  Many bacteria are motile by means of one or more rotating rigid helical
flagella, making them the only known organism to use rotation as a means of
propulsion. The rotation is supplied by the bacterial flagellar motor, a
particularly powerful rotary molecular machine. At the base of each flagellum
is the hook, a soft helical polymer that acts as a universal joint, coupling
rotation of the rigid membrane-spanning rotor to rotation of the rigid
extra-cellular flagellum. In multi-flagellated bacterial species, where thrust
is provided by a hydrodynamically coordinated bundle of flagella, the
flexibility of the hook is particularly crucial, as many of the flagella within
the bundle rotate significantly off-axis from their motor. But, consequently,
the thrust produced by a single rotating flagellum applies a significant
bending moment to the hook. So, the hook needs to simultaneously provide the
compliance necessary for off-axis bundle formation and the rigidity necessary
to withstand the large hydrodynamical forces of swimming. To elucidate how the
hook can fulfill this double functionality, measurements of the mechanical
behavior of individual hooks under dynamical conditions are needed. Here, via
new high-resolution measurements and a novel analysis of hook fluctuations
during in vivo motor rotation in bead assays, we resolve the elastic response
of single hooks under increasing torsional stress, revealing a clear dynamic
increase in their bending stiffness. Accordingly, the persistence length of the
hook increases by more than one order of magnitude with applied torque. Such
strain-stiffening allows the system to be flexible when needed yet reduce
deformation under high loads, allowing cellular motility at high speed.
