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Evolution of resistance and progression to disease during clonal expansion of cancer

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  • Durrett, Richard
  • Moseley, Stephen

Abstract

Inspired by previous work of Iwasa et al. (2006) and Haeno et al. (2007), we consider an exponentially growing population of cancerous cells that will evolve resistance to treatment after one mutation or display a disease phenotype after two or more mutations. We prove results about the distribution of the first time when k mutations have accumulated in some cell, and about the growth of the number of type-k cells. We show that our results can be used to derive the previous results about a tumor grown to a fixed size.

Suggested Citation

  • Durrett, Richard & Moseley, Stephen, 2010. "Evolution of resistance and progression to disease during clonal expansion of cancer," Theoretical Population Biology, Elsevier, vol. 77(1), pages 42-48.
    • Handle: RePEc:eee:thpobi:v:77:y:2010:i:1:p:42-48
    DOI: 10.1016/j.tpb.2009.10.008
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    Citations

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    Cited by:

    1. Burden, Conrad J. & Wei, Yi, 2018. "Mutation in populations governed by a Galton–Watson branching process," Theoretical Population Biology, Elsevier, vol. 120(C), pages 52-61.
    2. Sophie Pénisson & Amaury Lambert & Cristian Tomasetti, 2022. "Evaluating cancer etiology and risk with a mathematical model of tumor evolution," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    3. Foo, Jasmine & Leder, Kevin & Schweinsberg, Jason, 2020. "Mutation timing in a spatial model of evolution," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6388-6413.
    4. Durrett, Rick & Foo, Jasmine & Leder, Kevin & Mayberry, John & Michor, Franziska, 2010. "Evolutionary dynamics of tumor progression with random fitness values," Theoretical Population Biology, Elsevier, vol. 78(1), pages 54-66.
    5. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    6. Hwai-Ray Tung & Rick Durrett, 2021. "Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective," PLOS Computational Biology, Public Library of Science, vol. 17(2), pages 1-12, February.
    7. Michael D Nicholson & Tibor Antal, 2019. "Competing evolutionary paths in growing populations with applications to multidrug resistance," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-25, April.

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