Converting amino acid alignment scores into measures of evolutionary time: A simulation study of various relationships

Amino acid substitution tables are essential for the proper alignment of protein sequences, and alignment scores based on them can be transformed into distance measures by various means. In the simplest case, the negative log of the score is used. This Poisson relationship assumes that all sites are equally likely to change, however. A more accurate relationship would correct for different rates of change at each residue position. Recently, Grishin (J. Mol. Evol. 41:675-679, 1995) published a set of simple equations that correct for various circumstances, including different rates of change at different sites. We have used these equations in conjunction with similarity scores that take into account constraints on amino acid interchange. Simulation studies show a linear relationship between these calculated distances and the numbers of allowed mutations based on the observed variation of rate at all sites in various proteins.