Kinetic constants Km and Vmax

A mechanism provides a description of individual chemical steps that make up the overall reaction. How fast each reaction occurs is governed by the rate constant for the reaction. The observable kinetic constants Km and Vmax are related to the individual rate constants for the individual steps by a bunch of algebra. 

The measurable activity reflects the biocatalytic efficiency of an immobilized enzyme. In homogeneous solution the initial rate of substrate conversion rises linearly with enzyme concentration. The reaction rate is influenced by substrate diffusion only at extremely large degrees of conversion. With immobilized enzymes the measured reaction rate depends not only on the substrate concentration and the kinetic constants Km and vmax but also on so-called immobilization effects. These effects are due to the following alterations of the enzyme by the immobilization process (Kobayashi and Laidler, 1974). 

Perhaps the second most elementary (and very common) consideration regarding the kinetic profiling of an enzyme reaction is to assess whether or not it can be fitted to the Michaehs-Menten model. This assessment is not always taken as seriously as it should. Rather than truly assess whether or not the data conform to a Michaehs-Menten model, it is often simply stated (or bhndly assumed) that they do, and various linear transformations are conducted to arrive at estimations of the kinetic constants Km and Vmax-... 

Determination of kinetic constants. Km and Vmax determinations for the acyl-ACP substrates were performed in reactions which contained 0.25 M MOPS, pH 7.4, sn-G3P at 8 mM (3.05 mCi/mmol) and unlabelled acyl-ACP at various concentrations. No BSA was present in these reactions, which were carried out for 15 minutes at 25°C with appropriately diluted enzyme preparations. The enzyme diluent was 50% glycerol in 10 mM Tris (pH 7.8), 2.5 mM DTT. Reactions were terminated and processed as for the general ATI assay. 

The simplest substrate in general use for measurement of the kinetic constants, Km and Vmax for bacterial sialidase has been sialyllactose, that particular isomer in which sialic acid is in a, 2 3 linkage to... 

Drugs can inhibit enzymes through several general mechanisms. The mechanism by which inhibition occurs dictates the approach by which the inhibition should be quantified. Inhibitors may act to alter Km, or Vmax) or both in this context, alter may mean that the true values of Km and Vmax really have been altered, or it may mean that these values have apparently changed in the presence of the inhibitor but that, in actual fact, they have not. In either case, it is vital that before any inhibitor has been introduced to a system, a robust and reproducible assay to measure Km and is in place, and good estimates for these kinetic constants have been obtained. 

In the determination of steady state reaction kinetic constants of enzyme-substrate reactions, FABMS also provides some very unique capabilities. Since these studies are best performed in the absence of glycerol in the reaction mixture, the preferred method is that which analyzes aliquots which are removed from a batch reaction at timed intervals. Quantitation of the reactants and products of interest is essential. When using internal standards, generally, the closer in mass the ion of interest is to that of the internal standard, the better is the quantitative accuracy. Using these techniques in the determination of kinetic constants of trypsin with several peptide substrates, it was found that these constants could be easily measured (8). FABMS was used to follow the decrease in the reactant substrate and/or the increase in the products with time and with varying concentrations of substrate. Rates of reactions were calculated from these data for each of the several substrate concentrations used and from the Lineweaver-Burk plot, the values of Km and Vmax are obtained. 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

The Michaelis constant is equal to substrate concentration at which the rate of reaction is equal to one-half the maximum rate. The parameters Km and Vmax characterize the enzymatic reactions that are described by Michaelis-Menten kinetics. Vmax is dependent on total enzyme concentration CET (Equation 11-10), whereas Km is not. 

Substances that cause enzyme-catalyzed reactions to proceed more slowly are termed inhibitors, and the phenomenon is termed inhibition. When an enzyme is subject to inhibition, the reaction still may obey Michaelis-Menten kinetics but with apparent Km and Vmax values that vary with the inhibitor concentration. If the inhibitor acts only on the apparent Km, it is a competitive inhibitor if it affects only the apparent Vmax, it is a noncompetitive inhibitor and if it affects both constants, it is an uncompetitive inhibitor. 

Based on in vitro studies of hepatic microsomal-catalysed oxidative reactions, using liver specimens from a variety of animal species including man, and marker substrates for the various reactions, it can be concluded that neither the measured levels of cytochrome P450 and cytochrome nor the activity of NADPH-cytochrome c reductase accounts for species variations in the capacity of oxidative reactions (McManus and Ilett, 1976 Dalvi et al., 1987 Souhaili-El-Amri et al., 1986). However, species variations could be attributed to differences in values of the kinetic parameters (Michaelis constant, Km, and the maximum reaction velocity, Vmax) associated with individual reactions. 

Simultaneous to the graph creation, kinetic properties in each vRxn are used to create the appropriate reaction rate equations (ordinary differential equations, ODE). These properties include rate constants (e.g., Michaelis constant, Km, and maximum velocity, Vmax, for enzyme-catalyzed reactions, and k for nonenzymatic reactions), inhibitor constants, A) and modes of inhibition or allosterism. The total set of rate equations and specified initial conditions forms an initial value problem that is solved by a stiff ODE equation solver for the concentrations of all species as a function of time. The constituent transforms for the each virtual enzyme are compiled by carefully culling the literature for data on enzymes known to act on the chemicals and chemical metabolites of interest. 

Note that the ternary complex EAB can be formed in two different ways. If the formation of EAB can occur with either substrate binding first, the reaction is known as a random single-displacement reaction. Many reactions catalyzed by phosphotransferases are of this type. If a particular substrate must bind first with the enzyme before the second substrate can bind, the reaction is known as an ordered single-displacement reaction. Many reactions catalyzed by dehydrogenases are of this type. The values for Km and Vmax for each substrate can be obtained from experiments in which the concentration of one substance is held constant at saturating levels while the concentration of the second substrate is varied. Kinetic analyses can distinguish between these types of reactions. 

The answer is b. (Murray, pp 48-73. Scriver, pp 4571-4636. Sack, pp 3-17. Wilson, pp 287-317.) When an enzyme obeys classic Michaelis-Menten kinetics as seen in the figure presented in question 154, the Michaelis constant (Km) and the maximal rate (V ax) can be readily derived. By plotting a reciprocal of the Michaelis-Menten equation, a straight-line Lineweaver-Burk plot is produced. The y intercept is l/Vmax, while the x intercept is —l/K . Thus, a reciprocal of these absolute values yields Vjnax and Kn. 

Liver is the principal site of D-fructose metabolism. D-Fructose is transported to the liver from the small intestine by way of the portal blood-vessel. Experiments with perfused pig and rat livers revealed that the rate of elimination of D-fructose from blood is a function of the sugar concentration,26,27 and follows Michaelis-Menten kinetics.27,28 Carrier-mediated, liver-membrane transport of D-fructose has a high29 Km and Vmax, in comparison to the intracellular phosphorylation constants of D-fructose in both pigeon and rat livers.27,28 For example, the calculated rat-liver transport for D-fructose has a Km of 67 mM and a Vmax of 30 /u,mole.min. g-1, in contrast to the lower, calculated fruc-tokinase Km of 1.0 mM and Vmax of 10.3 pmole. min r1. g 1 with D-fruc-tose and Km of 0.54 mM with adenosine 5 -triphosphate (ATP). In perfused pig-liver,28 the transport Km for D-fructose is only ten times that of intracellular phosphorylation by fructokinase. Hence, D-fructose-transport values suggested that, at physiological D-fructose concentrations, membrane transport limits the rate of uptake, thereby protecting the liver from severe depletion of adenine nucleotide.28,29... 

It is hard to get every rate constant experimentally, but simulation (as exemplified above for Km and Vmax) does not always require every rate constant to be known. The system it describes can often replace many rate constants by a single effective rate constant or another kind of quantity relating to the overall or part behavior of the kinetic system, and that single number can often be determined experimentally. A simple example of general... 

Activation energies and kinetic constants (Km, Vmax) were calculated for inorganic pyrophosphatases in several soils. Some residual activity remained after steam sterilization and formaldehyde treatment of soils. Enzyme activities were significantly correlated with organic C of soil profiles, and with organic C and clay contents of acidic top soils ". ... 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

The enzymatic activities of intercalated GOx-AM P layered nanocomposites at various pH values and temperatures were compared with the native enzyme in aqueous solution. In both cases, characteristic linear plots consistent with Michalis-Menton kinetics were obtained. The Lineweaver-Burk plots indicated that the reaction rates (Vmax) for free and intercalated GOx (3.3 and 4.0 pM min 1 respectively), were comparable, suggesting that the turnover rate at substrate saturation was only marginally influenced by entrapment between the re-assembled organoclay sheets. However, the dissociation constant (Km) associated with the activity of the enzyme was higher for intercalated GOx (6.63 mM) compared to native GOx (2.94 mM), suggesting... 

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. 

The important kinetic constants, Vmax and KM, can be graphically determined as shown in Figure E5.1. Equation E5.2 and Figure E5.1 have all of the disadvantages of nonlinear kinetic analysis. Vmax can be estimated only because of the asymptotic nature of the line. The value of Ku, the substrate concentration that results in a reaction velocity of VmJ2, depends on Vmax, so both are in error. By taking the reciprocal of both sides of the Michaelis-Menten equation, however, it is converted into the Lineweaver-Burk relationship (Equation E5.3). 

Some kinetic constants for several substrates are given in Table III Km values for each substrate are roughly comparable for the enzyme from each organism, and Vmax values indicate the degree of reactivity for each substrate. Several kinetic studies have provided evidence that... 

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