- Email: [email protected]
Antagonism of receptor-activated biological effects mediated by second messenger pathways
Life Sciences, Vol. 38, pp. 251-257 Printed in the U.S.A.
Pergamon Press
ANTAGONISM OF RECEPTOR-ACTIVATED BIOLOGICAL EFFECTS MEDIATED BY SECOND MESSENGER PATHWAYS Robert B. Raffa and C. Paul Bianchi D e p a r t m e n t of P h a r m a c o l o g y , J e f f e r s o n M e d i c a l C o l l e g e Thomas J e f f e r s o n U n i v e r s i t y , P h i l a d e l p h i a , P A 19107 (Received in final form October 30, 1985) SUMMARY It is g e n e r a l l y held that m a n y b i o l o g i c a l l y a c t i v e compounds produce their effects through a sequence of events that are initiated when the substances combine with s e l e c t i v e r e c e p t o r s located on the cell s u r f a c e m e m b r a n e . A c t i v a t i o n of these r e c e p t o r s p r o d u c e s a s t i m u l u s that is somehow transmitted intracellularly. The t r a n s d u c t i o n b e t w e e n the s t i m u l u s and the r e s p o n s e is n o w k n o w n to be mediated, in many systems, by an intracellular intermediary or second messenger. A m o d e l d e s c r i b i n g the r e l a t i o n of agonist concentration, receptor o c c u p a t i o n , and b i o l o g i c a l r e s p o n s e in such a s y s t e m is h e r e i n e x t e n d e d to i n c l u d e antagonist binding at two target sites (i) the cell-surface receptor and (ii) the receptor for the second messenger. It is demonstrated that the shift of an agonist's dose-response curve is characteristic of the site of antagonism and that analysis of this shift can reveal the existence of a second m e s s e n g e r p a t h w a y or, if this is known, the site of a c t i o n of the antagonist. In the past few years, evidence has accumulated suggesting that the biological effects of many drugs, hormones, and neurotransmitters are m e d i a t e d by s p e c i f i c i n t r a c e l l u l a r p a t h w a y s in w h i c h second m e s s e n g e r s play an i m p o r t a n t role. For example, several r e c e p t o r systems appear to utilize a common second messenger pathway involving polyphosphoinositides and Ca ++ (1-3). The phosphoinositides, although a quantitatively m i n o r g r o u p of m e m b r a n e lipids, can have a s i g n i f i c a n t e f f e c t on c e l l u l a r p r o c e s s e s for t w o reasons: (i) activation of the polyphosphoinositide system results in two products, inositol triphosphate and diacylglycerol, both of which act as second messengers and (ii) the signal is amplified through cascade reactions activated by each second messenger. A characteristic feature of the receptors for which the system operates is that they mediate multiple c e l l u l a r responses, i n c l u d i n g m o b i l i z a t i o n of Ca %+, a c t i v a t i o n of protein kinase C, the release of arachidonic acid, and the activation of guanylate cyclase (2). A simplified description of o n e p r o p o s e d model for the involvement of inositol triphosphate (IP 3) and diacylglycerol (DG) in C a + + - l i n k e d , r e c e p t o r - a c t i v a t e d b i o l o g i c a l responses is as follows. B i n d i n g of a s p e c i f i c ligand to its r e c e p t o r a c t i v a t e s an e n z y m e (a p h o s p h o d i e s t e r a s e ) that h y d r o l y z e s a polyphosphoinositide precursor ++ ++ (PIP 2) to IP 3 and DG. IP 3 raises intracellular Ca by releasing Ca 0024-3205/86 $3.00 + .00 Copyright (c) 1986 Pergamon Press Ltd.
252
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
ions from internal storage sites, presumably sarcoplasmic reticulum. C o n c u r r e n t l y , DG s t i m u l a t e s p r o t e i n p h o s p h o r y l a t i o n by a c t i v a t i n g protein kinase C. A model that describes the relation between ligand concentration, r e c e p t o r occupancy, and the m a g n i t u d e of b i o l o g i c a l r e s p o n s e in s y s t e m s d e p e n d e n t upon s e c o n d m e s s e n g e r s has been p r e s e n t e d by S t r i c k l a n d and Loeb (4). In this model, the ligand (A) i n t e r a c t s reversibly with its cell-surface receptor (R) in accord with the Law of Mass Action (A+R ~ AR). The formation of ligand-receptor complexes p r o d u c e s the b i o l o g i c a l e f f e c t by f o r m a t i o n of an i n t r a c e l l u l a r i n t e r m e d i a t e (I) that b i n d s to its o w n i n t r a c e l l u l a r r e c e p t o r (N) a c c o r d i n g to I+N ~ IN, w i t h an e q u i l i b r i u m d i s s o c i a t i o n c o n s t a n t designated K (=[I][N]/[IN]). S t r i c k l a n d and Loeb p o s t u l a t e that the c o n c e n t r a t i o n of i n t r a c e l l u l a r m e d i a t o r is p r o p o r t i o n a l to the c o n c e n t r a t i o n of the AR c o m p l e x (i.e., I = a[AR]*) and that the biological response is p r o p o r t i o n a l to t h e c o n c e n t r a t i o n of intermediate-receptor complex (i.e., R=b[IN]). One consequence of the model, as r e p o r t e d by S t r i c k l a n d and Loeb, is that the n a t u r e of the coupling between ligand and receptor can be inferred by comparison of the m a g n i t u d e s of the d i s s o c i a t i o n c o n s t a n t of the l i g a n d - r e c e p t o r interaction (KA) to the dissociation constant of the overall process (KR). If K R = K A, then it is l i k e l y that there is a d i r e c t c o u p l i n g of r e c e p t o r and response. But K R m u s t be less than K A w h e n there is an intracellular mediator. It is the p u r p o s e of the p r e s e n t p a p e r to e x t e n d the m o d e l of Strickland and Loeb to include antagonists to the ligand receptor or to the i n t r a c e l l u l a r m e d i a t o r of ligand action. We consider two cases: (i) a n t a g o n i s m of the l i g a n d - r e c e p t o r i n t e r a c t i o n and (ii) antagonism of t h e m e d i a t o r - r e c e p t o r interaction. The r e s u l t s p r e s e n t e d here i n d i c a t e that the shape and d i s p l a c e m e n t p a t t e r n s of a g o n i s t d o s e - r e s p o n s e curves (DRC) o b t a i n e d in the p r e s e n c e of antagonist can yield information about the site of antagonism. THEORY In m o s t t h e o r i e s of d r u g action, it is a s s u m e d that the ligand (A) i n t e r a c t s w i t h its r e c e p t o r (R) in a second order, r e v e r s i b l e reaction. The ligand-receptor complex r e a c h e s an e q u i l i b r i u m concentration, [AR]e, given by the expression [AR]e = [A]Rt/([A ] + KA),
[i]
w h e r e [A] is free ligand c o n c e n t r a t i o n , R t is the total n u m b e r of s u r f a c e receptors, and K A is the d i s s o c i a t i o n c o n s t a n t of this reaction (with units of concentration). In s y s t e m s m e d i a t e d by s e c o n d - m e s s e n g e r p a t h w a y s , the ligandreceptor complex stimulates second-messenger formation intracellulary (e.g., IP 3 in the case of the p o l y p h o s p h o i n o s i t i d e s ) . If the second m e s s e n g e r (I) also b i n d s w i t h its i n t r a c e l l u l a r r e c e p t o r (N) in a
*As an aside, this is an interesting possible physical interpretation of the concept introduced by Stephenson (5) of a biological stimulus directly proportional to the number of drug-receptor complexes.
Vol. 38, No. 3, 1986
Analysis of Second-messenger Antagonism
253
s e c o n d order, r e v e r s i b l e reaction, a c c o r d i n g to I + N # IN, t h e n the equilibrium concentration of IN complex is given by, [IN] e = [I] Nt/([I]
[II]
+ K),
where [I] is free intermediate concentration, N t is the total number of intracellular receptors, and K is the dissociation constant of this reaction. W i t h the a s s u m p t i o n that [I] = aJAR], the r e l a t i o n b e t w e e n the e x t r a c e l l u l a r l i g a n d c o n c e n t r a t i o n and s e c o n d - m e s s e n g e r b i n d i n g is given by [IN]e = aNtRt[A]/I(K
+ aRt)[A]
which was derived by Strickland
+ KKA} ,
and Loeb
[III]
(4).
W e n o w e x a m i n e the i m p a c t of c o m p o u n d s that c o m b i n e w i t h receptors, but that lack the intrinsic ability to activate them. Such antagonists interfere with the binding of the active ligand and, thus, r e d u c e the m a g n i t u d e of the e f f e c t of the ligand. For e f f e c t s mediated by second messengers, two sites of antagonism are possible: o n e at t h e c e l l s u r f a c e ligand receptor, the other at t h e intracellular second-messenger receptor. RESULTS Case i.
Reversible
Antagonism
of the Li@and's
Cell-Surface
Receptors
In the p r e s e n c e of an a n t a g o n i s t that c o m p e t e s w i t h the l i g a n d for c e l l - s u r f a c e r e c e p t o r s , the ligand, A, and the a n t a g o n i s t , B, react reversibly with a c o m m o n receptor according to A+R = AR and B+R = BR. The c o n c e n t r a t i o n of l i g a n d - r e c e p t o r c o m p l e x e s is g i v e n by modification of equation [I] to [AR] e = [A]Rt/{[A]
+ KA(I + [B]/KB)},
[IV]
w h e r e [B] is the c o n c e n t r a t i o n of free a n t a g o n i s t and K B is the d i s s o c i a t i o n c o n s t a n t of the a n t a g o n i s t - r e c e p t o r i n t e r a c t i o n (6). When this expression is substituted for equation [I], the relationship between free ligand concentration and intracellular receptor occupation, equation [III], becomes, [IN]e = aNtRt[A]/{(K
+ aRt)[A]
+ KKA(I + [B]/KB) }.
[v]
Thus, the presence of an antagonist at the cell surface receptor reduces [IN] e in a dose-dependent manner according to the (i + [B]/K B) term in the denominator of equation [V]. If we now use the Null Method and equate equiactive IN complexes in the p r e s e n c e (equation [V]) and the a b s e n c e (equation [III]) of antagonist, [A]' = 1 + [B]
[VI]
where [A]' represents the concentration of agonist (greater than [A]) that is r e q u i r e d to p r o d u c e the s a m e [IN] e in the p r e s e n c e of antagonist as [A] in the absence of antagonist. Equation [VI] is the
254
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
c o n v e n t i o n a l d o s e - r a t i o e q u a t i o n (7-9). Hence, the p r e s e n c e of a reversible antagonist at the surface receptor site has the effect of p r o d u c i n g a p a r a l l e l s h i f t to the r i g h t of the a g o n i s t ' s DRC w h e t h e r or not second messengers are involved. Case 2.
Reversible Antagonism of the Second-Messenger's
Receptors
In the p r e s e n c e of an a n t a g o n i s t t h a t c o m p e t e s w i t h the s e c o n d m e s s e n g e r for intracellular receptors, equation [II] is modified, in analogy to the case of cell surface receptors, to [I]N t
a[AR] e N t
[IN] e =
:
[VII]
[I] + K(I + [C]/K C)
a[AR] e + K(I + [C]/K C)
w h e r e [C] is the c o n c e n t r a t i o n of free a n t a g o n i s t and K C is the dissociation constant for the interaction b e t w e e n the antagonist and the r e c e p t o r for the s e c o n d m e s s e n g e r (e.g., IP3). S u b s t i t u t i o n for [AR] e y i e l d s the r e l a t i o n b e t w e e n second-messenger b i n d i n g and extracellular ligand concentration: [IN] e = aNRt[A]/{K[A](I+[C]/K C) + aRt[A] The N u l l M e t h o d , relating [A] and
in t h i s case, [A]',
[A]' = 1 + [C] {([A]'/KA) KC
results
+ KKA(I+[C]/Kc) ~.
in the f o l l o w i n g
[VIII]
expression
+ i}. [IX]
Hence, the p r e s e n c e of a c o m p o u n d t h a t r e v e r s i b l y b l o c k s the intracellular second m e s s e n g e r at its receptor produces a rightward, b u t n o t p a r a l l e l s h i f t of an a g o n i s t ' s DRC. Instead, the d o s e - r a t i o increases at h i g h e r v a l u e s of [A]' a n d t h e E m a x is d e p r e s s e d (masquerading as i r r e v e r s i b l e antagonism). S u c h a s h i f t is c h a r a c t e r i s t i c for r e s p o n s e s t h a t are m e d i a t e d by s e c o n d - m e s s e n g e r p a t h w a y s , b u t is not u n i q u e to t h e m (at l e a s t as t h e y w e r e n a r r o w l y d e f i n e d for the p r e s e n t d e r i v a t i o n ) . Indeed, our r e s u l t s for this case are formally identical to the indirect antagonism model of Black, Jenkinson, and Kenakin (i0) in which an antagonist blocks the action of an i n d i r e c t a g o n i s t , i.e., one (like t y r a m i n e ) t h a t c a u s e s the r e l e a s e of a n o t h e r a g o n i s t that, in turn, d i r e c t l y p r o d u c e s the o b s e r v e d effect. In t h e i r e l e g a n t p r e s e n t a t i o n , t h e s e a u t h o r s a l s o consider several variants of t h e i r m o d e l , i n c l u d i n g one t h a t incorporates a non-linear relationship b e t w e e n ligand-receptor complex and response. Case 3.
Irreversible A n t a g o n i s m at the Cell-Surface Receptor
I r r e v e r s i b l e o c c l u s i o n of a p o r t i o n of the t o t a l c e l l - s u r f a c e receptor population leaves a fraction of the total, qRt, available for interaction with ligand. In the presence of such antagonism, equation (III) is modified to [IN]e = qaNtRt[A]'/{(K w h e r e all this c a s e I/[A]
+ aRt)[A]' + KKA I '
terms have been defined l e a d s to = i/q[A]'
+
previously.
(i/q - I)/KA,
[x] The N u l l M e t h o d
for
[XI]
Vol. 38, No. 3, 1986
Analysis of Second-messenger Antagonism
which is no different from that observed messenger pathway, namely, a rightward agonist dose-response curve (ii). Case 4.
255
in the absence of a secondand d o w n w a r d s h i f t of the
Irreversible Antagonism of Second-Messenger Receptors
Occlusion of all but q'N t receptors of the second messenger to the expression
leads
[IN] e = q'aNtRt/ { (K + aRt)[A]' + KKAI
[xi1]
I/[A]
[XIII]
and = i/q'[A]' + (i/q - I)(K + aRt)/KK A.
Hence, irreversible antagonism of second-messenger receptors produces a r i g h t w a r d and d o w n w a r d shift of the a g o n i s t ' s d o s e - r e s p o n s e c u r v e i n d i s t i n g u i s h a b l e f r o m C a s e 3. H o w e v e r , e s t i m a t i o n of the a g o n i s t d i s s o c i a t i o n c o n s t a n t (KA) f r o m (slope-l)/y-intercept would actually be in error by the factor q(l-q')/q'(l-q)(l+aRt/K). These results are summarized
in tabular form in table I.
TABLE 1 E f f e c t of Site and T y p e of A n t a g o n i s m Curve
on an A g o n i s t ' s D o s e - R e s p o n s e
Without a Second Messenger
With a Second Messenger
Shift
Shift
Site of Antagonism
Type of Antagonism
Cell Surface Receptor
Reversible
parallel to right
no change
parallel to right
Irreversible
rightward
decrease
rightward decrease
Reversible
N.A.
rightward decrease*
Irreversible
N.A.
rightward decrease
2nd Messenger Receptor
*If K A <
Emax
from
parallelism
Emax no change
may
not
be
DISCUSSION Several models have been proposed to explain the initial event of d r u g - i n d u c e d e f f e c t s , i.e., the i n t e r a c t i o n of ligand with receptor, but less is k n o w n a b o u t the s e q u e n c e of r e a c t i o n s t h a t f o l l o w the f o r m a t i o n of the d r u g - r e c e p t o r c o m p l e x . These reactions have been t e r m e d the "black box" in p h a r m a c o l o g y in a r e c e n t c o m p r e h e n s i v e
256
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
t h e o r e t i c a l t r e a t m e n t by G e r o (12) of the t r a n s d u c t i o n of drugreceptor association into pharmacologic effect. The relation between agonist concentration, receptor occupancy, and biological response in s y s t e m s d e p e n d e n t u p o n s e c o n d m e s s e n g e r s as r e c e n t l y p r e s e n t e d by S t r i c k l a n d and Loeb (4) lead to an i n t e r e s t i n g e x p l a n a t i o n for nonlinearity between receptor occupancy and biological response that is often observed experimentally (13-15). The treatment presented here extends this model to encompass the p o s s i b i l i t y of s e l e c t i v e a n t a g o n i s m at either the c e l l - s u r f a c e receptor or the intracellular receptor for the second messenger. In the case of a r e v e r s i b l e a n t a g o n i s t at the cell s u r f a c e receptor, there is no d i f f e r e n c e f r o m c o n v e n t i o n a l theory: the d o s e - r a t i o e q u a t i o n holds, and the a n t a g o n i s t p r o d u c e s a p a r a l l e l shift to the right of the agonist's dose-response curve. Thus, the use of such an agent would not be expected to shed light on whether an intracellular m e d i a t o r of r e c e p t o r r e s p o n s e w a s involved. Likewise, irreversible a n t a g o n i s m of e i t h e r c e l l - s u r f a c e or second m e s s e n g e r r e c e p t o r s produces a righward and downward shift of an agonist's dose-response curve. However, in the case of a r e v e r s i b l e a n t a g o n i s t at the intracellular receptor of the second messenger, the conventional doseratio e q u a t i o n does not apply, and such an a g o n i s t w o u l d p r o d u c e a rightward, but n o n - p a r a l l e l and n o n - s u r m o u n t a b l e , shift in the agonist's d o s e - r e s p o n s e curve. Hence, the use of such an a n t a g o n i s t would be expected to uncover a second messenger pathway. Conversely, if the system is known to be mediated by such a pathway, then analysis of the shift p r o d u c e d by an a n t a g o n i s t w o u l d suggest its site of action. ACKNOWLEDGEMENT The authors wish to thank Elaine Collins for help in preparation of the manuscript. NOTE ADDED IN PROOF One of the reviewers of the manuscript has kindly brought to our attention a treatment of shifts in concentration-response curves with r e s p e c t to the link b e t w e e n a g o n i s t - r e c e p t o r c o m p l e x e s and c a l c i u m c h a n n e l s (16) and has p o i n t e d out the f o l l o w i n g special case of the present analysis. If K<
R.H. MICHELL, Biochim. et Biophys. A c t a 415 81-147 (1975). M.J. BERRIDGE, Biochem. J. 220 345-360 (1984). K. HIRASAWA and Y. NISHIZUKA, Ann. Rev. Pharmacol. Toxicol. 25 147 -170 (1985). S. S T R I C K L A N D and J.N. LOEB, Proc. Natl. Acad. Sci. USA 78 13661370 (1981). R.P. S T E P H E N S O N , Br. J. P h a r m a c o l . ii 379-393 (1956). R.J. TALLARIDA and L.S. JACOB, The Dose-Response Relation in P h a r m a c o l o g y , S p r i n g e r - V e r l a g , N e w Y o r k (1979).
Vol. 38, No. 3, 1986
7. 8. 9. 10. ii. 12. 13. 14. 15. 16.
Analysis of Second-messenger Antagonism
257
H.O. S C H I L D , Br. J. P h a r m a c o l . 2 1 8 9 - 2 0 6 (1947). E.J. A R I E N S and J.M. V A N R O S S U M ~ A r c h . int. P h a r m a c o d y n . 110 2 7 5 299 (1957). J.H. G A D D U M , P h a r m a c o l . Revs. 9 2 1 1 - 2 6 8 (1957). J.W. BLACK, D.H. J E N K I N S O N and T.P. K E N A K I N , Eur. J. P h a r m a c o l . 65, i-i0 (1980). R.F. F U R C H G O T T , Advs. Drug. Res. 3 2 1 - 5 5 (1966). A. GERO, J. Theo. Biol. 104 249-559 (1983). T.P. K E N A K I N , P h a r m a c o l . Revs. 36 1 6 5 - 2 2 2 (1984). R.B. RAFFA, R.J. T A L L A R I D A and A. GERO, Arch. int. P h a r m a c o d y n . 241 1 9 7 - 2 0 7 (1979). R.B. RAFFA, F. P O R R E C A , A. C O W A N and R.J. T A L L A R I D A , Eur. J. Pharmacol. 79 11-16 (1982). L. H U R W I T Z and J. W E I S S I N G E R , J. P h a r m a c o l . Exp. Ther. 214 5 8 1 588 (1980).
Pergamon Press
ANTAGONISM OF RECEPTOR-ACTIVATED BIOLOGICAL EFFECTS MEDIATED BY SECOND MESSENGER PATHWAYS Robert B. Raffa and C. Paul Bianchi D e p a r t m e n t of P h a r m a c o l o g y , J e f f e r s o n M e d i c a l C o l l e g e Thomas J e f f e r s o n U n i v e r s i t y , P h i l a d e l p h i a , P A 19107 (Received in final form October 30, 1985) SUMMARY It is g e n e r a l l y held that m a n y b i o l o g i c a l l y a c t i v e compounds produce their effects through a sequence of events that are initiated when the substances combine with s e l e c t i v e r e c e p t o r s located on the cell s u r f a c e m e m b r a n e . A c t i v a t i o n of these r e c e p t o r s p r o d u c e s a s t i m u l u s that is somehow transmitted intracellularly. The t r a n s d u c t i o n b e t w e e n the s t i m u l u s and the r e s p o n s e is n o w k n o w n to be mediated, in many systems, by an intracellular intermediary or second messenger. A m o d e l d e s c r i b i n g the r e l a t i o n of agonist concentration, receptor o c c u p a t i o n , and b i o l o g i c a l r e s p o n s e in such a s y s t e m is h e r e i n e x t e n d e d to i n c l u d e antagonist binding at two target sites (i) the cell-surface receptor and (ii) the receptor for the second messenger. It is demonstrated that the shift of an agonist's dose-response curve is characteristic of the site of antagonism and that analysis of this shift can reveal the existence of a second m e s s e n g e r p a t h w a y or, if this is known, the site of a c t i o n of the antagonist. In the past few years, evidence has accumulated suggesting that the biological effects of many drugs, hormones, and neurotransmitters are m e d i a t e d by s p e c i f i c i n t r a c e l l u l a r p a t h w a y s in w h i c h second m e s s e n g e r s play an i m p o r t a n t role. For example, several r e c e p t o r systems appear to utilize a common second messenger pathway involving polyphosphoinositides and Ca ++ (1-3). The phosphoinositides, although a quantitatively m i n o r g r o u p of m e m b r a n e lipids, can have a s i g n i f i c a n t e f f e c t on c e l l u l a r p r o c e s s e s for t w o reasons: (i) activation of the polyphosphoinositide system results in two products, inositol triphosphate and diacylglycerol, both of which act as second messengers and (ii) the signal is amplified through cascade reactions activated by each second messenger. A characteristic feature of the receptors for which the system operates is that they mediate multiple c e l l u l a r responses, i n c l u d i n g m o b i l i z a t i o n of Ca %+, a c t i v a t i o n of protein kinase C, the release of arachidonic acid, and the activation of guanylate cyclase (2). A simplified description of o n e p r o p o s e d model for the involvement of inositol triphosphate (IP 3) and diacylglycerol (DG) in C a + + - l i n k e d , r e c e p t o r - a c t i v a t e d b i o l o g i c a l responses is as follows. B i n d i n g of a s p e c i f i c ligand to its r e c e p t o r a c t i v a t e s an e n z y m e (a p h o s p h o d i e s t e r a s e ) that h y d r o l y z e s a polyphosphoinositide precursor ++ ++ (PIP 2) to IP 3 and DG. IP 3 raises intracellular Ca by releasing Ca 0024-3205/86 $3.00 + .00 Copyright (c) 1986 Pergamon Press Ltd.
252
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
ions from internal storage sites, presumably sarcoplasmic reticulum. C o n c u r r e n t l y , DG s t i m u l a t e s p r o t e i n p h o s p h o r y l a t i o n by a c t i v a t i n g protein kinase C. A model that describes the relation between ligand concentration, r e c e p t o r occupancy, and the m a g n i t u d e of b i o l o g i c a l r e s p o n s e in s y s t e m s d e p e n d e n t upon s e c o n d m e s s e n g e r s has been p r e s e n t e d by S t r i c k l a n d and Loeb (4). In this model, the ligand (A) i n t e r a c t s reversibly with its cell-surface receptor (R) in accord with the Law of Mass Action (A+R ~ AR). The formation of ligand-receptor complexes p r o d u c e s the b i o l o g i c a l e f f e c t by f o r m a t i o n of an i n t r a c e l l u l a r i n t e r m e d i a t e (I) that b i n d s to its o w n i n t r a c e l l u l a r r e c e p t o r (N) a c c o r d i n g to I+N ~ IN, w i t h an e q u i l i b r i u m d i s s o c i a t i o n c o n s t a n t designated K (=[I][N]/[IN]). S t r i c k l a n d and Loeb p o s t u l a t e that the c o n c e n t r a t i o n of i n t r a c e l l u l a r m e d i a t o r is p r o p o r t i o n a l to the c o n c e n t r a t i o n of the AR c o m p l e x (i.e., I = a[AR]*) and that the biological response is p r o p o r t i o n a l to t h e c o n c e n t r a t i o n of intermediate-receptor complex (i.e., R=b[IN]). One consequence of the model, as r e p o r t e d by S t r i c k l a n d and Loeb, is that the n a t u r e of the coupling between ligand and receptor can be inferred by comparison of the m a g n i t u d e s of the d i s s o c i a t i o n c o n s t a n t of the l i g a n d - r e c e p t o r interaction (KA) to the dissociation constant of the overall process (KR). If K R = K A, then it is l i k e l y that there is a d i r e c t c o u p l i n g of r e c e p t o r and response. But K R m u s t be less than K A w h e n there is an intracellular mediator. It is the p u r p o s e of the p r e s e n t p a p e r to e x t e n d the m o d e l of Strickland and Loeb to include antagonists to the ligand receptor or to the i n t r a c e l l u l a r m e d i a t o r of ligand action. We consider two cases: (i) a n t a g o n i s m of the l i g a n d - r e c e p t o r i n t e r a c t i o n and (ii) antagonism of t h e m e d i a t o r - r e c e p t o r interaction. The r e s u l t s p r e s e n t e d here i n d i c a t e that the shape and d i s p l a c e m e n t p a t t e r n s of a g o n i s t d o s e - r e s p o n s e curves (DRC) o b t a i n e d in the p r e s e n c e of antagonist can yield information about the site of antagonism. THEORY In m o s t t h e o r i e s of d r u g action, it is a s s u m e d that the ligand (A) i n t e r a c t s w i t h its r e c e p t o r (R) in a second order, r e v e r s i b l e reaction. The ligand-receptor complex r e a c h e s an e q u i l i b r i u m concentration, [AR]e, given by the expression [AR]e = [A]Rt/([A ] + KA),
[i]
w h e r e [A] is free ligand c o n c e n t r a t i o n , R t is the total n u m b e r of s u r f a c e receptors, and K A is the d i s s o c i a t i o n c o n s t a n t of this reaction (with units of concentration). In s y s t e m s m e d i a t e d by s e c o n d - m e s s e n g e r p a t h w a y s , the ligandreceptor complex stimulates second-messenger formation intracellulary (e.g., IP 3 in the case of the p o l y p h o s p h o i n o s i t i d e s ) . If the second m e s s e n g e r (I) also b i n d s w i t h its i n t r a c e l l u l a r r e c e p t o r (N) in a
*As an aside, this is an interesting possible physical interpretation of the concept introduced by Stephenson (5) of a biological stimulus directly proportional to the number of drug-receptor complexes.
Vol. 38, No. 3, 1986
Analysis of Second-messenger Antagonism
253
s e c o n d order, r e v e r s i b l e reaction, a c c o r d i n g to I + N # IN, t h e n the equilibrium concentration of IN complex is given by, [IN] e = [I] Nt/([I]
[II]
+ K),
where [I] is free intermediate concentration, N t is the total number of intracellular receptors, and K is the dissociation constant of this reaction. W i t h the a s s u m p t i o n that [I] = aJAR], the r e l a t i o n b e t w e e n the e x t r a c e l l u l a r l i g a n d c o n c e n t r a t i o n and s e c o n d - m e s s e n g e r b i n d i n g is given by [IN]e = aNtRt[A]/I(K
+ aRt)[A]
which was derived by Strickland
+ KKA} ,
and Loeb
[III]
(4).
W e n o w e x a m i n e the i m p a c t of c o m p o u n d s that c o m b i n e w i t h receptors, but that lack the intrinsic ability to activate them. Such antagonists interfere with the binding of the active ligand and, thus, r e d u c e the m a g n i t u d e of the e f f e c t of the ligand. For e f f e c t s mediated by second messengers, two sites of antagonism are possible: o n e at t h e c e l l s u r f a c e ligand receptor, the other at t h e intracellular second-messenger receptor. RESULTS Case i.
Reversible
Antagonism
of the Li@and's
Cell-Surface
Receptors
In the p r e s e n c e of an a n t a g o n i s t that c o m p e t e s w i t h the l i g a n d for c e l l - s u r f a c e r e c e p t o r s , the ligand, A, and the a n t a g o n i s t , B, react reversibly with a c o m m o n receptor according to A+R = AR and B+R = BR. The c o n c e n t r a t i o n of l i g a n d - r e c e p t o r c o m p l e x e s is g i v e n by modification of equation [I] to [AR] e = [A]Rt/{[A]
+ KA(I + [B]/KB)},
[IV]
w h e r e [B] is the c o n c e n t r a t i o n of free a n t a g o n i s t and K B is the d i s s o c i a t i o n c o n s t a n t of the a n t a g o n i s t - r e c e p t o r i n t e r a c t i o n (6). When this expression is substituted for equation [I], the relationship between free ligand concentration and intracellular receptor occupation, equation [III], becomes, [IN]e = aNtRt[A]/{(K
+ aRt)[A]
+ KKA(I + [B]/KB) }.
[v]
Thus, the presence of an antagonist at the cell surface receptor reduces [IN] e in a dose-dependent manner according to the (i + [B]/K B) term in the denominator of equation [V]. If we now use the Null Method and equate equiactive IN complexes in the p r e s e n c e (equation [V]) and the a b s e n c e (equation [III]) of antagonist, [A]' = 1 + [B]
[VI]
where [A]' represents the concentration of agonist (greater than [A]) that is r e q u i r e d to p r o d u c e the s a m e [IN] e in the p r e s e n c e of antagonist as [A] in the absence of antagonist. Equation [VI] is the
254
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
c o n v e n t i o n a l d o s e - r a t i o e q u a t i o n (7-9). Hence, the p r e s e n c e of a reversible antagonist at the surface receptor site has the effect of p r o d u c i n g a p a r a l l e l s h i f t to the r i g h t of the a g o n i s t ' s DRC w h e t h e r or not second messengers are involved. Case 2.
Reversible Antagonism of the Second-Messenger's
Receptors
In the p r e s e n c e of an a n t a g o n i s t t h a t c o m p e t e s w i t h the s e c o n d m e s s e n g e r for intracellular receptors, equation [II] is modified, in analogy to the case of cell surface receptors, to [I]N t
a[AR] e N t
[IN] e =
:
[VII]
[I] + K(I + [C]/K C)
a[AR] e + K(I + [C]/K C)
w h e r e [C] is the c o n c e n t r a t i o n of free a n t a g o n i s t and K C is the dissociation constant for the interaction b e t w e e n the antagonist and the r e c e p t o r for the s e c o n d m e s s e n g e r (e.g., IP3). S u b s t i t u t i o n for [AR] e y i e l d s the r e l a t i o n b e t w e e n second-messenger b i n d i n g and extracellular ligand concentration: [IN] e = aNRt[A]/{K[A](I+[C]/K C) + aRt[A] The N u l l M e t h o d , relating [A] and
in t h i s case, [A]',
[A]' = 1 + [C] {([A]'/KA) KC
results
+ KKA(I+[C]/Kc) ~.
in the f o l l o w i n g
[VIII]
expression
+ i}. [IX]
Hence, the p r e s e n c e of a c o m p o u n d t h a t r e v e r s i b l y b l o c k s the intracellular second m e s s e n g e r at its receptor produces a rightward, b u t n o t p a r a l l e l s h i f t of an a g o n i s t ' s DRC. Instead, the d o s e - r a t i o increases at h i g h e r v a l u e s of [A]' a n d t h e E m a x is d e p r e s s e d (masquerading as i r r e v e r s i b l e antagonism). S u c h a s h i f t is c h a r a c t e r i s t i c for r e s p o n s e s t h a t are m e d i a t e d by s e c o n d - m e s s e n g e r p a t h w a y s , b u t is not u n i q u e to t h e m (at l e a s t as t h e y w e r e n a r r o w l y d e f i n e d for the p r e s e n t d e r i v a t i o n ) . Indeed, our r e s u l t s for this case are formally identical to the indirect antagonism model of Black, Jenkinson, and Kenakin (i0) in which an antagonist blocks the action of an i n d i r e c t a g o n i s t , i.e., one (like t y r a m i n e ) t h a t c a u s e s the r e l e a s e of a n o t h e r a g o n i s t that, in turn, d i r e c t l y p r o d u c e s the o b s e r v e d effect. In t h e i r e l e g a n t p r e s e n t a t i o n , t h e s e a u t h o r s a l s o consider several variants of t h e i r m o d e l , i n c l u d i n g one t h a t incorporates a non-linear relationship b e t w e e n ligand-receptor complex and response. Case 3.
Irreversible A n t a g o n i s m at the Cell-Surface Receptor
I r r e v e r s i b l e o c c l u s i o n of a p o r t i o n of the t o t a l c e l l - s u r f a c e receptor population leaves a fraction of the total, qRt, available for interaction with ligand. In the presence of such antagonism, equation (III) is modified to [IN]e = qaNtRt[A]'/{(K w h e r e all this c a s e I/[A]
+ aRt)[A]' + KKA I '
terms have been defined l e a d s to = i/q[A]'
+
previously.
(i/q - I)/KA,
[x] The N u l l M e t h o d
for
[XI]
Vol. 38, No. 3, 1986
Analysis of Second-messenger Antagonism
which is no different from that observed messenger pathway, namely, a rightward agonist dose-response curve (ii). Case 4.
255
in the absence of a secondand d o w n w a r d s h i f t of the
Irreversible Antagonism of Second-Messenger Receptors
Occlusion of all but q'N t receptors of the second messenger to the expression
leads
[IN] e = q'aNtRt/ { (K + aRt)[A]' + KKAI
[xi1]
I/[A]
[XIII]
and = i/q'[A]' + (i/q - I)(K + aRt)/KK A.
Hence, irreversible antagonism of second-messenger receptors produces a r i g h t w a r d and d o w n w a r d shift of the a g o n i s t ' s d o s e - r e s p o n s e c u r v e i n d i s t i n g u i s h a b l e f r o m C a s e 3. H o w e v e r , e s t i m a t i o n of the a g o n i s t d i s s o c i a t i o n c o n s t a n t (KA) f r o m (slope-l)/y-intercept would actually be in error by the factor q(l-q')/q'(l-q)(l+aRt/K). These results are summarized
in tabular form in table I.
TABLE 1 E f f e c t of Site and T y p e of A n t a g o n i s m Curve
on an A g o n i s t ' s D o s e - R e s p o n s e
Without a Second Messenger
With a Second Messenger
Shift
Shift
Site of Antagonism
Type of Antagonism
Cell Surface Receptor
Reversible
parallel to right
no change
parallel to right
Irreversible
rightward
decrease
rightward decrease
Reversible
N.A.
rightward decrease*
Irreversible
N.A.
rightward decrease
2nd Messenger Receptor
*If K A <
Emax
from
parallelism
Emax no change
may
not
be
DISCUSSION Several models have been proposed to explain the initial event of d r u g - i n d u c e d e f f e c t s , i.e., the i n t e r a c t i o n of ligand with receptor, but less is k n o w n a b o u t the s e q u e n c e of r e a c t i o n s t h a t f o l l o w the f o r m a t i o n of the d r u g - r e c e p t o r c o m p l e x . These reactions have been t e r m e d the "black box" in p h a r m a c o l o g y in a r e c e n t c o m p r e h e n s i v e
256
Analysis of Second-messenger Antagonism
Vol. 38, No. 3, 1986
t h e o r e t i c a l t r e a t m e n t by G e r o (12) of the t r a n s d u c t i o n of drugreceptor association into pharmacologic effect. The relation between agonist concentration, receptor occupancy, and biological response in s y s t e m s d e p e n d e n t u p o n s e c o n d m e s s e n g e r s as r e c e n t l y p r e s e n t e d by S t r i c k l a n d and Loeb (4) lead to an i n t e r e s t i n g e x p l a n a t i o n for nonlinearity between receptor occupancy and biological response that is often observed experimentally (13-15). The treatment presented here extends this model to encompass the p o s s i b i l i t y of s e l e c t i v e a n t a g o n i s m at either the c e l l - s u r f a c e receptor or the intracellular receptor for the second messenger. In the case of a r e v e r s i b l e a n t a g o n i s t at the cell s u r f a c e receptor, there is no d i f f e r e n c e f r o m c o n v e n t i o n a l theory: the d o s e - r a t i o e q u a t i o n holds, and the a n t a g o n i s t p r o d u c e s a p a r a l l e l shift to the right of the agonist's dose-response curve. Thus, the use of such an agent would not be expected to shed light on whether an intracellular m e d i a t o r of r e c e p t o r r e s p o n s e w a s involved. Likewise, irreversible a n t a g o n i s m of e i t h e r c e l l - s u r f a c e or second m e s s e n g e r r e c e p t o r s produces a righward and downward shift of an agonist's dose-response curve. However, in the case of a r e v e r s i b l e a n t a g o n i s t at the intracellular receptor of the second messenger, the conventional doseratio e q u a t i o n does not apply, and such an a g o n i s t w o u l d p r o d u c e a rightward, but n o n - p a r a l l e l and n o n - s u r m o u n t a b l e , shift in the agonist's d o s e - r e s p o n s e curve. Hence, the use of such an a n t a g o n i s t would be expected to uncover a second messenger pathway. Conversely, if the system is known to be mediated by such a pathway, then analysis of the shift p r o d u c e d by an a n t a g o n i s t w o u l d suggest its site of action. ACKNOWLEDGEMENT The authors wish to thank Elaine Collins for help in preparation of the manuscript. NOTE ADDED IN PROOF One of the reviewers of the manuscript has kindly brought to our attention a treatment of shifts in concentration-response curves with r e s p e c t to the link b e t w e e n a g o n i s t - r e c e p t o r c o m p l e x e s and c a l c i u m c h a n n e l s (16) and has p o i n t e d out the f o l l o w i n g special case of the present analysis. If K<
R.H. MICHELL, Biochim. et Biophys. A c t a 415 81-147 (1975). M.J. BERRIDGE, Biochem. J. 220 345-360 (1984). K. HIRASAWA and Y. NISHIZUKA, Ann. Rev. Pharmacol. Toxicol. 25 147 -170 (1985). S. S T R I C K L A N D and J.N. LOEB, Proc. Natl. Acad. Sci. USA 78 13661370 (1981). R.P. S T E P H E N S O N , Br. J. P h a r m a c o l . ii 379-393 (1956). R.J. TALLARIDA and L.S. JACOB, The Dose-Response Relation in P h a r m a c o l o g y , S p r i n g e r - V e r l a g , N e w Y o r k (1979).
Vol. 38, No. 3, 1986
7. 8. 9. 10. ii. 12. 13. 14. 15. 16.
Analysis of Second-messenger Antagonism
257
H.O. S C H I L D , Br. J. P h a r m a c o l . 2 1 8 9 - 2 0 6 (1947). E.J. A R I E N S and J.M. V A N R O S S U M ~ A r c h . int. P h a r m a c o d y n . 110 2 7 5 299 (1957). J.H. G A D D U M , P h a r m a c o l . Revs. 9 2 1 1 - 2 6 8 (1957). J.W. BLACK, D.H. J E N K I N S O N and T.P. K E N A K I N , Eur. J. P h a r m a c o l . 65, i-i0 (1980). R.F. F U R C H G O T T , Advs. Drug. Res. 3 2 1 - 5 5 (1966). A. GERO, J. Theo. Biol. 104 249-559 (1983). T.P. K E N A K I N , P h a r m a c o l . Revs. 36 1 6 5 - 2 2 2 (1984). R.B. RAFFA, R.J. T A L L A R I D A and A. GERO, Arch. int. P h a r m a c o d y n . 241 1 9 7 - 2 0 7 (1979). R.B. RAFFA, F. P O R R E C A , A. C O W A N and R.J. T A L L A R I D A , Eur. J. Pharmacol. 79 11-16 (1982). L. H U R W I T Z and J. W E I S S I N G E R , J. P h a r m a c o l . Exp. Ther. 214 5 8 1 588 (1980).