Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

Shum, H.; Gaffney, E. A.; Smith, D. J.

Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

Type

Article

Authors

Shum, H.
Gaffney, E. A.
Smith, D. J.

KAUST Grant Number

KUK-C1-013-04

Online Publication Date

2010-01-13

Print Publication Date

2010-06-08

Date

2010-01-13

Abstract

We describe a boundary-element method used to model the hydrodynamics of a bacterium propelled by a single helical flagellum. Using this model, we optimize the power efficiency of swimming with respect to cell body and flagellum geometrical parameters, and find that optima for swimming in unbounded fluid and near a no-slip plane boundary are nearly indistinguishable. We also consider the novel optimization objective of torque efficiency and find a very different optimal shape. Excluding effects such as Brownian motion and electrostatic interactions, it is demonstrated that hydrodynamic forces may trap the bacterium in a stable, circular orbit near the boundary, leading to the empirically observable surface accumulation of bacteria. Furthermore, the details and even the existence of this stable orbit depend on geometrical parameters of the bacterium, as described in this article. These results shed some light on the phenomenon of surface accumulation of micro-organisms and offer hydrodynamic explanations as to why some bacteria may accumulate more readily than others based on morphology. © 2010 The Royal Society.

Citation

Shum H, Gaffney EA, Smith DJ (2010) Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466: 1725–1748. Available: http://dx.doi.org/10.1098/rspa.2009.0520.

Acknowledgements

This publication is based on work supported in part by award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). D.J.S. acknowledges the MRC (Special Training Fellowship G0600178 in Computational Biology). The authors would like to thank Prof. John Blake of the School of Mathematics, University of Birmingham, Dr Jackson Kirkman- Brown of the Centre for Human Reproductive Science, Birmingham Women's Hospital and Mr Hermes Gadeha of the Mathematical Institute, University of Oxford for invaluable discussions.