Protein Folding Kinetics Under Force from Molecular Simulation

Despite a large number of studies on the mechanical unfolding of proteins, there are still relatively few successful attempts to refold proteins in the presence of a stretching force. We explore refolding kinetics under force using simulations of a coarse-grained model of ubiquitin. The effects of force on the folding kinetics can be fitted by a one-dimensional Kramers theory of diffusive barrier crossing, resulting in physically meaningful parameters for the height and location of the folding activation barrier. By comparing parameters obtained from pulling in different directions, we find that the unfolded state plays a dominant role in the refolding kinetics. Our findings explain why refolding becomes very slow at even moderate pulling forces and suggest how it could be practically observed in experiments at higher forces.