Rapid equilibrium, enzyme kinetic modeling

Enzyme reaction kinetics were modelled on the basis of rapid equilibrium assumption. Rapid equilibrium condition (also known as quasi-equilibrium) assumes that only the early components of the reaction are at equilibrium.8-10 In rapid equilibrium conditions, the enzyme (E), substrate (S) and enzyme-substrate (ES), the central complex equilibrate rapidly compared with the dissociation rate of ES into E and product (P ). The combined inhibition effects by 2-ethoxyethanol as a non-competitive inhibitor and (S)-ibuprofen ester as an uncompetitive inhibition resulted in an overall mechanism, shown in Figure 5.20. 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

Figure 8.1 Model energy diagrams for non-enzymic reactions (A), enzymic reaction following the rapid equilibrium mechanism (see Table 8.1) (B) and enzymic reaction following Briggs-Haldane kinetics (C). E represents the activation energy of transition and the positive and...

Schuster, R. and Schuster, S. (1991) Relationships between modal-analysis and rapid-equilibrium approximation in the modeling of biochemical networks. Syst. Anal. Model. Simul. 8, 623-633. Segel, I.H. (1993) Enzyme kinetics Behavior andAnalysis of Rapid Equilibrium and Steady-state Enzyme Systems. (New York John Wiley Sons, Inc.). 

London and Steck (1969) have developed a general model, based on rapid equilibrium assumptions, for a monosubstrate enzyme that combines with substrate, activator, and a substrate-activator complex. The kinetic model for this type of activation is rather complex (Reaction (7.7)). 

It is important to note, and should always be remembered, that all the rate and binding equations for cooperative and allosteric enzymes were derived under rapid equilibrium assumption. Therefore, all kinetic models for the cooperative phenomena can be equally well applied to enzyme reactions that are in the rapid equilibrium and to the binding of ligands to enzymes and proteins. 

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