Size and structure of the sequence space of repeat proteins

Abstract

The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occuring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of ~ 30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of fustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family, and suggests new strategies for protein design.

References in corpus (8)

• Direct-coupling analysis of residue co-evolution captures native contacts across many protein families
• Identification of direct residue contacts in protein-protein interaction by message passing
• Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
• Coevolutionary landscape inference and the context-dependence of mutations in beta-lactamase TEM-1
• Protein design: A perspective from simple tractable models
• Inter-residue, inter-protein and inter-family coevolution: bridging the scales
• On the entropy of protein families
• Understanding hierarchical protein evolution from first principles