Stochastic dynamics of model proteins on a directed graph

TL;DR

This paper introduces a graph-based method to analyze protein energy landscapes, enabling efficient estimation of folding times and distinguishing between fast and slow folders through topological and dynamical properties.

Contribution

The authors develop a novel graph representation of protein energy landscapes that preserves key dynamical features and allows for renormalization, improving analysis of folding kinetics.

Findings

Graph representation accurately estimates folding and equilibration time scales.

Renormalization preserves topological and dynamical properties of the landscape.

Distinct kinetic features differentiate fast and slow folding proteins.

Abstract

A method for reconstructing the energy landscape of simple polypeptidic chains is described. We show that we can construct an equivalent representation of the energy landscape by a suitable directed graph. Its topological and dynamical features are shown to yield an effective estimate of the time scales associated with the folding and with the equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined by a temperature dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs", while redefining their connectivity. We show that both topological and dynamical properties are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to obtain a clear distinction between a "fast folder" and a "slow folder" in the heteropolymers one has to look at kinetic features of the directed graph. We find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time, while for the bad folder these time scales are comparable. Accordingly, we can conclude that the strategy described in this paper can be successfully applied also to more realistic models, by studying their renormalized dynamics on the directed graph, rather than performing lengthy molecular dynamics simulations.