Terminology summary
Reference agonist(s) for Emax: When no single reference ligand with full efficacy across all compared pathways is available, different reference ligands can be used to define Emax in each pathway. The reference ligand and all tested ligands should have their efficacy compared (e.g. % or value 0-1) to the reference agonist(s) for Emax.

Special recommendation for biased inverse agonism in compared pathways

Recommendation 14: When a ligand acts as an inverse agonist in two pathways compared for bias, a bias factor can in theory be calculated in the same way as for agonists. However, the reference ligand would need to be another inverse agonist, i.e., in this case it would be warranted to not use the endogenous ligand, as it typically is an agonist (agouti is a rare example of an endogenous inverse agonist).
Reason: Inverse agonists inhibiting the non-ligand-dependent constitutive activity of a receptor may, just as well as biased agonists do, act differentially on pathways by stabilizing distinct receptor conformations. This is only evident for receptors with constitutive activity in the absence of an agonist. The minimum condition needed to quantify bias would be concentration-response curves in two pathways and this condition can be met for an inverse agonist ligand. For receptors with a high constitutive activity, biased inverse agonism could be valuable to understand fundamental signaling and to exploit this therapeutically.
Further reading: Specific discussion of the actual methods to quantify bias for inverse agonists are beyond the scope of this paper, as they involve differences in agonist-mediated and constitutively mediated efficacy (Ehlert, Suga & Griffin, 2011). Specifically, it is known that constitutively active receptors themselves possess an efficacy that can be different from agonist-mediated efficacy; this is manifest in the phenomenon of protean agonism whereby a low efficacy partial agonist demonstrates positive agonism in quiescent systems and inverse agonism in constitutively active systems (Chidiac, Nouet & Bouvier, 1996; Kenakin, 1997). This is due to the fact that the agonist-mediated active state is of lower efficacy than the constitutively active state. Such phenomena must be considered to ascribe an efficacy to an inverse agonist.

Special recommendation for bias-inducing allosteric modulators

Recommendation 15: For bias-inducing allosteric modulators, it is essential to specify which combination of allosteric modulator and orthosteric ligand was used to determine bias of the latter (Slosky, Caron & Barak, 2021).
Reason: For bias-inducing allosteric modulators, which do not convey agonism on their own, the functional outcome can vary for different orthosteric ligands, in line with the probe dependency of bias. As no concentration-response curves can be measured for such an allosteric ligand on its own, bias cannot be attributed to it individually.

Comparing ligand bias across studies and systems using rank orders

Recommendation 16: We recommend using ligand rank orders of bias factors (rather than quantitative bias values) for comparisons of ligand bias across studies using different experimental systems. When comparing more than two pathways, the preferentially activated pathway must be identical and the second pathway should be the next-most efficacious, which could differ for two ranked ligands or studies.
Reason: Bias values obtained from different experimental systems are typically not comparable on a quantitative level. For example, a bias value above 2.0 in one system may be below 2.0 for the same pathways when studied in another system differing by e.g., cell line, measured molecules or process (Figure 3). Achieving a more consistent assessment of which ligand is the most biased towards a given pathway is important to identify functionally selective probes that can be used to dissect a distinct effect. This provides information about which pathways should be targeted or avoided in the design of drugs with higher efficacy and fewer side effects.
Disclaimer: The relative ligand bias rank orders may also differ across systems (Figure 3B). However, they are expected to differ less than detailed quantitative values.

Special recommendation for agonism versus antagonism in compared pathways (‘non-quantitative bias’)

Recommendation 17: When agonism and no agonism (neutral antagonism or inverse agonism), respectively, are observed in two pathways compared, it is not possibly to quantify bias using the above models. This is because calculation of a quantitated bias factor requires two concentration-response curves with the same modality (agonism or inverse agonism). However, the bias can be described as a non-quantitative term, “non-quantitative bias”.
Alternatively, it can be approximated by measuring an affinity to limit bias or describe it in a “bias is larger than” relationship (Kenakin, 2015; Stahl, Ehlert & Bohn, 2019; Stahl, Zhou, Ehlert & Bohn, 2015). Specifically, the affinity (determined from functional antagonism) is used to determine receptor occupancy and a very low level of efficacy is assumed to generate a simulated curve (i.e. maximal response of 5%) which is then used to calculate bias. This yields the lowest possible bias (it could be greater than this if the efficacy is lower than the assumed one giving 5% maximal response).
Reason: In this case, there is no need to quantify bias to claim bias. Thus, a non-quantitative statement would be good enough to specify the case.
Disclaimer: Although a very low ligand efficacy cannot be detected in one system, it may be detected in another functional system with higher sensitivity. Hence, the statement should be understood as a practical qualification, in the sense that the efficacy of the ligand is close to zero within the detection limits of the given system. I.e., some partial agonists may appear to be neutral antagonists.