Protein folding tames chaos

TL;DR

This paper introduces molecular nonlinear dynamics as a framework to analyze protein folding, revealing that folding reduces chaos, increases stability, and can predict structural temperature factors.

Contribution

It presents a novel theoretical approach linking chaos theory with protein folding, including the discovery of ILDMs and a new method for predicting temperature factors.

Findings

Folding reduces the chaoticity of protein dynamics.

Existence of low dimensional manifolds in folded proteins.

New algorithm for predicting temperature factors.

Abstract

Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderliness and relative energies of folded, misfolded and unfolded protein states. Finally, we exploit chaos for protein flexibility analysis and develop a robust chaotic algorithm for the prediction of Debye-Waller factors, or temperature factors, of protein structures.