# Invariance properties of bacterial random walks in complex structures

## TL;DR

This paper demonstrates that the mean residence time of swimming bacteria in complex microstructures can be predicted by a generalized invariance property of random walks, linking geometry to bacterial behavior.

## Contribution

It introduces a generalized invariance property for bacterial random walks that predicts mean residence times based solely on free volume to surface ratio.

## Key findings

- Mean residence time is constrained by free volume to surface ratio.
- Structural disorder affects path length distributions but not mean residence time.
- Predicts bacterial colonization behavior based on geometric properties.

## Abstract

Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. This interplay of internal and external noise sources gives rise to a complex dynamical behavior that can be strongly sensitive to details and hard to model quantitatively. In striking contrast to this general picture we show that the mean residence time of swimming bacteria inside artificial complex microstructures, can be quantitatively predicted by a generalization of a recently discovered invariance property of random walks. We find that variations in geometry and structural disorder have a dramatic effect on the distributions of path length while mean values are strictly constrained by the sole free volume to surface ratio. Biological implications include the possibility of predicting and controlling the colonization of complex natural environments using only geometric informations.