Hook stiffness as a mechanical switch for torque regulation in the bacterial flagellar motor.

The bacterial flagellar motor drives cell motility by rotating the flagellar filament and converting ion flux into mechanical work. At low counterclockwise (CCW) rotational speeds, the motor operates near the thermodynamic reversible limit, where torque remains nearly constant against rotation speed for an extended range. Earlier models based on thermodynamic reversibility predict qualitatively similar behavior in the clockwise (CW) direction, regardless of the underlying mechanism of torque generation. Structural studies further support this symmetry by showing that the torque-generation machinery in the two directions is essentially mirror reversed. However, single-molecule measurements reveal a striking asymmetry: CCW rotation shows a torque plateau, whereas CW rotation displays a linear decrease in torque with increasing speed. Here, we identify that this asymmetry has a mechanical origin in the rotation-dependent elasticity of the hook rather than in the motor's torque-generating units. In CCW rotation, the hook remains bent and compliant, maintaining a separation of timescales between motor stepping and load response and thereby preserving the torque plateau in the nearly thermodynamic reversible region. In CW rotation, the hook straightens and stiffens, collapsing the timescale separation and generating the observed linear torque-speed relationship. A mathematical model that varies only the hook's bending stiffness quantitatively reproduces the experimental torque-speed curves in both directions. These results resolve the long-standing puzzle of torque-speed asymmetry and identify hook elasticity as a key physical regulator of torque transmission in rotary molecular machines.