the favorable entropic contribution from desolvation of the protein binding pocket that one would predict in a 
hydrophobic interaction is absent in mup , since the occluded binding pocket is substantially desolvated prior to binding.(2 ) this phenomenon has subsequently been observed in other proteins . in the case of rrahbp2(d24r ) , the dominant favorable entropic contribution to binding again derives from ligand desolvation , with a significant contribution from protein degrees of freedom .
however , the overall entropic contribution to binding is still unfavorable , leading to the suggestion that the entropic contribution from desolvation of the protein binding pocket is strongly unfavorable .
further insight into the possible source of this contribution can be had by examining the solvation of the binding pocket of rrahbp2(d24r ) and its reorganization on binding histamine during the course of the above md simulations .
an average of five to six water molecules is observed in the binding pocket of the protein over the time - course of the simulation of rrahbp2(d24r ) in the absence of ligand .
analysis of the diffusion and rotational correlation functions of these solvent molecules suggests that their dynamics are very similar to those of bulk water ( figure 4 ) .
( left ) typical mean square displacements of solvent water molecules in the binding pocket of uncomplexed rrahbp2(d24r ) ( red , green , and blue traces ) in comparison with bulk water ( black trace ) .
( right ) typical mean square displacements of solvent water molecules in the binding pocket of rrahbp2(d24r ) in complex with histamine ( red , green , blue , and gray traces ) . in both panels
thus , the return of these water molecules to bulk solution on ligand binding would be expected to offer no significant contribution to the binding entropy .
in contrast , four solvent water molecules are sequestered in the binding pocket in the complex , whose diffusion ( measured by mean square displacement ) is indicative of a degree of order substantially higher than bulk ; unlike solvent water molecules in the binding pocket of the uncomplexed protein , these water molecules have residence times extending to 20 ns or more during the simulation ( figure 4 ) . given that the translation entropy represents the dominant contribution to the overall entropy of water,(54 ) these data
indicate that the presence of ligand results in the sequestration of water molecules into the binding pocket with significantly lower entropy than bulk water .
this is also borne out by the rotational correlation times of the water molecules in the complex , which do not decay to zero on a time - scale of 50 ps or more , with one water molecule ( gray trace in figure 4 ) that appears to be very ordered indeed .
these results are consistent with stabilization of waters in the bound state by a hydrogen - bonding network subtended by the combined presence of the polar side chains of glu 135 , asp 110 , and tyr 100 together with the charged amide group of the ligand .
it is difficult to estimate the entropic contribution from these water molecules , but it is possible to set limits .
recent theoretical considerations suggest that the total entropy of liquid water at 298 k is ca .
waters.(54 ) on the other hand , on the basis of the experimental entropies of salt hydrates , dunitz estimated that the entropy cost of transferring a water molecule from bulk solvent to protein is in the region from zero to ca .
10 kj / mol , with the higher values corresponding to water molecules that are most firmly bound to metal centers or polar groups .
thus , the unfavorable entropic contribution from sequestration of four ordered water molecules in the rrahbp2(d24r)-histamine complex can be estimated as ca .
30 to 40 kj / mol , which is not inconsistent with the data in table 5 considering sources of error .
these observations are also qualitatively consistent with the observed sign of cp on binding ( see above ) . using the qualitative relationship derived by spolar et al.,(55 )
+ 400 j / mol / k , i.e. , a contribution of 400 j / mol / k to cp on binding .
in addition , the sequestration of water molecules into the binding pocket amounts to a net solvation of polar groups , which is known to make a negative contribution to cp.(56 ) our studies suggest that this contribution is on the order of 300 j / mol / k , but this value must be interpreted with caution since there are potentially a number of other contributions to cp that the present studies are unable to capture.(57 ) in reaching the conclusion that the sequestration of solvent water molecules in the complex contributes to the unfavorable entropic binding signature , we were struck with parallels with carbohydrateprotein interactions .
these systems typically exhibit extreme enthalpyentropy compensation , with very large unfavorable entropies of binding.(58 ) over a decade ago , in seeking to rationalize this phenomenon , and on the basis of the extremely limited data that were available at the time , lemieux proposed(59 )  at nonpolar surfaces ... an organized layer of molecules is formed that , on being released to bulk , provides an increase in entropy .
in contrast , the liberation of water molecules from polyamphiphilic surfaces causes important decreases in both h and ts ....  given that this hypothesis has yet to find experimental support to the best of our knowledge , the present data suggest that an alternative explanation might entail the sequestration of solvent water molecules on complexation .
 in the present study we characterize the thermodynamics of binding of histamine to recombinant histamine - binding protein ( rrahbp2 ) , a member of the lipocalin family isolated from the brown - ear tick rhipicephalus appendiculatus . 
 the binding pocket of this protein contains a number of charged residues , consistent with histamine binding , and is thus a typical example of a  hydrophilic  binder . 
 in contrast , a second member of the lipocalin family , the recombinant major urinary protein ( rmup ) , binds small hydrophobic ligands , with a similar overall entropy of binding in comparison with rrahbp2 . 
 having extensively studied ligand binding thermodynamics for rmup previously , the data we obtained in the present study for hbp enables a comparison of the driving forces for binding between these classically distinct binding processes in terms of entropic contributions from ligand , protein , and solvent . in the case of rrahbp2 
 , we find favorable entropic contributions to binding from desolvation of the ligand ; however , the overall entropy of binding is unfavorable due to a dominant unfavorable contribution arising from the loss of ligand degrees of freedom , together with the sequestration of solvent water molecules into the binding pocket in the complex . 
 this contrasts with binding in rmup where desolvation of the protein binding pocket makes a minor contribution to the overall entropy of binding given that the pocket is substantially desolvated prior to binding . 
Introduction
Materials and Methods
Results and Discussion