Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process.
Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process.
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DOI：
10.1007/s10955-014-1143-3
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发表时间：
2015-02
影响因子：
1.6
通讯作者：
Levine H
中科院分区：
文献类型：
--
作者：
Kessler DA;Levine H
很久以前，Luria和Delbrück提出了一种最流行的模型，用于定量了解细菌菌落和恶性肿瘤中耐药性的出现。在这里，个体抗性突变体在指数增长的敏感群体的出生事件中随机出现。当群体规模N很大，突变率很低时，这个过程会出现一个最有趣的极限，但与1/N相比，突变率不一定很小。这里我们提供了一个在这个极限下有效的标度解，它与Levy α稳定分布理论相联系，特别是朗道很久以前讨论过的那个。这种关联的一个后果是，分布的矩在表征典型行为时具有高度误导性。使我们的解决方案成为可能的一个关键见解是，在固定人口规模的集合中工作与在固定时间的集合中工作是不一样的。我们的一些结果已经在前面以简短的形式提出
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 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 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 α-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 shortened form