%0 Journal Article
%T Mutant number distribution in an exponentially growing population
%A Peter Keller
%A Tibor Antal
%J Quantitative Biology
%D 2014
%I arXiv
%R 10.1088/1742-5468/2015/01/P01011
%X We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grows stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the "large population-small mutation"-limit we recover recent results of Kessler and Levin for a fully stochastic version of the process.
%U http://arxiv.org/abs/1410.3307v1