Simple Stochastic Theory of Stem Cell Differentiation is not Simultaneously Consistent with Crypt Extinction Probability and the Expansion of Mutated Clones

It is shown that a simple Galton-Watson branching process model of the stem-cell pool in intestinal crypts is not simultaneously consistent with observations of the dynamics of replacement of normal by mutant crypt stem cells and other observations which put limits on the probability of crypt loss through extinction of all stem cells. This is because the limits on extinction probability forces the probability that a stem-cell division yields only non-stem cells to be small, but such a small probability makes it unlikely that a mutant stem-cell clone would expand while the normal stem-cell clones decay (it is more likely that both normal and mutant clones persist). It is suggested that the fundamental assumptions of independence and constancy of stem-cell behavior are flawed.