Combining equations (2.9) and (2.10) yields
Equation (2.11) indicates a hyperbolic relationship between the effect and the concen-
tration of free drug. The ED 50 is therefore equal to KD. Incidentally, equation (2.11) is
identical to the Michaelis–Menten relationship in enzyme kinetics, with Emaxrepresent-
ingVmax. Dose–response curves usually show effect versus the logarithm of the total
drug concentration [DT], assuming that the concentration of bound drug is so small as
to be negligible and that [DT]≅[D]. However, if the receptor concentration [RT]
becomes large relative to KD, then
meaning that, at a high bound-drug concentration, the total concentration of drug may
exceed KDby an amount equal to one-half the total receptor concentration. It seems that
the case ED 50 =KDis rather exceptional. If occupation of some of the receptors is suf-
ficient for a maximal response, as often happens,spare receptors will be present and
and the true value of KD(and thus the affinity of the drug for the receptor) will be under-
estimated. This case may be an indication that an “induced fit” takes place, since it
seems that a small number of agonist molecules can trigger a conformational change in
many receptors, leading to the activation of a larger number of receptors than seems to
be warranted. The “spare” receptor concept can be tied to the idea of efficacy or intrin-
sic activity, meaning that some drugs may have to activate fewer receptors than others
to elicit a full pharmacological effect, and are thus said to be more efficacious.
Agonists that yield parallel dose–response curves with the same maximum are
assumed to act on the same site but with different affinities. Nonreceptor binding to
a “site of loss” (sometimes called a “silent” receptor) can thus be distinguished from
relevant binding.
Schild extended these ideas to the description of effects when a competitive antago-
nist(A) is present. If Yis the proportion of receptors occupied, that is, if
and the AR complex is inactive, then
whereKA, is the association constant of the antagonist. If the same biological response
is achieved at a lower drug concentration [d] in the absence of the antagonist, then
RECEPTORS: STRUCTURE AND PROPERTIES 79E=
Emax[D]
KD+[D](2.11)
ED 50 =KD+ 0 .5[RT] (2.12)
ED 50
KD< 1
(2.13)
Y=
[DR]
[RT]
(2.14)
KD
[D]
=
( 1 +[A]KA)Y
1 −Y
(2.15)
KD[d]=