Exact solution of a two-type branching process: Clone size distribution in cell division kinetics

TL;DR

This paper presents an exact mathematical solution for a two-type branching process modeling cell division, providing insights into clone size distribution and cell dynamics in skin tissue without assuming stem cell support.

Contribution

It derives an exact solution for a simplified progenitor cell model, enabling precise analysis of cell division and differentiation processes.

Findings

Exact generating function solutions for cell number distributions

Asymptotic behaviors of clone sizes at large times

Validation of diffusion approximation against exact results

Abstract

We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells. We derive an exact solution of this model in terms of generating functions for the total number of cells, and for the number of cells of different types. We also deduce large time asymptotic behaviors drawing on our exact results, and on an independent diffusion approximation.