Enzyme kinetics Michaelis constant

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

The kinetic parameters of an enzyme—the Michaelis constant, and the maximal velocity, Fmax—should provide both qualitative and quantitative information concerning variation of an enzyme due to the change in the enzyme s kinetic properties brought about by conformational changes in the tertiary structure of the enzyme induced by substitutions, deletions, or addition of amino acids. Since the of an enzyme is a quali-... 

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]. 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

The kinetic data below were reported for an enzyme catalyzed reaction of the type E + S ES E + P. Since the data pertain to initial reaction rates, the reverse reaction may be neglected. Use a graphical method to determine the Michaelis constant and Fmax for this system at the enzyme concentration employed. 

Another type of inhibitor combines with the enzyme at a site which is often different from the substrate-binding site and as a result will inhibit the formation of the product by the breakdown of the normal enzyme-substrate complex. Such non-competitive inhibition is not reversed by the addition of excess substrate and generally the inhibitor shows no structural similarity to the substrate. Kinetic studies reveal a reduced value for the maximum activity of the enzyme but an unaltered value for the Michaelis constant (Figure 8.7). There are many examples of non-competitive inhibitors, many of which are regarded as poisons because of the crucial role of the inhibited enzyme. Cyanide ions, for instance, inhibit any enzyme in which either an iron or copper ion is part of the active site or prosthetic group, e.g. cytochrome c oxidase (EC 1.9.3.1). 

Figure 8.7 The kinetic effects of a non-competitive inhibitor. The effect of a noncompetitive inhibitor is not reversed by high concentrations of substrate and the enzyme reaction shows a reduced value for the maximum velocity. The enzyme remaining is unaltered and gives the same value for the Michaelis constant as originally shown by the uninhibited enzyme.

In contrast to the kinetics of isosteric (normal) enzymes, allosteric enzymes such as ACTase have sigmoidal (S-shaped) substrate saturation curves (see p. 92). In allosteric systems, the enzyme s af nity to the substrate is not constant, but depends on the substrate concentration [A]. Instead of the Michaelis constant Km (see p. 92), the substrate concentration at half-maximal rate ([AJo.s) is given. The sigmoidal character of the curve is described by the Hill coef cient h. In isosteric systems, h = 1, and h increases with increasing sigmoid icity. 

A procedure to simplify the experimental method in the kinetic analysis of three-substrate, enzyme-catalyzed reactions ". In this method, the concentration of one substrate is varied while the other two substrates are kept in a constant ratio and in which the individual concentrations of these two substrates are in the neighborhood of their respective Michaelis constants. The experi-... 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

ENZYME KINETIC EQUATIONS MICHAELIS CONSTANT UNI UNI MECHANISM Koppel-Palm solvent parameters,... 

If enzymes are described under tbe aspect of reaction mechanisms, the maximal rate of turnover Vmax. the Michaelis and Menten constant Km, the half maximal inhibitory concentration ICso, and tbe specific enzyme activity are keys of characterization of the biocatalyst. Even though enzymes are not catalysts in a strong chemical sense, because they often undergo an alteration of structure or chemical composition during a reaction cycle, theory of enzyme kinetics follows the theory of chemical catalysis. 

Data in Fig. 9 show that ferrocene is the most reactive in this family of HRP substrates. The rate constant k7 of 2 x 105 M-1 s 1 at pH 7 and 25 °C indicates that its reactivity is comparable with the frequently used electron donors of HRP. Ferrocene follows first-order kinetics and k7 should be compared with the ratio cat/ 4Vb where kc t and Km are the catalytic and the Michaelis constants for substrates obeying the Michaelis-Menten kinetics, respectively. Such are iodide, guaiacol, and ABTS (2,2 -azino-bis(3-ethylbenzothiazoline-6 -sulfonic acid) (128). The available ratios of 0.15 x 105, 1.3 x 105, and 34 x 105 M 1 s-1, respectively (129), indicate that ferrocene is more reactive than iodide and comparable with guaiacol. High reactivity of ferrocene makes it a convenient analytical reagent for routine assays of H2O2 in the presence of HRP by monitoring the enzymically produced ferricenium dye at 617 nm (113). 

The Fc-HRP activity was quantified using two different substrates of HRP, i.e., ABTS and water-soluble ferrocene derivatives. Rate laws and kinetic parameters for native HRP and Fc-HRP have been compared. The native and the reconstituted enzymes catalyze the oxidation of ABTS in accordance with the Michaelis-Menten kinetics the inverse rate versus [ABTS]-1 plots are linear and the values of the maximum rates Vm and the Michaelis constant Km are summarized... 

Before NMR spectroscopy and mass spectrometry revolutionized the structural elucidation of organic molecules, UV spectroscopy was an important technique and was used to identify the key chromophore of an unknown molecule. The importance of UV is much diminished nowadays, but it still retains its place in certain applications, such as the determination of kinetic parameters, (the Michaelis constant) and A cat (the turnover rate of an enzyme, in molecules per second), for a number of enzymic reactions and in the analysis of pharmaceuticals. 

KiMM is given the subscript, MM, to remind us that it reflects Michaelis-Menten enzyme kinetics as distinguished from KiM used above to model microbial growth kinetics (see Monod cases above). Note, is the same as KE in Box 12.2 when it s value represents the reciprocal of the equilibrium constant for the binding step. 

Tlie kinetic parameters of Eq. 9-44 are Vf, the maximum velocity in the forward direction, the two Michaelis constants, KmB and KmA, and the equilibrium constant Ke, for reversible dissociation of the complex EA and which is equal to k2/k1. The relationship between the parameters of Eq. 9-44 (Km s, V s, and KeqA s) and the rate constants /q- kw is not obvious. However, remember that the parameters are experimental quantities determined by measurements on the enzyme. Sometimes, but not always, it is possible to deduce some of the values of individual rate constants from the experimental parameters. 

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