Kinetic measurements, enzyme reactions

After the operator has selected the desired method menu of the relevant samples and has started the instrument, all subsequent steps are fully automated. Since 1987 it is also possible to effect a direct identification of the sample so that there are no longer any problems in respect of a dialogue with a central EDP system. The samples are taken from the sample vessel by means of disposable single use pipette tips that are used for one sample only and exchanged via a computer-monitored pipetting unit. This method excludes the possibility of a carry-over between samples. In accordance with the preset conditions, the required slides are automatically moved to the sample dosage unit (see Fig. 23). Samples of 11 pi serum or plasma will be sufficient for kinetic measurements (enzymes), 10 pi of sample for all other tests. As soon as application of the sample has been completed, the slide is moved to the appropriate incubation chamber by means of the slide rotor (see Fig. 23). The chemical reactions take place in these chambers. This is followed by measurement either by reflectometer (end point or kinetic) or a potentiometric measurement unit. 

Describe the effects of competitive and noncompetitive inhibitors on the kinetics of enzyme reactions. Apply kinetic measurements and analysis to determine the nature of an inhibitor. 

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

This equation is fundamental to all aspects of the kinetics of enzyme action. The Michaelis-Menten constant, KM, is defined as the concentration of the substrate at which a given enzyme yields one-half of its maximum velocity. is the maximum velocity, which is the rate approached at infinitely high substrate concentration. The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It provides the quantitative calculation of enzyme characteristics and the analysis for a specific substrate under defined conditions of pH and temperature. KM is a direct measure of the strength of the binding between the enzyme and the substrate. For example, chymotrypsin has a Ku value of 108 mM when glycyltyrosinylglycine is used as its substrate, while the Km value is 2.5 mM when N-20 benzoyltyrosineamide is used as a substrate... 

Other automated systems may be purchased for a specific purpose and are called dedicated instruments, e.g. glucose analyser. Others have fairly restricted applications, an example being the reaction rate analysers which are specifically designed for the kinetic measurements of enzyme activity. Some of the more recently developed instruments employ individual pre-prepared disposable test packs or strip devices which contain all the reagents for each particular assay in a dry form. 

Coupled enzyme assays provide a good alternative to chemical modification and permit a kinetic technique to be employed. In a coupled assay, the rate at which the product is formed is measured by using the product of the reaction as a substrate for a second enzyme reaction which can be monitored more easily. Coupled assays offer great flexibility in enzyme methodology while still retaining all the advantages of continuous monitoring techniques and are illustrated by Procedure 8.5. 

The use of fluorescent substrates or products permits sensitive kinetic measurement of enzyme reactions to be undertaken and although there are relatively few natural fluorescent substrates, analogues can sometimes be used (Table 8.7). Some products can be converted to fluorescent compounds and can be used in fixed time assays. 

Carbon kinetic isotope effects on enzyme-catalyzed decarboxylations are among the most intensively studied enzyme reactions. This is because of the central role that carbon dioxide plays in plant metabolism and also because precise kinetic measurements are relatively easy to obtain since the carbon dioxide liberated in the reaction can be immediately analyzed using isotope ratio mass spectrometry. 

It has already been stated that a suitable quantitative assay technique must be available to measure the reaction of interest and it is assumed that the experimenter has determined optimal reaction conditions for the enzyme of interest. All kinetic assay techniques assume that v is a variable and that [S] is known as such, preparation of substrate must be meticulous in terms of ensuring that concentrations are correct, and this in turn will rely upon factors such as good weighing and pipetting techniques with calibrated instruments capable of precise, accurate, and sufficiently sensitive measurement. 

For reactions in which one or more reactants or products is a gas, manometry (the measurement of pressure differences) can provide a convenient means for monitoring the course and kinetics of the reaction Thus, enzymes that can be assayed with this method include oxidases, urease, carbonic anhydrase, hydrogenase, and decarboxylases. For example, bacterial glutamate decarboxylase is readily assayed by utilizing a Warburg flask and measuring the volume of gas evolved at different times using a constant-pressure respirometer. ... 

Because enzymic reactions are so sensitive to variations in temperature, suitable care must be exercised such that the temperature of the system is constant and under adequate control. Ideally, the temperature-regulated water bath and/or circulator should reduce any variability to within less than 0.1°C. Before initiating any reaction kinetic measurement, all samples should be thermally equilibrated. This process may take several minutes, depending on the nature of the sample container and the volume of the sample. 

Urea in kidney dialysate can be determined by immobilizing urease (via silylation or with glutaraldehyde as binder) on commercially available acid-base cellulose pads the process has to be modified slightly in order not to alter the dye contained in the pads [57]. The stopped-flow technique assures the required sensitivity for the enzymatic reaction, which takes 30-60 s. Synchronization of the peristaltic pumps PI and P2 in the valveless impulse-response flow injection manifold depicted in Fig. 5.19.B by means of a timer enables kinetic measurements [62]. Following a comprehensive study of the effect of hydrodynamic and (bio)chemical variables, the sensor was optimized for monitoring urea in real biological samples. A similar system was used for the determination of penicillin by penicillinase-catalysed hydrolysis. The enzyme was immobilized on acid-base cellulose strips via bovine serum albumin similarly as in enzyme electrodes [63], even though the above-described procedure would have been equally effective. 

Figure 10.2 One of the procedures for entrapping an enzyme, E, (or any other solute) inside liposomes. The non-entrapped enzyme is eliminated by size exclusion chromatography, then the substrate (ADP in this case) is left to permeate throughout, the ADP excess is again eliminated chromatographically, and the reaction kinetics - due to the internalized enzyme reaction - measured. (From Walde et al., 1994b.)...

Rates for this reaction may easily be measured by disappearance of azide UV absorption. Most importantly, kinetic saturation behavior is noted with sufficient amounts of the reactants cycloaddition velocity becomes independent of substrate concentration. As is familiar from enzyme catalysis, this indicates complete occupancy of all available cucurbituril by reacting species. In actuality, the rate of the catalyzed reaction under conditions of saturation was found to be the same as that for release of the product from cucurbituril. Such a stoichiometric triazole complex was independently prepared and its kinetics of dissociation were examined by the displacement technique previously outlined, giving the identical rate constant of 1.7xl0 s under the standard conditions. (It is not uncommon for product release to be rate-limiting in enzymic reactions). 

Rates of hydrolysis of /)-nitrophenyl-P-D-glucopyranoside by P-glucosidase, an irreversible unimolecular reaction, were measured at several concentrations of the substrate. The initial reaction rates were obtained as given in Table 3.2. Determine the kinetic parameters of this enzyme reaction. 

Steady state kinetic measurements on an enzyme usually give only two pieces of kinetic data, the KM value, which may or may not be the dissociation constant of the enzyme-substrate complex, and the kcM value, which may be a microscopic rate constant but may also be a combination of the rate constants for several steps. The kineticist does have a few tricks that may be used on occasion to detect intermediates and even measure individual rate constants, but these are not general and depend on mechanistic interpretations. (Some examples of these methods will be discussed in Chapter 7.) In order to measure the rate constants of the individual steps on the reaction pathway and detect transient intermediates, it is necessary to measure the rate of approach to the steady state. It is during the time period in which the steady state is set up that the individual rate constants may be observed. 

Inhibition kinetics are included in the second category of assay applications. An earlier discussion outlined the kinetic differentiation between competitive and noncompetitive inhibition. The same experimental conditions that pertain to evaluation of Ku and Vmax hold for A) estimation. A constant level of inhibitor is added to each assay, but the substrate concentration is varied as for Ku determination. In summary, a study of enzyme kinetics is approached by measuring initial reaction velocities under conditions where only one factor (substrate, enzyme, cofactor) is varied and all others are held constant. 

The hypothetical reaction mechanism shown in Fig. 10 is a variation of Scheme (3), and is consistent with the redox and pH dependence of the EPR-detectable nickel species (65). Hydrogen is known to undergo heterolytic cleavage (81) it is proposed that this is an intramolecular reaction, leading to the formation of a nickel (II) hydride and a protonated base in the enzyme (Step 1 in Fig. 10). The Ni-C species is postulated to be a protonated Ni(I) species. An alternative formulation for this state would be a dihydrogen complex, Ni(III) H2, as suggested by Crabtree (104). Ultimately the exact mechanism can only be determined by kinetic measurements. 

Studies on the kinetic behaviour of nucleoside and nucleotide complexes are less common than those on structural aspects. This arises because of the rapid rates of the formation and dissociation reactions, requiring NMR or temperature-jump relaxation measurements. The number of species that can coexist in solution also hinders interpretation. The earlier kinetic studies have been reviewed by Frey and Stuehr.127 Two important biological reactions of the nucleotides are phosphoryl and nucleotidyl group transfers. Both reactions are catalytic nucleophilic reactions and they both require the presence of a divalent metal ion, in particular Mg2+. Consequently, one of the main interests has been in understanding the catalytic mechanism of the metal ion involvement. This has mainly involved studies on related non-enzymic reactions.128... 

Kinetic analysis was used to characterize enzyme-catalyzed reactions even before enzymes had been isolated in pure form. As a rule, kinetic measurements are made on purified enzymes in vitro. But the properties so determined must be referred back to the situation in vivo to ensure they are physiologically relevant. This is important because the rate of an enzymatic reaction can depend strongly on the concentrations of the substrates and products, and also on temperature, pH, and the concentrations of other molecules that activate or inhibit the enzyme. Kinetic analysis of such effects is indispensable to a comprehensive picture of an enzyme. 

Measurements of reactions that occur in less than a few seconds require special techniques to speed up the mixing of the enzyme and substrate. One way to achieve this is to place solutions containing the enzyme and the substrate in two separate syringes. A pneumatic device then is used to inject the contents of both syringes rapidly into a common chamber that resides in a spectrophotometer for measuring the course of the reaction (fig. 7.5). Such an apparatus is referred to as a stopped-flow device because the flow stops abruptly when the movement of the pneumatic driver is arrested. In this type of apparatus it is possible to make kinetic measurements within about 1 ms after mixing of enzyme and substrate. 

Enzymes that catalyze reactions with two or more 7T) substrates work in a variety of ways. In some cases, the intermolecular reaction occurs when all the substrates are bound in a common enzyme-substrate complex in others, the substrates bind and react one at a time. A frequent application of kinetic measurements is to distinguish between such alternatives. 

It should be noted that this solution procedure requires the knowledge of elementary rate constants, klt k2, and k3. The elementary rate constants can be measured by the experimental techniques such as pre-steady-state kinetics and relaxation methods (Bailey and Ollis, pp. 111 -113, 1986), which are much more complicated compared to the methods to determine KM and rmax. Furthermore, the initial molar concentration of an enzyme should be known, which is also difficult to measure as explained earlier. However, a numerical solution with the elementary rate constants can provide a more precise picture of what is occurring during the enzyme reaction, as illustrated in the following example problem. 

---