Quantifying the entropy of binding for water molecules in protein cavities by computing correlations.

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.Acknowledgments go to the Cambridge High Performance Computing Service for technical assistance, Professor Mike Gilson for helpful discussions, and Professor Bruce Tidor for support. This work was supported by the MRC under grant ML/L007266/1. All calculations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/) provided by Dell, Inc., using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and were funded by the EPSRC under grants EP/F032773/1 and EP/J017639/1.This is the final published version. It first appeared in Biophysics Journal, Volume 108 February 2015, 928–936 DOI: http://dx.doi.org/10.1016/j.bpj.2014.12.035