Unfolding times for proteins in a force clamp

TL;DR

This paper models protein unfolding times under constant force as a diffusion process on the energy landscape, revealing a force-dependent transition in escape-time distributions and providing a unified expression for unfolding times.

Contribution

It introduces a diffusion-based model for protein unfolding times that unifies weak and strong force regimes and explains experimental observations.

Findings

Unfolding times follow exponential or inverse Gaussian distributions depending on force strength.

A single formula describes average unfolding time across force regimes.

The model aligns with experimental data for ddFLN4 and ubiquitin.

Abstract

The escape process from the native valley for proteins subjected to a constant stretching force is examined using a model for a Beta-barrel. For a wide range of forces, the unfolding dynamics can be treated as one-dimensional diffusion, parametrized in terms of the end-to-end distance. In particular, the escape times can be evaluated as first passage times for a Brownian particle moving on the protein free-energy landscape, using the Smoluchowski equation. At strong forces, the unfolding process can be viewed as a diffusive drift away from the native state, while at weak forces thermal activation is the relevant mechanism. An escape-time analysis within this approach reveals a crossover from an exponential to an inverse Gaussian escape-time distribution upon passing from weak to strong forces. Moreover, a single expression valid at weak and strong forces can be devised both for the average unfolding time as well as for the corresponding variance. The analysis offers a possible explanation of recent experimental findings for ddFLN4 and ubiquitin.