Michaelis fractional conversions

The Michaelis-Menten equation relates the initial velocity of the reaction (V ) to the concentration of enzyme substrate complexes (ES). This equation is derived for a reaction in which a single substrate, S, is converted to a single product, P. The enzyme (E) and S associate to form ES with the rate constant of k,. The complex dissociates with the rate constant of kj, or is converted to P with the rate constant kj. Under conditions in which [S] [E], [P] is negligible, and the rate of conversion of ES to an enzyme-product complex is very fast, v, = kj [ES]. The concentration of ES is a fraction of Ej, the total amount of enzyme present as ES and E. 

One may postulate isomerisations of EA preceding the release of products, but the basic point is that a specific, stoichiometric enzyme-substrate complex is formed. This fact is now so totally taken for granted by biochemists that it is easy to forget that its establishment was the first major milestone in enzyme kinetics. The analysis of Scheme 1 by Brown [1] and Henri [2] and subsequently by Michaelis and Men ten [3] and Briggs and Haldane [4] provided an explanation of the previously puzzling observation that the rate of a typical enzyme reaction plotted as a function of substrate concentration increases asymptotically to a maximum (Fig. 1). In Scheme 1 the overall rate of the catalysed reaction, i.e. of product formation, is proportional to [EA]/([E]-h [EA]), the fraction of the total enzyme present as the productive complex EA at low substrate concentration this fraction is proportional to [A], whereas at high substrate concentration the fraction approaches 1, and the rate is then limited only by the rate constant for conversion of EA to E + products. 

The Michaelis-Menten equation was a large step forward in our ability to imderstand how biological systems control chemical processes. This equation linked the rate of enzymatic substrate catalysis to a mass action process relying on the fractional association between the substrate and the enzyme population. That is, the maximum conversion rate of substrate to product (Vmax) could be directly related to the concentration of the enzyme ([E]) present and the catalytic rate at which individual enzymes converted substrate molecules to product (kcat Equation 2). 

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