d_N/d_S-H, a New Test to Distinguish Different Selection Modes in Protein Evolution and Cancer Evolution

One of the most popular measures in the analysis of protein sequence evolution is the ratio of nonsynonymous distance (d_N) to synonymous distance (d_S). Under the assumption that synonymous substitutions in the coding region are selectively neutral, the d_N/d_S ratio can be used to statistically detect the adaptive evolution (or purifying selection) if d_N/d_S > 1 (or d_N/d_S < 1) significantly. However, due to strong structural constraints and/or variable functional constraints imposed on amino acid sites, most encoding genes in most species have demonstrated d_N/d_S < 1. Consequently, the statistical power for testing d_N/d_S = 1 may be insufficient to distinguish between different selection modes. In this paper, we propose a more powerful test, called d_N/d_S-H, in which a new parameter H, a relative measure of rate variation among sites, was introduced. Given the condition of strong purifying selections at some sites, the d_N/d_S-H model predicts d_N/d_S = 1-H for neutral evolution, d_N/d_S < 1-H for nearly neutral selection, and d_N/d_S > 1-H for adaptive evolution. The potential of this new method for resolving the neutral-adaptive debates is illustrated by the protein sequence evolution in vertebrates, Drosophila and yeasts, as well as somatic cancer evolution (specialized as the C_N/C_S-H test).