Codon substitution in evolution and the 'saturation' of synonymous changes

A mathematical model for codon substitution is presented, taking into account unequal mutation rates among different nucleotides and purifying selection. This model is constructed by using a 61x61 transition probability matrix for the 61 nonterminating codons. Under this model, a computer simulation is conducted to study the numbers of silent (synonymous) and amino acid-altering (nonsynonymous) nucleotide substitutions when the underlying mutation rates among the four kinds of nucleotides are not equal. It is assumed that the substitution rates are costant over evolutionary time, the codon frequencies being in equilibrium, and, thus, the numbers of synonymous and nonsynonymous substitutions both increase linearly with evolutionary time. It is shown that, when the mutation rates are not equal, the estimate of synonymous substitutions obtaind by F. Perler, A. Efstratiadis, P. Lomedico, W. Gilbert, R. Kolodner and J. Dodgson's 'Percent Corrected Divergence' method increases nonlinearly, although the true number of synonymous substitutions increases linearly. It is, therefore, possible that the 'saturation' of synonymous substitutions observed by Perler et al. is due to the inefficiency of their method to detect all synonymous substitutions.