ENZYME KINETICS in .NET

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Figure 2.11. Pyridoxal phosphate at the active site of aspartate aminotransferase.
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In these cases, the third term in the denominator (Km12/[S1] [S2] in Eq. 2.36) is absent because no ternary E  S1  S2 complex is formed. The individual values of Km1 and Km2 may be found in two separate experiments in which S1 and S2 are varied under saturating conditions of S2 and S1, respectively, so that the second and rst terms in the denominator become vanishingly small. 2.5.6. Examples of Enzyme-Catalyzed Reactions and Their Treatment It is not always immediately apparent from an enzymatic reaction whether it should be treated with single- or dual-substrate enzyme kinetic expressions. Lactose hydrolase, which catalyzes the hydrolysis of lactose according to Lactose H2 O D-Galactose D-Glucose ! 2:33
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is best (and perhaps obviously) treated by simple one-substrate Michaelis Menten kinetics, since H2O may be safely ignored as a second substrate. Glucose oxidase catalyzes a two- substrate reaction, however,
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O2 d-D-Gluconolactone H2 O2 !
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2:34
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and must be treated with two-substrate kinetics; it has been shown that the ping pong mechanism applies in this case. Lactate dehydrogenase (misnamed since it usually functions in the reverse direction and so would be more aptly named pyruvate hydrogenase) represents a yet more complicated system: Pyruvate NADH H L-Lactate NAD ! 2:35
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In this case, the question is whether H should be considered a third substrate. It has, in fact, been treated in this manner by researchers, who have shown that if both pyruvate and NADH concentrations are maintained at saturating levels, the initial rate of the enzymatic reaction is pH dependent, showing a Gaussian-like curve over the pH range 6 8. Data taken on the alkaline side of this curve may be used to obtain a KmH value, or, alternately, the alkaline pH value at Vmax /2 value may be read
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directly from the n versus pH curve. Research has shown that, in general, Vmax /2 occurs at a pH value that is at least two orders of magnitude (two pH units) alkaline of the optimum pH for the reaction, where n Vmax . This nding means that, at the pH optimum, H % 100 KmH , so that the deviation of n from Vmax is <1%. Furthermore, in a buffered solution, [H ] is constant, so that deviations of n from Vmax , even at an unusually narrow pH optimum, appear as constants in the kinetic expressions. It has therefore been concluded that, for all practical purposes, H may be safely ignored as a second or third substrate. It must also be remembered that enzymes have structures that depend on pH. Under excessively acid or alkaline conditions, denaturation of the tertiary protein structure will occur due to disruption of the normal hydrogen bonding modes, and this denaturation will have dramatic effects on enzyme activity. 2.6. ENZYME ACTIVATORS A large variety of chemical and biochemical compounds are known to affect the activity of enzymes without themselves being involved in the enzyme-catalyzed reaction. Activators are species that increase enzyme activity; they may be necessary for the enzyme to possess any catalytic activity (such as a prosthetic group), or they may increase the speci c activity of an already active enzyme (e.g., ions such as Ca2 and Mg2 that interact with phosphate-containing substrates). At constant, saturating levels of substrate(s), increasing concentrations of activator yield increasing initial reaction rates, with a limiting rate reached at high activator concentrations. In some cases, such as for prosthetic group activation, the following sequence of reactions may be used as a model for kinetic descriptions: ! A Einactive Eactive ! ! S Eactive S  Eactive Eactive P 2:36 2:37
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where A represents the activator species. Parallel reaction sequences must be considered if the enzyme is catalytically active in the absence of activator. With the exception of prosthetic group activation, activators are not usually speci c, and several species may have similar activating effects on an enzyme. For example, isocitrate dehydrogenase is activated by both Mn2 and Mg2 ; it has been shown that, in the absence of Mg2 , Mn2 levels as low as 5 ppb may be determined via measurement of isocitrate dehydrogenase activity. Anions are also relatively nonspeci c activators, and the activation of a-amylase by buffer anions (especially Cl ) has been studied in detail. An exception to this nonspeci c ion activation occurs with pyruvate kinase: This enzyme is activated by K , but is inhibited by Na . While activator concentrations may be quantitated through activity assays, the presence of unknown concentrations of activators in samples requiring substrate or enzyme quantitation represents a signi cant source of error. If activators are present or suspected in such samples, activators are added in excess to both samples and calibration standards.
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