Many applications require the calculation of site-specific evolutionary rates from alignments of amino-acid sequences. For example, catalytic residues in enzymes and interface regions in protein complexes can be inferred from observed relative rates. While numerous approaches exist to calculate amino-acid rates, however, it is not entirely clear what physical quantities the inferred rates represent and how these rates relate to the underlying fitness landscape of the evolving protein. Further, amino-acid rates can be calculated in the context of different amino-acid exchangeability matrices, such as JTT, LG, or WAG, and again it is not known how the choice of the matrix influences the physical interpretation of the inferred rates. Here, we develop a theory of measurement for site-specific evolutionary rates, but analytically solving the maximum-likelihood equations for rate inference performed on sequences evolved under a mutation–selection model. We demonstrate that the measurement process can only recover the true expected rates of the mutation–selection model if rates are measured relative to a naïve exchangeability matrix, in which all exchangeabilities are equal to one. Rate measurements using other matrices are quantitatively close but not mathematically correct. Our results demonstrate that insights obtained from phylogenetic-tree inference do not necessarily apply to rate inference, and best practices for the former may be deleterious for the latter.
Peer Review #2 of "Calculating site-specific evolutionary rates at the amino-acid or codon level yields similar rate estimates (v0.1)"
