Explicit and fully automatic analysis of magnetotactic bacteria motion reveals the magnitude and length scaling of magnetic moments

Magnetotactic bacteria (MTB) are a diverse group of microorganisms whose movement can be directed via a magnetic field, which makes them attractive for applications in medicine and microfluidics. One of their key properties is the magnetic moment $m$, which is challenging to measure experimentally. We perform optical imaging experiments with MSR-1 MTB, and derive both the $m$ statistics and the scaling of $m$ with the MTB size using an explicit and fully automated method to determine $m$ from the MTB trajectories via the U-turn protocol, which measures $m$ based on the U-shaped trajectories exhibited by the MTB in an applied alternating magnetic field. The proposed method is an alternative to the standard U-turn time-based moment calculation and uses the theoretical U-turn shape function we have derived. This directly accounts for the U-turn geometry and determines the moment from the U-turn branch width. We couple this approach with a robust U-turn decomposition algorithm that detects U-turns from MTB tracks regardless of their orientations. We report a linear dependence of $m$ on the size of the bacteria, accounting for the bacteria velocity variations during the U-turns. We also demonstrate that the new U-turn shape-based and the conventional time-based methods produce significantly different results. The proposed method can be used to differentiate between various types of MTB within the same population based on their velocity and magnetic moments, and to precisely characterize the magnetic properties of a culture.