- Email: [email protected]
Correlation between affinity and efficacy
Update
TRENDS in Pharmacological Sciences
Vol.24 No.1 January 2003
5
| Letters
Correlation between affinity and efficacy Piet van der Graaf Discovery Biology, IPC 619, Pfizer Global Research and Development, Sandwich CT13 9NJ, UK
In a recent TiPS article [1], Kenakin and Onaran presented a probabilistic model of protein conformation that describes efficacy and affinity as a function of agonist- and G-protein-induced perturbations of receptor states. In a simulation, the authors demonstrated that the model predicts a negative correlation between affinity and efficacy for different ligands acting in the same system, although homoscedacity in the model parameters allows for different agonists having identical efficacies with different affinities and identical affinities with different efficacies. The authors comment that the model contains too many parameters to use it to fit experimental data. Additionally, it seems very difficult to verify their simulated example experimentally because: (1) it would be practically impossible to test each compound in the same assay; and (2) a very large number of compounds would have to be synthesized and screened to reveal a correlation that is not overshadowed by the homoscedacity in the relationship as a result of between-assay variability. An alternative, perhaps more feasible, approach would be to use the inherent between-assay variability to test the predictions of the probabilistic model of receptor function with a single ligand. There are several examples in the literature indicating that it is indeed possible to reveal correlations between affinity and efficacy for a single agonist. For example, our analysis [2] with the operational model of agonism [3] of noradrenaline responses in rat small mesenteric arteries before and after phenoxybenzamine treatment revealed a highly significant, negative correlation between operational affinity (pKA) and efficacy
(log t), consistent with the predictions of the probability model. A similar conclusion can be inferred [2] from data reported for the effects of carbachol and pilocarpine in guinea-pig ileum [4], 5-HT in rabbit aorta [5], 5-methylfurmethide in guinea-pig trachea [6] and phenylephrine in rat tail artery [7]. Although it cannot be excluded that such observations are due to a statistical rather than a pharmacological phenomenon and reflect the issue of over-parameterization inherent to mechanistic models of agonism [2], it is tempting to suggest that they are examples of experimental evidence for the conformational selection hypothesis of agonist action. References 1 Kenakin, T. and Onaran, O. (2002) The ligand paradox between affinity and efficacy: can you be there and not make a difference? Trends Pharmacol. Sci. 23, 275– 280 2 Van der Graaf, P.H. and Stam, W.B. (1999) Analysis of inactivation experiments with the operational model of agonism yields correlated estimates of agonist affinity and efficacy. J. Pharmacol. Toxicol. Meth. 41, 117 – 125 3 Black, J.W. and Leff, P. (1983) Operational models of pharmacological agonism. Proc. R. Soc. Lond. B 220, 141 – 162 4 Henry, A. et al. (1992) Graphical assessment of the operational model of agonist action. FASEB J. 6, A1561 5 Leff, P. et al. (1990) Estimation of agonist affinity and efficacy by direct, operational model-fitting. J. Pharmacol. Meth. 23, 225 – 237 6 Leff, P. et al. (1985) Application of the operational model of agonism to establish conditions when functional antagonism may be used to estimate agonist dissociation constants. Br. J. Pharmacol. 85, 655 – 663 7 Tabernero, A. et al. (1996) Endothelial modulation of a1-adrenoceptor contractile responses in the tail artery of spontaneous hypertensive rats. Br. J. Pharmacol. 119, 765– 771 Corresponding author: Piet van der Graaf ([email protected]). PII: S0165-6147(02)00003-2
Correlation between affinity and efficacy Response from Kenakin and Onaran
Terry P. Kenakin1 and H. Ongun Onaran2 1
Systems Research, GlaxoSmithKline Research and Development, Research Triangle Park, NC 27709, USA Department of Pharmacology and Clinical Pharmacology and Antibody Research and Development Unit, Faculty of Medicine, Ankara University, Ankara, Turkey 2
Van der Graaf raises some excellent points of discussion around the issues of affinity and efficacy; there are two ideas worth exploring here. The first is that ‘pure’ macroscopic affinity estimates are essential in experimental Corresponding author: Terry P. Kenakin ([email protected]).
determinations of the relationship between affinity and efficacy. This is a practical problem in experimental approaches such as the method of Furchgott [1] to estimate agonist efficacy. In fact, the relationships in the literature described by van der Graaf are a little surprising in view of the affinity-enhancing effect of receptor isomerization as
http://tips.trends.com 0165-6147/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
6
Update
TRENDS in Pharmacological Sciences
a result of efficacy. As discussed by Colquhoun [2] and generalized by the probabilistic model [3], it would be predicted that observed affinity will be affected by the efficacy of the ligand. Hence, it would be expected that a relationship between affinity and efficacy might be observed. However, unveiling this hidden correlation between the two entities might not be possible in experiments where only the macroscopic constants can be measured. Theory has the luxury of dealing with possibly non-measurable micro-constants whereas experiment must deal with what nature provides as a looking glass into complex systems, and it is possible that true experimental verification of the theoretical prediction might not be feasible. The second idea is more fundamental and concerns the system independence of affinity and efficacy. Both affinity and efficacy are supposedly chemically based terms that are unique to the molecule and not subject to vagaries of different receptor system set-points. Variation in agonist potencies and intrinsic activities for a given agonist in preparations of the same tissues ostensibly involves variation in t (in terms of the operational model) with special regard to receptor density and the tissue component of KE as a result of differences in the efficiency of receptor coupling, and not true differences in molecular affinity and/or intrinsic efficacy. In this regard it might be more likely to conclude that the relationship between affinity and efficacy in a given tissue for a single agonist is due to intrinsic statistical problems of the estimation procedure as postulated by van der Graaf and Stam [4]. As long as the molecular efficacy of a ligand – receptor pair is seen as a result of a conformational difference between bound and free receptor, part of the macroscopic affinity of the binary complex should be determined by this conformational difference. This implies a correlation between the two entities in the sense that they are dependent. This (hidden) dependence might not appear as a correlation between the two measures. The independent parts of these
Vol.24 No.1 January 2003
measures are also subject to stochastic or systematic variations across ligands, which might theoretically mask the expected correlation when they are measured experimentally. This dependence is there to be observed when the resting macroscopic state of the protein molecule is modified. Such modifications in the resting state of the receptor are expected to change affinity and efficacy in a correlated way. The resting state of the receptor is affected by changes in the chemical environment or by any conceivable modification of the environmental factors that interact with the receptor molecule. The relationship shown also unveils the potential fallacy of choosing data from stochastic relationships to make law statements. In our case, we chose values of constant affinity or efficacy to show independence; another judicious choice of data could show a strict dependence. The point is that the energies and forces that control both affinity and efficacy are the same and thus it is a given that they must be related. The simulation shows what such a system can do in terms of showing either a correlation or not between these two properties: that is, there is no dichotomy in observing either. Thus, in this case, the law statement is that there is no law. References 1 Furchgott, R.F. (1966) The use of b-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants of receptor– agonist complexes. Advances in Drug Research (Vol. 3) (Harper, N.J. and Simmonds, A.B. eds), pp. 21 – 55, Academic Press 2 Colquhoun, D. (1985) Imprecision in presentation of binding studies. Trends Pharmacol. Sci. 6, 197 3 Onaran, H.O. and Costa, T. (2001) Intramolecular dynamics and ligandinduced conformational changes: a stochastic model of receptor action. In Biomedical Applications of Computer Modelling (Christopoulos, A., ed.), pp. 109 – 134, CRC press 4 Van der Graff, P.H. and Stam, W.B. (1999) Analysis of inactivation experiments with the operational model of agonism yields correlated estimates of agonist affinity and efficacy. J. Pharmacol. Toxicol. Meth. 41, 117 – 125 PII: S0165-6147(02)00002-0
Articles of interest in other journals Elevated levels of GluR1 in the midbrain: a trigger for sensitization to drugs of abuse? W.A. Carlezon, Jr and E.J. Nestler, Trends in Neurosciences 25, 610 – 615 Hyperacidification in cystic fibrosis: links with lung disease and new prospects for treatment J. Poschet et al., Trends in Molecular Medicine 8, 512 – 519 Drugs targeting functional bowel disorders: insights from animal studies G.J. Sanger and G.A. Hicks, Current Opinion in Pharmacology 2, 678– 683 Drug targeting to specific vascular sites E. Ruoslahti, Drug Discovery Today 7, 1138 – 1143 Therapy of autoimmune diseases: clinical trials and new biologics G.T. Nepom, Current Opinion in Immunology 14, 812 – 815 Botulinum and tetanus neurotoxins: structure, function and therapeutic utility K. Turton et al., Trends in Biochemical Sciences 27, 552– 558 Proteomics: drug target discovery on an industrial scale T.E. Ryan and S.D. Patterson, Trends in Biotechnology 20, S45 – S51 Somatostatin analogs in the diagnosis and treatment of cancer S.W.J. Lamberts et al., Trends in Endocrinology and Metabolism 13, 451– 457 Growth factor treatment of demyelinating disease: at last, a leap into the light R.M. Ransohoff et al., Trends in Immunology 23, 512 – 516 Private prescription: rat of the month R.C. Rowe, Drug Discovery Today 7, 1118– 1119 http://tips.trends.com
TRENDS in Pharmacological Sciences
Vol.24 No.1 January 2003
5
| Letters
Correlation between affinity and efficacy Piet van der Graaf Discovery Biology, IPC 619, Pfizer Global Research and Development, Sandwich CT13 9NJ, UK
In a recent TiPS article [1], Kenakin and Onaran presented a probabilistic model of protein conformation that describes efficacy and affinity as a function of agonist- and G-protein-induced perturbations of receptor states. In a simulation, the authors demonstrated that the model predicts a negative correlation between affinity and efficacy for different ligands acting in the same system, although homoscedacity in the model parameters allows for different agonists having identical efficacies with different affinities and identical affinities with different efficacies. The authors comment that the model contains too many parameters to use it to fit experimental data. Additionally, it seems very difficult to verify their simulated example experimentally because: (1) it would be practically impossible to test each compound in the same assay; and (2) a very large number of compounds would have to be synthesized and screened to reveal a correlation that is not overshadowed by the homoscedacity in the relationship as a result of between-assay variability. An alternative, perhaps more feasible, approach would be to use the inherent between-assay variability to test the predictions of the probabilistic model of receptor function with a single ligand. There are several examples in the literature indicating that it is indeed possible to reveal correlations between affinity and efficacy for a single agonist. For example, our analysis [2] with the operational model of agonism [3] of noradrenaline responses in rat small mesenteric arteries before and after phenoxybenzamine treatment revealed a highly significant, negative correlation between operational affinity (pKA) and efficacy
(log t), consistent with the predictions of the probability model. A similar conclusion can be inferred [2] from data reported for the effects of carbachol and pilocarpine in guinea-pig ileum [4], 5-HT in rabbit aorta [5], 5-methylfurmethide in guinea-pig trachea [6] and phenylephrine in rat tail artery [7]. Although it cannot be excluded that such observations are due to a statistical rather than a pharmacological phenomenon and reflect the issue of over-parameterization inherent to mechanistic models of agonism [2], it is tempting to suggest that they are examples of experimental evidence for the conformational selection hypothesis of agonist action. References 1 Kenakin, T. and Onaran, O. (2002) The ligand paradox between affinity and efficacy: can you be there and not make a difference? Trends Pharmacol. Sci. 23, 275– 280 2 Van der Graaf, P.H. and Stam, W.B. (1999) Analysis of inactivation experiments with the operational model of agonism yields correlated estimates of agonist affinity and efficacy. J. Pharmacol. Toxicol. Meth. 41, 117 – 125 3 Black, J.W. and Leff, P. (1983) Operational models of pharmacological agonism. Proc. R. Soc. Lond. B 220, 141 – 162 4 Henry, A. et al. (1992) Graphical assessment of the operational model of agonist action. FASEB J. 6, A1561 5 Leff, P. et al. (1990) Estimation of agonist affinity and efficacy by direct, operational model-fitting. J. Pharmacol. Meth. 23, 225 – 237 6 Leff, P. et al. (1985) Application of the operational model of agonism to establish conditions when functional antagonism may be used to estimate agonist dissociation constants. Br. J. Pharmacol. 85, 655 – 663 7 Tabernero, A. et al. (1996) Endothelial modulation of a1-adrenoceptor contractile responses in the tail artery of spontaneous hypertensive rats. Br. J. Pharmacol. 119, 765– 771 Corresponding author: Piet van der Graaf ([email protected]). PII: S0165-6147(02)00003-2
Correlation between affinity and efficacy Response from Kenakin and Onaran
Terry P. Kenakin1 and H. Ongun Onaran2 1
Systems Research, GlaxoSmithKline Research and Development, Research Triangle Park, NC 27709, USA Department of Pharmacology and Clinical Pharmacology and Antibody Research and Development Unit, Faculty of Medicine, Ankara University, Ankara, Turkey 2
Van der Graaf raises some excellent points of discussion around the issues of affinity and efficacy; there are two ideas worth exploring here. The first is that ‘pure’ macroscopic affinity estimates are essential in experimental Corresponding author: Terry P. Kenakin ([email protected]).
determinations of the relationship between affinity and efficacy. This is a practical problem in experimental approaches such as the method of Furchgott [1] to estimate agonist efficacy. In fact, the relationships in the literature described by van der Graaf are a little surprising in view of the affinity-enhancing effect of receptor isomerization as
http://tips.trends.com 0165-6147/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
6
Update
TRENDS in Pharmacological Sciences
a result of efficacy. As discussed by Colquhoun [2] and generalized by the probabilistic model [3], it would be predicted that observed affinity will be affected by the efficacy of the ligand. Hence, it would be expected that a relationship between affinity and efficacy might be observed. However, unveiling this hidden correlation between the two entities might not be possible in experiments where only the macroscopic constants can be measured. Theory has the luxury of dealing with possibly non-measurable micro-constants whereas experiment must deal with what nature provides as a looking glass into complex systems, and it is possible that true experimental verification of the theoretical prediction might not be feasible. The second idea is more fundamental and concerns the system independence of affinity and efficacy. Both affinity and efficacy are supposedly chemically based terms that are unique to the molecule and not subject to vagaries of different receptor system set-points. Variation in agonist potencies and intrinsic activities for a given agonist in preparations of the same tissues ostensibly involves variation in t (in terms of the operational model) with special regard to receptor density and the tissue component of KE as a result of differences in the efficiency of receptor coupling, and not true differences in molecular affinity and/or intrinsic efficacy. In this regard it might be more likely to conclude that the relationship between affinity and efficacy in a given tissue for a single agonist is due to intrinsic statistical problems of the estimation procedure as postulated by van der Graaf and Stam [4]. As long as the molecular efficacy of a ligand – receptor pair is seen as a result of a conformational difference between bound and free receptor, part of the macroscopic affinity of the binary complex should be determined by this conformational difference. This implies a correlation between the two entities in the sense that they are dependent. This (hidden) dependence might not appear as a correlation between the two measures. The independent parts of these
Vol.24 No.1 January 2003
measures are also subject to stochastic or systematic variations across ligands, which might theoretically mask the expected correlation when they are measured experimentally. This dependence is there to be observed when the resting macroscopic state of the protein molecule is modified. Such modifications in the resting state of the receptor are expected to change affinity and efficacy in a correlated way. The resting state of the receptor is affected by changes in the chemical environment or by any conceivable modification of the environmental factors that interact with the receptor molecule. The relationship shown also unveils the potential fallacy of choosing data from stochastic relationships to make law statements. In our case, we chose values of constant affinity or efficacy to show independence; another judicious choice of data could show a strict dependence. The point is that the energies and forces that control both affinity and efficacy are the same and thus it is a given that they must be related. The simulation shows what such a system can do in terms of showing either a correlation or not between these two properties: that is, there is no dichotomy in observing either. Thus, in this case, the law statement is that there is no law. References 1 Furchgott, R.F. (1966) The use of b-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants of receptor– agonist complexes. Advances in Drug Research (Vol. 3) (Harper, N.J. and Simmonds, A.B. eds), pp. 21 – 55, Academic Press 2 Colquhoun, D. (1985) Imprecision in presentation of binding studies. Trends Pharmacol. Sci. 6, 197 3 Onaran, H.O. and Costa, T. (2001) Intramolecular dynamics and ligandinduced conformational changes: a stochastic model of receptor action. In Biomedical Applications of Computer Modelling (Christopoulos, A., ed.), pp. 109 – 134, CRC press 4 Van der Graff, P.H. and Stam, W.B. (1999) Analysis of inactivation experiments with the operational model of agonism yields correlated estimates of agonist affinity and efficacy. J. Pharmacol. Toxicol. Meth. 41, 117 – 125 PII: S0165-6147(02)00002-0
Articles of interest in other journals Elevated levels of GluR1 in the midbrain: a trigger for sensitization to drugs of abuse? W.A. Carlezon, Jr and E.J. Nestler, Trends in Neurosciences 25, 610 – 615 Hyperacidification in cystic fibrosis: links with lung disease and new prospects for treatment J. Poschet et al., Trends in Molecular Medicine 8, 512 – 519 Drugs targeting functional bowel disorders: insights from animal studies G.J. Sanger and G.A. Hicks, Current Opinion in Pharmacology 2, 678– 683 Drug targeting to specific vascular sites E. Ruoslahti, Drug Discovery Today 7, 1138 – 1143 Therapy of autoimmune diseases: clinical trials and new biologics G.T. Nepom, Current Opinion in Immunology 14, 812 – 815 Botulinum and tetanus neurotoxins: structure, function and therapeutic utility K. Turton et al., Trends in Biochemical Sciences 27, 552– 558 Proteomics: drug target discovery on an industrial scale T.E. Ryan and S.D. Patterson, Trends in Biotechnology 20, S45 – S51 Somatostatin analogs in the diagnosis and treatment of cancer S.W.J. Lamberts et al., Trends in Endocrinology and Metabolism 13, 451– 457 Growth factor treatment of demyelinating disease: at last, a leap into the light R.M. Ransohoff et al., Trends in Immunology 23, 512 – 516 Private prescription: rat of the month R.C. Rowe, Drug Discovery Today 7, 1118– 1119 http://tips.trends.com