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Rapidly dividing tissues, like intestinal crypts, are frequently chosen toinvestigate the process of tumor initiation, because of their high rate ofmutations. To study the interplay between normal and mutant as well as immortalcells in the human colon or intestinal crypt, we developed a 4-compartmentalstochastic model for cell dynamics based on current discoveries. Recent studiesof the intestinal crypt have revealed the existence of two stem cell groups.Therefore, our model incorporates two stem cell groups (central stem cells(CeSCs) and border stem cells (BSCs)), plus one compartment for transitamplifying (TA) cells and one compartment of fully differentiated (FD) cells.However, it can be easily modified to have only one stem cell group. We findthat the worst-case scenario occurs when CeSCs are mutated, or an immortal cellarises in the TA or FD compartments. The probability that the progeny of asingle advantageous CeSC mutant will take over the entire crypt is more than$0.2$, and one immortal cell always causes all FD cells to becomeimmortals.Moreover, when CeSCs are either mutants or wild-type (w.t.)individuals, their progeny will take over the entire crypt in less than 100days if there is no immortal cell. Unexpectedly, if the CeSCs are wild-type,then non-immortal mutants with higher fitness are washed out faster than thosewith lower fitness. Therefore, we suggest one potential treatment for coloncancer might be replacing or altering the CeSCs with the normal stem cells.

New Insights into Initiation of Colon and Intestinal Cancer: The Significance of Central Stem Cells in the Crypt