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Locomotion of a single-flagellated bacterium

Published online by Cambridge University Press:  21 November 2018

Yunyoung Park
Department of Mathematics, Chung-Ang University, Dongjakgu, Heukseokdong, Seoul 06974, Republic of Korea
Yongsam Kim*
Department of Mathematics, Chung-Ang University, Dongjakgu, Heukseokdong, Seoul 06974, Republic of Korea
Sookkyung Lim
Department of Mathematical Sciences, University of Cincinnati, 4199 French Hall West, Cincinnati, OH 45221, USA
Email address for correspondence:


Single-flagellated bacteria propel themselves by rotating a flagellar motor, translating rotation to the filament through a compliant hook and subsequently driving the rotation of the flagellum. The flagellar motor alternates the direction of rotation between counterclockwise and clockwise, and this leads to the forward and backward directed swimming. Such bacteria can change the course of swimming as the hook experiences its buckling caused by the change of bending rigidity. In this paper, we present a comprehensive model of a monotrichous bacterium as a free swimmer in a viscous fluid. We describe a cell body as a rigid body using the penalty method and a flagellum as an elastic rod using Kirchhoff rod theory. The hydrodynamic interaction of the bacterium is described by the regularized Stokes formulation. Our model of a single-flagellated micro-organism is able to mimic a swimming pattern that is well matched with the experimental observation. Furthermore, we find the critical thresholds of the rotational frequency of the motor and the bending modulus of the hook for the buckling instability, and investigate the dependence of the buckling angle and the reorientation of the swimming cell after buckling on the physical and geometrical parameters of the model.

JFM Papers
© 2018 Cambridge University Press 

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Park et al. supplementary movie 1

The backward and forward swimming motions of a monotrichous bacterium without a hook. The motor first rotates CW till t=50 ms and then switches to CCW rotation. When the motor rotates CW (CCW), the cell body counterrotates and the bacterium swims backward (forward).

Download Park et al. supplementary movie 1(Video)
Video 9 MB

Park et al. supplementary movie 2

The run-reverse-flick movement of a bacterium with a flexible hook. The rotation of motor changes CW to CCW at t= 20 ms, and the hook is more flexible (relaxed) from t=20 ms till t=50 ms. During this time period, there occurs a buckling instability of the hook and the flicking of the cell body. At t=50 ms, the hook becomes less flexible (loaded) again, and the helical filament begins to be aligned with the cell body.

Download Park et al. supplementary movie 2(Video)
Video 10 MB
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