Extreme statistics of mutation accumulations in stem cell populations: a model for cancer initiation risk

Abstract: 

Cancer can be initiated by a single cell in a tissue if a critical constellation of mutations triggers over-proliferation of that cell. Thus, within a large population of tissue cells, the one cell which is closest to a critical accumulation of mutations is determining the probability of triggering cancer. When considering the risk of cancer initiation by random mutations, it is therefore important to study the statistics of extreme accumulations of mutations within a cell population, rather than population averages. In this talk I will present some results on the extreme value statistics of mutation numbers in a dividing stem cell population, represented by a Moran process, to compare the risk of cancer initiation under different modes of stem cell divisions (symmetric vs. asymmetric divisions). While for asymmetric divisions the accumulation of mutations occurs independently in each stem cell, which allows the approximation by a Generalised Extreme Value Distribution, such a canonical approach to the problem is not possible under symmetric divisions. I will show how to retrieve approximate results for statistics of the maximum number of mutations in the latter situation, by an analogy between the cell population’s genealogical tree and a branching random walk.