Compressibility of the protein-water interface.

The compressibility of a protein relates to its stability, flexibility, and hydrophobic interactions, but the measurement, interpretation, and computation of this important thermodynamic parameter present technical and conceptual challenges. Here, we present a theoretical analysis of protein compressibility and apply it to molecular dynamics simulations of four globular proteins. Using additively weighted Voronoi tessellation, we decompose the solution compressibility into contributions from the protein and its hydration shells. We find that positively cross-correlated protein-water volume fluctuations account for more than half of the protein compressibility that governs the protein's pressure response, while the self correlations correspond to small (∼0.7%) fluctuations of the protein volume. The self compressibility is nearly the same as for ice, whereas the total protein compressibility, including cross correlations, is ∼45% of the bulk-water value. Taking the inhomogeneous solvent density into account, we decompose the experimentally accessible protein partial compressibility into intrinsic, hydration, and molecular exchange contributions and show how they can be computed with good statistical accuracy despite the dominant bulk-water contribution. The exchange contribution describes how the protein solution responds to an applied pressure by redistributing water molecules from lower to higher density; it is negligibly small for native proteins, but potentially important for non-native states. Because the hydration shell is an open system, the conventional closed-system compressibility definitions yield a pseudo-compressibility. We define an intrinsic shell compressibility, unaffected by occupation number fluctuations, and show that it approaches the bulk-water value exponentially with a decay "length" of one shell, less than the bulk-water compressibility correlation length. In the first hydration shell, the intrinsic compressibility is 25%-30% lower than in bulk water, whereas its self part is 15%-20% lower. These large reductions are caused mainly by the proximity to the more rigid protein and are not a consequence of the perturbed water structure.