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

We study a two-type branching process which provides an excellent description of experimental data on cell dynamics in skin tissue. The model involves only a single type of progenitor cell, that is it 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 for the generating function of the number of cells of different types. The generating function is then used to numerically determine the time dependent probability distribution of the numbers of the two types of cells. We also deduce large time asymptotic behaviors drawing on exact results and on a diffusion approximation.