Theoretical foundations for quantitative paleogenetics. III - The molecular divergence of nucleic acids and proteins for the case of genetic events of unequal probability

Theoretical equations are derived for molecular divergence with respect to gene and protein structure in the presence of genetic events with unequal probabilities: amino acid and base compositions, the frequencies of nucleotide replacements, the usage of degenerate codons, the distribution of fixed base replacements within codons and the distribution of fixed base replacements among codons. Results are presented in the form of tables relating the probabilities of given numbers of codon base changes with respect to the original codon for the alpha hemoglobin, beta hemoglobin, myoglobin, cytochrome c and parvalbumin group gene families. Application of the calculations to the rabbit alpha and beta hemoglobin mRNAs and proteins indicates that the genes are separated by about 425 fixed based replacements distributed over 114 codon sites, which is a factor of two greater than previous estimates. The theoretical results also suggest that many more base replacements are required to effect a given gene or protein structural change than previously believed.