Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation

TL;DR

This paper develops a comprehensive kinetic framework for structured populations, specifically cells characterized by age and size, integrating stochastic growth and demographic variability into PDE and birth-death models.

Contribution

It introduces a full kinetic equation approach that unifies deterministic PDE and stochastic birth-death models for structured populations.

Findings

Derived kinetic equations for age and size structured populations.

Showed how stochastic growth influences population dynamics.

Unified PDE and birth-death process descriptions within a single framework.

Abstract

We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer" model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations.