Enzymes in reversed micelles: 4. Theoretical analysis of a one‐substrate/one‐product conversion and suggestions for efficient application

Abstract

Abstract A detailed analysis of the conversion of polar and apolar substrates in an heterogeneous medium is given. The enzyme is assumed to follow the mechanism: E + S⇌ES⇌E + P. The effects of various parameters, both enzymic and those of the microemulsion, are presented. In an extension to the model presented earlier, analysis of this simplified case reveals why a large difference is observed between the K m in aqueous solution and its value in microemulsions, suggesting increased affinity of the enzyme for a hydrophilic substrate and decreased affinity for an apolar substrate. It also demonstrates why, in contrast to studies in aqueous solutions, the rate constant of the reverse reaction ( k ‐2 ) affects the initial rate of the reaction in microemulsions. Furthermore, it is explained that the bell‐shaped relationship between the initial reaction rate and the water content of the microemulsion can depend on the value of the rate constant of the reverse reaction and on the relationship between the radius of the micelle and the molar ratio of detergent to water ( w 0 ) in the system. The model presented here predicts that bell‐shaped curves will only be observed in the conversion of substrates which are, at lea partially, confined to the water pool of the microemulsion. In order to illustrate the dependence of the rate of the reaction on the composition of the microemulsion, the example of δ‐chymotrypsin was chosen. Using this example, the effects of micellar parameters not accessible to systematic experimental variation can be calculated. The results of this analysis show that detailed knowledge of both microemulsion and enzymic parameters is necessary for an adequate description of the reaction rate. Based on the results of this analysis, advice to optimize the enzymatic conversion of both hydrophilic and hydrophobic substrates in heterogenic media is presented.