细胞分化的结构化群体模型
A Structured Population Model of Cell Differentiation
摘要：
我们介绍并分析了一种新的细胞分化模型的几个方面。它假定祖细胞的分化是一个连续的过程。从数学的观点看，它是建立在输运型的偏微分方程基础上的。具体地说，它由一个结构化的人口方程与非线性反馈回路。这模拟了由于调节分化和增殖过程的细胞因子引起的信号传导过程。我们将连续模型与其离散模型进行比较，离散模型是Marciniak-Czochra等人最近在2009年提出的一种离散细胞亚群集合的多房室模型，用于研究造血系统的动力学。我们得到的解决方案的统一界限，稳定状态的解决方案，并分析其线性化的稳定性。我们展示了如何持久性或灭绝可能会发生根据值的参数特征的干细胞自我更新。我们还进行了数值模拟，并讨论了连续模型与离散模型的定性行为。
英文摘要：
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.
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