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Universal Asymptotic Clone Size Distribution for General Population Growth

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria–Delbrück or Lea–Coulson mode...

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Detalles Bibliográficos
Autores principales: Nicholson, Michael D., Antal, Tibor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5090018/
https://www.ncbi.nlm.nih.gov/pubmed/27766475
http://dx.doi.org/10.1007/s11538-016-0221-x
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author Nicholson, Michael D.
Antal, Tibor
author_facet Nicholson, Michael D.
Antal, Tibor
author_sort Nicholson, Michael D.
collection PubMed
description Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria–Delbrück or Lea–Coulson model, is often assumed but seldom realistic. In this article, we generalise this model to different types of wild-type population growth, with mutants evolving as a birth–death branching process. Our focus is on the size distribution of clones—that is the number of progeny of a founder mutant—which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. Additionally, for a large class of population growth, we prove that the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. Considering metastases in cancer as the mutant clones, upon analysing a data-set of their size distribution, we indeed find that a power-law tail is more likely than an exponential one.
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spelling pubmed-50900182016-11-17 Universal Asymptotic Clone Size Distribution for General Population Growth Nicholson, Michael D. Antal, Tibor Bull Math Biol Original Article Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria–Delbrück or Lea–Coulson model, is often assumed but seldom realistic. In this article, we generalise this model to different types of wild-type population growth, with mutants evolving as a birth–death branching process. Our focus is on the size distribution of clones—that is the number of progeny of a founder mutant—which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. Additionally, for a large class of population growth, we prove that the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. Considering metastases in cancer as the mutant clones, upon analysing a data-set of their size distribution, we indeed find that a power-law tail is more likely than an exponential one. Springer US 2016-10-20 2016 /pmc/articles/PMC5090018/ /pubmed/27766475 http://dx.doi.org/10.1007/s11538-016-0221-x Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Original Article
Nicholson, Michael D.
Antal, Tibor
Universal Asymptotic Clone Size Distribution for General Population Growth
title Universal Asymptotic Clone Size Distribution for General Population Growth
title_full Universal Asymptotic Clone Size Distribution for General Population Growth
title_fullStr Universal Asymptotic Clone Size Distribution for General Population Growth
title_full_unstemmed Universal Asymptotic Clone Size Distribution for General Population Growth
title_short Universal Asymptotic Clone Size Distribution for General Population Growth
title_sort universal asymptotic clone size distribution for general population growth
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5090018/
https://www.ncbi.nlm.nih.gov/pubmed/27766475
http://dx.doi.org/10.1007/s11538-016-0221-x
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