An Alternative Method to Evaluate the Nature of an Antagonist and
Its Potency: A Theoretical Approach
Vincenzo Calderone
Istituto Policattedra di Discipline Biologiche, Facolta ` di Farmacia, Universita ` degli Studi di Pisa, via Bonanno 6, 56126 Pisa, Italy
The Schild analysis is certainly the most reliable method for antagonism studies. The Schild
regression allows one to determine the parameter of the Schild-slope, which represents a
powerful diagnostic tool when investigating the nature of an antagonist and, consequently, to
evaluate its potency. Nevertheless, in functional pharmacology, often practical reasons lead
the experimenter to obtain an inhibition curve for the antagonist and calculate its potency by
means of equations, which can be considered as a derivation of the Cheng-Prusoff analysis.
This approach is considered theoretically invalid, because it does not allow to know the exact
nature of the antagonism, and thus the evaluation of the antagonist dissociation constant can
be meaningless. In this paper, a new method is proposed, which, by means of an equation
closely similar to the Schild one, permits one to obtain a linear regression analysis, giving a
slope value absolutely equivalent to the Schild-slope. This method allows us to determine both
the nature and the potency of an antagonist, and requires an experimental procedure
substantially analogous to the one performed to obtain an inhibition curve. © 1998 Elsevier
Science Inc.
Key Words: Antagonist; Dissociation constant; Competitive antagonism
Introduction
Both the evaluation of the pharmacological proper-
ties of developmental drugs and the classification of
receptors, need a reliable estimation of the potency of
the competitive antagonists. This value is usually ex-
pressed as the equilibrium dissociation constant (Kb),
which represents a parameter linked to the chemical
forces of the antagonist–receptor reversible interaction
and ideally independent of the receptor location and
function (Kenakin, 1984a).
Two of the most widely used methods for the estima-
tion of the Kb in functional studies are the Schild
analysis (Arunlakshana and Schild, 1959) and the
Cheng-Prusoff analysis (Cheng and Prusoff, 1973), both
based on equations which can be considered as a devel-
opment of the following two experimental logistic equa-
tions, closely related to the Gaddum’s classic formula-
tion of the competitive antagonism (Gaddum, 1937,
1943) and describing the concentration–response curves
(CRCs) for an agonist, respectively in the absence
(equation 1) or in the presence (equation 2) of a
competitive antagonist:
Eff =
E max
1 +
EC
50
A
n
(1)
Eff =
E max
1 +
EC
50
1 +
B
Kb
A
n
2 ,
in which Eff is the functional response evoked by the
concentration A of an agonist, with a determined EC
50
value; Emax is the maximal response evoked by the
agonist; n is the slope factor of the curve; B and Kb are,
respectively, the concentration of a competitive antago-
nist and its dissociation constant.
The Schild analysis requires the construction of full
CRCs for an agonist in the absence and the presence of
several increasing concentrations of antagonist. The
observation of an antagonist-induced rightward parallel
shift of the CRCs (without a depression of the maximal
effect, which indicates different possible situations, such
as a noncompetitive antagonism) is the first necessary
Address reprint requests to author at above address.
Received December 9, 1997; revised January 28, 1998; accepted
February 19, 1998.
Journal of Pharmacological and Toxicological Methods 39, 129 –135 (1998)
© 1998 Elsevier Science Inc. All rights reserved. 1056-8719/98/$19.00
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