A Structured Population Model of Cell Differentiation

TL;DR

This paper presents a new continuous structured population model for cell differentiation based on PDEs, compares it with a discrete model, and analyzes stability, persistence, and extinction scenarios through mathematical and numerical methods.

Contribution

It introduces a novel PDE-based model for cell differentiation with nonlinear feedback and compares it to existing discrete models, providing new insights into system dynamics.

Findings

Uniform bounds for solutions established

Steady states characterized and stability analyzed

Numerical simulations illustrate model behavior

Abstract

We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential equations of transport type. Specifically, it consists of a structured population equation with a nonlinear feedback loop. This models the signaling process due to cytokines, which regulate the differentiation and proliferation process. We compare the continuous model to its discrete counterpart, a multi-compartmental model of a discrete collection of cell subpopulations recently proposed by Marciniak-Czochra et al. in 2009 to investigate the dynamics of the hematopoietic system. We obtain uniform bounds for the solutions, characterize steady state solutions, and analyze their linearized stability. We show how persistence or extinction might occur according to values of parameters that characterize the stem cells self-renewal. We also perform numerical simulations and discuss the qualitative behavior of the continuous model vis a vis the discrete one.