Michaelis-Menten mechanism

According to this expression, a plot of 1/v, versus l/[SJo will yield a straight line if the data follow the Michaelis-Menten mechanism. This line has a slope given by Km/Vmax, a y intercept of 1/Vmax, and an x intercept of -1 fKm. This is also illustrated in Fig. 4-7. Again, this treatment is valid when Eq. (4-107) applies whether or not the catalyst is an enzyme. The Lineweaver-Burk plot, Fig. 4-lb, is convenient for visualization but statistically unreliable for data fitting the form in Eq. (4-107) should be used for numerical analysis. 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that, when the concentration of substrate is low, the rate of an enzyme-catalyzed reaction increases with the concentration of the substrate, as shown in the plot in Fig. 13.41. However, when the concentration of substrate is high, the reaction rate depends only on the concentration of the enzyme. In the Michaelis-Menten mechanism of enzyme reaction, the enzyme, E, and substrate, S, reach a rapid preequilibrium with the bound enzyme-substrate complex, ES ... 

Michaelis constant (KM) A constant in the rate law for the Michaelis—Menten mechanism. 

Michaelis—Menten mechanism A model of enzyme catalysis in which the enzyme and its substrate reach a rapid pre-equilibrium with the bound substrate-enzyme complex. 

The simplest kinetic model applied to describe lipase catalyzed reactions is based on the classic Michaelis-Menten mechanism [10] (Table 3). To test this model Belafi-Bakd et al. [58] studied kinetics of lipase-catalyzed hydrolysis of tri-, di-, and mono-olein separately. All these reactions were found to obey the Michaelis-Menten model. The apparent parameters (K and V ) were determined for global hydrolysis. 

The kinetics of the general enzyme-catalyzed reaction (equation 10.1-1) may be simple or complex, depending upon the enzyme and substrate concentrations, the presence/absence of inhibitors and/or cofactors, and upon temperature, shear, ionic strength, and pH. The simplest form of the rate law for enzyme reactions was proposed by Henri (1902), and a mechanism was proposed by Michaelis and Menten (1913), which was later extended by Briggs and Haldane (1925). The mechanism is usually referred to as the Michaelis-Menten mechanism or model. It is a two-step mechanism, the first step being a rapid, reversible formation of an enzyme-substrate complex, ES, followed by a slow, rate-determining decomposition step to form the product and reproduce the enzyme ... 

Note that written in this form Eq. (106) retains the linear dependency of the rate on the total enzyme concentration Ej, typical for most Michaelis Menten mechanisms. The dependence on the substrate concentrations is approximated by a sum of nonlinear logarithmic terms [85, 86, 318, 320],... 

The subscript on kcat in Equation 11.19 abbreviates catalyzed . Vmax is connected with the rate determining step. For desorption much faster than catalysis, ks >> k3, Vmax = k3 [E]0 which is the result found for the simpler Michaelis-Menten mechanism, Section 11.2.1. If, however, ks is commensurate with k3 the intrinsic catalysis is damped by the weighting function ks/(k3+ks). Note that Vmax/KM sees events through the first irreversible step as illustrated in Fig. 11.3. The same is true for the isotope effects. These points are discussed in considerable detail by Northrop (see reading list). 

The rate form of Eq. 57 and some of its generalizations are used to represent a number of widely different kinds of reactions. For example, in homogeneous systems this form is used for enzyme-catalyzed reactions where it is suggested by mechanistic studies (see the Michaelis-Menten mechanism in Chap. 2 and in Chap. 27). It is also used to represent the kinetics of surface-catalyzed reactions. 

The potential energy diagram of the Michaelis Menten mechanism, drawn... 

For an enzyme-substrate system obeying the simple Michaelis Menten mechanism, the rate of product formation when the substrate concentration is very large, has the limiting value 0.02 mol dmJ. At a substrate concentration of250 mg dnu, the rate is half this value, K/K assuming that K2 K j, calculated ... 

Fig. 7.1 15. The basis of the Michaelis-Menten mechanism of enzyme action. Only a fragment of the large enzyme molecule E is shown. (Reprinted with permission from P. W. Atkins, Physical Chemistry, 5th ed., W. H. Freeman, 1994, p. 890, Fig. 25.12.)...

The quantity Vmax also varies greatly from one enzyme to the next. If an enzyme reacts by the two-step Michaelis-Menten mechanism, Vmax = k2[Et], where k2 is rate-limiting. However, the number of reaction steps and the identity of the rate-limiting step(s) can vary from enzyme to enzyme. For example, consider the quite common situation where product release, EP — E + P, is rate-limiting. Early in the reaction (when [P] is low), the overall reaction can be described by the scheme... 

The Michaelis-Menten mechanism assumes that the enzyme-substrate complex is in thermodynamic equilibrium with free enzyme and substrate. This is true only if, in the following scheme, k2 < ... 

It is extremely common for intermediates to occur after the initial enzyme-substrate complex, as in equation 3.19. However, it is often found for physiological substrates that these intermediates do not accumulate and that the slow step in equation 3.19 is k2. (A theoretical reason for this is discussed in Chapter 12, where examples are given.) Under these conditions, KM is equal to Ks, the dissociation constant, and the original Michaelis-Menten mechanism is obeyed to all intents and purposes. The opposite occurs in many laboratory experiments. The enzyme kineticist often uses synthetic, highly reactive substrates to assay enzymes, and covalent intermediates frequently accumulate. 

In the simple Michaelis-Menten mechanism in which there is only, one enzyme-substrate complex and all binding steps are fast, cat is simply the first-order rate constant for the chemical conversion of the ES complex to the EP... 

The most-studied enzyme in this context is chymotrypsin. Besides being well characterized in both its structure and its catalytic mechanism, it has the advantage of a very broad specificity. Substrates may be chosen to obey the simple Michaelis-Menten mechanism, to accumulate intermediates, to show nonproductive binding, and to exhibit Briggs-Haldane kinetics with a change of rate-determining step with pH. 

Interpretation of the kinetic phenomena for single-substrate reactions The Michaelis-Menten mechanism... 

Although it is only for the simple Michaelis-Menten mechanism or in similar cases that Ku = Ks, the true dissociation constant of the enzyme-substrate complex, Km may be treated for some purposes as an apparent dissociation constant. For example, the concentration of free enzyme in solution may be calculated from the relationship... 

If an inhibitor I binds reversibly to the active site of the enzyme and prevents S binding and vice versa, I and S compete for the active site and I is said to be a competitive inhibitor. In the case of the simple Michaelis-Menten mechanism (equation 3.4, where Ku = Ks), an additional equilibrium must be considered, i.e.,... 

It may be shown from the Michaelis-Menten mechanism—in the simplifying case in which the dissociation constant of S from EIS is the same as that from i ES (i.e., Km = K m) but in which ESI does not react (i.e., k = 0)—that... 

This is known as nonproductive binding. The effect of such binding on the Michaelis-Menten mechanism is. to lower both the kcat and the Ku. The kcu is lowered since, at saturation, only a fraction of the substrate is bound productively. The Km is lower than the Ks because the existence of additional binding modes must lead to apparently tighter binding. 

The first possibility is substrate inhibition. A second molecule of substrate binds to give an ES2 complex that is catalytically inactive. If, in a simple Michaelis-Menten mechanism, the second dissociation constant is K s, then... 

We shall now analyze some of the simple examples, beginning with the Michaelis-Menten mechanism. We can make four simplifying assumptions that may break down in some circumstances but that often hold in practice ... 

The theory predicts that unless there is a change of rate-determining step with pH, the pH dependence of kcJKM for all non-ionizing substrates should give the same pKa that for the free enzyme. With one exception, this is found (Table 5.2). At 25°C and ionic strength 0.1 M, the pKa of the active site is 6.80 0.03. The most accurate data available fit very precisely the theoretical ionization curves between pH 5 and 8, after allowance has been made for the fraction of the enzyme in the inactive conformation. The relationship holds for amides with which no intermediate accumulates and the Michaelis-Menten mechanism holds, and also for esters with which the acylenzyme accumulates. 

This scheme is analogous to that of the Michaelis-Menten mechanism, and the reaction should thus show saturation kinetics with increasing inhibitor concentration. The kinetics were solved in Chapter 4, equation 4.46. For the simple case of pre-equilibrium binding followed by a slow chemical step, the solution reduces to... 

Michaelis constant KM A constant that occurs in the Michaelis-Menten mechanism. 

Enzymes are a special kind of catalyst, proteins of MW 6,000—400,000 which are found in living matter. They have two remarkable properties (1) they are extremely selective to the given substrate and (2) they are extraordinarily effective in increasing the rates of reactions. Thus, they combine the recognition and amplification steps. A general, enzymatically catalyzed reaction can be described by the Michaelis-Menten mechanism, in which E is the enzyme, S is the substrate, and P is the product, formed from the intermediate complex ES. 

In an enzyme reaction, initially free enzyme E and free substrate S in their respective ground states initially combine reversibly to an enzyme-substrate (ES) complex. The ES complex passes through a transition state, AGj, on its way to the enzyme-product (EP) complex and then on to the ground state of free enzyme E and free product P. From the formulation of the reaction sequence, a rate law, properly containing only observables in terms of concentrations, can be derived. In enzyme catalysis, the first rate law was written in 1913 by Michaelis and Menten therefore, the corresponding kinetics is named the Michaelis-Menten mechanism. The rate law according to Michaelis-Menten features saturation kinetics with respect to substrate (zero order at high, first order at low substrate concentration) and is first order with respect to enzyme. 

What reactions have linear mechanisms Primarily these are enzyme reactions [43, 44]. A typical scheme for enzyme catalysis is the Michaelis Menten mechanism (1) E + A -> ES (2) ES - P + S, where S and P are the initial substrate and product, respectively, and E and ES are various forms of enzymes. 

Let us apply estimate (94) to the various mechanisms of class 1 given above. For the Michaelis-Menten mechanism, the brutto-reaction is of the form S = P, nln = 1, nprod = 1, and s = 1 + 1 = 2. For CO conversion, the brutto-equation takes the form... 

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