A simple stochastic model for cell population dynamics in colonic crypts

Cells in colonic crypts are identified as stem, transit-amplifying (TA), or fully differentiated (FD), depending on their proliferation capability. It has been experimentally observed that the numbers of TA and FD cells vary significantly from crypt to crypt, resulting in considerable variance in the total crypt size in healthy tissue. In the present work, we propose a simple stochastic branching process to model the population dynamics of the aforementioned three cell types in a colonic crypt. We solve the model analytically, obtaining the probability distributions for the numbers of TA and FD cells, as well as the total number of cells in the crypt. For values of model parameters that correspond to healthy human crypts, all three probability distributions for TA, FD and total cell populations are in good agreement with experimental data. Furthermore, by taking into consideration the effects of APC and KRAS mutations on the number and proliferation characteristics of epithelial cells, our model is able to explain the increase in crypt size observed in early stages of colorectal tumorigenesis. Our stochastic cell population model contributes to the understanding of the mechanisms that maintain crypt size in homeostasis, and the quantification of the effects of oncogenic mutations on cell populations in the crypt. ### Competing Interest Statement The authors have declared no competing interest.