Inferring Site-Specific Evolutionary Rates: Bayesian Methods are Superior

Not all sites in protein sequences evolve at the same rate during the course of evolution. The working hypothesis assumes that evolutionary conserved sites in a protein sequence point to functionally important regions. Thus, identifying conserved regions in a protein impacts such areas as functional annotation studies, drug design, quaternary structure prediction, and protein biochemistry [1]. Conservation levels are typically inferred from multiple sequence alignment (MSA) of homologous proteins. Recently, ‘Rate4Site’ [2] was developed as a tool for the identification of functional regions in proteins using the maximum likelihood (ML) criteria. However, Bayesian rate inference techniques are also plausible. When considering a Bayesian rate inference a few alternatives exist: (1) the inferred rate is the expectation of the rate over the posterior rate distribution (BAYES-EXP), and (2) the rate yielding the highest posterior probability is chosen (BAYES-MAP). When considering a Bayesian rate inference one must assume a prior distribution of rates. The most commonly used distribution for modeling rate variation across sites is the gamma distribution [3]. This distribution is used here as the prior for both the BAYES-EXP and BAYES-MAP methods. The purpose of this study is to compare three different likelihood-based inference methods: ML, BAYES-MAP and BAYES-EXP by using simulations. We studied the effect of the number of discrete gamma categories on the performance of the BAYES-EXP method. We also studied the effect of various evolutionary parameters, such as the number of taxonomic units, branch lengths and rate distributions on the quality of predictions. Finally, we discuss confidence intervals for inferred rates. We conclude with a biological example.