The Steady State Approximation in Enzyme Kinetics: Reflections in Its Centennial Year

The now-called quasi- (or pseudo-) steady state (QSS) approximation was introduced by Briggs and Haldane in an analysis of an unusual kinetic scheme for an enzyme-catalysed reaction, it had no product binding. The approximation, though perhaps not the kinetic scheme used, was well founded, and led to a solution of the rate equation of an enzyme-substrate intermediate. That in turn allowed the derivation of the well-known equation describing the kinetics of many enzymes, the Henri-Michaelis-Menten equation. Unfortunately, in more realistic kinetic schemes with product binding, the application of the QSS approximation leads to an uncertainty in the nature of kinetic constants as described by rate constants. It is shown here that for reasonable special cases of two kinetic schemes, first analysed by Haldane, that during the pre-steady state the reverse reaction may cause the concentration of the enzyme-substrate intermediate to rise to give a QSS essentially that of its final equilibrium concentration. This leads to a revision of the structure of kinetic constants (as describe by rate constants), and is sufficient to show the Haldane Relationship between catalytic constants and the equilibrium constant of the reaction is not generally true.