Mechanical property of the helical configuration for a twisted intrinsically straight biopolymer

Bistability of a helical filament confined on a cylinder

The natural configuration of an intrinsically curved and twisted filament is uniquely a helix so that it can be referred to as a helical filament. We find that confining a helical filament on a cylinder can create a bistable state. When c_{0}R=0.5, where c_{0} is the intrinsic curvature of filament and R is the radius of cylinder, the phase diagram for the stability of a helix contains three regimes. Regime I has a small intrinsic twisting rate (ITR) and exhibits a bistable state which consists of two isoenergic helices. In regime II, the filament has a moderate ITR and the bistable state consists of a metastable low-pitch helix and a stable nonhelix. In regime III, the helix is unstable, owing to a large ITR. A similar phenomenon occurs when c_{0}R∼0.5. Monte Carlo simulation confirms these conclusions and indicates further that there are bistable nonhelices in regime III. This bistable system offers a prospective green material since the wide range of parameters and distinctive configurations for bistable states favor its realization and application.

Crucial role of the intrinsic twist rate for the size of an intrinsically curved semiflexible biopolymer

We study the effects of the intrinsic curvature (IC), intrinsic twist rate (ITR), anisotropic bending rigidities, sequence disorder, and temperature (T) on the persistence length (l_{p}) of a two- or three-dimensional semiflexible biopolymer. We develop some general expressions to evaluate exactly these effects. We find that a moderate IC alone reduces l_{p} considerably. Our results indicate that the centerline of the filament keeps as a helix in a rather large range of T when ITR is small. However, a large ITR can counterbalance the effect of IC and the result is insensitive to the twist rigidity. Moreover, a weak randomness in IC and ITR can result in an "overexpanded" state. Meanwhile, when ITR is small, l_{p} is not a monotonic function of T but can have either minimum or maximum at some T, and in the two-dimensional case the maximum is more obvious than that in the three-dimensional case. These results reveal that to obtain a proper size at a finite T for an intrinsically curved semiflexible biopolymer, proper values of bending rigidities and ITR are necessary but a large twist rigidity may be only a by-product. Our findings are instructive in controlling the size of a semiflexible biopolymer in organic synthesis since the mean end-to-end distance and radius of gyration of a long semiflexible biopolymer are proportional to l_{p}.