Michaelis-Menten approach

If the slower reaction, Eq. (2.6), determines the overall rate of reaction, the rate of product formation and substrate consumption is proportional to the concentration of the enzyme-substrate complex as 4 

Unless otherwise specified, the concentration is expressed as molar unit, such as kmol/m3 or mol/L. The concentration of the enzyme-substrate complex CES in Eq. (2.7), can be related to the substrate concentration Cs and the free-enzyme concentration CE from the assumption that the first reversible reaction Eq. (2.5) is in 

4 It seems that the rate of substrate consumption should be expressed as 

it gives a contradictory result that the substrate concentration stays constant (dCs/dt = 0) because the first reversible reaction, Eq. (2.5), is assumed to be in equilibrium (kf CSCE - k2 CES = 0). Since the rate of reaction is determined by the second slower reaction, Eq. (2.6), the preceding expression is wrong. Instead, the rate of substrate consumption must also be written by the second reaction as 

For the Briggs-Haldane approach, the rate expression for substrate can be expressed by the first reversible reaction as explained in the next section. 

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Some of the more important assumptions of the Michaelis-Menten approach are given below [264] ... 

Michaelis-Menten Approach In enzyme reactions, the total molar concentration of the free and combined enzyme, Cpg (kmol m ) should be constant that is. 

This expression by Briggs-Haldane is similar to Equation 3.28, obtained by the Michaelis-Menten approach, except that is equal to (Ar i -F These... 

Note that the biological transformation is assumed to be first order. If river sections with higher concentrations were considered, a Michaelis-Menten approach (Box 12.2) would have to be taken (see Wanner et al., 1989). 

The rates of such bisubstrate reactions can also be analyzed by the Michaelis-Menten approach. Hexokinase has a characteristic Km for each of its substrates (Table 6-6). 

Michaelis-Menten approach (Michaelis and Menten, 1913) It is assumed that the product-releasing step, Eq. (2.6), is much slower than the reversible reaction, Eq. (2.5), and the slow step determines the rate, while the other is at equilibrium. This is an assumption which is often employed in heterogeneous catalytic reactions in chemical kinetics.3 Even though the enzyme is... 

Derive the rate equation by employing (a) the Michaelis-Menten and (b) the Briggs-Haldane approach. Explain when the rate equation derived by the Briggs-Haldane approach can be simplified to that derived by the Michaelis-Menten approach. 

As shown in the previous section, the rate equation can be derived by employing the Michaelis-Menten approach as followsrwhere... 

Develop a rate expression using (a) the Michaelis-Menten approach and (b) the Bnggs-Haldane approach. 

Develop suitable rate expression using (a) the Michaelis-Menten approach and (b) Bnggs-Haldane approach. Please note that the rate constants of the second equilibrium reaction are the same as those of the third reaction. 

The Michaelis-Menten approach assumes that the product releasing step is much slower than the first complex forming step of the simple enzyme-reaction mechanism ... 

Derive a rate equation for the following partially competitive inhibition using the Michaelis-Menten approach. 

The kinetic parameters for a free enzyme in solution are readily derived using the Michaelis-Menten approach describing pseudo-steady-state conversions. Consider Equation (31.1) representing the conversion of a substrate S into a product P, catalyzed by an enzyme E. The rate of formation of an enzyme/substrate complex, ES, is denoted as ku the reverse reaction by and the rate of subsequent conversion to the free product by k2. 

It is at this point that the Langmuir and Michaelis-Menten approaches diverge. The development of the Langmuir isotherm (Eqn. 7.7) was based on the adsorption coefficient of the catalyst-substrate complex (Eqn. 7.4) while the Michaelis-Menten equation is based on the dissociation constant of this complex (Eqn. 7.16). 

In addition to the preceding assumptions, there are three different approaches to derive the rate equation Michaelis-Menten approach [10], Briggs-Haldane approach [11], and numerical solution. 

The formation of an enzyme-inhibitor complex reduces the amount of enzyme available for interaction with the substrate and, hence, the rate of reaction decreases. Based on the above mechanism, the rate of product formation can be derived by using the Michaelis-Menten approach to give... 

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