Moran process version of the tug-of-war model: Behavior revealed by mathematical analysis and simulation studies

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dc.citation.firstpage4532
dc.citation.issueNumber8
dc.citation.journalTitleDiscrete and Continuous Dynamical Systems - B
dc.citation.lastpage4563
dc.citation.volumeNumber28
dc.contributor.authorBobrowski, Adam
dc.contributor.authorKimmel, Marek
dc.contributor.authorKurpas, Monika K.
dc.contributor.authorRatajczyk, Elżbieta
dc.date.accessioned2023-04-25T14:47:37Z
dc.date.available2023-04-25T14:47:37Z
dc.date.issued2023
dc.description.abstractIn a series of publications McFarland and co-authors introduced the tug-of-war model of evolution of cancer cell populations. The model is explaining the joint effect of rare advantageous and frequent slightly deleterious mutations, which may be identifiable with driver and passenger mutations in cancer. In this paper, we put the tug-of-war model in the framework of a denumerable-type Moran process and use mathematics and simulations to understand its behavior. The model is associated with a time-continuous Markov Chain (MC), with a generator that can be split into a sum of the drift and selection process part and of the mutation process part. Operator semigroup theory is then employed to prove that the MC does not explode, as well as to characterize a strong-drift limit version of the MC which displays 'instant fixation' effect, which was an assumption in the original McFarland's model. Mathematical results are confirmed by simulations of the complete and limit versions. Simulations also visualize complex stochastic transients and genealogies of clones arising in the model.
dc.identifier.citationBobrowski, Adam, Kimmel, Marek, Kurpas, Monika K., et al.. "Moran process version of the tug-of-war model: Behavior revealed by mathematical analysis and simulation studies." <i>Discrete and Continuous Dynamical Systems - B,</i> 28, no. 8 (2023) Amerian Institute of Mathematical Sciences: 4532-4563. https://doi.org/10.3934/dcdsb.2023029.
dc.identifier.digital10-3934_dcdsb-2023029
dc.identifier.doihttps://doi.org/10.3934/dcdsb.2023029
dc.identifier.urihttps://hdl.handle.net/1911/114808
dc.language.isoeng
dc.publisherAmerian Institute of Mathematical Sciences
dc.rightsThis is an open access article under the CC BY-NC-ND license
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleMoran process version of the tug-of-war model: Behavior revealed by mathematical analysis and simulation studies
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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