Lineweaver-Burk plot, enzyme inhibition

Michaelis-Menten Kinetics Lineweaver-Burk Plots Enzyme Inhibition... 

Figure 3-5. Lineweaver-Burk plots for inhibition of an enzyme-catalyzed reaction. Km and Vm L> the altered values representing the effect of the inhibitors.

The three reversible mechanisms for enzyme inhibition are distinguished by observing how changing the inhibitor s concentration affects the relationship between the rate of reaction and the concentration of substrate. As shown in figure 13.13, when kinetic data are displayed as a Lineweaver-Burk plot, it is possible to determine which mechanism is in effect. 

Competitive and non-eompetitive inhibitions are easily distinguishable from the Lineweaver-Burk plot. In the ease of eompetitive inhibitors, the intereept on tlie 1/Cg axis inereases while tlie intereept of tlie 1/v axis remains unehanged by the addition of the inhibitor. Conversely, with a non-eompetitive inhibitor, only the 1/v axis intereept inereases. The effeet of eompetitive inhibitors ean be reversed by inereasing the substrate eoneentration. Where the enzyme or the enzyme substrate eomplex is made inaetive, a non-eompetitive inhibitor deereases of the enzyme, but remains eonstant. 

Pure noncompetitive inhibition occurs if Ki = Ki. This situation is relatively uncommon the Lineweaver-Burk plot for such an instance is given in Eigure 14.15. Note that K is unchanged by I (the x-intercept remains the same, with or without I). Note also that Tmax decreases. A similar pattern is seen if the amount of enzyme in the experiment is decreased. Thus, it is as if I lowered [E],... 

Enzymes can be used not only for the determination of substrates but also for the analysis of enzyme inhibitors. In this type of sensors the response of the detectable species will decrease in the presence of the analyte. The inhibitor may affect the vmax or KM values. Competitive inhibitors, which bind to the same active site than the substrate, will increase the KM value, reflected by a change on the slope of the Lineweaver-Burke plot but will not change vmax. Non-competitive inhibitors, i.e. those that bind to another site of the protein, do not affect KM but produce a decrease in vmax. For instance, the acetylcholinesterase enzyme is inhibited by carbamate and organophosphate pesticides and has been widely used for the development of optical fiber sensors for these compounds based on different chemical transduction schemes (hydrolysis of a colored substrate, pH changes). 

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. 

Figure 10.4 Lineweaver-Burk plot illustrating comparison of competitive inhibition with no inhibition of enzyme activity...

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 8.11 Substrate inhibition. The enzyme L-amino acid oxidase (EC 1. 4. 3. 2) suffers substrate inhibition at concentrations of L-leucine above 3.0 mmol 1 1. A Lineweaver-Burk plot shows the characteristic bend to the usual straight line.

For example, experimental data might reveal that a novel enzyme inhibitor causes a concentration-dependent increase in Km, with no effect on and with Lineweaver-Burk plots indicative of competitive inhibition. Flowever, even at very high inhibitor concentrations and very low substrate concentrations, it is observed that the degree of inhibition levels off when some 60% of activity still remains. Furthermore, it has been confirmed that only one enzyme is present, and all appropriate blank rates have been accounted for. It is clear that full competitive inhibition cannot account for such observations because complete inhibition can be attained at infinitely high concentrations of a full competitive inhibitor. Thus, it is likely that the inhibitor binds to the enzyme at an allosteric site. 

Full and partial competitive inhibitory mechanisms, (a) Reaction scheme for full competitive inhibition indicates binding of substrate and inhibitor to a common site, (b) Lineweaver-Burk plot for full competitive inhibition reveals a common intercept with the 1/v axis and an increase in slope to infinity at infinitely high inhibitor concentrations. In this example, Ki = 3 pM. (c) Replot of Lineweaver-Burk slopes from (b) is linear, confirming a full inhibitory mechanism, (d) Reaction scheme for partial competitive inhibition indicates binding of substrate and inhibitor to two mutually exclusive sites. The presence of inhibitor affects the affinity of enzyme for substrate and the presence of substrate affects the affinity of enzyme for inhibitor, both by a factor a. (e) Lineweaver-Burk plot for partial competitive inhibition reveals a common intercept with the 1/v axis and an increase in slope to a finite value at infinitely high inhibitor concentrations. In this example, Ki = 3 pM and = 4. (f) Replot of Lineweaver-Burk slopes from (e) is hyperbolic, confirming a partial inhibitory mechanism... 

O Figure 4-10a shows a reaction scheme for interactions of enzyme and substrate with a full noncompetitive inhibitor. The inhibitor interacts with a site distinct from the active site, and the ESI complex is incapable of yielding product. It is thus possible, at saturating concentrations of inhibitor, to drive all enzymes to a nonproductive form, and so activity can be completely inhibited. Furthermore, the affinity of the inhibitor for the saturable allosteric inhibitory site remains independent of substrate concentration. A Lineweaver-Burk plot (O Figure 4-1 Ob) reveals a common intersection point on the 1/ [ S] axis for the data obtained at different inhibitor concentrations. It can be seen that as inhibitor concentration increases toward infinity, the slope of the Lineweaver-Burk plot increases toward infinity. Thus, a replot of the slopes versus inhibitor concentrations (O Figure 4-lOc) generates a straight line, which intersects the [i] axis at a value equal to —Ki. 

In partial (hyperbohc) mixed inhibition (O Figure 4-12d), binding of inhibitor to a site distinct from the active site results in altered affinity of enzyme for substrate (by a factor, ot) as well as a change (by a factor, /i) in the rate at which product can be released from ESI. The effects of a partial mixed inhibitor on a Lineweaver-Burk plot depend upon the actual values, and on the relative values, of ot and fl. Once again, inhibitor plots can intersect the control plot above or below, but not on, the oeaxis, and to the left or to the right of, but not on, the y-axis. Because Vmax cannot be driven to zero, a maximum Lineweaver-Burk slope is reached at infinitely high inhibitor concentrations beyond which no further increase occurs. 

Once the four anionic fractions were isolated (Bi, B2, Xi, X2), their activities were investigated using ferulic or / -fluoroferulic isopropylamine salts as substrates. Rates were plotted as a function of substrate concentration. The Lineweaver-Burk plots obtained (Fig. 4) were not always strictly linear as already reported in the case of ferulic acid and scolopetin oxidation (10,11)- An estimation was made of the apparent Km using the linear part of the plots and results were compared with those obtained for TMB. The values found in this case were in the same order of magnitude, about 0.5 X 10-3 to 1 x 10-3 M. In all extracts, / -fluoroferulic salt inhibited enzyme activity for concentrations higher than 0.25 X 10-2 M. 

A. Effect of a competitive inhibitor on the reaction velocity (v0) versus substrate [S] plot. B. Lineweaver-Burke plot of competitive inhibition of an enzyme. 

Second, an enzyme assay may be used to measure the kinetic properties of an enzyme such as Ku, Vmax, and inhibition characteristics. In this situation, different experimental conditions must be used. If Ku for a substrate is desired, the assay conditions must be such that the measured initial rate is first order in substrate. To determine Ku of a substrate, constant amounts of enzyme are incubated with varying amounts of substrate. A Lineweaver-Burk plot (1/v vs. 1/[S]) or direct linear plot may be used to determine Ku and V. If a reaction involves two or more substrates, each must be evalu-... 

Flo. 5.14. Graphical representation of enzyme inhibition, (a) Eadie-Hofstee and (b) Lineweaver-Burk plots of different types of inhibition. The bold line indicates initial reaction rate in the absence of the inhibitor the lighter lines show initial rates in the... 

Uncompetitive inhibition has seldom been reported in studies of xenobiotic metabolism. It occurs when an inhibitor interacts with an enzyme-substrate complex but cannot interact with free enzyme. Both Km and Vmax change by the same ratio, giving rise to a family of parallel lines in a Lineweaver-Burke plot. 

An uncompetitive inhibitor is much like a noncompetitive inhibitor except that an uncompetitive inhibitor binds only the enzyme-substrate complex (Scheme 4.14). The inhibitor-bound ternary complex cannot form product. Uncompetitive inhibitors cause both Vmax and Km to decrease by the same factor (Figure 4.17). Because the slope of a Lineweaver-Burk plot is Km/Vmxi, the slope of the line of an inhibited enzyme is unchanged from the uninhibited enzyme.4... 

Fig. 2. The characteristics of competitive inhibition, (a) A competitive inhibitor competes with the substrate for binding at the active site (b) the enzyme can bind either substrate or the competitive inhibitor but not both (c) Lineweaver-Burk plot showing the effect of a competitive inhibitor on Km and Vmax.

Allopurinol is a drug given to gout sufferers. It inhibits an enzyme of the purine degradation pathway called xanthine oxidase by acting in the capacity of a substrate. However, its product, oxidized allopurinol, is not able to leave the active site of the enzyme, thus blocking it. Is there a name for this type of substrate What inhibition kinetics would you observe with a Lineweaver-Burk plot, and why ... 

An inhibition of an Mg2+ ATPase on corn root plasma membrane was also observed. Kinetic data on aluminum inhibition present a competitive pattern, as demonstrated by the Lineweaver-Burk plot with an apparent inhibition constant (K,) of 40 pM [44]. These results were obtained at pH 6.6. The authors suggested that the inhibition may be a result of either the formation of an inefficient substrate (Al-ATP) or an interaction directly with the enzyme structure. 

The inhibitor constants, Kj, may be determined by measuring the variation of v with [S] at different concentrations of the inhibitor. Lineweaver—Burk plots can then be used to find K/ from measurements made in the presence, and absence, of inhibitor (see Fig. 2 and Table I). The kinetics of the inhibition of such enzymes as alpha-amylase, hefo-amylase, and phosphorylase have been studied, and inhibitor constants evaluated. 

It can be seen from this equation that competitive inhibitors have no effect on the Vmax of the enzyme, but alter the apparent Km. In the presence of inhibitor, Km will be increased by a factor of (1 + /K ). Lineweaver-Burk plots constructed at various inhibitor concentrations provide a useful diagnostic for this type of inhibition. Figure 2.13 shows that identical y intercepts (l/Vmax) are obtained at different inhibitor concentrations, while x intercepts (reciprocal of apparent Km) decrease with increasing [I], and are equal to — / Km + [1]/ ). ... 

Fig. 3. p-Glucosidase inhibition shown by Lineweaver-Burk plot (reproduced from [2]). Lineweaver-Burk plot of kinetic data from peak 2 cellobiase ((3-glucosidase) at several product inhibitor levels. This is an example of noncompetitive inhibition where the product is not only completing for binding in the active site but also binding to a secondary site on the enzyme that alters the enzyme catalytic ability... 

Figure 7-13 Lineweaver-Burk plots fur three types of enzyme inhibition.

Which of these plots should be used To generally understand the behavior of enzymes, use the simple graph of initial velocity against substrate concentration. The linearized forms are useful for calculation of ATM and Fmax. The Lineweaver-Burke plot is useful for distinguishing between types of inhibition (Chapter 8). The Eadie-Hofstee plot is better than the Lineweaver-Burke plot at picking up deviations from the Michaelis-Menten equation. 

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