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72 ESSENTIAL PHARMACOLOGY
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
I = 10
–6
[D], molar
10
–5
10
–4
I = 10
–4
10
–3
10
–2
% of maximal effect
I = 0
Figure9.5
−6
K
−6
−7
−6
−4
We can draw a schematic diagram for the action of a noncompet-
itive antagonist by allowing for an extra form of the receptor– one
that has bound both the agonist and the antagonist– on the lower
right (Figure9.4). Even though in this form the receptor is bound by
an agonist, the simultaneous binding of the noncompetitive antag-
onist blocks activation of the receptor by the bound agonist.
The behavior of this system can be described, just as before, by
expressing DR in terms of the dissociation constants and drug (ago-
nist, D, and antagonist, I) concentrations. The result is:
%MAX EFFECT
D
DK
I
K
d
i
100 1
1
An example is plotted as follows for K
d
= 10
−6
, K
i
= 10
−6
,
[I]=10
−7
, 10
−6
, 10
−4
M (Figure 9.5):
D + IR
⇌
IDR
D + R ⇌ DR Effect
+
I
⇋
+
I
⇋
Figure9.4
Pharmacodynamics III 73
Notice that in the presence of a noncompetitive antagonist,
the agonist appears to have reduced efficacy (lower maximum
response). The power, and potential risk, in using the noncompeti-
tive antagonists is that the body cannot overcome their effect by sim-
ply producing more agonist (see in particular the curve for 10
−4
M
antagonist above that is almost zero (almost indistinguishable from
the horizontal axis in this figure) even at the highest concentrations
of agonist).
9.4 Irreversible Antagonists
Some drugs form a covalent or irreversible bond with their target.
In this case the pharmacodynamic equations we have developed
do not strictly apply since they were derived assuming reversible
binding reactions. However, the behavior of irreversible antago-
nists will be similar to that of noncompetitive antagonists because
they make the receptor unavailable for reaction with agonists. In
some cases the irreversible antagonist binds to the same site as the
agonist. In this case the presence of large amounts of the agonist
can delay the onset of inhibition by the antagonist by a “competi-
tive” effect at the drug binding site. However, in time, the irre-
versible antagonist must gain access to the receptor and when it
does, it permanently inactivates it, and the effect will appear non-
competitive.
9.5 Partial Agonists
Some agonists produce a lower maximal response than do others
acting at the same receptor, despite the fact that they competi-
tively displace both agonists and antagonists from recognition
sites of well- characterized receptor systems. We call such drugs
“partial” agonists. They are quite common in current therapeu-
tic settings. As drugs are modified, perhaps to make them more
easily absorbed, more stable, or more potent, the design changes
74 ESSENTIAL PHARMACOLOGY
sometimes lead to the sacrifice of some level of efficacy. Such
drugs can play paradoxical roles in therapy: if adminis-
tered when only a small amount of endogenous agonist is
present, they will activate the target receptors and down-
stream systems and appear to be acting as agonists; how-
ever, if there is a high level of the endogenous agonist
present, they may compete with the endogenous agonist
and by virtue of being less effective lead to the reduction
of the activity of the receptor, appearing to act as antago-
nists. The behavior of the drug will therefore depend upon
the prior history and treatment of the patient.
Here we will present two models that reproduce this behavior.
Unless molecular details of the mechanism are understood for a
particular drug/receptor/effector system, it is not possible to say
which model is more “correct.” The first model simply assigns a
different proportionality constant to the relationship between a
receptor bound to one drug and the effect and a receptor bound to
another drug and the effect. The implication is that one drug may
be more efficient at promoting the “coupling” between the receptor
and the effector mechanisms.
The mixed agonist/antagonist character of a partial agonist can
be visualized by generating some dose- –response curves for systems
in which full agonists and partial agonists compete for receptors.
Aschematic for such a system is given below, Figure 9.6 in which
we indicate that the effect due to the occupation of the receptor by
the full agonist (D) is Em, which is larger than the effect Ei due to
the occupation of the receptor by the partial agonist (I), which is
competing for binding to the same site on the receptor.
IR
D + R ⇌ DR
+
I
⇋
Eff
ect
Ei(weak)
Em
Figure9.6
Pharmacodynamics III 75
This system can be solved as before to yield an expression for
the net effect. The net effect is the sum of the effects due to the par-
tial agonist (Ei) and the effect due to the full agonist (Em):
EFFECT
ED
DK
I
K
EI
IK
D
K
m
d
i
i
i
d
1
1
If E
m
> E
i
, then the maximum effect is E
m
, occurring, for exam-
ple, when I=0 and D is very large. The effect can be normalized to
E
m
to determine a % maximum effect.
Here is an example for this model with K
d
=10
−6
, K
i
=10
−6
,
I=0, 10
−4
, 10
−3
M, E
m
=100, and E
i
=20 (Figure 9.7).
Now suppose we have the same conditions, but reverse the titra-
tion to titrate the partial agonist I in the absence of the full agonist
(D=0) and the presence of two concentrations of the full agonist
D, 10
−3
and 10
−4
M (Figure 9.8).
Notice in these sets of curves that a partial agonist can thus
appear to be an antagonist if used in the presence of a full, or
more efficacious, agonist. In Figure9.7, the partial agonist causes
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
[D], molar
10
–5
10
–4
10
–3
10
–2
% of maximal effect
10
–4
10
–3
I = 0
Figure9.7
−4
−3
76 ESSENTIAL PHARMACOLOGY
a rightward shift of the titration curve for the full agonist, just as a
competitive antagonist would cause.
In Figure9.8, the partial agonist causes a decrease in the effi-
cacy of the full agonist by displacing the full agonist.
An important clinical example of this behavior is seen
with the partial opiate agonist buprenorphine. Buprenor-
phine is used to treat patients who have an addiction to opiates.
Since it is a partial agonist, it tends not to be addictive but can
provide some relief from withdrawal symptoms in a treatment
program to reduce opiate dependence. However, if buprenor-
phine is given to an addict who has high blood levels of a full ago-
nist like heroin, buprenorphine may have the unpleasant effect
of displacing the full agonist, causing an immediate withdrawal
from the full agonist. Its use must therefore be tailored carefully
to patient history.
This complex phenomenology of partial agonists compet-
ing with full agonists is very common in clinical pharmacology.
As mentioned above, many of our synthetic agonists are ‘imper-
fect” copies of known endogenous agonists since they have been
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
[I], molar
10
–5
10
–4
10
–4
10
–3
10
–3
10
–2
% of maximal effect
D = 0
Figure9.8
−4
−3
Pharmacodynamics III 77
modified to enhance such features as bioavailability, potency, or
stability, and possibly to reduce toxicity. Therefore, it is not unusual
for our imperfect partial agonists to have to compete with the body’s
“perfect” full agonists.
9.6 The Allosteric Model forDrug–Receptor
Interaction
We have seen that the simple occupancy model does not provide
a straightforward explanation of the phenomenon of partial ago-
nism since both full and partial agonists can completely occupy
the agonist binding site but lead to different magnitudes of effects.
This type of behavior of receptors can be more readily explained in
another model for receptor activation, the allosteric model. This
more contemporary model attempts to explain receptor activation
in terms of a change in the selection of conformation states of a
population of receptors as driven by the binding of the agonist.
It includes concepts that are very much in line with our present
understanding of the physical behavior of large protein molecules.
As in the development of any new theory in science, the predictions
of the allosteric model under certain conditions are indistinguish-
able from those of the older simple occupancy model, but the new
model can also explain phenomena outside the scope of the simple
occupancy model.
The allosteric model assumes that receptors fluctuate between
“active” and “inactive” states spontaneously, and agonists tend to
bind more tightly to the “active” form, thus increasing the concen-
tration of the “active” form. We will see that the phenomenon of
partial agonism is explained naturally in this model in terms of the
relative affinity of the drug for the active versus inactive receptor.
The notion of multiple conformations of receptors gains credence
from electrophysiological experiments using “patch- clamp” tech-
niques. The behavior of individual ion channels can be followed by
this technique, and both spontaneous and agonist- induced open-
ings can be observed and analyzed.
78 ESSENTIAL PHARMACOLOGY
In summary, the following concepts underlie the allos-
teric model:
a. Large proteins can assume multiple conformations in solution
(aqueous or lipid)– the conformer at the lowest energy state will
be favored, and almost all of the molecules will be in this state
most of the time (ground state)
b. The ground state is “inactive” (e.g., closed acetylcholine- gated
ion channels), but an “active” (e.g., open) conformation briefly
occurs spontaneously from time to time
c. Agonists increase the frequency (i.e., concentration) of the active
conformation in a concentration- dependent fashion, but antago-
nists have little or no effect.
d. Presumably, agonists bind preferentially to the active conformer,
thereby “pulling” the population of molecules into this state (via
mass action)
e. Antagonists have no preference, but by binding to either state
prevent the agonist from binding.
Partial agonists (also sometimes called “agonist- antagonists”)
are explained in the allosteric model as follows:
a. Visualized as having less preference than full agonists for binding
to the active state (i.e., some binding occurs to the ground state)
b. Even at high partial agonist concentration, some ground- state
conformer persists, thereby decreasing the fraction of molecules
that reach the active state
c. The preference for the active conformer can vary widely, leading
to a different fraction of receptors “kept out” of the active state
by various partial agonists
We have implied that antagonists won’t have a visible effect
on a system unless an agonist is present and attempting to acti-
vate the receptor. However, there may be a few circumstances in
which a considerable fraction of receptors are spontaneously in
the active state (e.g., the GABA- activated chloride channel that
is the benzodiazepine “receptor”). In this event, there would be
a difference between those antagonists that had no preference
for one or another conformer and those that greatly preferred
Pharmacodynamics III 79
ground- state molecules. The former would produce no effect by
themselves and would behave as “pure” antagonists, while the
latter would cause an effect opposite to that of agonists (so- called
“inverse agonists,” or “negative agonists”).
In the schematic for this model, shown in Figure9.9, R
on
rep-
resents the active form of the receptor, which leads to an effect
whether or not drug is bound. R
off
is the inactive receptor. The
active and inactive forms of receptor are in equilibrium. In the
absence of drug, the constant for this equilibrium is K
M
=R
off
/R
on
which is much greater than 1, so most receptors are “off.”
K
D,on
and K
D, off
are dissociation constants for the binding of the
drug to the active and inactive receptors, respectively. For an ago-
nist, K
D,on
< K
D,off
(because the agonist binds the active form with
a higher affinity (lower K
D
)). The equations describing the behav-
ior of this system are derived exactly as in the previous models,
by manipulation of the equations that define the various equilib-
rium/dissociation constants in terms of the concentrations of the
various species. The result is shown below.
%MAX EFFECT
RDR
RR DR DR
K
D
K
ON ON
ON OFFO
NO
FF
M
D,OF
100
100
1
1
FF
DON
D
K
1
,
D +
R
OFF
DR
OFF
D +
R
ON
DR
ON
K
D, ON
K
m
K
D, OFF
Effect
Effect
Figure9.9
80 ESSENTIAL PHARMACOLOGY
You can check that this expression makes sense by considering
some examples:
1. D=0 (no drug present), then % MAX EFFECT=100/(1 + K
M
),
which approaches 0 if K
M
is large
2. K
D,on
=K
D,off
then % MAX EFFECT=100/(1 + K
M
), the same
result as when no drug is present; to have an effect, the drug
must have different affinities for the “on” and “off” states.
3. K
M
very small, then %MAX EFFECT approaches 100% as all the
receptors are spontaneously in the active state
Let’s run this model on the computer now for a couple of differ-
ent conditions. For comparison we’ll also plot the simple receptor
occupancy model for a drug binding to a receptor with K
d
=10
−6
M
(curve A in each case).
1. Curve B: K
M
=5, K
D,on
=10
−6
, K
D,off
=10
−4
M
Notice in Figure 9.10 that there is activity of the receptor in the
allosteric model even in the absence of the drug, or at very low drug
concentrations, because of spontaneous activity of the receptor, and
that full activation is never achieved. Drug B is a partial agonist,
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
[D], molar
10
–5
10
–4
10
–3
10
–2
% of maximal effect
A
B
Figure9.10
−6
M
−6
−4
Pharmacodynamics III 81
although it is nearly as active as the full agonist using the values
assigned to the binding constants.
Now let’s compare this system to one in which the drug has
greater affinity for the receptor in the “off” state than in the “on”
state (acting as an inverse agonist, Figure9.11). Curve A: The sim-
ple occupancy model, as above with Kd=10
−6
M.
Curve B: K
M
=5, K
D,on
=10
−4
, K
D,off
=10
−6
M
Notice that in this case in the allosteric model drug B is acting as
an inverse agonist because of its higher affinity for the off state of the
receptor rather than the on state. In the absence of the drug, or at very
low levels, the receptor remains active due to spontaneous activity.
9.7 “Spare Receptors”
In some instances it has been found that agonists cause maximum
effects when only a small fraction of the total population of recep-
tors is occupied. The additional receptors seem not to be used, or are
spare. This is again a deviation from the simple occupancy model
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
[D], molar
10
–5
10
–4
10
–3
10
–2
% of maximal effect
A
B
Figure9.11
M
K
−4
−6