A Game-theoretical Approach to the Analysis of Microbial Metabolic Pathways

1. A Game-theoretical Approach to the Analysis of Microbial Metabolic Pathways Stefan Schuster and Gunter NeumannFriedrich Schiller University Jena, Dept. of BioinformaticsErnst-Abbe-Pl. 2, 07743 Jena, Germanyemail: (schuster, gfneuman)@minet.uni-jena.de • Introduction • Bacteria and other micro-organisms can form complex ecosystems • Both competition and cooperation play a role • Microbial species or strains can be considered as players in the sense of game theory • Evolutionary game theory has often been used in biology [1] • Advantage: computation of stable equilibria without the need to simulate the time course of reaching these equilibria • Only recently, game theory has been used for analysing metabolic pathways [2-4] • More than two strains: more complicated games are possible. Rock-Scissors-Paper Game between Bacteria Three-player game: „RSP“ - rock beats scissors, scissors beats paper, and paper beats rock. For each subpopulation, the Competitive Exclusion Principle holds while for all together, a permanent cyclic coexistence is observed. Example from microbiology: Bacteriocin producing bacteria: Producers win against sensitives, resistant win against producers (because of lower metabolic costs), sensitives win against resistant (even lower costs). Can be modelled by competitive Lotka-Volterra equations [5]. • Conclusions • Microbes can be trapped in Prisoner‘s Dilemma w.r.t. • use of inefficient metabolic pathways • However, many micro-organisms sich as Kluyveromyces • species use respiration (cooperative strategy) • Bacteria producing bacteriocins can „play“ a game of rock-scissors-paper, in which the weakest strain (sensitive) does not get extinct. Extension and „solution“ of the Prisoner‘s Dilemma. • Distinction between competition and cooperation not always clear-cut • Game theory may be promising for analysing cross-feeding (consortium pathways) between different microbes First Example: Respiration vs. Fermentation Respiration: High ATP:glucose yield (> 30), but low ATP production rate Fermentation: Low ATP:glucose yield (2), but high ATP production rate Glukose Strain A Strain B Respiration or fermentation?Respiration or fermentation? Outcome of each strategy depends also on strategy of other strain Results in Prisoner‘s Dilemma with payoff matrix References [1] Hofbauer, J. and Sigmund, K. (1998). Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge [2] T. Pfeiffer, S. Schuster, S. Bonhoeffer: Cooperation and competition in the evolution of ATP-producing pathways. Science 292 (2001) 504-507. [3] T. Frick, S. Schuster: An example of the prisoner's dilemma in biochemistry. Naturwissenschaften 90 (2003) 327-331. [4] T. Pfeiffer, S. Schuster: Game-theoretical approaches to studying the evolution of biochemical systems. Trends Biochem. Sci. 30 (2005) 20-25. [5] Neumann, G. and Schuster, S. (2006). Continuous model for the rock- scissors-paper game between bacteriocin producing bacteria. Submitted to J. Math. Biol. B (Numbers are arbitrary just to show the order relations.) It would be advantageous for both strains to respire (cooperative usage of resource). However, they end up in the inefficient state where both strains use fermentation (Nash equilibrium) [3]. Resp Ferm A 3/3 0/5 Resp 5/0 Ferm 2/2