Scatchard equation/plot

Equation E3.5 in this experiment can be used to determine / values, but hyperbolic plots are obtained. Can you convert Equation E3.5 into an equation that will yield a linear plot without going through all the changes necessary for the Scatchard equation Hint Study the conversion of the Michaelis-Menten equation to the Lineweaver-Burk equation. 

Two other possible transformations of saturation binding data mentioned earlier are the Hofstee (B versus B/F) and Woolf Plots (F/B versus / ). As with the Scatchard equation, these equations can be derived from algebraic manipulations of the equations listed above. 

Fig. 8.1. Scatchard (A), Langmuir (B and C) and Sips (D) forms of the Law of Mass Action for antibody-antigen interactions. The abbreviations and the derivation of the equations are given in Section 8.3. Polyclonal sera yield curved lines in A, B and C, whereas the interrupted lines represent homogeneous interaction. In the Scatchard (1949) plot, three of the different populations of antibodies are indicated by dotted lines low afTinity (K is small) at r = 2, intermediate ( average ) affinity, Aoat r = 1 and high affinity at small r. The Langmuir (1918) adsorption isotherm can be graphically presented if the total amount of antibody is known (B) or not (C). In the latter case b represents bound antibody (Abt d) and n/r in eq. 9 is substituted by Abio,ai/Abbo d to obtain ...

Usually Eq. (3) is converted into Eq. (4) (Scatchard equation), and Bbound/C is plotted against... 

It is often true that I > > RI and thus I = L. In this case, a and b of the Scatchard equation for inhibition mechanism I are constant and plotting B/L against B yields a straight line. Different lo yield different linear forms. All lines go through the point with the coordinates B/L = 0 B = Bmax and thus form a ray pattern (see Figure 2.20). 

The Scatchard plot is bound free (/i/ L, y-axis) vs. bound (B, x-axis) (the Eadie-Hofstee plot is bound vs. bound/free). If this equation is applicable (i.e., the binding represents a simple bimolecular... 

The Scatchard formalism can of course be applied to the binding of any small molecule to any biomacromolecule, such as the binding of a substrate or inhibitor to an enzyme, or the binding of a metal ion to an apoprotein. In receptor research, the determination of Kd typically requires labeling of the substrate by radioactivity or by fluorescence. However, we might just as well choose paramagnetism as the label, and this then makes the EPR spectrometer the detector for the determination of binding equilibria. The Scatchard plot in Equation 13.4 has two experimental observables [L] and [RL], and so we must find ways to determine these quantities from EPR spectra. 

As seen in equations (32)-(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, As, corresponding to the formation of M — Rcen following measurement of [M] and (M —Rceii. For example, a (Scatchard) plot of (M — RCeii /[M] versus (M — RCeii should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]). 

Figure 19.11. A plot of —(1 — g)/m2 against from the freezing point data for potassium nitrate (KNO3) solutions in water. Data from G. Scatchard, S. S. Prentice, and P. T. Jones, J. Am. Chem. Soc. 54, 2690 (1932). See Equation (19.63).

LINKED FUNCTIONS SCATCHARD PLOT HILL EQUATION AND PLOT Ligand binding,... 

SCATCHARD PLOT KLOTZ PLOT ALLOSTERISM COOPERATIVITY HILL EQUATION AND PLOT WOMACK-COLOWICK DIALYSIS METHOD... 

Merging both equations and transformation of the result gives the Scatchard graph, characterized by plotting [B]/[F] on ordinate and 1/Kd on abscissa. The constant Bmax represents that concentration of L needed for complete saturation of all binding sites at the receptor and the maximal number of binding sites, respectively. 

C. The appropriate Scatchard plot is a graph of AA/[X versus AA (Equation 19-16). 

The Scatchard plot is the best of the various linear transformations of the saturation equation and is preferred to "double reciprocal plots" analogous to that shown in Fig. 9-3. 

Equation (3.171a) is known as the Scatchard plot. Plotting Y/[D] against Y gives a straight line with a slope of —K and an intercept of nK. Equation (3.171b) is known as the Hames plot. A plot of [D /Y vs. [D] yields a straight line of slope 1/n and intercept 1/nK. 

Figure 3.27 illustrates a rectangular hyperbolic plot [Equation (3.169)], doublereciprocal plot [Equation (3.170)], Scatchard plot [Equation (3.171a)], and Hames plot [Equation (3.171b)] for the binding of NADH to rabbit muscle lactate dehydrogenase. 

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. 

Scatchard plots. Stability constants for the binding of Ou by a model ligand (histidine) and by natural organic ligands in river water were computed using Scatchard plot diagrams as described previously by Mantoura and Riley (1 ). The general equation for this analysis was ... 

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