Abstract

Many species of bacteria possess a single helical flagellar filament, which is connected to a motor embedded in the cell body via a short flexible segment known as a ‘hook’. As the motor rotates it winds up the hook, and this twist is in turn transmitted to the filament, which rotates the filament and leads to a propulsive force on the cell body. However, this propulsive force only allows the cell to swim forwards or backwards along a straight path (in the absence of noise); to change direction and efficiently explore their environment, several species of marine bacteria have been observed to exploit a strategy known as ‘flicking’. Flicking is an elastic instability in which the hook buckles under the compressive force generated by the filament and forms a kink, which acts to rotate the cell before the hook eventually unbuckles and the cell resumes straight swimming along a different path. 

While many studies have considered static aspects of the flicking instability, much remains unknown about its dynamics. It has been hypothesised that the hook eventually unbuckles because it stiffens under the twist applied by the motor, though the timescale of the flicking is much slower than what would be expected based on this mechanism alone. I will present a reduced mathematical model for the flicking instability, which aims to elucidate the key features of its dynamics. In particular, the model explains what limits how quickly cells can regain their maximum swimming speed once the motor reverses direction, which in turn controls how efficiently bacteria may explore their environment by flicking.