Modeling amino acid substitution patterns in orthologous and paralogous genes

We study to what degree patterns of amino acid substitution vary between genes using two models of protein-coding gene evolution. The first divides the amino acids into groups, with one substitution rate for pairs of residues in the same group and a second for those in differing groups. Unlike previous applications of this model, the groups themselves are estimated from data by simulated annealing. The second model makes substitution rates a function of the physical and chemical similarity between two residues. Because we model the evolution of coding DNA sequences as opposed to protein sequences, artifacts arising from the differing numbers of nucleotide substitutions required to bring about various amino acid substitutions are avoided. Using 10 alignments of related sequences (five of orthologous genes and five gene families), we do find differences in substitution patterns. We also find that, although patterns of amino acid substitution vary temporally within the history of a gene, variation is not greater in paralogous than in orthologous genes. Improved understanding of such gene-specific variation in substitution patterns may have implications for applications such as sequence alignment and phylogenetic inference.