Structural Determinant of Protein Designability

TL;DR

This paper develops an analytical theory linking protein structure contact matrices to the distribution of low-energy sequences, validated by simulations, and suggests criteria for foldability and designability of protein structures.

Contribution

It introduces a new analytical approach connecting contact matrix eigenvalues to protein designability, supported by Monte Carlo simulations on lattice proteins.

Findings

Structures with certain contact matrix eigenvalues have more low-energy sequences.

Simulation results agree with the analytical predictions.

Proposes a method to test real protein foldability based on the theory.

Abstract

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structure's contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.