2.5. Calculation of bias factor

In order to determine ligand bias, we followed the operational model equation in Graphpad Prism 8 (RRID:SCR_002798, GraphPad Software, La Jolla, CA) to calculate Log R (τ/KA; Table S1), ΔLogR, and ΔΔLogR as previously described (van der Westhuizen, Breton, Christopoulos, & Bouvier, 2014). Subsequently, bias factors (10^ΔΔLogR) were calculated using DAMGO, leu‐enkephalin, and U50,488 as reference compounds for μOP, δOP, and κOP, respectively. All three reference compounds were more potent in the cAMP (G protein) assay than in the β‐arrestin 2 recruitment assay and thus were not unbiased but G protein‐biased to begin with. A bias factor >1 meant that the agonist was more G protein‐biased than the reference compound; a bias factor <1 meant that the agonist was less G protein‐biased than the reference compound. Bias factors for compounds with <30% efficacy for β‐arrestin 2 recruitment could not reliably be calculated and are listed as undeterminable (Table ​(Table1),1), which indicates that these agonists can be considered to be efficacy dominant for G protein signalling (Kenakin, 2015).

Pharmacological characterization of kratom alkaloids and synthetic G protein‐biased opioids at the μ, δ and κ opioid receptor

Note. cAMP inhibition potencies (pIC_50, drug concentration at 50% maximal efficacy) and efficacies (α, % inhibition at maximal efficacy normalized to DAMGO [μOP], leu‐enkephalin [δOP], or U50,488 [κOP]) for OP agonists to inhibit cAMP production are indicated ±SEM. β‐arrestin 2 recruitment potencies (pEC₅₀) and efficacies (α, normalized to DAMGO, leu‐enkephalin, or U50,488) of OP agonists to recruit β‐arrestin 2 are indicated ±SEM. The number of repetitions for each drug is indicated in parentheses. ND, not detectable. For Log R (τ/KA) values with confidence intervals, see Table S1.