Combining game theory and graph theory to model interactions between cells in the tumor microenvironment

Mathematical concepts of graph theory and game theory both influence models of biological systems. We combine these two approaches to understand how game-like interactions influence the cellular topology of a planar tissue. We review the literature on the role of cell to cell interactions in tumourigenesis and survey the mathematical approaches that have been used to simulate such cell-cell interactions. We present how this game-graph approach can be used to simulate epithelial tissue growth and how it can foster our understanding of the role of cell-cell communication in the early stages of cancer development. We present computational models that we use to test how cooperating and non-cooperating cells build planar tissues and compare the simulated tissue topologies with literature data. We further discuss how such system could be used to model microenviromental communications between cancer cells and the surrounding tissue.