Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis
Abstract
We present an asymptotic analysis of a stochastic two-compartmental cell division system with regulatory mechanisms inspired by Getto et al. (2013). The hematopoietic system is modeled as a two-compartment system, where the first compartment consists of dividing cells in the bone marrow, referred to as type cells, and the second compartment consists of post-mitotic cells in the blood, referred to as type cells. Division and self-renewal of type cells are regulated by the population density of type cells. By scaling up the initial population, we demonstrate that the scaled dynamics converges in distribution to the solution of a system of ordinary differential equations (ODEs). This system of ODEs exhibits a unique non-trivial equilibrium that is globally stable. Furthermore, we establish that the scaled fluctuations of the density dynamics converge in law to a linear diffusion process with time-dependent coefficients. When the initial data is Gaussian, the limit process is a Gauss-Markov process. We analyze its asymptotic properties to elucidate the joint structure of both compartments over large times. This is achieved by proving exponential convergence in the 2-Wasserstein metric for the associated Gaussian measures on an Hilbert space. Finally, we apply our results to compare the effects of regulating division and self-renewal of type cells, providing insights into their respective roles in maintaining hematopoietic system stability.
Keywords
Cite
@article{arxiv.2404.19041,
title = {Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis},
author = {Ren-Yi Wang and Marek Kimmel and Guodong Pang},
journal= {arXiv preprint arXiv:2404.19041},
year = {2025}
}