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

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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, average selective constraints 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 a protein family are
approximated as a linear function of a given estimate of the
average selective constraints.
AIC values indicate that 
allowing multiple nucleotide changes leads the model to a better fit.
Also, the ML estimates of
transition-transversion bias from these empirical matrices
are not so large as previously estimated. 
The present model provides a good fit to substitution data
even for chloroplast and mitochondrial proteins.
Reference: doi:10.1371/PLoS One, 6, e17244, 2011.