On the Distribution of Mutants in Cell populations with Both Forward and Backward Mutation
W. Y. Tan · SIAM Journal on Applied Mathematics · 1989
Consider a population of cells, such as bacteria, consisting of nonmutant cells and k types of mutants. Recognizing that the mutation-birth-death process can be modeled as a $(k + 1)$-dimensional multivariate branching process, in this paper the probability distribution of the number of mutant cells whenthe cell population is subjected to mutation and stochastic birth and death is derived. The probability generating functions, the cumulants, and an iterative formula for computing probabilities are obtained; a representation formula for the number of mutants is also derived. The results obtained in this paper will be useful for stochastic modeling of many mutagenicity and carcinogenesis assays.