Nucleotide substitution rate estimation in enterobacteria: approximate and maximum-likelihood methods lead to similar conclusions.

Synonymous mutations are ‘‘silent’’ with regard to the amino acid sequence of a protein, but a wealth of evidence indicates that, at least in species with large effective population sizes, synonymous mutations are subject to translational selection (Akashi and EyreWalker 1998). One line of evidence for translational selection has been the perceived negative correlation between codon bias and synonymous substitution rates (KS), reported in both Drosophila (Shields et al. 1988) and enterobacteria (Sharp and Li 1987a). The reasoning behind this interpretation of the correlation between KS and codon bias is straightforward. Translational selection means that certain codons are favored over others, so selection causes an increased codon bias with a preponderance of favored codons, which means that most synonymous mutations are selectively disfavored and so selection also reduces KS. The selective interpretation of the correlation between KS and codon bias in Drosophila has been questioned recently on both theoretical and methodological grounds. It seems that translational selection is weak relative to genetic drift in Drosophila (Akashi and Schaeffer 1997), but theoretical models show that when selection for codon usage is weak there is unlikely to be a strong relationship between codon bias and KS (McVean and Charlesworth 1999). Furthermore, the reported relationship between codon bias and KS in Drosophila (Shields et al. 1988) has recently been shown to be a methodological artifact of approximate substitution rate estimation methods which fail to account fully for biased codon usage and transition/transversion biases (Dunn, Bielawski, and Yang 2001). When more realistic maximum-likelihood (ML) methods are used to estimate substitution rates, no relationship between KS and codon bias is found (Dunn, Bielawski, and Yang 2001). Given these new findings for Drosophila, we investigated the methodological sensitivity of the correlation between KS and codon bias in enterobacteria. We used a set of 128 aligned protein-coding sequences from Escherichia coli and Salmonella typhimurium (EyreWalker and Bulmer 1995). Codon bias was measured by the codon adaptation index (CAI), which gives a measure of how closely codon usage approaches that found in highly expressed genes. CAI was calculated only for the E. coli genes using the method of Sharp and Li