Evolution of resistance and progression to disease during clonal expansion of cancer. (English) Zbl 1403.92171
Summary: Inspired by previous work of Y. Iwasa [“Evolution of resistance during clonal expansion”, Genetics 172, No. 4, 2557–2566 (2005; doi:10.1534/genetics.105.049791)] and H. Haeno et al. [“The evolution of two mutations during clonal expansion”, Genetics 177, No. 4, 2209–2221 (2007; doi:10.1534/genetics.107.078915)], 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.
MSC:
| 92D15 | Problems related to evolution |
| 92C50 | Medical applications (general) |
| 92D10 | Genetics and epigenetics |
| 60J85 | Applications of branching processes |
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