Mutant number distribution in an exponentially growing population. (9th January 2015)

• Record Type: Journal Article
• Authors: Keller, Peter; Antal, Tibor
• Is Part Of: Journal of statistical mechanics. (2015:Jan.)
• Publication Date: 2015-01-09
• Subjects: 9 -- 10; 9/300 -- 10/300 -- 10/380; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/01/P01011
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491–511) 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 grow 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 Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3 ) for a fully stochastic version of the process.