Fig. 7

Simulations for the human colon crypt. a Division probability distribution functions for human colon crypt. Each cell depending on its location has a different probability of division p _div (i). Here, the total number of cells in a row is 80. The location x=0 corresponds to the top of the crypt and x=79 corresponds to the bottom of the crypt. We consider five different theoretical division probability functions and one experimentally measured function. The human experimental function obtained from the positional BrdU label index in the human colon crypt from [44]. b In this plot, we assume only cells at the location x=0 die. c Here, 10 % of the time a uniform random cell death happens within the crypt. At each updating time step with probability 0.1 a location x, where 0<x<n−1, is chosen uniformly randomly for cells death. When two cells at the location x die, then a random cell located lower than the dead cells divide. This implies, the death cannot happen at very bottom of the crypt, i.e. the location x=n−1, because there is no cells located lower than this location to divide. The location of the division is chosen based on the normalized division probability function. For example, if the cells at the location x=a die, then the location of the divisions is chosen based on the probability function \(\frac {p_{div}(x)}{S}\), where a<x<n and \(S=\sum _{i=a}^{n-1} p_{div}(x)\). In both plots (b) and (c), we obtain the probability of 2-hit mutant generation \(P_{2 hit}^{gen}(T)\) at least in one location as the probability of symmetric division σ is varied. Other parameters are t=4000, u ₁=0.001, u ₂=0.01, n=80. In these simulations, we model an entire human colon crypt (i.e. 12 two-rows), so the total number of cells is 1920