Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers
Figure 6
Fixation and exponential growth of two-mutation cells with dedifferentiation for variable stem cell population size.
A: Observed growth rate of the stem cell population (black curve) and the semi-analytic approximation Eq. (18) (green) for
,
, and
. The vertical line denotes
. B: Analytically predicted critical dedifferentiation rate
as a function of asymmetric division probability
and the growth advantage
of the two-mutation progenitor population. Exponential growth occurs for
. C: Normalized histogram (stars) of waiting times for exponential growth of the stem cell population with stochastic homeostasis and dedifferentiation for
,
. For comparison the histogram (red and black dots) as well as the analytical distributions of times to fixation given strict homeostasis for
and
are also shown. D: The median and inter-quantile range of times to first occurrence of
two-mutation stem cells, given stochastic homeostasis and a range of dedifferentiation rates
. For comparison, the waiting times to fixation for
given strict homeostasis (shaded areas) for the equivalent value of
are also shown. E: The probability that the first two-mutation stem cell arose from mutation in the stem cell compartment, rather than dedifferentiation. Vertical line denotes
. Parameters for all simulations given in Table 1.