Page 22 - 20dynamics of cancer

INTRODUCTION 7

chemical carcinogenesis experiments. I follow with the separate line of
mathematical multistage theory that developed in the 1950s to explain
the patterns of incidence curves. Ashley (1969a) and Knudson (1971)
provided the most profound empirical test of multistage progression.
They reasoned that if somatic mutation is the normal cause of progres-
sion, then individuals who inherit a mutation would have one less step
to pass before cancer arises. By the mathematical theory, one less step
shifts the incidence curve to earlier ages and reduces the slope (accel-
eration) of failure. Ashley (1969a) compared incidence in normal indi-
viduals and those who inherit a single mutation predisposing to colon
cancer: he found the predicted shift in incidence to earlier ages among
the predisposed individuals. Knudson (1971) found the same predicted
shift between inherited and noninherited cases of retinoblastoma.
I continue Chapter 4 with various developments in the theory of multi-
stage progression. One common argument posits that somatic mutation
alone pushes progression too slowly to account for incidence; however,
the actual calculations remain ambiguous. Another argument empha-
sizes the role of clonal expansion, in which a cell at an intermediate
stage divides to produce a clonal population that shares the changes
suffered by the progenitor cell. The large number of cells in a clonal
population raises the target size for the next failure that moves pro-
gression to the following stage. I then discuss various consequences
of cell lineage history and processes that influence the accumulation of
change in lineages. I end by returning to the somatic mutation rate, and
how various epigenetic changes such as DNA methylation or histone
modification may augment the rate of heritable change in cell lineages.

Part II turns to the dynamics of progression and the causes of the in-
cidence curve. I first present extensive, original developments of multi-
stage theory. I then apply the theory to comparisons between differ-
ent genotypes that predispose to cancer and to different treatments of
chemical carcinogens. I also apply the quantitative theory of age-specific
failure to other causes of death besides cancer; the expanded analysis
provides a general theory of aging.
Chapter 5 sets the background for the quantitative analysis of inci-
dence. Most previous theory fit specific models to the data of incidence
curves. However, fitting models to the data provides almost no insight;