Development of a population of cancer cells: Observation and modeling by a Mixed Spatial Evolutionary Games approach

Eco-evolutionary causes and consequences of temporal changes in intratumoural blood flow

Temporal changes in blood flow are commonly observed in malignant tumours, but the evolutionary causes and consequences are rarely considered. We propose that stochastic temporal variations in blood flow and microenvironmental conditions arise from the eco-evolutionary dynamics of tumour angiogenesis in which cancer cells, as individual units of selection, can influence and respond only to local environmental conditions. This leads to new vessels arising from the closest available vascular structure regardless of the size or capacity of this parental vessel. These dynamics produce unstable vascular networks with unpredictable spatial and temporal variations in blood flow and microenvironmental conditions. Adaptations of evolving populations to temporally varying environments in nature include increased diversity, greater motility and invasiveness, and highly plastic phenotypes, allowing for broad metabolic adaptability and rapid shifts to high rates of proliferation and profound quiescence. These adaptive strategies, when adopted in cancer cells, promote many commonly observed phenotypic properties including those found in the stem phenotype and in epithelial-to-mesenchymal transition. Temporal variations in intratumoural blood flow, which occur through the promotion of cancer cell phenotypes that facilitate both metastatic spread and resistance to therapy, may have substantial clinical consequences.

Cancer heterogeneity and multilayer spatial evolutionary games

Background

Evolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. Our model contains four main phenotypes. Moreover, in a standard approach only heterogeneity of populations is studied, while cancer cells remain homogeneous. A multilayer approach proposed in this paper enables to study heterogeneity of single cells.

Method

In the extended model presented in this paper we consider four strategies (phenotypes) that can arise by mutations. We propose multilayer spatial evolutionary games (MSEG) played on multiple 2D lattices corresponding to the possible phenotypes. It enables simulation and investigation of heterogeneity on the player-level in addition to the population-level. Moreover, it allows to model interactions between arbitrary many phenotypes resulting from the mixture of basic traits.

Results

Different equilibrium points and scenarios (monomorphic and polymorphic populations) have been achieved depending on model parameters and the type of played game. However, there is a possibility of stable quadromorphic population in MSEG games for the same set of parameters like for the mean-field game.

Conclusion

The model assumes an existence of four possible phenotypes (strategies) in the population of cells that make up tumour. Various parameters and relations between cells lead to complex analysis of this model and give diverse results. One of them is a possibility of stable coexistence of different tumour cells within the population, representing almost arbitrary mixture of the basic phenotypes.

Reviewers

This article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.