Accurate Estimates of Free Energy Changes in Charge Mutations

The ability to determine the effect of charge changes on the free energy is necessary for fundamental studies of the electrostatic contribution to protein binding and stability. Currently, calculations of differences in free energy for charge mutations carried out in systems with periodic boundary conditions must include an approximate self-energy correction that can be on the same order of magnitude as the calculated free energy change. Here, a new method for accurately calculating the free energy change associated with any alchemical mutation, regardless of charge, is presented. In this method, paired mutations of opposite charge exactly cancel the self-energy term because of its quadratic charge dependence. Since the self-energy term implicitly cancels within the method, a correction never needs to be applied, and the statistical uncertainty associated is thereby removed. An implementation procedure is described and applied to the free energy of ionic hydration and a charged amino acid mutation.