Analysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles

TL;DR

This paper develops and analyzes a linear model for structured cell populations with unidirectional motion, providing explicit formulas and applying it to ovarian follicle morphogenesis, with parameter estimation from biological data.

Contribution

It introduces a novel analytical framework for a multi-type age-dependent cell population model with unidirectional motion, including explicit formulas and biological application.

Findings

Explicit formulas for cell number moments and age distribution.

Model parameter identifiability for age-independent division rates.

Successful fitting of model to ovarian follicle development data.

Abstract

We analyze a multi-type age dependent model for cell populations subject to unidirectional motion, in both a stochastic and deterministic framework. Cells are distributed into successive layers; they may divide and move irreversibly from one layer to the next. We adapt results on the large-time convergence of PDE systems and branching processes to our context, where the Perron-Frobenius or Krein-Rutman theorem can not be applied. We derive explicit analytical formulas for the asymptotic cell number moments, and the stable age distribution. We illustrate these results numerically and we apply them to the study of the morphodynamics of ovarian follicles. We prove the structural parameter identifiability of our model in the case of age independent division rates. Using a set of experimental biological data, we estimate the model parameters to fit the changes in the cell numbers in each layer during the early stages of follicle development.