X reciprocal plot

The calculated binding constants assuming a 1 1 interaction are listed in Table 3. There is a clear difference between the plotting methods. Only by using the x-reciprocal plot does it become clear that there seem to be higher order equilibria between the compounds. The nonlinear regression leads to similar results as with the y-reciprocal fit. The double reciprocal... 

Equation 1-111 is known as the Lineweaver-Burk or reciprocal plot. If the data fit this model, a plot of l/V versus 1/Cg will he linear with a slope K /V x intercept l/V x-... 

FIGURE 5.19 Method of Barlow for measurement of affinity of a partial agonist, (a) Guinea pig ileal smooth muscle contraction to histamine (filled circles) and partial histamine receptor agonist E-2-P (N,N-diethyl-2-(l-pyridyl)ethylamine (open circles). Dotted lines show equiactive concentrations of each agonist used for the double reciprocal plot shown in panel b. (b) Double reciprocal plot of equiactive concentrations of histamine (ordinates) and E-2-P (abscissae). Linear plot has a slope of 55.47 and an intercept of 1.79 x 10s. This yields a KB (1 — tp/ta) = 30.9 pM. (c) Variant of double reciprocal plot according to Equation 5.8. (d) Variant of double reciprocal plot according to Equation 5.10. Data redrawn from [10],... 

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... 

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)...

For either of the ternary complex mechanisms described above, titration of one substrate at several fixed concentrations of the second substrate yields a pattern of intersecting lines when presented as a double reciprocal plot. Hence, without knowing the mechanism from prior studies, one can not distinguish between the two ternary complex mechanisms presented here on the basis of substrate titrations alone. In contrast, the data for a double-displacement reaction yields a series of parallel lines in the double reciprocal plot (Figure 2.15). Hence it is often easy to distinguish a double-displacement mechanism from a ternary complex mechanism in this way. Also it is often possible to run the first half of the reaction in the absence of the second substrate. Formation of the first product is then evidence in favor of a doubledisplacement mechanism (however, some caution must be exercised here, because other mechanistic explanations for such data can be invoked see Segel, 1975, for more information). For some double-displacement mechanisms the intermediate E-X complex is sufficiently stable to be isolated and identified by chemical and/or mass spectroscopic methods. In these favorable cases the identification of such a covalent E-X intermediate is verification of the reaction mechanism. 

A Scatchard plot of the data is shown in Figure 5.10C. For convenience, the fitted line is the regression of B/F on B (though, as noted earlier, this is statistically unsound) and provides an estimate for Bmax ( -intercept) of 0.654 fmol/mg dry wt. and an estimate for KL (-1/slope) of 132 pM. A Lineweaver-Burk (double-reciprocal) plot is provided for comparison in Figure 5.10D. Linear regression gives another estimate for Bmax (I v-intercept see Eq. (5.29)) of 0.610 fmol/mg dry wt. The estimate of KL from this plot (slope x Bmax) is 114 pM. 

In vitro dieldrin production increased proportionally to larval concentration (enzyme concentration) up to 5 larvae/ml and each 10X increase in substrate (aldrin) concentration tripled and doubled, respectively, dieldrin formation. An approximation of 2 X 10-5 M aldrin as the Km value for midge epoxidase was obtained from a double reciprocal plot of data in Table VII, which closely corresponds to values for aldrin epoxidase in the house fly (28) and the southern armyworm (11). 

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. 

Figure 2 shows a plot of equilibrium dissociation pressure vs. the reciprocal temperature for TiCuH x. The plot was obtained by selecting a composition near the middle of the plateau in Figure 1 and measuring the dissociation pressure as a function of temperature. Since the volume of the system was very small and a large sample was used, the sample composition was nearly constant during the measurements. The enthalpy of Reaction 7 determined by this method is —75 kj/mol H2, and the entropy change is —113 J/deg mol H2. 

Repeat Question 11, but graph the data as a linear, double reciprocal plot in the spirit of the Lineweaver-Burk equation (see Chapter 4). Plot l/ATm vs. 1 /(N/nt) and perform a linear regression to determine the best-fit line (Equation 4.a). The x-intercept corresponds to the KD of the DNA-netropsin complex. The KD value from this method should be more accurate than the estimation in Question 11. 

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. 

Using the Living Graphs for Equation 6-30 and the Lineweaver-Burk equation in Box 6-1, create Lineweaver-Burk (double-reciprocal) plots for all the cases in (a) and (b). When a = 2.0, does the x intercept move to the right or to the left If a = 2.0 and a = 3.0, does the x intercept move to the right or to the left ... 

Application of a least-squares method to the linearized plots (e.g., Scatchard and Hames) is not reasonable for analysis of drug-protein binding or other similar cases (e.g., adsorption) to obtain the parameters because the experimental errors are not parallel to the y-axis. In other words, because the original data have been transformed into the linear form, the experimental errors appear on both axes (i.e., independent and dependent variables). The errors are parallel to the y-axis at low levels of saturation and to the x-axis at high levels of saturation. The use of a double reciprocal plot to determine the binding parameters is recommended because the experimental errors are parallel to the y-axis. The best approach to this type of experimental data is to carry out nonlinear regression analysis on the original equation and untransformed data. 

This relationship is graphically represented as a double reciprocal plot known as a Lineweaver-Burk plot (Figure 31.7) where the x-intercept is —l/Km, the y-intercept is l/vmax and the slope Km/Fmax. 

Figure 4. Sorption of p-galactosidase by collagen preparations (samples as in Figure 2) at different degrees of lysine content as a double reciprocal plot for control, Ac — 14 X 10 6 for 15% modification, A0 — 0.53 X 10 6 for 30% modification, Ac = 0.41 X 10 6 for upper curve, A = 0.18 X 10 6 mol/g collagen,...

The energy-transfer term 0 x is unity under conditions of infinite DPA concentration. What is typically done is that one measures the DPA-enhanced chemiluminescence intensity (/dpa) function of DPA concentrations and constructs a plot of 1//dpa vs. 1/[DPA]. The intercept of such a double reciprocal plot represents the DPA-enhanced chemiluminescence intensity at infinite DPA concentration, that is, /foPA] - The DPA-enhanced chemiluminescence quantum yield that is calculated from this emission intensity, that is, 0fDPA] > represents complete singlet-singlet energy transfer, that is, 0 x is unity. 

A reciprocal plot shows that the of the enzyme present in the serum is 3 x 10" M. Thus, liver damage is a more likely diagnosis than strenuous exercise (assuming the absence of inhibitors or activators that might alter the value). 

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