Page 78 - 20dynamics of cancer

HISTORY OF THEORIES 63

with age. Second, what happens to any particular individual appears to
be highly stochastic, yet simple patterns emerge at the population level.
In a rarely cited paper, Charles and Luce-Clausen (1942) developed
what may be the first quantitative multistage theory. They analyzed
observations on skin tumors from mice painted repeatedly with ben-
zopyrene. They assumed that benzopyrene causes a mutation rate, u,
and that cancer arises by knockout of a single gene following two mu-
tations, one to each of the two alleles. If t is the time since the start
of painting with the carcinogen, then the probability of mutation to a
single allele is roughly ut, and the probability of two hits to a cell is
2
2
(ut) . They assumed that painting affects N cells, so that N(ut) cells
are transformed, and that the time between the second genetic hit and
growth of the transformed cell into an observable papilloma is i.
From these assumptions, the number of tumors per mouse after the
2
time of first treatment is n = N[u(t − i)] . This formula gave a good
fit to the data with reasonable values for the parameters. Thus, Charles
and Luce-Clausen (1942) provided a clearly formulated multistage the-
ory based on two genetic mutations to a single locus and fit the theory
to the age-specific incidence of tumors in a population of individuals.
They assumed that both genetic hits must happen to a single cell, after
which the single transformed cell grows into a tumor.
Muller (1951, p. 131) mentioned the need for multiple genetic hits:
“There are, however, reasons for inferring that many or most cancerous
growths would require a series of mutations in order for the cells to
depart sufficiently from the normal.” However, Muller did not connect
his statement about multiple genetic hits to age-specific incidence.
The next theoretical developments followed directly from the obser-
vation that several cancers increase in incidence roughly with a power of
age, t n−1 , where t is age and the theories suggested that n is the number
of rate-limiting carcinogenic events required for transformation. Fitting
the data yielded n ≈ 6–7 distinct events.
Whittemore and Keller (1978) usefully separate explanations for the
exponential increase of incidence with age between multicell and multi-
stage theories.
The multicell theory assumes that the distinct carcinogenic events
happen to n ≈ 6–7 different cells in a tissue (Fisher and Hollomon 1951).
If the carcinogenic events occur independently in the different cells, then
this process would yield an age-specific incidence proportional to t n−1 ,