### Mathematical Biosciences and Engineering

2017, Issue 5&6: 1379-1397. doi: 10.3934/mbe.2017071

# A mathematical model of stem cell regeneration with epigenetic state transitions

• Received: 18 May 2016 Accepted: 15 January 2017 Published: 01 October 2017
• MSC : Primary: 92B05, 34D20; Secondary: 92D25

• 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.

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

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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