Journal of Mathematical Chemistry

, Volume 3, Issue 1, pp 25–42 | Cite as

A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

  • Stefan Schuster
  • Ronny Schuster


A generalization of Wegschcider's condition concerning equilibrium constants in chemically reacting systems is formulated, which is then proved to be a necessary and sufficient condition for detailed balancing. In order to include a large multitude of rate laws, a generalized mass action kinetics is considered which comprises usual mass action kinetics and all reversible enzyme kinetics and which is consistent with basic postulates of irreversible thermodynamics for ideal mixtures. Reaction systems of arbitrary stoichiometry are considered. They may contain reactants with fixed concentrations, as is characteristic for models of biochemical reaction networks. Existence, uniqueness, and global asymptotic stability of equilibrium states for reaction systems endowed with generalized man action kinetics are proved. Using these results, he generalized Wegscheider condition is shown to be a sufficient criterion for the applicability of the quasi-steady-state approximation.


Asymptotic Stability Reaction Network Generalize Mass Enzyme Kinetic Detailed Balance 
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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1989

Authors and Affiliations

  • Stefan Schuster
    • 1
  • Ronny Schuster
    • 2
  1. 1.Sektion Biologie, Bereich BiophysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für BiochemieHumboldt-Universität zu BerlinBerlinGermany

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