Page 287 - 20dynamics of cancer

272 CHAPTER 13

13.1 Mutations during Development

Renewing tissues typically have two distinct phases in the history of
their cellular lineages. Early in life, cellular lineages expand exponen-
tially to form the tissue. For the remainder of life, stem cells renew the
tissue by dividing to form a nearly linear cellular history. Figure 13.1
shows a schematic diagram of the exponential and linear phases of cel-
lular division.
Mutations accumulate differently in the exponential and linear phases
of cellular division (Frank and Nowak 2003). During the exponential
phase of development, a mutation carries forward to many descendant
cells. The initial stem cells derive from the exponential, developmental
phase: one mutational event during development can cause many of the
initial stem cells to carry and transmit that mutation. During the renewal
phase, a mutation transmits only to the localized line of descent in that
tissue compartment: one mutational event has limited consequences.
Development occurs over a relatively short fraction of the human
lifespan. However, a significant fraction of cancer risk may arise from
mutations during development, because the shape of cell lineage history
differs during development from that in later periods of tissue renewal
(Frank and Nowak 2003).

MUTATIONAL EVENTS VERSUS THE NUMBER OF MUTATED CELLS
Individuals begin life with one cell. At the end of development, a re-
newing tissue may have millions of stem cells. To go from one precursor
cell to N initial stem cells requires at least N − 1 cell divisions, because
each cell division increases the number of cells by one.
If the mutation rate per locus in each cellular generation is u, then how
many of the initial N stem cells carry a mutation at a particular locus?
This general kind of problem was first studied in microbial populations
by Luria and Delbrück (Luria and Delbrück 1943; Zheng 1999, 2005).
They wanted to estimate the mutation rate, u, in microbial populations
by observing the fraction of the final N cells that carry a mutation.
The Luria-Delbrück problem plays a central role in the study of can-
cer, because progression depends on how heritable changes accumulate
in cell lineages. The Luria-Delbrück analysis focuses on one aspect of