Enzyme reciprocating

This equation successfully describes the kinetic behavior of a surprisingly large number of reac tions of different enzymes. Taking reciprocals of both sides gives ... 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

Reactions that fit this model are called ping-pong or double-displacement reactions. Two distinctive features of this mechanism are the obligatory formation of a modified enzyme intermediate, E, and the pattern of parallel lines obtained in double-reciprocal plots (Figure 14.19). 

A competitive inhibitor and substrate exert reciprocal effects on the concentration of the EI and ES complexes. Since binding substrate removes free enzyme available to combine with inhibitor, increasing the [S] decreases the concentration of the EI complex and raises the reaction velocity. The extent to which [S] must be increased to completely overcome the inhibition depends upon the concentration of inhibitor present, its affinity for the enzyme K-, and the of the enzyme for its substrate. 

For simple noncompetitive inhibition, E and EI possess identical affinity for substrate, and the EIS complex generates product at a negligible rate (Figure 8-10). More complex noncompetitive inhibition occurs when binding of the inhibitor does affect the apparent affinity of the enzyme for substrate, causing the tines to intercept in either the third or fourth quadrants of a double reciprocal plot (not shown). 

In this scheme, EOH is the enzyme, IX is the inhibitor (either a carbamate or an organophosphate). EOH(IX) is analogous to the Michaelis Menton comploc seen with the substrate reaction. EOI is the acyl-enzyme intermediate for carbamates or a phosphoro-enzyme intermediate for the organophosphates. The equilibrium constant for this reaction (K ) is defined as k /k and the phosphorylation or carbamylation constant is defined as k2- In this study 42)y ANTX-A(S) was found to be more specific for AChE than BUChE. The double reciprocal and Dixon plot of the inhibition of electric eel AChE indicated that the toxin is a non-competitive inhibitor decreases, k remains unchanged) (Figure 2). 

Figure 3. Plot of V against total enzyme [ET] showing the irreversible inhibition of el tric eel acetylcholinesterase (AChE) by ANTX-A(S). The enzymes were incubated with 0.32 fig/mL ANTX-A(S) for 1.0 min and acetylthiocholine (final concentrations 2.5, 4.7, 6.3, and 7.8 X 10 M) was added. V was determined from the double reciprocal plots (not shown). Key (o) control ( ) ANTX-A(S). (Reproduced with permission from Ref. 42. Copyright 1987 Pergamon Press)...

When the initial LA concentration is large, the quantity of substrate transferred to the aqueous phase allows the lipoxygenation to progress. This reaction consumes LA and produces HP, which favor the transfer of residual substrate between the two phases. Then catalysis and transfer have a reciprocal influence on each other. We demonstrated that the use of a non-allosteric enzyme in a compartmentalized medium permits the simulation of a co-operativity phenomenon. The optimal reaction rate in the two-phase system is reached for a high initial LA concentration 14 mM. Inhibition by substrate excess is observed in two-phase medium. 

We can now relate the kinetic constants kCM, Ku, and kcJKM to specific portions of the enzyme reaction mechanism. From our discussions above we have seen that the term kCM relates to the reaction step of ES conversion to ES. Hence experimental perturbations (e.g., changes in solution conditions, changes in substrate identity, mutations of the enzyme, and the presence of a specific inhibitor) that exclusively affect kCM are exerting their effect on catalysis at the ES to ES transition step. The term KM relates mainly to the dissociation reaction of the encounter complex ES returning to E + S. Conversely, the reciprocal of Ku (1IKU) relates to the association step of E and S to form ES. Inhibitors and other perturbations that affect the... 

Figure 3.3 Substrate titration of steady state velocity for an enzyme in the presence of a competitive inhibitor at varying concentrations. (A) Untransformed data (B) data as in (A) plotted on a semilog scale (C) data as in (A) plotted in double reciprocal form. For all three plots the data are fit to Equation (3.1).

Mutual exclusivity can also be tested for by the effects of combinations of two inhibitors on the activity of a target enzyme. The advantage of this approach is that it does not require any special labeling of either compound, and only catalytic quantities of enzyme are required for the studies. There are a number of graphical methods that can be used to determine the effects of inhibitor combinations on enzyme velocity (see Copeland, 2000). The most popular of these was introduced by Yonetani and Theorell (1964) and is based on the following reciprocal equation ... 

Figure 7.6 Double reciprocal plot for a tight binding competitive enzyme inhibitor, demonstrating the curvature of such plots. The dashed lines represent an attempt to fit the data at lower substrate concentrations to linear equations. This highlights how double reciprocal plots for tight binding inhibitors can be misleading, especially when data are collected only over a limited range of substrate concentrations.

If the inhibitor combines with an enzyme form different from one with which the variable substrate combines, the vertical intercept of the corresponding reciprocal plot will be affected. 

First-order rate constants are used to describe reactions of the type A — B. In the simple mechanism for enzyme catalysis, the reactions leading away from ES in both directions are of this type. The velocity of ES disappearance by any single pathway (such as the ones labeled k2 and k3) depends on the fraction of ES molecules that have sufficient energy to get across the specific activation barrier (hump) and decompose along a specific route. ES gets this energy from collision with solvent and from thermal motions in ES itself. The velocity of a first-order reaction depends linearly on the amount of ES left at any time. Since velocity has units of molar per minute (M/min) and ES has units of molar (M), the little k (first-order rate constant) must have units of reciprocal minutes (1/min, or min ). Since only one molecule of ES is involved in the reaction, this case is called first-order kinetics. The velocity depends on the substrate concentration raised to the first power (v = /c[A]). 

The turnover number, or kCM (pronounced kay kat ), is another way of expressing Vmax. It s Vmax divided by the total concentration of enzyme (Vmax/E,). The kcat is a specific activity in which the amount of enzyme is expressed in micromoles rather than milligrams. The actual units of kcat are micromoles of product per minute per micromole of enzyme. Frequently, the micromoles cancel (even though they re not exactly the same), to give you units of reciprocal minutes (min-1). Notice that this has the same units as a first-order rate constant (see later, or see Chap. 24). The kcat is the first-order rate constant for conversion of the enzyme-substrate complex to product. For a very simple mechanism, such as the one shown earlier, kcat would be equal to k3. For more complex... 

The useful thing about the Lineweaver-Burk transform (or double reciprocal) is that the y intercept is related to the first-order rate constant for decomposition of the ES complex to E + P (7ccat or Vmax) and is equal to the rate observed with all of the enzyme in the ES complex. The slope, in contrast, is equal to the velocity when the predominant form of the enzyme is the free enzyme, E (free meaning unencumbered rather than cheap). 

At low concentrations of substrate ([S] < Km), the enzyme is predominantly in the E form. The competitive inhibitor can combine with E, so the presense of the inhibitor decreases the velocity when the substrate concentration is low. At low substrate concentration ([S] < Km), the velocity is just Vmay IKm. Since the inhibitor decreases the velocity and the velocity at low substrate concentration is proportional to Vmax/Km, the presence of the inhibitor affects the slopes of the Lineweaver-Burk plots the slope is just the reciprocal of Vmax/Km. Increasing the inhibitor concentration causes Km/Vmax to increase. The characteristic pattern of competitive inhibition can then be rationalized if you simply remember that a competitive inhibitor combines only with E. 

At very low substrate concentration ([S] approaches zero), the enzyme is mostly present as E. Since an uncompetitive inhibitor does not combine with E, the inhibitor has no effect on the velocity and no effect on Vmsa/Km (the slope of the double-reciprocal plot). In this case, termed uncompetitive, the slopes of the double-reciprocal plots are independent of inhibitor concentration and only the intercepts are affected. A series of parallel lines results when different inhibitor concentrations are used. This type of inhibition is often observed for enzymes that catalyze the reaction between two substrates. Often an inhibitor that is competitive against one of the substrates is found to give uncompetitive inhibition when the other substrate is varied. The inhibitor does combine at the active site but does not prevent the binding of one of the substrates (and vice versa). 

An analysis of the influence of errors shows clearly that the double-reciprocal plot according to Lineweaver-Burk [32] is the least suitable. Although it is by far the most widely used plot in enzyme kinetics, it cannot be recommended, because it gives a grossly misleading impression of the experimental error for small values of v small errors in v lead to enormous errors in 1/y but for large values of v the same small errors in v lead to barely noticeable errors in 1/17 [23]. Due to the error distribution, that is much more uniform, the plot according to Hanes (Eq. (7)), is the most favored. 

We point out that in enzyme kinetics TON is understood as TOF It is also sometimes called the turnover number, because it is a reciprocal time and defines the number of catalytic cycles (or turnovers ) that the enzyme can undergo in unit time, or the number of molecules of substrate that one molecule of enzyme can convert into products in one unit of time. Quotation from [23]. 

As discussed above, the degree of inhibition is indicated by the ratio of k3/k and defines an inhibitor constant (Kj) [Eq. (3.19)], whose value reports the dissociation of the enzyme-inhibitor complex (El) [Eq. (3.20)]. Deriving the equation for competitive inhibition under steady-state conditions leads to Eq. (3.21). Reciprocal plots of 1/v versus 1/5 (Lineweaver-Burk plots) as a function of various inhibitor concentrations readily reveal competitive inhibition and define their characteristic properties (Fig. 3.5). Notice that Vmax does not change. Irrespective of how much competitive inhibitor is present, its effect can be overcome by adding a sufficient amount of substrate, i.e., substrate can be added until Vmax is reached. Also notice that K i does change with inhibitor concentration therefore the Km that is measured in the presence of inhibitor is an apparent Km- The true KM can only be obtained in the absence of inhibitor. 

FIGURE 3.5 Reciprocal plot of the rate of substrate turnover by an enzyme in the presence of different concentrations of competitive inhibitor. 

A reciprocal plot of the effect of varying concentrations of a noncompetitive inhibitor on enzyme-catalyzed substrate turnover readily reveals the nature and characteristics of this type of inhibition (Fig. 3.6). Notice that in this case, the properties that characterize noncompetitive inhibition are virtually opposite of those that characterize competitive inhibition. With a noncompetitive inhibitor Emax does change but KM is constant. 

PDH is a multi-enzyme complex consisting of three separate enzyme units pyruvate decarboxylase, transacetylase and dihydrolipoyl dehydrogenase. Serine residues within the decarboxylase subunit are the target for a kinase which causes inhibition of the PDH the inhibition can be rescued by a phosphatase. The PDH kinase (PDH-K) is itself activated, and the phosphatase reciprocally inhibited, by NADH and acetyl-CoA. Figure 3.12(a and b) show the role and control of PDH. 

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