# 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.

## Key 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.