Spatially Resolved Single-Water Entropy around Amino Acids and Its Link to Hydropathy

The hydrophobic effect is a crucial guiding force in biological processes such as protein folding, molecular recognition, and structural stability. The enthalpy-entropy interplay at the hydration shell offers key insights into these phenomena. Although molecular dynamics simulations estimate enthalpy, determining entropic contributions, especially at the single-particle level, remains a challenge. This study calculates the translational (trans) and rotational (rot) entropies of water molecules around amino acids and compares the results with those of existing theoretical studies. By applying a permutation reduction technique to the water molecules in molecular dynamics trajectories and using the quasiharmonic approach, we computed the translational entropy of individual molecules. The rotational entropy was calculated using the angular orientation distribution of individual permuted water molecules. The solvation entropy calculated from individual contributions in our method agrees well with that from thermal integration (TI) and grid inhomogeneous solvation theory (GIST). We analyzed the spatial distribution of water entropy around amino acid backbones and side chains, observing a consistent loss of entropy near backbone atoms across all amino acids. Charged residues were associated with greater reductions in the water entropy compared to uncharged ones. Interestingly, a higher reduction in translational water entropy is observed near positively charged amino acids, whereas negatively charged residues reduce the rotational entropy to a greater extent. In general, the total water entropy loss (trans + rot) exhibits an inverted parabolic dependence on the hydropathy index of the amino acids. This study lays the groundwork for calculating water entropy around full protein surfaces, thereby advancing our understanding of hydration-driven processes in biomolecular systems. It also provides a foundation for exploring entropic behavior in molecular recognition, including protein-drug interactions.