Practical guide for calculating and representing biased signaling by GPCR ligands: A stepwise approach

In vitro pharmacological characterization of a novel unbiased NOP receptor‐selective nonpeptide agonist AT‐403

“…The concentration response curves of each compound were fitted to the Black–‐Leff operational model described by (Nagi and Pineyro ):where [A] is the agonist concentration, the maximal response of the system is given by E m , n is a fitting parameter for the slope, the affinity of the agonist is represented by the equilibrium dissociation constant of the agonist‐receptor complex ( K A ), and the efficacy of the agonist is defined by τ . τ and K A are descriptive parameters of intrinsic efficacy and binding affinity and may be directly obtained by fitting experimental data to the operational equation and can be expressed as “transduction coefficients” log( τ / K A ).…”

“…The concentration response curves of each compound were fitted to the Black--Leff operational model described by (Nagi and Pineyro 2016):…”

In vitro functional characterization of novel nociceptin/orphanin FQ receptor agonists in recombinant and native preparations

“…Bias factors were calculated by choosing the standard NOP agonist N/OFQ, as standard unbiased ligand. The concentration response curves of each compound were fitted to the Black-Leff operational model described in Nagi and Pineyro (2016): $$\text{italicresponse}=\frac{false[A^{n}false]{\mathrm{\tau }}^n{E}_m}{{false[Afalse]}^n{\mathrm{\tau }}^n+{false(false[Afalse]+K_{A}false)}^n}$$ where [A] is the agonist concentration, the maximal response of the system is given by E m , n is a fitting parameter for the slope, the affinity of the agonist is represented by the equilibrium dissociation constant of the agonist-receptor complex (K A ), and the efficacy of the agonist is defined by τ. τ and K A are descriptive parameters of intrinsic efficacy and binding affinity and may be directly obtained by fitting experimental data to the operational equation and can be expressed as “transduction coefficients” log(τ/K A ). The relative efficiency of agonists producing activation of any pathways can thus be quantified with a “normalized” transduction coefficient, namely Δlog(τ/K A ).…”

Molecular Pharmacology ofδ-Opioid Receptors

“…The operational model developed by Black and Leff (1983) has been proposed as an analytical tool to estimate such a parameter in the form of the transduction coefficient (log)t/K A , where t is the ligand's efficacy and K A is its "functional affinity," corresponding to the theoretical affinity the ligand would have for the active state(s) of the receptor responsible for the response (Black and Leff, 1983;Rajagopal et al, 2011;Kenakin and Christopoulos, 2013;Onaran et al, 2014). A detailed account of the steps involved in obtaining these parameters from experimental data has been presented elsewhere, both from a general theoretical viewpoint (Kenakin et al, 2012;Kenakin, 2015) and within the context of DOPr signaling (Charfi et al, 2014Nagi and Pineyro, 2016). Here, we will mention two aspects in relation to the quality of information provided by quantitative approaches compared with identification of ligand bias through comparison of single maximal responses.…”