  In order to fulfill cell proliferation and differentiation through cellular
hierarchy, stem cells can undergo either asymmetric or symmetric divisions.
Recent studies pay special attention to the effect of different modes of stem
cell division on the lifetime risk of cancer, and report that symmetric
division is more beneficial to delay the onset of cancer. The fate uncertainty
of symmetric division is considered to be the reason for the cancer-delaying
effect. In this paper we compare asymmetric and symmetric divisions of stem
cells via studying stochastic stem cell models with mutations. Specially, by
using rigorous mathematical analysis we find that both asymmetric and symmetric
models show the same statistical average, but symmetric model shows higher
fluctuation than asymmetric model. We further show that the difference between
the two models would be more remarkable for lower mutation rates. Our work
quantifies the uncertainty of cell division and highlights the significance of
stochasticity for distinguishing between different modes of stem cell division.
