Multistable dynamics of an elastic filament with off-tangent self-propulsion

Rotational motion in active matter can arise not only from active agents with chiral equilibrium shape, but also from agents of achiral shape that exert chiral active forces. Motivated by observations of rotational motion and filament curvature in gliding assays of microtubules, which have helical microstructures, we model the dynamics of an elastic filament with a particular form of chiral active force: The self-propulsion is rotated relative to the local tangent by a fixed angle. Can such filaments move steadily along straight or curved trajectories? To answer this question, we construct a theoretical framework for the over-damped dynamics of a one-dimensional elastic filament moving over the plane with off-tangent self-propulsion. We show that the resulting equations of motion are capable of supporting multiple stationary solutions in a co-moving frame, i.e. that these filaments exhibit dynamic multi-stability in their shapes and motions. We also present simulations that confirm many of our theory's predictions while revealing additional complexity.