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Mathematical Biosciences and Engineering (MBE)
 

A mathematical model of stem cell regeneration with epigenetic state transitions

Pages: 1379 - 1397, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017071

 
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Qiaojun Situ - Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China (email)
Jinzhi Lei - Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084, China (email)

Abstract: 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.

Keywords:  Stem cell, population dynamics, epigenetic state, histone modification, DNA methylation, stability.
Mathematics Subject Classification:  Primary: 92B05, 34D20; Secondary: 92D25.

Received: May 2016;      Accepted: January 2017;      Available Online: May 2017.

 References