A simple reaction-diffusion system as a possible model for the origin of chemotaxis

TL;DR

This paper introduces a reaction-diffusion model inspired by cell polarity regulators to explain the emergence of chemotaxis, demonstrating through analysis and simulations that directed movement speed correlates with chemical gradient size.

Contribution

It presents a novel reaction-diffusion framework for chemotaxis origin, analyzing its mathematical properties and linking movement speed to chemical gradient, inspired by cell polarity mechanisms.

Findings

Global regularity proven in 1D and 2D cases.

Simulations show movement speed proportional to chemical gradient.

Model aligns with Keller-Segel chemotaxis behavior.

Abstract

Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur based on purely reaction-diffusion equations reflecting inner working of the cells. The model is inspired by the well-studied role of the rho-GTPase Cdc42 regulator of cell polarity, in particular in yeast cells. We analyze several versions of the model in order to better understand its analytic properties, and prove global regularity in one and two dimensions. Using computer simulations, we demonstrate that in the framework of this model, at least in certain parameter regimes, the speed of the directed movement appears to be proportional to the size of the gradient of signalling chemical. This coincides with the form of the chemical drift in the most studied mean field model of chemotaxis, the Keller-Segel equation.