Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908424339456000 |
|---|---|
| author | Wang, Ren-Yi Kimmel, Marek Pang, Guodong |
| author_facet | Wang, Ren-Yi Kimmel, Marek Pang, Guodong |
| contents | 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 $0$ cells, and the second compartment consists of post-mitotic cells in the blood, referred to as type $1$ cells. Division and self-renewal of type $0$ cells are regulated by the population density of type $1$ 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 $L^{2}$ Hilbert space. Finally, we apply our results to compare the effects of regulating division and self-renewal of type $0$ cells, providing insights into their respective roles in maintaining hematopoietic system stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis Wang, Ren-Yi Kimmel, Marek Pang, Guodong Populations and Evolution 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 $0$ cells, and the second compartment consists of post-mitotic cells in the blood, referred to as type $1$ cells. Division and self-renewal of type $0$ cells are regulated by the population density of type $1$ 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 $L^{2}$ Hilbert space. Finally, we apply our results to compare the effects of regulating division and self-renewal of type $0$ cells, providing insights into their respective roles in maintaining hematopoietic system stability. |
| title | Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis |
| topic | Populations and Evolution |
| url | https://arxiv.org/abs/2404.19041 |