Network Structure of Protein Folding Pathways

TL;DR

This paper introduces a network-based approach to analyze protein folding pathways, revealing scale-free network structures and energy landscape correlations that influence folding dynamics and differ from random models.

Contribution

It presents a novel network model for protein folding pathways, linking conformation space structure to energy landscape correlations and folding behavior.

Findings

Folding pathways form scale-free networks.

Energy landscape correlations are crucial for network structure.

High temperature alters the folding network's exponent.

Abstract

The classical approach to protein folding inspired by statistical mechanics avoids the high dimensional structure of the conformation space by using effective coordinates. Here we introduce a network approach to capture the statistical properties of the structure of conformation spaces. Conformations are represented as nodes of the network, while links are transitions via elementary rotations around a chemical bond. Self-avoidance of a polypeptide chain introduces degree correlations in the conformation network, which in turn lead to energy landscape correlations. Folding can be interpreted as a biased random walk on the conformation network. We show that the folding pathways along energy gradients organize themselves into scale free networks, thus explaining previous observations made via molecular dynamics simulations. We also show that these energy landscape correlations are essential for recovering the observed connectivity exponent, which belongs to a different universality class than that of random energy models. In addition, we predict that the exponent and therefore the structure of the folding network fundamentally changes at high temperatures, as verified by our simulations on the AK peptide.