TABLE 4

Methods to quantify biased signaling

No.MethodProcedureAdvantagesDisadvantagesReference
1Transducer coefficients [ΔLog(τ/KA)]Fit DR curves to operational model/calculate ratios of Log(τ/KA) within each pathway (Δlog(τ/KA); calculate Log bias as ΔΔLog(τ/KA) across pathwaysSensitive/system independentPossible difficulties in fitting Black/Leff operational model to DR curvesKenakin et al. (2012)
Quantifiable to yield a scale
High throughput
Statistically verifiable/bounded
Accommodates full agonists
Theoretically sound
2ΔLog (max/EC50)Calculate Log(max/EC50) of DR curves; calculate ΔLog(max/EC50) within each pathway; calculate ΔΔLog(max/EC50) across pathways for Log biasSensitive/system independent Cannot be used if n << 1 and/or intrinsic activity <30%Kenakin (2017)
Simple/quantifiable yielding a scale
High throughput
Statistically verifiable/bounded
Accommodates full agonists
No difficulties fitting curves to operational model
Theoretically sound
3Relative efficacy [ΔLog(τ)]Fit DR curves for both functional pathways with a single measurement of affinity (binding) to obtain efficacy (τ values); express bias as relative Log(τ) valuesSensitive/system independent Not theoretically sound (ignores possible Δaffinity)Rajagopal et al. (2011)
Quantifiable to yield scaleBinding affinity must be used for full agonists
High throughputPossible difficulties in fitting Black/Leff operational model to DR curves
Statistically verifiable/bounded
4RAEquiactive concentrations from DR curves for two agonists are compared with null methods in each pathway to yield RA values. Bias is then evaluated through Δlog(RA) valuesSensitive/system independent Not high throughput (need dual agonist simultaneous comparison) Ehlert (2008)
Quantifiable to yield a scaleWorks best with divergent curves (i.e., full vs. partial agonist)
Statistically variable/bounded
No difficulties fitting curves to operational model
Theoretically sound
5Method of Barlow, Scott, and StephensonDouble-reciprocal plot of equiactive concentrations of two agonists in a functional system are used to yield a ratio of efficacy and affinity in each pathway. These ratios are then compared across pathways to yield estimate of biasSensitive/system independent Not high throughput (need dual agonist simultaneous comparison) Barlow et al. (1967)
Quantifiable to yield scaleNeeds divergent curves (i.e., full vs. partial agonist)
Theoretically soundDouble-reciprocal plots often skewed and yield erroneous parameters
No difficulties fitting curves to operational model
6Trajectory and rank orderMaximal responses to a range of agonists plotted for each pathway to determine trajectory relationship defining system bias. Outliers (either from plot itself or rank order) identified as biasedModel independentNo quantifiable scale Onaran et al. (2017)
Sensitive/system independentRequires a range of agonist intrinsic activities to define trajectory
No difficulties fitting curves to operational modelIgnores affinity (may miss bias in some compounds)
Theoretically sound
  • DR, dose response.