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.

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

Living cells, like whole living organisms during evolution, communicate with their neighbors, interact with the environment, divide, change their phenotypes, and eventually die. The development of specific ways of communication (through signaling molecules and receptors) allows some cellular subpopulations to survive better, to coordinate their physiological status, and during embryonal development to create tissues and organs or in some conditions to become tumors. Populations of cells cultured in vitro interact similarly, also competing for space and nutrients and stimulating each other to better survive or to die.

Multidimensional extended spatial evolutionary games.

The goal of this paper is to study the classical hawk-dove model using mixed spatial evolutionary games (MSEG). In these games, played on a lattice, an additional spatial layer is introduced for dependence on more complex parameters and simulation of changes in the environment. Furthermore, diverse polymorphic equilibrium points dependent on cell reproduction, model parameters, and their simulation are discussed.

Application of evolutionary games to modeling carcinogenesis.

We review a quite large volume of literature concerning mathematical modelling of processes related to carcinogenesis and the growth of cancer cell populations based on the theory of evolutionary games. This review, although partly idiosyncratic, covers such major areas of cancer-related phenomena as production of cytotoxins, avoidance of apoptosis, production of growth factors, motility and invasion, and intra- and extracellular signaling. We discuss the results of other authors and append to them some additional results of our own simulations dealing with the possible dynamics and/or spatial distribution of the processes discussed.