Many biological active agents respond to gradients of environmental cues by redirecting their motion. In addition to the well-studied prominent examples such as phototaxis and chemotaxis, there has been considerable recent interest in topotaxis, i.e., the ability to sense and follow topographic environmental cues. A trivial topotaxis is achievable through a spatial gradient of obstacle density, though over limited length scales. Here, we introduce a type of topotaxis based on sliding of particles along obstacles—as observed, e.g., in bacterial dynamics near surfaces. We numerically demonstrate how imposing a gradient in the angle of sliding along pillars breaks the spatial symmetry and biases the direction of motion, resulting in an efficient topotaxis in a uniform pillar park. By repeating blocks of pillars with a strong gradient of sliding angle, we propose an efficient method for guiding particles over arbitrary long distances. We provide an explanation for this spectacular phenomenon based on effective reflection at the borders of neighboring blocks. Our results are of technological and medical importance for design of efficient taxis devices for living agents.

• Received 3 May 2023
• Revised 31 October 2023
• Accepted 16 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013178

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society