We study the effect of an intrinsic curvature on the mechanical property of two-dimensional semiflexible biopolymers and find that it can induce a discontinuous transition in extension. At zero temperature, we accurately show that the extension of an intrinsically curved semiflexible biopolymer of finite length can undergo a multiple-step discontinuous transition regardless of bending rigidity. The transition is accompanied by unwinding loops, and the critical force reaches a limit quickly with decreasing number of loops so that, in the experiment, it is possible to observe the almost simultaneous opening of several loops. However, the fluctuation or configurational average at a finite temperature suppresses the sharp transition so that there is no discontinuous transition in a system of finite size. However, our results obtained from Monte Carlo simulation reveal that, at a finite temperature, the extension of a biopolymer can undergo a one-step first-order transition in the thermodynamical limit if the biopolymer has a sufficiently large bending rigidity. The critical force increases with increasing intrinsic curvature or bending rigidity.

We apply a Monte Carlo simulation method to lattice systems to study the effect of an intrinsic curvature on the mechanical property of a semiflexible biopolymer. We find that when the intrinsic curvature is sufficiently large, the extension of a semiflexible biopolymer can undergo a first-order transition at finite temperature. The critical force increases with increasing intrinsic curvature. However, the relationship between the critical force and the bending rigidity is structure-dependent. In a triangle lattice system, when the intrinsic curvature is smaller than a critical value, the critical force increases with the increasing bending rigidity first, and then decreases with the increasing bending rigidity. In a square lattice system, however, the critical force always decreases with the increasing bending rigidity. In contrast, when the intrinsic curvature is greater than the critical value, the larger bending rigidity always results in a larger critical force in both lattice systems.

We study two-dimensional disordered semiflexible biopolymers with finite mean intrinsic curvature (MIC). We find exact distribution function of orientational angle for the system with short-range correlation (SRC) in intrinsic curvatures. We show that with a finite MIC, our theoretical end-to-end distances can be fitted well to some experimental data of DNA with long-range correlation (LRC) in sequences. Moreover, we find that the variance of the orientational angle has the same power-law behavior as that of the bending profile for DNA with LRC in sequences. Our results provide a way to evaluate MIC and suggest that the LRC in sequences can result in a SRC in intrinsic curvatures.

We study the effect of an intrinsic curvature to the mechanical property of a semiflexible biopolymer by using Monte Carlo simulation method. We find that under external force and with moderate intrinsic curvature and bending rigidity, the extension of a semiflexible biopolymer can undergo a sharp transition at finite temperature. The critical force increases with increasing intrinsic curvature or bending rigidity.