Arrestin Pathways as Drug Targets - Progress in Molecular Biology and Translational Science - page 460

2.2. Quantifying GPCR ligand ”

Ligand bias can range from relatively modest deviations in rank order of
potency 22,23 to frank reversal of efficacy, wherein the classification of a
ligand as agonist, antagonist, or inverse agonist becomes assay depen-
dent. 20,24 In such cases, a more complete characterization of ligand efficacy
is required. The most generalizable method for quantifying ligand bias uses
the Black/Leff operational model, 12 which relates the equilibrium dissoci-
ation constant ( K A ) of the ligand, a direct measure of receptor occupancy,
to a coupling efficiency factor (

“ bias

), which encompasses both the intrinsic effi-
cacy of the agonist and system-dependent factors such as receptor density
and coupling efficiency. 10,25 Since the latter factors are constant for any
given signaling pathway assayed in the same cell background, the ratio of
t

t

values for any two agonists yields a measure of intrinsic efficacy that is inde-
pendent of receptor number or coupling efficiency. Once determined for
each agonist and pathway of interest, t / K A ratios can be used to quantify
bias relative to a reference agonist. The advantages of the operational model
are its ability to quantify the full range of agonism, from submaximal effects
to effects in very sensitive systems with receptor reserve, and that once t / K A
ratios have been determined in one system they are applicable to all systems
without the need to individually quantify functional selectivity in each.
Variation in receptor density and coupling efficiency between systems might
change the ability of all agonists targeting a given receptor to activate a
particular pathway, but it will not change the pathway-selective “bias” of
different ligands relative to one another. 9,10
A simpler, but more limited, approach to visualizing ligand bias is to
determine the intrinsic Relative Activity (RA i ) of a series of ligands using
multiple readouts of receptor activation. RA i is a measure of the microscopic
affinity constant of an agonist for the active state of the receptor expressed
relative to that of a reference agonist, and can be estimated from empirically
determined EC 50 and E max values using the formula shown in
Fig. 18.1 B. 10,25 This method yields results similar to the operational model,
provided that the Hill slope of the ligand concentration-response curves is
close to 1.0, that is, that the observed EC 50 is proportional to the degree of
receptor occupancy needed to elicit the response. As an illustration,
Fig. 18.1 B depicts a multiaxial plot of experimentally determined RA i esti-
mates using a panel of six different peptide ligands for the human type 1 para-
thyroid hormone receptor (hPTH 1 R) in three different assays of receptor
activation; cAMP production, intracellular calcium release, and ERK1/2