Measurement of the Internal Frictional Drag of the Bacterial Flagellar Motor by Fluctuation Analysis

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.

Dynamic stiffening of the flagellar hook

For many bacteria, motility stems from one or more flagella, each rotated by the bacterial flagellar motor, a powerful rotary molecular machine. The hook, a soft polymer at the base of each flagellum, acts as a universal joint, coupling rotation between the rigid membrane-spanning rotor and rigid flagellum. In multi-flagellated species, where thrust arises from a hydrodynamically coordinated flagellar bundle, hook flexibility is crucial, as flagella rotate significantly off-axis. However, consequently, the thrust applies a significant bending moment. Therefore, the hook must simultaneously be compliant to enable bundle formation yet rigid to withstand large hydrodynamical forces. Here, via high-resolution measurements and analysis of hook fluctuations under dynamical conditions, we elucidate how it fulfills this double functionality: the hook shows a dynamic increase in bending stiffness under increasing torsional stress. Such strain-stiffening allows the system to be flexible when needed yet reduce deformation under high loads, enabling high speed motility.

Bacterial motility relies on the mechanics of the “hook” the 60 nm biopolymer at the base of rotating flagella. Here, authors observe the hook stiffening as it is twisted by the rotation of the flagellum, a mechanical feat evolved for its function.