Skip to main content
Log in

On the Higgins model of glycolysis

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A study was made of Higgins’ model of glycolysis incorporating molecular diffusion of intermediates, utilizing an earlier conjecture due to Landau. Conditions for the existence of asymptotically stable spatio-temporal periodic solutions are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Chance, B., E. K. Pye, A. Ghosh and B. Hess. 1973.Biological and Biochemical Oscillators. New York: Academic Press.

    Google Scholar 

  • Eckhaus, W. 1965.Studies in Nonlinear Stability Theory. Berlin: Springer.

    Google Scholar 

  • Haken, H. 1977.Synergetics. Berlin: Springer.

    Google Scholar 

  • Higgins, J. 1964. “A Chemical Mechanism for Oscillations of Glycolytic Intermediates in Yeast Cells.”Proc. natn. Acad. Sci. U.S.A.,51, 989–994.

    Article  Google Scholar 

  • Ibanez, J. L., V. Faiven and M. G. Velarde. 1976. “Limit Cycles and Dissipative Structures in a Simple Biomolecular Non-Equilibrium Reactional Scheme with Enzyme.”Phys. Lett. 58A, 364–366.

    Google Scholar 

  • — and M. G. Velarde. 1978. “Multiple Steady States in a Simple Reaction-Diffusion Model with Michaelis-Menten (First-Order Hinshelwood Langmuir) Saturation Law: The Limit of Large Separation in Two Diffusion Constants.”J. math. Phys.,19, 151–156.

    Article  Google Scholar 

  • Kogelman, S. and R. C. diPrima. 1970. “Stability of Spatially Periodic Supercritical Flows in Hydrodynamics.”Phys. Fluids,13, 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  • Landau, L. D. 1959.Fluid Dynamics, p. 103. New York: Pergamon Press.

    Google Scholar 

  • Nicolis, G. and I. Prigogine. 1977.Self Organization in Non-Equilibrium Systems. New York: John Wiley.

    Google Scholar 

  • Zhabotinsky, A. M. and A. N. Zaikin. 1970. “Concentration Wave Propagation in a Two Dimensional Liquid Phase Self-Oscillating System.”Nature,225, 535–537.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhargava, S.C. On the Higgins model of glycolysis. Bltn Mathcal Biology 42, 829–836 (1980). https://doi.org/10.1007/BF02461061

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02461061

Keywords

Navigation