LogisticCrypt — A logistic model of intestinal crypt structure

Cancer - uncontrolled cell proliferation, is caused by the deregulation of key genes that control cellular mechanisms, including division, differentiation, apoptosis, and movement. Here, we introduce LogisticCrypt, a logistic model on crypt structure at specific time points, which focuses on cell division, differentiation and apoptosis rates and on cell competition in crypt space. Comparative analysis of time-intervals for occurrence of the crypt phenomena is performed with respect to deregulation in intestinal cell number between the colon and small intestine crypts, obtained during cancer initiation and when carcinogen influence applies. Results are found to be more variable for the colon crypt, compared with the small intestine crypt, suggesting that the former is more sensitive to alterations in stem cell division rate than the latter. In addition, significantly higher carcinogen impact on crypt dynamics is evident in the colon crypt, compared with the small intestine crypt: cell proliferation time was observed to decrease by factors of 13 and 4.50 respectively, compared to situations when only the progenitor compartment was affected.