标题： 年龄结构多阶段细胞周期表示的等价框架 显示英文标题

标题： An equivalence framework for an age-structured multi-stage representation of the cell cycle

摘要： 我们建立了分年龄的个体细胞种群的随机模型和确定性模型之间的理论等价关系。 具体而言，我们建立了一个分层方程系统，描述了用于近似细胞周期时间分布的分年龄多阶段马尔可夫过程的完整动力学。 我们进一步证明，在长时间尺度上，所得的平均行为等价于经典的麦肯德里克-冯·福斯特积分-偏微分方程。 最后，我们将这一框架扩展到空间情境，促进了行进波现象和细胞介导的模式形成的建模。 更一般地，这种方法可以扩展到众多反应扩散过程，其中个体的年龄对动力学是相关的。 显示英文摘要

摘要： We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multi-stage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behaviour is equivalent, over large timescales, to the classical McKendrick-von Foerster integro-partial differential equation. We conclude by extending this framework to a spatial context, facilitating the modelling of travelling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.