  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.
