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.