Empirical substitution matrices represent the average tendencies of substitutions over various protein families by sacrificing gene-level resolution. We develop a codon-based model, in which mutational tendencies of codon, a genetic code, and the strength of selective constraints against amino acid replacements can be tailored to a given gene. First, selective constraints averaged over proteins are estimated by maximizing the likelihood of each 1-PAM matrix of empirical amino acid (JTT, WAG, and LG) and codon (KHG) substitution matrices. Then, selective constraints specific to given proteins are approximated as a linear function of those estimated from the empirical substitution matrices. Akaike information criterion (AIC) values indicate that a model allowing multiple nucleotide changes fits the empirical substitution matrices significantly better. Also, the ML estimates of transition-transversion bias obtained from these empirical matrices are not so large as previously estimated. The selective constraints are characteristic of proteins rather than species. However, their relative strengths among amino acid pairs can be approximated not to depend very much on protein families but amino acid pairs, because the present model, in which selective constraints are approximated to be a linear function of those estimated from the JTT/WAG/LG/KHG matrices, can provide a good fit to other empirical substitution matrices including cpREV for chloroplast proteins and mtREV for vertebrate mitochondrial proteins. The present codon-based model with the ML estimates of selective constraints and with adjustable mutation rates of nucleotide would be useful as a simple substitution model in ML and Bayesian inferences of molecular phylogenetic trees, and enables us to obtain biologically meaningful information at both nucleotide and amino acid levels from codon and protein sequences.
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