  Motivated by diverse phenomena in cellular biophysics, including bacterial
flagellar motion and DNA transcription and replication, we study the overdamped
nonlinear dynamics of a rotationally forced filament with twist and bend
elasticity. Competition between twist injection, twist diffusion, and writhing
instabilities is described by a novel pair of coupled PDEs for twist and bend
evolution. Analytical and numerical methods elucidate the twist/bend coupling
and reveal two dynamical regimes separated by a Hopf bifurcation: (i)
diffusion-dominated axial rotation, or twirling, and (ii) steady-state
crankshafting motion, or whirling. The consequences of these phenomena for
self-propulsion are investigated, and experimental tests proposed.
