Journal of Mathematical Chemistry

, Volume 3, Issue 1, pp 25-42

First online:

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

  • Stefan SchusterAffiliated withSektion Biologie, Bereich Biophysik, Humboldt-Universität zu Berlin
  • , Ronny SchusterAffiliated withInstitut für Biochemie, Humboldt-Universität zu Berlin

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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.