Forum Can Adding Constitutive Receptor Activity Redefine Biased Signaling Quantification? Bin Zhou, 1,2,3 David A. Hall, 4 and Jesús Giraldo 1,2,3, * Biased signaling, the differential activation of distinct signaling pathways, is currently at the center of pharmacology. Reliable charac- terization of biased ligands requires robust scales applicable to all ligand classes: agonists, neu- tral antagonists, and inverse ago- nists. To this end, constitutive receptor activity should be included in the models. Quantification of G Protein- Coupled Receptor (GPCR) Biased Signaling GPCRs are key players in cell signaling that are found inserted in the cell mem- brane and transmit the signals embodied in the structure of ligands from outside to inside the cell [1]. GPCRs signal not only through G proteins but also through other proteins (e.g., b-arrestin) [2]. Differential engagement of these multiple signaling pathways (biased agonism) may have therapeutic implications. For example, typical opioid analgesics (e.g., morphine) directed to the m-opioid receptor yield beneficial effects through the G protein but unwanted effects through b-arrestin [3]. Similarly, it was suggested that anti- psychotic drugs selectively activating b-arrestin via the dopamine D2 receptor might present benefits versus simple inverse agonists [4]. Likewise, b-adreno- ceptor blockers like carvedilol functioning as antagonists of G protein-mediated sig- naling and agonists of b-arrestin- mediated signaling can have clinical ben- efits [5]. Moreover, it has been reported that b-arrestin-biased agonists of the angiotensin type I receptor stimulate car- diac contractility while also antagonizing some harmful effects of the receptor, mediated through G proteins [5]. Robust scales to quantify biased ago- nism are a fundamental need in pharma- cology. These scales should have certain properties, as pointed out by Kenakin et al. [6]: ‘It is essential for such a scale not to be affected by differences in receptor density, as these are system factors that often vary between cell types’. To define a scale of biased ago- nism, a mathematical model is needed. The Black and Leff operational model of agonism (Box 1) considers two steps for the generation of a pharmacological effect [7]: the binding of agonist to the receptor and transduction of binding into effect. A single parameter in the model, t or operational efficacy, quantifies the ability to generate a pharmacological effect. t determines the maximum response to a particular agonist, thus differentiating full and partial agonists (Box 1, Equation V) and also affects the potency of the ligand (Box 1, Equa- tion VI). Because t is proportional to receptor density (Box 1, Equation III), Dlog(t) between two agonists in a particular pathway isindependent of receptor density and provides a scale with which to quantify differences between agonists. If we take one of these agonists as the reference ligand, DDlog(t) may serve as a scale for biased agonism between pathways [8]. However, the concentration–effect curve is also influenced by the equilibrium dis- sociation constant K A because, as a com- ponent of agonist potency (Box 1, Equation VI), it too determines the loca- tion of the curve along the concentration axis. Consequently, the ratio of t to K A , termed the transduction coefficient, log (t/K A ), has been proposed to quantify biased agonism [6]. For the reasons out- lined above, since Dlog(t/K A ) is indepen- dent of receptor density in a given pathway it is an appropriate scale to quantify the differences between the ago- nist of interest and the reference ligand. Finally, DDlog(t/K A ) measures biased agonism between two pathways for the particular agonist. The classical operational model of ago- nism [7] (Box 1) does not account for constitutive receptor activity (i.e., signal- ing by receptors in the absence of ligands) and thus inverse agonists – ligands that yield a response lower than the constitu- tive receptor activity – are excluded from the analysis of biased agonism. Since inverse agonists are part of the ligand space, their potential therapeutic effects should not be excluded from routine screening analyses of biased agonism. In a recent paper [9], we used a model, the Slack and Hall operational model [10], that includes constitutive receptor activity (Box 2) and allows the quantification of ligand bias independently of ‘system bias’. Both the free receptor and the ligand-bound receptor produce a stimu- lus (Box 2, Equation II). e is the intrinsic efficacy of the ligand; the value of e deter- mines whether ligands are agonists (e > 1), neutral antagonists (e = 1), or inverse agonists (e < 1). It was proposed [9] that log(e) and log(e/K A ) can work as scales for biased agonism. Importantly, because both e and K A are ligand–recep- tor molecular properties, these scales do not depend on receptor density and thus a reference compound is not required to eliminate system dependence. Receptor Bias We refer to the inherent bias of the recep- tor in the absence of ligands as ‘receptor bias’. As shown in Box 2, Equation V, the basal response depends on E m , n, and x. E m is the maximum response of the TIPS 1581 No. of Pages 4 Trends in Pharmacological Sciences, Month Year, Vol. xx, No. yy 1