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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer US
2016
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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. |
format | Online Article Text |
id | pubmed-5090018 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
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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