From principal component to direct coupling analysis of coevolution in proteins: Low-eigenvalue modes are needed for structure prediction

TL;DR

This paper introduces the Hopfield-Potts model, bridging PCA and DCA, to improve protein contact prediction by utilizing low-eigenvalue modes often discarded by PCA, enabling accurate predictions with fewer parameters.

Contribution

The authors develop the Hopfield-Potts model, a novel approach that interpolates PCA and DCA, highlighting the importance of low-eigenvalue modes for structural information in proteins.

Findings

Low-eigenvalue modes are crucial for structural contact prediction.

The Hopfield-Potts model reduces parameters needed for accurate predictions.

Low-eigenvalue patterns are localized and correspond to close contacts in 3D structures.

Abstract

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.