# B07 - Inferring active particle dynamics by data assimilation

This project started with the second funding period in July 2021.

## Objectives

This interdisciplinary research project is placed at the interface of stochastic modelling, statistical inference, and data assimilation applied to bacterial motility. Bacterial motility is a subject related to essential biological functions such as the spreading of infections or the formation of biofilms. We will combine experimental studies of a bacterial model swimmer with data assimilation techniques to develop a modelling framework for the complex, stochastic motility patterns of active swimmers given observations of their trajectories. The central question of how to systematically infer dynamical models of actively driven entities based on trajectory data is not specific to the motility of bacteria but of general interest in the field of active matter.

Active motion in biology is inherently stochastic and dominated by fluctuations. Flagellated bacteria, for example, can switch randomly between different modes of motility, each of them characterised by a distinct speed and typical fluctuations. These may have different causes, such as the internal stochasticity in the regulatory biochemical pathways, or the complex nature of the flagellar dynamics. Notably, variability in motility characteristics implies that population-averaged quantities can qualitatively differ from the actual behaviour of individuals. Moreover, experimental observations are often limited in spatial and temporal resolution. Dedicated data assimilation methods are therefore needed to disentangle the different sources of fluctuations and disorder, and to handle limited amounts of trajectory data.

Using the soil bacterium *Pseudomonas putida* as a model organism, we will bring data assimilation techniques to the field of active matter in this project. Our goal is the development of a modelling framework for the complex, stochastic motility patterns of bacterial swimmers given observations of their trajectories. A particular focus is the assessment of cell-to-cell variability in the motility parameters within a bacterial population. We are specifically planning to combine experimental particle tracking and stochastic modeling to also unveil the motility pattern of this bacterial swimmer as a function of the environmental conditions (quorum sensing). For more information on our previous research on *P. putida*, we refer to Refs. [1-4]. The experimental part of the project is complemented by the development of algorithms for the systematic inference of Langevin-type models for the dynamics of active swimmers. This includes the order of the differential equation as well as the properties of temporal fluctuations. Disentangling different sources of noise and determining the distributions of motility parameters across a population are central challenges in this context. To this end, maximum likelihood estimation and Bayesian parameter inference will be employed.

References and further reading

[1] M. Theves et al. “A bacterial swimmer with two alternating speeds of propagation“ *Biophys. J.***105** 1915

[2] M. Hintsche et al. “A polar bundle of flagella can drive bacterial swimming by pushing, pulling and coiling around the cell body“ *Sci. Rep.***7** 16771

[3] Z. Alirezaeizanjani et al. “Chemotaxis strategies of bacteria with multiple run modes” *Sci. Adv.***6** eaaz6153

[4] L.G. Nava et al. “A novel approach to chemotaxis: Active particles guided by internalclocks” *Europhys. Lett.***130** 68002

## Preprints

Datta, A., Beta, C. and Großmann, R. (2024).

*The random walk of intermittently self-propelled particles.*arXiv:2406.15277 (2024)Albrecht, J. and Reich, S. (2024).

*Robust parameter estimation for partially observed second-order diffusion processes.*arXiv:2406.14738

## Publications

V. Pfeifer, V. Muraveva, and Beta, C. (2024).

*Flagella and Cell Body Staining of Bacteria with Fluorescent Dyes*in*Cell Motility and Chemotaxis: Methods and Protocols*, edited by Carsten Beta and Cristina Martinez-Torres (Springer, 2024), p.79-85.R. Großmann et al. (2024).

*Non-Gaussian Displacements in Active Transport on a Carpet of Motile Cells.*Phys. Rev. Lett.**132**(8) 088301. doi: 10.1103/PhysRevLett.132.088301Pfeifer, V., Beier, S., Alirezaeizanjani, Z., and Beta, C. (2022).

*Role of the two flagellar stators in swimming motility of Pseudomonas putida.*Mbio**13**(6) e02182-22, doi: 10.1128/mbio.02182-22.