Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution

Kepler, Thomas B. and Oprea, Mihaela. (2001) Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution. Theoretical population biology, 59 (1). pp. 41-48.

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Official URL: http://edoc.unibas.ch/49777/

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The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.
Faculties and Departments:05 Faculty of Science > Departement Biozentrum > Computational & Systems Biology > Bioinformatics (Zavolan)
UniBasel Contributors:Zavolan, Mihaela
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Academic Press
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:14 Nov 2017 15:14
Deposited On:14 Nov 2017 15:14

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