Quantification of Drug Action V

Concentration-Binding Curves
In order to elicit their effect, drug molecules
must be bound to the cells of the
effector organ. Binding commonly occurs
at specific cell structures, namely,
the receptors. The analysis of drug binding
to receptors aims to determine the
affinity of ligands, the kinetics of interaction,
and the characteristics of the
binding site itself.
In studying the affinity and number
of such binding sites, use is made of
membrane suspensions of different tissues.
This approach is based on the expectation
that binding sites will retain
their characteristic properties during
cell homogenization. Provided that
binding sites are freely accessible in the
medium in which membrane fragments
are suspended, drug concentration at
the “site of action” would equal that in
the medium. The drug under study is radiolabeled
(enabling low concentrations
to be measured quantitatively),
added to the membrane suspension,
and allowed to bind to receptors. Membrane
fragments and medium are then
separated, e.g., by filtration, and the
amount of bound drug is measured.
Binding increases in proportion to concentration
as long as there is a negligible
reduction in the number of free binding
sites (c = 1 and B ! 10% of maximum
binding; c = 2 and B ! 20 %). As binding
approaches saturation, the number of
free sites decreases and the increment
in binding is no longer proportional to
the increase in concentration (in the example
illustrated, an increase in concentration
by 1 is needed to increase
binding from 10 to 20 %; however, an increase
by 20 is needed to raise it from 70
to 80 %).

The differing affinity of different ligands
for a binding site can be demonstrated
elegantly by binding assays. Although
simple to perform, these binding
assays pose the difficulty of correlating
unequivocally the binding sites concerned
with the pharmacological effect;
this is particularly difficult when more
than one population of binding sites is
present. Therefore, receptor binding
must not be implied until it can be
shown that
• binding is saturable (saturability);
• the only substances bound are those
possessing the same pharmacological
mechanism of action (specificity);
• binding affinity of different substances
is correlated with their pharmacological
potency.
Binding assays provide information
about the affinity of ligands, but they do
not give any clue as to whether a ligand
is an agonist or antagonist . Use of
radiolabeled drugs bound to their receptors
may be of help in purifying and
analyzing further the receptor protein.

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Quantification of Drug Action IV

Disadvantages are:
1. Unavoidable tissue injury during dissection.
2. Loss of physiological regulation of
function in the isolated tissue.
3. The artificial milieu imposed on the
tissue.
Concentration-Effect Curves (B)
As the concentration is raised by a constant
factor, the increment in effect diminishes
steadily and tends asymptotically
towards zero the closer one comes
to the maximally effective concentration.
The concentration at which a maximal
effect occurs cannot be measured
accurately; however, that eliciting a
half-maximal effect (EC50) is readily determined.
It typically corresponds to the
inflection point of the concentration–
response curve in a semilogarithmic
plot (log concentration on abscissa).
Full characterization of a concentration–
effect relationship requires determination
of the EC50, the maximally
possible effect (Emax), and the slope at
the point of inflection.

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Quantification of Drug Action III

Concentration-Effect Relationship (A)
The relationship between the concentration
of a drug and its effect is determined
in order to define the range of active
drug concentrations (potency) and
the maximum possible effect (efficacy).
On the basis of these parameters, differences
between drugs can be quantified.
As a rule, the therapeutic effect or toxic
action depends critically on the response
of a single organ or a limited
number of organs, e.g., blood flow is affected
by a change in vascular luminal
width. By isolating critical organs or tissues
from a larger functional system,
these actions can be studied with more
accuracy; for instance, vasoconstrictor
agents can be examined in isolated
preparations from different regions of
the vascular tree, e.g., the portal or
saphenous vein, or the mesenteric, coronary,
or basilar artery. In many cases,
isolated organs or organ parts can be
kept viable for hours in an appropriate
nutrient medium sufficiently supplied
with oxygen and held at a suitable temperature.
Responses of the preparation to a
physiological or pharmacological stimulus
can be determined by a suitable recording
apparatus. Thus, narrowing of a
blood vessel is recorded with the help of
two clamps by which the vessel is suspended
under tension.
Experimentation on isolated organs
offers several advantages:
1. The drug concentration in the tissue
is usually known.
2. Reduced complexity and ease of relating
stimulus and effect.
3. It is possible to circumvent compensatory
responses that may partially
cancel the primary effect in the intact
organism — e.g., the heart rate increasing
action of norepinephrine
cannot be demonstrated in the intact
organism, because a simultaneous
rise in blood pressure elicits a counter-
regulatory reflex that slows cardiac
rate.
4. The ability to examine a drug effect
over its full rage of intensities — e.g.,
it would be impossible in the intact
organism to follow negative chronotropic
effects to the point of cardiac
arrest.

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Quantification of Drug Action II

To illustrate this point, we consider
an experiment in which the subjects individually
respond in all-or-none fashion,
as in the Straub tail phenomenon
. Mice react to morphine with excitation,
evident in the form of an abnormal
posture of the tail and limbs. The dose
dependence of this phenomenon is observed
in groups of animals (e.g., 10
mice per group) injected with increasing
doses of morphine. At the low dose,
only the most sensitive, at increasing
doses a growing proportion, at the highest
dose all of the animals are affected
. There is a relationship between the
frequency of responding animals and
the dose given. At 2 mg/kg, one out of 10
animals reacts; at 10 mg/kg, 5 out of 10
respond. The dose-frequency relationship
results from the different sensitivity
of individuals, which as a rule exhibits
a log-normal distribution (C, graph at
right, linear scale). If the cumulative frequency
(total number of animals responding
at a given dose) is plotted
against the logarithm of the dose (abscissa),
a sigmoidal curve results .
The inflection point of the curve lies at
the dose at which one-half of the group
has responded. The dose range encompassing
the dose-frequency relationship
reflects the variation in individual sensitivity
to the drug. Although similar in
shape, a dose-frequency relationship
has, thus, a different meaning than does
a dose-effect relationship. The latter can
be evaluated in one individual and results
from an intraindividual dependency
of the effect on drug concentration.
The evaluation of a dose-effect relationship
within a group of human subjects
is compounded by interindividual
differences in sensitivity. To account for
the biological variation, measurements
have to be carried out on a representative
sample and the results averaged.
Thus, recommended therapeutic doses
will be appropriate for the majority of
patients, but not necessarily for each individual.
The variation in sensitivity may be
based on pharmacokinetic differences
(same dose ! different plasma levels)
or on differences in target organ sensitivity
(same plasma level !different effects).

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Quantification of Drug Action I

Dose–Response Relationship
The effect of a substance depends on the
amount administered, i.e., the dose. If
the dose chosen is below the critical
threshold (subliminal dosing), an effect
will be absent. Depending on the nature
of the effect to be measured, ascending
doses may cause the effect to increase in
intensity. Thus, the effect of an antipyretic
or hypotensive drug can be quantified
in a graded fashion, in that the extent
of fall in body temperature or blood
pressure is being measured. A dose-effect
relationship is then encountered.
The dose-effect relationship may
vary depending on the sensitivity of the
individual person receiving the drug,
i.e., for the same effect, different doses
may be required in different individuals.
Interindividual variation in sensitivity is
especially obvious with effects of the
“all-or-none” kind.

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