Description of enzyme kinetics in reversed micelles. 1. Theory

In the literature measurements of kinetic data of enzymes in reversed micelles have been interpreted in two ways. In the first, all enzyme parameters are expressed with respect to the total volume of the reversed micellar solution. In the second, the enzymatic conversion is related only to the fraction of the volume consisting of aqueous solution (pseudophase model). In this paper equations are derived describing the rate of an enzymatic reaction for three different kinds of enzymes: enzymes obeying Michaelis-Menten kinetics, enzymes following a ping-pong bi-bi mechanism and enzymes which convert substrates according to an ordered mechanism. In deriving these equations, a distinction is made between intermicellar exchange reactions of substrate(s) and product(s) and the enzymatic reaction which takes place in the waterpool of a reversed micelle. In the description, all intrinsic rate constants of the enzyme are assumed to be independent of its environment. The rate equations show that the presence and efficiency of the intermicellar exchange reaction, which supplies the enzyme with substrate and removes product, can affect the rate of an enzymatic reaction under common experimental conditions. Whereas kinetic parameters derived from double-reciprocal plots often seem to be affected by enclosure in reversed micelles, these apparent deviations from kinetics in aqueous media can be explained by the model presented here as arising from exchange phenomena. Neither the experimentally determined maximum enzyme velocity, vmax, nor the Michaelis constants are affected by the incorporation of the enzyme in reversed micelles. The deviations of kinetic parameters from the aqueous values are shown to depend strongly on the concentration of reversed micelles, the intermicellar exchange rate and the volume fraction of water, a dependence in agreement with findings reported in the literature.