J. theor. Biol. (1995) 175, 577–582

0022–5193/95/160577+06 $12.00/0 7 1995 Academic Press Limited

A Model of Non-Exclusive Binding of Agonist and Antagonist on G-Protein

Coupled Receptors

J J

Institute of Chemical Physics, University of Tartu, 2 Jakobi Str., EE-2400 Tartu, Estonia

(Received on 21 October 1994, Accepted in revised form on 3 February 1995)

A modified concept of functioning of G-protein coupled receptors is presented, on the assumption thatagonistic and antagonistic effects of drugs are related to their interaction with two separate receptor sitesthat exist simultaneously on a single receptor molecule and possess different ligand-specificity patterns.This proposal distinguishes between agonists and antagonists as binding at one of these sites triggers thereceptor response, whereas the other site elicits another response leading to the receptor blockade. Asthese sites are simultaneously present on a single receptor molecule the formation of a ternary complexbetween agonist, antagonist and receptor is possible. Practical consequences of this concept are analysedwith reference to experimental data on muscarinic acetylcholine receptors.

7 1995 Academic Press Limited

Introduction

Drugs that interact with plasma membrane receptorshave generally been divided into two major groups:agonists, which trigger off biological responses, andantagonists, which block the action of the agonists.As a simple binding isotherm can be used to describethe dose–response data in different physiological andpharmacological tests, the classical receptor theoryassumes that agonists and antagonists bind reversiblyto the receptor (Clark 1926; Gaddum, 1936) andcompete for the same binding site (Clark, 1937;Colquhoun, 1973; Gaddum, 1936). Thus it is assumedthat the antagonist drugs inhibit the receptor responseby preventing agonist binding with the receptor.

Further, the presence of separate binding sites foragonists and antagonists on the receptor molecule wassuggested in connection with the ‘‘allosteric receptormodel’’ as well as in the case of different versions of the‘‘two-state receptor models’’ (for review see: Ariens& De Miranda, 1979). The drugs which bind moreeffectively at the agonistic site and less effectively at theantagonistic site elicit a physiological response and,therefore, are known as agonists. Other compounds,which interact more effectively with the inhibitory site,are known as antagonists. Thus, these concepts offer

a clearer formulation of the principles of distinctionbetween agonistic and antagonistic drugs on thebasis of their different affinity for the appropriatebinding sites, which in its turn should reveal different‘‘specificity patterns’’. At the same time, all theseapproaches follow the principle of competitivemechanism of interaction of agonists and antagonistswith the receptor, including the possibility of thereceptor blockade by allosteric exclusion of agonistbinding by antagonist, and therefore lead toproportionality between response and agonist bindingto the receptor, described by a rectangular hyperbolicshape of the dose–response plots.

However, in several cases ‘‘bell-shaped’’ dose–response curves have been observed. Examples of suchdata were published by Stephenson (1956), Paton(1961), Ariens (1964), but also more recently by Jarvet al. (1993). Therefore the mechanisms which lead tothis phenomenon are of general interest for receptortheory and have attracted much attention.

The first attempt at theoretical analysis of thesenon-conventional dose–response curves was made bySzabadi (1977), who analysed a system, consisting ofone agonist and two different receptors. He showedhow this model can be used to analyse bell-shapeddose–response curves, if the receptors involved

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mediate opposite effects, one stimulatory and anotherinhibitory. The same model was revisited by Rovatiand Nicosia in 1994.

In contrast to this ‘‘two-receptor model’’, bell-shaped dose–response curves have been analysedproceeding from the idea of the presence of twodifferent binding sites on one receptor molecule (Jarv,1992; Jarv et al., 1993). These sites should beresponsible for evoking and inhibiting the receptorresponse, respectively.

It is important to emphasize that in both thesemodels at least two ligand molecules should beinvolved in the process to cause bell-shaped dose–response curves. Formally speaking, this is inagreement with the fact that two inflection points canbe seen in these plots.

Finally, the downturn phase of the dose–responserelationships was analysed by Pliska (1994), proceed-ing from the idea of multiple state cell-signalling path-ways. However, in this compilation of the question ofstoichiometry of the drug-receptor complex(es) is notclearly formulated and hampers further analysis of thekinetic aspects of the model.

In the present paper I discuss the receptor concept,based on the assumption that there are two differentbinding sites on the receptor molecule, responsible forevoking and inhibiting the receptor response.

The Two-site Receptor Model

The basic idea of two different ligand-binding siteson one receptor molecule (see Ariens & De Miranda,1979) can be modified by assuming that:

(i) drug molecules may bind independently withthese sites on the receptor and, consequently, forma ternary complex including the receptor and twoligand molecules;

(ii) the binding of a ligand molecule at the agonisticsite triggers off the receptor response, while ligandbinding at the antagonistic site inhibits this responsethrough initiating another ‘‘inhibitory’’ response,which switches off the normal signal transductionmechanism (conformational transition), induced bythe ligand binding with the agonistic receptor site.

This situation can be represented as follows:

Agonistic Antagonisticsite site

‘‘Switching off’’the signal

UtransductionTmechanism

Normal receptorresponse

It is important to emphasize that in this paperthe receptor concept is discussed on the level of aformal kinetic model, independently of the particularmolecular mechanisms of transmission of neuro-transmitter effects to the responding system, structureof the particular binding sites and the possibilitythat the receptor–G-protein interactions modulate theeffectiveness of ligand binding, as pointed out bySchutz & Freissmuth (1992). The influence of theseadditional factors could be taken into consideration byintroducing extra terms into the mathematicalexpressions based on the present concept, i.e. byincreasing the number of the dimensions of the model.

On the other hand, on this basic level the proposedmodel suggests the existence of bell-shaped dose–response curves not only for partial agonists, whichelicit only weak responses, but also for full agonists.

Formalization of the Model

In general, the molecules of drug A may bind at bothagonistic and antagonistic sites on the receptorR.Hereit is assumed that both of these processes follow the lawofmass action at both sites and the affinity of the ligandfor these sites is given by the dissociation constantsKagon and Kantag, respectively. As ligand binding at theagonistic site triggers off the receptor effect and theoccupation of the antagonistic site inhibits the receptoractivity, the observed effect can be expressed as thedifference of the two corresponding dose–responsecurves. This statement can be formalized by means ofthe following equation:

EA=[RA]−[AR]

[R]0=

1Kagon/[Ai ]+1

−1

Kantag/[Ai ]+1,

(1)

where EA is the relative effect, equal to the ratio ofthe observed and maximal responses, RA and ARstand for complexes of the drug A with the agonisticand antagonistic sites on receptor R, Kagon and Kantag arethe appropriate dissociation constants.

It should be emphasized that this equation is basedon the assumption that there is direct interrelationshipbetween the extent of ligand binding and theappropriate response. But if necessary, the modelcan be updated by the introduction of someproportionality constants into the both terms ofeqn (1) by analogy with the ligand intrinsic activity(Ariens, 1954) or efficacy parameters (Stephenson,1956) in the classical receptor theory. The lattermodification of the model seems to be important if theagonistic effect is not completely inhibited by thebinding of a drug molecule at the antagonistic bindingsite. Such incomplete receptor inhibition should cause

11

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–log [A]

Rel

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e ef

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–1.00

1.00

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0.00

–0.50

1 2 3 4 6 7 8 9 10

A

B

C

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agonistic effects at high concentrations of thosecompounds that are recognized as typical antagonistsat their low concentrations.

Theoretical Analysis

It is evident from eqn (1) that the type of theobserved activity of a drug is determined by the affinityof the compound for the agonistic and antagonisticreceptor sites, characterized by the values of thedissociation constants Kagon and Kantag, respectively.Therefore the drug should reveal agonistic activity ifKagonQKantag, and antagonistic activity if the ratio ofthese constants is opposite. For a clearer presentationof the behaviour of this function, theoreticaldose–response curves were calculated for the followingcases.

First, for a typical antagonist, which has highaffinity for the antagonistic site and lower affinityfor the agonistic site, the values of pKantag=7.0 andpKagon=3.0 were used for the simulation of thedose-response curve. Figure 1 shows that no positivereceptor response can be observed in this case(curve A), as the relative effect is zero or has negativevalue within the whole drug concentration interval.Formally this means that antagonists can be describedas ligands revealing negative intrinsic activity asregards the agonistic response.

Second, for a typical agonist, which has highaffinity for the agonistic site and low affinity for theantagonistic site, the values pKagon=7.0 andpKantag=3.0 were used to simulate behaviour of thefunction (1). It appears from Fig. 1 (curve C) that aconventional dose–response curve can be obtained atligand concentrations around the Kagon value, while

an inhibitory effect is revealed when the agonistconcentration approaches the Kantag value. This meansthat at high concentration the agonistic drug behaveslike an antagonist. As this prediction of ‘‘dualism’’ ofthe actionof an agonistic drug follows directly from theproposed receptor model, all agonists must cause aninhibitory effect whenever their concentration is highenough to approach the Kantag value. It can be assumedthat at least in some cases this concentration intervalcan be reached in practice that provides the possibilityfor experimental evaluation of the suggested model.

Finally, a special case can be analysed when the drugreveals close affinity for the agonistic and antagonisticsites, i.e. activation and inhibition of the receptor canbe observed within the same concentration interval.For the simulation of this situation the constantspKagon=7.0 and pKantag=6.0 were used to calculate thedose–response curve. It can be seen in Fig. 1 (curve B)that in this case the ligand causes only a moderateeffect, which is typical of partial agonists. Thus, thepresent concept does not require the introduction ofextra parameters, like the intrinsic activity or efficacy,to describe the partial agonistic activity. Moreover,the simulated dose–response curve reveals a clearmaximum, which cannot be explained by the con-ventional receptor theories, but seems to be typical ofthe latter compounds.

In summary, the proposed receptor theory consider-ably simplifies the understanding of the principles ofdrug action and describes the behaviour of partialagonists on the basis of their affinity for agonistic andantagonistic receptor sites, i.e. by the same twoparameters Kagon and Kantag as in the case of typicalagonists.

Extension of the Model for Two or More Ligands

The principles presented above can be extended toanalyse receptor interaction with two or more differentdrugs. In this case the Kagon and Kantag values of each ofthe compounds must be taken into account, and theappropriate equation can be presented as the sum ofthe pairs of the dose–response curves. For n differentcompounds A0 . . . An we have:

EA=si=n

i=0

[RAi ]−[AiR][R]0

=si=n

i=0 0 1Ki

agon/[Ai ]+1−

1Ki

antag/[Ai ]+11, (2)

where the meaning of the parameters involvedcorresponds to eqn (1). However, it is quite reasonable

F. 1. Simulated dose–response curves for antagonist (A), partialagonist (B) and agonist (C) as predicted by eqn (1) in text.

100

6

30

Molecular refractivity

Aff

init

y (p

K)

5

4

25 50 75

1110

98

76

5

43

21

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to predict that in practice only the significant termsof this equation must be taken into account. Thisapparently leads to the common picture of agonist–antagonist competition in which case both ligandsare characterized by only one dissociation constant.Within the framework of the present model, however,these constants refer to the interaction of drugs withdifferent binding sites.

It is also important to emphasize that in the simplestcase, if the ‘‘response’’ is directly related to the receptoroccupancy, the formalism presented above should bevalid for binding curves of drugs.

Some Implications of the Two-site Model for

Muscarinic Receptor

The key point of the present receptor concept is theexistence of separate agonist and antagonist bindingsites on the receptor molecule and the possibilityof the formation of an agonist–antagonist–receptorternary complex. Kinetic evidence, suggesting simul-taneous binding of agonist and antagonist withthe same receptor molecule, has been obtained inthe case of muscarinic acetylcholine receptors bymeans of systematic kinetic study of receptor–ligandinteraction. A typical muscarinic antagonist, [3H]N-methylpiperidinyl benzilate, and two agonists, car-bamoylcholine and oxotremorine, were used in theseexperiments (Jarv et al., 1980).

This study was based on the fact that potentmuscarinic antagonists, including N-methylpiper-idinyl benzilate, interact with the receptor by acomplex mechanism, involving fast formation ofantagonist–receptor complex and the following‘‘isomerization’’ of this complex into another, slowlydissociating complex (Jarv et al., 1979). It has beenfound that carbamoylcholine and oxotremorine hadno effect on [3H]N-methylpiperidinyl benzilate bind-ing, but inhibited the ‘‘isomerization’’ step (Jarv et al.,1980). This means that the antagonist binds equallywell to the free receptor and to the receptor–agonistcomplex, suggesting formation of the ternaryagonist–antagonist–receptor complex. At the sametime inhibition of the ‘‘isomerization’’ step by theagonists gives the impression of competition betweenthe agonist and antagonist in the radioligand indisplacement experiments. For this reason theconventional equilibrium binding studies cannotreveal the formation of the agonist–antagonist–receptor ternary complexes (Jarv, 1991; Jarv, 1992)and extension of systematic kinetic studies for otherreceptor systems seems to be one of the possible waysfor evaluation of the present receptor concept.

The second example illustrates the consequences

from the two-site receptor model, related to differentspecificity of the agonistic and antagonistic sites.These differences are rather clear in the case oftetraalkylammonium ions, which are the simplestdrugs interacting with muscarinic receptors as agonistsor antagonists, while the type of their activity as wellas their affinity seems to depend upon the size of thealkyl groups. This dependence can be formalized as alinear correlation between affinity of ligands (pK) andthe molar refraction constants MR, which quantify the‘‘bulkiness’’ of these molecules, as was discussedelsewhere (Jarv & Eller, 1989; Jarv, 1992).

Figure 2 shows that the pK vs. MR plots formuscarinic agonists and antagonists reveal differentslopes and the ‘‘bulkiness’’ of ligands has contraryinfluence on the binding affinity of alkylammoniumions at agonistic and antagonistic receptor sites. Thismeans that the increase in size of molecules increasesaffinity of antagonists and decreases affinity of agonistsin the case of this particular example. Certainly, thegenuine specificity patterns of both of these sites onmuscarinic receptor must be more complex andprobably involve several structural factors whichmay be rather different in the case of agonists andantagonists.

On the other hand, the presence of commonspecificity-determining factors in the case of the

F. 2. Relationship between the affinity (pK) of alkylammoniumcompounds for the muscarinic receptor and the ‘‘bulkiness’’ ofthese compounds, as characterized by the molar refraction constantsMR. The data for the guinea pig ileum receptor are drawn fromStephenson (1956) and from Abramson et al. (1969). Agonists (q):(1) N+Me4 (tetramethylammonium); (2) EtN+Me3 (ethyltrimethyl-ammonium); (3) PrN+Me3 (propyltrimethylammonium); (4)PentN+Me3 (pentyltrimethylammonium). Partial agonist (R): (5)PentMeN+ (pentylmethylpyrrolidinium). Antagonists (r): (6)PentN+MeEt2 (pentyldiethylmethylammonium); (7) PentN+Et3

(pentyltrimethylammonium); (8) Ph(CH2)5N+Me3 (phenylpentyl-trimethylammonium); (9) Ph(CH2)5N+Me2Et (phenylpentyl-dimethylethylammonium); (10) Ph(CH2)5N+MeEt2 (phenylpentyl-methyldiethylammonium); (11) Ph(CH2)5N+Et3 (phenylpentyltri-ethylammonium).

0–log [carbachol]

Inh

ibit

ion

(%

)

5

40

30

20

10

1 2 3 4 6

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agonistic and antagonistic sites removes the necessityof absolute distinction between these drugs. Thereforesome compounds may have close affinity for both ofthese sites. In this case these compounds stimulate andinhibit the receptor simultaneously, as is characteristicof the action of partial agonists. This situation isillustrated in Fig. 2 where the point for a partial agonistlies close to the intersection point of the two lines,conventionally describing the specificity of theagonistic and antagonistic sites in this simplifiedexample. A more complex plot of the same type wasdiscussed elsewhere (Jarv, 1992).

Dual Effect of Agonists

According to the two-site receptor model thedistinction between agonists and antagonists by thereceptor is based on different affinity of thesecompounds for the agonistic and antagonistic bindingsites. However, this distinction cannot be absoluteif some common interaction mechanisms (hydro-phobicity, ion–ion interactions, H-bonds, etc) areinvolved for molecular recognition of ligands in thesesites. Therefore it can be predicted that agonistsmay also bind to the antagonistic site at sufficientlyhigh drug concentrations. This, in turn, should lead toblockade of the receptor response elicited at lowerconcentrations of the same ligand. Thus the two-sitemodel predicts dual effects of agonists and thebell-shaped forms of the dose–response curves.

For example, this was demonstrated in the caseof the muscarinic receptor mediated inhibition ofadenylate cyclase activity, measured at non-conven-tionally wide carbamoylcholine concentration interval(Jarv et al., 1993). Figure 3 shows that at low agonist

concentration this compound inhibited the cAMPsynthesis in a dose-dependent manner with theEC50-value 11 mM. The further increase in carbamoyl-choline concentration revealed the bell-shaped natureof this plot, indicating that the inhibitory effect ofagonist was blocked and the adenylate cyclase activitywas restored at a high ligand concentration. Thedownturn phase of this plot is also dose-dependent andthe effect of carbamoylcholinewas characterized by theIC50 value 4 mM. Thus, the effect of carbamoylcholineon the agonistic and antagonistic sites differs by almostthree powers of magnitude. This is large enough tomake the agonistic behaviour of this compoundobservable at submillimolar concentrations.

The present receptor concept predicts that therecould be some drugs that are initially recognized asantagonists, but in spite of that reveal agonistic activityat very high concentrations. This means that theagonistic activity of these drugs is not completelyinhibited by their antagonistic effect. Formally thissituation can be described by introducing respective‘‘intrinsic activity’’ parameters aagon and aantag to expressdrug interaction with the agonistic and antagonisticsites. As a result of this, eqn (1) can be presented asfollows:

EA=[RA]−[AR]

[R]0

=aagon

Kagon/[Ai ]+1−

aantag

Kantag/[Ai ]+1. (3)

In the case of such ‘‘late’’ agonistic activity ofantagonists aagonqaantag, and the difference between thefirst and the second terms of eqn (3) becomes positiveat sufficiently high ligand concentration. Thus themaximal value of the ‘‘late’’ agonistic effect of anantagonistic drug is determined by the differencebetween the parameters aagon and aantag.

Concluding Remarks

In this paper only the formal kinetic model of thenon-exclusive mechanism of agonist and antagonistinteraction with receptor molecule has been formu-lated. This means that the two independent bindingsites cannot be related to any particular areas ofthe receptor molecule without additional experiments,which design, in turn, can be stimulated by theproposed model. On the other hand, it can be expectedthat the presentation of this receptor model in the formof the equations above opens the possibility for dataprocessing as well as for theoretical analysis of various

F. 3. Carbachol-mediated inhibition of the adenylate cyclaseactivity in rat cerebral cortex membrane fragments, demonstratingligand interaction with the agonistic and antagonistic sites on themuscarinic receptor. Data taken from Jarv et al. (1993).

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situations, caused by different types of ligands andtheir combinations.

The experimental results discussed above arepresented for illustration of the possible ways ofapplication of the two-site receptor model and concernonly muscarinic acetylcholine receptors. This limi-tation is, at least partially, caused by the fact that in thiscase the kinetic aspects of the receptor–ligandinteraction have been analysed more systematicallyif compared with other receptors. But hopefully theprinciples, formulated within the present model,will stimulate similar studies with other receptorsystems, providing concrete ways for evaluation of theproposed model.

Part of this work was supported by EMBO Grant EE111-1992 and the Estonian Science Foundation.

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