Multiscale Analysis of a Kinetic Equation for Mechanotaxis
by Benoît Perthame, Francesco Salvarani, Shugo Yasuda.
Read the paper
How do billions of individual cells coordinate to form the complex, beautiful patterns seen in nature? The answer lies in how they physically "feel" and navigate the surfaces beneath them. Bridging microscopic physics and macroscopic biology, our study introduces a mathematical framework for mechanotaxis: cells actively modify the substrate, which then feeds back on their mobility through friction. We show how this feedback can trigger self-organization, producing stripes and spots like those in bacterial colonies. Because cell motion on surfaces is central to development, cancer, wound healing, and tissue engineering, this framework offers a new way to understand how collective behavior emerges from individual rules.
Image Description: Mechanical feedback between cells and their substrate can generate diverse population-level patterns. Cells locally modify the substrate, which in turn alters their mobility and spatial organization. Our multiscale model connects these cell-scale interactions to collective behavior and shows how the strength of substrate modification can produce periodic patterns, phase-separated states, or localized clusters.
