Page 290 - 20dynamics of cancer

STEM CELLS: POPULATION GENETICS 275

consider how the stochastic process of mutational events translates into
the number of final cells that carry a mutation at a particular locus
(Zheng 1999; Frank 2003b; Zheng 2005). For example, how do muta-
tions during development translate into the number of initially mutated
stem cells at the end of development?

NUMBER OF INITIALLY MUTATED STEM CELLS

A small number of somatic mutations during development can lead to
a significant fraction of stem cells carrying a mutation that predisposes
to cancer. How much of the risk of cancer can be attributed to mutations
that arise in development?
No one has tried to measure developmental risk. But a few simple
calculations based on standard assumptions about cell division and mu-
tation rate show that developmental risk may be important (Frank and
Nowak 2003).
8
Suppose that N = 10 stem cells must be produced during devel-
opment to seed the colon. Exponential growth of one cell into N cells
requires about ln(N) cellular generations in the absence of cell death.
8
In this case, ln(10 ) ≈ 18. If the mutation rate per locus per cell divi-
sion during exponential growth is u e , then the probability that any final
stem cell carries a mutation at a particular locus, x, is roughly the mu-
tation rate per cell division multiplied by the number of cell divisions,
x = u e ln(N). This probability is usually small: for example, if u e = 10 −6 ,
then x is of the order of 10 −5 .
The frequency of initially mutated stem cells may be small, but the
number may be significant. The average number of mutated cells at a
particular locus is the number of cells, N, multiplied by the probability of
3
mutation per cell, x. In this example, Nx ≈ 10 , or about one thousand.
I have focused on mutations at a single locus. Mutations at many
different loci may predispose to cancer. Suppose mutations at L differ-
ent loci can contribute to predisposition. We can get a rough idea of
how multiple loci affect the process by simply adjusting the mutation
rate per cell division to be a genome-wide rate of predisposing muta-
tions, equal to u e L. The number of loci that may affect predisposition
2
may reasonably be around L ≈ 10 and perhaps higher. Following the
2
calculation in the previous paragraph, with L ≥ 10 , the number of ini-
tial stem cells carrying a predisposing mutation would on average be at