A Simple Method for Derivation of Rate Equations for Enzyme-catalyzed Reactions under the Rapid Equilibrium Assumption or Combined Assumptions of Equilibrium and Steady State

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.