Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1983 Sep;80(18):5455–5459. doi: 10.1073/pnas.80.18.5455

Multiple steady states and oscillatory behavior of a compartmentalized phosphofructokinase system.

J F Hervagault, M C Duban, J P Kernevez, D Thomas
PMCID: PMC384276  PMID: 6225119

Abstract

This paper discusses interacting diffusion and reaction in an open enzyme system. The enzyme, rabbit muscle phosphofructokinase (PFK; ATP:D-fructose-6-phosphate 1-phosphotransferase, EC 2.7.1.11), is inhibited strongly by excess of the substrate ATP. Metabolites diffuse through an inert membrane separating the enzyme from the bulk reacting medium. We demonstrate that such a simple system is able to account for the existence of both oscillatory behavior (limit cycle) and multiple steady states (hysteresis) as well as for the sudden transitions between stable and periodic behaviors. Experimental evidence for time oscillations is given.

Full text

PDF
5455

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Boiteux A., Goldbeter A., Hess B. Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: a model and experimental study. Proc Natl Acad Sci U S A. 1975 Oct;72(10):3829–3833. doi: 10.1073/pnas.72.10.3829. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bunow B. Enzyme kinetics in cells. Bull Math Biol. 1974 Apr;36(2):157–169. doi: 10.1007/BF02458600. [DOI] [PubMed] [Google Scholar]
  3. Cambou B., Laurent M., Hervagault J. F., Thomas D. Modulation of phosphofructokinase behavior by chemical modifications during the immobilization process. Eur J Biochem. 1981 Dec;121(1):99–104. doi: 10.1111/j.1432-1033.1981.tb06436.x. [DOI] [PubMed] [Google Scholar]
  4. Caplan S. R., Naparstek A., Zabusky N. J. Chemical oscillations in membrane. Nature. 1973 Oct 19;245(5425):364–366. doi: 10.1038/245364a0. [DOI] [PubMed] [Google Scholar]
  5. Eschrich K., Schellenberger W., Hofmann E. In vitro demonstration of alternate stationary states in an open enzyme system containing phosphofructokinase. Arch Biochem Biophys. 1980 Nov;205(1):114–121. doi: 10.1016/0003-9861(80)90089-2. [DOI] [PubMed] [Google Scholar]
  6. Frenkel R. DPNH oscillations in glycolyzing cell free extracts from beef heart. Biochem Biophys Res Commun. 1965 Dec 9;21(5):497–502. doi: 10.1016/0006-291x(65)90411-0. [DOI] [PubMed] [Google Scholar]
  7. Friboulet A., Thomas D. Electrical excitability of artificial enzyme membranes. III. Hysteresis and oscillations observed with immobilized acetylcholinesterase membranes. Biophys Chem. 1982 Oct;16(2):153–157. doi: 10.1016/0301-4622(82)85017-5. [DOI] [PubMed] [Google Scholar]
  8. Ghosh A., Chance B. Oscillations of glycolytic intermediates in yeast cells. Biochem Biophys Res Commun. 1964 Jun 1;16(2):174–181. doi: 10.1016/0006-291x(64)90357-2. [DOI] [PubMed] [Google Scholar]
  9. HIGGINS J. A CHEMICAL MECHANISM FOR OSCILLATION OF GLYCOLYTIC INTERMEDIATES IN YEAST CELLS. Proc Natl Acad Sci U S A. 1964 Jun;51:989–994. doi: 10.1073/pnas.51.6.989. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hahn H. S., Nitzan A., Ortoleva P., Ross J. Threshold excitations, relaxation oscillations, and effect of noise in an enzyme reaction. Proc Natl Acad Sci U S A. 1974 Oct;71(10):4067–4071. doi: 10.1073/pnas.71.10.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Hahn H. S., Ortoleva P. J., Ross J. Chemical oscillations and multiple steady states due to variable boundary permeability. J Theor Biol. 1973 Oct;41(3):503–521. doi: 10.1016/0022-5193(73)90058-1. [DOI] [PubMed] [Google Scholar]
  12. Hervagault J. F., Friboulet A., Kernevez J. P., Thomas D. Spatiotemporal behaviors in immobilized enzyme systems. Biochimie. 1980;62(5-6):367–373. doi: 10.1016/s0300-9084(80)80167-2. [DOI] [PubMed] [Google Scholar]
  13. Hess B., Boiteux A. Mechanism of glycolytic oscillation in yeast. I. Aerobic and anaerobic growth conditions for obtaining glycolytic oscillation. Hoppe Seylers Z Physiol Chem. 1968 Nov;349(11):1567–1574. doi: 10.1515/bchm2.1968.349.2.1567. [DOI] [PubMed] [Google Scholar]
  14. Ibsen K. H., Schiller K. W. Control of glycolysis and respiration in substrate-depleted Ehrlich ascites tumor cells. Arch Biochem Biophys. 1971 Mar;143(1):187–203. doi: 10.1016/0003-9861(71)90199-8. [DOI] [PubMed] [Google Scholar]
  15. Kernevez J. P., Joly G., Duban M. C., Bunow B., Thomas D. Hysteresis, oscillations, and pattern formation in realistic immobilized enzyme systems. J Math Biol. 1979 Jan 23;7(1):41–56. doi: 10.1007/BF00276413. [DOI] [PubMed] [Google Scholar]
  16. MONOD J., WYMAN J., CHANGEUX J. P. ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. J Mol Biol. 1965 May;12:88–118. doi: 10.1016/s0022-2836(65)80285-6. [DOI] [PubMed] [Google Scholar]
  17. Naparstek A., Thomas D., Caplan S. R. An experimental enzyme-membrane oscillator. Biochim Biophys Acta. 1973 Nov 16;323(4):643–646. doi: 10.1016/0005-2736(73)90176-4. [DOI] [PubMed] [Google Scholar]
  18. Olsen L. F., Degn H. Oscillatory kinetics of the peroxidase-oxidase reaction in an open system. Experimental and theoretical studies. Biochim Biophys Acta. 1978 Apr 12;523(2):321–334. doi: 10.1016/0005-2744(78)90035-9. [DOI] [PubMed] [Google Scholar]
  19. Pettigrew D. W., Frieden C. Rabbit muscle phosphofructokinase. A model for regulatory kinetic behavior. J Biol Chem. 1979 Mar 25;254(6):1896–1901. [PubMed] [Google Scholar]
  20. Pettigrew D. W., Frieden C. Rabbit muscle phosphofructokinase. Modification of molecular and regulatory kinetic properties with the affinity label 5'-p-(fluorosulfonyl)benzoyl adenosine. J Biol Chem. 1978 May 25;253(10):3623–3627. [PubMed] [Google Scholar]
  21. Pettigrew D. W., Frieden C. Treatment of enzyme kinetic data. Extension of the concerted allosteric model to the two-substrate case. J Biol Chem. 1977 Jul 10;252(13):4546–4551. [PubMed] [Google Scholar]
  22. Rapoport T. A., Heinrich R., Rapoport S. M. 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. 1976 Feb 15;154(2):449–469. doi: 10.1042/bj1540449. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Schellenberger W., Eschrich K., Hofmann E. Selforganization of a glycolytic reconstituted enzyme system: alternate stable stationary states, hysteretic transitions and stabilization of the energy charge. Adv Enzyme Regul. 1980;19:257–284. doi: 10.1016/0065-2571(81)90019-4. [DOI] [PubMed] [Google Scholar]
  24. Sel'kov E. E. Stabilization of energy charge, generation of oscillations and multiple steady states in energy metabolism as a result of purely stoichiometric regulation. Eur J Biochem. 1975 Nov 1;59(1):151–157. doi: 10.1111/j.1432-1033.1975.tb02436.x. [DOI] [PubMed] [Google Scholar]
  25. Termonia Y., Ross J. Oscillations and control features in glycolysis: numerical analysis of a comprehensive model. Proc Natl Acad Sci U S A. 1981 May;78(5):2952–2956. doi: 10.1073/pnas.78.5.2952. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Thomas D., Bourdillon C., Broun G., Kernevez J. P. Kinetic behavior of enzymes in artificial membranes. Inhibition and reversibility effects. Biochemistry. 1974 Jul 2;13(14):2995–3000. doi: 10.1021/bi00711a032. [DOI] [PubMed] [Google Scholar]
  27. Tornheim K., Lowenstein J. M. The purine nucleotide cycle. Control of phosphofructokinase and glycolytic oscillations in muscle extracts. J Biol Chem. 1975 Aug 25;250(16):6304–6314. [PubMed] [Google Scholar]
  28. Tornheim K. Oscillations of the glycolytic pathway and the purine nucleotide cycle. J Theor Biol. 1979 Aug 21;79(4):491–541. doi: 10.1016/0022-5193(79)90240-6. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES