Transcript Elementary-Modes Analysis of Lysine Production in

A Game-theoretical Approach
to the Analysis of Microbial Metabolic Pathways
Stefan Schuster and Gunter Neumann
Friedrich Schiller University Jena, Dept. of Bioinformatics
Ernst-Abbe-Pl. 2, 07743 Jena, Germany
email: (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.
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
A
B Resp Ferm
Resp
3/3 0/5
Ferm 5/0 2/2
(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].
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
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 rockscissors-paper game between bacteriocin producing bacteria. Submitted
to J. Math. Biol.