Detecting active L\'evy particles using differential dynamic microscopy

TL;DR

This paper extends differential dynamic microscopy to detect active Levy particles with algebraic run-time distributions, validated on synthetic data and applied to biological experiments, distinguishing between different bacterial motility types.

Contribution

The authors develop a method to identify active Levy particles using differential dynamic microscopy, capable of analyzing biological systems with algebraic run-time distributions.

Findings

E. coli does not show Levy walk signatures.

E. gracilis is better described as active Levy particles.

Detection requires accessing length scales much larger than persistence length.

Abstract

Detecting L\'evy flights of cells has been a challenging problem in experiments. The challenge lies in accessing data in spatiotemporal scales across orders of magnitude, which is necessary for reliably extracting a power-law scaling. Differential dynamic microscopy has been shown to be a powerful method that allows one to acquire statistics of cell motion across scales, which is a potentially versatile method for detecting L\'evy walks in biological systems. In this article, we extend the differential dynamic microscopy method to self-propelled L\'evy particles, whose run-time distribution has an algebraic tail. We validate our protocol using synthetic imaging data and show that a reliable detection of active L\'evy particles requires accessing length scales of an order of magnitude larger than its persistence length, if the variability in particle speed is moderate. Applying the protocol to experimental data of E. coli and E. gracilis, we find that E. coli does not exhibit a signature of L\'evy walks, while E. gracilis is better described as active L\'evy particles.