Determining Elementary Modes of Functioning in Biochemical Reaction Networks at Steady State

  • S. Schuster
  • C. Hilgetag
  • R. Schuster


In the modelling of biochemical reaction systems, analysis of steady states plays an important role, because virtually stationary regimes are frequently encountered in experimental settings and under in-vivo conditions. Since in steady states, all intermediates have to be balanced with respect to inputs and outputs, the vector, V, of stationary reaction rates (called fluxes below) has to be situated in the null-space (kernel)of the stoichiometry matrix, N (cf. Clarke, 1980, 1988; Thomas and Fell, 1993).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Clarke, B.L.: Stability of complex reaction networks. In: Advances in Chemical Physics, vol. 43, Prigogine, I. and Rice, S.A. (Eds.), Wiley, New York 1980, 1–216.CrossRefGoogle Scholar
  2. 2.
    Clarke, B.L.: Stoichiometric network analysis. Cell Biophys. 12 (1988), 237–253.Google Scholar
  3. 3.
    Fell, D.A.: Substrate cycles: theoretical aspects of their role in metabolism. Comments on theor. Biol. 6 (1990), 1–14.Google Scholar
  4. 4.
    Fell, D.A.: Metabolic Control Analysis: a survey of its theoretical and experimental development, Biochem. J. 286 (1992), 313–330.Google Scholar
  5. 5.
    Fell, D. A., The analysis of flux in substrate cycles. In: Modern Trends in Biothermokinetics, Schuster, S., Rigoulet, M., Ouhabi, M., and Mazat, J.P. (Eds.), Plenum Press, New York and London 1993, 97–101.Google Scholar
  6. 6.
    Groetsch, C.W. and King, J.T.: Matrix methods and applications. Prentice-Hall, Englewood Cliffs 1988.Google Scholar
  7. 7.
    Leiser, J. and Blum J.J.: Plenum Press, New York and London, Cell Biophys. 11 (1987), 123–138.Google Scholar
  8. 8.
    Mavrovouniotis, M.L., Stephanopoulos, G. and Stephanopoulos, G.: Computer-aided synthesis of biochemical pathways. Biotechn. Bioengng. 36 (1990), 1119–1132.CrossRefGoogle Scholar
  9. 9.
    Mavrovouniotis, MX.: Synthesis of reaction mechanisms consisting of reversible and irreversible steps. 2. Formalization and analysis of the synthesis algorithm. Ind. Eng. Chem. Res. 31 (1992) 1637–1653.CrossRefGoogle Scholar
  10. 10.
    Nožička, F., Guddat, J., Hollatz, H., and Bank, B.: Theorie der linearen parametrischen Optimierung. Akademie-Verlag, Berlin 1974.zbMATHGoogle Scholar
  11. 11.
    Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton 1970.zbMATHGoogle Scholar
  12. 12.
    Schuster, S. and Heinrich, R.: Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks. I. Theoretical analysis. J. Math. Biol. 29 (1991), 425–442.zbMATHCrossRefGoogle Scholar
  13. 13.
    Schuster, S. and Hilgetag, C: On elementary flux modes in biochemical reactions systems at steady state. J. Biol. Syst. (1994), in press.Google Scholar
  14. 14.
    Schuster, R. and Schuster, S.: Refined algorithm and computer program for calculating all non-negative fluxes admissible in steady states of biochemical reaction systems with or without some flux rates fixed. Comp. Appl. Biosci. 9 (1993), 79–85.Google Scholar
  15. 15.
    Seressiotis, A. and Bailey, J.E.: MPS: an artificially intelligent software system for the analysis and synthesis of metabolic pathways. Biotechn. Bioengng. 31 (1988), 587–602.CrossRefGoogle Scholar
  16. 16.
    Thomas, S. and Fell, D.A.: A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis. Biochem. J. 292 (1993), 351–360.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

Authors and Affiliations

  • S. Schuster
  • C. Hilgetag
  • R. Schuster

There are no affiliations available

Personalised recommendations