Understanding the dependence on the pulling speed of the unfolding pathway of proteins

The dependence of the unfolding pathway of proteins on the pulling speed is investigated. This is done by introducing a simple one-dimensional chain comprising $N$ units, with different characteristic bistable free energies. These units represent either each of the modules in a modular protein or each of the intermediate "unfoldons" in a protein domain, which can be either folded or unfolded. The system is pulled by applying a force to the last unit of the chain, and the units unravel following a preferred sequence. We show that the unfolding sequence strongly depends on the pulling velocity $v_{p}$. In the simplest situation, there appears a critical pulling speed $v_{c}$: for pulling speeds $v_{p}<v_{c}$, the weakest unit unfolds first, whereas for $v_{p}>v_{c}$ it is the pulled unit that unfolds first. By means of a perturbative expansion, we find quite an accurate expression for this critical velocity.