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dc.contributor.authorMontgomery-Smith, Stephen ( Orcid Icon 0000-0003-1979-5520 )
dc.contributor.authorOveys, Hesam ( )
dc.date.accessioned2021-08-27T16:01:03Z
dc.date.available2021-08-27T16:01:03Z
dc.date.issued2021-06-23
dc.identifier.citationMontgomery-Smith, S. J., & Oveys, H. (2021). Age-dependent branching processes and applications to the Luria-Delbruck experiment. Electronic Journal of Differential Equations, 2021(56), pp. 1-22.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14466
dc.description.abstractMicrobial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and Max Delbrück that won them a Nobel Prize in 1969 confirmed that mutations don't occur out of necessity, but instead can occur many generations before there is a selective advantage, and thus organisms follow Darwinian evolution instead of Lamarckian. Since then, new areas of research involving microbial evolution have spawned as a result of their experiment. Determining the mutation rate of a cell is one such area. Probability distributions that determine the number of mutants in a large population have been derived by Lea, Coulson, and Haldane. However, not much work has been done when time of cell division is dependent on the cell age, and even less so when cell division is asymmetric, which is the case in most microbial populations. Using probability generating function methods, we rigorously construct a probability distribution for the cell population size given a life-span distribution for both mother and daughter cells, and then determine its asymptotic growth rate. We use this to construct a probability distribution for the number of mutants in a large cell population, which can be used with likelihood methods to estimate the cell mutation rate.en_US
dc.formatText
dc.format.extent22 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectProbability generating functionen_US
dc.subjectFluctuation analysisen_US
dc.subjectAsymmetric cell divisionen_US
dc.subjectLaplace transformen_US
dc.titleAge-dependent branching processes and applications to the Luria-Delbruck experimenten_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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