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Mutation frequencies in a birth-death branching process. (English) Zbl 1404.60122
Summary: First, we revisit the stochastic Luria-Delbrück model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously published cancer genomic data.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J28 Applications of continuous-time Markov processes on discrete state spaces
92D10 Genetics and epigenetics
92C50 Medical applications (general)
92D20 Protein sequences, DNA sequences
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