Table 1.

Parameters and their estimated order of magnitude (18, 31–36)

Symbol	Parameter	Value
u	Mutation rate per gene	≈10−7
nc	Number of dominant CIN genes	10–100
p0	Rate of LOH in normal cells	≈10−7
p	Rate of LOH in CIN cells	≈10−2
r	Reproductive rate of CIN cells	?
a	Reproductive rate of APC−/− cells	>1
n	Effective population size of crypt	1–1,000

For the validity of our analysis only two conditions are important: (i) we need u ≪ 1/N² (otherwise the stochastic dynamics do not proceed via mostly homogeneous states), and (ii) we need the selective advantage of APC^−/− cells, a, to be sufficiently large such that the probability of fixation of such a cell in a crypt is close to 1 (otherwise the dynamics of tunneling is very complex). Both conditions are very plausible. Only for a simple representation of the final results do we need a separation of time scales of the form ut ≪ 1, u_ct ≪ 1, and pt ≫ 1, where t is the time scale of human life in days divided by the time of cell division of the colon cells that are at risk of becoming cancer cells. The mutation rates and LOH rates are expressed per gene per cell division. The relative reproductive rate of CIN cells, r, should be <1 if there is a cost of CIN. Certain carcinogens, however, can select for CIN, which would imply r > 1.