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Journal of Molecular Evolution

, Volume 71, Issue 5–6, pp 346–355 | Cite as

Revisiting the Thermodynamic Theory of Optimal ATP Stoichiometries by Analysis of Various ATP-Producing Metabolic Pathways

  • Sarah Werner
  • Gabriele Diekert
  • Stefan SchusterEmail author
Article

Abstract

The stoichiometry of ATP-producing metabolic pathways had been analysed theoretically by several authors by using evolutionary arguments and optimality principles. Waddell et al. (Biochem Educ 27:12–13, 1999) analysed (lactate-producing) glycolysis and used linear irreversible thermodynamics. The result was that half of the free-energy difference should be converted into free-energy of ATP and the remaining half should be used to drive the pathway. The calculated stoichiometry is in agreement with the observed yield of two moles of ATP per mole of glucose. Using the same approach, we here analyse eight other metabolic pathways. Although the deviation is not very large, the calculated values do not fit as nicely as for glycolysis as leading to lactate. For example, for O2 respiration, the theoretical ATP yield equals 27.9. The real value varies among organisms between 26 and 38. For mixed-acid fermentation in Escherichia coli, the theoretical and experimental values are 2.24 and 2, respectively. For arginine degradation in M. pneumoniae, the calculated value is 2.43 mol of ATP, while in vivo only one mole is produced. During evolution, some pathways may not have reached their optimal ATP net production because energy yield is not their only function. Moreover, it should be acknowledged that the approach by linear irreversible thermodynamics is a rough approximation.

Keywords

Arginine degradation ATP-producing metabolic pathway Entner–Doudoroff pathway Linear irreversible thermodynamics Mixed-acid fermentation Molar yield Optimal ATP stoichiometry Phosphoketolase pathway Respiratory pathway 

Notes

Acknowledgments

We thank Peter Ruoff (Stavanger, Norway) for very helpful suggestions. St. S. is very grateful to the late Reinhart Heinrich, who was his academic teacher and aroused his interest for optimality calculations. Financial support by the Deutsche Forschungsgemeinschaft within the framework of the Jena School of Microbial Communication is gratefully acknowledged.

References

  1. Alberty RA (2003) Thermodynamics of biochemical reactions. Wiley, Hoboken, NJCrossRefGoogle Scholar
  2. Aledo JC, Esteban del Valle A (2002) Glycolysis in wonderland: the importance of energy dissipation in metabolic pathways. J Chem Educ 79:1336–1339CrossRefGoogle Scholar
  3. Angulo-Brown F, Santillan M, Calleja-Quevedo E (1995) Thermodynamic optimality in some biochemical reactions. Nuovo Cim 17D:87–90Google Scholar
  4. Bai FW, Anderson WA, Moo-Young M (2008) Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnol Adv 26:89–105CrossRefPubMedGoogle Scholar
  5. Bartl M, Li P, Schuster S (2010) Modelling the optimal timing in metabolic pathway activation – Use of Pontryagin’s Maximum Principle and role of the golden section. Biosystems 101:67–77CrossRefPubMedGoogle Scholar
  6. Calhoun MW, Oden KL, Gennis RB, de Mattos MJ, Neijssel OM (1993) Energetic efficiency of Escherichia coli: effects of mutations in components of the aerobic respiratory chain. J Bacteriol 175:3020–3025PubMedGoogle Scholar
  7. Christoffersen J, Christoffersen MR, Hunding A (1998) Comments on optimization of glycolysis. Biochem Educ 26:290–291CrossRefGoogle Scholar
  8. Cornish-Bowden A (1976) The effect of natural selection on enzymic catalysis. J Mol Biol 101:1–9CrossRefPubMedGoogle Scholar
  9. Cornish-Bowden A (1983) Metabolic efficiency: is it a useful concept? Biochem Soc Trans 11:44–45PubMedGoogle Scholar
  10. Cornish-Bowden A (2004) The pursuit of perfection: aspects of biochemical evolution. Oxford University Press, OxfordGoogle Scholar
  11. Diekert G (1997) Grundmechanismen des Stoffwechsels und der Energiegewinnung. In: Ottow JCG, Bidlingmeier W (eds) Umweltbiotechnologie. Fischer, Stuttgart, pp 1–38Google Scholar
  12. Ebenhöh O, Heinrich R (2001) Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems. Bull Math Biol 63:21–55CrossRefPubMedGoogle Scholar
  13. Ederer M, Gilles ED (2007) Thermodynamically feasible kinetic models of reaction networks. Biophys J 92:1846–1857CrossRefPubMedGoogle Scholar
  14. Esteban del Valle A, Aledo JC (2006) What process is glycolytic stoichiometry optimal for? J Mol Evol 62:488–495CrossRefGoogle Scholar
  15. Fraenkel D (1987) Glycolysis, pentose phosphate pathway, and Entner–Doudoroff pathway. In: Neidhardt FC (ed) Escherichia coli and Salmonella typhimurium. American Society for Microbiology, Washington, pp 142–150Google Scholar
  16. Garrigues C, Loubiere P, Lindley ND, Cocaign-Bousquet M (1997) Control of the shift from homolactic acid to mixed-acid fermentation in Lactococcus lactis: predominant role of the NADH/NAD+ ratio. J Bacteriol 179:5282–5287PubMedGoogle Scholar
  17. Garrigues C, Goupil-Feuillerat N, Cocaign-Bousquet M, Renault P, Lindley ND, Loubiere P (2001) Glucose metabolism and regulation of glycolysis in Lactococcus lactis strains with decreased lactate dehydrogenase activity. Metab Eng 3:211–217CrossRefPubMedGoogle Scholar
  18. Gupta S, Clark DP (1989) Escherichia coli derivatives lacking both alcohol dehydrogenase and phosphotransacetylase grow anaerobically by lactate fermentation. J Bacteriol 171:3650–3655PubMedGoogle Scholar
  19. Heinrich R, Schuster S (1996) The regulation of cellular systems. Chapman & Hall, LondonGoogle Scholar
  20. Heinrich R, Montero F, Klipp E, Waddel TG, Meléndez-Hevia E (1997) Theoretical approaches to the evolutionary optimization of glycolysis: thermodynamic and kinetic constraints. Eur J Biochem 243:191–201CrossRefPubMedGoogle Scholar
  21. Ibarra RU, Edwards JS, Palsson BO (2002) Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420:186–189CrossRefPubMedGoogle Scholar
  22. Kacser H, Beeby R (1984) Evolution of catalytic proteins. Or: On the origin of enzyme species by means of natural selection. J Mol Evol 20:38–51CrossRefPubMedGoogle Scholar
  23. Kedem O, Caplan SR (1965) Degree of coupling and its relation to efficiency of energy conversion. Trans Faraday Soc 61:1897–1911CrossRefGoogle Scholar
  24. Lehninger AL, Nelson DL, Cox MM (1993) Principles of biochemistry. Worth Publishers, New YorkGoogle Scholar
  25. Lemasters JJ, Billica WH (1981) Non-equilibrium thermodynamics of oxidative phosphorylation by inverted inner membrane vesicles of rat liver mitochondria. J Biol Chem 256:12949–12957PubMedGoogle Scholar
  26. Manchester KL (1998) Optimization of energy coupling: what is all the argument about? Biochem Educ 28:18–19CrossRefGoogle Scholar
  27. Maniloff J, McElhany R, Fynch L, Baseman J (eds) (1992) Mycoplasmas: molecular biology and pathogenesis. American Society for Microbiology, Washington, D.CGoogle Scholar
  28. Mavrovouniotis ML (1991) Estimation of standard Gibbs energy changes of biotransformations. J Biol Chem 266:14440–14445PubMedGoogle Scholar
  29. Meléndez-Hevia E, Waddell TG, Heinrich R, Montero F (1997) Theoretical approaches to the evolutionary optimization of glycolysis. Chemical analysis. Eur J Biochem 244:527–543CrossRefPubMedGoogle Scholar
  30. Molenaar D, van Berlo R, de Ridder D, Teusink B (2009) Shifts in growth strategies reflect tradeoffs in cellular economics. Mol Syst Biol 5:323CrossRefPubMedGoogle Scholar
  31. Nelson DL, Cox MM (2005) Lehninger. Principles of biochemistry. Worth Publishers, New YorkGoogle Scholar
  32. Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems: from dissipative structures to order through fluctuations. Wiley, Hoboken, NJGoogle Scholar
  33. Ogino T, Arata Y, Fujiwara S, Shoun H, Beppu T (1978) Proton correlation nuclear magnetic resonance study of anaerobic metabolism of Escherichia coli. Biochemistry 17:4742–4745CrossRefPubMedGoogle Scholar
  34. Oliveira AP, Nielsen J, Förster J (2005) Modeling Lactococcus lactis using a genome-scale flux model. BMC Microbiol 5:39CrossRefPubMedGoogle Scholar
  35. Pfeiffer T, Schuster S, Bonhoeffer S (2001) Cooperation and competition in the evolution of ATP-producing pathways. Science 292:504–507CrossRefPubMedGoogle Scholar
  36. Pollack JD (1992) Carbohydrate metabolism and energy conservation. In: Maniloff J, McElhaney RN, Finch LR, Baseman JB (eds) Mycoplasmas—molecular biology and pathogenesis. American Society for Microbiology, Washington, D.C., pp 181–200Google Scholar
  37. Sander R (1999) Compilation of Henry’s law constants for inorganic and organic species of potential importance in environmental chemistry (Version 3). http://www.henrys-law.org
  38. Schuetz R, Kuepfer L, Sauer U (2007) Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol Syst Biol 3:119CrossRefPubMedGoogle Scholar
  39. Schuster S, Pfeiffer T, Moldenhauer F, Koch I, Dandekar T (2002) Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18:351–361CrossRefPubMedGoogle Scholar
  40. Schuster S, Pfeiffer T, Fell DA (2008) Is maximization of molar yield in metabolic networks favoured by evolution? J Theor Biol 252:497–504CrossRefPubMedGoogle Scholar
  41. Stephani A, Nuño JC, Heinrich R (1999) Optimal stoichiometric designs of ATP-producing systems as determined by an evolutionary algorithm. J Theor Biol 199:45–61CrossRefPubMedGoogle Scholar
  42. Stucki JW (1980) The optimal efficiency and the economic degrees of coupling of oxidative phosphorylation. Eur J Biochem 109:269–283CrossRefPubMedGoogle Scholar
  43. Thauer RK, Jungermann K, Decker K (1977) Energy conservation in chemotrophic anaerobic bacteria. Bacteriol Rev 41:100–180PubMedGoogle Scholar
  44. Waddell TG, Repovic P, Meléndez-Hevia E, Heinrich R, Montero F (1997) Optimization of glycolysis: a new look at the efficiency of energy coupling. Biochem Educ 25:204–205CrossRefGoogle Scholar
  45. Waddell TG, Repovic P, Meléndez-Hevia E, Heinrich R, Montero F (1999) Optimization of glycolysis: new discussion. Biochem Educ 27:12–13CrossRefGoogle Scholar
  46. Wagner N, Pross A, Tannenbaum E (2010) Selection advantage of metabolic over non-metabolic replicators: a kinetic analysis. Biosystems 99:126–129CrossRefPubMedGoogle Scholar
  47. White D (1995) The physiology and biochemistry of prokaryotes. Oxford University Press, New York, pp 281–284Google Scholar
  48. Wise R, Hoober JK (eds) (2006) The structure and function of plastids. Springer, DordrechtGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Sarah Werner
    • 1
  • Gabriele Diekert
    • 2
  • Stefan Schuster
    • 1
    Email author
  1. 1.Jena Centre for BioinformaticsFriedrich Schiller University JenaJenaGermany
  2. 2.Institute of MicrobiologyFriedrich Schiller University JenaJenaGermany

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