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arXiv · 2108.02249

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

Joshua C. Kynaston·Chris Guiver·Christian A. Yates
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Abstract

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.

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Joshua C. Kynaston, Chris Guiver, Christian A. Yates. 2022-06-28. An equivalence framework for an age-structured multi-stage representation of the cell cycle. https://doi.org/10.1103/physreve.105.064411

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