Recommendation 6
At the present time, we are unable to recommend a single quantification
method due to the lack of consensus in the community, with new or
refined methods are still being proposed. Many methods are based on the
null principle of equieffective concentrations of agonist producing
equal responses first described by (Barlow, Scott & Stephenson, 1967).
Thus, simultaneous comparison of the concentration-response curves of
two agonists gives ratios of the efficacy and affinities of the two
agonists which form the basis of methods to quantify bias. The two
commonly used quantities, i.e. relative-relative
Log(Emax/EC50) (Ehlert, 2008) and
relative-relative Log(τ/KA), emanate from this work.
These quantities are theoretically justified within the framework of the
Black-Leff operational model (Black & Leff, 1983), a specific
implementation of the classical theory, which provides a fitting
equation for concentration response curves. The two models first compare
the tested ligand relative to the reference ligand in each pathway and
then compare across the two pathways. When the slope factors (Hill
coefficient) of ligand concentration-response-curves are 1 (Figure 2)
the Log(Emax/EC50) values are identical to
Log(τ/KA) values. However, when they are not, the
Log(Emax/EC50) values have the disadvantage that their
bias factors are less comparable, as they are influenced by different
receptor expression in the pathway experiments whereas the
Log(τ/KA) values take into account receptor density and
coupling within a system.
We may refer readers to (Kenakin, 2019) for a comprehensive review of
available implementations of bias quantification and Onaran & Costa,
2021 (Onaran & Costa, 2021) for a critical review of the detailed
principles, on which specific implementations are based.
Disclaimer: Quantification of bias using different methods,
even those based on the same theory, can in some cases lead to different
conclusions on the biased/unbiased nature of a ligand (and system)
(Onaran et al., 2017; Rajagopal et al., 2011) or to a different relative
bias rank order of a set of tested ligands. Hence, results will be more
definitive when bias is quantified using multiple models. Furthermore,
none of the available strategies can provide an absolute bias value of a
given ligand at a given receptor. Only bias values relative to a
reference ligand are accessible with current quantitation techniques.
Avoid: A large degree of caution is advisable for describing
ligands with only weak bias or absolute efficacy, as these compounds are
more likely to produce system-dependent biased effects (see section
Special recommendation for low efficacy agonists). Such agonists are
therefore more likely to be spuriously identified as biased, as both
methods outlined above rely on best-fit parameters. Weak partial
agonists will result in relatively poor fits (but still with excellent
R2) with Emax/EC50 or
τ/KA values that grossly underestimate the errors of the
derived bias factors. One can use a bias plot to confirm
non-quantitatively that bias exists between two compounds, but one
should never rely on bias factors alone.
Pathway-preference without a reference
ligand (e.g., pathway ΔLog(Emax/EC50) or
ΔLog(τ/KA))
Recommendation 7: Investigation of a ligand’s differential
activity across pathways (e.g. pathway
ΔLog(Emax/EC50) or
ΔLog(τ/KA) values), but not relative to a reference
ligand, is herein not considered a biased ligand/signaling study but
instead defined as ‘pathway-preference’. As no reference ligand is used,
the comparison must be made ideally using the same or otherwise
near-identical systems and assays.