Natural tristability of a confined helical filament with anisotropic bending rigidities

Abstract

AbstractWe find that when $$c_0 R\sim 0.5$$ c 0 R ∼ 0.5 and $$\tau _0R<0.11<c_0R$$ τ 0 R < 0.11 < c 0 R , confining a helical filament with anisotropic bending rigidities within a cylindrical tube of radius R can create a natural tristable status which is consisted of two low-pitch helices and one high-pitch helix, where a helical filament is referred to as a filament that has both an intrinsic curvature ($$c_0$$ c 0 ) and an intrinsic twist rate ($$\tau _0$$ τ 0 ). The formation of the tristable status also requires that the filament has a significant difference between two bending rigidities and a large twisting rigidity. The relative heights of two low-pitch helices in a tristable status are close to zero, and the smaller the intrinsic twisting angle, the smaller the difference between these two heights. Moreover, at a large intrinsic twisting angle, two low-pitch helices display a large energy difference, and the energy difference increases with decreasing $$\tau _0$$ τ 0 . Meanwhile, the relative height of the high-pitch helix is always close to that of a straight line. Finally, at some specific intrinsic parameters, the tristable status can include an isoenergic status with two helices of the same energy but distinct pitches.