Michaelis-Menten enzymatic reaction

Some reactions have to be "pseudomonomolecular". Their constants depend on concentrations of outer components, and are constant only under condition that these outer components are present in constant concentrations, or change sufficiently slow. For example, the simplest Michaelis-Menten enzymatic reaction is E+S ES->E+P (E here stands for enzyme, S for substrate and P for product), and the linear catalytic cycle here is S ES S. Hence, in general we must consider nonlinear systems. 

Elementary reaction. The term elementary reaction has been defined. Sometimes two or more elementary reactions are added, as for example the elementary steps in a Michaelis-Menten enzymatic reaction, and listed as a pseudo-elementary reaction. Catalyst. Acatalyst may be necessary for an elementary reaction to occur at a reasonable rate, as well as positive and negative effectors on the catalyst. We shall be concerned mostly with isothermal reactions. 

Lipases have also been used as initiators for the polymerization of lactones such as /3-bu tyro lac tone, <5-valerolactone, e-caprolactone, and macrolides.341,352-357 In this case, the key step is the reaction of lactone with die serine residue at the catalytically active site to form an acyl-enzyme hydroxy-terminated activated intermediate. This intermediate then reacts with the terminal hydroxyl group of a n-mer chain to produce an (n + i)-mer.325,355,358,359 Enzymatic lactone polymerization follows a conventional Michaelis-Menten enzymatic kinetics353 and presents a controlled character, without termination and chain transfer,355 although more or less controlled factors, such as water content of the enzyme, may affect polymerization rate and the nature of endgroups.360... 

The Michaelis constant is equal to substrate concentration at which the rate of reaction is equal to one-half the maximum rate. The parameters and characterize the enzymatic reactions that are described by Michaelis-Menten kinetics. is dependent on total... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

It is revealing to compare the equation for the uninhibited case. Equation (14.23) (the Michaelis-Menten equation) with Equation (14.43) for the rate of the enzymatic reaction in the presence of a fixed concentration of the competitive inhibitor, [I]... 

Michaelis-Menten kinetics, in 1913 L. Michaelis and M. Men ten realized that the rate of an enzymatic reaction... 

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. 

On the other hand, the macrolides showed unusual enzymatic reactivity. Lipase PF-catalyzed polymerization of the macrolides proceeded much faster than that of 8-CL. The lipase-catalyzed polymerizability of lactones was quantitatively evaluated by Michaelis-Menten kinetics. For all monomers, linearity was observed in the Hanes-Woolf plot, indicating that the polymerization followed Michaehs-Menten kinetics. The V, (iaotone) and K,ax(iaotone)/ m(iaotone) values increased with the ring size of lactone, whereas the A (iactone) values scarcely changed. These data imply that the enzymatic polymerizability increased as a function of the ring size, and the large enzymatic polymerizability is governed mainly by the reachon rate hut not to the binding abilities, i.e., the reaction process of... 

In case of two —stage enzymatic reactions, which did not obey Michaelis— Menten equ — ation reaction speed was at its maximum and then decreased.Graph of speed of substrate hyd —rolysis against In concentration acquired a shape of symmetric or asymmetric bell (Figure 4). 

In kinetic studies of enzymatic reactions, rate data are usually tested to determine if the reaction follows the Michaelis-Menten model of enzyme-substrate interaction. Weetall and Havewala [Biotechnol. and Bioeng. Symposium 3 (241), 1972] have studied the production of dextrose from cornstarch using conventional... 

As the above discussion indicates, assigning mechanisms to simple anation reactions of transition metal complexes is not simple. The situation becomes even more difficult for a complex enzyme system containing a metal cofactor at an active site. Methods developed to study the kinetics of enzymatic reactions according to the Michaelis-Menten model will be discussed in Section 2.2.4. 

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

Such a relationship between the polymer yield and the mass of feeded MMA is similar to that in the enzymatic reaction. Therefore, the result was applied to Michaelis-Menten equation and in the case of PVPA, the result shown in Fig. 5 was obtained. 

In order to understand the mechanisms of the enzymatic process and also predict the reaction characteristics, one needs to understand the kinetics of the reaction. The important factor that effects the enzyme reaction is the availability and concentration of the substrates. An important model that gives a mathematical relationship is the Michaelis-Menten and Hill equation. The equation is denoted as... 

The required enantiomeric excess of (S)-chloropropionic acid is 98%. Which of the two reactions will give the highest yield of the target compound Both enzymatic reactions can be described with irreversible Michaelis-Menten kinetics. 

Regulation of enzymic activity occurs via two modes (cf. Ref. 50) alteration of the substrate binding process and/or alteration of the catalytic efficiency (turnover number) of the enzyme. The initial rate of a simple enzymatic reaction v is governed by the Michaelis-Menten equation... 

It can be readily shown that the specificity constant ksp = kcat/KM can be taken to act as a (pseudo) second-order rate constant in the rate equation for an enzymatic reaction that follows minimal Michaelis-Menten kinetics ... 

The enzymatic activity of the L-19 IVS ribozyme results from a cycle of transesterification reactions mechanistically similar to self-splicing. Each ribozyme molecule can process about 100 substrate molecules per hour and is not altered in the reaction therefore the intron acts as a catalyst. It follows Michaelis-Menten kinetics, is specific for RNA oligonucleotide substrates, and can be competitively inhibited. The kcat/Km (specificity constant) is 10s m- 1 s lower than that of many enzymes, but the ribozyme accelerates hydrolysis by a factor of 1010 relative to the uncatalyzed reaction. It makes use of substrate orientation, covalent catalysis, and metalion catalysis—strategies used by protein enzymes. 

A simple example is the so-called Michaelis-Menten kinetics for enzymatic reactions A + E +C->B + E, which, when the pseudo-steady-state hypothesis is invoked, gives for the concentration of A, for instance, a,... 

The Henri-Michaelis-Menten Treatment Assumes That the Enzyme-Substrate Complex Is in Equilibrium with Free Enzyme and Substrate Steady-State Kinetic Analysis Assumes That the Concentration of the Enzyme-Substrate Complex Remains Nearly Constant Kinetics of Enzymatic Reactions Involving Two Substrates... 

The hyperbolic saturation curve that is commonly seen with enzymatic reactions led Leonor Michaelis and Maude Men-ten in 1913 to develop a general treatment for kinetic analysis of these reactions. Following earlier work by Victor Henri, Michaelis and Menten assumed that an enzyme-substrate complex (ES) is in equilibrium with free enzyme... 

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 parameters of the Michaelis-Menten type kinetics were calculated for the reactions and are summarized in Table II. The apparent Michaelis constant values (Km) are rather large, indicating that the concentration of the complex at the equilibrium state is not high, unlike ordinary enzymatic reactions. The ratio of kJKm against the second-order rate constant with sulfuric acid (k2) can be considered to be an indication of the rate enhancement. The ratio increased with increasing mole fraction of the vinyl alcohol repeating unit in the copolymer and with... 

During the enzymatic reaction of an immobilized enzyme, the rate of substrate transfer is equal to that of substrate consumption. Therefore, if the enzyme reaction can be described by the Michaelis-Menten equation,... 

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. 

When the pH-dependent Michaelis-Menten equation (2.22) is substituted for the pH-dependent reaction term 9ipn(Q), we obtain for the substrate S at any point inside the enzymatic gel layer... 

As it diffuses in, it reacts according to a general Michaelis-Menten equation (2.21), and the molar heat equal to the enthalpy of that reaction is evolved. For an enzymatic reaction... 

In Fig. 2.10, the boundary between the enzyme-containing layer and the transducer has been considered as having either a zero or a finite flux of chemical species. In this respect, amperometric enzyme sensors, which have a finite flux boundary, stand apart from other types of chemical enzymatic sensors. Although the enzyme kinetics are described by the same Michaelis-Menten scheme and by the same set of partial differential equations, the boundary and the initial conditions are different if one or more of the participating species can cross the enzyme layer/transducer boundary. Otherwise, the general diffusion-reaction equations apply to every species in the same manner as discussed in Section 2.3.1. Many amperometric enzyme sensors in the past have been built by adding an enzyme layer to a macroelectrode. However, the microelectrode geometry is preferable because such biosensors reach steady-state operation. 

Using the model in Scheme 4.7, Michaelis and Menten were able to generate an equation that related the rate of an enzymatic reaction to the concentration of the substrate. The second step is rate determining, so the rate of the reaction (V) as determined by the formation of the product (d[P]/dt) is given by Equation 4.1.4... 

Although the Michaelis-Menten equation places emphasis on V max, published kinetic studies of enzymes generally do not disclose the V max for specific enzymatic reactions. Instead papers report kcaV Deep in the experimental section, a paper will mention the total concentration of the enzyme, [Et], used in the kinetic study. Since k2 = kcat, with both kcat and [Et], one may use Equation 4.10 to estimate Vmax for the reaction of interest. 

Originally published in 1913 as a rate law for enzymatic sugar inversion [19], the Michaelis-Menten rate equation is also used frequently for describing homogeneously catalyzed reactions. It describes a two-step cycle (Eqs. (2.34) and (2.35)) the catalyst (the enzyme, E) first reacts reversibly with the substrate S, forming an enzyme-substrate complex ES (a catalytic intermediate). Subsequently, ES decomposes, giving the enzyme E and the product P. This second step is irreversible. 

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