Page 162 - 20dynamics of cancer

GENETICS OF PROGRESSION 147

at which a somatic mutation occurs in the tissue at a particular age,
subsuming all the details that together determine that rate.
In particular, we take our estimate for age-specific bilateral incidence
as our estimate for the rate at which second hits occur in the tissue
at a particular age. Clearly, this simplifies the real process; for exam-
ple, bilateral cases require at least one hit in each eye. However, the
probability of two second hits leading to bilateral cases is fairly high at
roughly 0.1–0.3 (Figure 2.6c), thus the probability of one second hit is
√ √
about 0.1– 0.3, the same order of magnitude as the probability of two
second hits. So let’s proceed with the simple approach that I B (t), the
incidence of bilateral cases at age t, provides a rough estimate of the
rate of second hits to the tissue at age t.
The incidence of unilateral cases can be written as

I U (t) ≈ f(t) I B (t) ,

where f(t) is the fraction of somatic cells at age t that carry one somatic
mutation, and I B (t) is approximately the rate at which the second hit
occurs and leads to a detectable tumor. The strongest prediction of
multistage theory arises from the comparison of sporadic and inherited
cases, so we analyze the ratio of unilateral to bilateral incidence at each
age:
I U (t)
R = ≈ f(t) ;
I B (t)
in words, the ratio of unilateral to bilateral rates should be roughly f(t),
the fraction of cells at time t that carry the first hit in individuals that
do not inherit a mutation. For example, if f(t) = 0.1, then one-tenth of
somatic cells have a first mutation, and the susceptibility for sporadic
cases is about one-tenth of the susceptibility for inherited cases.
The expected number of somatic mutational events suffered by a gene
in a particular cell is the mutation rate per cell division, v, multiplied by
the number of cell divisions going back to the embryo. Let the number
of cell divisions at age t be C(t), so that vC(t) is the expected number
of mutational events. For most assumptions, vC(t) << 1, so we can
take vC(t) ≈ f(t) as the fraction of cells at time t that carry a somatic
mutation, and thus
I U (t)
R = ≈ vC (t) . (8.1)
I B (t)