Differential Bending Stiffness of the Bacterial Flagellar Hook under Counterclockwise and Clockwise Rotations

The bacterial hook, as a universal joint coupling rotation of the flagellar motor and the filament, is an important component of the flagellum that propels the bacteria to swim. The mechanical properties of the hook are essential for the flagellum to achieve normal functions. In multiflagellated bacteria such as Escherichia coli, the hook must be compliant so that it can bend for the filaments to form a coherently rotating bundle to generate the thrust when the motor rotates counterclockwise (CCW), yet it also must be rigid so that the bundle can disrupt for the bacteria to tumble to change swimming direction when the motor rotates clockwise (CW). Here, by combining an elastic rod model with high-resolution bead assay to accurately measure the bending stiffness of the hook under CCW or CW rotation in vivo, we elucidate how the hook accomplishes this dual functionality: the hook stiffens under CW rotation, with bending stiffness under CW rotation twice as large as that under CCW rotation. This enables a robust run-and-tumble swimming motility for multiflagellated bacteria.