Structure and Dynamics of the Isozymes II and IX of Human Carbonic Anhydrase

Human carbonic anhydrases (HCAs) are responsible for the pH control and sensing in our body and constitute key components in the central pH paradigm connected to cancer therapeutics. However, little or no molecular level studies are available on the pH-dependent stability and functional dynamics of the known isozymes of HCA. The main objective of this Article is to report the first bench-marking study on the structure and dynamics of the two most efficient isozymes, HCA II and IX, at neutral pH using classical molecular dynamics (MD) and constant pH MD (CpHMD) simulations combined with umbrella sampling, transition path sampling, and Markov state models. Starting from the known crystal structures of HCA II and the monomeric catalytic domain of HCA IX (labeled as HCA IX-c), we have generated classical MD and CpHMD trajectories (of length 1 μs each). In all cases, the overall stability, RMSD, and secondary structure segments of the two isozymes are found to be quite similar. Functionally important dynamics of these two enzymes have been probed in terms of active site hydration, coordination of the Zn(II) ion to a transient excess water, and the formation of putative proton transfer paths. The most important difference between the two isozymes is observed for the side-chain fluctuations of His-64 that is expected to shuttle an excess proton out of the active site as a part of the rate-determining intramolecular proton transfer reaction. The relative stability of the stable inward and outward conformations of the His-64 side-chain and the underlying free energy surfaces are found to depend strongly on the isozyme. In each case, a lower free energy barrier is detected between predominantly inward conformations from predominantly outward ones when simulated under constant pH conditions. The kinetic rate constants of interconversion between different free energy basins are found to span 107–108 s–1 with faster conformational transitions predicted at constant pH condition. The estimated rate constants and free energies are expected to validate if the fluctuation of the His-64 side-chain in HCA IX may have a significance similar to that known in the multistep catalytic cycle of HCA II.


Supplementary Information
Determination of starting structure of the catalytic domain of HCA IX Among the existing high-resolution crystallographic structures deposited in the protein databank, the structures closest to the catalytic domain of the wild-type HCA IX are the PDB identities: 3IAI S1 (1 mutation), 4ZAO S2 (7 mutations), 5DVX S3 (6 mutations) and 6FE2 S4 (1 mutation). The PDB code 6FE2 was chosen to be the starting structure. Utilizing the Multiseq S5 analysis of Visual molecular dynamics (VMD) S6 package, and sequential superimposition of the structures have been carried out, keeping 6FE2 as the reference highlighted in Table S1 and Figure S1 . The Q H S7 value is a metric for structural homology. The Q H value measures structural conservations where Q H =1 implies that structures are identical and 0.1<Q H <0.3 implies poorly aligned structures.

Structural alignment in different MD simulations
To investigate the structural similarities among the systems sampled in different pH conditions, we have aligned all the structures in pair using Multiseq plugin of VMD.
S-2 Figure S1: Superimposition of the high-resolution crystallographic structures of HCA IX (PDB id: 6FE2 S4 ) with (a) 3IAI S1 (b) 4ZAO S2 and, (c) 5DVX. S3 The blue areas indicate that the molecules are structurally conserved at those points. If there is no correspondence in structural proximities, the regions appear red.)

Structural stability in protein
The structural stability of the protein structure following a 1 µs classical molecular dynamics simulation for HCA IX-c as well as HCA II has been defined in terms of the mass-weighted root mean square deviations (RMSD) and radius of gyration (R g ). The RMSD and R g plots of HCA IX-c highlighted in Figure S2(a,b) from MD and Figure S3(a,b) from CpHMD as well as those of HCA II highlighted in Figure S4(a,b) and Figure S5 as well as HCA II ( Figure S4(d), S5(d)). An exact mapping of which was not observed owing to the finite temperature and solvent effects. The RMSF values thus obtained from the simulations correctly identify the flexible regions of the enzyme.  Table S3. It is to be noted that even in the presence of such a highly acidic pH, the core of the protein remains almost intact with only minor changes to be observed. S-4

Choice of secondary order parameters
Now that the primary and secondary order parameters have been identified for both the systems, these can serve as the input for dimensionality-reduction methods. In this work, we have used time-structure independent components analysis (tICA) to carry out dimension reduction.
Towards this end, we have optimized the two slowest collective variables (T IC 1 and T IC 2 ) as a linear combination of the given input degrees of freedom. The relative weights of the OPs are the coefficients in T IC 1 and T IC 2 .
As the T IC 1 preserves the maximum kinetic variance along the projection, it supposedly has more time-lagged correlations along the time series. Thus, it is generally assumed that T IC 1 takes more time to de-correlate than its other counterparts. For HCA II, the T IC 1 variable indeed takes more time to de-correlate when compared with T IC 2 . However, for HCA IX-c, it is T IC 2 which is kinetically more sluggish. We have checked the individual S-5   has maximum contribution coming from χ 1 and χ 1 also takes more time to de-correlate than the other OPs, making T IC 1 to capture the maximum kinetic variance in input data. χ 2 takes more time to de-correlate in HCA IX-c, and it has a maximum contribution to T IC 2 , making the T IC 2 variable kinetically slowest. The details of which are presented in the Figure S8.
S-7 Table S4: List of all candidates for primary and secondary OPs.
S-8 Figure S6: Population distribution of (a) χ 2 of His-64, d 1 , d 2 , and d 3 as secondary order parameters for HCA IX-c from classical MD, (b) χ 2 of His-64, d 1 and d 2 as secondary order parameters for HCA IX-c from CpHMD, (c) d 1 and d 2 as secondary order parameters for HCA II from classical MD, and (d) d 1 and d 2 as secondary order parameters for HCA II from CpHMD.  The Markov models that have been built at some specified lag times for the system were validated further using the Chapman-Kolmogorov test. The standard test computes the transition probability between metastable states for different lag times. The Chapman-Kolmogorov test was found to be sufficiently validated for all the systems ( Figure S10).