Gamma-MYN: a new algorithm for estimating Ka and Ks with consideration of variable substitution rates

Over the past two decades, there have been several approximate methods that adopt different mutation models and used for estimating nonsynonymous and synonymous substitution rates (Ka and Ks) based on protein-coding sequences across species or even different evolutionary lineages. Among them, MYN method (a Modified version of Yang-Nielsen method) considers three major dynamic features of evolving DNA sequences-bias in transition/transversion rate, nucleotide frequency, and unequal transitional substitution but leaves out another important feature: unequal substitution rates among different sites or nucleotide positions.

We incorporated a new feature for analyzing evolving DNA sequences-unequal substitution rates among different sites-into MYN method, and proposed a modified version, namely gamma (gamma)-MYN, based on an assumption that the evolutionary rate at each site follows a mode of gamma-distribution. We applied gamma-MYN to analyze the key estimator of selective pressure omega (Ka/Ks) and other relevant parameters in comparison to two other related methods, YN and MYN, and found that neglecting the variation of substitution rates among different sites may lead to biased estimations of omega. Our new method appears to have minimal deviations when relevant parameters vary within normal ranges defined by empirical data.

Our results indicate that unequal substitution rates among different sites have variable influences on omega under different evolutionary rates while both transition/transversion rate ratio and unequal nucleotide frequencies affect Ka and Ks thus selective pressure omega.