Sorbonne Université, Université Paris-Diderot, CNRS, INRIA, Laboratoire Jacques-Louis Lions, F-75005 Paris, France.
Sorbonne Université, Institut de biologie Paris-Seine (IBPS), UMR 7238 CNRS Laboratoire de Biologie Computationnelle et Quantitative, F-75005 Paris, France.
Math Biosci Eng. 2019 May 29;16(5):4818-4845. doi: 10.3934/mbe.2019243.
We propose a mathematical model to describe the evolution of hematopoietic stem cells (HSCs) and stromal cells in considering the bi-directional interaction between them. Cancerous cells are also taken into account in our model. HSCs are structured by a continuous phenotype characterising the population heterogeneity in a way relevant to the question at stake while stromal cells are structured by another continuous phenotype representing their capacity of support to HSCs. We then analyse the model in the framework of adaptive dynamics. More precisely, we study single Dirac mass steady states, their linear stability and we investigate the role of parameters in the model on the nature of the evolutionary stable distributions (ESDs) such as monomorphism, dimorphism and the uniqueness properties. We also study the dominant phenotypes by an asymptotic approach and we obtain the equation for dominant phenotypes. Numerical simulations are employed to illustrate our analytical results. In particular, we represent the case of the invasion of malignant cells as well as the case of co-existence of cancerous cells and healthy HSCs.
我们提出了一个数学模型来描述造血干细胞（HSCs）和基质细胞的演化，同时考虑了它们之间的双向相互作用。我们的模型还考虑了癌细胞。HSCs 由一种连续的表型来构建，这种表型以与问题相关的方式描述了群体异质性，而基质细胞则由另一种连续的表型来构建，这种表型代表了它们对 HSCs 的支持能力。然后，我们在自适应动力学的框架内分析了该模型。更准确地说，我们研究了单个 Dirac 质量稳态，它们的线性稳定性，以及研究了模型中参数对进化稳定分布（ESD）的性质的影响，如单态、双态和唯一性特征。我们还通过渐近方法研究了主要表型，并得到了主要表型的方程。数值模拟用于说明我们的分析结果。特别是，我们代表了恶性细胞入侵的情况，以及癌细胞和健康 HSCs 共存的情况。
