On the motion of magnetotactic bacteria: theoretical predictions and experimental observations

The movement of magnetotactic bacteria is done in a viscous media in the low Reynolds number regime. In the present research, the simple model for magnetotactic bacteria motion, proposed by Nogueira and Lins de Barros (Eur Biophys J 24:13-21, 1995), was used to numerically simulate their trajectory. The model was done considering a spherical bacterium with a single flagellum and a magnetic moment positioned in the sphere center and parallel to the flagella. The numerical solution shows that the trajectory is a cylindrical helix and that the body Euler angles have linear dependencies on time. Using that information, analytical expressions were obtained for the first time for the center-of-mass coordinates, showing that the trajectories are helixes oriented to the magnetic field direction. They also show that the magnetic moment does not align to the magnetic field, but it precesses around it, being fully oriented only for very high magnetic fields. The analytical solution obtained permits to relate for the first time the flagellar force to the axial velocity and helical radius. Trajectories of uncultivated magnetotactic bacteria were registered in video and the coordinates were obtained for several bacteria in different magnetic fields. The trajectories showed to be a complex mixture of two oscillating functions: one with frequency lower than 5 Hz and the other one with frequency higher than 10 Hz. The simple model of Nogueira and Lins de Barros shows to be incomplete, because is unable to explain the trajectories composed of two oscillating functions observed in uncultivated magnetotactic bacteria.