An efficient methodology has been developed to quantify water energetics by analysis of explicit solvent molecular simulations of organic and biomolecular systems. The approach, grid cell theory (GCT), relies on a discretization of the cell theory methodology on a three-dimensional grid to spatially resolve the density, enthalpy, and entropy of water molecules in the vicinity of solute(s) of interest. Entropies of hydration are found to converge more efficiently than enthalpies of hydration. GCT predictions of free energies of hydration on a data set of small molecules are strongly correlated with thermodynamic integration predictions. Agreement with the experiment is comparable for both approaches. A key advantage of GCT is its ability to provide from a single simulation insightful graphical analyses of spatially resolved components of the enthalpies and entropies of hydration.

Excess free energies, enthalpies and entropies of water in protein binding sites were computed via classical simulations and Grid Cell Theory (GCT) analyses for three pairs of congeneric ligands in complex with the proteins scytalone dehydratase, p38α MAP kinase and EGFR kinase respectively. Comparative analysis is of interest since the binding modes for each ligand pair differ in the displacement of one binding site water molecule, but significant variations in relative binding affinities are observed. Protocols that vary in their use of restraints on protein and ligand atoms were compared to determine the influence of protein-ligand flexibility on computed water structure and energetics, and to assess protocols for routine analyses of protein-ligand complexes. The GCT-derived binding affinities correctly reproduce experimental trends, but the magnitude of the predicted changes in binding affinities is exaggerated with respect to results from a previous Monte Carlo Free Energy Perturbation study. Breakdown of the GCT water free energies into enthalpic and entropic components indicates that enthalpy changes dominate the observed variations in energetics. In EGFR kinase GCT analyses revealed that replacement of a pyrimidine by a cyanopyridine perturbs water energetics up three hydration shells away from the ligand.

A previously developed cell theory model of liquid water was used to evaluate the excess thermodynamic properties of confined clusters of water molecules. The results are in good agreement with reference thermodynamic integration calculations, suggesting that the model is adequate to probe the thermodynamic properties of water at interfaces or in cavities. Next, the grid cell theory (GCT) method was applied to elucidate the thermodynamic signature of nonpolar association for a range of idealized host-guest systems. Polarity and geometry of the host cavities were systematically varied, and enthalpic and entropic solvent components were spatially resolved for detailed graphical analyses. Perturbations in the thermodynamic properties of water molecules upon guest binding are restricted to the immediate vicinity of the guest in solvent-exposed cavities, whereas longer-ranged perturbations are observed in buried cavities. Depending on the polarity and geometry of the host, water displacement by a nonpolar guest makes a small or large enthalpic or entropic contribution to the free energy of binding. Thus, no assumptions about the thermodynamic signature of the hydrophobic effect can be made in general. Overall the results warrant further applications of GCT to more complex systems such as protein-ligand complexes.

Molecular dynamics simulations have been analyzed with the Grid Cell Theory (GCT) method to spatially resolve the binding enthalpies and entropies of water molecules at the interface of 17 structurally diverse proteins. Correlations between computed energetics and structural descriptors have been sought to facilitate the development of simple models of protein hydration. Little correlation was found between GCT-computed binding enthalpies and continuum electrostatics calculations. A simple count of contacts with functional groups in charged amino acids correlates well with enhanced water stabilization, but the stability of water near hydrophobic and polar residues depends markedly on its coordination environment. The positions of X-ray-resolved water molecules correlate with computed high-density hydration sites, but many unresolved waters are significantly stabilized at the protein surfaces. A defining characteristic of ligand-binding pockets compared to nonbinding pockets was a greater solvent-accessible volume, but average water thermodynamic properties were not distinctive from other interfacial regions. Interfacial water molecules are frequently stabilized by enthalpy and destabilized entropy with respect to bulk, but counter-examples occasionally occur. Overall detailed inspection of the local coordinating environment appears necessary to gauge the thermodynamic stability of water in protein structures.

Correction for ‘Evaluation of water displacement energetics in protein binding sites with grid cell theory’ by G. Gerogiokas et al., Phys. Chem. Chem. Phys., 2015, 17, 8416–8426.