Classification and stability analysis of polarising and depolarising travelling wave solutions for a model of collective cell migration

TL;DR

This paper analyzes four types of travelling wave solutions in a 1D model of collective cell migration, examining their stability through spectral theory and numerical methods, with implications for understanding cell sheet behaviors.

Contribution

It identifies and classifies four distinct travelling wave solutions in a cell migration model and assesses their stability using spectral analysis and Evans function computations.

Findings

Four types of travelling waves characterized in the model.

Stability of these waves determined through spectral analysis.

Most Evans function computations performed explicitly.

Abstract

We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent polarisation and depolarisation waves resulting from either colliding or departing cell sheets as observed in model wound experiments. We study the linear stability of the travelling wave solutions numerically and using spectral theory. This involves the computation of the Evans function most of which we are able to carry out explicitly, with one final step left to numerical simulation.