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Equivalence framework for an age-structured multistage representation of the cell cycle
OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/e62baa84-8cbc-4662-b1fa-64f95600e0f2 • DOI: https://doi.org/10.1103/PhysRevE.105.064411
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 multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation. We conclude by extending this framework to a spatial context, facilitating the modeling of traveling 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.