For competitive inhibition

Show that for competitive inhibition the equation for the rate of reaction is... 

Plot both sets of data as a Lineweaver-Burk plot for competitive inhibition (see Fig. 

These three classes of inhibition can be distinguished by virtue of the effect of variations in inhibitor concentration on the slopes and intercepts of reciprocal plots. For competitive inhibition only the slope varies. For uncompetitive inhibition only the intercept varies, while for noncompetitive inhibition both the slope and the intercept vary. 

Wilderdyke, M.R., Smith, D.A. and Brashears, M.M. (2004) Isolation, identification, and selection of lactic acid bacteria from alfalfa sprouts for competitive inhibition of foodbome pathogens. Journal of Food Protection, 67, 947-951. 

Figure 8 Plot of the initial rate of the enzyme-catalyzed oxidation of 1-phenylpropanol as a function of % ee. The solid line represents a fit of the data to the Michaelis-Menten formalism for competitive inhibition where [S] = [ -(60)] and [ ] = [ -(60)]. The total alcohol concentration was maintained constant at lOmM.100...

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. 

For competitive inhibition, the intrinsic clearance of a substrate by an inhibited enzyme can be described with the following equation ... 

Furthermore, we can account for additional competitive inhibition by metabolites I by assuming a polynomial of the form F(S,P,I,Km). In this case, the intervals for competitive inhibition correspond to the intervals obtained for the products of a reaction. 

Reactions proceeding through S CD inclusion complexes should show competitive inhibition (Fersht, 1985) in the presence of additives which bind in the CD cavity. Such behaviour has been observed for the cleavage of mNPA by a-CD (VanEtten et al., 1967a) and by /3-CD (Tee and Hoeven, 1989), supportive of the mechanism in Scheme 2A. In sharp contrast, with many potential inhibitors, the cleavage of pNPA is not retarded to the extent expected for competitive inhibition, and in a few cases slight rate enhancements are observed (Tee and Hoeven, 1989 Tee et al., 1993b). 

Use the data in the table above to plot Michaelis-Menten, Lineweaver-Burke and Eadie-Hofstee graphs to determine Km and Vm DC values. State the type of inhibitor which is present. Calculate the K based on Equations 2.10 (for competitive inhibition) or 2.11 (non-competitive inhibition) asappropriate assuming the [I] = 10mmol/l. 

Figure 3. Kinetics of conq)etitivc inhibition of Clostridium thermohydrosuljur-icum strain 39E purified amylopuUulanase activity with mixed substrates. The solid lines A and C indicate the theoretical plots for competitive inhibition at amylose ccmcentrations of 0.6 and 2.4 mg/ml, respectively. Lines B and D are the theoretical plots for the absence of inhibition at the same respective amylose ccmcentrations. PuUulan was used at concentrations of 0.4, 0.8, 1.2, 1.6, 2.0, 2.4 mg/ml. For clarity, only two sets of data points were used in the above plot. ( ) and (A) are the practical data points obtained at 0.6 and 2.4 mg/ml amylose concentrations. All reaction mixtures contained 5% (v/v) dimethyl sulfoxide for solubility of amylose. [S] = [A] + [P], where S is the total substrate ccmcentration. A and P are the concentrations of amylose and pullulan, respectively. (Reproduced with permissiem from Ref. 13. Copyright 1990 Academic Press, Inc.)...

The intersecting line pattern observed for competitive inhibition (top plot) can be distinguished from the action of a noncompetitive inhibitor characterized by K, = Ka. However, if K, is much less than Ka, the observed pattern cannot be distingished. 

Keller and coworkers341 proposed that tunicamyein is a reversible, tight-binding, and, therefore, competitive inhibitor of the GlcNAc 1-P transferase. The association rate-constant was 7 x 104 M s 1 (at 23°). Inhibition can be overcome by increasing the proportion of enzyme, and, because preincubation of the enzyme with UDP-GlcNAc prevented inhibition by tunicamyein,341 some experimental support for competitive inhibition was obtained. The known affinity of the antibiotic for phosphonolipids323 may facilitate its access to the membrane-bound enzyme, but the lipids do not prevent inhibition of the enzyme by tunicamyein.340... 

Another action of phenothiazines is to compete with NADPH for the oxidase, an inference which was based on fulfillment of the criteria for competitive inhibition in double reciprocal plots of 1/[NADPH] vs. 1/rate of formation of O in the presence and absence of inhibitor It seems worth considering that all the effects of phenothiazines might be mediated through this effect and that the process of activation represents the presentation of substrate to the enzyme from which, in the resting state, the substrate is kept separate. 

Deriving a Rate Equation for Competitive Inhibition The rate equation for an enzyme subject to competitive inhibition is... 

A commonly used test for competitive inhibition is to plot 1 / v vs 1 / [S] (Eq. 9-61), both in the absence of inhibitor and in the presence of one or more fixed concentrations of I. The result, in each case, is a family of lines of varying slope (Fig. 9-10) that converge on one of the axes at the value 1/Vmax. We see that the maximum velocity is unchanged by the presence of inhibitor. If sufficient substrate is added, the enzyme will be saturated with substrate and the inhibitor cannot bind. The value of Kt can be calculated using Eq. 9-61 from the change in slope caused by addition of inhibitor. 

Product inhibition (Section A,12) can also provide information about mechanisms. For example, if 1 / v is plotted against 1 / [A] in the presence and absence of the product Q, the product will be found to compete with A and to give a typical family of lines for competitive inhibition. On the other hand, a plot of 1 / v vs 1 / [B] in the presence and absence of Q will indicate noncompetitive inhibition if the binding of substrates is ordered (Eq. 9-43). In other words, only the A-Q pair of substrates are competitive. Product inhibition is also observed with enzymes having ping-pong kinetics (Eq. 9-47) as a result of formation of nonproductive complexes. 

The steady state solution has the Michaelis-Menten form for competitive inhibition... 

One standard equation for competitive inhibition is given in Eq. (6). This equation shows that the presence of the inhibitor modifies the observed Km but not the observed Vm. A double reciprocal plot gives an x intercept of — 1 Km and a y intercept of 1/Vrn. 

For IC5o determinations, the substrate concentration should be close to the Am for the marker reaction. As discussed previously, this choice of substrate concentration allows an estimate of the A) value because IC50 = 2A) for competitive inhibition and IC50 = A, for noncompetitive inhibition. For A) determinations, a common substrate concentration scheme is Am/3, Am, 3Am, 6Am, and 10Am. Assuming that the Km for the reaction has been accurately determined, this range of substrate concentrations will provide an adequate spread of data on an Eadie-Hofstee plot to readily observe the mechanism of direct inhibition. For some substrates, solubility can become limiting at concentrations >2Am. In such cases, it becomes necessary to choose alternate concentrations so that no fewer than five concentrations are used in a A, determination. The choice of substrate... 

Table 3. Constants for competitive inhibition of acid phosphatases by phosphate and its analogues8...

There may be observed a noncompetitive type of inhibition in which it is assumed that the inhibitor S operates cither by being sorbed on a site adjacent to the substrate, where it slows down the rate-controlling step 3, or inhibiting the sorption of a coenzyme or other species on this adjacent site. The rate expressions in such a case have a form different from that just given for competitive inhibitions. ... 

For competitive inhibition with single-step external pathway, eqn 8.65 is directly applicable, except that the inhibitor concentration replaces that of the free ligand. For noncompetitive inhibition by reaction with Xj5 A must be replaced by Djj, the sum of the elements of row j +1 of the Christiansen matrix. Both cases are covered by ... 

Here, Km is the equilibrium constant of the inhibition reaction inh + Xj — S, and index j refers to the cycle member with which the inhibitor reacts (j = 0 for competitive inhibition, and j 0 for noncompetitive inhibition). The extension to external pathways consisting of more than one step is as in eqn 8.67. 

Fig. 2.—Graphical Determination of the Maximum Velocity, V, and the Michaelis Constant, K . [(o) v against [S] (f>) t) against[S], Lineweaver—Burk plot (c) a Line-weaver—Burk plot for competitive inhibition (d) a Lineweaver—Burk plot for noncompetitive inhibition.]...

Competitive inhibitors. A competitive inhibitor often has structural features similar to those of the substrates whose reactions they inhibit. This means that a competitive inhibitor and enzyme s substrate are in direct competition for the same binding site on the enzyme. Consequently, binding of the substrate and the inhibitor are mutually exclusive. A kinetic scheme for competitive inhibition is shown in Equation 17.15. 

Potential interactions through the cytochrome P450 CYP 2D6 and CYP 3A4 enz)unes can be noted from Tables 19.2a and 19.2b. The combination of drugs that are substrates of the same enzyme creates potential for competitive inhibition of their metabolism with unexpected elevation of plasma concentration. Similarly, potent inhibitors, e.g. fluoxetine and paroxetine (CYP 2D6), fluoxetine and nefazodone (CYP 3A4) and fluvoxamine (CYP 1A2), may cause adverse effects by reducing metabolic breakdown of co-prescribed drugs that are used in standard doses. Antidepressants are commonly prescribed with antipsychotics in a depressive... 

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