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

Kynaston, Joshua C.; Guiver, Chris; Yates, Christian A.


Joshua C. Kynaston

Christian A. Yates


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.

Journal Article Type Article
Acceptance Date May 26, 2022
Online Publication Date Jun 21, 2022
Publication Date Jun 21, 2022
Deposit Date May 27, 2022
Publicly Available Date Jun 21, 2022
Print ISSN 1539-3755
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 105
Issue 6
Public URL


An Equivalence Framework For An Age-structured Multi-stage Representation Of The Cell Cycle (accepted version) (2.6 Mb)

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