Michaelis-Menten equation, derivation rapid equilibrium assumption

For most enzymes, the rate of reaction can be described by the Michaelis-Menten equation which was originally derived in 1913 by Michaelis and MENTEN 21 . Its derivation can be achieved by making one of two assumptions, one of which is a special case of the more general Briggs-Haldane scheme, whilst the alternative is the rapid-equilibrium method given in Appendix 5.3(2 ). 

Appendix 5.3. Derivation of the Michaelis-Menten Equation using the Rapid Equilibrium Assumption... 

Even this scheme represents a complex situation, for ES can be arrived at by alternative routes, making it impossible for an expression of the same form as the Michaelis-Menten equation to be derived using the general steady-state assumption. However, types of non-competitive inhibition consistent with the Michaelis-Menten type equation and a linear Linweaver-Burk plot can occur if the rapid-equilibrium assumption is valid (Appendix S.A3). In the simplest possible model, involving simple linear non-competitive inhibition, the substrate does not affect the inhibitor binding. Under these conditions, the reactions... 

If the rate constant k2 is much smaller than the rate constant k., of the enzyme, the substrate and the enzyme-substrate complex are in equilibrium, which is not disturbed by the decomposition of ES into E and P ( rapid equilibrium-assumption ). Based on this assumption, Michaelis and Menten derived the following rate equation (Eq. (17)) ... 

In the following sections the extension of Eq. (18) to more complex reaction schemes is described. Again the rapid equilibrium assumption is used to show how more complex rate equations are derived from simple Michaelis-Menten kinetics. Attention is focused on some typical rate equations that are useful to describe enzyme kinetics with respect to a desired process optimization. The whole complexity of enzyme kinetics is of importance for a basic understanding of the enzyme mechanism, but it is not necessary for the fitting of kinetic data and the calculation of reactor performance. 

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