Non-Negative Matrix Factorization for Learning Alignment-Specific Models of Protein Evolution

Ben Murrell,Konrad Scheffler,Gerdus Benade,Tristan Hands,Sasha Moola,Robert Ketteringham,Thomas Weighill,Jan Buys,Daniel Kaliski,Lise Du Buisson,Thomas Mailund

doi:10.1371/journal.pone.0028898

Abstract

Models of protein evolution currently come in two flavors: generalist and specialist. Generalist models (e.g. PAM, JTT, WAG) adopt a one-size-fits-all approach, where a single model is estimated from a number of different protein alignments. Specialist models (e.g. mtREV, rtREV, HIVbetween) can be estimated when a large quantity of data are available for a single organism or gene, and are intended for use on that organism or gene only. Unsurprisingly, specialist models outperform generalist models, but in most instances there simply are not enough data available to estimate them. We propose a method for estimating alignment-specific models of protein evolution in which the complexity of the model is adapted to suit the richness of the data. Our method uses non-negative matrix factorization (NNMF) to learn a set of basis matrices from a general dataset containing a large number of alignments of different proteins, thus capturing the dimensions of important variation. It then learns a set of weights that are specific to the organism or gene of interest and for which only a smaller dataset is available. Thus the alignment-specific model is obtained as a weighted sum of the basis matrices. Having been constrained to vary along only as many dimensions as the data justify, the model has far fewer parameters than would be required to estimate a specialist model. We show that our NNMF procedure produces models that outperform existing methods on all but one of 50 test alignments. The basis matrices we obtain confirm the expectation that amino acid properties tend to be conserved, and allow us to quantify, on specific alignments, how the strength of conservation varies across different properties. We also apply our new models to phylogeny inference and show that the resulting phylogenies are different from, and have improved likelihood over, those inferred under standard models.

Highlights

Empirical models of protein evolution, as pioneered by Dayhoff and colleagues [1,2], have found wide use across varied domains: sequence alignment [3], phylogenetics [4], and as baseline models against which positive selection is detected [5]
We investigate a compromise between generalist and specialist models by first extracting, from a large dataset, the important dimensions of variation in amino acid substitution rates, and using these to constrain our models
Using a separate test dataset, we show that models estimated through our procedure outperform existing models in terms of Akaike’s information criterion (AIC) on all but one of 50 alignments tested

Summary

Introduction

Empirical models of protein evolution, as pioneered by Dayhoff and colleagues [1,2], have found wide use across varied domains: sequence alignment [3], phylogenetics [4], and as baseline models against which positive selection is detected [5]. Whelan and Goldman [8] made use of a maximum likelihood approach which, unlike the counting methods mentioned above, finds the amino acid substitution matrix while simultaneously optimizing the branch lengths of the phylogeny, incorporating the possibility of multiple substitutions taking place along any given branch. In constructing their WAG matrix, they applied an approximation of this technique to a large dataset

Methods

Results

Conclusion