Mathematical modeling of monoclonal conversion in the colonic crypt.

A novel spatial multiscale model of a colonic crypt is described, which couples the cell cycle (including cell division) with the mechanics of cell movement. The model is used to investigate the process of monoclonal conversion under two hypotheses concerning stem cell behavior. Under the first hypothesis, 'stem-ness' is an intrinsic cell property, and the stem cell population is maintained through asymmetric division. Under the second hypothesis, the proliferative behavior of each cell is governed by its microenvironment through a biochemical signalling cue, and all cell division is symmetric. Under each hypothesis, the model is used to run virtual experiments, in which a harmless labeling mutation is bestowed upon a single cell in the crypt and the mutant clonal population is tracked over time to check if and when the crypt becomes monoclonal. It is shown that under the first hypothesis, a stable structured cell population is not possible without some form of population-dependent feedback; in contrast, under the second hypothesis, a stable crypt architecture arises naturally. Through comparison with an existing spatial crypt model and a non-spatial stochastic population model, it is shown that the spatial structure of the crypt has a significant effect on the time scale over which a crypt becomes monoclonal.