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Understanding the Links Between Affinity and Efficacy

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Understanding the Links Between Affinity and Efficacy CORRESPONDENCE LINK TO ORIGINAL ARTICLE LINK TO AUTHOR’S REPLY Nature Reviews Drug Discovery | AOP, published online 17 May 2013; doi:10.1038/nrd3954-c1 of this ternary complex by an agonist is associated with a high-affinity binding state Quantifying biased agonism: of the ligand for the receptor–transducer complex that is related to pharmacological understanding the links efficacy6 (FIG. 1). I believe that a limitation of the approach between affinity and efficacy favoured by Kenakin and Christopoulos to measure biased agonism is that they use a pharmacological model (the operational Sudarshan Rajagopal model) but use an allosteric ‘conditional affinity’ (that is, an estimate of the affinity of In the March issue of Nature Reviews Drug complex to result in a downstream signalling a ligand for a GPCR when a G protein trans- Discovery, a Perspective article by Kenakin response) (FIG. 1a). The stimulus for initiating ducer is bound that attempts to account for and Christopoulos (Nature Rev. Drug Discov. signalling is related to ligand efficacy and formation of a ternary complex). Although 12, 205–216; 2013)1 reviewed a number of to the concentration of the agonist–receptor the use of a conditional affinity value com- important developments in our understand- complex, and this relationship differs pensates for the fact that pharmacological ing of biased agonism at G protein-coupled depending upon the pharmacological model models underestimate receptor occupancy, receptors (GPCRs; also known as seven chosen to describe the system. I believe that the use of a conditional affinity transmembrane receptors) over the past Allosteric models explicitly account for value will necessarily lead to a gross under- decade. In my opinion, the authors have erred signalling by the formation of an agonist– estimate of agonist efficacy (FIG. 1). in their presentation of which approaches are receptor–transducer ternary complex6–8 Kenakin and Christopoulos use the most useful for measuring biased signalling at (FIG. 1b). Unlike pharmacological models in operational model to determine so-called GPCRs. Such models can be broadly consid- which the agonist–receptor complex results transduction coefficients (τ/KA; the transducer ered as pharmacological or allosteric models. in a different stimulus depending on the ago- ratio divided by the conditional affinity). In pharmacological models2–5 a ligand is nist, the ternary complex results in an equal Although transduction coefficients can be considered to have two properties: affinity stimulus for signalling regardless of which useful in comparing the relative signalling of (the ability of a ligand to form an ligand is used; the efficacy of a ligand is ligands, as well as for determining the rank agonist–receptor complex) and efficacy defined by its ability to form this signalling- order of biased signalling for a set of biased (the ability of the agonist–receptor competent ternary complex. The formation agonists9, they are problematic when trying to measure the efficacy of agonists that pro- duce maximal effects in a given signalling a Pharmacological models b Allosteric models system (full agonists). Fitting concentration– response data for full agonists to transduc- Agonist and receptor Agonist and receptor tion coefficients is inherently ambiguous, and may require non-physiological con- Affinity Kd Low affinity Kd straints to be used, such as setting log KA values to zero so that a fit to the data can be Agonist–receptor Agonist–receptor achieved10. Under such conditions, the use of a conditional affinity value may become K1* K2* meaningless. Therefore, I believe that the use of transduction coefficients is an erroneous Transducer 1 High Transducer 2 approach to determine ligand bias. affinity Also, I do not agree with the statement ε , τ ε , τ 1 1 2 2 made by the authors that: “The transduction coefficient scale reduces the measurement Efficacy Agonist–receptor–transducer 1 Agonist–receptor–transducer 2 of agonism to a single number…”. Instead, I believe that the measurement of agonism is encapsulated by the term τ (transducer ratio) in the operational model described 5 Signalling Signalling Signalling Signalling by Black and Leff . Indeed, Kenakin and via via via via Christopoulos demonstrate that there pathway 1 pathway 2 pathway 1 pathway 2 are situations in which the transduction coefficient scale lacks utility as an absolute Figure 1 | Pharmacological and allosteric models for interpreting receptor signalling. a | In scale of agonism. pharmacological models, formation of an agonist–receptor complex (quantified by affinity) results in signalling, encapsulated by efficacy, such as that described by ε values or by τ values. b | In an Nature Reviews | Drug Discovery Other models to quantify ligand bias allosteric model, the initial binding of an agonist to the receptor in the absence of transducers occurs in a low-affinity binding state. A high-affinity binding state results from transducer binding and the I believe that other models for quantifying formation of a ternary complex. In an allosteric model, ligand efficacy can be calculated from ligand bias are superior to the approach the difference between the low-affinity dissociation constant (Kd) obtained under conditions that advocated by Kenakin and Christopoulos. prevent transducer coupling and the affinity associated with transducer (T) coupling, equal to I and my co-workers9 favour calculating Kd/(1+([T]/K*)) in this simplified model. bias factors using one of two approaches. NATURE REVIEWS | DRUG DISCOVERY www.nature.com/reviews/drugdisc © 2013 Macmillan Publishers Limited. All rights reserved CORRESPONDENCE The first approach, which Kenakin and between potencies of partial agonists deter- 1. Kenakin, T. & Christopoulos, A. Signalling bias in new drug discovery: detection, quantification and Christopolous also note has merit, is based mined in signalling and binding assays, thereby therapeutic impact. Nature Rev. Drug Discov. 12, on intrinsic relative activity values. Relative limiting the utility of this second approach. 205–216 (2013). 2. Ariens, E. J. Affinity and intrinsic activity in the affinity values are calculated from the maxi- In the systems to which I have applied this theory of competitive inhibition. I. Problems and mal effect produced by a ligand (E value) approach, such differences have been minor. theory. Arch. Int. Pharmacodyn. Ther. 99, 32–49 max (1954). and the concentration of ligand that pro- However, if larger differences were noted, 3. Stephenson, R. P. A modification of receptor duces half-maximal response (EC value) I would suggest that the operational model theory. Br. J. Pharmacol. Chemother. 11, 379–393 50 (1956). from concentration–response curves that should not be used, as partial agonists would 4. Furchgott, R. F. in Advances in Drug Research have slopes equal to unity. For agonists that not be predicted to cause a large shift in the (eds Harper, N. J. & Simmonds, A. B.) 21–55 (Academic Press, 1966). produce concentration–response curves that functional affinity associated with formation 5. Black, J. W. & Leff, P. Operational models of have slopes of 1, intrinsic relative activities of a ternary complex. In this situation, relative pharmacological agonism. Proc. R. Soc. Lond. 9 B Biol. Sci. 220, 141–162 (1983). are identical to transduction coefficients, activity values could be used . 6. De Lean, A., Stadel, J. M. & Lefkowitz, R. J. but the estimates of bias obtained using this A ternary complex model explains the agonist-specific Moving forward binding properties of the adenylate cyclase-coupled approach are not limited by the problematic β-adrenergic receptor. J. Biol. Chem. 255, 7108–7117 fitting routine required for transduction At present there is debate as to the optimal (1980). 7. Samama, P., Cotecchia, S., Costa, T. & Lefkowitz, R. J. coefficients. methods to use to quantify ligand bias. A mutation-induced activated state of the beta A second approach is based on τ values To move forward, we need to directly com- 2-adrenergic receptor. Extending the ternary complex model. J. Biol. Chem. 268, 4625–4636 (1993). that are obtained from fitting the operational pare the different methodologies to the 8. Weiss, J. M., Morgan, P. H., Lutz, M. W. & model using a ligand dissociation constant same simulated and real data to assess which Kenakin, T. P. The cubic ternary complex receptor-occupancy model. III. Resurrecting efficacy. that is determined under conditions that approach yields the best estimate of ligand J. Theor. Biol. 181, 381–397 (1996). prevent formation of a ternary complex. bias, as well as looking towards developing 9. Rajagopal, S. et al. Quantifying ligand bias at seven- transmembrane receptors. Mol. Pharmacol. 80, This allows affinity and efficacy to be sepa- model-free approaches for understanding 367–377 (2011). rated in a pharmacological model. While this and quantifying ligand bias. 10. Kenakin, T. et al. A simple method for quantifying functional selectivity and agonist bias. ACS Chem. approach does require a separate dissocia- Neurosci. 3, 193–203 (2012). tion constant to be determined from binding Sudarshan Rajagopal is at the Department of Medicine, Duke University Medical Center, Acknowledgements assays, it does yield an estimate of the efficacy Durham, North Carolina 27710, USA. The author thanks R. Lefkowitz, T. Costa and O. Onaran for invaluable discussions. of a ligand, σlig. Systematic differences in e‑mail: [email protected] experimental conditions between signalling doi:10.1038/nrd3954-c1 Competing interests statement and binding assays can cause discrepancies Published online 17 May 2013 The author declares no competing financial interests. NATURE REVIEWS | DRUG DISCOVERY www.nature.com/reviews/drugdisc © 2013 Macmillan Publishers Limited. All rights reserved.
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