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Empirical substitution matrices represent the average tendencies ofsubstitutions over various protein families by sacrificing gene-levelresolution. We develop a codon-based model, in which mutational tendencies ofcodon, a genetic code, and the strength of selective constraints against aminoacid replacements can be tailored to a given gene. First, selective constraintsaveraged over proteins are estimated by maximizing the likelihood of each 1-PAMmatrix of empirical amino acid (JTT, WAG, and LG) and codon (KHG) substitutionmatrices. Then, selective constraints specific to given proteins areapproximated as a linear function of those estimated from the empiricalsubstitution matrices.  Akaike information criterion (AIC) values indicate that a model allowingmultiple nucleotide changes fits the empirical substitution matricessignificantly better. Also, the ML estimates of transition-transversion biasobtained from these empirical matrices are not so large as previouslyestimated. The selective constraints are characteristic of proteins rather thanspecies. However, their relative strengths among amino acid pairs can beapproximated not to depend very much on protein families but amino acid pairs,because the present model, in which selective constraints are approximated tobe a linear function of those estimated from the JTT/WAG/LG/KHG matrices, canprovide a good fit to other empirical substitution matrices including cpREV forchloroplast proteins and mtREV for vertebrate mitochondrial proteins.  The present codon-based model with the ML estimates of selective constraintsand with adjustable mutation rates of nucleotide would be useful as a simplesubstitution model in ML and Bayesian inferences of molecular phylogenetictrees, and enables us to obtain biologically meaningful information at bothnucleotide and amino acid levels from codon and protein sequences.

Selective Constraints on Amino Acids Estimated by a Mechanistic Codon Substitution Model with Multiple Nucleotide Changes