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

Gopinath Sadhu, Philip K Maini, Mohit Kumar Jolly

TL;DR

A connection is established 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.

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.

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

TL;DR

A connection is established 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.

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.
Paper Structure (8 sections, 21 equations, 1 figure)

This paper contains 8 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A two population go-or-grow model
  3. A single-equation formulation for the coupled phenotypes model
  4. Connecting $D(c)$ and $r(c)$ with $\mu(c)$, $\lambda_1(c)$, and $\lambda_2(c)$
  5. The conditions $D'(c)<0$ and $r'(c)>0$ are satisfied for the mixed phenotype single equation
  6. Numerical results
  7. Model analysis for limiting cases
  8. Discussion and future direction

Figures (1)

  • Figure 1: Time evolution of the proliferative ($p$), migratory cell ($m$) and total (sum of proliferative and migratory cells) and mixed phenotype cell density ($n$) in (A) fast phenotype regimes and (B) rapid oxygen oscillation regimes. Here, $D_m=0.01$, $\lambda_{pm}=10$,$\lambda_{mp}=20$, $\mu_p=1$, $L=10, K=1, c_H=0.5$ and the hill coefficient $k=3$. The period of cyclic hypoxia ($T_{\mathrm{oxy}}$) is 10 in (A) and 0.001 in (B).