Modeling force-induced bio-polymer unfolding

TL;DR

This paper presents an exactly solvable statistical mechanics model for bio-polymer unfolding under force, revealing multiple intermediate states, ensemble differences, and behaviors akin to experimental protein unfolding.

Contribution

It introduces a simple, exactly solvable model capturing force-induced unfolding of bio-polymers, including effects of stiffness and ensemble differences, aligning with experimental observations.

Findings

Force-extension curves show multiple plateaus at low temperatures.

Different responses in constant force and constant distance ensembles.

Stiff chains exhibit saw-tooth unfolding behavior.

Abstract

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 $N \to \infty$ 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 wiyh temperature. Finally, the force-extension curve for stiff chains exhibits "saw-tooth" like behavior, as observed in protein unfolding experiments.