Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

The extensive intratumor heterogeneity revealed by sequencing cancer genomes is an essential determinant of tumor progression, diagnosis, and treatment. What maintains heterogeneity remains an open question because competition within a tumor leads to a strong selection for the fittest subclone. Cancer cells also cooperate by sharing molecules with paracrine effects, such as growth factors, and heterogeneity can be maintained if subclones depend on each other for survival. Without strict interdependence between subclones, however, nonproducer cells can free-ride on the growth factors produced by neighboring producer cells, a collective action problem known in game theory as the “tragedy of the commons,” which has been observed in microbial cell populations. Here, we report that similar dynamics occur in cancer cell populations. Neuroendocrine pancreatic cancer (insulinoma) cells that do not produce insulin-like growth factor II (IGF-II) grow slowly in pure cultures but have a proliferation advantage in mixed cultures, where they can use the IGF-II provided by producer cells. We show that, as predicted by evolutionary game theory, producer cells do not go extinct because IGF-II acts as a nonlinear public good, creating negative frequency-dependent selection that leads to a stable coexistence of the two cell types. Intratumor cell heterogeneity can therefore be maintained even without strict interdependence between cell subclones. Reducing the amount of growth factors available within a tumor may lead to a reduction in growth followed by a new equilibrium, which may explain relapse in therapies that target growth factors

Multi-Player Diffusion Games on Graph Classes

We study competitive diffusion games on graphs introduced by Alon et al. [1] to model the spread of influence in social networks. Extending results of Roshanbin [8] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibrium for three players on (m x n) grids with min(m, n) >= 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.Comment: Extended version of the TAMC 2015 conference version now discussing hypercube results (added details for the proof of Proposition 1

Evolutionary games between epithelial cells: the impact of population structure and tissue dynamics on the success of cooperation

Cooperation is usually understood as a social phenomenon. However, it also occurs on the cellular level. A number of key mutations associated with malignancy can be considered cooperative, as they rely on the production of diffusible growth factors to confer a fitness benefit. Evolutionary game theory provides a framework for modelling the evolutionary dynamics of these cooperative mutations. This thesis uses evolutionary game theory to examine the evolutionary dynamics of cooperation within epithelial cells, which are the origin point of most cancers. In particular, we consider how the structure and dynamics of an epithelium affect cooperative success. We use the Voronoi tessellation model to represent an epithelium. This allows us much greater flexibility, compared to evolutionary graph theory models, to explore realistic dynamics for population updating. Initially, we consider a model where death and division are spatially decoupled. We analyse pairwise social dilemma games, focussing on the additive prisoner’s dilemma, and multiplayer public goods games. We calculate fixation probabilities, and conditions for cooperative success, by simulation, as well as deriving quasi-analytic results. Comparing with results for graph structured populations with spatially coupled birth and death, or well-mixed populations, we find that in general cooperation is promoted by local game play, but global competition for offspring. We then introduce a more realistic model of population updating, whereby death and division are spatially coupled as a consequence of contact inhibition. The strength of this coupling is positively correlated with the strength of contact inhibition. However, the extent to which strong spatial coupling inhibits cooperation depends on mechanical properties of the tissue

Cooperative success in epithelial public goods games

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.Comment: 29 Pages, 13 Figure