Many microorganisms propel themselves through their viscous surroundings by rotating slender filamentous appendages called flagella. Flagella are typically helical, and it is tempting to put this down to Purcell's "scallop theorem": a straight filament rotated at one end in a viscous environment (i.e. at zero Reynolds number) cannot generate net forward thrust, but helical filaments can. But, as a recent study showed, this is true only for rigid filaments, and initially straight semi-flexible filaments can in fact generate thrust, provided the applied torque is high enough. Beyond a critical value of torque, such filaments undergo a wrapping transition to a twisted shape which allows them to then act as propellers.

We use detailed simulations and simplified lumped-parameter models to show that an intrinsic helicity in the filament rest-shape does confer advantages to both singly- and multiply-flagellated microbial swimmers.

In single filaments twirled at their ends, the wrapping transition and associated hysteresis is less pronounced, and eventually disappears completely as intrinsic helicity is increased. This allows for smoother operating characteristics in single flagella. In many species, multiple flagella "bundle" together when rotated in the same direction to achieve unidirectional runs, and "unbundle" if counterrotated to cause tumbling to change directions. The greater hydrodynamic attraction in more twisted filament pairs is shown to play a crucial role in this behaviour.