Closed-loop control of magnetotactic bacteria

Abstract

Realization of point-to-point positioning of a magnetotactic bacterium (MTB) necessitates the application of a relatively large magnetic field gradients to decrease its velocity in the vicinity of a reference position. We investigate an alternative closed-loop control approach to position the MTB. This approach is based on the characterization of the magnetic dipole moment of the MTB and its response to a field with alternating direction. We do not only find agreement between our characterized magnetic dipole moment and previously published results, but also observe that the velocity of the MTB decreases by 37% when a field with alternating direction is applied at 85 Hz. The characterization results allow us to devise a null-space control approach which capitalizes on the redundancy of magnetic-based manipulation systems. This approach is based on two inputs. The first controls the orientation of the MTB, whereas the second generates a field with alternating direction to decrease its velocity. This control is accomplished by the redundancy of our magnetic-based manipulation system which allows for the projection of the second input onto the null-space of the magnetic force-current map of our system. A proportional–derivative control system positions the MTB at an average velocity and region of convergence of 29 μm s−1 and 20 μm, respectively, while our null-space control system achieves an average velocity and region of convergence of 15 μm s−1 and 13 μm, respectively.