期刊
JOURNAL OF STATISTICAL PHYSICS
卷 158, 期 4, 页码 783-805出版社
SPRINGER
DOI: 10.1007/s10955-014-1143-3
关键词
Luria-Delbruck; Mutants; Growth; Alpha-stable distribution
资金
- NSF Center for Theoretical Biological Physics [PHY-1308264]
- CPRIT Scholar program of the State of Texas
- Israeli Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1427654, 1308264] Funding Source: National Science Foundation
One 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 Delbruck. 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 N is large and mutation rates are low, but not necessarily small compared to 1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy alpha-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 form [12].
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