Modeling Protein Evolution with Several Amino Acid Replacement Matrices Depending on Site Rates

Abstract

Most protein substitution models use a single amino acid replacement matrix summarizing the biochemical properties of amino acids. However, site evolution is highly heterogeneous and depends on many factors that influence the substitution patterns. In this paper, we investigate the use of different substitution matrices for different site evolutionary rates. Indeed, the variability of evolutionary rates corresponds to one of the most apparent heterogeneity factors among sites, and there is no reason to assume that the substitution patterns remain identical regardless of the evolutionary rate. We first introduce LG4M, which is composed of four matrices, each corresponding to one discrete gamma rate category (of four). These matrices differ in their amino acid equilibrium distributions and in their exchangeabilities, contrary to the standard gamma model where only the global rate differs from one category to another. Next, we present LG4X, which also uses four different matrices, but leaves aside the gamma distribution and follows a distribution-free scheme for the site rates. All these matrices are estimated from a very large alignment database, and our two models are tested using a large sample of independent alignments. Detailed analysis of resulting matrices and models shows the complexity of amino acid substitutions and the advantage of flexible models such as LG4M and LG4X. Both significantly outperform single-matrix models, providing gains of dozens to hundreds of log-likelihood units for most data sets. LG4X obtains substantial gains compared with LG4M, thanks to its distribution-free scheme for site rates. Since LG4M and LG4X display such advantages but require the same memory space and have comparable running times to standard models, we believe that LG4M and LG4X are relevant alternatives to single replacement matrices. Our models, data, and software are available from http://www.atgc-montpellier.fr/models/lg4x.

Exploring Phylogenetic Relationships within Myriapoda and the Effects of Matrix Composition and Occupancy on Phylogenomic Reconstruction

“…Individual gene trees were run in RAxML 8.1.3 (Stamatakis 2014b) for each gene in each matrix. The best-fitting model in each case was selected using a custom script modified to permit testing of LG4M and LG4X models (Le et al 2012). Best-scoring ML trees were inferred for each gene under the selected model from 100 replicates of parsimony starting trees.…”

Evolutionarily Conserved Alternative Splicing Across Monocots

“…Protein sequences were aligned with MUSCLE (version 3.8.31) using default parameters (Edgar 2004). The alignments were used to construct a maximum likelihood phylogenetic tree with RAxML (version 8.1.12) software using a gamma distribution and LG4X model (Le et al 2012;Stamatakis 2014). Conserved AS events in SR families between maize and sorghum exon-intron gene structure were visualized by Fancygene version 1.4 (Rambaldi and Ciccarelli 2009).…”

Causes of evolutionary rate variation among protein sites

“…This heterogeneity likely emerges from the differing functional and/or biophysical constraints affecting different sites. Accurately modeling this among-site heterogeneity is critically important in evolutionary studies, particularly in phylogenetic inference 2-8 . Phylogenetic models which allow for among-site rate heterogeneity universally provide better fits to data than do models which assume constant rates across sites 3;9-13 .…”