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

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

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.

Citation

Kynaston, J. C., Guiver, C., & Yates, C. A. (2022). An equivalence framework for an age-structured multi-stage representation of the cell cycle. Physical Review E, 105(6), https://doi.org/10.1103/PhysRevE.105.064411

• 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
• DOI: https://doi.org/10.1103/PhysRevE.105.064411
• Public URL: http://researchrepository.napier.ac.uk/Output/2874534