Sequence Entropy and the Absolute Rate of Amino Acid Substitutions

The evolution of model proteins under selection for thermodynamic stability suggests parallels between evolutionary behavior and chemical reaction kinetics. We developed a statistical mechanics theory of protein evolution by dividing amino acid interactions into site-specific and ‘bath’ components, and show that substitutions between two amino acids occur when their site-specific contributions to stability are nearly identical. Fluctuating epistatic interactions drive stabilities into and out of these regions of near neutrality, with the time spent in the neutral region and thus the rate of substitution governed by physicochemical similarities between the amino acids. We derive a theoretical framework for how site-specific stabilities are determined, and demonstrate that substitution rates and the magnitude of the evolutionary Stokes shift can be predicted from biophysics and the effect of sequence entropy alone. Population genetics underlays our analysis, but population size does not determine the absolute rate of amino acid substitutions.