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280 CHAPTER 13

parents from earlier generations is f, then the approximation expands
to un p /(un p + un g + f). My point here is simply that, as long as f is
small, a significant fraction of important de novo mutations may hap-
pen developmentally rather than be inherited from parents.
Few estimates exist for n p , the number of precursor cell generations.
The little bit known about retinal development and the inherited can-
cer syndrome retinoblastoma raises some interesting issues. Retino-
blastoma usually occurs before the age of five. Without modern medi-
cal treatment, the disease would often be fatal, so the affected individ-
ual would not reproduce. The inherited syndrome includes early onset
and multiple independent tumors, usually with tumors in both eyes.
According to the analysis here, the inherited syndrome would derive
from developmental mutations approximately in a proportion of cases
n p /(n p + n g ).
The number of retinal precursor generations, n p , remains unknown.
Zaghloul et al. (2005) recently reviewed the subject of retinal develop-
ment and concluded that, based on the Xenopus model, the left and right
retina diverge rather late in development. Thus, there may be a sig-
nificant number of precursor generations, n p , before divergence of the
common retinal precursors into the left and right eye. A developmen-
tal mutation before left-right divergence could predispose to bilateral
retinoblastoma, a symptom usually attributed to an inherited mutation.

13.2 Stem-Transit Design
Mutations in transit cells usually get washed out as the transit cells
slough at the surface (Cairns 1975). Most cell divisions occur in the
transit lineages, and those divisions pose relatively little cancer risk. Be-
cause of the mutational washout advantage of transit lineages, it would
seem that natural selection would favor a stem-transit separation with
short-lived transit lineages. But adaptation may be more subtle.
Figure 13.5 shows the possibilities for design of a stem-transit archi-
tecture (Frank et al. 2003). Suppose a tissue requires k new cells over a
certain period to renew itself. For now, assume that no other constraints
exist with regard to renewal. To make k cells starting from one cell, the
tissue may use n 1 stem cell divisions leading to n 1 transit lineages, each
transit lineage dividing n 2 times to produce 2 n 2 final cells, for a total of
k = n 1 2 n 2 cells.