Enzymes Michaelis-Menten approach

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

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... 

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 ... 

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. 

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... 

This expression by Briggs-Haldane is similar to Equation 3.28, obtained by the Michaelis-Menten approach, except that Km is equal to (k 1+k2)/k1. These two approaches become identical, if k 1 k2, which is the case of most enzyme reactions. 

The Eadie-Hofstee plot does a betterjob than the Line-weaver-Burke plot in evenly distributing the data points over the entire substrate concentration range, and can be a useful visual technique for ascertaining whether enzyme kinetics are typical (as shown) or atypical (see Figure 8.18, B and G). The Michaelis-Menten approach basically assumes that enzymes present a single binding site to each substrate. Estimates of V x of drug... 

In non-competitive inhibition, an inhibitor is considered to combine with both an enzyme and the enzyme-substrate complex. Thus, a further reaction is added to the competitive inhibition mechanism and, assuming that the equilibrium constants of the two inhibition reactions are equal in many cases, the following rate equation can be obtained by the Michaelis-Menten approach ... 

There are two approaches in deriving an expression for the reaction rate. In the first approach (Michaelis-Menten approach), the first reaction is assumed to be in equilibrium. The decomposition of the enzyme-substrate complex ES to form E and P is the rate-determining step. In the second approach, it is assumed that after an initial period, the rate of change of the concentration of the enzyme-suhstrate complex is essentially zero mathematically, this can be expressed as ... 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

The necessity of developing approximate kinetics is unclear. It is sometimes argued that uncertainties in precise enzyme mechanisms and kinetic parameters requires the use of approximate schemes. However, while kinetic parameters are indeed often unknown, the typical functional form of generic rate equations, namely a hyperbolic Michaelis Menten-type function, is widely accepted. Thus, rather than introducing ad hoc functions, approximate Michaelis Menten kinetics can be utilized an approach that is briefly elaborated below. 

It has been found experimentally that in most cases v is directly proportional to the concentration of enzyme [.E0] and that v generally follows saturation kinetics with respect to the concentration of substrate [limiting value called Vmax. This is expressed quantitatively in the Michaelis-Menten equation originally proposed by Michaelis and Menten. Km can be seen as an apparent dissociation constant for the enzyme-substrate complex ES. The maximal velocity Vmax = kcat E0. ... 

Analyses of enzyme reaction rates continued to support the formulations of Henri and Michaelis-Menten and the idea of an enzyme-substrate complex, although the kinetics would still be consistent with adsorption catalysis. Direct evidence for the participation of the enzyme in the catalyzed reaction came from a number of approaches. From the 1930s analysis of the mode of inhibition of thiol enzymes—especially glyceraldehyde-phosphate dehydrogenase—by iodoacetate and heavy metals established that cysteinyl groups within the enzyme were essential for its catalytic function. The mechanism by which the SH group participated in the reaction was finally shown when sufficient quantities of purified G-3-PDH became available (Chapter 4). 

The curve expressing the relationship between [S] and Vo (Fig. 6-11) has the same general shape for most enzymes (it approaches a rectangular hyperbola), which can be expressed algebraically by the Michaelis-Menten... 

For an enzyme with typical Michaelis-Menten kinetics, the value of e ranges from about 1 at substrate concentrations far below Km to near 0 as Vmax is approached. Allosteric enzymes can have elasticities greater than 1.0, but not larger than their Hill coefficients (p. 167). 

The maximum rate of a reaction (V ) is attained when all the enzyme active sites are saturated with substrate molecules. For the rate to approach VmiX> the substrate concentration must be high in fact, it must be much greater than KM. When [S] > Ku, the Michaelis-Menten equation becomes... 

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