From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction

By Simona Cocco, Rémi Monasson, Martin Weigt. 2012

109 citations recorded by the source corpus.

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant ‘patterns’ of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold.

Subfields: Condensed Matter Physics, Molecular Biology, Statistical and Nonlinear Physics

Citations in the corpus

Revealing evolutionary constraints on proteins through sequence analysis (2018, neutral): “Note that we do not use inference methods specific to low-rank coupling matrices [34,35] because we wish to retain generality, with the application to real sequence data in mind.”
Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners (2014, neutral): “do-count-corrected covariance matrix of [10] with pseudo-count parameter . Indeed, identifying with =(+ M), this instance allows us to recast the estimation of as = U+ (1 )C+ (1 )(x )T (x ) (14) and J= 1 becomes the same as in the mean-eld Potts model. Manifestly from here, the eect of the prior is ”
Protein contact prediction by integrating joint evolutionary coupling analysis and supervised learning (2013, neutral): “Contact: j3xu@ttic.edu Supplementary information: Supplementary data are available at Bioinformatics online.”
Learning protein constitutive motifs from sequence data (2018, unknown): “We ﬁnd a variety of structural (including pairwise contacts as in weights 1 and 2) and phylogenetic (dedicated to few, evolutionary close sequences as hidden unit 5) features; the latter include in particular stretches of gaps, mostly located at the extremities of the sequence [30].”
Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences (2014, unknown): “The Hopﬁeld-Potts inference of [26] has, as far as we are aware, only been performed using the mean-ﬁeld method, and then works from less well to equally well as the method of [13] (but with many fewer parameters).”
Patterns of coevolving amino acids unveil structural and dynamical domains (2017, unknown): “DCA and statistical coupling analysis share nevertheless important conceptual similarities (89, 90), and, therefore, similarities between EDs and sectors can be expected in specific contexts.”
Evolution-Based Functional Decomposition of Proteins (2015, unknown): “Using mathematical analyses that explore diﬀerent aspects of this matrix (7; 8), studies have exposed tertiary structural contacts in protein structures (Direct Coupling Analysis, or DCA, (4; 9)), determinants of binding speciﬁcity in paralogous protein complexes (5), and larger, collectively…”