J. Phys. Chem. 1994,98, 1515-1 5 18
1515
Enthalpy-Entropy Compensation in Drug-Receptor Binding Paola Gilli, Valeria Ferretti, and Gastone Gilli' Dipartimento di Chimica, Universith di Ferrara, 441 00 Ferrara, Italy
Pier Andrea Borea Istituto di Farmacologia, Universith di Ferrara, 441 00 Ferrara, Italy Received: August 10, 1993; In Final Form: November 5, 1993"
The thermodynamic parameters (AGO, AHo, ASo)of the drug-receptor binding equilibrium derived from equilibrium constant measurements a t different temperatures and van't Hoff plots are reviewed. The analysis involves 186 independent experiments performed on 136 ligands binding to 10 biological receptors and, for comparison, to DNA and to two different enzymes. AHo and ASo values correlate according to the regression equation AHo (kcal mol-') = -9.5 278ASO (kcal K-l mol-') with a correlation coefficient of 0.981. The correlating equation is of the form AHo = BASo and is expected for a case of enthalpy-entropy compensation with a compensation temperature p = 278 K. The AH-AS correlation is carefully examined in terms of transmission of the experimental errors and of the representativeness of the experimental sample utilized. The correlation can be considered a true physical constraint for which, in spite of the relatively wide intervals of AHo and ASoallowed, the drug-receptor dissociation constant, KD, can never be smaller than some 10 pM. The physicochemical origin of the A H - h s compensation is probably related to a n intrinsic property of the hydrogen bond, which is the main force determining the association of the participants (drug, receptor binding site, water) in the drug-receptor binding equilibrium.
+
Introduction A drug can be defined as a xenobiotic substance which is able to modify the equilibrium conditions of living beings.' Many drugs interact with specific macromolecular targets which are called receptors and are located inside the cell (cytoplasmatic receptors) or on the cell surface (membrane receptors). Specific endogenous ligands (neurotransmitters, hormones, autacoids, modulators) bind to such receptors and, by modifying the receptor's conformation, trigger the chain of events leading to the final biological response. In such a way, a limited number of small molecules can control all inter- and intracellular communications by diffusing into the body fluids. It is such a complex network which can be artificially modified and corrected by the action of drugs. Two basic concepts of drug action theory2 are those of efficacy and affinity. In efficacy, drugs able to bind to the receptor and to mimic the effects of the endogenous ligand are called ngonists, while those which bind without producing any intrinsic effect are called antagonists (they just prevent the effect of agonists). The affinity is defined as the ability of a drug to selectively bind to a given receptor and is measured by the value of its drug-receptor association constant (affinity constant, KA). Rational development of new drugs (drug design) aims a t identifying new chemicals able to interact with the highest selectivity and affinity with the biologically relevant receptor, and it is not surprising that thousands of potential drugs have been investigated for their receptorial binding properties. The affinity of a drug, D, for a receptorial binding site, R, is most frequently measured by saturation radiochemical experiments carried out in uitro on whole cells or tissue homogenates. The following binding equilibrium is studied: KA
R
+ D*t R-D*
(1)
KD
= [R] [D*]/[R-D*] aretheassociation whereKAand KD= ~ / K A and dissociation constants and D* is the radiolabeled drug under
* To whom correspondence should be addressed. a
Abstract published in Aduance ACS Abslracts, December 15, 1993.
investigation. When the drug is not available in labeled form, a displacement or inhibition experiment is performed, and the following equilibria are studied
R + L* + R-L* R-L*
+ D F= R-D + L*
(2b)
where L* is a suitable radioligand of high affinity and selectivity and D is the drug under examination. When ICs0 is defined as the drug concentration able to displace the 50% of L* from the binding site, KD* = [R] [L*]/[R-L*] is the dissociation constant of R-L*, and KD = ~ / K A= [R][D]/[R-D] is the dissociation constant of R-D, it is easy to show3 that, under controlled experimental conditions, KD = ZCSo/(I + [L*]O/KD*) (3) where [L*]O is the concentration of labeled ligand initially added. While a large number of values of the standard free energy of the binding equilibrium are available as AGO = -RT In KA = R T In KD, relatively few measurements of its thermodynamic components (AGO = AHo - T U o ) are known in spite of their remarkable physical importance. In fact, the standard enthalpy AHo can be considered a quantitative indicator of the changes in intermolecular bond energies (hydrogen bonding and van der Waals interactions) occurring during the binding, while the standard entropy ASo is most likely a good indicator of the rearrangements undergone by thesolvent (water) molecules during the same process. This lack of data is mostly due to the extremely low concentrations of receptors present in biological tissues (typically 1-100 fM/mg of tissue for most neurotransmitter receptors4) which has so far made any microcalorimetric determination of AHo impossible. Nevertheless, methods based on KD measurements over a range of temperatures combined with van't Hoff plots have been successfully applied, as discussed in recent critical apprai~als.5-~ These applications are particularly successful for the case of essentially linear plots, that is, for systems whose ACpo is nearly zero. Fortunately, this is the case for all receptorial systems so far investigated. The only known exceptions are the binding of insulin to its membrane receptors* and the
0022-3654/94/2098-1515$04.50/0 0 1994 American Chemical Society
Gilli et al.
1516 The Journal of Physical Chemistry, Vol. 98, No. 5, 199 TABLE 1: Drug-Receptor Equilibria Whose Thermodynamic Parameters Are Known'
30
ligand
macromolecular system 1. D-2 dopamine R 2. antidepressant R 3. opiate R 4. AI-adenosine R 5. benzodiazepine R 6.8-adrenergic R 7. cholinergic muscarinic R 8. cholinergic nicotinic R 9. serotonine (S-HTI, 5-HT2) R 10. latelet activating ictor 11. DNA (binding of anthraquinones) 12. renin (inhibition) 13. dehydrofolatereductase (inhibition)
TOT
A
ANT
t o ("C)
ref
MR MR MR MR MR MR MR
20 4 7 26 10 37 7
4
16
5 136 7
2 13 3c 23d 7
21,25 25 20,25 25,37 0,20,37 10,25,37 20,30
10a 1Ob 1Oc 1Od 10e 10f log
MR
4
2
2 2 5
10h
MR
2
2
25
1Oi
MR
1
1
25
1Oj
DNA
3
25
10k
13 2
37 10
101 1Om
type
enzyme enzyme
146
All AH" values determined by the linear part of van't Hoff plots within the maximum temperature range 0 I t I 37 OC; R = receptor, MR = membrane receptor, A = agonists, ANT = antagonists, TOT = Q
total number of ligands investigated; t o is the temperature at which thermodynamical parameters are given. Including one partial agonist. Including one inverse agonist. d Including 10 partial agonists. binding of steroids to the cytoplasmatic glucocorticoid r e ~ e p t o r . ~ These two last cases have been excluded from the present analysis. In this paper, thermodynamic results collected on drug-receptor binding equilibria are reviewed and discussed from the point of view of their most striking feature: their remarkable enthalpyentropy compensation behavior. Experimental Data A summary of the systems so far investigated, including the number of ligands tested and the temperatures at which equilibrium thermodynamic parameters are given, is reported in Table 1 . Cases 1-10 are concerned with binding to typical membrane receptors, case 1 1 with binding of chemicals to DNA, and cases 12 and 13 with binding of inhibitors to enzymes. The last three cases have been included to show that the phenomena described are not confined to receptor binding but probably involve most ligand-macromolecule interactions as well. N o attempt, however, has been made to perform a complete literature search in this last area. The van't Hoff plots are essentially linear in the range of temperatures investigated (0 It I37 "C), indicating that AC," is not far from zero. Sometimes the linear region is shorter (0 It I30 "C),probably because of thermal denaturation of the receptors. A complete list of the papers in which AGO, AHo, and ASovalues were extracted is given in ref 10. The total number of compounds studied is 136, and the number of independent measurements is 186.
Discussion Figure 1 shows the scatter plot of AHo uersus ASo for all compounds investigated. The two parameters appear to be strongly correlated according to the regression equation: AHo (kcal mol-') = -9.5(*0.2)
+
278(f4)ASo (kcal K-I mol-') (4)
( n = 186,r = 0.981,s = 2.06,P 50.001) This equation is of the form AHo = @AS0and is expected for a case of enthalpy-entropy compensation11 with compensation temperature j3 of 278 K. The regression seems remarkable in
3
2
20
10
t d
0
s
- 0
x 4 -10 -20 -0.05
0.00
0.05
0.10
0.15
A S" (kcal/K/mol) Figure 1. Scatter plot of the standard enthalpies, AHo, uersus standard entropies, A!?",for the binding equilibria of 136 different ligands to 10 biological receptors, one DNA, and two enzymes. These data are summarized in Table 1. The two dashed lines indicate the loci of the points for which the ligand-macromolecule dissociation constants, KD, are 10 pM and 100 fiM; the continuous line is a linear regression and has a correlation coefficient of 0.98 1.
view of its high correlation coefficient and because of the large number of measurements (186). These measurements were carried out on as many as 136 different ligands binding to 13 macromolecular systems. The observed enthalpy-ntropy compensation seems to bestrongly indicativeof a common mechanism which is able to control the binding process, irrespective of the nature of ligands and of their macromolecular targets. Several authors, however, have remarked" that a strong correlation between AHo and ASois not, by itself, a proof of true AH-AS compensation arising from chemical causality but that instead it could be an artifact due to the transmission of experimental errors. In fact, ASo is essentially obtained by calculating it from the equation AGO = AHo - T U o . Thevalue of AGO is derived from the equilibrium constant, and that of AHo is determined by either van't Hoff plots or calorimetric measurements. As a consequence, any error on AHo,a m , will affect the error on ASo, Q M ~through , the equation as0 = ( I / p ' ) o w (wherep'is the mean experimental temperature). Theconfidence intervals of each point in the AH-AS plot will become lines of slope p', with length proportional to a w and whose superimposition could simulate the enthalpy-ntropy compensation phenomenon. Krug et al.llc* have proposed two conditions which, when fulfilled, are sufficient (but not necessary) to prove the prevalence of chemical causality over the error transmission effects: (i) the compensation temperature j3 must be significantly different from the average experimental temperature p'; (ii) AHo values should be linearly correlated with the corresponding AGO values. In the present case, the first condition is not fulfilled because j3 = 278 f 4 K (eq 4), and this value is too close to the average experimental temperature @' = 288 K. The second condition is not fulfilled because AGO and AHo for the complete set of data are totally uncorrelated. Therefore, the correlation of Figure 1 and eq 4 cannot be considered as strictly an enthalpy-entropy compensation. On the other hand, such AGO-AHo correlations would implylifthatthere is a common mechanism controlling the the binding of all ligands to all receptors, which frankly seems to be too strict of a condition to hold because of the extraordinary chemical variety of known ligands. A common mechanism, however, will be required if the binding process were totally determined by the properties of the solvent (as maintained, for instance, by Lumry and Rajenderl*). The idea that the observed AH-AS correlation is completely due to the transmission of experimental errors is not in agreement with the facts. We attempted to evaluate the errors on AHo
The Journal of Physical Chemistry, Vol. 98, No. 5, 1994 1517
Drug-Receptor Binding Equilibrium estimates for the binding of several drugs to the A1 and A2 adenosine receptors13 and found that the error is in the range 1-2 kcal mol-' and is therefore too small for determining the overall appearance of the scatter plot of Figure 1. Moreover, ligands of these two receptors are thermodynamically discriminated according to their efficacy, in the sense that the binding of agonists is entropy driven while that of antagonists is mostly enthalpy driven.14 Accordingly, agonist and antagonist data cluster into two different regions of the A H O - A S O space, but the points belonging to the two clusters are on the same correlation line of Figure 1. This phenomenon is also observed for the ligands of the @-adrenergicreceptor (where binding of agonists is enthalpy driven and that of antagonists is entropy driven'O9 and seems to be a clear indication of a specific chemical causality, because no typeof data error or mistreatment seems able to simulate a similar distribution of the experimental points. The nature of the AH-AS correlation can be better understood by writing eq 4 in the form
AHo - 278AS" = -9.5 kcal mol-' = AGO
(5) which immediately shows that the regression line is the locus of the points for which AGO = -9.5 kcal mol-' (or K ~ ( 2 9 8K) = 108 nM). Let us consider now that the highest-affinity drugs never display KDvalues smaller than 10 pM (AGO = -1 5.0 kcal mol-I), while those having KD 1 100 pM (AGO = -5.4 kcal mol-') are not considered of practical importance and are discarded. We can then draw the loci of the points defined by eq 5 and corresponding to these extreme values of KD (dashed lines encompassing the correlation line in Figure 1). These two lines are seen to delineate a narrow band where all experimental points are confined. The meanings of the upper and lower confinements are, however, quite different. The upper one is essentially an artifact arising from the biased composition of the sample, while the lower one reflects a true physicochemical constraint to which all molecular ligands binding to biological macromolecules in water solution apparently must conform. This constraint can be summarized by saying that, though binding enthalpies and entropies may be distributed over relatively wide intervals (approximately -22 IAHo I34 kcal mol-' and -35 IASo I 143 cal K-I mol-'), the resulting AGO = AH" - TASO can never be smaller than some -15 kcal mol-1 (or KD smaller than some 10 pM) because of an enthalpy-entropy compensation effect for which any decrease of binding enthalpy is compensated by a parallel decrease of binding entropy, and vice versa. The physical origin of such a constraint is not very well-known though it is sometimes imputed to some property of the solvent. We suggest a different explanation which seems particularly attractive in view of its extreme simplicity, being based only on the properties of the hydrogen bond as principal force controlling the intermolecular association in solution. The binding equilibrium of eq 1 is better describedL5as the transfer of drug molecules from their cage of water molecules inside the solvent to a second cage, the receptor binding site, which is probably already filled up with other water molecules. At the end of the transfer, the drug (D) will occupy the receptor binding site (RBS) cavity, while the water molecules (W), previously organized around the drug and the binding site, are released according to the reaction D-W,,
+ RBS-W,,
+ D-RBS
+ (nl + n2)W
(6)
We have already shown15 that AHo values are most likely determined by the energetic balance of the hydrogen bonds formed by the reaction partners before and after the binding event, a consideration strongly supported by the fact that all hydrogen bond donors and acceptors on D and RBS are already saturated by water molecules before the binding. On the other hand, the release of water molecules, which is generally considered the main factor affecting ASo values, is essentially a redistribution
of hydrogen bonds. This fact suggests the interesting possibility that both AHo and AS" are controlled by the hydrogen bond rearrangements occurring during the binding and that the two quantities can be interrelated according to the same extrathermodynamic rules which apply to hydrogen bond formation among simple molecules in solution. In a detailed study16 on the hydrogen bonds formed by phenol with amides, amines, ketones, ethers, and aldehydes in CC14 solutions, a definite enthalpy-entropy compensation effect was observed for all the chemical classes. On the average, the formation of a hydrogen bond having a AH of -5 kcal mol-' was found to produce a loss of entropy, AS, of -12 cal K-' mol-'. The present regression equation (eq 4) gives a AS of -1 8 cal K-I mol-' for the same AHchange, a difference which is not too large. This difference can be easily accounted for because the loss of degrees of freedom occurring in the immobilization of the drug within the receptor binding site is certainly greater than that produced by the association of two molecules in C C 4solutions. These findings seem to point to the idea that the enthalpy-entropy compensation found (Figure 1 and eqs 4 and 5) arises from an intrinsic property of the hydrogen bond, which is the main force determining the association of the participants (water, drug, binding site) in the drug-receptor binding equilibrium. This idea simply reflects the more basic fact that any tightening of the intermolecular bonds (the enthalpic factor) is compensated by a loss of degrees of freedom (the entropic factor), or vice versa. Acknowledgment. We thank the C.N.R., Progetto Finalizzato Chimica Fine I1 (Rome), for financial support. References and Notes (1) Goodman and Gilman's. The PharmacologicalBasisof Therapeutics, 8th ed.; Goodman Gilman, A., Rall, T. W., Nies, A. S., Taylor, P., Eds.; Pergamon Press: New York, 1990. (2) Pratt, W. B.; Taylor, P. Principles of Drug Action: The Basis of Pharmacology; Churchill Livingstone: New York, 1990. (3) Cheng, Y.; Prusoff, W. H. Biochem. Pharmacol. 1973, 22, 3099. (4) Bylund, D. B.; Yamamura, H. I. In Methods in Neurotransmitter Receptor Analysis; Yamamura, H. I., Enna, S.J., Kuhar, M. J., Eds.; Raven Press: New York, 1990; pp 1-36. (5) Testa, B.; Jenner, P.; Kilpatrick, G. J.; el Tayar, N.; van de Waterbeemd, H.; Marsden, C. D. Biochem. Pharmacol. 1987, 36, 4041. (6) Hitzemann, R. TIPS 1988, 9, 408. (7) Raffa, R. B.; Porreca, F. Lije Sci. 1989, 44, 245. (8) Waelbroeck, M.; Van Obberghen, E.; De Meyts, P. J. Biol. Chem. 1979, 254, 7736. (9) Wolff, M. E.; Baxter, J. D.; Kollman, P. A.; Lee, D. L.; Kuntz, I. D.; Bloom, E.; Matulich, D. T.; Morris, J. Biochemistry 1978,17,3201. Eliard, P. H.; Rousseau, G. G. Biochem. J. 1984, 218, 395. (10) (a) Zahniser, N. R.; Molinoff, P. B. Mol. Pharmacol. 1983,23,303.
Kilpatrick, G. J.; el Tayar, N.; van de Waterbeemd, H.; Jenner, P.; Testa, B.; Marsden, C. D. Mol. Pharmacol. 1986,30, 226. Duarte, E. P.; Oliveira, C. R.; Carvalho, A. P. Eur. J . Pharmacol. 1988, 147,227. (b) Reith, M. E. A.; Sershen, H.; Lajtha, A. Biochem. Pharmacol. 1984, 33, 4101. (c) Nicolas, P.; Hammonds, R. G., Jr.; Gomez, S.;Li, C. H. Arch. Biochem. Biophys. 1982,217,80. Hitzemann, R. J.; Murphy, M.; Curell, J. Eur. J. Pharmacol. 1985, 108, 171. Borea, P. A.; Bertelli, G. M.; Gilli, G. Eur. J . Pharmacol. 1988,146,247. (d) Murphy, K. M. M.;Snyder, S.H. Mol. Pharmacol. 1982, 22,250. Lohse, M. J.; Lenschow, V.; Schwabe, U. Mol. Pharmacol. 1984, 26, 1. Borea, P. A.; Varani, K.; Guerra, L.; Gilli, P.; Gilli, G. Mol. Neuropharmacol. 1992, 2, 273. (e) MBhler, H.; Richards, J. G. Nature (London) 1981,294,763. Kochman, R. L.; Hirsch, J. D. Mol. Pharmacol. 1982,22,335. (f) Weiland, G. A,; Minneman, K. P.;Molinoff, P. B. Nature (London) 1979, 281, 114. Weiland, G. A.; Minneman, K. P.; Molinoff, P. B. Mol. Pharmacol. 1980,18, 341. Bannister, R.; Boylston, A. W.; Davies, I. B.; Mathias, C. J.; Sever, P. S.; Sudera, D. J. Physiol. 1981, 319, 369. Contreras, M. L.; Wolfe, B. B.; Molinoff, P. B. J. Pharmacol. Exp. Ther. 1986,237,154. Contreras, M. L.; Wolfe, B. B.; Molinoff, P. B.J. Pharmacol. Exp. Ther. 1986, 237, 165. Bree, F.; el Tayar, N.; van de Waterbeemd, H.; Testa, B.; Tillement, J.-P. J. Recept. Res. 1986, 6, 381. Takayanagi, I.; Ogishima, M.; Koike, K. Gen. Pharmacol. 1990,21,303. (g) Barlow, R. B.; Birdsall,N. J. M.; Hulme, E. C. Br.J. PharmacoI. 1979,66,587. (h) Maelicke, A.; Fulpius, B. W.; Klett, R. P.; Reich, E. J . Biol. Chem. 1977, 252, 4811. (i) Todd, R. D.; Babinski, J. J. Neurochem. 1987,49, 1480. (j) Borea, P. A.; Montesi, L.; Muzzolini, A.; Fantozzi, R. Biochem. Pharmacol. 1991,41,629. (k) Bell, A,; Brown, J. R.; Neidle, S . Biochem. Phormacol. 1989, 38, 216. Accurate calorimetric measurements of DNA binding enthalpies are also known (Breslauer, K. J.; Remeta, D. P.; Chou, W. Y.; Ferrante, R.; Curry,
1518 The Journal of Physical Chemistry, Vol. 98, No. 5, 1994 J.; Zaunczkowski, D.;Snyder, J. G.; Marky, L. A. Proc. Natl. Acad. Sci. U.S.A. 1987,84,8922. Remeta, D. P.; Mudd, C. P.; Berger, R. L.; Breslauer, K. J. Biochemistry 1993, 32, 5064); these data were not used for eq 4 and Figure 1 becausenot derived fromvan't Hoff plots, but perfectly fit theobserved AH-AS correlation. (1) Epps, D. E.; Cheney, J.; Schostarez, H.; Sawyer, T. K.; Prairie, M.; Krueger, W. C.; Mandel, F. J . Med. Chem. 1990,33, 2080. (m) Gilli, R. M.; Sari, J. C.; Sica, L. M.; Briand, C. M. Biochim. Biophys. Acta 1988, 964, 53. (1 I ) (a) Leffler, J. E.; Grunwald, E. Rares and Equilibria of Organic Reactions; Wiley: New York, 1963. (b) Exner, 0. Prog. Phys. Org. Chem. 1973,10,414. (c) Krug, R. R.; Hunter, W. G.; Grieger, R. A. J. Phys. Chem. 1976, 80, 2335. (d) Krug, R. R.; Hunter, W. G.; Grieger, R. A. J . Phys. Chem. 1976,80,2341. (e) Krug, R. R.; Hunter, W. G.; Grieger, R. A. Nature
Gilli et al. (London) 1976,261,566. (f) Tomlinson, E. In?.J. Pharmaceutics 1983,13, 115. (g) Petersen, R. C. J. Org. Chem. 1964, 29, 3133. (12) Lumry, R.; Rajender, S. Eiopolymers 1970, 9, 1125. (13) Borea,P. A.; Dalpiaz, A.; Varani, K. Private communication. The typical experimental errors in KD are 3-796; estimated standard deviations in Lwo and ASo are 0.5-1.7 kcal mol-' and 2-5 cal K-1 mol-', respectively. (14) Borea, P. A.; Varani, K.; Guerra, L.; Gilli, P.; Gilli, G. Mol. Neuropharmacol. 1992, 2, 273. (1 5) Gilli, G.; Borea,P. A. In The AppltcationofChargeDensity Research to Chemistry and Drug Design; Jeffrey, G. A., Piniella, J. F.,Eds.; Plenum Press: New York, 1991. (16) Pimentel, G. C.; McClellan. A. L. Annu. Rev. Phys. Chem. 1971,22, 341.
ADDITIONS AND CORRECTIONS 1993,Volume 97 C. Chipot, J. G. Angyan, B. Maigret, and H. A. Scberaga': Modeling Amino Acid Side Chains. 3. Influence of Intra- and Intermolecular Environment on Point Charges Page 9799. In the first column, the 21st line from the bottom should read as follows: IqHv I0.209 ecu to be compared to qHV = 0.140 ecu in CHI). Vincent S. J. Craig, Barry W. Ninbam, and Richard M. Pashley': The Effect of Electrolytes on Bubble Coalescence in Water Page 10196. The correct version of Figure 10 is shown below.
-200
!
I
1
10
Separationlnm
100
