Stochastic Models For De-differentiation In Hierarchical Tumor Tissues

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 cancerdelaying 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.