Protein folding: Complex potential for the driving force in a two-dimensional space of collective variables

TL;DR

This paper introduces a complex potential for protein folding in a two-dimensional collective variable space, decomposing the folding fluxes into source, sink, and vorticity components, and illustrates this with a model beta-hairpin protein.

Contribution

It presents a novel complex potential framework for analyzing protein folding fluxes using Helmholtz decomposition in a 2D collective variable space.

Findings

Decomposition of folding fluxes into source, sink, and vorticity components.

Application of the theoretical framework to a beta-hairpin protein model.

Insights into flow canalization between unfolded and native states.

Abstract

Using the Helmholtz decomposition of the vector field of folding fluxes in a two-dimensional space of collective variables, a potential of the driving force for protein folding is introduced. The potential has two components. One component is responsible for the source and sink of the folding flows, which represent, respectively, the unfolded states and the native state of the protein, and the other, which accounts for the flow vorticity inherently generated at the periphery of the flow field, is responsible for the canalization of the flow between the source and sink. The theoretical consideration is illustrated by calculations for a model $\beta$-hairpin protein.