A thermodynamic model of protein structure evolution explains empirical amino acid rate matrices

Abstract

Proteins evolve under a myriad of biophysical selection pressures that collectively control the patterns of amino acid substitutions. Averaged over time and across proteins, these evolutionary pressures are sufficiently consistent to produce global substitution patterns that can be used to successfully find homologues, infer phylogenies, and reconstruct ancestral sequences. Although the factors which govern the variation of protein substitution rates has received much attention, the influence of thermodynamic stability constraints remains unresolved. Here we develop a simple model to calculate amino acid rate matrices from evolutionary dynamics controlled by a fitness function that reports on the thermodynamic effects of amino acid mutations in protein structures. This hybrid biophysical and evolutionary model accounts for nucleotide transition/transversion rate bias, multi-nucleotide codon changes, the number of codons per amino acid, and thermodynamic protein stability. We find that our theoretical model accurately recapitulates the complex pattern of empirical rates observed in common global amino acid substitution matrices used in phylogenetics. These results suggest that selection for thermodynamically stable proteins, coupled with nucleotide mutation bias filtered by the structure of the genetic code, is the primary global driver behind the amino acid substitution patterns observed in proteins throughout the tree of life.