Age-dependent branching processes and applications to the Luria-Delbruck experiment

Electronic Journal of Differential Equations

article

Stephen J. Montgomery-Smith¹  Hesam Oveys² 

[1] Department of Mathematics University of Missouri Columbia MO 65211;Courant Institute of Mathematical Sciences New York University New York

关键词: Probability generating function;    fluctuation analysis;    asymmetric cell division;    Laplace transform.;   

DOI  :  10.58997/ejde.2021.56

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

Microbial populations adapt to their environment by acquiring advantageous mutations,but in the early twentieth century, questions about how these organisms acquire mutationsarose. The experiment of Salvador Luria and Max Delbrück that won them a Nobel Prizein 1969 confirmed that mutations don't occur out of necessity, but instead can occur manygenerations before there is a selective advantage, and thus organisms follow Darwinianevolution instead of Lamarckian. Since then, new areas of research involving microbialevolution have spawned as a result of their experiment. Determining the mutation rateof a cell is one such area. Probability distributions that determine the number of mutantsin 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 microbialpopulations. Using probability generating function methods, we rigorously construct aprobability distribution for the cell population size given a life-span distribution forboth 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 largecell population, which can be used with likelihood methods to estimate the cell mutation rate.

【 授权许可】

CC BY