Advertisement

Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics

  • Andrej DobovišekEmail author
  • Paško Županović
  • Milan Brumen
  • Davor Juretić
Chapter
First Online:
Part of the Understanding Complex Systems book series (UCS)

Abstract

There have been many attempts to use optimization approaches to study the biological evolution of enzyme kinetics. Our basic assumption here is that the biological evolution of catalytic cycle fluxes between enzyme internal functional states is accompanied by increased entropy production of the fluxes and increased Shannon information entropy of the states. We use simplified models of enzyme catalytic cycles and bioenergetically important free-energy transduction cycles to examine the extent to which this assumption agrees with experimental data. We also discuss the relevance of Prigogine’s minimal entropy production theorem to biological evolution.

Keywords

Entropy Production Metabolic Flux Forward Rate Proton Motive Force Thermodynamic Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Wiley, New York (1967)Google Scholar
  2. 2.
    Martyushev, L.M., Seleznev, V.D.: Maximum entropy production principle in physics, chemistry and biology. Phys. Rev. 426, 1–45 (2006)MathSciNetGoogle Scholar
  3. 3.
    Onsager, L.: Reciprocal relations in irreversible processes I. Phys. Rev. 37, 405–426 (1931)CrossRefGoogle Scholar
  4. 4.
    Onsager, L.: Reciprocal relations in irreversible processes II. Phys. Rev. 38, 2265–2279 (1931)CrossRefzbMATHGoogle Scholar
  5. 5.
    Glansdorff, P., Prigogine, I.: Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley, New York (1971)zbMATHGoogle Scholar
  6. 6.
    Voet, D., Voet, J.G.: Biochemistry, 3rd edn. Wiley, New York (2004)Google Scholar
  7. 7.
    Ross, J., Vlad, M.O.: Exact solutions for the entropy production rate of several irreversible processes. J. Phys. Chem. A 109, 10607–10612 (2005)CrossRefGoogle Scholar
  8. 8.
    Metzner, H.: Bioelectrochemistry of photosynthesis: a theoretical approach. Bioelectrochem. Bioenerg. 13, 183–190 (1984)CrossRefGoogle Scholar
  9. 9.
    Andriesse, C.D., Hollestelle, M.J.: Minimum entropy production in photosynthesis. Biophys. Chem. 90, 249–253 (2001)CrossRefGoogle Scholar
  10. 10.
    Andriesse, C.D.: On the relation between stellar mass and luminosity. Astrophys. J. 539, 364–365 (2000)CrossRefGoogle Scholar
  11. 11.
    Jennings, R.C., Engelmann, E., Garlaschi, F., Casazza, A.P., Zucchelli, G.: Photosynthesis and negative entropy production. Biochim. Biophys. Acta Bioenerg. 1709, 251–255 (2005)CrossRefGoogle Scholar
  12. 12.
    Lavergne, L.: Commentary on photosynthesis and negative entropy production by Jennings and coworkers. Biochim. Biophys. Acta 1757, 1453–1459 (2006)CrossRefGoogle Scholar
  13. 13.
    Knox, R.S., Parson, W.W.: Entropy production and the second law in photosynthesis. Biochim. Biophys. Acta 1767, 1189–1193 (2007)CrossRefGoogle Scholar
  14. 14.
    Heinrich, R., Schuster, S., Holzhütter, H.G.: Mathematical analysis of enzymic reaction systems using optimization principles. Eur. J. Biochem. 201, 1–21 (1991)CrossRefGoogle Scholar
  15. 15.
    Albery, W.J., Knowles, J.R.: Evolution of enzyme function and the development of catalytic efficiency. Biochemistry 15, 5631–5640 (1976)CrossRefGoogle Scholar
  16. 16.
    Pettersson, G.: Effect of evolution on the kinetic properties of enzymes. Eur. J. Biochem. 184, 561–566 (1989)CrossRefGoogle Scholar
  17. 17.
    Christensen, H., Martin, M.T., Waley, G.: β-lactamases as fully efficient enzymes. Determination of all the rate constants in the acyl-enzyme mechanism. Biochem. J. 266, 853–861 (1990)Google Scholar
  18. 18.
    Pettersson, G.: Evolutionary optimization of the catalytic efficiency of enzymes. Eur. J. Biochem. 206, 295–298 (1992)CrossRefGoogle Scholar
  19. 19.
    Suarez, R.K., Staples, J.F., Lighton, J.R.B., West, T.G.: Relationships between enzymatic flux capacities and metabolic flux rates in muscles: nonequilibrium reactions in muscle glycolysis. Proc. Natl. Acad. Sci. 94, 7065–7069 (1997)CrossRefGoogle Scholar
  20. 20.
    Taylor, C.R., Weibel, E.R.: Design of the mammalian respiratory system. I. Problem and strategy. Respir. Physiol. 44, 1–10 (1981)CrossRefGoogle Scholar
  21. 21.
    Diamond, J.M.: Evolution of biological safety factors: a cost/benefit analysis. In: Weibel, E.R., Taylor, C.R., Bolis, L.C. (eds.) Principles of Animal Design: The Optimization and Symmorphosis Debate, pp. 21–27. Cambridge University Press, Cambridge (1998)Google Scholar
  22. 22.
    Suarez, R.K., Darveau, C.A.: Multi-level regulation and metabolic scaling. J. Exp. Biol. 208, 1627–1634 (2005)CrossRefGoogle Scholar
  23. 23.
    Reaves, M.L., Rabinowitz, J.L.: Metabolomics in systems microbiology. Curr. Opin. Biotechnol. 22, 17–25 (2011)CrossRefGoogle Scholar
  24. 24.
    Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)CrossRefGoogle Scholar
  25. 25.
    Dewar, R.C., Maritan, A.: The theoretical basis of maximum entropy production. In: Dewar, R.C., Lineweaver, C.H., Niven, R.K., Regenauer-Lieb, K. (eds.) Beyond the Second Law: Entropy Production and Non-Equilibrium Systems. Springer, Berlin (2013)Google Scholar
  26. 26.
    Dobovišek, A., Županović, P., Brumen, M., Bonačić-Lošić, Ž., Kuić, D., Juretić, D.: Enzyme kinetics and the maximum entropy production principle. Biophys. Chem. 154, 49–55 (2011)CrossRefGoogle Scholar
  27. 27.
    Hill, T.L.: Free Energy Transduction in Biology. The Steady State Kinetic and Thermodynamic Formalism. Academic Press, New York (1977)Google Scholar
  28. 28.
    Meszena, G., Westerhoff, H.V.: Non-equilibrium thermodynamics of light absorption. J. Phys. A: Math. Gen. 32, 301–311 (1999)CrossRefzbMATHGoogle Scholar
  29. 29.
    Juretić, D., Županović, P.: Photosynthetic models with maximum entropy production in irreversible charge transfer steps. J. Comp. Biol. Chem. 27, 541–553 (2003)CrossRefzbMATHGoogle Scholar
  30. 30.
    Lukács, A., Papp, E.: Bacteriorhodopsin photocycle kinetics analyzed by the maximum entropy method. J. Photochem. Photobiol., B 77, 1–16 (2004)Google Scholar
  31. 31.
    Kakareka, J.W., Smith, P.D., Pohida, T.J., Hendler, R.W.: Simultaneous measurements of fast optical and proton current kinetics in the bacteriorhodopsin photocycle using an enhanced spectrophotometer. J. Biochem. Biophys. Methods 70, 1116–1123 (2008)CrossRefGoogle Scholar
  32. 32.
    Juretić, D., Westerhoff, H.V.: Variation of efficiency with free-energy dissipation in models of biological energy transduction. Biophys. Chem. 28, 21–34 (1987)CrossRefGoogle Scholar
  33. 33.
    Michel, H., Oesterhelt, D.: Electrochemical proton gradient across the cell membrane of Halobacterium halobium: Effect of N, N’-dicyclohexylcarbodiimide, relation to intracellular adenosine triphosphate, adenosine diphosphate, and phosphate concentration, and influence of the potassium gradient. Biochemistry 19, 4607–4619 (1980)CrossRefGoogle Scholar
  34. 34.
    Boylestad, R.: Introductory Circuit Analysis. Prentice-Hall, Upper Saddle River (1999)Google Scholar
  35. 35.
    Hendler, R.W., Shrager, R.I., Bose, S.: Theory and practice for finding a correct kinetic model for the bacteriorhodopsin photocycle. J. Phys. Chem. B 105, 3319–3328 (2001)CrossRefGoogle Scholar
  36. 36.
    Chizhov, I., Chernavskii, D.S., Engelhard, M., Mueller, K.H., Zubov, B.V., Hess, B.: Spectrally silent transitions in the bacteriorhodopsin photocycle. Biophys. J. 71, 2329–2345 (1996)CrossRefGoogle Scholar
  37. 37.
    Lanyi, J.K.: Proton transfers in the bacteriorhodopsin photocycle. Biochim. Biophys. Acta 1757, 1012–1018 (2006)CrossRefGoogle Scholar
  38. 38.
    Juretić, D., Županović, P.: The free-energy transduction and entropy production in initial photosynthetic reactions. In: Kleidon, A., Lorenz, R.D. (eds.) Non-Equilibrium Thermodynamics and the Production of Entropy, pp. 161–171. Springer, Berlin (2005)CrossRefGoogle Scholar
  39. 39.
    Boyer, P.D.: The ATP synthase –a splendid molecular machine. Ann. Rev. Biochem. 66, 717–749 (1997)CrossRefGoogle Scholar
  40. 40.
    Pänke, O., Rumberg, B.: Kinetic modeling of rotary CF0F1-ATP synthase: storage of elastic energy during energy transduction. Biochim. Biophys. Acta 1412, 118–128 (1999)CrossRefGoogle Scholar
  41. 41.
    Pänke, O., Rumberg, B.: Kinetic modelling of the proton translocating CF0CF1-ATP synthase from spinach. FEBS Lett. 383, 196–200 (1996)CrossRefGoogle Scholar
  42. 42.
    Dewar, R.C., Juretić, D., Županović, P.: The functional design of the rotary enzyme ATP synthase is consistent with maximum entropy production. Chem. Phys. Lett. 430, 177–182 (2006)CrossRefGoogle Scholar
  43. 43.
    Turina, P., Samoray, D., Graeber, P.: H +/ATP ratio of proton transport-coupled ATP synthesis and hydrolysis catalysed by CF0F1-liposomes. Eur. Mol. Biol. Org. J. 22, 418–426 (2003)Google Scholar
  44. 44.
    Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 620–630 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Jaynes, E.T.: Information theory and statistical mechanics II. Phys. Rev. 108, 171–190 (1957)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Prigogine, I., Wiame, J.M.: Biologie et thermodynamique des phénomènes irréversibles. Experientia 2, 451–453 (1946)CrossRefGoogle Scholar
  47. 47.
    Kondepudi, D., Prigogine, I.: Modern Thermodynamics: From Heat Engines to Dissipative Structures. Wiley, Chichester (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrej Dobovišek
    • 1
    Email author
  • Paško Županović
    • 2
  • Milan Brumen
    • 1
    • 3
  • Davor Juretić
    • 2
  1. 1.Natural Sciences and Mathematics, Medicine, and Health SciencesUniversity of MariborMariborSlovenia
  2. 2.Department of Physics, Faculty of ScienceUniversity of SplitSplitCroatia
  3. 3.Jožef Stefan InstituteLjubljanaSlovenia

Personalised recommendations

Cite chapter

Buy options