A Single Equation Explains Go-or-Grow Dynamics in Cyclic Hypoxia

TL;DR

This paper develops a minimal mathematical model to explain how tumor cells switch between migratory and proliferative states under cyclic hypoxia, linking phenotype-specific dynamics to a simplified single-equation framework.

Contribution

It introduces a reduced single-equation model capturing go-or-grow tumor dynamics under cyclic hypoxia, simplifying the analysis of phenotypic switching.

Findings

The reduced model accurately replicates phenotype-specific dynamics.

Numerical simulations validate the theoretical reduction.

The model elucidates oxygen's role in phenotype transitions.

Abstract

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes linear diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether these two coupled phenotype-specific equations can be reduced to a single mixed-phenotype equation under cyclic hypoxia. We establish a connection between the minimal go-or-grow model with distinct phenotypic populations and a reduced model describing a single-cell population with oxygen-dependent diffusion and proliferation in the fast-phenotypic-switching regime. This theoretical reduction is validated through numerical simulations.