On the swimming motion of spheroidal magnetotactic bacteria

We investigate, via both theoretical and experimental methods, the swimming motion of magnetotactic bacteria having the shape of an elongated prolate spheroid in a viscous liquid under the influence of an imposed magnetic field. A fully three-dimensional Stokes flow, driven by the translation and rotation of a swimming bacterium, exerts a complicated viscous drag/torque on the motion of a non-spherical bacterium. By assuming that the body of the bacterium is non-deformable and that the interaction between different bacteria is weak and hence negligible, we have derived a system of 12 coupled nonlinear ordinary differential equations that govern both the motion and the orientation of a swimming spheroidal magnetotactic bacterium. The focus of the study is on how the shape of a non-spherical magnetotactic bacterium, marked by the size of its eccentricity, affects the pattern of its swimming motion. It is revealed that the pattern/speed of a swimming spheroidal magnetotactic bacterium is highly sensitive not only to the direction of its magnetic moment but also to its shape. We also compare the theoretical pattern obtained from the solutions of the 12 coupled differential equations with that observed in the laboratory experiments using the magnetotactic bacteria found in Lake Miyun near Beijing, China, showing that the observed pattern can be largely reproduced with an appropriate set of parameters in our theoretical model. (paper)