A kinetic mechanism inducing oscillations in simple chemical reactions networks

@article{Coatlven2008AKM,
  title={A kinetic mechanism inducing oscillations in simple chemical reactions networks},
  author={Julien Coatl{\'e}ven and Claudio Altafini},
  journal={2008 47th IEEE Conference on Decision and Control},
  year={2008},
  pages={1771-1776}
}
It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the onset of oscillations in sufficiently simple reaction networks. 

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References

SHOWING 1-10 OF 21 REFERENCES

Limit-cycle oscillations and chaos in reaction networks subject to conservation of mass.

A cyclic network of autocatalytic reactions involving an unbuffered cofactor and a number of components subject to conservation of mass displays a surprising richness of dynamical behaviors.

Limit-cycles in enzyme-systems with nonlinear negative feedback

  • A. Hunding
  • Biology
    Biophysics of structure and mechanism
  • 2004
TLDR
Computer-simulations suggest that this criterion is sufficient for the occurrence of oscillating reactions in multi-enzyme systems with end-product inhibition, since limit-cycles arise whenever the criterion is violated with a cycle-time in good agreement with the theoretically derived estimate.

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

  • E. Sel'kov
  • Biology
    European journal of biochemistry
  • 1968
TLDR
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.

Structural kinetic modeling of metabolic networks

TLDR
This work proposes a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations.

A synthetic oscillatory network of transcriptional regulators

TLDR
This work used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli, which periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells.

The effect of slow allosteric transitions in a coupled biochemical oscillator model.

TLDR
It is found that slowed allosteric transitions suppress complex dynamic modes such a bursting, quasi-periodicity and chaos and may contribute significantly to the dynamics of biological control mechanisms.

Cell-signalling dynamics in time and space

  • B. Kholodenko
  • Biology, Environmental Science
    Nature Reviews Molecular Cell Biology
  • 2006
TLDR
Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.

Control analysis for autonomously oscillating biochemical networks.