Unfolding times for proteins in a force clamp

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