Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact

TL;DR

This paper links microscopic stochastic models of cell movement with macroscopic equations, revealing how chemotaxis and cell shape fluctuations influence tissue growth and structure formation.

Contribution

It derives a nonlinear diffusion equation from microscopic cell dynamics incorporating excluded volume effects, connecting stochastic models to continuum descriptions.

Findings

Nonlinear diffusion coefficient depends on cellular volume fraction.

Macroscopic equations prevent cellular density collapse.

Good agreement between Monte Carlo simulations and macroscopic solutions.

Abstract

A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.