  Peritrichously-flagellated bacteria, such as Escherichia coli, self-propel in
fluids by using specialised motors to rotate multiple helical filaments. The
rotation of each motor is transmitted to a short flexible segment called the
hook which in turn transmits it to a flagellar filament, enabling swimming of
the whole cell. Since multiple motors are spatially distributed on the body of
the organism, one would expect the propulsive forces from the filaments to push
against each other leading to negligible swimming. We use a combination of
computations and theory to show that the swimming of multi-flagellated bacteria
is enabled by an elastohydrodynamic bending instability occurring for hooks
more flexible than a critical threshold. Using past measurements of hook
bending stiffness, we demonstrate how the design of real bacteria allows them
to be safely on the side of this instability that promotes systematic swimming.
