Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process

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dc.citation.firstpage783en_US
dc.citation.issueNumber4en_US
dc.citation.journalTitleJournal of Statistical Physicsen_US
dc.citation.lastpage805en_US
dc.citation.volumeNumber158en_US
dc.contributor.authorKessler, David A.en_US
dc.contributor.authorLevine, Herberten_US
dc.contributor.orgCenter for Theoretical Biological Physicsen_US
dc.date.accessioned2017-06-15T15:30:09Z
dc.date.available2017-06-15T15:30:09Z
dc.date.issued2015en_US
dc.description.abstractOne of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size NN is large and mutation rates are low, but not necessarily small compared to 1/N1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy αα-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated formen_US
dc.identifier.citationKessler, David A. and Levine, Herbert. "Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process." <i>Journal of Statistical Physics,</i> 158, no. 4 (2015) Springer: 783-805. http://dx.doi.org/10.1007/s10955-014-1143-3.
dc.identifier.doihttp://dx.doi.org/10.1007/s10955-014-1143-3en_US
dc.identifier.urihttps://hdl.handle.net/1911/94865
dc.language.isoengen_US
dc.publisherSpringer
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer.en_US
dc.subject.keywordLuria-Delbrucken_US
dc.subject.keywordalpha-stable distributionen_US
dc.subject.keywordgrowthen_US
dc.subject.keywordmutantsen_US
dc.titleScaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Processen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpost-printen_US
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