Abstract

Can we accurately predict a protein’s native structure from amino-acid sequence data alone? A major breakthrough has been the discovery of the imprint of evolutionary constraints in correlated mutations of protein sequences which can be used to predict residues in contact in 3D space. However, many approaches regard protein family sequences as independent samples from a distribution. This is not true – protein sequences share an evolutionary history (phylogeny), which ‘pollutes’ the correlation signal. Here, we develop a theory of the eigenvalue distribution as a function of phylogeny, and furthermore by using Random Matrix Theory we discover how to predict this shape. This allows us to determine precise thresholds on the parameters governing evolution and establish parameter regimes where evolutionary effects are important.