An evolutionary-game model of tumour-cell interactions: possible relevanceto gene therapy

Evolutionary games have been applied as simple mathematical models of popul ations where interactions between individuals control the dynamics. Recentl y, it has been proposed to use this type of model to describe the evolution of tumour cell populations with interactions between cells. We extent the analysis to allow for synergistic effects between cells. A mathematical mod el of a tumour cell population is presented in which population-level syner gy is assumed to originate through the interaction of triplets of cells. A threshold of two cooperating cells is assumed to be required to produce a p roliferative advantage. The mathematical behaviour of this model is explore d. Even this simple synergism (minor clustering effect) is sufficient to ge nerate qualitatively different cell-population dynamics from the models pub lished previously. The most notable feature of the model is the existence o f an unstable internal equilibrium separating two stable equilibria. Thus, cells of a malignant phenotype can exist in a stable polymorphism, but may be driven to extinction by relatively modest perturbations of their relativ e frequency. The proposed model has some features that may be of interest t o biological interpretations of gene therapy. Two prototypical strategies f or gene therapy are suggested, both of them leading to extinction of the ma lignant phenotype: one approach would be to reduce the relative proportion of the cooperating malignant cell type below a certain critical value. Anot her approach would be to increase the critical threshold value without redu cing the relative frequency of cells of the malignant phenotype. (C) 2001 E lsevier Science Ltd. All rights reserved.