Modeling and Optimization Analysis of Single Flagellum
Bacterial Motion
Edgar
Lobaton and Alexandre Bayen
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to appear in the 2007 American Control Conference - New York, July 2007
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presented at the Modeling
and control of physical networks workshop, satelite event from the Hybrid
Systems, Computation and Control (HSCC 2007) workshop, Pisa, Italy, April
2007.
| Abstract | Bacteria such as Rhodobacter sphaeroides
use a single flagellum for propulsion and change of orientation. Simple organisms
such as this have inspired nanorobotic designs with potential applications in
medicine which motivates the present work. In this article, an elastic model for
a single flagellum bacterium is presented and followed by an analysis of the system
based on optimization. The model is based on the method of Regularized Stokeslet
which allows for a discretization of the system into particles which are connected
by spring forces. An optimal elasticity distribution that maximizes the mean forward
speed is obtained. These elasticity coefficients are obtained through the use
of an adjoint-based optimization scheme. The results are illustrated through a
simulation showing improvement on the swimming patter of the bacteria. | |  |
Movies
(Click on Images)
| | Real swimming bacteria.
Short section of a swimming cell with the flagellum labeled with a
fluorescent dye. Courtesy of Judith P. Armitage, University
of Oxford. | | |
| | |
Change of configuration
of virtual bacteria. This movie shows the deformation on the flagellum
in slow motion from its rest state as the torque is applied at its base. Animated
Picture (GIF) | |
| | 3D
motion (left) and path of center of mass (right). The torque is reversed
and t=500, and reset at t=530. A change of orientation of about
30 degrees is observed. Animated Pictures (GIF1 - GIF2) | | |
| | | Optimization
results. Comparison between initial uniform distribution (top) and
optimal distribution (bottom). The mean forward speed has increased by a factor
of 76%. Animated Picture (GIF) | |
