Travelling waves in a minimal go-or-grow model of cell invasion

TL;DR

This paper analyzes a minimal model of cell invasion where cells switch between proliferating and moving states, revealing that wave speeds are bounded by the Fisher-KPP model, with implications for understanding invasion dynamics.

Contribution

It introduces a density-dependent go-or-grow model and derives bounds on wave speeds using a connection to Fisher-KPP equations.

Findings

Wave speed in the go-or-grow model is always bounded by Fisher-KPP wave speed.

The model simplifies to a reaction-diffusion equation with density-dependent terms.

Traveling wave solutions are characterized and bounded in the minimal model.

Abstract

We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis in the fast switching regime shows that the total cell density in the two-population go-or-grow model can be described in terms of a single reaction-diffusion equation with density-dependent diffusion and proliferation. Using the connection to single-population models, we study travelling wave solutions, showing that the wave speed in the go-or-grow model is always bounded by the wave speed corresponding to the well-known Fisher-KPP equation.