Br. J. Pharmacol. (1992), 106, 710-716
f,'.
Macmillan Press Ltd, 1992
Construction of antagonist dose-response curves for estimation of pA2-values by Schild-plot analysis and detection of allosteric interactions 'Gerald Poch, Friedrich Brunner & Elisabeth Kuihberger Institut
fur
Pharmakologie und Toxikologie, Universitat Graz, Univ. pl. 2, A-8010 Graz, Austria
1 One aim of this paper is to show an alternative approach for the determination of antagonist affinity estimates, KB and pA2, by construction and evaluation of antagonist dose-response curves (DRCs), using the curve-fitting programme, ALLFIT. 2 Parallel antagonist DRCs were derived by vertical analysis of families of conventional agonist DRCs in the presence and absence of an antagonist at a certain agonist concentration above its EDM. The latter represents a chosen, i.e. fixed dose-ratio (DR). The antagonist concentration that reduces an agonist effect to its Emax/2 was termed B,. It corresponds to B, the fixed antagonist concentration, tested to obtain DR 1, conventionally. 3 The dissociation constant was calculated as KB= BX/DR 1, analogous to the conventional approach (KB= B/DR 1). Likewise, pA2-values were estimated by plotting log B", obtained by the alternative approach, vs log (DR 1) in an 'alternative Schild plot'. 4 Experimental agonist DRCs from our laboratory and from the literature were analysed and KB- and pA2-values obtained by the alternative approach were compared with those obtained by the conventional method. The results showed a very good agreement (correlation) between the pA2-values obtained by either method (slope = 1.02, r = 0.99, n = 9), in agreement with theoretical DRCs. 5 Besides estimation of KB and pA2, antagonist DRCs were also evaluated qualitatively. The most important finding was that allosteric antagonists or competitive antagonists with an allosteric component, such as gallamine, showed a significant reduction in the maximum of the antagonist DRCs (Imax). The evaluation of antagonist DRCs appears to be a sensitive procedure to detect allosteric interactions. 6 This alternative approach can supplement or replace the conventional approach for the evaluation of antagonists on a quantitative and qualitative basis. The alternative approach appears of special advantage where the supply and/or the solubility of the agonist is limited, resulting in incomplete agonist DRCs. 7 For rapid screening of potential antagonists, a single antagonist DRC at the maximum effective agonist concentration may be constructed to calculate KB reliably. Keywords: Antagonists; dose-response curves; KB; pA2; competitive; allosteric -
-
-
-
Introduction The dissociation constant KB of a competitive antagonist is derived from the shift of an agonist dose-response curve (DRC), i.e. the dose-ratio (DR) of equieffective agonist concentrations at a fixed antagonist concentration of B. A plot of log (DR - 1) vs log B (Schild plot), gives a straight line and allows calculation of - log KB = pA2 for a dose-ratio x = 2 (Arunlakshana & Schild, 1959). If the regression of log (DR - 1) vs log B is linear and has a slope of unity, a competitive antagonism between agonist and antagonist at the receptor is inferred. More than 40 years after Schild's formulation, the Schild regression is still a powerful tool in experimental pharmacology and provides a cornerstone of receptor classification (Tallarida et al., 1979; Kenakin, 1987). The present paper, while adhering to the derivation of the model by Schild (1947, 1957) and the pA2-analysis by Schild regression (Arunlakshana & Schild, 1959), describes an alternative approach by estimating the antagonist concentration B, which reduces the agonist response to its Emax/2 at a fixed agonist concentration, i.e. at a fixed DR, rather than estimating values of DR - 1 at a fixed antagonist concentration B. This procedure requires the conventional testing of an agonist in the absence and presence of a fixed concentration
I
Author for correspondence.
of an antagonist. Also, the (chosen) fixed dose-ratio corresponds to the agonist concentration in the absence and presence of an antagonist, routinely determined at the 50% effect level of the agonist. In order to differentiate between the fixed concentration of the antagonist B and the antagonist concentration which reduces an agonist effect to its Emax/2, to be determined from antagonist DRCs, the latter was termed B,. As a major advantage, this procedure is also applicable to incomplete agonist DRCs, which may be due to limited agonist availability and/or solubility. Besides this practical aspect, it was hoped that the direct presentation of antagonist effects in form of DRCs might provide better information as to the type of antagonism exerted by a particular blocker in a given test tissue. Thus, purely competitive antagonists as well as antagonists with a competitive and an allosteric component were selected and tested in a simple experimental set-up. In addition, published data of several authors were analysed to give DRCs of various antagonists at different receptors, obtained in different laboratories. The inclusion of literature data for this paper served the purpose of examining our new approach for a variety of different receptors with different agonists and antagonists to exclude a possible biased interpretation derived only from interactions at muscarinic and P-adrenoceptors of the bovine heart and tracheal muscle, respectively.
ANTAGONIST DOSE-RESPONSE CURVES
The results provide evidence that this new approach is advantageous both from a practical and theoretical point of view: even incomplete dose-response curves give reliable affinity estimates. In some cases, the type of antagonism that is operative in a given experiment, is clearly more easily discerned than in the conventional approach of agonist DRCs. In this paper we use the expressions 'conventional Schild plot' and 'alternative Schild plot' to indicate that the values for the antagonist concentrations and for DR - 1 were obtained by the conventional and by the present alternative approach, respectively. A preliminary account of this work has appeared in abstract form (P6ch et al., 1990).
a Fixed DR = 10 0) C Co
0 a1)
711
Co in c
co
00-a) .0 0._ Co
4)
_
C ° c
0 C) 4._
Co
Co C
0CD 4-00 0.U
CoC
.0 0) C
Methods Isolated organ preparations used in our laboratory Trabecular muscles Left bovine atria were obtained from the local slaughterhouse. Trabeculae (length 4-5 mm, diameter 1-2 mm) were rapidly excised from the auricular appendix and suspended in 5 ml organ baths filled with a modified Tyrode solution of the following composition (mmol 1-'): NaCl 137, KCI 5.4, CaCl2 4.8, MgCl2 1.1, NaH2PO4 0.4, NaHCO3 11.9 and glucose 10.1, gassed with carbogen and kept under constant temperature of 32'C. Muscles were electrically stimulated (frequency 1 Hz; duration 5 ms; 5 fold threshold voltage) at a resting tension of 1.5 g by means of a HSE 215/I-stimulator (Hugo Sachs Elektronik, Freiburg, Germany). Contractile force was recorded isometrically with Gould transducers connected to a Watanabe multichannel recorder. Preparations were allowed to stabilize for 45 min. DRCs for the negative inotropic effect of the muscarinic agonist methacholine were established by adding the drug cumulatively to the organ bath. After 30 min equilibration, the trabeculae were pretreated with antagonists for 45 min and cumulative DRCs to methacholine were repeated (10 nmol 1- to 30 mmol 1V'). For a given antagonist, each muscle was exposed to all three or four antagonist concentrations in ascending order. Each concentration was tested on three to four different trabeculae derived from one heart, and for each antagonist, three to four hearts were used. The negative inotropic effect was quantitated as percentage of the control contraction, i.e. after tissue equilibration and before administration of methacholine. Bovine tracheal muscle strips were prepared and treated as described earlier (Pdch & Zimmermann, 1988). The muscles were precontracted by 27 mmol 1` KCI in order to study the relaxant effects of the P-adrenoceptor agonist orciprenaline in the absence and in the presence of 0.075, 0.375, and 3.75 ftmol 1` propranolol.
Drugs Orciprenaline sulphate was a gift of Boehringer Ingelheim, Germany, propranolol was kindly supplied by ICI, Wilmslow, Cheshire, England. Methacholine bromide and gallamine triethiodide were purchased from Sigma Chemical Co., Munich, Germany. Pirenzepine dihydrochloride was a generous gift from Dr R. Hammer, di Angeli, Milano, Italy, and AF-DX 116 (11-1j2-[(diethylamino) methyl]-l-piperidinyl] acetyl]-5,1 1-dihydro-6H-pyrido [2,3-b][1,4] benzodiazepine-6one) from Dr Thomae GmbH, Biberach, Germany.
Construction of agonist- and antagonist dose-response curves The construction of antagonist DRCs is illustrated in Figure 1, which shows the basic difference between the conventional
&
2-
pA2 =0
2-
pA2=
0
0 0
1
2
log B
0 0
1
log
2
3
B,
Figure 1 Theoretical dose-response curves (DRCs) of an agonist A alone and in the presence of a competitive antagonist B at concentrations of 5, 20, 100 and 300 (a,c). DRCs of inhibitory effects of the antagonist in the presence of agonist concentrations of 10 (b) and 300(d). The antagonist DRC in (b) was derived from (a) by vertical evaluation of inhibition of agonist response (right scale) at the agonist concentration of 10, corresponding to a fixed DR = 10. The antagonist DRC in (d) was derived analogously by vertical evaluation at the agonist concentration of 300, corresponding to DR = 300. Schild plots derived from the agonist DRCs in the upper panel are shown in (e), from antagonist DRCs in the lower panel in (f), supplemented by values obtained at DR = 30 (*).
and the alternative approach, exemplified with idealized curves. First, agonist DRCs were constructed as usual (Figure la,lc); second, in the submaximum to maximum dose-range of the agonist, vertical lines were drawn at fixed dose-ratios, exemplified for DR = 10 (Figure la) and for DR = 300 (Figure Ic). The inhibitory effects of the antagonist B were then calculated as indicated in Figure la and Figure lb. They were determined by using experimental points of the agonist DRCs, rather than points of the fitted
DRCs, when possible. With the values of inhibition obtained graphically, antagonist DRCs were constructed, shown in Figure lb and Figure Id, by the ALLFIT programme package (De Lean et al., 1988), analogously to the agonist DRCs. Bx, the concentration which reduced the effect of the agonist to its Emax/2, corresponds to an inhibitory effect of 44.7% in Figure la and to 50% in Figure Ic. Hence, Figure 1 shows that if Bx is determined from antagonist DRCs at submaximum effective agonist concentrations (Figure la,b), it corresponds to a value lower than B50, i.e. to a value 0.05). The observed deviations ranged from 0.87 to 1.27 and 0.89 to 1.26, respectively.
Discussion An alternative method for the evaluation of agonistantagonist interactions is described in this paper. It is based on the usual DRCs of an agonist in the absence and in the presence of fixed concentrations of an antagonist. Antagonist DRCs were constructed at a submaximum to maximum effective control response to the agonist by expressing the inhibitory effects as a percentage of the maximum possible inhibitory effect. The antagonist concentration which reduced the control effect of the agonist to its Ema,,/2 was termed B. in order to differentiate it from the fixed antagonist concentration B used for testing the agonist in its presence. As can be seen from Figure 1, Bx equals B50 = IC50 of the antagonist at the maximum effect of the agonist, only. At submaximum effective concentrations of the agonist, B,, corresponds to values lower than IC50. Hence, the antagonist concentration was determined at fixed agonist concentrations, and hence at fixed DR, by 'vertical examination' of agonist DRCs, rather than the DR - 1 at fixed antagonist concentrations. The procedure outlined in this paper has in part been used by others. In an attempt to measure the potency with which muscarinic antagonists inhibit muscarinic agonist-stimulated phosphoinositol breakdown, Lazareno & Roberts (1987) have calculated KB = IC50/[(fixed agonist concentration/EC50)1], with [(fixed agonist concentration/EC50)-1] corresponding to DR - 1. The approach of these authors was to test the responses to a fixed concentration of agonist in the presence of various concentrations of antagonist. In addition, in each experiment a concentration-effect curve to the agonist alone was obtained. The authors pointed out in their paper (Lazareno & Roberts, 1987) that using the principles of dose ratio analysis, it need only be assumed that equieffective agonist concentrations correspond to equal receptor occupancy of agonist. Since they measured the IC50- and EC50values at the same effect level, their mathematical treatment is identical to the one used in this paper. The experimental procedure of Lazareno & Roberts (1987) is, however, limited to a single fixed agonist concentration and thus does not extend to Schild plots. Another attempt at quantifying functional inhibition data was presented by Eglen & Whiting (1989), who tested the dose response of inhibitory effects of the antagonist in the presence of a maximum effective concentration of an agonist, and calculated dissociation constants by inappropriately applying (Lazareno & Roberts, 1987; Lazareno, in preparation) the Cheng-Prusoff equation for the determination of enzyme inhibitor constants (Ki) (Cheng & Prusoff, 1973). Our approach allowed antagonist DRCs to be derived from experimental data points of incomplete agonist DRCs, as exemplified in Figure 4, as an alternative to an estimation of DR-1 which then yields only a few or extrapolated points for a conventional Schild plot (Figure 4c). Although dose ratios may be estimated at the 50% or lower effect level, estimated values are likely to have a higher variation at low compared with the half maximum effect level. Antagonist DRCs can be determined from experimental data points of incomplete agonist curves, as in Figure 4, in the same way as from complete agonist curves (e.g. Figure 4). In this example, as in others not shown, the pA2- or KB-values derived by the present procedure were in good agreement with those
715
obtained from incomplete agonist DRCs (Figure 4c vs d) which were complemented, i.e. extrapolated by fitting the experimental points to complete DRCs by ALLFIT. The procedure of assessment of antagonist DRCs can thus meaningfully supplement an investigation or can be chosen as an attractive alternative. It is noteworthy that even in the case of complete experimental agonist DRCs, the antagonist DRCs were determined as if they were incomplete. Where possible, as in Figures 3 and 5, antagonist DRCs were assessed up to concentrations of the agonist exhibiting effects lower than 50% in the presence of the antagonist, in order to obtain rather complete DRCs for the inhibition of agonist response. The antagonist DRCs also allow a qualitative evaluation of various aspects of DRCs, e.g. with respect to slope and Imax. In theory, DRCs of competitive antagonists give parallel DRCs with a common slope and Im,, = 100% inhibition of agonist effects, independent of agonist concentrations. The experimental DRCs shown in Figures 3 and 4 are in accordance with the theory. Allosteric antagonists or competitive antagonists with an allosteric component exhibit antagonist DRCs with reduced Imax. Experimental results with gallamine (Figure 5) share this phenomenon with theoretical antagonist DRCs of an allosteric antagonist (Figure 2). As a matter of fact, the depression of Imax of the antagonist DRCs appears to be a sensitive indicator of allosteric interaction. The results obtained with gallamine support this view, since deviations from a straight line in the conventional Schild plot were hardly detectable (Figure Sc) while the reduction in Im.. of the DRC of the inhibitory effects of gallamine against methacholine was clearly seen (Figure 5b). In the literature, allosteric interaction by gallamine with binding of agonists or antagonists to muscarinic receptors has been described by various groups, either as the sole mechanism or as an additional property of this muscarinic antagonist at higher concentrations (Ehlert, 1988b; Lee & El-Fakahany, 1988; Roffel et al., 1989; Michel et al., 1990). A drawback of the alternative Schild plot is that deviations from linearity at high antagonist concentrations are more difficult to detect since the highest antagonist concentrations B,, plotted are somewhat lower than B in conventional Schild plots. This disadvantage appears to be more than compensated for by the sensitive depression of Imax of antagonist DRCs since deviation from linearity in the respective Schild plots with gallamine was barely seen while Imax was significantly reduced from 100 to 78% (Figure 5). A comparison between KB and pA2-values obtained by either method showed an excellent agreement (Figure 6, Table 1). The values for DR-I and B by the conventional approach were determined from more or less complete experimental agonist DRCs. B,,-values at a fixed DR were obtained from antagonist DRCs which in principle were assessed from incomplete DRCs. For example, the agonist response above 50 pmol 1` methacholine in Figure 3 was not taken into consideration for the determination of antagonist DRCs. However, it appears that the alternative approach leads to KB and pA2-values which are at least as precisely estimated as by the conventional approach. This means that accurate affinity estimates can be obtained from incomplete DRCs. This finding appears of practical importance where incomplete experimental agonist DRCs have to be evaluated, e.g. due to limited supply and/or solubility of the agonist. The KB-values determined by the alternative approach showed small differences between those obtained at the submaximum to maximum effective range of agonist concentrations (Table 1). Hence, it appears reasonable to estimate rapidly KB-values of antagonists in screening experiments by the assessment of a single antagonist DRC at a maximum effective agonist concentration. This procedure is applicable irrespective of whether or not the experimental data points correspond to complete or incomplete agonist DRCs.
716
G. P6CH et al.
The excellent technical assistance of Mrs Heike Stessel and Mrs Betty Oberer is gratefully acknowledged. We thank Dr Sebastian
Lazareno for showing us his manuscript in preparation, referred to in the Discussion.
References ARIENS, E.J., VAN ROSSUM, J.M. & SIMONIS, A.M. (1956). A theoretical basis of molecular pharmacology. Part I: Interaction of one or two compounds with one receptor system. Arzneim.Forsch. (Drug Res.), 6, 282-293. ARUNLAKSHANA, 0. & SCHILD, H.O. (1959). Some quantitative uses
of drug antagonists. Br. J. Pharmacol. Chemother., 14, 48-58. CHENG, Y.-C. & PRUSOFF, W.H. (1973). Relationship between the inhibition constant (Ki) and the concentration of inhibitor which causes 50 per cent inhibition ('50) of an enzymatic reaction. Biochem. Pharmacol., 22, 3099-3108. DE LEAN, A., MUNSON, P.J., GUARDABASSO, V. & RODBARD, D.
(1988). A User's Guide to ALLFIT. Lab. Theoret. Physical Biol., Nat'l Inst. Child Hlth, NIH, Bethesda, MD 20892, USA. EGLEN, R.M. & WHITING, R.L. (1989). Problems associated with the application of the Cheng-Prusoff relationship to estimate atropine affinity constants using functional tissue responses. Life Sci., 44, 81-94. EHLERT, F.J. (1988a). Estimation of the affinities of allosteric ligands using radioligand binding and pharmacological null methods. Mol. Pharmacol., 33, 187-194. EHLERT, F.J. (1988b). Gallamine allosterically antagonizes muscarinic receptor-mediated inhibition of adenylate cyclase activity in the rat myocardium. J. Pharmacol. Exp. Ther., 247, 596-602. KENAKIN, T.P. (1982). Theoretical and practical problems with the assessment of intrinsic efficacy of agonists: efficacy of reputed beta-I selective adrenoceptor agonists for beta-2 adrenoceptors. J. Pharmacol. Exp. Ther., 223, 416-423. KENAKIN, T.P. (1987). Pharmacologic Analysis of Drug-Receptor Interaction. New York: Raven Press. LAZARENO, S. & ROBERTS, F.F. (1987). Measuring the potency with which muscarinic antagonists inhibit muscarinic agonist stimulated phosphoinositide breakdown in rat cortical slices. In International Symposium on Muscarinic Cholinergic Mechanisms. ed. Cohen, S. & Sokolovsky, M. pp. 272-277. London: Freund Publ. House Ltd.
LEE, N.H. & EL-FAKAHANY, E.E. (1988). Influence of ligand choice on the apparent binding profile of gallamine to cardiac muscarinic receptors. Identification of three main types of gallaminemuscarinic receptor interactions. J. Pharmacol. Exp. Ther., 246, 829-838. MICHEL, A.D., DELMENDO, R.E., LOPEZ, M. & WHITING, R.L.
(1990). On the interaction of gallamine with muscarinic receptor subtypes. Eur. J. Pharmacol., 182, 335-345. PERSSON, C.G.A., KARLSON, J.-A. & ERJEFALT, I. (1982). Differentiation between bronchodilation and universal adenosine antagonism among xanthine derivatives. Life Sci., 30, 2181-2189. POCH, G., BRUNNER, F. & KOHBERGER, E. (1990). Alternative approach to the Schild plot analysis. Eur. J. Pharmacol., 183, 2135. POCH, G. & ZIMMERMANN, I. (1988). Simple pA2 estimation of partial agonists: comparison with the Kaumann-Blinks method. J. Pharmacol. Methods, 19, 47-56. RODBARD, D. (1974). Statistical quality control and routine data processing for radioimmunoassays and immunoradiometric assays. Clin. Chem., 20, 1255-1270. ROFFEL, A.F., ELZINGA, C.R.S., MEURS, H. & ZAAGSMA, J. (1989). Allosteric interactions of three muscarine antagonists at bovine tracheal smooth muscle and cardiac M2 receptors. Eur. J. Pharmacol., 172, 61-70. SCHILD, H.O. (1947). pA, a new scale for the measurement of drug antagonism. Br. J. Pharmacol. Chemother., 2, 189-206. SCHILD, H.O. (1957). Drug antagonism and pA,. Pharmacol. Rev., 9,
242-256. TALLARIDA, R.J., COWAN, A. & ADLER, M.W. (1979). pA2 and receptor differentiation: A statistical analysis of competitive antagonism. Life Sci., 25, 635-654.
(Received December 11, 1991 Revised January 17, 1992 Accepted March 17, 1992)
f,'.
Macmillan Press Ltd, 1992
Construction of antagonist dose-response curves for estimation of pA2-values by Schild-plot analysis and detection of allosteric interactions 'Gerald Poch, Friedrich Brunner & Elisabeth Kuihberger Institut
fur
Pharmakologie und Toxikologie, Universitat Graz, Univ. pl. 2, A-8010 Graz, Austria
1 One aim of this paper is to show an alternative approach for the determination of antagonist affinity estimates, KB and pA2, by construction and evaluation of antagonist dose-response curves (DRCs), using the curve-fitting programme, ALLFIT. 2 Parallel antagonist DRCs were derived by vertical analysis of families of conventional agonist DRCs in the presence and absence of an antagonist at a certain agonist concentration above its EDM. The latter represents a chosen, i.e. fixed dose-ratio (DR). The antagonist concentration that reduces an agonist effect to its Emax/2 was termed B,. It corresponds to B, the fixed antagonist concentration, tested to obtain DR 1, conventionally. 3 The dissociation constant was calculated as KB= BX/DR 1, analogous to the conventional approach (KB= B/DR 1). Likewise, pA2-values were estimated by plotting log B", obtained by the alternative approach, vs log (DR 1) in an 'alternative Schild plot'. 4 Experimental agonist DRCs from our laboratory and from the literature were analysed and KB- and pA2-values obtained by the alternative approach were compared with those obtained by the conventional method. The results showed a very good agreement (correlation) between the pA2-values obtained by either method (slope = 1.02, r = 0.99, n = 9), in agreement with theoretical DRCs. 5 Besides estimation of KB and pA2, antagonist DRCs were also evaluated qualitatively. The most important finding was that allosteric antagonists or competitive antagonists with an allosteric component, such as gallamine, showed a significant reduction in the maximum of the antagonist DRCs (Imax). The evaluation of antagonist DRCs appears to be a sensitive procedure to detect allosteric interactions. 6 This alternative approach can supplement or replace the conventional approach for the evaluation of antagonists on a quantitative and qualitative basis. The alternative approach appears of special advantage where the supply and/or the solubility of the agonist is limited, resulting in incomplete agonist DRCs. 7 For rapid screening of potential antagonists, a single antagonist DRC at the maximum effective agonist concentration may be constructed to calculate KB reliably. Keywords: Antagonists; dose-response curves; KB; pA2; competitive; allosteric -
-
-
-
Introduction The dissociation constant KB of a competitive antagonist is derived from the shift of an agonist dose-response curve (DRC), i.e. the dose-ratio (DR) of equieffective agonist concentrations at a fixed antagonist concentration of B. A plot of log (DR - 1) vs log B (Schild plot), gives a straight line and allows calculation of - log KB = pA2 for a dose-ratio x = 2 (Arunlakshana & Schild, 1959). If the regression of log (DR - 1) vs log B is linear and has a slope of unity, a competitive antagonism between agonist and antagonist at the receptor is inferred. More than 40 years after Schild's formulation, the Schild regression is still a powerful tool in experimental pharmacology and provides a cornerstone of receptor classification (Tallarida et al., 1979; Kenakin, 1987). The present paper, while adhering to the derivation of the model by Schild (1947, 1957) and the pA2-analysis by Schild regression (Arunlakshana & Schild, 1959), describes an alternative approach by estimating the antagonist concentration B, which reduces the agonist response to its Emax/2 at a fixed agonist concentration, i.e. at a fixed DR, rather than estimating values of DR - 1 at a fixed antagonist concentration B. This procedure requires the conventional testing of an agonist in the absence and presence of a fixed concentration
I
Author for correspondence.
of an antagonist. Also, the (chosen) fixed dose-ratio corresponds to the agonist concentration in the absence and presence of an antagonist, routinely determined at the 50% effect level of the agonist. In order to differentiate between the fixed concentration of the antagonist B and the antagonist concentration which reduces an agonist effect to its Emax/2, to be determined from antagonist DRCs, the latter was termed B,. As a major advantage, this procedure is also applicable to incomplete agonist DRCs, which may be due to limited agonist availability and/or solubility. Besides this practical aspect, it was hoped that the direct presentation of antagonist effects in form of DRCs might provide better information as to the type of antagonism exerted by a particular blocker in a given test tissue. Thus, purely competitive antagonists as well as antagonists with a competitive and an allosteric component were selected and tested in a simple experimental set-up. In addition, published data of several authors were analysed to give DRCs of various antagonists at different receptors, obtained in different laboratories. The inclusion of literature data for this paper served the purpose of examining our new approach for a variety of different receptors with different agonists and antagonists to exclude a possible biased interpretation derived only from interactions at muscarinic and P-adrenoceptors of the bovine heart and tracheal muscle, respectively.
ANTAGONIST DOSE-RESPONSE CURVES
The results provide evidence that this new approach is advantageous both from a practical and theoretical point of view: even incomplete dose-response curves give reliable affinity estimates. In some cases, the type of antagonism that is operative in a given experiment, is clearly more easily discerned than in the conventional approach of agonist DRCs. In this paper we use the expressions 'conventional Schild plot' and 'alternative Schild plot' to indicate that the values for the antagonist concentrations and for DR - 1 were obtained by the conventional and by the present alternative approach, respectively. A preliminary account of this work has appeared in abstract form (P6ch et al., 1990).
a Fixed DR = 10 0) C Co
0 a1)
711
Co in c
co
00-a) .0 0._ Co
4)
_
C ° c
0 C) 4._
Co
Co C
0CD 4-00 0.U
CoC
.0 0) C
Methods Isolated organ preparations used in our laboratory Trabecular muscles Left bovine atria were obtained from the local slaughterhouse. Trabeculae (length 4-5 mm, diameter 1-2 mm) were rapidly excised from the auricular appendix and suspended in 5 ml organ baths filled with a modified Tyrode solution of the following composition (mmol 1-'): NaCl 137, KCI 5.4, CaCl2 4.8, MgCl2 1.1, NaH2PO4 0.4, NaHCO3 11.9 and glucose 10.1, gassed with carbogen and kept under constant temperature of 32'C. Muscles were electrically stimulated (frequency 1 Hz; duration 5 ms; 5 fold threshold voltage) at a resting tension of 1.5 g by means of a HSE 215/I-stimulator (Hugo Sachs Elektronik, Freiburg, Germany). Contractile force was recorded isometrically with Gould transducers connected to a Watanabe multichannel recorder. Preparations were allowed to stabilize for 45 min. DRCs for the negative inotropic effect of the muscarinic agonist methacholine were established by adding the drug cumulatively to the organ bath. After 30 min equilibration, the trabeculae were pretreated with antagonists for 45 min and cumulative DRCs to methacholine were repeated (10 nmol 1- to 30 mmol 1V'). For a given antagonist, each muscle was exposed to all three or four antagonist concentrations in ascending order. Each concentration was tested on three to four different trabeculae derived from one heart, and for each antagonist, three to four hearts were used. The negative inotropic effect was quantitated as percentage of the control contraction, i.e. after tissue equilibration and before administration of methacholine. Bovine tracheal muscle strips were prepared and treated as described earlier (Pdch & Zimmermann, 1988). The muscles were precontracted by 27 mmol 1` KCI in order to study the relaxant effects of the P-adrenoceptor agonist orciprenaline in the absence and in the presence of 0.075, 0.375, and 3.75 ftmol 1` propranolol.
Drugs Orciprenaline sulphate was a gift of Boehringer Ingelheim, Germany, propranolol was kindly supplied by ICI, Wilmslow, Cheshire, England. Methacholine bromide and gallamine triethiodide were purchased from Sigma Chemical Co., Munich, Germany. Pirenzepine dihydrochloride was a generous gift from Dr R. Hammer, di Angeli, Milano, Italy, and AF-DX 116 (11-1j2-[(diethylamino) methyl]-l-piperidinyl] acetyl]-5,1 1-dihydro-6H-pyrido [2,3-b][1,4] benzodiazepine-6one) from Dr Thomae GmbH, Biberach, Germany.
Construction of agonist- and antagonist dose-response curves The construction of antagonist DRCs is illustrated in Figure 1, which shows the basic difference between the conventional
&
2-
pA2 =0
2-
pA2=
0
0 0
1
2
log B
0 0
1
log
2
3
B,
Figure 1 Theoretical dose-response curves (DRCs) of an agonist A alone and in the presence of a competitive antagonist B at concentrations of 5, 20, 100 and 300 (a,c). DRCs of inhibitory effects of the antagonist in the presence of agonist concentrations of 10 (b) and 300(d). The antagonist DRC in (b) was derived from (a) by vertical evaluation of inhibition of agonist response (right scale) at the agonist concentration of 10, corresponding to a fixed DR = 10. The antagonist DRC in (d) was derived analogously by vertical evaluation at the agonist concentration of 300, corresponding to DR = 300. Schild plots derived from the agonist DRCs in the upper panel are shown in (e), from antagonist DRCs in the lower panel in (f), supplemented by values obtained at DR = 30 (*).
and the alternative approach, exemplified with idealized curves. First, agonist DRCs were constructed as usual (Figure la,lc); second, in the submaximum to maximum dose-range of the agonist, vertical lines were drawn at fixed dose-ratios, exemplified for DR = 10 (Figure la) and for DR = 300 (Figure Ic). The inhibitory effects of the antagonist B were then calculated as indicated in Figure la and Figure lb. They were determined by using experimental points of the agonist DRCs, rather than points of the fitted
DRCs, when possible. With the values of inhibition obtained graphically, antagonist DRCs were constructed, shown in Figure lb and Figure Id, by the ALLFIT programme package (De Lean et al., 1988), analogously to the agonist DRCs. Bx, the concentration which reduced the effect of the agonist to its Emax/2, corresponds to an inhibitory effect of 44.7% in Figure la and to 50% in Figure Ic. Hence, Figure 1 shows that if Bx is determined from antagonist DRCs at submaximum effective agonist concentrations (Figure la,b), it corresponds to a value lower than B50, i.e. to a value 0.05). The observed deviations ranged from 0.87 to 1.27 and 0.89 to 1.26, respectively.
Discussion An alternative method for the evaluation of agonistantagonist interactions is described in this paper. It is based on the usual DRCs of an agonist in the absence and in the presence of fixed concentrations of an antagonist. Antagonist DRCs were constructed at a submaximum to maximum effective control response to the agonist by expressing the inhibitory effects as a percentage of the maximum possible inhibitory effect. The antagonist concentration which reduced the control effect of the agonist to its Ema,,/2 was termed B. in order to differentiate it from the fixed antagonist concentration B used for testing the agonist in its presence. As can be seen from Figure 1, Bx equals B50 = IC50 of the antagonist at the maximum effect of the agonist, only. At submaximum effective concentrations of the agonist, B,, corresponds to values lower than IC50. Hence, the antagonist concentration was determined at fixed agonist concentrations, and hence at fixed DR, by 'vertical examination' of agonist DRCs, rather than the DR - 1 at fixed antagonist concentrations. The procedure outlined in this paper has in part been used by others. In an attempt to measure the potency with which muscarinic antagonists inhibit muscarinic agonist-stimulated phosphoinositol breakdown, Lazareno & Roberts (1987) have calculated KB = IC50/[(fixed agonist concentration/EC50)1], with [(fixed agonist concentration/EC50)-1] corresponding to DR - 1. The approach of these authors was to test the responses to a fixed concentration of agonist in the presence of various concentrations of antagonist. In addition, in each experiment a concentration-effect curve to the agonist alone was obtained. The authors pointed out in their paper (Lazareno & Roberts, 1987) that using the principles of dose ratio analysis, it need only be assumed that equieffective agonist concentrations correspond to equal receptor occupancy of agonist. Since they measured the IC50- and EC50values at the same effect level, their mathematical treatment is identical to the one used in this paper. The experimental procedure of Lazareno & Roberts (1987) is, however, limited to a single fixed agonist concentration and thus does not extend to Schild plots. Another attempt at quantifying functional inhibition data was presented by Eglen & Whiting (1989), who tested the dose response of inhibitory effects of the antagonist in the presence of a maximum effective concentration of an agonist, and calculated dissociation constants by inappropriately applying (Lazareno & Roberts, 1987; Lazareno, in preparation) the Cheng-Prusoff equation for the determination of enzyme inhibitor constants (Ki) (Cheng & Prusoff, 1973). Our approach allowed antagonist DRCs to be derived from experimental data points of incomplete agonist DRCs, as exemplified in Figure 4, as an alternative to an estimation of DR-1 which then yields only a few or extrapolated points for a conventional Schild plot (Figure 4c). Although dose ratios may be estimated at the 50% or lower effect level, estimated values are likely to have a higher variation at low compared with the half maximum effect level. Antagonist DRCs can be determined from experimental data points of incomplete agonist curves, as in Figure 4, in the same way as from complete agonist curves (e.g. Figure 4). In this example, as in others not shown, the pA2- or KB-values derived by the present procedure were in good agreement with those
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obtained from incomplete agonist DRCs (Figure 4c vs d) which were complemented, i.e. extrapolated by fitting the experimental points to complete DRCs by ALLFIT. The procedure of assessment of antagonist DRCs can thus meaningfully supplement an investigation or can be chosen as an attractive alternative. It is noteworthy that even in the case of complete experimental agonist DRCs, the antagonist DRCs were determined as if they were incomplete. Where possible, as in Figures 3 and 5, antagonist DRCs were assessed up to concentrations of the agonist exhibiting effects lower than 50% in the presence of the antagonist, in order to obtain rather complete DRCs for the inhibition of agonist response. The antagonist DRCs also allow a qualitative evaluation of various aspects of DRCs, e.g. with respect to slope and Imax. In theory, DRCs of competitive antagonists give parallel DRCs with a common slope and Im,, = 100% inhibition of agonist effects, independent of agonist concentrations. The experimental DRCs shown in Figures 3 and 4 are in accordance with the theory. Allosteric antagonists or competitive antagonists with an allosteric component exhibit antagonist DRCs with reduced Imax. Experimental results with gallamine (Figure 5) share this phenomenon with theoretical antagonist DRCs of an allosteric antagonist (Figure 2). As a matter of fact, the depression of Imax of the antagonist DRCs appears to be a sensitive indicator of allosteric interaction. The results obtained with gallamine support this view, since deviations from a straight line in the conventional Schild plot were hardly detectable (Figure Sc) while the reduction in Im.. of the DRC of the inhibitory effects of gallamine against methacholine was clearly seen (Figure 5b). In the literature, allosteric interaction by gallamine with binding of agonists or antagonists to muscarinic receptors has been described by various groups, either as the sole mechanism or as an additional property of this muscarinic antagonist at higher concentrations (Ehlert, 1988b; Lee & El-Fakahany, 1988; Roffel et al., 1989; Michel et al., 1990). A drawback of the alternative Schild plot is that deviations from linearity at high antagonist concentrations are more difficult to detect since the highest antagonist concentrations B,, plotted are somewhat lower than B in conventional Schild plots. This disadvantage appears to be more than compensated for by the sensitive depression of Imax of antagonist DRCs since deviation from linearity in the respective Schild plots with gallamine was barely seen while Imax was significantly reduced from 100 to 78% (Figure 5). A comparison between KB and pA2-values obtained by either method showed an excellent agreement (Figure 6, Table 1). The values for DR-I and B by the conventional approach were determined from more or less complete experimental agonist DRCs. B,,-values at a fixed DR were obtained from antagonist DRCs which in principle were assessed from incomplete DRCs. For example, the agonist response above 50 pmol 1` methacholine in Figure 3 was not taken into consideration for the determination of antagonist DRCs. However, it appears that the alternative approach leads to KB and pA2-values which are at least as precisely estimated as by the conventional approach. This means that accurate affinity estimates can be obtained from incomplete DRCs. This finding appears of practical importance where incomplete experimental agonist DRCs have to be evaluated, e.g. due to limited supply and/or solubility of the agonist. The KB-values determined by the alternative approach showed small differences between those obtained at the submaximum to maximum effective range of agonist concentrations (Table 1). Hence, it appears reasonable to estimate rapidly KB-values of antagonists in screening experiments by the assessment of a single antagonist DRC at a maximum effective agonist concentration. This procedure is applicable irrespective of whether or not the experimental data points correspond to complete or incomplete agonist DRCs.
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The excellent technical assistance of Mrs Heike Stessel and Mrs Betty Oberer is gratefully acknowledged. We thank Dr Sebastian
Lazareno for showing us his manuscript in preparation, referred to in the Discussion.
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(Received December 11, 1991 Revised January 17, 1992 Accepted March 17, 1992)
