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.Comment: Table 9 in this article includes corrections for errata in the Table
9 published in 10.1371/journal.pone.0017244. Supporting information is
attached at the end of the article, and a computer-readable dataset of the ML
estimates of selective constraints is available from
10.1371/journal.pone.001724