Enzymatic reactions Michaelis-Menten equation

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]... 

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. 

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... 

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. 

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,... 

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... 

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. 

The quantitative treatment of kinetic data is based on the pseudophase separation approach, i.e. the assumption that the aggregate constitutes a (pseudo)phase separated from the bulk solution where it is dispersed. Some of the equations below are reminiscent of the well-known Michaelis- Menten equation of enzyme kinetics [101]. This formal similarity has led many authors to draw a parallel between micelle and enzyme catalysis. However, the analogy is limited because most enzymatic reactions are studied with the substrate in a large excess over the enzyme. Even for systems showing a real catalytic behavior of micelles and/or vesicles, the above assumption of the aggregate as a pseudophase does not allow operation with excess substrate. The condition... 

Michaelis-Menten equations often do not apply for enzymatic reactions at surfaces, such as bacterial walls (McLaren and Packer, 1970). Precise kinetic parameters, which can only be obtained with well-characterized low molecular weight substrates, are complicated by non-productive binding of small substrates, i.e. binding outside of the catalytic site. 

Enzymatic reactions are usually characterized by a parameter, the Michaelis-Menten constant or KM, which is determined by the efficiency of the first equilibrium reaction for the formation of ES. That is, KM is the concentration in mM of S at which the initial rate of the overall process, V0, is one-half of the maximum rate, Vma possible. The maximum rate occurs when all of E is converted to ES. Each particular type and concentration of E and S, and each set of reactions conditions, has its own KM, and the Michaelis-Menten equation describes the relationship between Vo, [S] (the concentration of S), Vmax and Km for a given amount of E under a fixed set of conditions, as follows ... 

Other concepts follow from the Michaelis-Menten equation. When the velocity of an enzymatic reaction is one-half the maximal velocity ... 

The fundamental cornerstone of the kinetic characterization of enzymatic reactions has been and remains the Michaelis-Menten equation (Eq. 4.1). 

This expression is equivalent to Michaelis-Menten equation (rate equation for the one-substrate enzymatic reactions), i.e. 

The studies of the kinetics of bioelectrocatalytic transformations show that in some systems (for instance, adsorbed laccase ) the kinetic parameters correspond to the phenomenology of electrochemical kinetics, while in other systems (for instance, lactate oxidation they fit the phenomenology of enzymatic catalysis. In the latter case, we observe a hyperbolic dependence of anode current on the substrate concentration, as expected from the Michaelis-Menten equation. The absence of a general theory of bioelectrocatalysis does not permit us to examine the kinetics of electrochemical reactions in the presence of enzymes under different conditions. At present we can only try to estimate the scope of possible accelerations of electrochemical reactions by making some simple assumptions. 

This equation is the general reversible form of the Michaelis-Menten equation. If the enzymatic reaction is completely reversible, it can be started by mixing the substrate with the enzyme, or vice versa, by mixing the product with the enzyme. In the former case, P=o, and Eq. (3.27) reduces to the Michaelis-Menten equation in the forward direction ... 

The two independent kinetic parameters of the Michaelis-Menten equation are Ymax and Vroax/Km. Many enzymologists who have analyzed for isotopic effects have looked for rate reductions in Vmax. because Knax, for most enzymes, contains a rate term for the chemical step involving the covalent change being analyzed. In probing with a deuterated substrate, for instance, if V max(H)/l max(D)> then Y ax rates may be controlled totally or in part by a slow catalytic step involving C-H (C-D) fission. The magnitude of Ymax difference observed for substrate-deuterium kinetic isotope effects varies widely in enzymatic reactions. 

Using this equation, it is clear that continuous operation in a CSTR is superior to batch processing, especially when organisms with maximum growth rates of more than about 0.2 are used. Inserting the Michaelis-Menten equation (Equ. 2.54) for a poison-free enzymatic reaction into the performance equation of a single CSTR (Equ. 3.90) gives... 

A great number of enzymatic reactions can be described by the well-known Michaelis-Menten equation rate, which was initially proposed by Henri, and then improved by Briggs and Haldane (Bailey and Ollis, 1986 Laidler and Bunting, 1973). 

This is the Michaelis-Menten equation for the rate of a simple enzymatic reaction and Km = K lk is known as the Michaelis-Menten constant. At high reactant concentration Ca much larger than iQ, the rate levels off and becomes zero order with respect to the reactant, =k Cl- At low Q (1.5.1-8) degenerates into a first order rate equation. This equation is entirely similar to the Hougen-Watson rate equations that will be derived in Chapter 2 for reactions catalyzed by solids. 

Enzymatic reactions usually proceed as shown in Fig. 10.2. Initially, an enzyme-substrate complex is formed, which is then converted into an enzyme-product complex, followed by product release from the enzyme. Figure 10.2 shows the relationship between the reaction rate and the substrate concentration, following the Michaelis-Menten equation. Although one typical problem for chemical reactions in water maybe that the solubihty of hydrophobic... 

The kinetics of enzymatic reactions in microemulsions obey, as a rule, the classic Michaelis-Menten equation [6,26,35], but difhculties arise in interpreting the results because of the distribution of reactants, products, and enzyme molecules among the microphases of the microemulsion [8,36-38], In addition, there are some enzymes in reverse micelles that exhibit enhanced activity as compared to that expressed in water this has given rise to the concept of superactivity [6,26,39], The superactivity has been explained in terms of the state of water in reverse micelles, the increased rigidity of the enzymes caused by the surfactant layer, and the enhanced substrate concentration at the enzyme microenvironment [36,40],... 

The efficiency of solution-phase (two aqueous phase) enzymatic reaction in microreactor was demonstrated by laccase-catalyzed l-DOPA oxidation in an oxygen-saturated water solution, and analyzed in a Y-shaped microreactor at different residence times (Figure 10.24) [142]. Up to 87% conversions of l-DOPA were achieved at residence times below 2 min. A two-dimensional mathematical model composed of convection, diffusion, and enzyme reaction terms was developed. Enzyme kinetics was described with the double substrate Michaelis-Menten equation, where kinetic parameters from previously performed batch experiments were used. Model simulations, obtained by a nonequidistant finite differences numerical solution of a complex equation system, were proved and verified in a set of experiments performed in a microreactor. Based on the developed model, further microreactor design and process optimization are feasible. 

Interestingly, Eq. (5.21) is the differential equation commonly employed in the context of chemical kinetics to model the dynamics of a chemical species that is produced via a catalytic reaction and degraded linearly (Houston 2001). In particular, the first term on the right-hand side of Eq. (5.21) corresponds to Michaelis-Menten equation, which is commonly used to model the velocity of enzymatic reactions (Houston 2001 Lehninger et al. 2005). Let us close this section by stating that knowing how Eq. (5.21) can be deduced from a stochastic chemical dynamics approach, allows us to better understand its range of validity and its connection with the relevant quantities of the stochastic-description. 

The mechanisms of micelle-catalyzed reactions have been studied not only by analogy with the Michaelis-Menten equation for enzymatic reactions but also from the perspective of volume fractions of the two-part reaction system consisting of the micelles and the intermicellar bulk solutions.The kinetics of this reaction has been successfully used only when the micellar concentrations are much higher than the reactant concentrations. However, micellar concentrations near the CMC are often less than the reactant concentrations. In such cases, the distribution of reactants among micelles must be taken into consideration, which is essentially a thermodynamic problem (Chapter 9). Reactant is a better technical term than substrate for micelle-catalyzed reactions. 

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