Modeling force-induced bio-polymer unfolding

We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N = 55 using exact enumeration techniques. We analyze in details the differences between the constant force and constant distance ensembles for large but finite N . At low temperatures, and in the constant force ensemble, the force-extension curve shows multiple plateaus (intermediate states), in contrast with the abrupt transition to an extended state prevailing in the N → ∞ limit. In the constant distance ensemble, the same curve provides a unified response to pulling and compressing forces, and agrees qualitatively with recent experimental results. We identify a cross-over length, proportional to N , below which the critical force of unfolding decreases with temperature, while above, it increases with temperature. Finally, the force-extension curve for stiff chains exhibits “saw-tooth” like behavior, as observed in protein unfolding experiments.