Medicinal Chemistry

2.6.3 Double Reciprocal Plot

The hyperbolic direct plot can easily be straightened out, as analogies from classical
enzymology teach us. The most popular data treatment for yielding straight lines is the
double reciprocal plot, also known as the Lineweaver–Burke or Benesi–Hildebrand
plot. Here, we take the reciprocal of equation (2.24):

If one plots l/υagainst 1/[D],KDandυcan be obtained directly with good precision.

2.6.4 Dixon Plot

Another useful method of data reduction is the Dixon plot, where 1/υis plotted against
[I], the inhibitor concentration, at a fixed [D]. This allows for the determination of KD
without the need to determine the absolute concentration of [D]—a great advantage in
cases in which the substrate is a polynucleotide or a protein, as is often the case in
chemotherapy.

2.6.5 Scatchard Plot

Perhaps the most widely used method for extracting binding data is the Scatchard plot.
This is obtained from

Thus, plotting υ/[D] against υor, alternatively, [D]bound/[D]freeagainst [D]boundgives a
straight line. The slope is 1/KD(the binding constant); the abscissa intercept is the
number of binding sites if υis shown as mol υ/mol R.
The great advantage of the Scatchard plot is its linearity (i.e., all data are weighted
equally). Errors in measurement register on both axes and are therefore eliminated. The
Scatchard plot is most useful when there are multiple binding sites; in that case, how-
ever, the plot is not linear. This most commonly occurs in the case involving a small
population of receptors with a high affinity, accompanied by a large population with a
low affinity. The Scatchard plot is an excellent way of extracting binding-site constants
and numbers from experimental findings. However, it must be remembered that these
properties of the Scatchard plot are valid only if the binding sites are independent (that
is, if there is no cooperative interaction between them). Indeed, downward curvature of
the Scatchard plot may result from the underestimation of nonspecific binding, simul-
taneous binding on two sites, and other factors beside negative cooperativity and
differences in affinity.

2.6.6 Hill Plot

The cooperativity of receptor sites can be recognized from binding data. Cooperativity
means that binding to one receptor site facilitates binding to subsequent receptor sites

RECEPTORS: STRUCTURE AND PROPERTIES 83

1

v

= 1 +

KD

[D] (2.30)

v

[D]

=

1

KD

−

v

KD (2.31)