Random Matrix approach to collective behavior and bulk universality in protein dynamics

TL;DR

This paper applies Random Matrix Theory to analyze covariance matrices of protein displacements, revealing universal statistical properties that distinguish collective motions from localized vibrations, thus offering a new quantitative method for studying protein dynamics.

Contribution

It introduces a novel application of Random Matrix Theory to identify collective degrees of freedom in protein dynamics through bulk universality and eigenmode analysis.

Findings

Bulk universality in eigenmode spacing statistics with Brody distribution parameter ~0.8

A quantitative criterion to distinguish collective motions from localized vibrations

Support for the universality hypothesis in protein displacement covariance matrices

Abstract

Covariance matrices of amino acid displacements, commonly used to characterize the large-scale movements of proteins, are investigated through the prism of Random Matrix Theory. Bulk universality is detected in the local spacing statistics of noise-dressed eigenmodes, which is well described by a Brody distribution with parameter $\beta\simeq 0.8$. This finding, supported by other consistent indicators, implies a novel quantitative criterion to single out the collective degrees of freedom of the protein from the majority of high-energy, localized vibrations.