Medicinal Chemistry

in the same population. The classical example is oxygen binding by hemoglobin, which
is treated in every biochemistry text. In a direct plot, the curve of cooperative binding is
sigmoidal instead of hyperbolic.
If equation (2.24) is modified to incorporate ntheoretical sites on the receptor, then

from which

IfFis the fraction of occupied active sites, then the number of occupied sites becomes

and therefore

In logarithmic form, this becomes

and a straight line, the Hill plot, results if log F/(1−F) is plotted against log [D]. The
slope is n. Thus the Hill plot gives, approximately, the number of interacting sites. If
the slope of the Hill plot is less than unity, negative cooperativity is suspected (i.e., the
binding of the first ligand inhibits subsequent binding). The insulin receptor shows such
behavior. Positive or negative cooperativity would indicate a conformational change
that increases or decreases the affinity of the receptor site for the drug.

2.7 GENERAL MOLECULAR CONCEPTS

OF DRUG RECEPTOR ACTION

The preceding sections have explored classical pharmacological concepts based on the
dose–response relationships in tissue or organ preparations. The enormous complexity
of living systems and the remoteness of cause from effect (i.e., drug administration
from pharmacological action) introduce many complications and artefacts into the
study of such relationships.
Molecular pharmacologists and physical scientists have therefore sought to simplify
the experimental system as much as possible. This objective has been increasingly real-
ized as the methodology of quantitative binding experiments on membrane preparations
(and, later, on isolated receptors) has become more sophisticated, precise, and simple.
Isotopically labelled compounds of very high activity have made it possible to work
with physiological ligand concentrations down to the picomole level (10–12M). This has
allowed direct experimental access to receptor binding sites and has led to the develop-
ment of several complementary receptor models. Physical chemistry techniques (X-ray
crystallography, NMR conformational analysis, molecular modeling) are now enabling

84 MEDICINAL CHEMISTRY

v=

n[D]n

KD+[D]n

(2.32)

v

n−v

=

[D]n

KD

(2.33)

v=nF (2.34)

v

n−v

=

[D]n

KD

(2.35)

log

F

1 −F

=nlog [D]−logKD (2.36)