Elastic energy of proteins and the stages of protein folding

TL;DR

This paper introduces a universal elastic energy model for proteins based on physical principles, revealing three distinct folding stages with specific scaling behaviors and a phase transition during the folding process.

Contribution

It presents a novel elastic energy framework for proteins that captures folding stages and phase transition phenomena based on physical arguments and simulation data.

Findings

Identifies three folding stages with distinct scaling exponents.

Shows a phase transition from pre-globule to molten globule.

Provides a universal elastic energy model fitting simulation data.

Abstract

We propose a universal elastic energy for proteins, which depends only on the radius of gyration $R_{g}$ and the residue number $N$. It is constructed using physical arguments based on the hydrophobic effect and hydrogen bonding. Adjustable parameters are fitted to data from the computer simulation of the folding of a set of proteins using the CSAW (conditioned self-avoiding walk) model. The elastic energy gives rise to scaling relations of the form $R_{g}\sim N^{\nu}$ in different regions. It shows three folding stages characterized by the progression with exponents $\nu = 3/5, 3/7, 2/5$, which we identify as the unfolded stage, pre-globule, and molten globule, respectively. The pre-globule goes over to the molten globule via a break in behavior akin to a first-order phase transition, which is initiated by a sudden acceleration of hydrogen bonding.