Enzymes Lineweaver—Burk plots

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. 

Lineweaver-Burk plot a graphical means for evaluating enzyme kinetics, (p. 638)... 

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. 

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. ... 

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],... 

First draw both Lineweaver-Burk plots and Hanes-Woolf plots for the following a Monod-Wyman-Changeux allosteric K enzyme system, showing separate curves for the kinetic response in (1) the absence of any effectors (2) the presence of allosteric activator A and (3) the presence of allosteric inhibitor I. Then draw a similar set of curves for a Monod-Wyman-Changeux allosteric Uenzyme system. 

According to this expression, a plot of 1/v, versus l/[SJo will yield a straight line if the data follow the Michaelis-Menten mechanism. This line has a slope given by Km/Vmax, a y intercept of 1/Vmax, and an x intercept of -1 fKm. This is also illustrated in Fig. 4-7. Again, this treatment is valid when Eq. (4-107) applies whether or not the catalyst is an enzyme. The Lineweaver-Burk plot, Fig. 4-lb, is convenient for visualization but statistically unreliable for data fitting the form in Eq. (4-107) should be used for numerical analysis. 

Methods of plotting data obtained from enzyme catalyzed reactions, (a) Lineweaver-Burk plot, (b) Eadie or Hofstee plot, (c) Hanes plot. 

The enzymatic activities of intercalated GOx-AM P layered nanocomposites at various pH values and temperatures were compared with the native enzyme in aqueous solution. In both cases, characteristic linear plots consistent with Michalis-Menton kinetics were obtained. The Lineweaver-Burk plots indicated that the reaction rates (Vmax) for free and intercalated GOx (3.3 and 4.0 pM min 1 respectively), were comparable, suggesting that the turnover rate at substrate saturation was only marginally influenced by entrapment between the re-assembled organoclay sheets. However, the dissociation constant (Km) associated with the activity of the enzyme was higher for intercalated GOx (6.63 mM) compared to native GOx (2.94 mM), suggesting... 

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. 

Plotting 1/V versus 1/[S], one obtains a straight line having a slope of Km/Vmax with a y-axis intercept of l/VmAX and an x-intercept of - 1/Km as shown in Figure 2.13. Lineweaver-Burk plots of enzyme activity in the presence of an inhibitor can distinguish the type of inhibitor. Competitive inhibitors have a molecular structure similar to that of the substrate and will alter Km but not VnrAX because they compete with the substrate for binding at the enzyme s active site but do not change the enzyme s affinity for substrate. Noncompetitive inhibitors bear no structural similarity to the substrate but bind the free enzyme or enzyme-substrate... 

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. 

Lineweaver-Burk plot (Figure 8.11). In such cases the chosen substrate concentration must give the highest reaction velocity possible. It is important, when describing any enzyme assay, to report the percentage maximum velocity which the method will give. 

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. 

When data in the presence of an enzyme inhibitor are presented in the form of a Lineweaver-Burk plot, a series of straight lines should be obtained. The slopes of these hnes may or may not change, and the hnes may or may not intersect at a common point. The relationships between slopes, intersection points, and inhibitor mechanisms are outlined later. Further information regarding these mechanisms, including velocity equations describing data obtained in the presence of inhibitors with diverse mechanisms, can be found in (Segel, 1993). 

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. 

From a Lineweaver-Burk plot, the K and of this rate-limiting enzyme were calculated to be 4 X 10" M and 8 X 10 mmol/h, respectively. If the above experiment is repeated in the presence of simvastatin, which of the following values would be obtained ... 

First, the activity of the enzyme was measured and kinetic parameters were determined by Lineweaver-Burk plots, using phenyhnalonic acid as the substrate. The results are summarized in Tabled. Among four mutants, C188S showed a drastic decrease in the activity (k -jt/Kn,). The low activity was due to a decrease in the catalytic tirrnover number (k(.jt) rather than in affinity for the substrate (Km). 

Figure 6. Plot of relative log of apparent versus pH for Ghiioi mutant (filled circles) and wild-type (open circles) xylose isomerases. Apparent values at different pH were determined from a Lineweaver-Burk plot. The scale of relative log Vmax pp indicates the fraction of each experimental value at different pH relative to the maximal value. Both enzymes were stable under the assay conditions used. Reprinted with permission from ref. 22. Copyright 1990 American Society for Biochemistry and Molecular Biology.

Almost all enzymes—in contrast to the simplified description given on p. 92—have more than one substrate or product. On the other hand, it is rare for more than two substrates to be bound simultaneously. In bisubstrate reactions of the type A + B C+D, a number of reaction sequences are possible. In addition to the sequential mechanisms (see p.90), in which all substrates are bound in a specific sequence before the product is released, there are also mechanisms in which the first substrate A is bound and immediately cleaved. A part of this substrate remains bound to the enzyme, and is then transferred to the second substrate B after the first product C has been released. This is known as the ping-pong mechanism, and it is used by transaminases, for example (see p.l78). In the Lineweaver— Burk plot (right see p.92), it can be recognized in the parallel shifting of the lines when [B] is varied. 

Allosteric enzymes shift the target enzyme s saturation curve to the left (see p. 92). In Eadie-Hofstee and Lineweaver-Burk plots (see p. 92), allosteric enzymes are recognizable because they produce curved lines (not shown). 

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. 

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 main plots used in enzyme kinetics and receptor binding studies are the Scatchard plot, the Lineweaver-Burk plot, and the linearization for estimation of the Hill coefficient. This chapter gives a short survey of these transformations of enzyme kinetics or receptor binding data. 

Figure 8.4 The Lineweaver-Burk plot (A) and the Hanes plot (B) of typical enzyme kinetics in presence of a competitve (a) noncompetive (b), mixed type (c) and uncompetitive (d) inhibitor.

The mixed-type inhibitors combine the effects of the competitive and noncompetitive inhibitors binding at the active center decreases the affinity of the enzyme towards the substrate molecule and also decreases the rate of transformation of the bound substrate. In their presence, the straight line plots intersect in the fourth quarter of the Lineweaver-Burk plot, according to equation ... 

Uncompetitive inhibitors can bind to the enzyme-substrate complex only, but not to the free enzyme molecule. The Lineweaver-Burk plots in such cases give parallel straight lines for activity-substrate concentration profiles, measured at different concentrations of the inhibitor (Figure 8.4), according to equation ... 

Scatchard analysis is reliable for the simplest cases, but as with Lineweaver-Burk plots for enzymes, when the receptor is an allosteric protein, the plots deviate from linearity. 

When v0 is plotted against [S], it is not always possible to determine when Vmax has been achieved, because of the gradual upward slope of the hyperbolic curve at high substrate concentrations. However, if 1A/0 is plotted versus 1/[S], a straight line is obtained (Figure 5.11). This plot, the Lineweaver-Burke plot (also called a double-reciprocal plot) can be used to calculate Km and Vmax> as well as to determine the mechanism of action of enzyme inhibitors. 

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