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

Author:

Montgomery-Smith Stephen J.,Oveys Hesam

Abstract

Microbial 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. For more information see https://ejde.math.txstate.edu/Volumes/2021/56/abstr.html

Publisher

Texas State University

Subject

Analysis

Reference14 articles.

1. R. Bellman, T. E. Harris; On age-dependent binary branching processes, Annals of Mathematics, 55:280-295, 1952.

2. J. Diestel; Sequences and Series in Banach Spaces, volume 92 of Graduate Texts in Mathematics, Springer, 1984.

3. G. B. Folland; Real Analysis: Modern Techniques and Their Applications, Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley, 2013.

4. T. E. Harris; The Theory of Branching Processes, Courier Corporation, 2002.

5. D. E. Lea, C. A. Coulson; The distribution of the numbers of mutants in bacterial populations, Journal of Genetics, 49(3):264-285, 1949.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3