A Linear Steady-State Treatment of Enzymatic Chains

General Properties, Control and Effector Strength

Authors

  • Reinhart Heinrich,

    1. Institut für Physiologische und Biologische Chemie, Medizinischer Bereich der Humboldt-Universität, DDR-104 Berlin, Hessische Straße 3/4 German Democratic Republic
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  • Tom A. Rapoport

    1. Institut für Physiologische und Biologische Chemie, Medizinischer Bereich der Humboldt-Universität, DDR-104 Berlin, Hessische Straße 3/4 German Democratic Republic
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  • Note Added in Proof. (29.11.1973). Recently we received a paper by Kacser and Burns [Kacser, H. & Burns, J. A. (1973) in Rate Control of Biological Processes (Davies, D. D. ed.) pp. 65–104, Cambridge University Press] which dealt with the same problems. They made similar definitions of control parameters. It seems of particular interest that besides Eqn (48) the following relation holds

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Abstract

A theoretical analysis of linear enzymatic chains is presented. By linear approximation simple analytical solutions can be obtained for the metabolite concentrations and the flux through the chain for steady-state conditions. The equations are greatly simplified if the common kinetic constants are expressed as functions of two parameters, i.e. the thermodynamic equilibrium constant and the “characteristic time”. Three cardinal terms are proposed for the quantitative description of enzyme systems. The first two are the control strength and the control matrix; these indicate the dependence of the flux and the metabolite concentrations, respectively, on the kinetic properties of a given enzyme. The third is the effector strength, which defines the dependence of the velocity of an enzyme on the concentration of an effector; it expresses the importance of an effector. By linear approximation simple analytical expressions were derived for the control strength, the control matrix and the mass-action ratios. The effector strength was calculated for two cases: for a competitive inhibitor and for allosteric effectors according to the Monod (1965) model. The influence of an effector on the concentrations of the metabolites was considered.

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