Development of Enzyme Kinetics from Binding and Catalysis

Development of Enzyme Kinetics from Binding and Catalysis 

From the idea of enzyme kinetics as a binding and a reaction step with the corresponding course of the energy curve in the Gibbs free enthalpy-reaction coordinate (AG - E) diagram, the reaction scheme represented by Eq. (2.1) can be drawn. 

Among the several ways of verifying or disproving such a reaction scheme (Chapter 9, Section 9.2), the derivation of a rate law linking a product formation rate or substrate consumption rate with pertinent concentrations of reactants, products, and auxiliary agents such as catalysts probably has the greatest utility, as conversion to product can be predicted. A proper rate law contains only observables, and no intermediates or other unobservable parameters. In enzyme catalysis, the first rate law was written in 1913 by Michaelis and Menten (the corresponding kinetics is therefore aptly named the Michaelis-Menten (MM) mechanism). 

The kinetic scheme according to Michaelis-Menten for a one-substrate reaction (Michaelis, 1913) assumes three possible elementary reaction steps (i) formation of an enzyme-substrate complex (ES complex), (ii) dissociation of the ES complex into E and S, and (iii) irreversible reaction to product P. In this scheme, the product formation step from ES to E + P is assumed to be rate-limiting, so the ES complex is modeled to react directly to the free enzyme and the product molecule, which is assumed to dissociate from the enzyme without the formation of an enzyme-product (EP) complex [Eq. (2.2)]. 

In the derivation according to Michaelis and Menten, association and dissociation between free enzyme E, free substrate S, and the enzyme-substrate complex ES are assumed to be at equilibrium, fCs = [ES]/([E] [S]). [The Briggs-Haldane derivation (1925), based on the assumption of a steady state, is more general see Chapter 5, Section 5.2.1.] With this assumption and a mass balance over all enzyme components ([E]total = [E]free + [ES]), the rate law in Eq. (2.3) can be derived. 

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