Michaelis-Menten equation breakdown

Let us consider the basic enzyme catalysis mechanism described by the Michaelis-Menten equation (Eq. 2). It includes three elementary steps, namely, the reversible formation and breakdown of the ES complex (which does not mean that it is at equilibrium) and the decomposition of the ES complex into the product and the regenerated enzyme ... 

This is an assumption used to derive the Michaelis-Menten equation in which the velocity of ES formation is assumed to be equal to the velocity of ES breakdown. 

Here we develop the basic logic and the algebraic steps in a modern derivation of the Michaelis-Menten equation, which includes the steady-state assumption introduced by Briggs and Haldane. The derivation starts with the two basic steps of the formation and breakdown of ES (Eqns 6-7 and 6-8). Early in the reaction, the concentration of the product, [P], is negligible, and we make the simplifying assumption that the reverse reaction, P—>S (described by k 2), can be ignored. This assumption is not critical but it simplifies our task. The overall reaction then reduces to... 

In this case the Michaelis-Menten equation reflects a first-order reaction in which the rate of substrate breakdown depends on substrate concentration. In using a kinetic method for the determination of substrate concentration (cf. 2.6.1.3), the experimental conditions must be selected such that Equation 2.46 is valid. 

The effect of substrate concentration on enzymatic reaction was first put forward in 1903 (Henri, 1903), where the conversion into the product involved a reaction between the enzyme and the substrate to form a substrate-enzyme complex that is then converted to the product. However, the reversibility of the substrate-enzyme complex and its final breakdown into the substrate and free enzyme regeneration was generally ignored. In 1913, Michaelis and Menten took this into consideration and proposed the scheme shown in Equation 4.1 for a one-substrate enzymatic reaction. Experimental data, that is, the initial reaction rates, were collected to support their analysis. The reaction mechanism, which is one of the most common mechanisms in enzymatic reactions, was based on the assumption that only a single substrate and product are involved in the reaction. 

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