Bulletin of Mathematical Biology

, Volume 65, Issue 2, pp 323–357 | Cite as

Stoichiometric design of metabolic networks: Multifunctionality, clusters, optimization, weak and strong robustness

Article

Abstract

Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network’s functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barabasi, A. L. and R. Albert (1999). Emergence of scaling in random networks. Science 286, 509–512.MathSciNetCrossRefGoogle Scholar
  2. Binder, B. and R. Heinrich (2002). Dynamic stability of signal transduction networks depending on downstream and upstream specificity of protein kinases. Mol. Biol. Rep. 29, 51–55.CrossRefGoogle Scholar
  3. Ebeling, W., A. Engel and R. Feistel (1990). Physik der Evolutionsprozesse, Berlin: Akademie Verlag.Google Scholar
  4. Ebeling, W. and R. Feistel (1977). Stochastic theory of molecular replication processes with selection character. Ann. Phys. 34, 81–90.Google Scholar
  5. Ebenhöh, O., (2003). Structural analysis of metabolic systems. PhD thesis, Humboldt-University Berlin.Google Scholar
  6. Ebenhöh, O. and R. Heinrich (2001). Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems. Bull. Math. Biol. 63, 21–55.CrossRefGoogle Scholar
  7. Eigen, M. (1971). Selforganization of matter and the evolution of biological macromolecules. Die Naturwissenschaften 58, 465–523.CrossRefGoogle Scholar
  8. Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Reading: Addison-Wesley.Google Scholar
  9. Groetsch, C. W. and J. T. King (1988). Matrix Methods and Applications, Englewood Cliffs: Prentice-Hall.Google Scholar
  10. Heinrich, R., H. G. Holzhütter and S. Schuster (1987). A theoretical approach to the evolution and structural design of enzymatic networks: linear enzymatic chains, branched pathways and glycolysis of erythrocytes. Bull. Math. Biol. 49, 539–595.MathSciNetCrossRefGoogle Scholar
  11. 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
  12. Heinrich, R. and S. Schuster (1996). The Regulation of Cellular Systems, Chapman and Hall.Google Scholar
  13. Heinrich, R. and I. Sonntag (1981). Analysis of the selection equations for a multivariable population model: Deterministic and stochastic solutions and discussion of the approach for populations of self-reproducing biochemical networks. J. Theor. Biol. 93, 325–361.MathSciNetCrossRefGoogle Scholar
  14. Mavrovouniotis, M. L., G. Stephanopoulos and G. Stephanopoulos (1990). Computer-aided synthesis of biochemical pathways. Biotechnol. Bioeng. 36, 1119–1132.CrossRefGoogle Scholar
  15. Meléndez-Hevia, E. and N. V. Torress (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
  16. Meléndez-Hevia, E., T. G. Waddell and M. Cascante (1996). The puzzle of the Krebs citric acid cycle: assembling the pieces of chemically feasible reactions, and opportunism in the design of metabolic pathways during evolution. J. Mol. Evol. 43, 293–303.Google Scholar
  17. Mittenthal, J. E., B. Clarke, T. G. Waddell and G. Fawcett (2001). A new method for assembling metabolic networks with application to the Krebs citric acid cycle. J. Theor. Biol. 208, 361–382.CrossRefGoogle Scholar
  18. 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
  19. Mulquiney, P. J. and P. W. Kuchel (1999). 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
  20. Nuño, J. C., I. Sanchez-Valdenebro, C. Perez-Iratxeta, E. Meléndez-Hevia and F. Montero (1997). Network organization of cell metabolism: monosaccharide interconversion. Biochem. J. 324, 103–111.Google Scholar
  21. Rechenberg, U. I. (1989). Evolution Strategy: Nature’s Way of Optimization, Lecture Notes in Engineering, Vol. 47, Berlin: Springer.Google Scholar
  22. Rizzi, M., M. Baltes, U. Theobald and M. Reuss (1997). In vivo analysis of metabolic dynamics in Saccharomyces cervisiae: II. Mathematical model. Biotechnol. Bioeng. 55, 592–608.CrossRefGoogle Scholar
  23. Schilling, C. H. and B. O. Palsson (1998). The underlying pathway structure of biochemical networks. Proc. Natl Acad. Sci. 95, 4193–4198.CrossRefGoogle Scholar
  24. Schilling, C. H., S. Schuster, O. B. Palsson and R. Heinrich (1999). Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era. Biotechnol. Prog. 15, 296–303.CrossRefGoogle Scholar
  25. Schuster, S., T. Dandekar and D. A. Fell (1999). Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol. 17, 53–60.CrossRefGoogle Scholar
  26. Schuster, S. and C. Hilgetag (1994). On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165–182.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. Strogatz, S. H. (2001). Exploring complex networks. Nature 410, 268–276.CrossRefGoogle Scholar
  30. Teusink, B., J. Passarge, C. A. Reijenga, E. Esgalhado, C. C. van der Weijden, M. Schepper, M. C. Walsh, B. M. Bakker, K. van Dam, H. V. Westerhoff and J. L. Snoep (2000). Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur. J. Biochem. 267, 5313–5329.CrossRefGoogle Scholar
  31. Wagner, A. and D. A. Fell (2001). The small world inside large metabolic networks. Proc. R. Soc. B 268, 1803–1810.CrossRefGoogle Scholar
  32. Wolf, J. and R. Heinrich (2000). Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation. Biochem. J. 345, 321–334.CrossRefGoogle Scholar
  33. Wolf, J., H. Y. Sohn, R. Heinrich and H. Kuriyama (2001). Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisiae. FEBS Lett. 499, 230–234.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2003

Authors and Affiliations

  1. 1.Department of Theoretical Biophysics, Institute of BiologyHumboldt-UniversityBerlinGermany

Personalised recommendations