Abstract
A method is described by which rate equations for enzymic reactions under the equilibrium assumptions may be derived by inspecting the reaction pathways without solving simultaneous equations in the conventional way. Also described is a simple graphic method which combines the above technique with King and Altman's method. By the latter method, rate equations may be derived with minimal effort for complicated enzymic mechanisms in which some steps are considerably faster than the rest so that the enzymic species connected by those rapid steps may be at a near equilibrium while the over-all reaction is in a steady state. Rate equations are derived, for the purpose of illustration, for the reversible single substrate-single modifier system, the partial equilibrium ping-pong bi-bi mechanism, the general mechanism for two-substrate system, and a complicated three-substrate mechanism.
Highlights
A method is described by which rate equations for enzymic reactions under the equilibrium assumptions may be derived by inspecting the reaction pathways without solving simultaneous equations in the conventional way
The equilibrium rate equation, it is only an approximation of the true kinetics, is simpler and more convenient to use than the steady state equation, and it can offer valuable insight into the reaction mechanism
It is hoped that the use of the simple rules described in this paper may contribute to the derivation and the analysis of complicated enzymic mechanisms such as kinetics of regulatory enzymes
Summary
A method is described by which rate equations for enzymic reactions under the equilibrium assumptions may be derived by inspecting the reaction pathways without solving simultaneous equations in the conventional way. Described is a simple graphic method which combines the above technique with King and Altman’s method By the latter method, rate equations may be derived with minimal effort for complicated enzymic mechanisms in which some steps are considerably faster than the rest so that the enzymic species connected by those rapid steps may be at a near equilibrium while the over-all reaction is in a steady state. For the purpose of illustration, for the reversible single substrate-single modifier system, the partial equilibrium ping-pong bi-bi mechanism, the general mechanism for two-substrate three-substrate mechanism
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