Quantifying the Entropy of Binding for Water Molecules in Protein Cavities by Computing Correlations

Abstract

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.

Enhancing Structure Prediction and Design of Soluble and Membrane Proteins with Explicit Solvent-Protein Interactions

“…Given the aforementioned information, we assigned an entropic cost of 0.5 kcal mol -1 K -1 for each energetically favorable protein-water hydrogen bond. In our model, the entropic cost of burying a water molecule can be as low as 0.5, which is consistent with the findings reported independently by Huggins (Huggins, 2015). The combination of terms that have different intrinsic units to the same energy function is accomplished by weighing and optimizing each individual term with a scaling factor, as described with more details in later method sections.…”

The Impact of Binding Thermodynamics on Medicinal Chemistry Optimizations

“…Although an assignment of free-energy and its components to water molecules is an approximation it contributes to our understanding of the role of water in ligand binding. It appears that the enthalpic component of water repulsion can be both favorable and unfavorable while the entropic component is basically favorable [26,27,28]. This finding is in agreement with the increasing role of entropy gain for larger ligands.…”

“…Detailed thermodynamic and structural analyses of the water network and its perturbation by ligands can distinguish water molecules whose repulsion from the binding site is favorable or unfavorable in terms of their contribution to binding free energy and its components [22,23,24,25,26]. Although an assignment of free-energy and its components to water molecules is an approximation it contributes to our understanding of the role of water in ligand binding.…”

“…Next there are two options to improve the affinity of the fragment further. In one case a chlorine atom was introduced to the ortho position of the 2-methoxyphenyl ring (25) that was replaced by another methoxy group resulting the dimethoxyphenyl analogue (26). The other option replaces the methyl group of the aminopyrimidine ring by a chlorine (27) and the introduction of the second methoxy group yields the chloro analogue (28) of 26.…”

On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility

“…This is consistent with calorimetry measurements which showed that an increase in binding affinity was determined by an increase in enthalpy rather than entropy for aromatic molecules bound to protein receptor sites, 35 and that in protein binding sites unfavorable entropic changes can be overcome by favorable enthalpic changes. 36 On the molecular scale, the key to understanding this enhanced solubility for indole in methanol compared with water appears to be related to the solvation of the benzene ring. The results here indicate that methanol forms more ordered interactions around indole compared with water in ternary indole/water/methanol solution, that replaces the benzene water contacts which are present in the absence of methanol.…”