Enzyme concentration determination

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

Enzyme Assays. An enzyme assay determines the amount of enzyme present in sample. However, enzymes are usually not measured on a stoichiometric basis. Enzyme activity is usually determined from a rate assay and expressed in activity units. As mentioned above, a change in temperature, pH, and/or substrate concentration affects the reaction velocity. These parameters must therefore be carefully controlled in order to achieve reproducible results. 

Amylase enters the blood largely via the lymphatics. An increase in hydrostatic pressure in the pancreatic ducts leads to a fairly prompt rise in the amylase concentration of the blood. Neither an increase in volume flow of pancreatic juice nor stimulation of pancreatic enzyme production will cause an increase in senm enzyme concentration. Elevation of intraductal pressure is the important determinant. Stimulation of flow in the face of obstruction can, however, augment the entry of amylase into the blood, as can disruption of acinar cells and ducts. A functional pancreas must be present for the serum amylase to rise. Serum amylase determination is indicated in acute pancreatitis in patients with acute abdominal pain where the clinical findings are not typical of other diseases such as appendicitis, cholecystitis, peptic ulcer, vascular disease or intestinal obstruction. In acute pancreatitis, the serum amylase starts to rise within a few hours simultaneously with the onset of symptoms and remains elevated for 2 to 3 days after which it returns to normal. The peak level is reached within 24 hours. Absence of increase in serum amylase in first 24 hours after the onset of symptoms is evidence against a diagnosis of acute pancreatitis (76). 

Several tubidimetric methods (92, 93) have been described specifically for the kinetic determination of lipase in serum but these methods suffer from lack of linearity with increasing enzyme concentration, and instability of emulsions. 

Thus the best approach for HTS purposes is to experimentally determine the effect of enzyme titration on the observed reaction velocity, and to then choose to run the assay at an enzyme concentration well within the linear portion of the curve (as in Figure 4.6). Again, the other details of the assay conditions can affect the enzyme titration curve, so this experiment must be performed under the exact assay conditions that are to be used for library screening. 

Here m is the slope value and [ii]app is the apparent total enzyme concentration, typically estimated from protein assays and other methods (Copeland, 1994). Note from Equation (7.13) that when our estimate of enzyme concentration is incorrect, the slope of the best fit line of IC50 as a function of [E] will not be 1/2, as theoretically expected. Nevertheless, the v-intercept estimate of K pp is unaffected by inaccuracies in [ ]. In fact we can combine Equations (7.12) and (7.13) to provide an accurate determination of [ /]T from the slope of plots such as those shown in Figure 7.2. The true value of [ii]T is related to the apparent value [ TPP as... 

Use of Morrison s quadratic equation, together with Murphy s recommended dilution scheme, will allow accurate estimates of Kfpjpj as low as 100-fold below the total enzyme concentration. Based on Murphy s simulations, the most accurate determination of Kfpp is obtained for inhibitor titrations performed at / T = 10A I, (Murphy, 2004). 

These practical approaches are by no means mutually exclusive, and attempts should be made to combine as many of these as possible to improve ones ability to experimentally measure the K-pp of tight binding inhibitors. Thus one should always work at the lowest enzyme concentration possible, and drive the substrate concentration as high as possible, when dealing with competitive inhibitors. A long preincubation step should be used before activity measurements, or the progress curves should be fitted to Equation (6.2) so that accurate determinations of the steady state velocity at each inhibitor concentration can be obtained. Finally, the concentration-response data should be fitted to Morrison s quadratic equation to obtain good estimates of the value of Arfpp. 

In Section 7.2 we presented one method for determining E T from the effects of apparent enzyme concentration on the measured value of IC50 for tight binding inhibitors. Another convenient way to determine [E T derives from the nature of Morrison s equation. When the ratio E T/A (PP equals or exceeds 200, the fractional velocity decreases very steeply with increasing inhibitor concentration, in an essen-... 

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. 

At low temperatures, the nonenzymatic reaction is reduced to a larger extent than the enzymatic reaction. The mass transfer rate is reduced to a smaller extent. Mass transfer limitation is required for high enantiomeric excess and determines the conversion rate. Therefore, the volumetric productivity decreases at lower temperatures. The equilibrium constant is considerably higher at low temperatures, resulting in a higher extent of conversion or a lower HCN requirement. Both the volumetric productivity and the required enzyme concentration increase by increasing the reaction temperature and aqueous-phase volume while meeting the required conversion and enantiomeric excess [44]. The influence of the reaction medium (solvent and water activity) is much more difficult to rationalize and predict [45],... 

The enzyme concentration mE in a geochemical application is likely to represent in a general way the amount of biomass in the system. It is not common to attempt to determine values for k+ and mE separately instead, the product rmax of the two variables is generally reported, as was the case for Equation 17.16. As well, the... 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

Assay of Homogenate for Aldrin Epoxidation. The following experimental sequence was designed to determine the optimum in vitro conditions for aldrin epoxidation in larval whole body homogenates 1) the effect of component chemicals generally included in an incubation mixture, 2) a pH profile, 3) a temperature profile, 4) a molarity profile, 5) a reaction time profile, 6) a larval concentration (enzyme concentration) profile, 7) a substrate concentration profile, and 8) a restudy of the effects of component chemicals in the initial incubation mixture (Step 1) upon aldrin epoxidation under optimum conditions as defined by steps 2-7 above. The effect of PBO, FMN, and FAD upon enzyme activity was also tested. 

Figure 11.1 illustrates the behavior of Equation 11.6. By the assumption of rapid equilibrium the rate determining step is the unimolecular decomposition. At high substrate composition [S] KM and the rate becomes zero-order in substrate, v = Vmax = k3 [E0], the rate depends only on the initial enzyme concentration, and is at its maximum. We are dealing with saturation kinetics. The most convenient way to test mechanism is to invert Equation 11.6... 

The / -glucosidase activity was determined by measuring the release of p-nitrophenol from p-nitrophenyl-/i-D-glucopyranoside one unit of / -glucosidase activity (U) is defined as the amount of enzyme that releases 1 [mu] mol p-nitrophenol per minute. AU samples were assayed in potassium phosphate buffer (50 mM, pH 7.0) at 50 °C under conditions that activity was proportional to enzyme concentration. 

Plots devised by Dixon to determine K, for tight-binding inhibitors, (a) A primary plot of v versus total inhibitor present ([/Id yields a concave line. In this example, [S] = 3 x Km and thus v = 67% of Straight lines drawn from Vo (when [/It = 0) through points corresponding to Vq/2, Vq/3, etc. intersect with the x-axis at points separated by a distance /Cj app/ when inhibition is competitive. When inhibition is noncompetitive, intersection points are separated by a distance equivalent to K. The positions of lines for n = 1 and n = 0 can then be deduced and the total enzyme concentration, [EJt, can be determined from the distance between the origin and the intersection point of the n = 0 line on the x-axis. If inhibition is competitive, this experiment is repeated at several different substrate concentrations such that a value for K, app is obtained at each substrate concentration. (b) Values for app are replotted versus [S], and the y-intercept yields a value for /Cj. If inhibition is noncompetitive, this replot is not necessary (see text)... 

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