Pharmacological Research, Vol . 25, No . 4, 1992
325
GRAPHICAL ANALYSIS OF DATA FROM PHARMACOLOGY EXPERIMENTS JOSEP J . CENTELLES, MONTSERRAT BUSQUETS, ENRIC I . CANELA and RAFAEL FRANCO Departament de Bioquímica i Fisiologia, Facultat de Química, Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Catalunya, Spain Received in final form 8 November 1991
SUMMARY Dose-response curves are often used in the study of the interaction of hormones and receptors . From these plots, IC 50 or EC 50 values are calculated . In these pharmacological assays it is implicitly assumed that a single receptor predominates in a tissue . In this paper the interaction of a ligand with two receptors is studied from a theoretical point of view . It is assumed that the responses mediated by these receptors are qualitatively or quantitatively different . The theoretical direct and Scatchard plots display a high variety of shapes depending upon the difference in potency of the effect of the drug acting in both receptors and upon the magnitude and sign of the individual response . When dose-response curves taken from the literature have been transformed into direct or Scatchard plots new information has become available . With respect to this, it is shown that agonists of purinergic receptors seem to interact with two different populations of receptors . We claim that carefully designed experiments must provide valuable information concerning the number of subtypes of receptors present in a given system and the kind of response mediated by them . KEY WORDS :
Receptors, dose-response, interactions
INTRODUCTION Strategies for analysis of data from ligand-binding experiments have been described during the last 10 years . Rodbard and co-workers [1-3] have reviewed graphical methods for estimating parameters in ligand-binding or dose-response experiments and have prepared computer programs useful for obtaining the optimal estimates of `binding parameters' . For dose-response curves, strategies similar to those employed in ligandbinding experiments can be used for obtaining EC50 and IC 5o values . They can be Correspondence to : Dr Josep J . Centelles . 1043-6618/92/040325-10/$03 .00/0
© 1992 The Italian Pharmacological Society
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Pharmacological Research, Vol . 25, No . 4, 1992
used only when there is a single receptor interacting with the ligand or when there are two receptors interacting with the drug that qualitatively display the same response . But, commonly when a ligand interacts with two receptor subtypes the response is qualitatively different, i .e . one receptor mediates an excitatory response whereas another mediates an inhibitory response . The aim of the present report is to perform the analysis of dose-response curves to obtain more information for the case of a single ligand interacting with two receptor subtypes . In this study a normal steepness [normal steepness for dose-response (or binding plots) is the slope of the Langmuir isotherm and implies that the receptors present a uniform affinity for the ligand or hormone [4] ; it also implies a hyperbolic direct-plot and a linear Scatchard plot] for dose-response curves of a drug interacting with a single receptor subtype has been assumed . This assumption is based on the available experimental evidence obtained with receptors which can activate or deactivate the adenylate cyclase [4] . After the Clark hypothesis [5] which assumes that the effect is proportional to receptor occupation, two further hypotheses have arisen in order to explain the existence of spare receptors . One is the mobile receptor hypothesis of Bennett et al . [6] and DeHaen [7], where the receptor-ligand complex moves through the plasma membrane and associates adenylate cyclase . Although supported by some experimental evidence this hypothesis failed to explain the participation of GTP in the whole process . More recently the so-called allozyme hypothesis has been introduced by Macfarlane [8] and has permitted explanation of many of the processes occurring after the activation of a receptor which subsequently modifies the activity of the adenylate cyclase . It assumes the existence of ligand-occupied receptors which enzymatically activate the adenylate cyclase system, both in a GTP/GDP-dependent manner . This hypothesis and the assumptions made by Macfarlane [4, 8] have been used in this paper since, furthermore, it explains the normal steepness found, as mentioned above, in dose-response curves obtained with many systems coupled to adenylate cyclase . We suggest the use of Scatchard-like plots instead of plots commonly used in pharmacology (dose vs log [hormone]) . Furthermore, we provide a compendium of shapes for direct and Scatchard plots that can be obtained from pharmacological experiments (e .g . organ bath) in the case of a ligand interacting with two receptors . The model is very simple ; it consists of the study of the effect after the interaction of a drug with two receptors, each having a different (qualitative and/or quantitative) mediated response . This approach is supported by the enormous quantity of literature dealing with receptor heterogeneity, which states that almost every receptor class has at least two different subtypes that mediate qualitatively different responses . The approach is very useful to obtain further information when dose-response curves are analyzed . It should be noted that the common plot employed in pharmacology : % effect vs log [ligand] does not easily allow the calculation of EC3() or ICS(), which are better calculated by non-linear regression from direct plot . THEORY Let us consider two types of receptor (R, and R,) for the same ligand (L) . For a
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given ligand concentration, and considering a normal steepness of dose-response curves, we have a response proportional to : For receptor R, :
[L]/(K, + [L])
(1)
For receptor R 2 :
[L]/(K2 + [ L])
(2)
If the effect is the activation (or inactivation) of adenylate cyclase, K, and K, would correspond to the half-maximal effect on the adenylate cyclase . But in general terms, K, and K2 correspond to the EC 50 (IC 50) values for the effect mediated by R, and R 2 respectively . It should be noted that it is well established that a comparison between the three types of saturation curves-ligand binding, primary biochemical response and final biochemical response-usually reveals that the final response saturates at much lower concentrations than the primary response ; the latter may or may not saturate ahead of ligand saturation [9] . Though the present study is irrespective of the type of saturation curve it is focussed on that most commonly employed in organ-bath experiments, i .e . dose-final response curves . Considering that the partial responses are additive, the global response is :
Response =
E, [L]
E2 [L]
+ (3) K, + [L] K 2 + [L]
E, and E2 being the maximal effects mediated by R, and R 2 respectively . Parameters of R2 , can be given as functions of those of R, : E 2 = aE,
(4)
K2 =,8 K,
(5)
Where a can be negative (when the receptors mediate opposed responses) or positive (when both mediate the same response) ; ß must be always positive . The final equation is obtained replacing equations (4) and (5) in (3) and rearranging : Response =(1
+ a) E, [L] 2 + ( a+ ß) E, K, [L] [L] 22+(1 +P)K, [L] +ßK, 2
(6)
This equation is also valid when the receptors interact to give a cooperative response . In this case, a is a negative when cooperativity is negative and positive when it is positive .
RESULTS Theoretical possible curves
Pairs of values of responseAigand concentration were obtained by applying equation (6) and fixing the values of E, and K, equal to 1 (E,=1 response unit, K,=
Pharmacological Research, Vol . 25, No . 4, 1992
3 28
1 um) . These values of E, and K, permit us to obtain all the possible types of plots . For different values of a and ß, direct plots of `response vs ligand concentration' or Scatchard-like plots of `response/ligand concentration vs response' (being the ligand concentration in the range of 1 um to 100 mm) were constructed . Depending upon the values of a and ß, various types of direct (hyperbolic, with one inflection point, with one minimum and one inflection point or with one maximum and one inflection point) and Scatchard (linear, concave upward or concave downward) plots were encountered . Results are displayed in Figs I and 2 . Obviously, the only true linear (i .e . Michaelian-like) behaviour is found at the abscissa axis (when ß=1 and thus K2 =K,) . In this case, equation (6) becomes : + a) E, [L] 2 + ( a+ 1) E, K, [L] = Response = (1 [L] 2 + 2K, [L] + K 1 2 _(1 +a)El[L]([L] +K,) ([L] + K l ) 2
(1 +a)E l [L] ([L] + K,)
(7)
A linear Scatchard plot will be also found if there is one single receptor (a =0) . The line a=-ß separates curves with a positive response at very low ligand concentrations (zones 1 a, 2a, 4a, 3b and 5b) from curves with negative response at
a0
log ßO (zones 6a and 6b), i .e . when both types of receptors mediate activating responses, convex Scatchard plots are always found . However, in the direct plot it is difficult to note that the curve is not a true hyperbola . The set of results are summarized in Table 1 . The difference between zones l a and 2a is that in the latter the response is always positive whereas in zone la the response is positive at low substrate concentration and negative at high concentrations . This is due to two factors influencing the response in zone la : (i) the response mediated by R 2 is negative and quantitatively more potent than the positive response mediated by R, (al) . Similar differences appear in zones 2b and lb . In zone lb the response is always negative whereas in zone 2b the response changes from negative to positive as the ligand concentration increases . Furthermore, from graphical analysis some parameter constrictions can be evaluated, which makes it easier to fit the data to the suitable model by nonlinear regression analysis using the available programs [2, 10) . From this nonlinear regression analysis, parameter estimates and standard errors can be obtained . Obviously, nonlinear regression analysis should be followed by the classical tests to evaluate the goodness-of-fit of the model . Comparison between theoretical and experimental plots taken from the literature In order to correlate the data shown in Figs 1 and 2 with actual examples, dose-response plots or data from binding experiments corresponding to purinergic receptors have been analyzed . The Scatchard plot corresponding to data of binding of adenosine to rat brain membranes presented in the form of bound adenosine vs ligand concentration by Schwabe et al . [11] is given in Fig . 3 . The same shape (Fig . 4) is obtained for the
Table I Summary of plots for the different zones (all information presented in this table is taken from Figs 1 and 2) Direct plot
Zone
Scatchard plot
Null Maximum Minimum Sigmoid Hyperbola Linear Concave Convex response upward upward la lb 2a 2b 3a 3b 4a, 5a 4b, 5b 6a 6b
+ +
-
+ + + + + + -
-
-
-
*Apparent shape .
-
-
+(*) +(*) +(*) +(*)
-
-
+(*) +(*) -
+ + +
+ + + + + -
Pharmacological Research, Vol . 25, No . 4, 1992
33 1
Scatchard plot corresponding to data of percentage of maximal relaxation of rat duodenum vs log [adenosine] [12] . The shape of these curves (Figs 3 and 4) corresponds to zones 6a or 6b of Figs 1 and 2 and is indicative of an interaction of adenosine with two types of P, receptors . They are probably the A, and A, subtypes in the nomenclature of Van Calker et al. [13], or the R, and R, subtypes in the nomenclature of Londos and Wolff [14] . The Scatchard plot corresponding to data of percentage of maximum contraction of rabbit central ear artery (free from endothelium) vs log [a,,ß-Methylene ATP'
4
0 .2
0.1 B (nmol/mg protein)
Fig . 3 Scatchard plot constructed from binding data given by Schwabe et al. [11] . Scatchard plot corresponding to adenosine binding to rat brain membranes .
20
10
20
40
60
80
R (%)
Fig. 4 . Scatchard plot constructed from pharmacological data given by Franco et al . 1121 . Scatchard plot corresponding to the effect of adenosine on rat duodenum .
332
Pharmacological Research, Vol . 25, No . 4, 1992
200
J u
50
100
R (%)
Fig . 5 Scatchard plot constructed from pharmacological data given by Kennedy and Burnstock [151 . Scatchard plot corresponding to the effect of a,ß-Methylene ATP upon the isolated rabbit central ear artery .
[15] is given in Fig . 5 . a,ß-Methylene ATP is a presumptive agonist of P 2 purinoceptors (specific for ATP) [15] . The shape of the curve is similar to that encountered in zones 2a or 3b of Figs 1 and 2 . This suggests that the compound interacts with two different receptors . A combined interaction of a,ß-Methylene ATP with receptors specific for ATP (P2 ) and for adenosine (P,) cannot be ruled out .
DISCUSSION The present report provides a review of the theoretically possible plots that can be found when data from pharmacology (mainly organ bath) experiments are analyzed . Current plots used in pharmacology, such as response vs log [L], might hide some valuable information when interaction of a ligand with at least two different receptor subtypes occurs . However, if direct, reciprocal or Scatchard plots are used, information relative to the number of different receptors interacting with a ligand can be obtained . It should be noted that the theoretically possible plots obtained from pharmacological data agree with those obtained from binding data when a>O (i .e . right zone of Fig . 1) [1-3] . Obviously, in binding experiments negative binding cannot occur. Conversely, in organ-bath pharmacology, opposite effects with two receptor subtypes could be obtained . For instance, in the case of adenosine receptors, activation of A2 receptors leads to an increase of cyclic AMP levels whereas activation of A, receptors leads to a decrease of cyclic AMP [13] . Although there are typical examples of tissues having preferably one of these
Pharmacological Research, Vol. 25, No . 4, 1992
333
subtypes [16, 17], it is reasonable to assume that, irrespective of the tissue, both subtypes coexist . Although for other receptors data have not been given, other plots are also observed [18-20] . In some cases, when a ligand interacts with two receptors mediating opposite effects a maximum or a minimum (zones la, 2a, lb and 2b) could be found in direct plots . This singular point (maximum or minimum) appears at relatively low concentrations of ligand (see Figs 1 and 2) . Then, such zones (having either a maximum or a minimum) would be detected with difficulty when analyzing pharmacological data and could even have been rejected as discordant observations . However, carefully designed experiments, repeated until achieving 99% confidence levels in effect values, could be useful in obtaining accurate Scatchard plots (see ref . 21 for an example of experimental design useful in model discrimination) . These plots might be suitable for demonstrating to which extent two receptors for the same ligand coexist in a single tissue . When a Scatchard plot suggests the existence of two receptor subtypes in the tissue analyzed, confirmation should be carried out . In the most favourable case the shape of the curve must change when the experiment is repeated in the presence of a blocker specific for one of the subtypes . If there are no specific blockers for the different subtypes, displacement binding experiments using agonists specific either for one or other subtype are required .
REFERENCES I . DeLean A, Munson PJ, Rodbard D . Simultaneous analysis of families of sigmoidal curves : application to bioassay, radioligand assay, and physiological dose-response curves . Am J Physiol 1978 ; 235 : E97-E102 . 2 . Munson PJ, Rodbard D . Ligand : a versatile computerized approach for characterization of ligand-binding systems . Anal Biochem 1980 ; 107 : 220-39 . 3 . Thakur AK . Jaffe ML, Rodbard D . Graphical analysis of ligand-binding systems : evaluation by Monte Carlo studies . Anal Biochem 1980; 107 : 279-95 . 4 . Macfarlane DE . On the enzymic nature of receptors : the allozyme hypothesis . Trends Pharmacol Sci 1984; 5: 11-15 . 5 . Clark AJ . The mode of action of drugs on cells . London : Edward Arnold and Company, 1933 . 6 . Bennett GV, O'Keefe E, Cuatrecasas P . Mechanism of action of cholera toxin and the mobile receptor theory of hormone receptor-adenylate cyclase interactions . Proc Nail Acad Sci USA 1975 ; 72 : 33-7 . 7 . DeHaen C . The nonstoichiometric floating receptor model for hormone sensitive adenylyl cyclase . J Theor Biol 1976 ; 58 : 383-400 . 8 . Macfarlane DE . Bidirectional collision coupling in the regulation of the adenylate cyclase . The allozyme hypothesis for receptor function . Mol Pharmacol 1982 : 22 : 580-88 . 9 . Levitzki A . Receptors . A quantitative approach . Menlo Park : Benjamin Cummings . 1984 . 10 . Canela EI . A free derivative program for non-linear regression analysis of enzyme kinetics to be used on small computers . Int J Biomed Comput 1984 ; 15 : 121-30 . 11 . Schwabe U, Kiffe H, Puchstein C, Trost T . Specific binding of 3 H-adenosine to rat brain membranes . Naunyn-Schmiedeherg's Arch Pharmacol 1979 ; 310 : 59-67 . 12 . Franco R . Hoyle CHV, Centelles JJ, Burnstock G . Degradation of adenosine by extracellular adenosine deaminase in the rat duodenum . Gen Pharmacol 1988 : 19 : 679-81 .
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13 . Van Calker D, Mueller M, Hamprecht, B . Adenosine regulates via two different types of receptors, the accumulation of cyclic AMP in cultured brain cells . J Neurochem 1979 ; 33 : 999-1005 . 14 . Londos C, Wolff J . Two distinct adenosine-sensitive sites on adenylate cyclase . Proc Natl Acad Sci USA 1977 ; 74 : 5482-6 . 15 . Kennedy C, Burnstock G . ATP produces vasodilation via P, ppurinoceptors in the isolated rabbit central ear artery . Blood Vessels 1985 ; 22 : 145-55 . 16 . Burnstock G, Brown CM . In Burnstock G, ed . Purinergic receptors . London : Chapman and Hall, 1981 . 17 . Daly JW . In : Stefanovich V, Rudolphi K, Schubert P, eds . Adenosine : receptors and modulation of cell function . Oxford: IRL Press, 1985 : 31-46. 18 . Burnstock G, Hills JM, Hoyle CHV . Evidence that the P,-purinoceptor in the guinea-pig taenia coli is an A2 -subtype . Br J Pharmac 1984 ; 81 : 533-41 . 19 . Meldrum LA, Burnstock G . Evidence that ATP is involved as a co-transmitter in the hypogastric nerve supplying the seminal vesicle of the guinea-pig . Eur J Pharmacol 1985 ;110 :363-6 . 20 . Kennedy C, Burnstock G . Evidence for two types of P 2 -purinoceptor in longitudinal muscle of the rabbit portal vein . Eur J Pharmacol 1985 ; 111 : 49-56 . 21 . Franco R, Gavalda M-T, Canela EI . A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design . Biochem J 1986 ; 238 : 855-62 .
325
GRAPHICAL ANALYSIS OF DATA FROM PHARMACOLOGY EXPERIMENTS JOSEP J . CENTELLES, MONTSERRAT BUSQUETS, ENRIC I . CANELA and RAFAEL FRANCO Departament de Bioquímica i Fisiologia, Facultat de Química, Universitat de Barcelona, Marti i Franques 1, 08028 Barcelona, Catalunya, Spain Received in final form 8 November 1991
SUMMARY Dose-response curves are often used in the study of the interaction of hormones and receptors . From these plots, IC 50 or EC 50 values are calculated . In these pharmacological assays it is implicitly assumed that a single receptor predominates in a tissue . In this paper the interaction of a ligand with two receptors is studied from a theoretical point of view . It is assumed that the responses mediated by these receptors are qualitatively or quantitatively different . The theoretical direct and Scatchard plots display a high variety of shapes depending upon the difference in potency of the effect of the drug acting in both receptors and upon the magnitude and sign of the individual response . When dose-response curves taken from the literature have been transformed into direct or Scatchard plots new information has become available . With respect to this, it is shown that agonists of purinergic receptors seem to interact with two different populations of receptors . We claim that carefully designed experiments must provide valuable information concerning the number of subtypes of receptors present in a given system and the kind of response mediated by them . KEY WORDS :
Receptors, dose-response, interactions
INTRODUCTION Strategies for analysis of data from ligand-binding experiments have been described during the last 10 years . Rodbard and co-workers [1-3] have reviewed graphical methods for estimating parameters in ligand-binding or dose-response experiments and have prepared computer programs useful for obtaining the optimal estimates of `binding parameters' . For dose-response curves, strategies similar to those employed in ligandbinding experiments can be used for obtaining EC50 and IC 5o values . They can be Correspondence to : Dr Josep J . Centelles . 1043-6618/92/040325-10/$03 .00/0
© 1992 The Italian Pharmacological Society
326
Pharmacological Research, Vol . 25, No . 4, 1992
used only when there is a single receptor interacting with the ligand or when there are two receptors interacting with the drug that qualitatively display the same response . But, commonly when a ligand interacts with two receptor subtypes the response is qualitatively different, i .e . one receptor mediates an excitatory response whereas another mediates an inhibitory response . The aim of the present report is to perform the analysis of dose-response curves to obtain more information for the case of a single ligand interacting with two receptor subtypes . In this study a normal steepness [normal steepness for dose-response (or binding plots) is the slope of the Langmuir isotherm and implies that the receptors present a uniform affinity for the ligand or hormone [4] ; it also implies a hyperbolic direct-plot and a linear Scatchard plot] for dose-response curves of a drug interacting with a single receptor subtype has been assumed . This assumption is based on the available experimental evidence obtained with receptors which can activate or deactivate the adenylate cyclase [4] . After the Clark hypothesis [5] which assumes that the effect is proportional to receptor occupation, two further hypotheses have arisen in order to explain the existence of spare receptors . One is the mobile receptor hypothesis of Bennett et al . [6] and DeHaen [7], where the receptor-ligand complex moves through the plasma membrane and associates adenylate cyclase . Although supported by some experimental evidence this hypothesis failed to explain the participation of GTP in the whole process . More recently the so-called allozyme hypothesis has been introduced by Macfarlane [8] and has permitted explanation of many of the processes occurring after the activation of a receptor which subsequently modifies the activity of the adenylate cyclase . It assumes the existence of ligand-occupied receptors which enzymatically activate the adenylate cyclase system, both in a GTP/GDP-dependent manner . This hypothesis and the assumptions made by Macfarlane [4, 8] have been used in this paper since, furthermore, it explains the normal steepness found, as mentioned above, in dose-response curves obtained with many systems coupled to adenylate cyclase . We suggest the use of Scatchard-like plots instead of plots commonly used in pharmacology (dose vs log [hormone]) . Furthermore, we provide a compendium of shapes for direct and Scatchard plots that can be obtained from pharmacological experiments (e .g . organ bath) in the case of a ligand interacting with two receptors . The model is very simple ; it consists of the study of the effect after the interaction of a drug with two receptors, each having a different (qualitative and/or quantitative) mediated response . This approach is supported by the enormous quantity of literature dealing with receptor heterogeneity, which states that almost every receptor class has at least two different subtypes that mediate qualitatively different responses . The approach is very useful to obtain further information when dose-response curves are analyzed . It should be noted that the common plot employed in pharmacology : % effect vs log [ligand] does not easily allow the calculation of EC3() or ICS(), which are better calculated by non-linear regression from direct plot . THEORY Let us consider two types of receptor (R, and R,) for the same ligand (L) . For a
327
Pharmacological Research, Vol. 25, No . 4, 1992
given ligand concentration, and considering a normal steepness of dose-response curves, we have a response proportional to : For receptor R, :
[L]/(K, + [L])
(1)
For receptor R 2 :
[L]/(K2 + [ L])
(2)
If the effect is the activation (or inactivation) of adenylate cyclase, K, and K, would correspond to the half-maximal effect on the adenylate cyclase . But in general terms, K, and K2 correspond to the EC 50 (IC 50) values for the effect mediated by R, and R 2 respectively . It should be noted that it is well established that a comparison between the three types of saturation curves-ligand binding, primary biochemical response and final biochemical response-usually reveals that the final response saturates at much lower concentrations than the primary response ; the latter may or may not saturate ahead of ligand saturation [9] . Though the present study is irrespective of the type of saturation curve it is focussed on that most commonly employed in organ-bath experiments, i .e . dose-final response curves . Considering that the partial responses are additive, the global response is :
Response =
E, [L]
E2 [L]
+ (3) K, + [L] K 2 + [L]
E, and E2 being the maximal effects mediated by R, and R 2 respectively . Parameters of R2 , can be given as functions of those of R, : E 2 = aE,
(4)
K2 =,8 K,
(5)
Where a can be negative (when the receptors mediate opposed responses) or positive (when both mediate the same response) ; ß must be always positive . The final equation is obtained replacing equations (4) and (5) in (3) and rearranging : Response =(1
+ a) E, [L] 2 + ( a+ ß) E, K, [L] [L] 22+(1 +P)K, [L] +ßK, 2
(6)
This equation is also valid when the receptors interact to give a cooperative response . In this case, a is a negative when cooperativity is negative and positive when it is positive .
RESULTS Theoretical possible curves
Pairs of values of responseAigand concentration were obtained by applying equation (6) and fixing the values of E, and K, equal to 1 (E,=1 response unit, K,=
Pharmacological Research, Vol . 25, No . 4, 1992
3 28
1 um) . These values of E, and K, permit us to obtain all the possible types of plots . For different values of a and ß, direct plots of `response vs ligand concentration' or Scatchard-like plots of `response/ligand concentration vs response' (being the ligand concentration in the range of 1 um to 100 mm) were constructed . Depending upon the values of a and ß, various types of direct (hyperbolic, with one inflection point, with one minimum and one inflection point or with one maximum and one inflection point) and Scatchard (linear, concave upward or concave downward) plots were encountered . Results are displayed in Figs I and 2 . Obviously, the only true linear (i .e . Michaelian-like) behaviour is found at the abscissa axis (when ß=1 and thus K2 =K,) . In this case, equation (6) becomes : + a) E, [L] 2 + ( a+ 1) E, K, [L] = Response = (1 [L] 2 + 2K, [L] + K 1 2 _(1 +a)El[L]([L] +K,) ([L] + K l ) 2
(1 +a)E l [L] ([L] + K,)
(7)
A linear Scatchard plot will be also found if there is one single receptor (a =0) . The line a=-ß separates curves with a positive response at very low ligand concentrations (zones 1 a, 2a, 4a, 3b and 5b) from curves with negative response at
a0
log ßO (zones 6a and 6b), i .e . when both types of receptors mediate activating responses, convex Scatchard plots are always found . However, in the direct plot it is difficult to note that the curve is not a true hyperbola . The set of results are summarized in Table 1 . The difference between zones l a and 2a is that in the latter the response is always positive whereas in zone la the response is positive at low substrate concentration and negative at high concentrations . This is due to two factors influencing the response in zone la : (i) the response mediated by R 2 is negative and quantitatively more potent than the positive response mediated by R, (al) . Similar differences appear in zones 2b and lb . In zone lb the response is always negative whereas in zone 2b the response changes from negative to positive as the ligand concentration increases . Furthermore, from graphical analysis some parameter constrictions can be evaluated, which makes it easier to fit the data to the suitable model by nonlinear regression analysis using the available programs [2, 10) . From this nonlinear regression analysis, parameter estimates and standard errors can be obtained . Obviously, nonlinear regression analysis should be followed by the classical tests to evaluate the goodness-of-fit of the model . Comparison between theoretical and experimental plots taken from the literature In order to correlate the data shown in Figs 1 and 2 with actual examples, dose-response plots or data from binding experiments corresponding to purinergic receptors have been analyzed . The Scatchard plot corresponding to data of binding of adenosine to rat brain membranes presented in the form of bound adenosine vs ligand concentration by Schwabe et al . [11] is given in Fig . 3 . The same shape (Fig . 4) is obtained for the
Table I Summary of plots for the different zones (all information presented in this table is taken from Figs 1 and 2) Direct plot
Zone
Scatchard plot
Null Maximum Minimum Sigmoid Hyperbola Linear Concave Convex response upward upward la lb 2a 2b 3a 3b 4a, 5a 4b, 5b 6a 6b
+ +
-
+ + + + + + -
-
-
-
*Apparent shape .
-
-
+(*) +(*) +(*) +(*)
-
-
+(*) +(*) -
+ + +
+ + + + + -
Pharmacological Research, Vol . 25, No . 4, 1992
33 1
Scatchard plot corresponding to data of percentage of maximal relaxation of rat duodenum vs log [adenosine] [12] . The shape of these curves (Figs 3 and 4) corresponds to zones 6a or 6b of Figs 1 and 2 and is indicative of an interaction of adenosine with two types of P, receptors . They are probably the A, and A, subtypes in the nomenclature of Van Calker et al. [13], or the R, and R, subtypes in the nomenclature of Londos and Wolff [14] . The Scatchard plot corresponding to data of percentage of maximum contraction of rabbit central ear artery (free from endothelium) vs log [a,,ß-Methylene ATP'
4
0 .2
0.1 B (nmol/mg protein)
Fig . 3 Scatchard plot constructed from binding data given by Schwabe et al. [11] . Scatchard plot corresponding to adenosine binding to rat brain membranes .
20
10
20
40
60
80
R (%)
Fig. 4 . Scatchard plot constructed from pharmacological data given by Franco et al . 1121 . Scatchard plot corresponding to the effect of adenosine on rat duodenum .
332
Pharmacological Research, Vol . 25, No . 4, 1992
200
J u
50
100
R (%)
Fig . 5 Scatchard plot constructed from pharmacological data given by Kennedy and Burnstock [151 . Scatchard plot corresponding to the effect of a,ß-Methylene ATP upon the isolated rabbit central ear artery .
[15] is given in Fig . 5 . a,ß-Methylene ATP is a presumptive agonist of P 2 purinoceptors (specific for ATP) [15] . The shape of the curve is similar to that encountered in zones 2a or 3b of Figs 1 and 2 . This suggests that the compound interacts with two different receptors . A combined interaction of a,ß-Methylene ATP with receptors specific for ATP (P2 ) and for adenosine (P,) cannot be ruled out .
DISCUSSION The present report provides a review of the theoretically possible plots that can be found when data from pharmacology (mainly organ bath) experiments are analyzed . Current plots used in pharmacology, such as response vs log [L], might hide some valuable information when interaction of a ligand with at least two different receptor subtypes occurs . However, if direct, reciprocal or Scatchard plots are used, information relative to the number of different receptors interacting with a ligand can be obtained . It should be noted that the theoretically possible plots obtained from pharmacological data agree with those obtained from binding data when a>O (i .e . right zone of Fig . 1) [1-3] . Obviously, in binding experiments negative binding cannot occur. Conversely, in organ-bath pharmacology, opposite effects with two receptor subtypes could be obtained . For instance, in the case of adenosine receptors, activation of A2 receptors leads to an increase of cyclic AMP levels whereas activation of A, receptors leads to a decrease of cyclic AMP [13] . Although there are typical examples of tissues having preferably one of these
Pharmacological Research, Vol. 25, No . 4, 1992
333
subtypes [16, 17], it is reasonable to assume that, irrespective of the tissue, both subtypes coexist . Although for other receptors data have not been given, other plots are also observed [18-20] . In some cases, when a ligand interacts with two receptors mediating opposite effects a maximum or a minimum (zones la, 2a, lb and 2b) could be found in direct plots . This singular point (maximum or minimum) appears at relatively low concentrations of ligand (see Figs 1 and 2) . Then, such zones (having either a maximum or a minimum) would be detected with difficulty when analyzing pharmacological data and could even have been rejected as discordant observations . However, carefully designed experiments, repeated until achieving 99% confidence levels in effect values, could be useful in obtaining accurate Scatchard plots (see ref . 21 for an example of experimental design useful in model discrimination) . These plots might be suitable for demonstrating to which extent two receptors for the same ligand coexist in a single tissue . When a Scatchard plot suggests the existence of two receptor subtypes in the tissue analyzed, confirmation should be carried out . In the most favourable case the shape of the curve must change when the experiment is repeated in the presence of a blocker specific for one of the subtypes . If there are no specific blockers for the different subtypes, displacement binding experiments using agonists specific either for one or other subtype are required .
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