Page 88 - 20dynamics of cancer

HISTORY OF THEORIES 73

Log 10 (Somatic mutation rate) -4 2 3 4 6
-2

-6

-8

10 100 1,000 10,000
Stem cell divisions

Figure 4.2 Mutation rate per cell division required to explain observed cancer
incidence for various numbers of stages in multistage progression. The x axis
shows the number of cell divisions over a lifetime, d. The calculations follow a
simple multistage model with constant mutation rate per cell division, the same
mutation rate for each transition between stages, and no clonal expansion. Can-
cer arises only after the accumulation of n mutations within a single cell lineage.
The number attached to each line show the number of stages in progression,
n, from classical multistage theory. The shaded area highlights the commonly
accepted mutation rate per cell division. I calculated the required mutation
rate per cell division, u, by solving for the value of u that satisfies the equation
n−1

N(1 − i=0 P i (ud)) ≈ C, where N is the number of distinct cell lineages in the
tissue under study, P i (x) is the Poisson probability of i events given a mean of
x events, d is the number of cell divisions per cell lineage over a lifetime in that
tissue, and C is the probability that an individual develops cancer in that tissue.
8
For this figure, I used N = 10 and C = 0.05; results change little when varying
N up or down by a factor of 10 and when varying C over the range 0.01 − 0.1.
See Chapter 6 for the mathematical background.

The need for hypermutation seems to be widely accepted (but see
Sieber et al. 2005). However, my own calculations of the somatic muta-
tion rate required to get several hits contradicts the calculation given by
Stein (1991) and the strong conclusions drawn by Loeb (1991) and Beck-
man and Loeb (2005) on the sheer implausibility of multiple mutations
accumulating in a single cell lineage (see also Calabrese et al. 2004).
Figure 4.2 shows that a somatic mutation rate on the order of 10 −5
to 10 −6 may be sufficient to explain 4–6 hits. I used a model in which
stem cells renew tissues, as happens in colorectal, epidermal, and per-
haps several other epithelial tissues, in which most human cancers arise.