A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
E Horn and R. Jackson, Arch. Rational Mech. Anal. 47 (l972)8l.
J. Wei, J. Chem. Phys. 36 (1962)1578.
J.Z. Hearon, Bull. Math. Biophys. 15 (1953)121.
K. Hayashi and N. Sakamoto,Dynamic Analysis of Enzyme Systems (Japan Scientific Societies/Springer, Tokyo, Berlin, 1986).
B.L. Clarke, in:Advances in Chemical Physics, Vol. XLIII, ed. I. Prigogine and S.A. Rice (Wiley, New York, 1980) p. 1.
M. Feinberg, in:Dynamics and Modelling of Reactive Sytems, ed. W.E. Stewart, W.H. Ray and C.C. Conley (Academic Press, New York, 1980) p. 59; and in the volume given sub  p. 56.
H.G. Othmer, in:Modelling of Chemical Reaction Systems, ed. K.H. Ebert, P. Deuflhard and W. Jäger (Springer, Berlin, 1981) p. 2.
R. Heinrich, S.M. Rapoport and T.A. Rapoport, Progr. Biophys. Molec. Biol. 32 (1977)1.
S.W. Benson,The Foundations of Chemical Kinetics (McGraw-Hill, New York, 1960).
D. Park, J. Theor. Biol. 46 (1974)31.
M. Schauer and R. Heinrich, Math. Biosci. 65 (1983)155.
F. Battelli and C. Lazzari, Math. Biosci. 75 (1985)229.
G. Nicolis and I. Prigogine,Self-Organization in Non-Equilibrium Systems (Wiley, New York, 1977).
K. Denbigh,The Principles of Chemical Equilibrium (University Press, Cambridge, U.K., 1955).
I. Samohýl,Rational Thermodynamics of Chemically Reacting Mixtures (Academia, Prague, 1982) (in Czech).
J.D. Rawn,Biochemistry (Harper and Row, New York, 1983).
J.L. Willems,Stability Theory of Dynamical Systems (Nelson, London, 1970).
W. Wasow,Asymptotic Expansions for Ordinary Differential Equations (Wiley, New York, 1965).
H.G. Holzhütter, G. Jacobasch and A. Bisdorff, Eur. J. Biochem. 149 (1985)101.
- A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation
Journal of Mathematical Chemistry
Volume 3, Issue 1 , pp 25-42
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links