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0031-6997/95/4702-0255$03.00!0PHARMACOLOGICAL REVIEWS

Copyright © 1995 by The American Society for Pharmacology and Experimental Therapeutics

Vol. 47, No. 2

Printed in U.S.A.

International Union of Pharmacology Committee on

Receptor Nomenclature and Drug Classification.

Ix. Recommendations on Terms and Symbols in

Quantitative Pharmacology

DONALD H. JENKINSON,1 ERIC A. BARNARD,2 DANIEL HOYER,3 PATRICK P. A. HTJMPHREY4*, PAUL LEFF,5 AND

NIGEL P. SHANKLEY�

‘Department ofPharmacology, University College London, London, United Kingdom; 2Molecular Neurobiology Unit,

Royal Free Hospital School ofMedicine, London, United Kingdom; 3Sandoz Pharma Limited, Basel, Switzerland; 4Glaxo Institute of

Applied Pharmacology, University of Cambridge, Cambridge, United Kingdom; 5Fisons Pharmaceuticals, Leicestershire, United Kingdom;

6James Black Foundation, London, United Kingdom

I. Introduction 255

A. Members of the Technical Subcommittee 256

B. Corresponding Members 256

II. Recommendations 256

A. The expression of amount of drug: concentration and dose 256

1. Concentration 256

2. Dose 256

B. General terms used to describe drug action 257

C. Empirical measures of drug action 257

1. General measures 257

2. Agonists 258

3. Antagonists 259

D. Terms and procedures used in the analysis of drug action 260

1. The quantification of ligand-receptor interactions 260

2. Actions of agonists 262

3. Actions of antagonists 264

III. Appendix 266

A. Microscopic and macroscopic equilibrium constants 266

B. Schild equation and plot-further detail 266

C. The relationship between the Hill and logistic equations 266

IV. References 266

I. Introduction

The literature of pharmacology presents many incon-

sistencies in the use of nomenclature and symbols.These are particularly common in operational studies in

which receptors are characterized by quantitative mea-

surements of receptor-mediated function and of ligand

binding. The problem is compounded by the fact that

sometimes a given term is used in quite different senses.

For these reasons, it would, we believe, be helpful to

* To whom correspondence should be addressed: Glaxo Institute of

Applied Pharmacology, Department of Pharmacology, University of

Cambridge, Tennis Court Road, Cambridge CB2 1QJ, UK.

adhere to (so far as is practicable and reasonable) a

common terminology, set of definitions, and symbol us-

age. These issues have been addressed in most other

biological and physical sciences, and the approach taken

by the International Union of Pure and Applied Chem-

istry (IUPAC) seems particularly relevant to us (see, for

example, Mills et a!. 1993)

The recommendations that follow have been pre-

pared as one of the objectives of a Technical Subcom-

mittee set up by the International Union of Pharma-

co!ogy Committee on Receptor Nomenclature and

Drug Classification. The authors are most grateful to

the other subcommittee members and to a pane! of

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256 JENKINSON ET AL.

distinguished pharmacologists who served as corre-

sponding members. Al! provided invaluable comments

and suggestions for the improvement of successive

drafts. These consultations notwithstanding, the rec-

ommendations that follow are to be regarded as pro-visional in nature. Their aim is to aid communication

and ease of comprehension without being rigidly pre-

scriptive, and they will certainly require periodic re-

vision and updating as new ideas and information

arise. With this in mind, the Technical Subcommitteewelcomes comments and suggestions. Al! correspon-

dence should be addressed to the subcommittee chair-

man, P. P. A. Humphrey (see footnote).It should be added that variations from the suggested

notation and usage may well be desirable under partic-ular circumstances. For example, subscripts can be

omitted where no ambiguity would result, or additional

subscripts or superscripts may be added in the interests

of clarity. The only essential is that the new terms are

clearly defined.

A. Members of the Technical Subcommittee

E. A. Barnard

T. I. BonnerD. Hoyer

P. P. A. HumphreyD. H. JenkinsonP. Leff

J. LomasneyN. P. Shankley

B. Corresponding Members

R. B. Barlow

J. W. BlackD. E. ClarkeD. Colquhoun

R. F. FurchgottJ. P. GreenT. P. KenakinU. Trendelenburg

D. R. Waud

II. Recommendations

As a general principle, these follow the recommendationsof the International Union of Pure and Applied Chemistry

(Mills et a!., 1993), albeit with variations and extensions

prompted by the requirements of pharmacolog�.

A. The Expression ofAmount ofDrug: Concentration

and Dose

1. Concentration. It is recommended that the molar

concentration of substance X be denoted by either [XJ or

C�, with the former preferred. Decimal multipliersshould be indicated by the use of either Le Syst#{232}meInternational dljnit#{233}s (International System of Units)prefixes (e.g., iM, nrvi) or by powers often (e.g., 3 X 108 M),

with the former preferred.2. Dose. In some circumstances (e.g., in therapeutics

and clinical pharmacology, in in vivo experiments, and

when tissues are perfused in vitro and exposed to a bolus

application of drug), absolute drug concentrations areuncertain, and it becomes more appropriate to specify

the quantity of drug administered. This may be done in

terms ofeither mass or molar quantity. Units and routes

of administration should be specified. In the case of invivo experiments with animals, the quantity ofdrug is tobe expressed per unit of animal mass (e.g., mollkg, mg/kg). In therapeutics, mg/kg will normally be appropriate.

Negative indices should be used where confusion could

otherwise arise (e.g., mg min1 kg’).

B. General Terms Used to Describe Drug Action

Table 1.

C. Empirical Measures ofDrug Action

1. General measures. Table 2.

2. Agonists. Table 3.3. Antagonists. Table 4.

D. Terms and Procedures Used in the Analysis of Drug

Action

1. The quantification of ligand-receptor interactions.

Table 5.2. Action ofagonists. Table 6.

3. Action ofantagonists. Table 7.

QUANTITATIVE PHARMACOLOGY 257

TABLE 1

General terms used to describe drug action

Term Suggested usage Notes

Agonist A ligand that binds to receptors and thereby alters the proportion Agonists may act by combining either with the same

of them that are in an active form, resulting in a biological site(s) as the endogenous agonist or, less

response. Conventional agonists increase this proportion, commonly, with a different region of the receptor

whereas inverse agonists (which see) reduce it. macromolecule. Agonists in the second category

are sometimes referred to as allosteric agonists or

activators.

Some agonists (e.g., glutamate) may only be effective

in the presence of another ligand (e.g., glycine in

the case of glutamate) that binds to a different site

on the receptor macromolecule. Under these

circumstances, glutamate is referred to as the

primary agonist and glycine as a co-agonist.

Antagonist A drug that reduces the action of another drug, generally an The term physiological antagonism has also been

agonist. Many act at the same receptor macromolecule as the used to describe the action of a substance that

agonist. Antagonists of this kind may be surmountable or exerts an opposite effect to an agonist.insurmountable, depending on the experimental conditions (see

table 7). Antagonism may also result from combination with the

substance being antagonized (chemical antagonism), or the

production of an opposite effect through a different receptor

(functional antagonism) or as a consequence of competition for

the binding site of an intermediate that links receptor activation

to the effect observed (indirect antagonism). The term functional

antagonism is also used to describe a less well-defined category in

which the antagonist interferes with other events that follow

receptor activation.

Modulator A ligand that increases or decreases the action of an agonist by

combining with a distinct (allosteric) site on the receptor

macromolecule.

Receptor Cellular macromolecules that are concerned directly and specifically

in chemical signaffing between and within cells. Combination of a

hormone, neurotransmitter, drug or intracellular messenger with

its receptor(s) initiates a change in cell function.The regions of the receptor macromolecule to which endogenous

agonists bind are referred to collectively as the recognition site(s)of the receptor.

TABLE 2

Empirical measures ofdrug action: general


The relationship between In the following, drug action is expressed in terms of [A]50 in the Hill equation is sometimes denoted by

concentration and the effect, E, produced when an agent, A, is applied K, and E� by a. The choice between [Also and Keffect: Hill equation. at a concentration [A]. The relationship between E will depend on the directness of the measurement.

and [A] can often be described empirically by the The former is appropriate if an indirect action,

Hill equation which has the form: such as the contraction of an intact smooth muscle

E A ““ preparation, is observed. However, in a ligand- = [ ] binding experiment, K would be preferable,E� [A]� + [A]”H although whether the value ofK corresponds to a

. . . . single dissociation equilibrium constant (even ifwhere Em,,,, ‘� the maximal action of A, nfl is the nH is unity) will depend on the circumstances

Hill coefficient and [A]so 15 the concentration that � Ap�nii� ffl.A.).

produces an effect that is 50% Of Em,�.The Hill equation and the logistic equation are

closely related but not identical (see Appendix,

IH.C.).

Potency An expression of the activity of a drug, either in terms

of the concentration or amount needed to produce a

defined effect, or, less acceptably, with regard to the

maximal effect attainable. An imprecise term that

should always be further defined (see EC50, IC50,Maximal agonist effect, etc.).

ED50


work.

TABLE 3

Empirical measures of drug action: agonists


EC50 or [A]50 The molar concentration of an agonist that

produces 50% of the maximal possible

effect of that agonist. Other percentage

values (EC2O, EC40, etc.) can be specified.

The action of the agonist may be

stimulatory or inhibitory.

The mass concentration (g/l) to be used if the molecular

weight of the test substance is unknown.

It may sometimes be preferable to express the activity of a

drug in terms of the concentration that causes a

specified change in a baseline measurement (e.g., a 20-

mm Hg change in perfusion pressure; a 30% increase ina muscle twitch). If the EC� (or [A]�) terminology is to

be used in this context, the appropriate units must be

included (e.g., � or [A]3�) to avoid confusion with

EC20 or [A]30 as here defined.

Under some circumstances, it may become appropriate to

use these terms in a more general sense. For example,

the application of an antagonist to an intact tissue can

reduce the action of an endogenous agonist that exerts

an inhibitory effect. Thus, an a2-adrenoceptor

antagonist such as yohimbine will block inhibitory a2-

autoreceptors on noradrenergic nerve endings. The

outcome will be a rise in noradrenaline release. If this

release is measured, it will be increased in a graded

fashion by the antagonist. Under such circumstances,

when the agonist concentration is unknown, this action

of the antagonist can be characterized in terms of an

EC50 or [A]50. If, however, the concentration of agonist

is known, then the measures of antagonist action

considered in the next table (table 4) should be used.

Eitherthe dose of a drug that produces, on

average, a specified all-or-none response

in 50% of a test population

or, if the response is graded,

the dose that produces 50% of the

maximal response to that drug

Units (e.g., mg/kg, mmol/kg or mg/I, mmol/l when a tissue

is perfused) to be given.

Applicable to in vivo measurements and to those in vitro

experiments (e.g., with a perfused tissue) in which

absolute concentration is uncertain. Otherwise use

EC50.

In some circumstances, the maximum response will be

unknown. This will often be so in clinical pharmacology,

for considerations of safety. The effectiveness of a drug

may then be best expressed in terms of the dose that

causes, for example, a certain change in blood pressure

or heart rate. If the ED terminology is to be used for

such measurements, the appropriate units must beincluded (e.g., � to avoid confusion with the

usage recommended in the left column.

pEC50 or p[A]50 The negative logarithm to base 10 of the

EC50 of an agonist.

The term pD2 has also been used, particularly in the

earlier literature.

Maximal agonist effect, a The maximal effect that an agonist, whether

conventional or inverse, can elicit in a

given tissue under particular

experimental conditions, expressed as a

fraction of that produced by a full agonist

acting through the same receptors under

the same conditions.

Also referred to as intrinsic activity, although the term

maximal agonist effect is preferred.

See also Efficacy (table 6).

Equi-effective molar

concentration ratio,

EMR

The ratio of the molar concentrations of test

and reference substances that produce the

same biological effect (whether activation

or inhibition).

Should only be specified if the log concentration-effect

curves for the substances being compared are parallel.

Equi-effective dose ratio,

EDR

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266 JENKJNSON ET AL.

III. Appendix

A. Microscopic and Macroscopic Equilibrium Constants

Microscopic and macroscopic equilibrium constants

should be distinguished when describing complex equi-libria, as occur with all agonists. The latter refers to the

overall equilibrium (i.e., the value that would be ob-

tamed in a ligand binding experiment). For the scheme

K, K2

A+R ;=� AR �==� Mt*

the macroscopic dissociation equilibrium constant isgiven by

K1K2Keff � � K2

Here, K1 and � are the microscopic equilibrium con-

stants. Note that on this scheme, Furchgott’s (1966)irreversible antagonist method for determining the dis-

sociation equilibrium constant for an agonist would pro-vide an estimate OfKeff rather than K1.

This distinction is also important when considering

those receptors (e.g., ligand-gated ion channels) that

have more than one binding site for the agonist.

B. Schild Equation and Plot-Further Detail

The Schild equation is based on the assumptions that

(a) agonist and antagonist combine with the receptormacromolecule in a freely reversible but mutually exclu-sive manner, (b) equilibrium has been reached and that

the law of mass action can be applied, (c) a particular

level of response is associated with a unique degree ofoccupancy or activation of the receptors by the agonist,(d) the response observed is mediated by a uniform

population of receptors, and (e) the antagonist has noother relevant actions, e.g., on the relationship betweenreceptor and response.

For an antagonist to be classified as reversible and

competitive on the basis of experiments in which a bio-logical response is measured, the following criteria musthold:

a) in the presence of the antagonist, the log agonistconcentration-effect curve should be shifted to the rightin a parallel fashion.

b) the relationship between the extent of the shift (as

measured by the concentration ratio) and the concentra-tion of the antagonist should follow the Schild equationover as wide a range of antagonist concentrations as

practicable. Usually, the data are presented in the form

of the Schild plot, and adherence to the Schild equationis judged by the finding of a linear plot with unit slope.

Non-linearity and slopes other than unity can result

from many causes. For example, a slope greater than 1may reflect incomplete equilibration with the antagonist

or depletion of a potent antagonist from the medium, asa consequence either of binding to receptors or other

structures, or of partitioning into lipid. A slope that issignificantly less than 1 may indicate removal of agonist

by a saturable uptake process, or it may arise because

the agonist is acting at more than one receptor (theSchild plot may then be non-linear). See Kenakin (1993)

for a detailed account.The finding that the Schild equation is obeyed over a

wide range of concentrations does not prove that the

agonist and antagonist act at the same site. All that maybe concluded is that the results are in keeping with thehypothesis of mutually exclusive binding, which may of

course result from competition for the same site but can

also arise in other ways.

C. The Relationship Between the Hill and Logistic

Equations

The logistic function is defined by the equation

1

y = � � �

where a and b are constants. If a is redefined as

-log�(K”), and x as log5z, then

y = Kb +

which has the same form as the Hill equation.

REFERENCES

ARUNLAKSHANA, 0., �rw ScmLD, H. 0.: Some quantitative uses ofdrug antag-onists. Br. J. Pharmacol. 14: 48-58, 1959.

BLAcK, J. W., AND LEFF, P.: Operational models of pharmacological agonism.Proc. R. Soc. Lond. B Biol. Sci. 220: 141-162, 1983.

CoLQuHouN, D.: Affinity, efficacy and receptor classification: is the classicaltheory still useful? In Perspectives on Receptor Classification: ReceptorBiochemistry and Methodology, ed. by J. W. Black, D. H. Jenkinson andV. P. Gerskowitch, vol. 6, pp. 103-114, Alan R. Liss, New York, 1987.

DEL C�s’rua�o, J., �.Nn K.&rz, B.: Interaction at end-plate receptors betweendifferent choline derivatives. Proc. R. Soc. Lond. B Biol. Sci. 146: 369-381,1957.

DELEAN, A., STADEL, J. M., �i�r LEFKowirz, R. J.: A ternary complex modelexplains the agonist-specific binding properties of the adenylate cyclase-coupled f3-adrenergic receptor. J. Biol. Chem. 255: 7108-7117, 1978.

FURCHGOTF, R. F.: The use of (3-haloalkylamines in the differentiation ofreceptors and in the determination of dissociation constants of receptor-agonist complexes. Adv. Drug Res. 3: 21-55, 1966.

GADDUM, J. H.: The quantitative effects of antagonistic drugs. J. Physiol.(Lond.) 89: 7P, 1937.

GADDuM, J. H.: Introductory address. Part I. Biological aspects: the antago-nism of drugs. Trans. Faraday Soc. 39: 323-332, 1943.

KENAKIN, T. P.: PharmacologicAnalysis ofDrug-Receptor Interaction. 2nd Ed.,Raven Press, New York, 1993.

MILLS, I., CvITA�, T., H0MANN, K, KAu.�y, N. �rw KucHrrsu, K: Quantities,Units and Symbols in Physical Chemistry, published under the auspices ofthe International Union ofPure and Applied Chemistry, 2nd Ed., Blackwell,Oxford, 1993.

SAMAMA, P., CoTEccalA, S., COSTA, T., �ND LEFKOWITZ, R. J.: A mutation-induced activated state ofthe /32 -adrenergic receptor: extending the ternarycomplex model. J. Biol. Chem. 288: 4625-4636, 1993.

Sc}IILD, H. 0.: pA, a new scale for the measurement ofdrug antagonism. Br. J.Pharmacol. 2: 189-206, 1947.

ScmLD, H. 0.: pA,, and competitive drug antagonism. Br. J. Pharmacol. 4:277-280, 1949.

STEPHENSON, R. P.: A modification of receptor theory. Br. J. Pharmacol. 11:379-393, 1956.

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