Helical trajectories of swimming cells with a flexible flagellar hook

A model bacterium with a flexible flagellar hook generically swims along helical trajectory, even when incorporating detailed hydrodynamics. bifurcation in the hook's equilibrium bending angle below critical stiffness can have dramatic effect on trajectory's pitch angle. Analytical predictions for bifurcation's dependence spontaneous curvature, shape of cell body, and flagellum geometry are provided.