Papers

The wiggling trajectories of bacteria

Yunkyong Hyon^a1, Marcos^a2, Thomas R. Powers^a3, Roman Stocker^a4 and Henry C. Fu^a1 c1

^a1 Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA

^a2 School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore

^a3 School of Engineering and Department of Physics, Brown University, Providence, RI 02912, USA

^a4 Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

Many motile bacteria display wiggling trajectories, which correspond to helical swimming paths. Wiggling trajectories result from flagella pushing off-axis relative to the cell body and making the cell wobble. The spatial extent of wiggling trajectories is controlled by the swimming velocity and flagellar torque, which leads to rotation of the cell body. We employ the method of regularized stokeslets to investigate the wiggling trajectories produced by flagellar bundles, which can form at many locations and orientations relative to the cell body for peritrichously flagellated bacteria. Modelling the bundle as a rigid helix with fixed position and orientation relative to the cell body, we show that the wiggling trajectory depends on the position and orientation of the flagellar bundle relative to the cell body. We observe and quantify the helical wiggling trajectories of Bacillus subtilis, which show a wide range of trajectory pitches and radii, many with pitch larger than 4 . For this bacterium, we show that flagellar bundles with fixed orientation relative to the cell body are unlikely to produce wiggling trajectories with pitch larger than 4 . An estimate based on torque balance shows that this constraint on pitch is a result of the large torque exerted by the flagellar bundle. On the other hand, multiple rigid bundles with fixed orientation, similar to those recently observed experimentally, are able to produce wiggling trajectories with large pitches.

(Received May 27 2011)

(Reviewed March 11 2012)

(Accepted May 02 2012)

(Online publication June 15 2012)

Key Words:

• micro-organism dynamics;
• propulsion;
• swimming/flying

Correspondence:

^c1 Email address for correspondence: hfu@unr.edu