  Traditionally, it has been held that a central characteristic of stem cells
is their ability to divide asymmetrically. Recent advances in inducible genetic
labeling provided ample evidence that symmetric stem cell divisions play an
important role in adult mammalian homeostasis. It is well understood that the
two types of cell divisions differ in terms of the stem cells' flexibility to
expand when needed. On the contrary, the implications of symmetric and
asymmetric divisions for mutation accumulation are still poorly understood. In
this paper we study a stochastic model of a renewing tissue, and address the
optimization problem of tissue architecture in the context of mutant
production. Specifically, we study the process of tumor suppressor gene
inactivation which usually takes place as a sequence of two consecutive "hits",
and which is one of the most common patterns in carcinogenesis. We compare and
contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on
the rate at which double-hit mutants are generated. It turns out that
symmetrically-dividing cells generate such mutants at a rate which is
significantly lower than that of asymmetrically-dividing cells. This result
holds whether single-hit (intermediate) mutants are disadvantageous, neutral,
or advantageous. It is also independent on whether the carcinogenic double-hit
mutants are produced only among the stem cells or also among more
differentiated cells. We argue that symmetric stem cell divisions in mammals
could be an adaptation which helps delay the onset of cancers. We further
investigate the question of the optimal fraction of stem cells in the tissue,
and quantify the contribution of non-stem cells in mutant production. Our work
provides a hypothesis to explain the observation that in mammalian cells,
symmetric patterns of stem cell division seem to be very common.
