Two-state protein-like folding of a homopolymer chain

TL;DR

This study demonstrates that a simple homopolymer can undergo a direct, two-state folding transition similar to small proteins, characterized by a free-energy barrier and a dominant folding pathway, using advanced sampling techniques.

Contribution

It shows that homopolymer chains can exhibit two-state folding behavior with thermodynamics and kinetics akin to small proteins, using Wang-Landau and multi-canonical sampling methods.

Findings

Homopolymer undergoes a direct freezing transition similar to protein folding.

The transition involves a free-energy barrier and a dominant folding pathway.

Thermodynamics satisfy the van't Hoff criterion for two-state folding.

Abstract

Many small proteins fold via a first-order "all-or-none" transition directly from an expanded coil to a compact native state. Here we study an analogous direct freezing transition from an expanded coil to a compact crystallite for a simple flexible homopolymer. Wang-Landau sampling is used to construct the 1D density of states for square-well chains of length 128. Analysis within both the micro-canonical and canonical ensembles shows that, for a chain with sufficiently short-range interactions, the usual polymer collapse transition is preempted by a direct freezing or "folding" transition. A 2D free-energy landscape, built via subsequent multi-canonical sampling, reveals a dominant folding pathway over a single free-energy barrier. This barrier separates a high entropy ensemble of unfolded states from a low entropy set of crystallite states and the transition proceeds via the formation of a transition-state folding nucleus. Despite the non-unique homopolymer ground state, the thermodynamics of this direct freezing transition are identical to the thermodynamics of two-state protein folding. The model chain satisfies the van't Hoff calorimetric criterion for two-state folding and an Arrhenius analysis of the folding/unfolding free energy barrier yields a Chevron plot characteristic of small proteins.