Unbounded solutions of models for glycolysis

  title={Unbounded solutions of models for glycolysis},
  author={Pia Brechmann and Alan D. Rendall},
  journal={Journal of Mathematical Biology},
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally… 

Transient behavior towards the stable limit cycle in the Sel’kov model of Glycolysis: A physiological disorder

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A modification of the Selkov model was proposed here to study this problem of Glycolysis in more realistic way and it was observed that convergence time, studied as a function of the distance from the limit cycle, got saturated away from the cycle.

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Dynamics of the Selkov oscillator.

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In this work, we study the qualitative properties of the model proposed by Selkov Eur J Biochem 4: 79–86 (1968) for the description of the glycolytic oscillations. First we show that the Selkov’s

Early models of chemical oscillations failed to provide bounded solutions

  • T. Erneux
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2018
The findings support the conclusion that the Brusselator is the first minimal two-variable model explaining the onset of stable oscillations in a way fully compatible with thermodynamics and the law of mass action.

Globally attractive oscillations in open monosubstrate allosteric enzyme reactions

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Self-oscillations in glycolysis. 1. A simple kinetic model.

  • E. Sel'kov
  • Biology
    European journal of biochemistry
  • 1968
A comparison between the model and the phosphofructokinase reaction shows a close resemblance between their dynamical properties, which makes it possible to explain qualitatively most experimental data on single-frequency oscillations in glycolysis.

On the creation, growth and extinction of oscillatory solutions for a simple pooled chemical reaction scheme

The equations which govern a simple pooled chemical reaction scheme are analysed in detail in terms of a nondimensional parameter $\mu $, which represents the amount of the pooled chemical originally

Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: a model and experimental study.

Type and range of entrainment of glycolytic oscillations by a periodic source of substrate are determined experimentally in yeast extracts and indicates that the oscillatory dynamics of the gly colytic system can satisfactorily be described by the phosphofructokinase model.


  • J. Higgins
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1964
7 Browder, F. E., "Nonlinear elliptic boundary value problems, II," Trans.

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This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic