Bulletin of Mathematical Biology

, Volume 63, Issue 1, pp 21–55

Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems

  • Oliver Ebenhöh
  • Reinhart Heinrich
Article

Abstract

The structural design of ATP and NADH producing systems, such as glycolysis and the citric acid cycle (TCA), is analysed using optimization principles. It is assumed that these pathways combined with oxidative phosphorylation have reached, during their evolution, a high efficiency with respect to ATP production rates. On the basis of kinetic and thermodynamic principles, conclusions are derived concerning the optimal stoichiometry of such pathways. Extending previous investigations, both the concentrations of adenine nucleotides as well as nicotinamide adenine dinucleotides are considered variable quantities. This implies the consideration of the interaction of an ATP and NADH producing system, an ATP consuming system, a system coupling NADH consumption with ATP production and a system consuming NADH decoupled from ATP production. It is examined in what respect real metabolic pathways can be considered optimal by studying a large number of alternative pathways. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations. In this manner, the steady-state ATP production rate can be calculated for any possible ATP and NADH producing pathway. It is shown that most of the possible pathways result in a very low ATP production rate and that the very efficient pathways share common structural properties. Optimization with respect to the ATP production rate is performed by an evolutionary algorithm. The following results of our analysis are in close correspondence to the real design of glycolysis and the TCA cycle. (1) In all efficient pathways the ATP consuming reactions are located near the beginning. (2) In all efficient pathways NADH producing reactions as well as ATP producing reactions are located near the end. (3) The number of NADH molecules produced by the consumption of one energy-rich molecule (glucose) amounts to four in all efficient pathways. A distance measure and a measure for the internal ordering of reactions are introduced to study differences and similarities in the stoichiometries of metabolic pathways.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albery, W. J. and J. R. Knowles (1976). Evolution of enzyme function and the development of catalytic efficiency. Biochemistry 15, 5631–5640.CrossRefGoogle Scholar
  2. Angulo-Brown, F., M. Santillán and E. Calleja-Quevado (1995). Thermodynamic optimality in some biochemical reactions. Nuovo Cimento D 17, 87–90.Google Scholar
  3. Eigen, M., J. McCaskill and P. Schuster (1989). Molecular quasispecies. J. Phys. Chem. 92, 6881–6891.CrossRefGoogle Scholar
  4. Ferea, T. L., D. Botstein, P. O. Brown and R. F. Rosenzweig (1999). Systematic changes in gene expression patterns following adaptive evolution in yeast. Proc. Natl. Acad. Sci. USA 96, 9721–9726.CrossRefGoogle Scholar
  5. Florkin, M. and E. H. Stotz (Eds) (1969). Carbohydrate Metabolism, Amsterdam: Elsevier.Google Scholar
  6. Garfinkel, D. and B. Hess (1964). Metabolic control mechanism VII. A detailed computer model of the glycolytic pathway in ascites cells. J. Biol. Chem. 239, 971–983.Google Scholar
  7. Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Reading, MA: Addison-Wesley.Google Scholar
  8. Hamming, R. W. (1980). Coding and Information Theory, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  9. Heinrich, R. and E. Hoffmann (1991). Kinetic parameters of enzymatic reactions in states of maximal activity. An evolutionary approach. J. Theor. Biol. 151, 249–283.Google Scholar
  10. Heinrich, R., F. Montero, E. Klipp, T. G Waddell and E. Meléndez-Hevia (1997). Theoretical approaches to the evolutionary optimization of glycolysis; thermodynamic and kinetic constraints. Eur. J. Biochem. 243, 191–201.CrossRefGoogle Scholar
  11. Heinrich, R. and S. Schuster (1996). The Regulation of Cellular Systems, New York: Chapman & Hall.Google Scholar
  12. Heinrich, R., S. Schuster and H. G. Holzhütter (1991). Mathematical analysis of enzymic reaction systems using optimization principles. Eur. J. Biochem. 201, 1–21.CrossRefGoogle Scholar
  13. Joshi, A. and B. O. Palsson (1989). Metabolic dynamics in the human red cell. I and II. J. Theor. Biol. 141, 515–545.Google Scholar
  14. Joshi, A. and B. O. Palsson (1990). Metabolic dynamics in the human red cell. III and IV. J. Theor. Biol. 142, 41–85.Google Scholar
  15. Mavrovouniotis, M. L. and G. Stepanopoulos (1990). Estimation of upper bounds for the rates of enzymatic reactions. Chem. Eng. Commun. 93, 211–236.Google Scholar
  16. Meléndez-Hevia, E. and A. Isidoro (1985). The game of the pentose phosphate cycle. J. Theor. Biol. 117, 251–263.Google Scholar
  17. Meléndez-Hevia, E. and N. V. Torres (1988). Economy of design in metabolic pathways: further remarks on the game of the pentose phosphate cycle. J. Theor. Biol. 132, 97–111.Google Scholar
  18. Meléndez-Hevia, E., T. G. Waddell, R. Heinrich and F. Montero (1997). Theoretical approaches to the evolutionary optimization of glycolysis; chemical analysis. Eur. J. Biochem. 244, 527–543.CrossRefGoogle Scholar
  19. Mittenthal, J. E., A. Yuan, B. Clarke and A. Scheeline (1998). Designing metabolism; alternative connectivities for the pentose-phosphate pathway. Bull. Math. Biol. 60, 815–856.CrossRefGoogle Scholar
  20. Mulquiney, P. and P. W. Kuchel (1999a). Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement. Biochem. J. 342, 581–596.CrossRefGoogle Scholar
  21. Mulquiney, P. and P. W. Kuchel (1999b). Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: computer simulation and metabolic control analysis. Biochem. J. 342, 597–604.CrossRefGoogle Scholar
  22. Nuño, J. C., I. Sanchez-Valdenebro, C. Pereziratxeta, E. Meléndez-Hevia and F. Montero (1997). Network organization of cell metabolism; monosaccharide interconversion. Biochem. J. 324, 103–111.Google Scholar
  23. Pettersson, G. (1992). Evolutionary optimization of the catalytic efficiency of enzymes. Eur. J. Biochem. 206, 289–295.CrossRefGoogle Scholar
  24. Rapoport, T. A., R. Heinrich and S. M. Rapoport (1976). The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time dependent processes. Biochem. J. 154, 449–469.Google Scholar
  25. Rechenberg, I. (1989). Evolution Strategy: Nature’s Way of Optimization, Lecture Notes in Engineering, Vol. 47, Berlin: Springer.Google Scholar
  26. Rizzi, M., M. Baltes, U. Theobald and M. Reuss (1997). In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model. Biotechnol. Bioeng. 55, 592–608.CrossRefGoogle Scholar
  27. Stephani, A. and R. Heinrich (1998). Kinetic and thermodynamic principles determining the structural design of ATP-producing systems. Bull. Math. Biol. 60, 505–543.CrossRefGoogle Scholar
  28. Stephani, A., J. C. Nuño and R. Heinrich (1999). Optimal stoichiometric design of ATP-producing systems as determined by an evolutionary algorithm. J. Theor. Biol. 199, 45–61.CrossRefGoogle Scholar
  29. Stryer, L. (1988). Biochemistry, New York: W. H. Freeman and Company.Google Scholar
  30. Teusink, B., M. C. Walsh, K. van Dam and H. V. Westerhoff (1998). The danger of metabolic pathways with turbo design. Trends Biochem. Sci. 23, 162–169.CrossRefGoogle Scholar
  31. Varma, A. and B. O. Palsson (1993). Metabolic capabilities of Escherichia coli: I. Synthesis of biosynthetic precursors and cofactors. J. Theor. Biol. 165, 477–502.CrossRefGoogle Scholar
  32. Venables, W. N. and B. D. Ripley (1998). Modern Applied Statistics with S-PLUS, 2nd edn, New York: Springer.Google Scholar
  33. Waddell, T. G., P. Repovic, E. Meléndez-Hevia, R. Heinrich and F. Montero (1999). Optimization of glycolysis: new discussions. Biochem. Educ. 27, 12–13.CrossRefGoogle Scholar
  34. Werner, A. and R. Heinrich (1985). A kinetic model for the interaction of energy metabolism and osmotic states of human erythrocytes. Analysis of the stationary ‘in vivo’ state and of time dependent variations under blood preservation conditions. Biomed. Biochim. Acta 44, 185–212.Google Scholar
  35. Wilhelm, T., E. Hoffmann-Klipp and R. Heinrich (1994). An evolutionary approach to enzyme kinetics: optimization of ordered mechanisms. Bull. Math. Biol. 56, 65–106.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2001

Authors and Affiliations

  • Oliver Ebenhöh
    • 1
  • Reinhart Heinrich
    • 1
  1. 1.Institut für Biologie/Theoretische BiophysikHumboldt-Universität zu BerlinBerlinGermany

Personalised recommendations