Biology Reference
In-Depth Information
Effect
1.185
SEM [DRUG]
0.021
0.00
1.152
1.186
1.166
1.201
1.213
1.181
1.269
1.245
1.242
1.301
1.286
1.322
1.309
1.301
1.348
1.311
1.352
1.340
1.371
1.357
1.407
1.502
1.510
0.021
0.05
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.021
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
2.00
4.00
8.00
1.500
1.375
1.250
1.125
0
2
4
6
8
10
[Drug] or [Ligand]
FIGURE 8-3.
A typical example of a ligand-binding experimental measurement. The y-axis (arbitrary units)
corresponds to the measurements of a drug effect or some other response that can be assumed to
be proportional to the amount of the drug or other ligand that is bound. The x-axis is the
concentration of the unbound drug or other ligand. The vertical lines are centered on the observed
values and represent the 1 standard error of the measurement (SEM) of experimental
uncertainties for the particular data points.
could have different measurement errors. Thus, it is important to
consider a data point as a triplet (Y
i
, SEM
i
,X
i
) consisting of the
dependent variable, the precision of the dependent variable, and the
independent variable.
Historically, two general approaches have been applied to the analysis of
ligand-binding data. The earliest was to perform a transformation of the
data such that the transformed data were reasonably described by
a straight line. The resulting nearly linear data could then be analyzed by
fitting a straight line to it and deducing the desired properties from the
slope and intercept of that line. Now that high-speed computers are
ubiquitous, the more common and more statistically valid approach is to
fit the nonlinear equations to the original experimental data without
transformation. We illustrate the shortcomings of the first approach next,
and then examine the second approach in detail.
It is important to realize that transformation methods only apply to the
simplest models, such as Eq. (8-12), where there was a unique linearizing
transformation. In most other situations, this will not apply. Recall,
for example, Eq. (7-5) from Chapter 7:
½
Drug
=
K
d
Y
¼
K
d
:
(8-15)
1
þ½
Drug
=
If the data can adequately be described by the simple mechanism of
drug action represented by Eq. (8-15), then the da
ta
can be linearized
several ways, s
uc
h as a dou
bl
e reciprocal plot
ð
1
=
Yvs
:
1
=½
Drug
Þ
or a
Scatchard plot
. In addition, if the model contains more
than two parameters, it cannot be transformed into a two-parameter line.
ð
Y
=½
Drug
vs
:
Y
Þ
