Michaelis-Menten and Similar Kinetics

Suppose the reaction S — P occurs using an enzyme as a catalyst. The following reaction mechanism is postulated  

FIGURE 12.1 Effects of substrate (reactant) concentration on the rate of enzymatic reactions (a) simple Michaelis-Menten kinetics (b) substrate inhibition (c) substrate activation. 

Example 12.1 Suppose an enzymatic reaction has the following mechanism  

The two equilibrium relations and the rate expression allow the unknown surface concentrations [S E], [SE], and [E] to be eliminated. The result is 

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

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