Hook-transmitted torque drives spinning and precession of bacterial flagella

Bacterial propulsion is powered by torque generated by the flagellar motor and transmitted to the flagellum through the hook, a short deformable structure acting as a flexible joint. Despite the hook being essential for propulsion, the physical mechanism governing torque transmission remains poorly characterized. Here, we show that the torque consists of two components: one parallel to the flagellum, responsible for rapid spin, and another along the motor axis, which induces precession of the former component. Evidence of such a two-component torque also emerge in bead assay experiments, where the attached bead can exhibit complex trajectories rather than simple circular motion. We introduce a minimal mechanical model that captures both the spin/precession dynamics and the commonly observed circular orbits.