Stokesian dynamics simulations of a magnetotactic bacterium

Sarah Mohammadinejad,Damien Faivre,Stefan Klumpp

doi:10.1140/epje/s10189-021-00038-5

Abstract

The swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles (lesssim {20^{circ }}) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.Graphic abstract

Highlights

Can be steered by a magnetic field [10,11], which provides a promising biocompatible option for the remote control of swimming
The model incorporates the magnetic moment of the cell body, which interacts with the field, the helical structure of the flagellum as well as its elasticity and the torque due to the flagellar motor
We developed a detailed model for the propulsion and orientation of magnetotactic bacteria (MTB) based on Stokesian dynamics and investigated their swimming in the presence of an external magnetic field

Summary

Introduction

Can be steered by a magnetic field [10,11], which provides a promising biocompatible option for the remote control of swimming. Notable exceptions are studies on the coordination of two flagella at opposite poles in Magnetospirillum magneticum (AMB-1) [23], of two velocity modes in Magnetospirillum gryphiswaldense (MSR-1) [24] and of the cooperation of two flagellar bundles almost perpendicular to the magnetic moment in Magnetococcus marinus (MC-1) [9]. These studies are complemented by theoretical approaches. We present two scenarios that are relevant from an experimental point of view: we investigated the U-turns that are observed when the magnetic field is reversed and asked whether an inclination of the magnetic moment relative to the flagellar propulsion axis is detrimental to the swimming motion

Methods

Results

Conclusion