The relative contribution of mutation and selection to the amino acid substitution rates observed in empirical matrices is unclear. Herein, we present a neutral continuous fitness-stability model, inspired by the Arrhenius law (qij=aije-ΔΔGij). The model postulates that the rate of amino acid substitution (i→j) is determined by the product of a pre-exponential factor, which is influenced by the genetic code structure, and an exponential term reflecting the relative fitness of the amino acid substitutions. To assess the validity of our model, we computed changes in stability of 14,094 proteins, for which 137,073,638 in silico mutants were analyzed. These site-specific data were summarized into a 20 square matrix, whose entries, ΔΔGij, were obtained after averaging through all the sites in all the proteins. We found a significant positive correlation between these energy values and the disease-causing potential of each substitution, suggesting that the exponential term accurately summarizes the fitness effect. A remarkable observation was that amino acids that were highly destabilizing when acting as the source, tended to have little effect when acting as the destination, and vice versa (source → destination). The Arrhenius model accurately reproduced the pattern of substitution rates collected in the empirical matrices, suggesting a relevant role for the genetic code structure and a tuning role for purifying selection exerted via protein stability.
Keywords: amino acid substitution; fitness; genetic code; mutation; protein evolution; protein stability; replacement matrices; selection.