Bistable Helices

Abstract

We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.