Abstract
Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.
Highlights
There is an extensive literature on cancer modelling, which goes way beyond evolutionary game theory
Evolutionary game theory is increasingly used in cancer modelling (Rockne et al, 2019; Archetti and Pienta, 2019; Wölfl et al, 2020) both to elucidate tumorigenesis (Tomlinson and Bodmer, 1997; Bach et al, 2003; Basanta et al, 2008; Basanta et al, 2008; Archetti, 2016) and to inform potential treatment strategies (Basanta et al, 2012; Kaznatcheev et al, 2017; Zhang et al, 2009; West et al, 2018)
These cancers both originate in epithelial cells, of the lung and pancreas, respectively
Summary
Oncogenesis is a process of somatic evolution. In order to become cancerous there are certain key mutations which cells must obtain, corresponding to the hallmarks of cancer (Hanahan and Weinberg, 2000; Hanahan and Weinberg, 2011). Certain mutations can be considered cooperative, in that they invoke a cost to the cell which is recuperated as a shared benefit. This is evident when the benefit relies on the production of a diffusible growth factor (Jouanneau et al, 1994; Axelrod et al, 2006), as is the case for a number of the hallmarks of cancer, such as self-sufficiency in growth signalling and sustained angiogenesis. Cooperative mutations benefit the population as a whole; it is often the case that defection (e.g. not producing growth factor) results in higher individual fitness This is because the defector shares in the benefits without paying any fitness costs associated with cooperating. This is detrimental to the patient, and disrupting cooperation between cancer subclones, possibly by exploiting its evolutionary weaknesses, could be an important avenue for treatment (Archetti, 2013a; Zhou et al, 2017)
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