BCAM-Basque Center for Applied Mathematics, Bizkaia Technology Park, Derio, Spain.
J Biol Dyn. 2012;6 Suppl 1:2-18. doi: 10.1080/17513758.2011.558214. Epub 2011 Jun 24.
We study two- and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result.
我们研究了一个具有细胞分裂受成熟细胞水平调节的层次细胞生产系统的两室和三室模型。我们研究了平衡状态相对于参数的结构以及平衡状态的局部稳定性性质。为了解释结果，我们将生态学中众所周知的繁殖数的概念应用于干细胞群体动力学。在两室模型中，只要存在正平衡点，它就是稳定的。在三室模型中，我们发现分化的中间阶段是导致参数平面中不稳定性区域出现的原因。此外，我们证明了这个区域随着成熟细胞的死亡率增加而缩小，并讨论了这个结果。
