Page 262 - The Toxicology of Fishes

242 The Toxicology of Fishes

A 0.5
Bound Ligand 0.6
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2 2.5
Free Ligand Concentration
B
0.6
0.5
Bound Ligand 0.4
0.3
0.2
0.1
0
0.1 1 10
Free Ligand Concentration
FIGURE 5.3 Achieving saturating concentrations of labeled ligand. The same values of ligand bound to receptor are
represented in linear (A) and semilog (B) plots of ligand concentration. Although the receptor appears to be nearly saturated
in A, the semilog plot shows that that insufficient data have been collected.

5.3 describes a nonlinear function of ligand concentration, a transformation that yields a linear relation-
ship would be both visually satisfying and simpler to fit. By cross-multiplying the terms of Equation
5.6 and dividing throughout by [L]*K , such a linear relationship is established:
D
[LR [ R T]
[LR ] ]
=− + (5.4)
[] K D K D
L
A plot of bound ligand (or receptor) concentration divided by free ligand concentration on the y-axis
and bound ligand concentration on the x-axis yields a line with a slope of –1/K and an x-intercept of
D
R (Figure 5.4). An obviously nonlinear relationship for data plotted in this fashion is a sign that one
T
of the assumptions listed for Equation 5.3 is false.
Although the Scatchard plot is a useful tool for visually assessing the nature of the binding interaction
and easily computing R and K , it does have its drawbacks. The transformation necessary to achieve
T
D
the linear relationship includes both independent (ligand concentration) and dependent (binding) vari-
ables in the y-axis; therefore, data points from different ligand concentrations are weighted unequally,
with points at higher ligand concentrations receiving greater relative weight in the determination of the
binding constants. This typically leads to overestimation of both R and K .
T
D
Bound/Free (fmol/mg/nM) 60 y = –1.7304x + 66.386
70
50
40
30
20
10
0
0 5 10 15 20 35 30 35
Bound (fmol TCDD per mg protein)
FIGURE 5.4 Scatchard plot of ligand binding. The linear fit of binding data is shown, producing estimates of 0.58 nM
for K D and 38 fmol TCDD per mg protein for R T .