Page 163 - 20dynamics of cancer

148 CHAPTER 8

Few attempts have been made to measure the somatic mutation rate
per gene per cell division. Yeast provide a convenient model of sin-
gle eukaryotic cells. For yeast, the mutation rate has been estimated
as 10 −7 –10 −5 (Lichten and Haber 1989; Yuan and Keil 1990). In mice,
Kohler et al. (1991) estimated the frequency of somatic mutations as
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1.7 × 10 −5 . There are roughly 10 –10 divisions in a mouse cell lineage,
so this study suggests a somatic mutation rate per cell division on the
order of 10 −7 –10 −6 . I use the approximate value of 10 −6 per gene per
cell generation.
The number of cell divisions, C(t), is roughly in the range 15–40,
because there are probably about 15–25 cell divisions before the start of
retinal development, and it takes about 15 cellular generations to make
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the e 15 ≈ 10 –10 cells in the fully developed retina. Thus, I U (t)/I B (t) ≈
10 −4 –10 −5 , and this ratio may increase by a factor of about two during
early childhood as C(t) increases from around 15–25 at the start of
retinal development to roughly 30–40 in the final cellular generations in
the retina.
These rough calculations lead to two qualitative predictions (Frank
2005). First, the ratio of unilateral to bilateral age-specific incidence
should be roughly 10 −4 –10 −5 . Second, the ratio of unilateral to bilateral
incidence should approximately double with age over the period of reti-
nal growth as the number of cellular generations, C(t), increases with
time.
Figure 8.2b shows that the ratio of unilateral to bilateral incidence is
in the predicted range of 10 −4 –10 −5 , roughly the somatic mutation rate
multiplied by the number of cellular generations. This ratio approxi-
mately doubles from the earliest age of 0–1 to the latest age of 2–3 at
which sufficient numbers of bilateral cases occur to estimate incidence
rates. The increase of this ratio supports the prediction that unilateral
incidence increases relative to bilateral incidence as the number of cel-
lular generations increases.

DIFFERENCE BETWEEN SPORADIC AND INHERITED ACCELERATION

Individuals who inherit a mutation are born one step further along
than are individuals who do not inherit a mutation. Thus, my simple
theory predicted that the ratio of sporadic to inherited incidence would