Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding

TL;DR

This paper models protein folding energy landscapes using a dissipative Hookean spring system with noise, revealing a distribution of energy states that follows a modified Ornstein-Uhlenbeck process and aligns with real protein energy distributions.

Contribution

It introduces a novel dissipative model for protein energy landscapes that reproduces real protein energy distributions over a wide range of energies.

Findings

Energy distribution follows a modified Ornstein-Uhlenbeck process.

The model reproduces real protein energy distributions.

Sampling yields a family of energy and spacing distributions.

Abstract

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process and giving rise to the so called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.