Simulation of Biochemical Pathways and its Application to Biology and Medicine

  • Otto Richter
  • Augustin Betz
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 11)

Summary

In recent years quantitative data on biochemical pathways have accumulated up to a point where a detailed mathematical analysis of multi-enzymesystems concerning their dynamics and regulatory properties has become possible: the knowledge of the structure of a pathway, its metabolite scheme, the pool sizes involved, and the kinetic laws of its enzymes enable its mathematical description in terms of coupled non-linear differential equations.

In the following paper the general form of the basic kinetic equations containing all species of a multienzymesystem is represented. Assuming a stationary state hypothesis for the enzyme species these equations are reduced to a system of conservation equations for the fluxes of substrates and intermediates whose terms consist of the kinetic laws of the corresponding enzymes.

Two examples of application in biology and medicine are given: simulation of glycolytic oscillations and simulation of allopurinol-therapy in hyperuricemia, e. d., the action of allopurinol on the last two steps in purine degradation.

Keywords

Sugar Carbohydrate Enzymatic Degradation Purine Gout 

List of abbreviations

HK)

Hexokinase (E.C. 2.7.1.1)

PFK)

Phosphofructokinase (S.C. 2.7.1.11)

F6P)

Fructose-6-Phosphate

FDP)

Fructosediphosphate

ATP, ADP, AMP)

Adenosin (tri, di, mono) phosphate

XANT)

Xanthine

HYPO)

Hypoxanthine

Vx)

kinetic law of enzyme x

Allo)

Allopurinol

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References

  1. 1.
    Otten, H.A., and Duysens, L. N., J. theor. Biol. 39, 387–396 (1973)CrossRefGoogle Scholar
  2. 2.
    Reich, J. G., and Selkov, E. E., Biosystems 7,1,39–51 (1975)CrossRefGoogle Scholar
  3. 3.
    Tikhanov, A. N., Mat. Sb. 22,64,193–201 (1948)Google Scholar
  4. 4.
    Walter, C. F., J. theor. Biol. 27,259–272 (1970)CrossRefGoogle Scholar
  5. 5.
    Chance, B., Betz, A., and Hess, B., Biochem. Biophys. Res. Comm. 16,2 (1964)CrossRefGoogle Scholar
  6. 6.
    Tornheim, K., and Loewenstein, J. M., J. Biol. Chem. 249, 3241–47 (1974)Google Scholar
  7. 7.
    Frenkel, R., Arch. Biochem. Biophys. 125,157–165 (1968)CrossRefGoogle Scholar
  8. 8.
    Hess, B., Boiteux, A. and Krüger, J. in “Advances in Enzyme Regulation”, Vol. 7, 149–167 (1969)Google Scholar
  9. 9.
    Hess, B., Ergebnisse der exp. Med. 9,66–87 (1971)Google Scholar
  10. 10.
    Selkov, E. E., Eur.J.Biochem. 4,79–86 (1973)CrossRefGoogle Scholar
  11. 11.
    Goldbeter, A., FEBS Letters 43, 327–330 (1974)CrossRefGoogle Scholar
  12. 12.
    IBM Scientific Subroutine Package, Version III, Subrocutine HPCGGoogle Scholar
  13. 13.
    Kopperschläger, G., Bahr, M.L. and Hofmann, E., Acta biol. med. german. 19,691–704 (1967)Google Scholar
  14. 14.
    Lalanne, M. and Willemot, J., Int. J. Biochem. 6,479–484 (1975)CrossRefGoogle Scholar
  15. 15.
    Wyngaarden, J., in “Advances in Metabolic Disorders”, Vol. II, 1–67 (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1976

Authors and Affiliations

  • Otto Richter
    • 1
    • 2
  • Augustin Betz
    • 1
    • 2
  1. 1.Medizinische Einrichtungen, Institut für Medizinische Statistik und BiomathematikUniversität DüsseldorfDüsseldorfGermany
  2. 2.Botanisches InstitutUniversität BonnBonnGermany

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