Henri-Michaelis-Menten equation, derivation

Let s assume that the rate constant kcat for the formation of products on either subunit is the same, whether only that site or both catalytic sites are occupied. Suppose also that ES, SE, and SES are in equilibrium with the free enzyme and substrate. By following the same procedure that led to the Henri-Michaelis-Menten equation in chapter 7, we can derive an expression for the rate of the enzymatic reaction in terms of [S], AT], and K2. Here we just give the result. 

The linear relationship between v and [S] when [S] K can be derived from the Henri-Michaelis-Menten equation. 

An equation equivalent to the Michaelis-Menten rate law has been derived earlier by Henri (1902,1903) indeed, Michaelis and Menten in their original publication in 1913 honored the contribution of Henri. Therefore, in appreciation of the work of Henri, it is often also referred to as the Henri-Michaelis-Menten equation. 

THE RAPID-EQUILIBRIUM TREATMENT. The first rate equation for an enzyme-catalyzed reaction was derived by Henri and by Michaelis and Menten, based on the rapid-equilibrium concept. With this treatment it is assumed that there is a slow catalytic conversion step and the combination and dissociation of enzyme and substrate are relatively fast, such that they reach a state of quasi-equilibrium or rapid equilibrium. 

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