Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect

Objectives: The Warburg effect, a switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analysed the dynamics of cell proliferation and of resistance to therapies that target acidity, in a population of cells, under the Warburg effect. Materials and methods: The dynamics of mutant cells with increased glycolysis and motility has been assessed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment have been used to simulate the effect of therapies that target glycolysis. Results: The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to coexistence of glycolytic and non-glycolytic cells within a tumour. Mutants with increased motility can invade such a polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour cell proliferation, frequency-dependent selection enables it to adapt to the new conditions and can enable the tumour to restore its original levels of growth and invasiveness. Conclusions: The acidity produced by glycolysis acts as a non-linear public good that leads to coexistence of cells with high and low glycolysis within the tumour. Such a heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis.