Double reciprocal plots inhibitors

Double Reciprocal Plots Facilitate the Evaluation of Inhibitors... 

Double reciprocal plots distinguish between competitive and noncompetitive inhibitors and simpbfy evaluation of inhibition constants Aj. v, is determined at several substrate concentrations both in the presence and in the absence of inhibitor. For classic competitive inhibition, the lines that connect the experimental data points meet at they axis (Figure 8-9). Since they intercept is equal to IIV, this pattern indicates that wben 1/[S] approaches 0, Vj is independent of the presence of inhibitor. Note, however, that the intercept on the X axis does vary with inhibitor concentration—and that since is smaller than HK, (the apparent... 

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). 

Stem juice of Dieffenbachia maculata contains an inhibitor of fungal polygalacturonase. The inhibitor is non dializable and heat stable. The double reciprocal plot indicates that the inhibitor causes a mixed type of inhibition. The paper also describes the distribution of the inhibitor in different varieties of Dieffenbachia, and some of its properties. 

For compounds that conform to the mechanism of scheme C, an alternative method for defining inhibition modality is to measure progress curves (or preincubation effects vide supra) at varying inhibitor and substrate concentrations, and to then construct a double reciprocal plot of 1/v, as a function of l/[.Sj. Using the analysis methods and equations described in Chapter 3, one can then determine the modality of inhibition for the inhibitor encounter complex. Similarly, for inhibitors that conform to the mechanism of scheme B, a double reciprocal plot analysis of l/vs as a function of 1/[S] can be used to define inhibition modality. 

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.

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). 

When plotted on double reciprocal axes, inhibitor data for full inhibitory mechanisms cannot be distinguished easily from those for partial inhibitory mechanisms. However, with suitable data, careful inspection of Lineweaver-Burk plots may reveal subtle differences these become clear in secondary plots (replots) of slopes or intercepts, as shown later. The use of Ks rather than Km (later) reflects the convention employed by Segel (1993) as has been discussed earlier, this dissociation constant provides a good indication of the value of Km if rapid equilibrium conditions exist. 

Rule 1. Upon obtaining a double-reciprocal plot of 1/v vx. 1/[A] (where [A] is the initial substrate concentration and V is the initial velocity) at varying concentrations of the inhibitor (I), if the vertical intercept varies with the concentration of the reversible inhibitor, then the inhibitor can bind to an enzyme form that does not bind the varied substrate. For example, for the simple Uni Uni mechanism (E + A EX E -P P), a noncompetitive or uncompetitive inhibitor (both of which exhibit changes in the vertical intercept at varying concentrations of the inhibitor), I binds to EX, a form of the enzyme that does not bind free A. In such cases, saturation with the varied substrate will not completely reverse the inhibition. 

A limiting case of noncompetitive inhibition, characterized by f/iird-quadrant convergence of double-reciprocal plots of 1/v versus 1/[S] in the absence and presence of several constant levels of the inhibitor. 

Depressed catalytic activity occurring when an inhibitor binds more than once to a single enzyme form (or forms). While standard double-reciprocal plots are usually linear, secondary replots of the data (i.e., plots of slopes and/or intercepts vx. [I], the concentration of the inhibitor) will be nonlinear depending on the relative magnitude of the [I], [If,. .., and [If terms in the rate expression. 

Consider the standard Uni Uni mechanism (E + A EX E + P). A noncompetitive inhibitor, I, can bind reversibly to either the free enzyme (E) to form an El complex (having a dissociation constant K s), or to the central complex (EX) to form the EXl ternary complex (having a dissociation constant Xu). Both the slope and vertical intercept of the standard double-reciprocal plot (1/v vx. 1/[A]) are affected by the presence of the inhibitor. If the secondary replots of the slopes and the intercepts (thus, slopes or vertical intercepts vx [I]) are linear (See Nonlinear Inhibition), then the values of those dissociation constants can be obtained from these replots. If Kis = Xu, then a plot of 1/v vx 1/[A] at different constant concentrations of the inhibitor will have a common intersection point on the horizontal axis (if not. See Mixed-Type Inhibition). Note that the above analysis assumes that the inhibitor binds in a rapid equilibrium fashion. If steady-state binding conditions are present, then nonlinearity may occur, depending on the magnitude of the [I] and [A] terms in the rate expression. See also Mixed Type Inhibition... 

This term usually applies to reversible inhibition of an enzyme-catalyzed reaction in which nonlinearity is detected (a) in a double-reciprocal plot (i.e., 1/v versus 1/ [S]) in the presence of different, constant concentrations of inhibitor or (b) in replots of slope or intercept values obtained from primary plots of 1/v versus 1/[S]). Nonline-... 

This type of inhibition differs from that exhibited by classical competitive inhibitors, because the substrate can still bind to the El complex and the EIS complex can go on to form product (albeit at a slower rate) without the inhibitor being released from the binding site. While standard double-reciprocal plots of partial competitive inhibitors will be linear (except for some steady-state, i.e., non-rapid-equilibrium, cases), secondary slope replots will be nonlinear. See Nonlinear Inhibition... 

In the examples above, the secondary plots utilized the slopes or intercepts of the original plot. However, replots are secondary plots for any functional dependency using data obtained from a primary graphing procedure. Secondary replots can also be used with inhibition studies. In these cases, the slope or intercept of a double-reciprocal plot is graphed as a function of the inhibitor concentration. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

However, note that is replaced with Xia (the dissociation constant of A for the free enzyme) in the rapid-equilibrium equation. A standard double-reciprocal plot (1/v v. 1/[A]) at different concentrations of inhibitor will yield a series of parallel lines. A vertical intercept v. [I] secondary replot will provide a value for X on the horizontal axis. If questions arise as to whether the lines are truly parallel, one possibility is to replot the data via a Hanes plot ([A]/v v. [A]). In such a plot, the lines of an uncompetitive inhibitor intersect on the vertical axis. 

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. 

The double-reciprocal plot (see Box 6-1) offers an easy way of determining whether an enzyme inhibitor is competitive, uncompetitive, or mixed. Two sets of rate experiments are carried out, with the enzyme concentration held constant in each set. In the first set, [S] is also held constant, permitting measurement of the effect of increasing inhibitor concentration [I] on the initial rate V0 (not shown). In the second set, [I] is held constant but [S] is varied. The results are plotted as V0 versus 1/[S]. 

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. 

Figure 9-10 Effect of a competitive inhibitor on the Eadie-Hofstee plot (top) and on a double reciprocal plot (bottom). The apparent Km (Eq. 9-59) is increased by increasing [ I ], but E.naxis unchanged.

Competitive inhibition. A series of double-reciprocal plots (1/v versus 1/[S]) measured at different concentrations of the inhibitor (I) all intersect at the same point (on the ordinate. The slopes of the plots and the intercepts on the abscissa are simple, linear functions of [IJ/A j, where K, is the dissociation constant of the inhibitor-enzyme complex. 

Figure 12. Plot of the slopes of the double-reciprocal plots versus inhibitor (Tris) concentration. Adapted from data of Nelson et al. ( ll).

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. 

Two other examples of sigmoidal reactions that are made linear by an activator include a report by Johnson et al. (31), who showed that pregnenolone has a nonlinear double-reciprocal plot that was made linear by the presence of 5 pM 7,8-benzoflavone, and Ueng et al. (23), who showed that aflatoxin B1 has sigmoidal saturation curve that is made more hyperbolic by 7,8-benzoflavone. As with the effect of quinine on carbamazepine metabolism, 7,8-benzoflavone is an activator at low aflatoxin B1 concentrations and an inhibitor at high aflatoxin B1 concentrations. 

The characteristics of the double reciprocal plots given by Equation (5.149), Equation (5.154), and Equation (5.155) determine what kind of enzyme inhibition may occur competitive, noncompetitive, or uncompetitive. In a given concentration of enzyme and inhibitor, the substrate concentration is changed and the double reciprocal plot of 1/V against 1/[A] is drawn. Figure 5.24a illustrates the double... 

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