Sequence entropy of folding and the absolute rate of amino acid substitutions

Adequate representations of protein evolution should consider how the acceptance of mutations depends on the sequence context in which they arise. However, epistatic interactions among sites in a protein result in hererogeneities in the substitution rate, both temporal and spatial, that are beyond the capabilities of current models. Here we use parallels between amino acid substitutions and chemical reaction kinetics to develop an improved theory of protein evolution. We constructed a mechanistic framework for modelling amino acid substitution rates that uses the formalisms of statistical mechanics, with principles of population genetics underlying the analysis. Theoretical analyses and computer simulations of proteins under purifying selection for thermodynamic stability show that substitution rates and the stabilization of resident amino acids (the ‘evolutionary Stokes shift’) can be predicted from biophysics and the effect of sequence entropy alone. Furthermore, we demonstrate that s...