# Topotaxis of active Brownian particles

## TL;DR

This paper presents a toy model demonstrating that active Brownian particles can exhibit topotaxis, moving directionally due to spatial variations in obstacle spacing that modulate their persistence, highlighting persistence as a key driver.

## Contribution

The study introduces a simplified active particle model showing how topographical gradients induce directed motion through persistence modulation, advancing understanding of topotaxis mechanisms.

## Key findings

- Persistence varies with obstacle spacing
- Particles move toward regions of higher persistence
- Persistence alone can drive topotaxis

## Abstract

Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, is especially prominent among cells persistently crawling within a spatially varying distribution of cell-sized obstacles. In this article we introduce a toy model of topotaxis based on active Brownian particles constrained to move in a lattice of obstacles, with space-dependent lattice spacing. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles' persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells.