Mutant number distribution in an exponentially growing population
Abstract
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.
Keywords
Cite
@article{arxiv.1410.3307,
title = {Mutant number distribution in an exponentially growing population},
author = {Peter Keller and Tibor Antal},
journal= {arXiv preprint arXiv:1410.3307},
year = {2015}
}
Comments
23 pages, 8 figures