Symmetries in bacterial motility

Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order.