Key interaction patterns in proteins revealed by cluster expansion of the partition function

TL;DR

This paper uses a cluster expansion approach to identify key interaction patterns in proteins, revealing that even cycles are crucial while cliques are less favorable, impacting protein designability.

Contribution

It introduces a novel application of cluster expansion to analyze protein interaction networks and ranks elementary patterns by their importance in sequence design.

Findings

Even cycles are the most significant interaction patterns.

Cliques tend to be detrimental to protein stability.

Interaction patterns influence the evolutionary designability of proteins.

Abstract

The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence design. To achieve this goal, we employed a cluster expansion of the partition function in the space of sequences and evaluated numerically the statistical importance of each cluster. An important feature of this procedure is that it is applied to a dense, finite system. We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental. Each cluster also gives a contribute to the sequence entropy, which is a measure of the evolutionary designability of a fold. We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.