Dividing (2.15) by (2.16):
The Schild equation is thus obtained, where [D]/[d] is the “dose ratio.” From equation (2.17),
[A] 2 , the antagonist concentration necessitating a doubling of the agonist concentration
to achieve the pure agonist effect, is
and
which provides a convenient experimental method for measuring the “activity” of an
antagonist. This is, of course, analogous to the pD 2 =−logKDconcept.
The effect of a competitive inhibitor can also be expressed as an inhibitor affinity
constant(KI) by plotting the inhibitor concentration versus the reciprocal of the reac-
tion velocity, or versus the reciprocal concentration of a labeled ligand (the isotopically
radiolabeled agonist that is displaced by the antagonist). The intersect of the lines so
generated is −KI.
where IC 50 is the inhibitor concentration that displaces 50% of the labeled ligand, [L]
is the concentration of the labelled ligand, and Kis its dissociation constant. This is a
method that is particularly suited for in vitro binding experiments; however, it is not
suitable for organ preparations or whole-animal studies. Rapidly growing experimental
evidence that takes into account the latest in vitro binding experiments favors a modi-
fied form of the occupation theory of drug activity. There are, however, phenomena that
are unexplained by the occupation theory:
- The inability of partial agonists to elicit a full response while blocking the effect of
more active agents. - The existence of drugs that first stimulate and then block an effect.
- Desensitization ortachyphylaxis—diminution of the effect of an agonist with
repeated exposure to or higher concentrations of that agonist. - The concept of spare receptors.
To accommodate some or all of these phenomena, several alternatives to the occupation
theory have been proposed. None of them is entirely satisfactory, and some have no
physicochemical basis.
Therate theoryof Paton, as modified by Paton and Rang, rejects the assumption that
the response is proportional to the number of occupied receptors, and instead proposes
a relationship of response to the rateof drug–receptor complex formation. According
80 MEDICINAL CHEMISTRY
[D]
[d]= 1 +[A]KA (2.17)
[A] 2 =
1
KA
(2.18)
pA 2 =−logKA (2.19)KI=
IC 50
1 +[L∗]
K∗