Regularizing Binding Energy Distributions and the Hydration Free Energy of Protein Cytochrome C from All-Atom Simulations

By introducing an external field to temper short-range protein water interactions, we regularize the statistical problem of calculating the hydration free energy, μ(ex), of the protein cytochrome C using the potential distribution theorem. Using this approach, we calculate the nonelectrostatic (dispersion) and electrostatic contributions to μ(ex). The nonelectrostatic contribution interpreted within an accessible surface area approach leads to a surface energy parameter that is about twice the value based on the hydration of small alkanes: at the size scale of the protein, hydrophobic hydration is more stronger relative to small alkanes. The electrostatic contribution does not obey linear response behavior. Further, depending on the choice of the protein dielectric constant, continuum dielectric calculations of the electrostatic contribution differ from the all-atom result by between 6%-12% (in a net value of about -2000 kcal/mol). We conclude by indicating potential applications of the present physically transparent approach toward illuminating the role of water, ions, and osmolytes in protein solution thermodynamics, including in protein folding and aggregation.