An individual based computational model of intestinal crypt fission and its application to predicting unrestrictive growth of the intestinal epithelium.

Intestinal crypt fission is a homeostatic phenomenon, observable in healthy adult mucosa, but which also plays a pathological role as the main mode of growth of some intestinal polyps. Building on our previous individual based model for the small intestinal crypt and on in vitro cultured intestinal organoids, we here model crypt fission as a budding process based on fluid mechanics at the individual cell level and extrapolated predictions for growth of the intestinal epithelium. Budding was always observed in regions of organoids with abundant Paneth cells. Our data support a model in which buds are biomechanically initiated by single stem cells surrounded by Paneth cells which exhibit greater resistance to viscoelastic deformation, a hypothesis supported by atomic force measurements of single cells. Time intervals between consecutive budding events, as simulated by the model and observed in vitro, were 2.84 and 2.62 days, respectively. Predicted cell dynamics was unaffected within the original crypt which retained its full capability of providing cells to the epithelium throughout fission. Mitotic pressure in simulated primary crypts forced upward migration of buds, which simultaneously grew into new protruding crypts at a rate equal to 1.03 days(-1) in simulations and 0.99 days(-1) in cultured organoids. Simulated crypts reached their final size in 4.6 days, and required 6.2 days to migrate to the top of the primary crypt. The growth of the secondary crypt is independent of its migration along the original crypt. Assuming unrestricted crypt fission and multiple budding events, a maximal growth rate of the intestinal epithelium of 0.10 days(-1) is predicted and thus approximately 22 days are required for a 10-fold increase of polyp size. These predictions are in agreement with the time reported to develop macroscopic adenomas in mice after loss of Apc in intestinal stem cells.