Swimming motion of rod-shaped magnetotactic bacteria: the effects of shape and growing magnetic moment

We investigate the swimming motion of rod-shaped magnetotactic bacteria affiliated with the Nitrospirae phylum in a viscous liquid under the influence of an externally imposed, time-dependent magnetic field. By assuming that fluid motion driven by the translation and rotation of a swimming bacterium is of the Stokes type and that inertial effects of the motion are negligible, we derive a new system of the twelve coupled equations that govern both the motion and orientation of a swimming rod-shaped magnetotactic bacterium with a growing magnetic moment in the laboratory frame of reference. It is revealed that the initial pattern of swimming motion can be strongly affected by the rate of the growing magnetic moment. It is also revealed, through comparing mathematical solutions of the twelve coupled equations to the swimming motion observed in our laboratory experiments with rod-shaped magnetotactic bacteria, that the laboratory trajectories of the swimming motion can be approximately reproduced using an appropriate set of the parameters in our theoretical model.