Journal of Biological Physics

, Volume 34, Issue 1–2, pp 1–17 | Cite as

Use of Game-Theoretical Methods in Biochemistry and Biophysics

  • Stefan Schuster
  • Jan-Ulrich Kreft
  • Anja Schroeter
  • Thomas Pfeiffer


Evolutionary game theory can be considered as an extension of the theory of evolutionary optimisation in that two or more organisms (or more generally, units of replication) tend to optimise their properties in an interdependent way. Thus, the outcome of the strategy adopted by one species (e.g., as a result of mutation and selection) depends on the strategy adopted by the other species. In this review, the use of evolutionary game theory for analysing biochemical and biophysical systems is discussed. The presentation is illustrated by a number of instructive examples such as the competition between microorganisms using different metabolic pathways for adenosine triphosphate production, the secretion of extracellular enzymes, the growth of trees and photosynthesis. These examples show that, due to conflicts of interest, the global optimum (in the sense of being the best solution for the whole system) is not always obtained. For example, some yeast species use metabolic pathways that waste nutrients, and in a dense tree canopy, trees grow taller than would be optimal for biomass productivity. From the viewpoint of game theory, the examples considered can be described by the Prisoner’s Dilemma, snowdrift game, Tragedy of the Commons and rock–scissors–paper game.


Evolutionary game theory Metabolic pathways Prisoner’s dilemma Snowdrift game Transition to cooperation Tree growth 



We wish to thank David Fell (Oxford), Matjaz Perc (Maribor), Eytan Ruppin (Tel-Aviv) and Günter Theissen (Jena) for stimulating discussions. Financial support to A.S. by the German-Israeli Foundation is gratefully acknowledged. T.P. gratefully acknowledges support by Society in Science/The Branco Weiss Fellowship.


  1. 1.
    Kacser, H., Beeby, R.: Evolution of catalytic proteins or on the origin of enzyme species by means of natural selection. J. Mol. Evol. 20(1), 38–51 (1984). doi: 10.1007/BF02101984 CrossRefGoogle Scholar
  2. 2.
    Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Chapman & Hall, New York (1996)zbMATHGoogle Scholar
  3. 3.
    Meléndez-Hevia, E., Waddell, T.G., Heinrich, R., Montero, F.: Theoretical approaches to the evolutionary optimization of glycolysis – chemical analysis. Eur. J. Biochem. 244(2), 527–543 (1997). doi: 10.1111/j.1432-1033.1997.t01-1-00527.x CrossRefGoogle Scholar
  4. 4.
    Edwards, J.S., Ramakrishna, R., Palsson, B.O.: Characterizing the metabolic phenotype: a phenotype phase plane analysis. Biotechnol. Bioeng. 77(1), 27–36 (2002). doi: 10.1002/bit.10047 CrossRefGoogle Scholar
  5. 5.
    Ebenhöh, O., Heinrich, R.: Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems. Bull. Math. Biol. 63(1), 21–55 (2001). doi: 10.1006/bulm.2000.0197 CrossRefGoogle Scholar
  6. 6.
    Stucki, J.W.: The optimal efficiency and the economic degrees of coupling of oxidative phosphorylation. Eur. J. Biochem. 109(1), 269–283 (1980). doi: 10.1111/j.1432-1033.1980.tb04792.x CrossRefGoogle Scholar
  7. 7.
    Schuster, S., Heinrich, R.: Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks. I. Theoretical analysis. J. Math. Biol. 29(5), 425–442 (1991). doi: 10.1007/BF00160470 zbMATHCrossRefGoogle Scholar
  8. 8.
    Thompson, J.N.: The Coevolutionary Process. University of Chicago Press, Chicago (1994)Google Scholar
  9. 9.
    Maynard-Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)Google Scholar
  10. 10.
    Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)Google Scholar
  11. 11.
    Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  12. 12.
    Nowak, M.A., Sigmund, K.: Evolutionary dynamics of biological games. Science 303(5659), 793–799 (2004). doi: 10.1126/science.1093411 CrossRefADSGoogle Scholar
  13. 13.
    Eigen, M., Winkler, R.: Das Spiel. Naturgesetze steuern den Zufall. Pieper, München (1975)Google Scholar
  14. 14.
    Schieving, F., Poorter, H.: Carbon gain in a multispecies canopy: the role of specific leaf area and photosynthetic nitrogen-use efficiency in the tragedy of the commons. New Phytol. 143(1), 201–211 (1999). doi: 10.1046/j.1469-8137.1999.00431.x CrossRefGoogle Scholar
  15. 15.
    Falster, D.S., Westoby, M.: Plant height and evolutionary games. Trends Ecol. Evol. 18(7), 337–343 (2003). doi: 10.1016/S0169-5347(03)00061-2 CrossRefGoogle Scholar
  16. 16.
    Anten, N.P.R.: Optimal photosynthetic characteristics of individual plants in vegetation stands and implications for species coexistence. Ann. Bot. (Lond.) 95(3), 495–506 (2005). doi: 10.1093/aob/mci048 CrossRefGoogle Scholar
  17. 17.
    Pfeiffer, T., Schuster, S., Bonhoeffer, S.: Cooperation and competition in the evolution of ATP-producing pathways. Science 292(5516), 504–507 (2001). doi: 10.1126/science.1058079 CrossRefADSGoogle Scholar
  18. 18.
    Greig, D., Travisano, M.: The Prisoner’s Dilemma and polymorphism in yeast SUC genes. Proc. R. Soc. B-Biol. Sci. 271, S25–S26 (2004)CrossRefGoogle Scholar
  19. 19.
    Kreft, J.U.: Biofilms promote altruism. Microbiology 150, 2751–2760 (2004). doi: 10.1099/mic.0.26829-0 CrossRefGoogle Scholar
  20. 20.
    Pfeiffer, T., Schuster, S.: Game-theoretical approaches to studying the evolution of biochemical systems. Trends Biochem. Sci. 30(1), 20–25 (2005). doi: 10.1016/j.tibs.2004.11.006 CrossRefGoogle Scholar
  21. 21.
    Costa, E., Pérez, J., Kreft, J.U.: Why is metabolic labour divided in nitrification? Trends Microbiol. 14(5), 213–219 (2006). doi: 10.1016/j.tim.2006.03.006 CrossRefGoogle Scholar
  22. 22.
    Hauert, C., Doebeli, M.: Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428(6983), 643–646 (2004). doi: 10.1038/nature02360 CrossRefADSGoogle Scholar
  23. 23.
    Hardin, G.: The tragedy of the commons. Science 162(3859), 1243–1248 (1968). doi: 10.1126/science.162.3859.1243 CrossRefADSGoogle Scholar
  24. 24.
    Doebeli, M., Hauert, C., Killingback, T.: The evolutionary origin of cooperators and defectors. Science 306(5697), 859–862 (2004). doi: 10.1126/science.1101456 CrossRefADSGoogle Scholar
  25. 25.
    Voet, D., Voet, J.G.: Biochemistry. Wiley, New York (2004)Google Scholar
  26. 26.
    Veiga, A., Griffin, A.S., Gardner, A., Diggle, S.P.: Cyanide-resistant respiration is frequent, but confined to yeasts incapable of aerobic fermentation. FEMS Microbiol. Lett. 190(1), 93–97 (2000). doi: 10.1111/j.1574-6968.2000.tb09268.x CrossRefGoogle Scholar
  27. 27.
    Myerson, R.B.: Game Theory: Analysis of Conflict. Harvard University Press, Cambridge, MA (1991)zbMATHGoogle Scholar
  28. 28.
    West, S.A., et al.: Social evolution theory for microorganisms. Nat. Rev. Microbiol. 4(8), 597–607 (2006). doi: 10.1038/nrmicro1461 CrossRefGoogle Scholar
  29. 29.
    Frick, T., Schuster, S.: An example of the prisoner’s dilemma in biochemistry. Naturwissenschaften 90(7), 327–331 (2003). doi: 10.1007/s00114-003-0434-3 CrossRefADSGoogle Scholar
  30. 30.
    Murray, J.D.: Mathematical Biology. Springer, Berlin (2002)zbMATHGoogle Scholar
  31. 31.
    Rieck, C.: Spieltheorie. Eine Einführung. Christian Rieck Verlag, Eschborn (2006)Google Scholar
  32. 32.
    Wolfe, K.: Evolutionary genomics: yeasts accelerate beyond BLAST. Curr. Biol. 14(10), R392–R394 (2004). doi: 10.1016/j.cub.2004.05.015 CrossRefGoogle Scholar
  33. 33.
    Conant, G.C., Wolfe, K.H.: Increased glycolytic flux as an outcome of whole-genome duplication in yeast. Mol. Syst. Biol. 3, 129 (2007)CrossRefGoogle Scholar
  34. 34.
    MacLean, R.C., Gudelj, I.: Resource competition and social conflict in experimental populations of yeast. Nature 441(7092), 498–501 (2006). doi: 10.1038/nature04624 CrossRefADSGoogle Scholar
  35. 35.
    Cushing, J.M.: Periodic Lotka–Volterra competition equations. J. Math. Biol. 24(4), 381–403 (1986). doi: 10.1007/BF01236888 zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Kerr, B., Neuhauser, C., Bohannan, B.J., Dean, A.M.: Local migration promotes competitive restraint in a host-pathogen ‘tragedy of the commons’. Nature 442(7098), 75–78 (2006). doi: 10.1038/nature04864 CrossRefADSGoogle Scholar
  37. 37.
    Kreft, J.U.: Conflicts of interest in biofilms. Biofilms 1, 265–276 (2004). doi: 10.1017/S1479050504001486 CrossRefGoogle Scholar
  38. 38.
    Kreft, J.U., Bonhoeffer, S.: The evolution of groups of cooperating bacteria and the growth rate versus yield trade-off. Microbiology 151, 637–641 (2005). doi: 10.1099/mic.0.27415-0 CrossRefGoogle Scholar
  39. 39.
    Carlson, M., Botstein, D.: Organization of the SUC gene family in Saccharomyces. Mol. Cell. Biol. 3(3), 351–359 (1983)Google Scholar
  40. 40.
    Vulic, M., Kolter, R.: Evolutionary cheating in Escherichia coli stationary phase cultures. Genetics 158(2), 519–526 (2001)Google Scholar
  41. 41.
    Bonner, J.T.: First Signals: The Evolution of Multicellular Development. Princeton University Press, Princeton (2001)Google Scholar
  42. 42.
    Nelson, D.L., Cox, M.M.: Lehninger Principles of Biochemistry. Worth, New York (2003)Google Scholar
  43. 43.
    Pellerin, L.: How astrocytes feed hungry neurons. Mol. Neurobiol. 32(1), 59–72 (2005). doi: 10.1385/MN:32:1:059 CrossRefMathSciNetGoogle Scholar
  44. 44.
    Doebeli, M.: A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms. Popul. Ecol. 44(2), 59–70 (2002). doi: 10.1007/s101440200008 CrossRefGoogle Scholar
  45. 45.
    Pfeiffer, T., Bonhoeffer, S.: Evolution of cross-feeding in microbial populations. Am. Nat. 163(6), E126–E135 (2004). doi: 10.1086/383593 CrossRefGoogle Scholar
  46. 46.
    Warburg, O.: Origin of cancer cells. Science 123(3191), 309–314 (1956). doi: 10.1126/science.123.3191.309 CrossRefADSGoogle Scholar
  47. 47.
    Schulz, T.J., Thierbach, R., Voigt, A., Drewes, G., Mietzner, B., Steinberg, P., Pfeiffer, A.F., Ristow, M.: Induction of oxidative metabolism by mitochondrial frataxin inhibits cancer growth–Otto Warburg revisited. J. Biol. Chem. 281(2), 977–981 (2006). doi: 10.1074/jbc.M511064200 CrossRefGoogle Scholar
  48. 48.
    Gatenby, R.A., Vincent, T.L.: An evolutionary model of carcinogenesis. Cancer Res. 63(19), 6212–6220 (2003)Google Scholar
  49. 49.
    Gabriel, W., Burger, R.: Survival of small populations under demographic stochasticity. Theor. Popul. Biol. 41(1), 44–71 (1992). doi: 10.1016/0040-5809(92)90049-Y zbMATHCrossRefGoogle Scholar
  50. 50.
    Pfeiffer, T., Bonhoeffer, S.: An evolutionary scenario for the transition to undifferentiated multicellularity. Proc. Natl. Acad. Sci. USA 100(3), 1095–1098 (2003). doi: 10.1073/pnas.0335420100 CrossRefADSGoogle Scholar
  51. 51.
    Merrill, S.J.: Stochastic models of tumor growth and the probability of elimination by cytotoxic cells. J. Math. Biol. 20(3), 305–320 (1984). doi: 10.1007/BF00275990 zbMATHCrossRefMathSciNetGoogle Scholar
  52. 52.
    King, D.A.: The adaptive significance of tree height. Am. Nat. 135(6), 809–828 (1990). doi: 10.1086/285075 CrossRefGoogle Scholar
  53. 53.
    Bartel, H.G.: Considerations on the usefulness of the game-theory in chemistry. Z. Chem. 23(7), 269Google Scholar
  54. 54.
    Goodman, J.M.: Solutions for chemistry: synthesis of experiment and calculation. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 358(1766), 387–398 (2000)CrossRefADSGoogle Scholar
  55. 55.
    Kovács, I.A., Szalay, M.S., Csermely, P.: Water and molecular chaperones act as weak links of protein folding networks: Energy landscape and punctuated equilibrium changes point towards a game theory of proteins. FEBS Lett. 579(11), 2254–2260 (2005). doi: 10.1016/j.febslet.2005.03.056 CrossRefGoogle Scholar
  56. 56.
    Hauert, C., Szabo, G.: Game theory and physics. Am. J. Phys. 73(5), 405–414 (2005). doi: 10.1119/1.1848514 CrossRefADSMathSciNetGoogle Scholar
  57. 57.
    Perc, M.: Coherence resonance in a spatial prisoner’s dilemma game. New J. Phys. 8, 22 (2006)CrossRefADSGoogle Scholar
  58. 58.
    Aledo, J.C., Pérez-Claros, J.A., Esteban del Valle, A.: Switching between cooperation and competition in the use of extracellular glucose. J. Mol. Evol. 65(3), 328–339 (2007). doi: 10.1007/s00239-007-9014-z CrossRefGoogle Scholar
  59. 59.
    Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82(5), 1052–1055 (1999). doi: 10.1103/PhysRevLett.82.1052 zbMATHCrossRefADSMathSciNetGoogle Scholar
  60. 60.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999). doi: 10.1103/PhysRevLett.83.3077 zbMATHCrossRefADSMathSciNetGoogle Scholar
  61. 61.
    Klarreich, E.: Playing by quantum rules. Nature 414(6861), 244–245 (2001). doi: 10.1038/35104702 CrossRefADSGoogle Scholar
  62. 62.
    Czaran, T.L., Hoekstra R.F., Pagie, L.: Chemical warfare between microbes promotes biodiversity. Proc. Natl. Acad. Sci. USA 99(2), 786–790 (2002). doi: 10.1073/pnas.012399899 CrossRefADSGoogle Scholar
  63. 63.
    Neumann, G., Schuster, S.: Continuous model for the rock–scissors–paper game between bacteriocin producing bacteria. J. Math. Biol. 54(6), 815–846 (2007). doi: 10.1007/s00285-006-0065-3 zbMATHCrossRefMathSciNetGoogle Scholar
  64. 64.
    Fell, D.A., Small, J.R.: Fat synthesis in adipose-tissue – an examination of stoichiometric constraints. Biochem. J. 238(3), 781–786 (1986)Google Scholar
  65. 65.
    Watson, M.R.: A discrete model of bacterial metabolism. Comput. Appl. Biosci. 2(1), 23–27 (1986)Google Scholar
  66. 66.
    Varma, A., Palsson, B.O.: Metabolic capabilities of Escherichia coli: I. Synthesis of biosynthetic precursors and cofactors. J. Theor. Biol. 165(4), 477–502 (1993). doi: 10.1006/jtbi.1993.1202 CrossRefGoogle Scholar
  67. 67.
    Schuster, S., Fell, D.A.: In: Lengauer, T. (ed.) Bioinformatics: From Genomes to Therapies, pp. 755–805. Wiley-VCH, Weinheim (2007)Google Scholar
  68. 68.
    Schuster, S., Pfeiffer, T., Fell, D.A.: Is maximization of molar yield in metabolic networks favoured by evolution? J. Theor. Biol. 252, 497–504 (2008)CrossRefGoogle Scholar
  69. 69.
    Spotorno, A.E.: Evolutionary medicine: an emergent basic science. Rev. Med. Chil. 133(2), 231–240 (2005) (in Spanish)Google Scholar
  70. 70.
    Dawkins, R.: The Selfish Gene. Oxford University Press, Oxford (2006)Google Scholar
  71. 71.
    Keinan, A., Sandbank, B., Hilgetag, C.C., Meilijson, I., Ruppin, E.: Axiomatic scalable neurocontroller analysis via the Shapley value. Artif. Life 12(3), 333–352 (2006). doi: 10.1162/artl.2006.12.3.333 CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Stefan Schuster
    • 1
  • Jan-Ulrich Kreft
    • 2
  • Anja Schroeter
    • 1
  • Thomas Pfeiffer
    • 3
  1. 1.Department of BioinformaticsFriedrich Schiller UniversityJenaGermany
  2. 2.Centre for Systems Biology, School of BiosciencesUniversity of Birmingham, EdgbastonBirminghamUK
  3. 3.Program for Evolutionary DynamicsHarvard UniversityCambridgeUSA

Personalised recommendations