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A mathematical model of stem cell regeneration with epigenetic state transitions

. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

In this paper, we study a mathematical model of stem cell regeneration with epigenetic state transitions. In the model, the heterogeneity of stem cells is considered through the epigenetic state of each cell, and each epigenetic state defines a subpopulation of stem cells. The dynamics of the subpopulations are modeled by a set of ordinary differential equations in which epigenetic state transition in cell division is given by the transition probability. We present analysis for the existence and linear stability of the equilibrium state. As an example, we apply the model to study the dynamics of state transition in breast cancer stem cells.

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Keywords Stem cell; population dynamics; epigenetic state; histone modification; DNA methylation; stability

Citation: Qiaojun Situ, Jinzhi Lei. A mathematical model of stem cell regeneration with epigenetic state transitions. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1379-1397. doi: 10.3934/mbe.2017071

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