Crawling and turning in a minimal reaction-diffusion cell motility model: coupling cell shape and biochemistry

TL;DR

This paper presents a minimal reaction-diffusion model linking cell shape and biochemistry to explain persistent crawling and turning behaviors in eukaryotic cells, highlighting how simple mechanical-biochemical couplings can produce complex motility patterns.

Contribution

It introduces a coupled reaction-diffusion and mechanics model that explains cell shape, polarity, and turning behaviors, revealing how shape-biochemistry interactions induce motility instabilities.

Findings

Cells exhibit both straight and turning trajectories in the model.

Turning arises from coupling between reaction-diffusion polarity and cell shape.

Model suggests similar mechanisms may underlie polarity-driven motility in various cells.

Abstract

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability, and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.