Compressibility of Cavities and Biological Water from Voronoi Volumes in Hydrated Proteins

Abstract

This paper is concerned with the calculation of isothermal compressibilities of hydrated proteins via molecular dynamics simulation. New fluctuation formulas are derived to compute from one molecular dynamics simulation at a given pressure the protein intrinsic compressibility, β p , and the compressibility of surface, or biological, water, β p w . Changes in the Voronoi volumes of the protein and its residues are shown to be a direct measure of changes in the volume of the protein cavities. Compressions, i.e., relative volume changes, of the atomic core of the proteins studied here are sufficiently small, less than 3% of the total compression, to be neglected in the calculation of compressibility. Although this study finds that the averaged density of water near a protein surface is similar to that of the bulk, the compressibility of biological water, which is computed here for the first time, is 20-24% smaller than the compressibility of bulk water. The results of β p and β p w can be combined with the calculations of the protein and biological water volume fractions to estimate, with a small uncertainty, the apparent isothermal compressibility.