Measuring Initial Velocity

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 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. 

While this model explained the action of the brain enzyme on a number of hexose substrates and nonsubstrate inhibitory analogs, the mode had its weaknesses. It assumed that the other conformations of a hexose that are in equilibrium with the active conformer act as competitive inhibitors relative to this conformer. One cannot evaluate the effect of a competitive inhibitor which is present in a constant proportion relative to the active substrate by initial velocity measurements. Moreover, the use of apparent Michaelis constants may not provide accurate estimates of affinity, which is more directly related to a dissociation constant. The chief limitation of the model, however, is that an equally great number of experimental facts can be satisfactorily explained in terms of a simpler scheme involving the binding and phosphorylation of the Cl conformer. Furthermore, one can understand more directly how the enzyme can phosphorylate glucopyranose and fructofuranose equally well. 

Substrate concentration is yet another variable that must be clearly defined. The hyperbolic relationship between substrate concentration ([S ) and reaction velocity, for simple enzyme-based systems, is well known (Figure C1.1.1). At very low substrate concentrations ([S] ATm), there is a linear first-order dependence of reaction velocity on substrate concentration. At very high substrate concentrations ([S] A m), the reaction velocity is essentially independent of substrate concentration. Reaction velocities at intermediate substrate concentrations ([S] A"m) are mixed-order with respect to the concentration of substrate. If an assay is based on initial velocity measurements, then the defined substrate concentration may fall within any of these ranges and still provide a quantitative estimate of total enzyme activity (see Equation Cl. 1.5). The essential point is that a single substrate concentration must be used for all calibration and test-sample assays. In most cases, assays are designed such that [S] A m, where small deviations in substrate concentration will have a minimal effect on reaction rate, and where accurate initial velocity measurements are typically easier to obtain. 

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

Kinetic Study of Hydrolysis. It is of great interest to know the nature of the high enantioselectivity of the Arthrobacter lipase. The initial velocity measurements were conducted for the purpose of knowing which is the main factor of the enantioselectivity, the apparent Michaelis constant K m or the catalytic constant k cat. 

According to the kinetic treatment of Lavayre et al (10) on two insoluble enantiomeric isomers, the relative initial velocities, V/VR were plotted against various ratios in the (S)-enantiomer. All of the initial velocity measurements were made at 50°C instead of 40°C to avoid crystallization of the acetate of pure (R)-HMPC, and at pH 6.0 to prevent spontaneous hydrolysis of the substrate at 50°C. The result gives a concave type of curve as illustrated in Figure 3. This implies that K mS < K mR and that the (S)-enantiomer is a strong competitive inhibitor. Thus, it is concluded that a very high optical purity of (R)-HMPC liberated with Arthrobacter lipase is entirely the result of the great catalytic constant of the (R)-HMPC ester. 

Discussion on Binding Mode. The initial velocity measurements of the acetate of CPBA with various ratios of the (R)-enantiomer were observed to give almost the same line having a concave curve as illustrated for the acetate of HMPC in Figure 3. This result... 

Most enzymes react with two or more substrates. For this reason, the Michaelis-Menten equation is inadequate for a full kinetic analysis of these enzyme reactions. Nonetheless, the same general approach can be used to derive appropriate equations for two or more substrates. For example, most enzymes that react with two substrates, A and B, are found to obey one of two equations if initial velocity measurements are made as a function of the concentration of both A and B (with product concentrations equal to zero). These are... 

Initial velocity measurements for enzyme activity (through the purification and before kinetic experiments) were performed by a continuous spectrophotometric assay as described by Lockridge et al. (1972) and modifed by Frederick et al. (1990) with a Hewlett-Packard 8452A diode array spectrophotometer equipped with a thermostatted cell holder. 

Initial velocity measurements in kinetic experiments were carried out by following the oxygen consumption with an oxygen electrode (Yellow Spring Instruments 1 mL chamber). 

Determination of enthalpy of activation requires measurements of kcat under full substrate saturation over a significant temperature range. The initial velocity measurements were performed under pure oxygen atmosphere and with 0.5 M 2-deoxyglucose (> 8 Km) in 10 mM bis-tris propane buffer pH 9 as described under... 

Figiirc 4-44 Ordered Bi Bi system, (a) l/v versus 1/[A] at different fixed B concentrations, (b) 1/v-axis intercept repbt. (c) Slofei/A replot. Although the nomenclature is different. Figure 4-44 is identical to Figure 4-42. Thus, initial velocity measurements alone will not discriminate between random and ordered mechanisms. 

In another approach. Cash and Brahic (1986) quantitated ISH using initial velocity measurements and observed a linear relationship between the number of autoradiographic grains and the number of viral genomes per cell (between 600 and 60000). This method avoids the requirement of achieving saturation. 

Each of the components of the mixture was shown to improve the stability of the diluted enzyme the addition of BSA did not reduce the concentration of crotonyl-CoA in the assay mixture, as determined by initial velocity measurements of freshly prepared enzyme dilution in the presence and absence of BSA. 

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