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}.