Linearization Scatchard

In some cases more complex reaction schemes may give rise to linear Scatchard plots (Conners, 1987), and nonlinear plots may arise from a number of experimental artefacts, e.g., failure to reach equilibrium at low ligand concentrations. The interpretation of this particular linearisation approach has been the subject of many articles to which the reader is referred for further insight (Boeynaems and Dumont, 1975 Norby et al., 1980 Klotz, 1982, 1983 Hulme, 1992). 

K. E. Light (1984). Analyzing non-linear Scatchard plots. Science 223 16-11. 

In radioligand binding studies, non-linear Scatchard plots or competition curves that have abnormally steep slopes imply complex binding phenomena, possibly involving multiple receptor types or affinity states. In such cases, the thermodynamic parameters should be separately determined for each receptor type or affinity state. 

A novel new technique employing fluorescence correlation spectroscopy has confirmed specific interactions between a tetramethyirhodamine-labeled kavain derivative and human cortical neurons. Human cortical neurons were incubated with 1 nM of the dye-labeled kavain derivative. A total binding of 0.55 nM was found after an incubation period of 60 minutes. Fifty percent of the total binding was specifically displaced in the presence of 1 XM non-labeled (+)-kavain. Evidence for these specific interactions was verified by a saturation experiment. Both the non-linear Scatchard plot and the n value of 1.58 0.07 in the sigmoid Hill plot indicated binding sites with different binding affinities (Boonen etal., 2000). 

If nn = 1, this can (but does not have to) be due to the simple mechanism I, in that (for example) rnechanism III also yields nH = 1 at 4Kdi = Kd2- Similarly, mechanism IV at Kd3 -I- Kd4 = 2-7Kdi, Kd3, which can be a positive cooperative binding (i.e., with Kdi > Kd4)-The Scatchard plots for III and IV are linear at nH = 1, which means that linear Scatchard plots are no proof of the existence of only one binding site. In addition, it is difficult to distinguish between nn = 1 and nn 1, because the difference of nn and 1 is often small and indistinguishable from the experimental error. 

Assuming the validity of the assumptions upon which equations 1 and 2 are based a linear Scatchard plot will result. 

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. 

Scatchard analysis, a common linear transformation of saturation binding data used prevalently before the widespread availability of nonlinear fitting software. The Scatchard transformation (see Chapter 4.2.1), while easy to perform, can be misleading and lead to errors. 

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. 

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

A historically important graphical technique to describe binding data (see O Figure 10-2) is the Scatchard plot (1949). This is simply a linearization of the function ... 

Scatchard plot of the binding data shown inO Figure 10-la, illustrating how the Kd and R can be obtained from such a linearization procedure... 

See Double-Reciprocal Plot Hanes Plot Direct Linear Plot Dixon Plot Dixon-Webb Plot Eadie-Hofstee Plot Substrate Concentration Range Frieden Protocol Fromm Protocol Point-of-Convergence Method Dal-ziel Phi Relationships Scatchard Plots Hill Plots... 

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. 

Standard curves and serum samples are prepared in duplicate. In this study, standard curves were linear for values of B/B0 ranging from 0.1 to 0.9. The lower limit of sensitivity (B/B0= 0.9) was 0.6 pmol, the upper limit B/B0 = 0.1) was 37 pmol. A Scatchard plot revealed a linear relationship between the quotient bound to free antigen versus bound antigen, the binding capacity being 0.52 pmol/1 of serum. The coefficient of variation ranged between 12 and 20% and recovery from 100 to 111%. 

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. 

Figure 7-3 A Scatchard plot of the same data shown in Figs. 7-1 and 7-2. This is the best of the linear plots for studying binding.

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. 

If [X]b/ [P]t[X] is plotted against [X]b/ [P]t the resulting linear plot will have an intercept of Kt on the y axis and n on the x axis. Thus, n is directly apparent, whereas in Eq. 7-5 it is incorporated into Y. A problem arises if, as discussed in the next section, the multiple binding sites are not independent but interact. Curved Scatchard plots result and attempts to extract more than one binding constant can lead to very large errors. Before measuring saturation curves, the student should read additional articles or books on the subject.26-10... 

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