Equivalence framework for an age-structured multistage representation of the cell cycle

Area of Science:

• Mathematical Biology
• Theoretical Ecology
• Cellular Dynamics

Background:

• Stochastic and deterministic models offer different perspectives on population dynamics.
• Age stratification is crucial for understanding cell cycle progression and behavior.
• Classical models like the McKendrick-von Foerster equation are foundational but may not capture all stochastic elements.

Purpose of the Study:

• To develop theoretical equivalences between stochastic and deterministic models for age-stratified cell populations.
• To approximate cell cycle time distributions using a hierarchical system of equations for a multistage Markov process.
• To extend this framework to spatial contexts for modeling pattern formation.

Main Methods:

• Developed a hierarchical system of equations for an age-structured multistage Markov process.
• Demonstrated equivalence between the Markov process mean behavior and the McKendrick-von Foerster equation over large timescales.
• Extended the framework to incorporate spatial dimensions.

Main Results:

• Established theoretical equivalences between stochastic (Markov process) and deterministic (McKendrick-von Foerster) models.
• The developed hierarchical system accurately approximates cell cycle time distributions.
• The framework successfully extends to spatial contexts, enabling modeling of traveling waves and pattern formation.

Conclusions:

• The unified framework bridges stochastic and deterministic approaches in age-structured population dynamics.
• This methodology provides a robust tool for analyzing cell cycle and reaction-diffusion processes.
• The findings have broad implications for modeling various biological phenomena where individual age is a key factor.