Mechanical instability of a bistable helical filament confined on a cylinder

We study mechanical property of a helical filament confined on a cylinder. With appropri-ate parameters such a system exhibits a natural bistable state consisted of two isoenergic configurations. We find closed-form expressions for helical configuration of the filament and related stability criterion. Exact calculations reveal that the extension of filament can undergo a single-step abrupt transition because both extension and energy can be triple-value functions of external force or torque in a critical regime. The larger the ratio between twisting rigidity and bending rigidity, the larger the critical regime and the abrupt change in extension; but the larger the intrinsic twisting rate, the smaller the critical regime and the abrupt change. Moreover, we evaluate the energy barrier between two isoenergic configurations and find that to make the filament jump from a low pitch helix up to a configuration with a large extension it is more efficient to apply a stretching force; but to induce a collapse from a configuration with a large extension to a low pitch helix it is better to apply a positive torque.