Michaelis-Menten reaction

Enzyme-Catalyzed Batch Reactions. Michaelis-Menten theory assumes equih-brium between occupied and unoccupied sites ... 

MICHAELIS CONSTANT (APPARENT) MICHAELIS-MENTEN EQUATION L HOPITAL S RULE MICHAELIS CONSTANT MICHAELIS-MENTEN KINETICS PROGRESS CURVE ANALYSIS UNI UNI MECHANISM ZERO-ORDER REACTIONS MICHAELIS-MENTEN KINETICS MICHAELIS-MENTEN EQUATION UNI UNI MECHANISM... 

Box 12.2 An Enzyme-Catalyzed Reaction (Michaelis-Menten Enzyme Kinetics)... 

The simplest mechanism for an enzyme-catalysed reaction (Michaelis-Menten scheme) is... 

Another type of kinetic behavior that is very common for enzyme-catalyzed reactions (Michaelis-Menten kinetics) has also been observed in a number of homogeneous catalytic systems. The rate expression in such cases is given by... 

The assumption of uniformity is in fact justified for some realistic kinetic schemes, such as Langmuir isotherm catalyzed reactions, Michaelis-Menten kinetics, and others (Aris, 1989 Cicarelli et al, 1992). The assumption bears a more than superficial analogy with those systems termed pseudo-monomolecular by Wei and Prater (1962). Mathematically, it is a very powerful assumption By crossing out the dependence of F[ ] on x, its value has been reduced from an infinite-dimensional vector (a function of x) to a scalar. This simplification makes Eq. (102) a quasilinear one, and it can be integrated explicitly by introducing a warped time scale t(0. (0) = 0. The solution, as can be verified by inspection, is... 

Detection limits for enzyme-based potentiometric biosensors are governed by the iimate detection limits of the membrane electrode toward the product of the enzyme reaction, as well as the kinetics of the enzymatic reaction (Michaelis-Menten constant and turnover number of the enzyme), and mass transfer rate of substrate into the enzymatic layer. Carr and Bowers developed in detail the theory of how such parameters affect the response curves of such sensors [48]. Generally, enzyme-based potentiometric biosensors respond to target substrates over the concentration range of 0.01 mM to 10 mM. In the case of the urea example mentioned earlier, limited selectivity of the nonactin-based ammonium membrane electrode over potassium ions k ... 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

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... 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

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]. 

The turnover number of an enzyme, is a measure of its maximal catalytic activity, is defined as the number of substrate molecules converted into product per enzyme molecule per unit time when the enzyme is saturated with substrate. The turnover number is also referred to as the molecular activity of the enzyme. For the simple Michaelis-Menten reaction (14.9) under conditions of initial velocity measurements, Provided the concentration of... 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

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]... 

For a Michaelis-Menten reaction, ki = 7X10VAf- sec, /f i = 1 X lOVsec, and fe = 2 X lOVsec. What are the values of Ks and Does substrate binding approach equilibrium or does it behave more like a steady-state system ... 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

As with the Langmuir adsorption isotherm, which in shape closely resembles Michaelis-Menten type biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the concentration axis (the value of Km or the magnitude of the coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, Michaelis-Menten reactions can be written in the form... 

The operational model allows simulation of cellular response from receptor activation. In some cases, there may be cooperative effects in the stimulus-response cascades translating activation of receptor to tissue response. This can cause the resulting concentration-response curve to have a Hill coefficient different from unity. In general, there is a standard method for doing this namely, reexpressing the receptor occupancy and/or activation expression (defined by the particular molecular model of receptor function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes the concentration of response-producing receptor as the substrate for a Michaelis-Menten type of reaction, given as... 

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

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The initial reaction rate (v0) obtained from each substrate concentration was fitted to Michaelis-Menten kinetics using enzyme kinetics. Pro (EKP) Software (ChemSW product,... 

Kinetic data fitting the rate equation for catalytic reactions that follow the Michaelis-Menten equation, v = k A]/(x + [A]), with[A]0 = 1.00 X 10 J M, k = 1.00 x 10 6 s 1, and k = 2.00 X 10-J molL1. The left panel displays the concentration-time profile on the right is the time lag approach. 

The rates of many catalyzed reactions depend upon substrate concentrations, as shown in Fig. 4-7. The rate at high substrate concentrations is zeroth-order with respect to [S], falling until it shows a first-order dependence in the limit of low [S], This pattern is that of a rectangular hyperbola, defined by an empirical relation known as the Michaelis-Menten equation. 

One reaction scheme that leads to Michaelis-Menten kinetics is known as the Briggs-Haldane scheme. It consists of these reactions ... 

Almost every reaction scheme that gives rise to Michaelis-Menten kinetics will proceed at a rate directly proportional to [E]j. It is customary to express Emax as... 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

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 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 ... 

The Michaelis-Menten rate equation for enzyme reactions is typically written as the rate of formation of product (Eq. 19a). This equation implies that 1/Rate (where rate is the rate of formation of product) depends linearly on the inverse of the substrate concentration [S]. This relation allows KM to be determined. Derive this equation and sketch 1/Rate against 1/[S]. Label the axes, the y-intercept, and the slope with their corresponding functions. 

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