Scatchard plots

FIGURE 4.3 Erroneous estimation of maximal binding with Scatchard plots. The saturation binding curve shown to the left has no data points available to estimate the true Bmax. The Scatchard transformation to the right linearizes the existing points, allowing an estimate of the maximum to be made from the x-axis intercept. However, this intercept in no way estimates the true Bmax since there are no data to define this parameter. 

A Scatchard plot is a plot of B/x against B (where B is the amount of bound ligand and x is the ligand concentration), which is used to estimate the maximal binding, Bmax as well as the binding affinity (K). 

If BjX is plotted against B (the Scatchard plot) it should give a straight line (Fig. 5.2(b)) with the slope (1/A d) giving K and the intercept on the abscissa providing the maximal binding (.Smax) expressed as fmol per mg tissue protein. The steeper the slope, the higher the affinity. 

In water, Scatchard plots showed clear concave-shaped curves whatever the pectin origin (figure 4A). Nevertheless, differences between sugar-beet and citrus pectins appeared in presence of ionic strength. While citrus pectins exhibited convex-shaped curves whatever the metal ion, sugar-beet pectins display convexe curvature for Cu2+ and Pb2+ but concave-shaped curves for the other three cations (figure 4B, in the case of Ni2+). 

An anticooperative mode of interactions was assumed in case of concave-shaped Scatchard plots, as alrea% proposed by other authors (Mattai Kwak, 1986 Gamier et al, 1994). A convexe curvature of the plots indicated a cooperative binding process (figure 4). 

FIGURE 1. Scatchard plot of equilibrium-saturation binding of... 

H-(+)SKF-10,047 binding was also measured in the presence of 100 nM haloperidol. This approach yielded a Scatchard plot in which the density of the apparent high-affinity sites was decreased by... 

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... 

A plot of 1 IB vs. 1/[L] will give a straight line providing that Eq. (5.3) applies when 1 IB = 0, then 1/[L] = -1 IKl, and when 1/[L] = 0, then 1 IB = 1 /) max. A Lineweaver-Burk plot is shown in Figure 5.10, where it may be compared with the Scatchard plot of the same data. The double-reciprocal plot spreads the data very poorly and is inferior to the Scatchard plot. 

Construct a Scatchard plot of the data and derive new estimates of Kh and fimax. 

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. 

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. 

The binding density is the concentration of bound enzyme over the concentration of binding sites. The binding constant Kb is related to the affinity between the enzyme and the matrix, the greater Kb the higher the affinity. Figure 15.8 displays the Scatchard plot of Mb adsorbed on (A) a-ZrP and (B) magadiite, from Refs. [86] and [133], respectively. 

Fig. 15.8 Scatchard plots of myoglobin adsorbed on (A) a-ZrP and (B) magadiite, from Refs. [86] and [133]. respectively.

According to the synthetic strategy just described, a series of water-soluble carbosi-lane dendrimers were made, bearing peripheral galabiose trimers interspaced by 29 A, adjusted to the binding-site distances (Fig. 75).432 The binding affinity to SLT-I and SLT-II B subunits were determined by Scatchard plot analysis. Hexavalent compound 610 showed KD values of 1.3 and 1.6 /M for SLT-I and SLT-II,... 

Fig. 11. A Theoretical binding curve for an A + B = AB interaction. Black lines indicate a plot of signal vs [Atotal], Grey lines vs [Afree]. The dashed line shows an example of an active site titration. B Scatchard plot [154]...

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]). 

The above procedures imply that (1) there is only a single type of site (2) binding occurs only to the transporter site (usually not the case for trace metals), and (3) the internalisation flux is negligible for the equilibration times that are employed [197,198], These conditions are rarely fulfilled for metal transporters. The interpretation of Scatchard plots is especially ambiguous in the presence of several independent sites. On the other hand, in the biomedical literature, where nonspecific adsorption is generally not a problem, values of 104 to 106 carriers per cell (ca. 10-13 to 10 11 carriers cm-2 of cell surface area), with even lower numbers determined for some receptors (e.g. haematopoetic growth factor [199]), are typically reported. 

Traditionally, polyvalent cation-phytate complexes have been considered uniformly insoluble, and this dogma has been the basis of most methods for the determination of phytate (31). In 1976, however, soluble monoferric phytate was isolated (32), and most recently, Cai- and Ca2 phytate were also found to be soluble (27). Figure 2 shows a Scatchard plot of Ca2+ binding to phytate at pH 4.8. At a ratio of 2.2 to 2.4 the complex precipitates. This ratio is independent of the phytate concentration over a 100-... 

Figure 2. Scatchard plot of binding of Ca2+ to phytic acid. A solution of 3 04 mM phytic acid in 50 mM acetic acid pH 4.8 was titrated with 1.005 M CaCl at 40°C.

Proteins were quantitatively retained above the membrane while low molecular weight ligand passed through the membrane. Binding constants were determined by Scatchard plot analysis (24-26). 

Linear regression analysis was used to fit the points for the Scatchard plot. 

Figure 5. Scatchard plot of procyanidin trimer and bean globulin G1 at 19C.

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