Introduction
In lecture, we learned about some of the fundamentals of game theory and a few of its applications. Having such a narrowed-view of the applications of game theory, it is fascinating to see the different ways in which game theoretic notions apply themselves in different fields of research. The article I have chosen takes a closer look at one of these instances. In particular, Theocharopoulou et al propose a bio-inspired model of computation for a membrane system using game theoretic notions.
Context
The study focuses on modeling what is known as a P system which consists of a membrane structure and evolution rules. The P system has already been associated with various biomolecular processes as modeling methods, however, Theocharopoulou et al model an equivalent system using a game model and show how this model relates to the mitochondrial fusion-fission cycle. In our model of the P system, we are interested in maintaining equilibrium in the population of mitochondria within a cell because offsetting from this balance can be harmful for the cell. Moreover, this balance is regulated by biological processes known as mitochondrial fission (i.e division) and mitochondrial fusion.
Game Model of the P System
In our game, the population of mitochondria (N) in our system is divided into two groups wherein the first group is denoted by Player 1 and the second group is denoted by Player 2. Each player chooses between strategy Fuse (C) and strategy Divide (D), and receives their corresponding payoffs.
The payoff values that appear in our game are computed using a payoff function u that takes in a combination of player 1 and player 2’s strategies as input and returns some corresponding value, wherein the magnitude of the outputs have the following properties:
In the case of our game, these payoff values are later used to compute the rate of reproduction (i.e. fitness), wherein a higher payoff value is proportional to a higher level of fitness (which is optimal).
This model becomes especially useful when we consider a probability distribution over our set of strategies and solve for its mixed strategy equilibrium. The importance of this computation lies in the fact that researchers were able to conclude that (the ratio of the total mitochondrial population that fuses) = (d-b) / (d-b + a – c). In other words, the mixed-nash equilibrium of our model suggests that an adjustment process which allows players to reach equilibrium (in regards to its total population) exists.
With this being said, we can now extend our model of the single P system and imagine a multi-environment P system, wherein multiple populations of mitochondria are conducting their own games simultaneously. Within this multi-system, each game is affected by the population frequencies of neighboring games, which we have previously shown can tend towards equilibrium. Thus, we end up with a game theoretic model that precisely resembles the evolution of the mitochondrial fusion-fission cycle.
Conclusion
In conclusion, the applications of game theory in biology provides biological researchers with an interesting new way to model important biological processes. Naturally, modeling such processes with notions of game theory is unconventional because other techniques can model these biological processes in a more efficient and optimal manner. However, extending the forms of these simple games that consider iterative plays (as shown in the P system model) may be useful in modeling the dynamic changes that frequently arise in biological processes.
References
Theocharopoulou, G., Giannakis, K., Papalitsas, C., Fanarioti, S., & Andronikos, T. (2019). Elements of game theory in a bio-inspired model of computation. 2019 10th International Conference on Information, Intelligence, Systems and Applications (IISA). https://doi.org/10.1109/iisa.2019.8900768