Page 87 - 20dynamics of cancer

72 CHAPTER 4

Ashley (1969b) used the standard Armitage and Doll (1954) multi-
stage model to fit data for gastric cancer. He calculated n = 7 stages
and a mutation rate of 10 −3 . His calculations are a bit hard to follow,
but he seems to be using somatic mutation rate per year. He concluded
that the fitted mutation rate appears to be high, although he seemed
not to be aware of the scaling he used for his mutation rate estimate.
In any case, this high number may have influenced subsequent authors
by suggesting that the standard multistage theory requires a very high
mutation rate. For example, Knudson (1971) stated in his introduction:
“What is lacking, however, is direct evidence that cancer can ever arise
in as few as two steps and that each step can occur at a rate that is
compatible with accepted values for mutation rates.”
Stein (1991, p. 167) provides the following calculation to support his
argument that five or more hits are very unlikely based on standard
somatic mutation processes:

It is generally agreed that mutation rates in mammalian cells occur
with a frequency of some 10 −5 to 10 −6 mutations per cell genera-
tion (Evans 1984) [see also Lichten and Haber (1989), Yuan and Keil
(1990), Kohler et al. (1991)]. Thus, five independent, simultaneous
mutations will occur at a frequency of some 10 −25 to 10 −30 muta-
tions per cell generation. To score such a 5-hit event will require
the elapse of some 10 25 through 10 30 generations. Now the human
body, in an average lifetime, produces a total of only 10 16 cells, or
that number (minus one) of cell divisions. By this calculation, on a
5-hit model, cancer should seldom occur—indeed, in not more than
10 −9 down to 10 −14 of the population—that is, never. The model
requires mutation rates of some 10 −3 per cell division for it to be
applicable, rates which are most unlikely to be found.

The apparent contradiction between the commonly accepted somatic
mutation rate and those rates supposedly needed for a multiple-hit the-
ory may have played an important role in how the theory developed.
In particular, Loeb has emphasized that an early stage in carcinogenesis
must very often be mutation to the DNA repair system (Loeb 1991; Beck-
man and Loeb 2005). Subsequent hypermutation could then explain how
cancer cells obtain the multiple mutations that most tissues apparently
need for transformation (Rajagopalan et al. 2003; Michor et al. 2004).
The fact that many tumors have chromosomal instabilities supports the
hypermutation theory.