Trajectory of a model bacterium

It is well known that bacteria, such as Escherichia coli, propel themselves in aqueous media by rotating helically shaped flagella. While a number of theoretical approaches have been proposed to model the detailed swimming motion, a rigorous comparison with experimental data is lacking due to the difficulty in simultaneously visualizing the motion of the head and the flagella along with the resulting trajectory. To this end, we have built a macroscopic working model of a bacterium and visualized its detailed motion in high-viscosity liquid. We show that a small asymmetry in the mass distribution in the head can lead to helical trajectories with large pitch and radius, which are reminiscent of the wiggling trajectories observed for swimming bacteria. The detailed motion agrees well with the predictions from slender-body theory that accounts for the asymmetric mass distribution in the head. Our study shows that the trajectory consists of two helical trajectories of different length scales - a large one caused by the asymmetric mass distribution and set by the head rotation rate, and a smaller one caused by the rotating flagellum and set by its rotation rate. We discuss implications of these results on the wiggling trajectories of swimming bacteria