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The competitive and noncompetitive antagonism of receptor-mediated drug actions in the presence of spare receptors
JPM Vol. 29, No. 2 April 1993:85-91
The Competitive and Noncompetitive Antagonism of ReceptorMediated Drug Actions in the Presence of Spare Receptors Bao Ting Zhu Department of Pharmacology and Toxicology, The University of Texas Medical Branch, Galveston, Texas, U.S.A.
According to the original receptor occupancy theory proposed by Clark in the 1930s, the percent occupancy of total available receptors by an agonist is linearly related to the response (or effect). However, the first recognition of "receptor reserve" or "spare receptors" mainly by Furchgott and Stephenson in separate studies about two decades ago has profoundly modified the original receptor occupancy theory, that is, the receptor occupancy is not directly proportional to the responses, and the EDso (or ECso) could be much lower than the equilibrium dissociation constant (Kd). To date, the receptor reserve phenomenon has been characterized in an increasing number of receptor systems. In theory, spare receptors may influence the profile of dose-response (D-R) relationship as well as that of the competitive or noncompetitive antagonism of receptor-mediated drug actions.
Keywords: Spare receptor; Dose-response relationship; Competitive antagonism; Noncompetitive antagonism
Introduction By the original hypothesis of receptor occupancy theory as proposed by Clark (1926, 1933, 1937), the percent occupancy of total receptors is quantitatively proportional to the magnitude of the response, that is, 50% occupancy of the total receptors would generate half the maximum response elicited by the ligand-receptor complex, and 100% occupancy is necessary for the maximum response. However, later studies (Furchgott, 1955, 1966; Nickerson, 1955, Stephenson, 1956) revealed that in some receptor-mediated systems, maximum response was obtained with up to 95% of the total receptors presented on the cell membrane remaining unoccupied. This phenomenon was concluded as "receptor reserve" or "spare receptors." Although the existence of receptor reserve in several different receptor systems has been recognized for about two decades, its potential physiological or pharmacological roles have not been given appropriate con-
sideration. This communication primarily focused on the potential influence of existing spare receptors on the dose-response (D-R) profiles, and on the competitive or noncompetitive antagonism of receptormediated drug actions.
Basic Principles and Assumptions Basic Principles of LigandReceptor Interaction A vast number of good review articles or textbook chapters are available on this topic (for a quick review see Pratt and Taylor, 1990). For the purpose of clarity in the following discussion on the possible roles of spare receptors, some of the pertinent equations have been listed below. The ligand-receptor interaction shown in Equation (Eq.) 1 follows the Law of Mass Action, and all the other listed equations can be derived from Eqs. 1 and 2. k
L + R. I,LR
(1)
k- ~ [L][R] Kd = k--T- [LR]
(2)
k-1
Address reprint requests to Bao Ting Zhu, M.D., Ph.D., J-31, Department of Pharmacology and Toxicology, The University of Texas Medical Branch, Galveston, Texas 77555-1031, U.S.A. Received December 18, 1992; revised and accepted December 18, 1992. Journal of Pharmacological and Toxicological Methods 29, 85-91 (1993) © 1993 Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
At equilibrium,
1056-8719/93/$6.00
86
JPM Vol. 29, No. 2 April 1993:85-91
B
[L]
% occupancy - Bma~ - [L] + Kd
(3)
In the presence of a competitive antagonist,
B Bmax -
[L] ( [An]/ [L] + Kd 1 + ~ /
(4)
receptor reserve will be presumably seen. For the purpose of simplicity in the following discussion on the possible roles of spare receptors, we assume that before reaching the maximal response the occupancy of each receptor by an agonist can be transduced with equal efficiency into the intracellular biochemical process.
In the presence of a noncompetitive antagonist, B
[L]
Spare Receptors and the Sigmoid Dose-Response Curve
(5)
where variables are indicated as follows: L: ligand; R: receptors; k~: association rate constant of the ligand-receptor interaction; k_ ,: dissociation rate constant of the ligand-receptor interaction; Kd: equilibrium dissociation constant; B: number of receptors that are bound with ligand at equilibrium; Bma×: number of total receptors; [L]: free ligand concentrations at equilibrium; [R]: unbound receptor concentrations at equilibrium; [LR]: bound receptor concentrations at equilibrium; [An]: antagonist concentrations added; and Ki: equilibrium dissociation constant of an antagonist.
Some Assumptions It is assumed that spare receptors are not functionally or pharmacologically different from nonspare receptors, and they are not hidden or unavailable. Therefore, each individual receptor has the same possibility to become a spare receptor in the presence of an agonist concentration that is minimally needed to generate a maximum response. The percentage of total receptors that will become spare receptors can be experimentally determined by the method of Furchgott and Bursztyn (1967). Biochemically, the intracellular mechanisms accounting for the phenomenon of receptor reserve have not been elucidated. It is postulated that the number of total receptors on the cell surface does not always match the number of the relevant and functional intracellular transducers/effectors (e.g., G-protein, adenylate cyclase). If the ratio of total receptor number to that of the relevant and functional intracellular transducers/effectors is less than or equal to 1, then there would be no existing spare receptors, because the activated receptors can be simultaneously transduced into the intracellular biochemical process. However, if the ratio is greater than 1, that is, the total receptor number is greater than that of the relevant and functional intracellular transducers/effectors, then the activation of all receptors by ligand cannot be simultaneously transduced into the cell, and therefore, the phenomenon of
According to the original hypothesis of the receptor occupancy theory of drug action, the dose-response curve should be similar to the saturation curve in ligand-receptor binding studies, that is, a hyperbolic curve when both X axis (drug concentration) and Y axis (% of maximum response or % of maximum binding) are illustrated on a mathematic scale [Figure 1 (curve A)]. If the X axis is converted to a logarithmic scale with the Y axis unchanged (semilogarithmic scale), as the D - R curve is usually drawn, a symmetric sigmoid curve is produced [Figure 2 (curve A)]. This standard symmetric sigmoid pattern has been repeatedly demonstrated in studies of the D - R relationship of receptor-mediated drug actions when spare receptors are not present. In the presence of spare receptors the saturation profile in ligand-receptor binding studies will not change because the kinetic properties of ligand-receptor interaction, such as the Kd value, are not dependent on the total receptor numbers and only dependent on percent occupancy or binding (according to Eq. 3). However, in the presence of spare receptors, the calculated D-R curve will no longer look like a typical hy-
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Figure 1. The calculated D - R c u r v e s of an agonist on a mathematic scale in the absence (curve A) or presence (curves B and C) of different percentages of spare receptors. The Kd value is arbitrarily assigned to be 10 - 9 M, and this Kd value is also used in all the other illustrations. Curve A is drawn according to Eq. 3; c u r v e s B and C are drawn according to Eq. 6.
B. T. Z H U ROLE OF SPARE RECEPTORS IN DRUG ACTION
87
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Figure 2. The calculated D-R curves of an agonist on a semilogarithmic scale in the absence or presence of different percentages of spare receptors. The Kd value is equal to 10 - 9 M in this plot. In actuality, varied Kd values will have D-R curves of the same pattern if in the absence of spare receptors, that is, they are superimposable, and the only difference is a rightward or leftward shift. Curve A is drawn according to Eq. 3; curves B-E are drawn according to Eq. 6.
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perbolic [Figure 1 (curves B and C)] or symmetrical sigmoid curve [Figure 2 (curves B-E)], because the maximum response does not need to occupy 100% of the total receptors presented, but only needs to occupy a fraction of the total receptors. The percentage of total receptors that will produce a maximal response depends on the percentage of existing spare receptors. The equation used for drawing curves B and C in Figure 1 and curves B - E in Figure 2, as listed below, is derived from Eq. 3, [LI 1 E -- Emax " Kd + [L] " 1 - p (6) (self-explanation 1) where p is the percentage or fraction of existing spare receptors accounting for the total receptors. Figures 1 and 2 illustrate the calculated theoretical D-R curves either in the absence or presence of different fractions of spare receptors according to Eqs. 3 or 6, respectively. The following assumptions are made for simplicity of the model: 1. The response mediated by the ligand is linearly related to the occupancy of receptors before the maximum response has been reached. 2. The receptor concentration in comparison with that of the ligand should be less than 1%. Therefore, the total ligand concentration will be approximately equal to the free ligand concentration at equilibrium, and the concentrations of total ligand instead of free ligand can also be utilized in Eq. 4. 3. The ligand is not eliminated by any possible means, for instance, enzymatic degradation or uptake into the cells, and so on. Thus, the ECso will equal the physiological binding affinity in the absence of spare receptors. In theory, the standard semilogarithmic D - R curve in the absence of spare receptors should be characteristic of a symmetric sigmoid curve with the ECso point as a center for symmetry [Figure 2 (curve A)] (Goldstein, 1974). The slope of the curve increases continuously
8
6
( M)
from zero up to reaching the ECso point, and that point has the maximal slope value (equal to 0.576) and the highest degree of inflection (Goldstein, 1974). In principle, this maximal slope value is independent of receptor types and Kd values (Goldstein, 1974). After the ECso point, the slope of the D - R curve decreases in a way which is exactly the opposite process of the increase of the slope before reaching the ECs0 point. When the slope of the dose-response curve reverts to zero again, the maximum response is obtained. These features of the standard D - R curve have been applied as classical requirements in characterizing the D - R relationship of receptor-mediated drug actions (Goldstein, 1974). However, in the presence of spare receptors, the D - R curve will no longer exhibit a typical hyperbolic curve on a mathematic scale [Figure I (curves B and C)], or a symmetric sigmoid curve on a semilogarithmic scale [Figure 2 (curves B-E)]. The apparent change in the curve pattern becomes more pronounced with increasing percentages of spare receptors. If the percentage of spare receptors is equal to or greater than 50%, then the slope of the semilogarithmic D - R curve will continuously increase until reaching the maximum response, at which point a characteristic sharp turning angle will occur [Figure 2 (curves C-E)]. By contrast, if the percentage of spare receptors is less than 50%, then the maximal slope on the semilogarithmic D - R curve will be at the region between 50% and 100% of the maximum response. A higher percentage of the existing spare receptors (but still less than 50% of the total receptors) will move the point that has the maximal slope and inflection on the semilogarithmic D - R curve closer to the maximum response. The range of 10%-90% of the maximum response in the absence of spare receptors will cover approximately 2 log molar concentration units on a semilogarithmic D - R curve [Figure 2 (curve A)]. In the presence of spare receptors, the range of 10%-90% of
88
maximum response, and especially that of 50%-90%, will be dramatically narrowed. In other words, the semilogarithmic D - R curve will be much steeper, especially the 50%-100% of maximal response [as illustrated in Figure 2 (curves B - E ) . Therefore, each individual D - R curve is theoretically different in shape from another unless the percentages of the existing spare receptors are the same. H o w e v e r , the heterogeneity of D - R curves due to the presence of differential percentages of spare receptors are frequently inappropriately dealt with in the scientific publications. One of the causes is that almost all of the available computer programs for the simulation of D - R curves are designed according to the principles suitable for the situations in the absence of spare receptors. Consequently, all D - R curves are simulated to a symmetric sigmoid pattern. It is hoped that sophisticated computer programs will be available in the future for individualized simulation of D - R curves, so that the heterogeneity of each D - R curve could be determined, which may include the determination of following parameters: 1) the log molar concentration coverage for 10%-90% and for 50%-90% of maximal response; 2) location of the point that has the highest slope and inflection; 3) the ECso (EDso) value; and 4) the possibility of the existence of spare receptors.
Influence of Spare Receptors on Competitive and Noncompetitive Antagonism The concept and mechanism of competitive and noncompetitive antagonism of receptor-mediated action are similar to that of e n z y m e inhibition. The theoretical competitive inhibition of e n z y m e by an inhibitor means that the inhibitor competes with the substrate at the same site on the enzyme, so that the apparent binding affinity of substrate for the e n z y m e (characterized by 1/Kin) decreases, while the Vma~ does not change. In contrast, a noncompetitive inhibitor acts at different site(s) on the e n z y m e from that of the substrate. Therefore, a noncompetitive inhibitor does not change the binding affinity of substrate to enzyme, but it inhibits the Vma~ of the reaction. These characteristics of a competitive or noncompetitive interaction as discussed above are also frequently observed in D - R studies or in radioligand-receptor binding assays. The question as to what possible influence spare receptors may have on the profiles of a competitive or noncompetitive antagonism is a discussion worth expanding. Theoretically, spare receptors will have no influence on the profile of a competitive or noncompetitive antagonism in radioligand-receptor binding assays (usually determined on the Scatchard or E a d i e - H o f f s t e e plot). This is because the kinetic parameters (e.g., Kd value) are not dependent upon the receptor concentra-
J P M Vol. 29, N o . 2 April 1993:85-91
tions (according to Eq. 3), and the spare or nonspare receptors are not pharmacologically different with respect to their ligand binding properties. However, in the presence of spare receptors these characteristics of a competitive or noncompetitive antagonism will be dramatically altered in the D - R relationship studies.
Competitive Antagonism In the absence of spare receptors, the profile of a competitive or noncompetitive antagonism in D - R relationship studies will be theoretically the same as that in radioligand binding assays. It has been documented that in the absence of spare receptors, a pure competitive antagonist will produce a parallel shift of the D - R curve (on semilogarithmic scale) to the right [Figure 3 (curves A and B)]. As illustrated in Figure 2, in the presence of spare receptors the shape of a symmetrical sigmoid D - R curve is altered. H o w e v e r , the strict parallelism (parallel shift of the D - R curve to the right) and the magnitude of the parallel shift in the presence
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Figure 3. The influence of spare receptors on the theoretical D-R curve of an agonist in the presence of a competitive antagonist. The Kd value of the agonist and the Ki value of the competitive antagonist are both arbitrarily assigned to be l0 9 M. Curve A is the theoretical D-R curve in the absence of both spare receptors and a competitive antagonist; curve B is that in the absence of spare receptors but in the presence of a competitive antagonist with a concentration equal to its Ki, l0 -9 M. Curves A and B are drawn according to Eqs. 3 and 4, respectively. Curve B is parallel to curve A. The magnitude of rightward shift on the semilogarithmic scale depends on the Ki and concentration of the antagonist applied, and in this case it equals 1.0 log molar concentration unit. Curve C is the theoretical D-R curve in the presence of 90% of spare receptors (no antagonist); curve D is that in the presence of both spare receptors (90%) and a competitive antagonist (10 -9 M). Curves C and D are drawn according to Eqs. 6 and 7 (self-explanation l), respectively. Curve D is also strictly parallel to curve C, and the magnitude of rightward shift on the semilogarithmic scale also equals 1.0 log molar concentration unit.
T. ZHU
89
B. ROLE OF SPARE RECEPTORS IN DRUG ACTION
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Figure 4. The calculated inhibition curves of an agonist's action by a competitive antagonist in the absence or presence of spare receptors (90%). The agonist concentration in this plot is equal to its Kd, 10 - 9 M; the Ki of the competitive antagonist also is equal to 10 9 M.
of a competitive antagonist will not be influenced by the existing spare receptors [Figure 3 (curves C and D)] (self-explanation 2, below). In the inhibition studies, that is, the inhibition of the action elicited by a fixed concentration of agonist, the profile will be sometimes altered due to the presence of spare receptors (Figure 4). The difference in the inhibition curves as illustrated in Figure 4 are dependent on the agonist concentrations presented. In the presence of higher agonist concentrations, the difference will be more apparent, and vice versa. However, when the fixed agonist concentration is lower than that needed to occupy all the nonspare receptors for generating a maximum response, the difference mentioned above will be no longer seen (theoretical curves are not shown). Therefore, the presence of a large percentage of spare receptors could make an agonist's effect more difficult to be antagonized by a competitive antagonist, as compared to that in the absence of spare receptors. The possible significance of such phenomena could be exemplified by the spare [3 adrenoceptors in the heart which may play a crucial role in the maintenance of basal cardiac function. The [3 adrenoceptors in the heart contain a large population of spare receptors, and, therefore, they can be virtually fully activated by any low physiological concentrations of catecholamines, and the effect cannot be readily antagonized by low concentrations of antagonists. In other words, if this function could be easily blocked by low doses of a competitive antagonist like propranolol, then the complete collapse of the cardiovascular functions would be readily resulted. Therefore, the spare receptors could be viewed as the body's built-in compensatory design.
The presence of spare receptors will make a noncompetitive antagonism more complex than what we actually realize. A noncompetitive antagonist inhibits the maximal receptor binding (or occupancy), therefore, the maximum response mediated by receptors will be also suppressed if it occurs in the absence of spare receptors [Figure 5 (left panel)]. This is one of the characteristics of noncompetitive antagonism. In contrast, the maximum response does not need to occupy all the receptors if spare receptors are present, it is thus possible that the maximum response in the presence of a noncompetitive antagonist could be still obtained in some situations. In this context, two parameters are important: the percentage of existing spare receptors and the concentrations of the noncompetitive antagonist applied. If the suppressed maximal occupancy of receptor number in the presence of low concentrations of a noncompetitive antagonist is still greater than or equal to that required for producing a maximum response, then the maximum response may be still obtained. However, if the suppressed maximal occupancy in the presence of a noncompetitive antagonist is lower than that needed to produce a maximum response, then the maximum response could not be obtained. Figure 5 (right panel) illustrates the calculated D - R curves in the presence of different concentrations of a noncompetitive antagonist yet with the same amount of spare receptors presented. In the presence of spare receptors, low concentrations of a noncompetitive antagonist will shift the D - R curve to the right (but not strictly parallel) and result in an increase in the ECso value, but the maximum response could be still obtained [Figure 5 (curves A-D)]. Further increase of the concentrations of the noncompetitive antagonist will eventually suppress the maximum response [Figure 5 (curves E and F)]. Theoretically, as soon as the maximum response can be no longer obtained, the ECso value will keep constant, and this constant ECso value is equal to the real Kd value of the agonist. Therefore, in order to indirectly determine the Kd value from the classical D - R relationship studies in cases where spare receptors are present, the involvement of a noncompetitive antagonist (reversible or irreversible) would be helpful. In addition, influence of spare receptors on the inhibition of an agonist's action by increasing concentrations of a noncompetitive antagonist is similar to that with a competitive antagonist, as illustrated in Figure 4.
Experimental Indications for the Possible Existence of Spare Receptors About two decades ago, Furchgott and Bursztyn (1967) developed an elegant method for in vitro experi-
90
JPM Vol. 29, No. 2
April 1993:85-91
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Figure 5. (a) The calculated D-R curves of a noncompetitive antagonism in the absence of spare receptors. Both the Kd of an agonist and Ki of an antagonist are equal to 10 - 9 M in this plot. Curve A is in the absence of a competitive antagonist, which is drawn according to Eq. 3; Curves B, C, and D are in the presence of three different concentrations of a noncompetitive antagonist (0.33 × l0 - 9 M , l 0 - 9 M , and 3 × 10 - 9 M , respectively), all of which are drawn according to Eq. 5. (b) The calculated D-R curves of a noncompetitive antagonism in the presence of 90% spare receptors. Curve A is in the absence of a noncompetitive antagonist, drawn according to Eq. 6; Curves B, C, D, E, and F are in the presence of increasing concentrations of a noncompetitive antagonist (4 x 10 - 9 M, 7.33 x 10 - 9 M, 9 x l0 - 9 M, 19 x 10 - 9 M, and 24 x 10 - 9 M, respectively), all of which are drawn according to Eq. 8 (self-explanation 1).
mental quantitation of the existing spare receptors. That method has been successfully applied o v e r the years to identify receptor reserve in different receptor systems. Theoretically, Furchgott's method or the main idea of the method is still applicable and o f choice for most of the testing systems. Some experimental indications for the possible existence o f spare receptors are suggested below. If the EC5o (or EDso) value determined from a semilogarithmic D - R curve is much lower than its Kd value, which is usually determined by receptor binding studies, then the possibility of the existence of spare receptor should be considered. . If the maximum response of a full agonist has been experimentally well defined in the testing system, then the range of 10%-90% of the maximum response in the absence of spare receptors will theoretically c o v e r approximately 2 log molar concentration units on a semilogarithmic D - R curve (Figure 2). H o w e v e r , in the presence o f spare receptors, the range of 10%-90% of the maximum response, especially that of 50%-90%, will be dramatically narrowed. As a suggested practical parameter, if the 10%-90% range is less than 1 log molar concentration unit, or the 50%-90% is less than 0.5 log molar
concentration unit, then the existence of spare receptors is suggested. . In the in vitro testing system, if low concentrations of a specific noncompetitive antagonist cause an increase in the EC5o (or EDso) value of an agonist yet no influence on the maximum response, and higher concentrations of the same antagonist inhibit the maximum response in a dose-dependent manner yet no further increase in the ECso (or EDso) value (as illustrated in Figure 5), then the existence of spare receptors is very possible.
Self-Explanations 1. According to Eq. 3, %occupancyofreceptors
B _ [L] B max Kd + [L]"
Therefore, in the absence of spare receptors, E
B
Emax
Bmax
[L] Kd + [L]"
In the presence of spare receptors, all the nonspare receptors must be fully occupied in order to produce a maximum response, that is,
B. T. ZHU ROLE OF SPARE RECEPTORS IN DRUG ACTION
B
91
[L]
Bma----~= Kd + [L]
same agonist in the absence of the antagonist• Therefore,
1 - p,
where p means the percentage of existing spare receptors in total receptors. Therefore, E Emax
B 1 Braax 1 - p
[L] Kd
[L] + [LI'I
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+
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The magnitude of parallel shift on a semilogarithmic scale will be equal to log[L]' - log [L], (6)
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=
Emax"
[
Kd(1
[L] rAnl\ +---~-]L J/ + [L]
1 1 - p"
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E = Emax"
(8)
[Anl / . 1 (Kd + [L]) 1 + --K-i-] 1 - p
Mathematically, the value of E in Eqs. 6-8 could be greater than E~ax- But in a pharmacological sense, E actually is always less than or equal to E . . . . Thus, when the calculated value of E is greater than Emax, assign E = E . . . . 2. A. According to Eq. 6 (self-explanation 1), if the percentage of existing spare receptors is p, then [L] 1 E --- Ernax " K d + [L] " 1 - p" Therefore [L] =
E Kd (1 - p) Emax - E(1 - p)"
In addition, according to Eq. 7, in the presence of spare receptors, the competitive antagonism will be E = Emax"
ILl' [An] / K d 1 + ---K-]-] + [L]'
1 l-p
where [L]' is the agonist concentration which is needed in the presence of a competitive antagonist to generate the same magnitude of response elicited by a certain concentration [L] of the
-- constant•
B e c a u s e t h e v a l u e o f ( L o g [ L ] ' - L o g ILl) is e q u a l to a c o n s t a n t i n t h e p r e s e n c e o f c e r t a i n concentration of the antagonist, therefore the curves for equations 6 and 7 are parallel. B. I n t h e a b s e n c e o f s p a r e r e c e p t o r s , t h e log shift in t h e p r e s e n c e o f a c o m p e t i t i v e a n t a g o n i s t will [An]) b e a l s o e q u a l to log (1 + ~ . Therefore, the s a m e a n t a g o n i s t c o n c e n t r a t i o n will p r o d u c e a p a r a l l e l shift o f t h e s a m e m a g n i t u d e , e q u a l to
[An]), log (1 + ~ either in the presence or absence of spare receptors. The author thanks Dr. Dianne K. Hammond at the Department of Pharmacology and Toxicology, the University of Texas Medical Branch at Galveston (U.S.A.), for her valuable suggestions.
References Clark AJ (1926) The antagonism of acetylcholine by atropine. JPhysiol (Lond.) 61:547-556. Clark AJ (1933) The Mode of Action of Drugs on Cells London: E• Arnold Co. Clark AJ (1937) Handbuch der Experimentallen Pharmakologie, Band IV. Berlin: Springer-Verlag. Furchgott RF (1955) The pharmacology of vascular smooth muscle, Pharmacol Rev 7:183. Furchgott RF (1966) The use of [3-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants of receptor-agonist complexes. In: Advances in Drug Research, Vol• 3. Ed., NJ Harper, AB Simmonds. London: Academic Press, pp 21-55. Furchgott RF, Bursztyn P (1967) Comparison of dissociation constants and relative efficies of selected agonists acting on parasympathetic receptors. Ann. N.Y. Acad. Sci. 114:882-899. Goldstein A (1974) Principles of Drug Action New York: A Wiley Biochemical-Health Publication. Nickerson M (1955) Receptor occupancy and tissue response. Nature 178:697-698. Pratt WB, Taylor P (1990) Principles of Drug Action (3d ed.) New York, Edingburgh, London, Melbourne, Tokyo. Churchill Livingstone. Stephenson RP (1956) A modification of receptor theory. Br J Pharnacol 11:379-393.
The Competitive and Noncompetitive Antagonism of ReceptorMediated Drug Actions in the Presence of Spare Receptors Bao Ting Zhu Department of Pharmacology and Toxicology, The University of Texas Medical Branch, Galveston, Texas, U.S.A.
According to the original receptor occupancy theory proposed by Clark in the 1930s, the percent occupancy of total available receptors by an agonist is linearly related to the response (or effect). However, the first recognition of "receptor reserve" or "spare receptors" mainly by Furchgott and Stephenson in separate studies about two decades ago has profoundly modified the original receptor occupancy theory, that is, the receptor occupancy is not directly proportional to the responses, and the EDso (or ECso) could be much lower than the equilibrium dissociation constant (Kd). To date, the receptor reserve phenomenon has been characterized in an increasing number of receptor systems. In theory, spare receptors may influence the profile of dose-response (D-R) relationship as well as that of the competitive or noncompetitive antagonism of receptor-mediated drug actions.
Keywords: Spare receptor; Dose-response relationship; Competitive antagonism; Noncompetitive antagonism
Introduction By the original hypothesis of receptor occupancy theory as proposed by Clark (1926, 1933, 1937), the percent occupancy of total receptors is quantitatively proportional to the magnitude of the response, that is, 50% occupancy of the total receptors would generate half the maximum response elicited by the ligand-receptor complex, and 100% occupancy is necessary for the maximum response. However, later studies (Furchgott, 1955, 1966; Nickerson, 1955, Stephenson, 1956) revealed that in some receptor-mediated systems, maximum response was obtained with up to 95% of the total receptors presented on the cell membrane remaining unoccupied. This phenomenon was concluded as "receptor reserve" or "spare receptors." Although the existence of receptor reserve in several different receptor systems has been recognized for about two decades, its potential physiological or pharmacological roles have not been given appropriate con-
sideration. This communication primarily focused on the potential influence of existing spare receptors on the dose-response (D-R) profiles, and on the competitive or noncompetitive antagonism of receptormediated drug actions.
Basic Principles and Assumptions Basic Principles of LigandReceptor Interaction A vast number of good review articles or textbook chapters are available on this topic (for a quick review see Pratt and Taylor, 1990). For the purpose of clarity in the following discussion on the possible roles of spare receptors, some of the pertinent equations have been listed below. The ligand-receptor interaction shown in Equation (Eq.) 1 follows the Law of Mass Action, and all the other listed equations can be derived from Eqs. 1 and 2. k
L + R. I,LR
(1)
k- ~ [L][R] Kd = k--T- [LR]
(2)
k-1
Address reprint requests to Bao Ting Zhu, M.D., Ph.D., J-31, Department of Pharmacology and Toxicology, The University of Texas Medical Branch, Galveston, Texas 77555-1031, U.S.A. Received December 18, 1992; revised and accepted December 18, 1992. Journal of Pharmacological and Toxicological Methods 29, 85-91 (1993) © 1993 Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
At equilibrium,
1056-8719/93/$6.00
86
JPM Vol. 29, No. 2 April 1993:85-91
B
[L]
% occupancy - Bma~ - [L] + Kd
(3)
In the presence of a competitive antagonist,
B Bmax -
[L] ( [An]/ [L] + Kd 1 + ~ /
(4)
receptor reserve will be presumably seen. For the purpose of simplicity in the following discussion on the possible roles of spare receptors, we assume that before reaching the maximal response the occupancy of each receptor by an agonist can be transduced with equal efficiency into the intracellular biochemical process.
In the presence of a noncompetitive antagonist, B
[L]
Spare Receptors and the Sigmoid Dose-Response Curve
(5)
where variables are indicated as follows: L: ligand; R: receptors; k~: association rate constant of the ligand-receptor interaction; k_ ,: dissociation rate constant of the ligand-receptor interaction; Kd: equilibrium dissociation constant; B: number of receptors that are bound with ligand at equilibrium; Bma×: number of total receptors; [L]: free ligand concentrations at equilibrium; [R]: unbound receptor concentrations at equilibrium; [LR]: bound receptor concentrations at equilibrium; [An]: antagonist concentrations added; and Ki: equilibrium dissociation constant of an antagonist.
Some Assumptions It is assumed that spare receptors are not functionally or pharmacologically different from nonspare receptors, and they are not hidden or unavailable. Therefore, each individual receptor has the same possibility to become a spare receptor in the presence of an agonist concentration that is minimally needed to generate a maximum response. The percentage of total receptors that will become spare receptors can be experimentally determined by the method of Furchgott and Bursztyn (1967). Biochemically, the intracellular mechanisms accounting for the phenomenon of receptor reserve have not been elucidated. It is postulated that the number of total receptors on the cell surface does not always match the number of the relevant and functional intracellular transducers/effectors (e.g., G-protein, adenylate cyclase). If the ratio of total receptor number to that of the relevant and functional intracellular transducers/effectors is less than or equal to 1, then there would be no existing spare receptors, because the activated receptors can be simultaneously transduced into the intracellular biochemical process. However, if the ratio is greater than 1, that is, the total receptor number is greater than that of the relevant and functional intracellular transducers/effectors, then the activation of all receptors by ligand cannot be simultaneously transduced into the cell, and therefore, the phenomenon of
According to the original hypothesis of the receptor occupancy theory of drug action, the dose-response curve should be similar to the saturation curve in ligand-receptor binding studies, that is, a hyperbolic curve when both X axis (drug concentration) and Y axis (% of maximum response or % of maximum binding) are illustrated on a mathematic scale [Figure 1 (curve A)]. If the X axis is converted to a logarithmic scale with the Y axis unchanged (semilogarithmic scale), as the D - R curve is usually drawn, a symmetric sigmoid curve is produced [Figure 2 (curve A)]. This standard symmetric sigmoid pattern has been repeatedly demonstrated in studies of the D - R relationship of receptor-mediated drug actions when spare receptors are not present. In the presence of spare receptors the saturation profile in ligand-receptor binding studies will not change because the kinetic properties of ligand-receptor interaction, such as the Kd value, are not dependent on the total receptor numbers and only dependent on percent occupancy or binding (according to Eq. 3). However, in the presence of spare receptors, the calculated D-R curve will no longer look like a typical hy-
® 09
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(/) (D
~
50-
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----0
J o~1
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of
~
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i /
ig 25- 6
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o--,
50 % spore r e c e p t o r s
~--~
90 % spore r e c e p t o r s
o~ 0 Ligond
(nM)
Figure 1. The calculated D - R c u r v e s of an agonist on a mathematic scale in the absence (curve A) or presence (curves B and C) of different percentages of spare receptors. The Kd value is arbitrarily assigned to be 10 - 9 M, and this Kd value is also used in all the other illustrations. Curve A is drawn according to Eq. 3; c u r v e s B and C are drawn according to Eq. 6.
B. T. Z H U ROLE OF SPARE RECEPTORS IN DRUG ACTION
87
E
Figure 2. The calculated D-R curves of an agonist on a semilogarithmic scale in the absence or presence of different percentages of spare receptors. The Kd value is equal to 10 - 9 M in this plot. In actuality, varied Kd values will have D-R curves of the same pattern if in the absence of spare receptors, that is, they are superimposable, and the only difference is a rightward or leftward shift. Curve A is drawn according to Eq. 3; curves B-E are drawn according to Eq. 6.
D
C
r
._E
iI
'~, , -'~
t // /o o
x
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• /o
25q
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//
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No spare receptor 25 % spare receptors
e---• .... *---*
50 % spare receptors 90 % spare receptors 95 % spare receptors
o 12
11
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perbolic [Figure 1 (curves B and C)] or symmetrical sigmoid curve [Figure 2 (curves B-E)], because the maximum response does not need to occupy 100% of the total receptors presented, but only needs to occupy a fraction of the total receptors. The percentage of total receptors that will produce a maximal response depends on the percentage of existing spare receptors. The equation used for drawing curves B and C in Figure 1 and curves B - E in Figure 2, as listed below, is derived from Eq. 3, [LI 1 E -- Emax " Kd + [L] " 1 - p (6) (self-explanation 1) where p is the percentage or fraction of existing spare receptors accounting for the total receptors. Figures 1 and 2 illustrate the calculated theoretical D-R curves either in the absence or presence of different fractions of spare receptors according to Eqs. 3 or 6, respectively. The following assumptions are made for simplicity of the model: 1. The response mediated by the ligand is linearly related to the occupancy of receptors before the maximum response has been reached. 2. The receptor concentration in comparison with that of the ligand should be less than 1%. Therefore, the total ligand concentration will be approximately equal to the free ligand concentration at equilibrium, and the concentrations of total ligand instead of free ligand can also be utilized in Eq. 4. 3. The ligand is not eliminated by any possible means, for instance, enzymatic degradation or uptake into the cells, and so on. Thus, the ECso will equal the physiological binding affinity in the absence of spare receptors. In theory, the standard semilogarithmic D - R curve in the absence of spare receptors should be characteristic of a symmetric sigmoid curve with the ECso point as a center for symmetry [Figure 2 (curve A)] (Goldstein, 1974). The slope of the curve increases continuously
8
6
( M)
from zero up to reaching the ECso point, and that point has the maximal slope value (equal to 0.576) and the highest degree of inflection (Goldstein, 1974). In principle, this maximal slope value is independent of receptor types and Kd values (Goldstein, 1974). After the ECso point, the slope of the D - R curve decreases in a way which is exactly the opposite process of the increase of the slope before reaching the ECs0 point. When the slope of the dose-response curve reverts to zero again, the maximum response is obtained. These features of the standard D - R curve have been applied as classical requirements in characterizing the D - R relationship of receptor-mediated drug actions (Goldstein, 1974). However, in the presence of spare receptors, the D - R curve will no longer exhibit a typical hyperbolic curve on a mathematic scale [Figure I (curves B and C)], or a symmetric sigmoid curve on a semilogarithmic scale [Figure 2 (curves B-E)]. The apparent change in the curve pattern becomes more pronounced with increasing percentages of spare receptors. If the percentage of spare receptors is equal to or greater than 50%, then the slope of the semilogarithmic D - R curve will continuously increase until reaching the maximum response, at which point a characteristic sharp turning angle will occur [Figure 2 (curves C-E)]. By contrast, if the percentage of spare receptors is less than 50%, then the maximal slope on the semilogarithmic D - R curve will be at the region between 50% and 100% of the maximum response. A higher percentage of the existing spare receptors (but still less than 50% of the total receptors) will move the point that has the maximal slope and inflection on the semilogarithmic D - R curve closer to the maximum response. The range of 10%-90% of the maximum response in the absence of spare receptors will cover approximately 2 log molar concentration units on a semilogarithmic D - R curve [Figure 2 (curve A)]. In the presence of spare receptors, the range of 10%-90% of
88
maximum response, and especially that of 50%-90%, will be dramatically narrowed. In other words, the semilogarithmic D - R curve will be much steeper, especially the 50%-100% of maximal response [as illustrated in Figure 2 (curves B - E ) . Therefore, each individual D - R curve is theoretically different in shape from another unless the percentages of the existing spare receptors are the same. H o w e v e r , the heterogeneity of D - R curves due to the presence of differential percentages of spare receptors are frequently inappropriately dealt with in the scientific publications. One of the causes is that almost all of the available computer programs for the simulation of D - R curves are designed according to the principles suitable for the situations in the absence of spare receptors. Consequently, all D - R curves are simulated to a symmetric sigmoid pattern. It is hoped that sophisticated computer programs will be available in the future for individualized simulation of D - R curves, so that the heterogeneity of each D - R curve could be determined, which may include the determination of following parameters: 1) the log molar concentration coverage for 10%-90% and for 50%-90% of maximal response; 2) location of the point that has the highest slope and inflection; 3) the ECso (EDso) value; and 4) the possibility of the existence of spare receptors.
Influence of Spare Receptors on Competitive and Noncompetitive Antagonism The concept and mechanism of competitive and noncompetitive antagonism of receptor-mediated action are similar to that of e n z y m e inhibition. The theoretical competitive inhibition of e n z y m e by an inhibitor means that the inhibitor competes with the substrate at the same site on the enzyme, so that the apparent binding affinity of substrate for the e n z y m e (characterized by 1/Kin) decreases, while the Vma~ does not change. In contrast, a noncompetitive inhibitor acts at different site(s) on the e n z y m e from that of the substrate. Therefore, a noncompetitive inhibitor does not change the binding affinity of substrate to enzyme, but it inhibits the Vma~ of the reaction. These characteristics of a competitive or noncompetitive interaction as discussed above are also frequently observed in D - R studies or in radioligand-receptor binding assays. The question as to what possible influence spare receptors may have on the profiles of a competitive or noncompetitive antagonism is a discussion worth expanding. Theoretically, spare receptors will have no influence on the profile of a competitive or noncompetitive antagonism in radioligand-receptor binding assays (usually determined on the Scatchard or E a d i e - H o f f s t e e plot). This is because the kinetic parameters (e.g., Kd value) are not dependent upon the receptor concentra-
J P M Vol. 29, N o . 2 April 1993:85-91
tions (according to Eq. 3), and the spare or nonspare receptors are not pharmacologically different with respect to their ligand binding properties. However, in the presence of spare receptors these characteristics of a competitive or noncompetitive antagonism will be dramatically altered in the D - R relationship studies.
Competitive Antagonism In the absence of spare receptors, the profile of a competitive or noncompetitive antagonism in D - R relationship studies will be theoretically the same as that in radioligand binding assays. It has been documented that in the absence of spare receptors, a pure competitive antagonist will produce a parallel shift of the D - R curve (on semilogarithmic scale) to the right [Figure 3 (curves A and B)]. As illustrated in Figure 2, in the presence of spare receptors the shape of a symmetrical sigmoid D - R curve is altered. H o w e v e r , the strict parallelism (parallel shift of the D - R curve to the right) and the magnitude of the parallel shift in the presence
<2) o3 0 d:)_ o9 q) 05
E
(3
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75 i
./
5O
t
2~.
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~
",~
,~
,40
bo 0
12
11
10
9
-Log E higGnd ]
8
,7--
-~6
;
( M)
Figure 3. The influence of spare receptors on the theoretical D-R curve of an agonist in the presence of a competitive antagonist. The Kd value of the agonist and the Ki value of the competitive antagonist are both arbitrarily assigned to be l0 9 M. Curve A is the theoretical D-R curve in the absence of both spare receptors and a competitive antagonist; curve B is that in the absence of spare receptors but in the presence of a competitive antagonist with a concentration equal to its Ki, l0 -9 M. Curves A and B are drawn according to Eqs. 3 and 4, respectively. Curve B is parallel to curve A. The magnitude of rightward shift on the semilogarithmic scale depends on the Ki and concentration of the antagonist applied, and in this case it equals 1.0 log molar concentration unit. Curve C is the theoretical D-R curve in the presence of 90% of spare receptors (no antagonist); curve D is that in the presence of both spare receptors (90%) and a competitive antagonist (10 -9 M). Curves C and D are drawn according to Eqs. 6 and 7 (self-explanation l), respectively. Curve D is also strictly parallel to curve C, and the magnitude of rightward shift on the semilogarithmic scale also equals 1.0 log molar concentration unit.
T. ZHU
89
B. ROLE OF SPARE RECEPTORS IN DRUG ACTION
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25
1'1
lt3
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6
-Log [ Antagonist ] ( M )
Figure 4. The calculated inhibition curves of an agonist's action by a competitive antagonist in the absence or presence of spare receptors (90%). The agonist concentration in this plot is equal to its Kd, 10 - 9 M; the Ki of the competitive antagonist also is equal to 10 9 M.
of a competitive antagonist will not be influenced by the existing spare receptors [Figure 3 (curves C and D)] (self-explanation 2, below). In the inhibition studies, that is, the inhibition of the action elicited by a fixed concentration of agonist, the profile will be sometimes altered due to the presence of spare receptors (Figure 4). The difference in the inhibition curves as illustrated in Figure 4 are dependent on the agonist concentrations presented. In the presence of higher agonist concentrations, the difference will be more apparent, and vice versa. However, when the fixed agonist concentration is lower than that needed to occupy all the nonspare receptors for generating a maximum response, the difference mentioned above will be no longer seen (theoretical curves are not shown). Therefore, the presence of a large percentage of spare receptors could make an agonist's effect more difficult to be antagonized by a competitive antagonist, as compared to that in the absence of spare receptors. The possible significance of such phenomena could be exemplified by the spare [3 adrenoceptors in the heart which may play a crucial role in the maintenance of basal cardiac function. The [3 adrenoceptors in the heart contain a large population of spare receptors, and, therefore, they can be virtually fully activated by any low physiological concentrations of catecholamines, and the effect cannot be readily antagonized by low concentrations of antagonists. In other words, if this function could be easily blocked by low doses of a competitive antagonist like propranolol, then the complete collapse of the cardiovascular functions would be readily resulted. Therefore, the spare receptors could be viewed as the body's built-in compensatory design.
The presence of spare receptors will make a noncompetitive antagonism more complex than what we actually realize. A noncompetitive antagonist inhibits the maximal receptor binding (or occupancy), therefore, the maximum response mediated by receptors will be also suppressed if it occurs in the absence of spare receptors [Figure 5 (left panel)]. This is one of the characteristics of noncompetitive antagonism. In contrast, the maximum response does not need to occupy all the receptors if spare receptors are present, it is thus possible that the maximum response in the presence of a noncompetitive antagonist could be still obtained in some situations. In this context, two parameters are important: the percentage of existing spare receptors and the concentrations of the noncompetitive antagonist applied. If the suppressed maximal occupancy of receptor number in the presence of low concentrations of a noncompetitive antagonist is still greater than or equal to that required for producing a maximum response, then the maximum response may be still obtained. However, if the suppressed maximal occupancy in the presence of a noncompetitive antagonist is lower than that needed to produce a maximum response, then the maximum response could not be obtained. Figure 5 (right panel) illustrates the calculated D - R curves in the presence of different concentrations of a noncompetitive antagonist yet with the same amount of spare receptors presented. In the presence of spare receptors, low concentrations of a noncompetitive antagonist will shift the D - R curve to the right (but not strictly parallel) and result in an increase in the ECso value, but the maximum response could be still obtained [Figure 5 (curves A-D)]. Further increase of the concentrations of the noncompetitive antagonist will eventually suppress the maximum response [Figure 5 (curves E and F)]. Theoretically, as soon as the maximum response can be no longer obtained, the ECso value will keep constant, and this constant ECso value is equal to the real Kd value of the agonist. Therefore, in order to indirectly determine the Kd value from the classical D - R relationship studies in cases where spare receptors are present, the involvement of a noncompetitive antagonist (reversible or irreversible) would be helpful. In addition, influence of spare receptors on the inhibition of an agonist's action by increasing concentrations of a noncompetitive antagonist is similar to that with a competitive antagonist, as illustrated in Figure 4.
Experimental Indications for the Possible Existence of Spare Receptors About two decades ago, Furchgott and Bursztyn (1967) developed an elegant method for in vitro experi-
90
JPM Vol. 29, No. 2
April 1993:85-91
a
b
~oo1j
,~ , z
B
.~ !./v°;::..
o01
C ....
I z// E
/
oooO.... . . . . . . . . . ?
D
,
/ o +'. 12
. ...........
,,d::;o+:...:''"
o" i+
lo
+
+
-}
+
- L o g [ Ligand ] (M)
....
12
11
:
I
+o
+
+
+
+
-Log r Ligand ]
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1
+
(t,,4)
Figure 5. (a) The calculated D-R curves of a noncompetitive antagonism in the absence of spare receptors. Both the Kd of an agonist and Ki of an antagonist are equal to 10 - 9 M in this plot. Curve A is in the absence of a competitive antagonist, which is drawn according to Eq. 3; Curves B, C, and D are in the presence of three different concentrations of a noncompetitive antagonist (0.33 × l0 - 9 M , l 0 - 9 M , and 3 × 10 - 9 M , respectively), all of which are drawn according to Eq. 5. (b) The calculated D-R curves of a noncompetitive antagonism in the presence of 90% spare receptors. Curve A is in the absence of a noncompetitive antagonist, drawn according to Eq. 6; Curves B, C, D, E, and F are in the presence of increasing concentrations of a noncompetitive antagonist (4 x 10 - 9 M, 7.33 x 10 - 9 M, 9 x l0 - 9 M, 19 x 10 - 9 M, and 24 x 10 - 9 M, respectively), all of which are drawn according to Eq. 8 (self-explanation 1).
mental quantitation of the existing spare receptors. That method has been successfully applied o v e r the years to identify receptor reserve in different receptor systems. Theoretically, Furchgott's method or the main idea of the method is still applicable and o f choice for most of the testing systems. Some experimental indications for the possible existence o f spare receptors are suggested below. If the EC5o (or EDso) value determined from a semilogarithmic D - R curve is much lower than its Kd value, which is usually determined by receptor binding studies, then the possibility of the existence of spare receptor should be considered. . If the maximum response of a full agonist has been experimentally well defined in the testing system, then the range of 10%-90% of the maximum response in the absence of spare receptors will theoretically c o v e r approximately 2 log molar concentration units on a semilogarithmic D - R curve (Figure 2). H o w e v e r , in the presence o f spare receptors, the range of 10%-90% of the maximum response, especially that of 50%-90%, will be dramatically narrowed. As a suggested practical parameter, if the 10%-90% range is less than 1 log molar concentration unit, or the 50%-90% is less than 0.5 log molar
concentration unit, then the existence of spare receptors is suggested. . In the in vitro testing system, if low concentrations of a specific noncompetitive antagonist cause an increase in the EC5o (or EDso) value of an agonist yet no influence on the maximum response, and higher concentrations of the same antagonist inhibit the maximum response in a dose-dependent manner yet no further increase in the ECso (or EDso) value (as illustrated in Figure 5), then the existence of spare receptors is very possible.
Self-Explanations 1. According to Eq. 3, %occupancyofreceptors
B _ [L] B max Kd + [L]"
Therefore, in the absence of spare receptors, E
B
Emax
Bmax
[L] Kd + [L]"
In the presence of spare receptors, all the nonspare receptors must be fully occupied in order to produce a maximum response, that is,
B. T. ZHU ROLE OF SPARE RECEPTORS IN DRUG ACTION
B
91
[L]
Bma----~= Kd + [L]
same agonist in the absence of the antagonist• Therefore,
1 - p,
where p means the percentage of existing spare receptors in total receptors. Therefore, E Emax
B 1 Braax 1 - p
[L] Kd
[L] + [LI'I
E = E~.Kd
+
ILl' =
1 [L]
1 -
[An] / E K d 1 + -~-~--] (1 - p)
p
1 - p"
Emax - E(1 - p)
The magnitude of parallel shift on a semilogarithmic scale will be equal to log[L]' - log [L], (6)
[Anl)
log[L]' - log[L] = log(l + ~
Similar to the transformation from Eq. 3 (in the absence of spare receptors) to Eq. 6 (in the presence of spare receptors), the equation for the competitive antagonism in the presence of spare receptors will be E
=
Emax"
[
Kd(1
[L] rAnl\ +---~-]L J/ + [L]
1 1 - p"
(7)
The equation for the noncompetitive antagonism will be ILl
E = Emax"
(8)
[Anl / . 1 (Kd + [L]) 1 + --K-i-] 1 - p
Mathematically, the value of E in Eqs. 6-8 could be greater than E~ax- But in a pharmacological sense, E actually is always less than or equal to E . . . . Thus, when the calculated value of E is greater than Emax, assign E = E . . . . 2. A. According to Eq. 6 (self-explanation 1), if the percentage of existing spare receptors is p, then [L] 1 E --- Ernax " K d + [L] " 1 - p" Therefore [L] =
E Kd (1 - p) Emax - E(1 - p)"
In addition, according to Eq. 7, in the presence of spare receptors, the competitive antagonism will be E = Emax"
ILl' [An] / K d 1 + ---K-]-] + [L]'
1 l-p
where [L]' is the agonist concentration which is needed in the presence of a competitive antagonist to generate the same magnitude of response elicited by a certain concentration [L] of the
-- constant•
B e c a u s e t h e v a l u e o f ( L o g [ L ] ' - L o g ILl) is e q u a l to a c o n s t a n t i n t h e p r e s e n c e o f c e r t a i n concentration of the antagonist, therefore the curves for equations 6 and 7 are parallel. B. I n t h e a b s e n c e o f s p a r e r e c e p t o r s , t h e log shift in t h e p r e s e n c e o f a c o m p e t i t i v e a n t a g o n i s t will [An]) b e a l s o e q u a l to log (1 + ~ . Therefore, the s a m e a n t a g o n i s t c o n c e n t r a t i o n will p r o d u c e a p a r a l l e l shift o f t h e s a m e m a g n i t u d e , e q u a l to
[An]), log (1 + ~ either in the presence or absence of spare receptors. The author thanks Dr. Dianne K. Hammond at the Department of Pharmacology and Toxicology, the University of Texas Medical Branch at Galveston (U.S.A.), for her valuable suggestions.
References Clark AJ (1926) The antagonism of acetylcholine by atropine. JPhysiol (Lond.) 61:547-556. Clark AJ (1933) The Mode of Action of Drugs on Cells London: E• Arnold Co. Clark AJ (1937) Handbuch der Experimentallen Pharmakologie, Band IV. Berlin: Springer-Verlag. Furchgott RF (1955) The pharmacology of vascular smooth muscle, Pharmacol Rev 7:183. Furchgott RF (1966) The use of [3-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants of receptor-agonist complexes. In: Advances in Drug Research, Vol• 3. Ed., NJ Harper, AB Simmonds. London: Academic Press, pp 21-55. Furchgott RF, Bursztyn P (1967) Comparison of dissociation constants and relative efficies of selected agonists acting on parasympathetic receptors. Ann. N.Y. Acad. Sci. 114:882-899. Goldstein A (1974) Principles of Drug Action New York: A Wiley Biochemical-Health Publication. Nickerson M (1955) Receptor occupancy and tissue response. Nature 178:697-698. Pratt WB, Taylor P (1990) Principles of Drug Action (3d ed.) New York, Edingburgh, London, Melbourne, Tokyo. Churchill Livingstone. Stephenson RP (1956) A modification of receptor theory. Br J Pharnacol 11:379-393.