Enzymes initial velocity

One other simplification will be advantageous. Because enzymes accelerate the rate of the reverse reaction as well as the forward reaction, it would be helpful to ignore any back reaction by which E + P might form ES. The velocity of this back reaction would be given by = A 2[E][Pj. However, if we observe only the initial velocity for the reaction immediately after E and S are mixed in the absence of P, the rate of any back reaction is negligible because its rate will... 

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... 

The mechanism involved the overall conversion of [5] to [P], The reverse reaction is insignificant because only the initial velocity in one of the forward direction is concerned. The mass balance equation expressing the distribution of the total enzyme is ... 

Similarly to quantitative determination of high surfactant concentrations, many alternative methods have been proposed for the quantitative determination of low surfactant concentrations. Tsuji et al. [270] developed a potentio-metric method for the microdetermination of anionic surfactants that was applied to the analysis of 5-100 ppm of sodium dodecyl sulfate and 1-10 ppm of sodium dodecyl ether (2.9 EO) sulfate. This method is based on the inhibitory effect of anionic surfactants on the enzyme system cholinesterase-butyryl-thiocholine iodide. A constant current is applied across two platinum plate electrodes immersed in a solution containing butyrylthiocholine and surfactant. Since cholinesterase produces enzymatic hydrolysis of the substrate, the decrease in the initial velocity of the hydrolysis caused by the surfactant corresponds to its concentration. Amounts up to 60 pg of alcohol sulfate can be spectrometrically determined with acridine orange by extraction of the ion pair with a mixture 3 1 (v/v) of benzene/methyl isobutyl ketone [271]. 

ASSAYS OF ENZYME-CATALYZED REACTIONS TYPICALLY MEASURE THE INITIAL VELOCITY... 

Most measurements of the rates of enzyme-catalyzed reactions employ relatively short time periods, conditions that approximate initial rate conditions. Under these conditions, only traces of product accumulate, hence the rate of the reverse reaction is negligible. The initial velocity (vj) of the reaction thus is essentially that of... 

Figure 8-3. Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction.

If the enzyme concentration is fixed at a value well below the substrate concentration, and the concentration of substrate is then titrated, one finds that the initial velocity of the reaction varies as illustrated in Figure 2.7. At the lower substrate concentrations, the initial velocity tracks linearly with substrate concentration. At intermediate values of [5], the initial velocity appear to be a curvilinear function of [5], while at higher substrate concentrations, the initial velocity appears to reach a maximum level, as if the active site of all the enzyme molecules are saturated with... 

Figure 2.7 Plot of initial velocity as a function of substrate concentration for a typical enzyme.

In Chapter 2 we described the typical product progress curve for a well-behaved enzyme and introduced the concept of initial velocity. In assays designed to quantify the ability of a test compound to inhibit the target enzyme, it is critical to restrict... 

Figure 4.3 Product progress curves for an enzyme-catalyzed reaction in the absence (closed circles) and presence open circles) of an inhibitor at a concentration that reduces the reaction rate by 50%. Inset The initial velocity phase of these progress curves.

Deviations from linearity at high enzyme concentrations can also have multiple origins. The most common reason for an apparent deviation from linearity here is that the high enzyme concentrations speed up the reaction so much that one inadvertently moves out of the initial velocity phase of the reaction, and into a phase of... 

Enzymatic reactions are influenced by a variety of solution conditions that must be well controlled in HTS assays. Buffer components, pH, ionic strength, solvent polarity, viscosity, and temperature can all influence the initial velocity and the interactions of enzymes with substrate and inhibitor molecules. Space does not permit a comprehensive discussion of these factors, but a more detailed presentation can be found in the text by Copeland (2000). Here we simply make the recommendation that all of these solution conditions be optimized in the course of assay development. It is worth noting that there can be differences in optimal conditions for enzyme stability and enzyme activity. For example, the initial velocity may be greatest at 37°C and pH 5.0, but one may find that the enzyme denatures during the course of the assay time under these conditions. In situations like this one must experimentally determine the best compromise between reaction rate and protein stability. Again, a more detailed discussion of this issue, and methods for diagnosing enzyme denaturation during reaction can be found in Copeland (2000). 

Figure 8.1 Typical enzyme reaction progress curve in the presence of an irreversible enzyme inactivator, highlighting the initial velocity region (v ) and the fact that the terminal velocity (vs) is zero for such compounds.

The velocity is not necessarily the same at all times after you start the reaction. The depletion of substrate, inhibition by the product, or instability of the enzyme can cause the velocity to change with time. The initial velocity is measured early, before the velocity changes. Initial velocity measurements also let you assume that the amount of substrate has not changed and is equal to the amount of substrate that was added. 

The initial velocity is measured at a series of different substrate concentrations. In all cases the concentration of substrate used is much higher (by thousands of times, usually) than that of the enzyme. Each substrate concentration requires a separate measurement of the initial velocity. At low concentrations of substrate, increasing the substrate concentration increases the velocity of the reaction, but at high substrate concentrations, increasing the initial substrate concentration does not have much of an effect on the velocity (Fig. 8-4). 

Cooperative enzymes show sigmoid or sigmoidal kinetics because the dependence of the initial velocity on the concentration of the substrate is not Michaelis-Menten-like but gives a sigmoid curve (Fig. 8-7). 

The evaluation of results of assay optimization experiments such as those described above (see Section 6.4.2.1) also provides valuable information about enzymatic kinetic behavior. For example, the results shown in Figures 6.45 and 6.46 already provide information on enzymatic activity at each time point. In general, when evaluating enzyme kinetics, assays are designed to yield a measured conversion close to initial velocity.32... 

W. W. Cleland, The kinetics of enzyme catalyzed reactions with two or more substrates or products. III. Prediction of initial velocity and inhibition patterns by inspection. Biochim. Biophys. Acta. 67, 188 196 (1963). 

The use of spectrophotometry to monitor enzyme-catalysed reactions (Table 8.6) is a very convenient and popular method owing to the simplicity of the technique and the precision that is possible. The technique lends itself readily not only to temperature control using water-jacketed or electrically heated cell holders but also to the measurement of initial velocities by continuous monitoring and recording techniques or by automated analysis systems. 

Many methods have been developed in which a product of the reaction is chemically modified to produce a substance with a particular spectral property. The inorganic phosphate released by the hydrolysis of phosphate esters may be measured by simple chemical methods (Fiske and Subbarow) after the enzyme reaction has been stopped. Such techniques are often convenient but do not lend themselves to the measurement of initial velocity. 

Further experiments by Brown and particularly Henri were made with invertase. At that time the pH of the reactions was not controlled, mutarotation did not proceed to completion, and it is no longer possible to identify how much enzyme was used (Segal, 1959). Nevertheless, in a critical review of kinetic studies with invertase, Henri concluded (1903) that the rate of reaction was proportional to the amount of enzyme. He also stated that the equilibrium of the enzyme-catalyzed reaction was unaffected by the presence of the catalyst, whose concentration remained unchanged even after 10 hours of activity. When the concentration of the substrate [S] was sufficiently high the velocity became independent of [S]. Henri derived an equation relating the observed initial velocity of the reaction, Vq, to the initial concentration of the substrate, [S0], the equilibrium constant for the formation of an enzyme-substrate complex, Ks, and the rate of formation of the products, ky... 

If an approximate Km value for the enzyme-substrate combination of interest is known, a full-scale kinetic assay may be done immediately. However, often an approximate value is not known and it is necessary first to do a range finding or suck and see preliminary assay. For such an assay, a concentrated substrate solution is prepared and tenfold serial dilutions of the substrate are made so that a range of substrate concentrations is available within which the experimenter is confident the Km value lies. Initial velocities are determined at each substrate concentration, and data may he plotted either hyperholically (as V versus [S]) or with [S] values expressed as logio values. In the latter case, a sigmoidal curve is fitted to data with a three parameter logistic equation (O Eq. 4) ... 

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