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62 ESSENTIAL PHARMACOLOGY
consider the beta adrenergic antagonist propranolol that binds
to the norepinephrine receptor or the antiestrogenic drug
tamoxifen that binds to the estrogen receptor.
2. Inhibiting enzymes that are involved in generating or breaking
down signaling molecules, either “first” messengers (e.g., neu-
rotransmitters) or “second” messengers (e.g., calcium ions or
cyclic AMP). Examples include physostigmine, an inhibitor of the
enzyme that breaks down acetylcholine (a “first” messenger), and
sildenafil (Viagra), an inhibitor of a phosphodiesterase that breaks
down cyclic GMP (a “second” messenger). Ion channels in the cell
membrane may also be considered “enzymes” that are subject to
pharmacological manipulation. For example, verapamil blocks the
entry of calcium, a “second” messenger, into smooth muscle cells,
and the local anesthetic procaine inhibits the entry of sodium into
nerves, thus blocking action potentials.
In either mechanism, the drug binds to a given target (an
enzyme or a cell surface receptor), so the analysis of the interaction
is based in the physics and chemistry of the binding of small mol-
ecules (the drug) to large molecules (a protein).
1. In most situations, drugs are relatively “specific.” They exhibit
structure– activity relationships (only a limited number of related
chemicals are active on a given target).
2. They have a high affinity for their target. This enables them to
act at low concentrations in the body.
3. Their action is stereospecific– different isomers often differ 100-
fold or more in potency.
4. The specificity of drugs for targets is manifested as differential
affinities for different molecule classes.
5. They may have selective affinities for certain cell types
or tissues.
6. They often exhibit species specificity (e.g., host vs parasite).
7. These properties led to the concept of specific targets for drugs,
called “receptors.”
Pharmacodynamics II 63
1. Most drug receptors are proteins– enzymes, hormone receptors,
transporters, etc.
2. Other receptors include nucleic acids– bound for example, by
some cancer chemotherapeutic agents.
3. Phospholipids are considered targets of volatile anesthetic
agents, although this violates certain rules such as stereospeci-
ficity, and their specificity derives from general properties such
as hydrophobicity.
4. AGONISTS are drugs that mimic an endogenous compound by
activating the receptor.
5. ANTAGONISTS are drugs that interfere with the action of
agonists at their receptors.
6. Rates of cellular processes can be either increased or decreased
by receptor agonists.
7. Inhibitors of agonists (antagonists) are “directly” acting (i.e.,
compete with agonists at ligand- binding sites) and usually have
little or no apparent effect in the absence of agonists.
Drugs whose targets are not “real” receptors (e.g., enzymes,
transport proteins) generally have different characteristics:
Rates of target cellular processes are only decreased, not activated.
Agents that “reverse” the effects of such drugs usually do so only
indirectly (e.g., “physiological” antagonism, rescue by providing
the product of the inhibited enzyme).
64
Pharmacodynamics III:
Quantitative Analysis
of Drug–Receptor
Interactions
A
mathematical description of the effects of drugs that act as
enzyme inhibitors can be provided by classical Michaelis–
Menton kinetic analysis as introduced in biochemistry
courses. Here we will develop some of the mathematical tools
used to describe drug–receptor interactions where the receptor is
a “real” receptor for an endogenous hormone or neurotransmitter.
We assume that for the drug to cause an effect, it must bind to the
receptor. Therefore, much of the mathematical formalism has to do
Chapter 9
Pharmacodynamics III 65
with the equations that describe binding according to the law of
mass action. The development will look similar to the Michaelis–
Menton analysis of enzyme kinetics, which also involves a binding
event– that of substrate to enzyme. In drug receptor theory, how-
ever, the drug is generally not altered by the receptor. Instead, the
receptor itself is coupled to some subsequent cellular process that
is regulated by the binding of the drug to the receptor. Importantly,
receptors do not consume ligands; agonist- induced conforma-
tional changes in the receptor initiate the response.
9.1 The “Simple Occupancy Model”
The simple occupancy model is central to theories of drug action
through receptors.
The model is based on the chemical law of mass action.
It assumes the intensity of receptor response is directly propor-
tional to receptor occupancy by the drug. The maximal effect of a
drug occurs when 100% of the receptors are occupied. Stated as a
chemical equation, the model has the form given here:
DR DR EFFECT
D and R are the concentrations of free drug and receptor, respec-
tively. The model says that the effect is strictly proportional to the
concentration of the complex DR, i.e., Effect=k × DR where k is a
proportionality constant. We need to derive an expression for DR in
terms of the affinity of the drug for the receptor (embodied in the
dissociation constant) and the concentration of the drug. We will
assume the concentration of drug is much greater than the con-
centration of receptors so we can take the total drug concentration
as approximately equal to the free drug concentration. The equilib-
rium (dissociation) constant, K
d
is given by
K
DR
DR
d
(9.1)
66 ESSENTIAL PHARMACOLOGY
The total population of receptors, R
t
, is divided between free
and complexed forms,
RD
RR
t
From the definition of the dissociation constant, equation(9.1),
RK
DR
D
d
Therefore,
RDRK
DR
D
DR
K
D
DR
DK
D
DR
RD
DK
td
d
d
t
d
1
(9.2)
The Effect=k × DR (the effect is proportional to the concentra-
tion of occupied receptors).
The Maximal Effect will occur when DR=R
t
(all the receptors
are occupied)
Therefore Maximal Effect=k × R
t
and Effect/Maximal Effect=DR/R
t
=D/(D + K
d
) or
Effect MaximalEffect XD DK
d
/
If we define the Maximum Effect as 100%, then we can write
%/
of MaximumEffect DD K
d
100
This is analogous to the Michaelis–Menton equation,
Velocity vVSSK
mm
/
Pharmacodynamics III 67
where S is the substrate concentration, K
m
the Michaelis constant,
and V
m
the maximum velocity.
Let’s work out some numerical and graphical examples for the
%/
Effect DDK
d
100
If K
d
= 1 μM, this expression generates the classic sigmoid
log- dose curve shown in Figure 9.1.
When D=K
d
, then D/(D + K
d
)=1/2, 50% Maximal Effect (equals K
act
).
When D=0.1 K
d
, then D/(D + K
d
)=0.1/1.1=9.1% Maximal Effect.
When D=10 K
d
, then D/(D + K
d
)=10/11=91% Maximal Effect.
Thus, this model says that responses between 9% and 90% of
maximal occur with a 100- fold increase in drug concentration.
There are several concepts that emerge from this analysis that
have particular importance in the application of agonists as drugs
in clinical medicine. First of all, in order to achieve an effect, the
drug must be introduced at concentrations near or above the Kd of
the drug for the relevant receptor. Although this may seem obvious,
it is sometimes overlooked. If not enough of a given drug gets to the
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
Figure9.1
μM.
68 ESSENTIAL PHARMACOLOGY
target receptor, the system will be on the flat part of the curve on
the left, i.e., at zero effect. Too small an amount of even the best
medicine is of no benefit whatsoever.
Conversely, after one introduces a concentration of the drug
that is 10- fold above the Kd, little more benefit can be obtained
by administering more of the drug. The system is then on the flat
part of the curve to the right. If a patient is not responding to
the medication at this level, giving even more medicine is of
no benefit whatsoever. It is time then to think about using a
different drug.
9.2 “Competitive” or “Surmountable” Antagonists
Competitive antagonists are agents that inhibit the effects of ago-
nists, but raising the concentration of an agonist can overcome
(“surmount”) this inhibition completely. The simple occupancy
model considers this behavior as “competitive,” resulting from the
reversible combination of the agent with the same site that binds
the agonist, thereby preventing combination of the receptor with
the agonist.
In designing drugs to interact with receptors, often the only
clue we have is the structure of the endogenous agonists. There-
fore, many drugs in current use are structural analogs of hormones
or neurotransmitters. It is not surprising then that they bind to the
same binding pocket on the receptor as the endogenous agonist.
However, because their structure has been changed, some of these
compounds fail to activate the receptor. Instead, they “compete”
with the endogenous agonist for the binding pocket. Which com-
pound succeeds in binding to the receptor is completely determined
by the relative concentrations of the agonist and the antagonist and
their respective dissociation constants.
In our model competitive antagonists are designated “I” to
invoke their role as inhibitors of the receptor. Antagonists bind to
receptor sites without initiating a response, thereby reducing the
concentration of (R) available and forming the inactive species (IR)
Pharmacodynamics III 69
in a concentration- dependent fashion as indicated in the following
diagram (Figure 9.2):
The dissociation constant of the antagonist for the receptor
is given by
K
IR
IR
i
where Ki is the dissociation constant of the antagonist for the
receptor R.
We can now solve for the concentration of receptors bound to
agonist, DR, when both agonists and antagonists are present by
using the same tricks as before. First, the total number of receptors
is divided into three species:
RD
RRI
R
t
Then the equations for the agonist and antagonist dissociation
constants can be used to reduce this expression to one that describes
DR in terms of the agonist (D) and antagonist (I) concentrations
and the two dissociation constants. You may wish to try the algebra
yourselves. The result is given below.
DR
RD
DK
I
K
d
i
t
1
Therefore, we can see that increasing [I] has the effect of increas-
ing the apparent Kd by a factor of (1 + [I]/Ki) and that progressively
D + R ⇌ DR Effect
IR (no effect)
+
I
⇋
Figure9.2
70 ESSENTIAL PHARMACOLOGY
increasing [D] reduces the impact of a given [I] toward zero. The
normalized dose- response relationship then becomes:
%MAX EFFECT
D
DK
I
K
d
i
100
1
Let’s try an example (Figure 9.3):
Note that the increasing concentrations of antagonist cause
a parallel shift to the right of the log dose–response curve. In the
presence of a competitive antagonist, the agonist appears to
have reduced potency.
There are important therapeutic lessons embodied in these curves.
In this example it is seen that if the agonist is present at a concentra-
tion near its “true” dissociation constant (1 μM), then the antagonist
is very effective at shutting down the receptor. However, if the agonist
concentration is increased to much higher levels, then it can overcome
the effect of the antagonist and activate the receptor (see the curve
furthest to the right). This is exactly what the body may try to do in
10
–10
0
20
40
60
80
100
120
10
–9
10
–8
10
–7
10
–6
[D], molar
10
–5
10
–4
I = 10
–4
I = 0
10
–3
10
–2
% of maximal effect
Figure9.3
−6
−6
−7
−6
−4
Pharmacodynamics III 71
the presence of drugs that act as antagonists. Sensitive to the fact that
signals are no longer coming through the communication pathway,
the body may attempt to compensate by increasing the amount of ago-
nist released in the vicinity of the receptor. This can very significantly
reduce the effect of a given medication that acts as an antagonist. On
the one hand, this weakness of competitive antagonists might be seen
as a disadvantage. However, it can also be an advantage. There may be
situations where it is of physiological benefit for the body to be able
to “break through” the effect of the drug. For example, in the case of
reducing the output of the heart in the treatment of hypertension by
treatment with the β- adrenergic competitive antagonist propranolol,
the body would be able to force enough noradrenaline onto the heart
to increase heart rate and blood pressure if needed to respond to blood
loss or the need for quick action in an emergency.
9.3 “Noncompetitive” or “Insurmountable”
Antagonists
Noncompetitive antagonists also inhibit the effects of agonists by com-
bining with the same receptors that bind agonists. However, in this
case, progressively raising the concentration of the agonist never fully
overcomes the inhibition. This type of antagonist, also called an insur-
mountable antagonist, prevents the agonist from producing any effect
at a given receptor site. It accomplishes this while binding to a sepa-
rate site on the receptor from the agonist- binding site, so there is no
direct competition between the two compounds to access the receptor.
Since the binding site for the noncompetitive antagonist is dif-
ferent from the binding site for the agonist, such an antagonist typi-
cally bears no structural relationship to the agonist.
Therefore, knowledge of the structure of the agonist– a known
hormone or neurotransmitter– provides no clues as to how to design
a useful noncompetitive antagonist. For this reason, most of the
noncompetitive antagonists currently used in medicine were dis-
covered empirically by randomly screening unrelated compounds
for effects on a given tissue or its resident receptors.