Applications of evolutionary game theory to understanding cancer dynamics
This post will be talking about the use of evolutionary game theory to improve our understanding of cancer dynamics. The study that I am looking at specifically, this article, looks to analyze the interaction between malignant and normal cells in a multiple myeloma (MM) model.
Game theory in general has numerous applications in the field of medicine where even at a rudimentary level, it can be used as a vessel of mathematical exploration between rational entities in order to make predictable and reproducible choices. This type of exploration has subsequently developed many mathematical formulae to describe such characteristics and how outputs change with varying inputs. Since both players make reproducible and rational choices this allows for the prediction of equilibrium states in games that are played repeatedly over time. Concordantly, an equilibrium state is steady when the payoffs or Utils of both players are maximized. What makes this especially tricky and interesting is that there can be many possible equilibrium states for any one game; and conversely, this means that there is always at least one equilibrium state for any game that is finite and that allows for mixed strategies.
“The idea of an equilibrium state has been successfully applied to evolutionary theory, most notably in the development of evolutionary stable strategies (ESSs) by George Price and John Maynard Smith. An ESS is essentially a strategy with a symmetric equilibrium state, except that it is also more stable than any possible alternative strategy to the game. This requirement provides the necessary evolutionary pressure against invasion from other competing strategies that would destabilize this equilibrium.” (this article)
When looking at cancer dynamics, these ESSs act as very efficient heuristics in that they can theoretically be used to understand and manipulate the process of cancer growth and our ability to understand its dynamics. By having these abilities, we can potentially predict and effectively improve survival by changing the strategies and payoffs of a “game” that we create when tracking cancer. This article does just that, by showing that when you reduce the payoff of malignant cells compared with the payoff of normal cells, you can potentially eradicate the cancer cell by natural selection.
This game that you create can be proven to be applicable to cancer dynamics by breaking it up into its logical components. You would have the aggressive malignant cell compete with a passive normal cell for biological energy: you would numerically express these strategies by their payoffs or Utils. Two interacting passive normal cells have a hypothetical payoff of 2 Utils each when they are sharing the energy, 1 Util each if both are aggressive malignant cells, and 4 to 0 Utils if one player is a malignant cell and the other is a normal cell, respectively. The resulting game theory ESS would be an interaction in which all players become malignant, which is a fundamental concept in game theory as it is more beneficial to be both normal. Concordantly, the minute possibility of malignant cells dooms the normal cells to their deaths. This game produces a similar result as was observed in this paper, and resemble the end result of untreated cancer, in which malignant cells overcome normal cells. Therefore, one can use backwards induction to deduce that this is a reasonable model for cancer dynamics.
Cancer Article: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2768082/
Analysis Article: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2795450