  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.
