A stochastic model of cell proliferation and death across a sequence of compartments

Abstract: Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by cellular division and cellular differentiation, events which lead to a population of cells with unique characteristics. In this paper, we model the dynamics of cells over time across a sequence of compartments. Cells within a compartment may represent being at the same spatial location or sharing the same phenotype. In this sequence of compartments, cells can either die, divide or enter an adjacent compartment. We analyse a set of ordinary differential equations to describe the evolution of the average number of cells in each compartment over time. We also focus on the progeny of a founder cell in terms of a stochastic process and analyse several summary statistics to bring insights into the lifespan of a single cell, the number of divisions during its lifespan, and the probability to die in each compartment. Numerical results inspired by cellular immune processes allow us to illustrate the applicability of our techniques.