论文标题
干细胞的随机模型及其后代在不同的临界假设下
Stochastic Models of Stem Cells and Their Descendants under Different Criticality Assumptions
论文作者
论文摘要
我们研究具有指数分布的寿命的时间连续分支过程，两种类型的细胞根据二进制裂变而增殖。考虑了一系列可能的系统动力学，每种动力学的特征是原始细胞的突变速率和改变的细胞后代的生存概率。对于每个系统，我们为细胞计数的联合概率生成函数得出封闭形式的表达，并对细胞群的行为进行渐近分析，特别关注灭绝概率。我们的一部分结果使用不同的方法证实了分支过程的已知特性，而其他方法是原始的。虽然该模型最适合对分化干细胞的命运进行建模，但我们讨论了这些系统动力学可能适用于现实生活中的其他情况。我们还讨论了该主题的历史。
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized by the mutation rate of the original cells and the survival probability of the altered cells' progeny. For each system, we derive a closed-form expression for the joint probability generating function of cell counts, and perform asymptotic analysis on the behaviors of the cell population with particular focus on probability of extinction. Part of our results confirms known properties of branching processes using a different approach while other are original. While the model is best suited for modeling the fate of differentiating stem cells, we discuss other scenarios in which these system dynamics may be applicable in real life. We also discuss the history of the subject.
