How pairwise coevolutionary models capture the collective residue variability in proteins

TL;DR

This paper demonstrates that pairwise coevolutionary models, inferred via Boltzmann-machine learning, effectively capture the complex collective residue variability in proteins, challenging the need for more complex models.

Contribution

The study provides a systematic analysis showing pairwise models are sufficient for modeling residue variability, supported by a new inference scheme and structural insights.

Findings

Correlations are built through multiple coupling paths based on 3D structure

Pairwise models accurately predict three-residue correlations

Models capture the structure of protein families in sequence space

Abstract

Global coevolutionary models of homologous protein families, as constructed by direct coupling analysis (DCA), have recently gained popularity in particular due to their capacity to accurately predict residue-residue contacts from sequence information alone, and thereby to facilitate tertiary and quaternary protein structure prediction. More recently, they have also been used to predict fitness effects of amino-acid substitutions in proteins, and to predict evolutionary conserved protein-protein interactions. These models are based on two currently unjustified hypotheses: (a) correlations in the amino-acid usage of different positions are resulting collectively from networks of direct couplings; and (b) pairwise couplings are sufficient to capture the amino-acid variability. Here we propose a highly precise inference scheme based on Boltzmann-machine learning, which allows us to systematically address these hypotheses. We show how correlations are built up in a highly collective way by a large number of coupling paths, which are based on the protein's three-dimensional structure. We further find that pairwise coevolutionary models capture the collective residue variability across homologous proteins even for quantities which are not imposed by the inference procedure, like three-residue correlations, the clustered structure of protein families in sequence space or the sequence distances between homologs. These findings strongly suggest that pairwise coevolutionary models are actually sufficient to accurately capture the residue variability in homologous protein families.