Data analysis was performed in GraphPad Prism 6 (GraphPad) to produce sigmoidal concentration-response curves by using the standard three-parameter equation. Agonist stimulation was determined and presented by normalizing all values to the top of the maximum response (Emax) produced by U69,593 or by normalizing to vehicle to show the fold over vehicle. The values of half maximal effective concentration (EC50) and Emax for all drugs were obtained from the average of n ≥ 3 from individual experiment and presented as means ± SEM. For receptor internalization assays in primary striatal neurons, the limited number of neurons from each preparation permitted a limited number of KOR agonist concentrations to be tested, along with vehicle, for each experiment. The EC50 and Emax values for KOR internalization in primary striatal neuron were estimated by fitting the averaged data points from each experiment.

For comparison of the results between each cell-based functional assay, each data set was fit to the operational model using GraphPad Prism 6. Specifically, the agonist that produced the greatest maximal response was fit to Eq. 1 (72, 73):Response = Bottom +Emax Bottom1+(1+10X10(X+LogRReference))n(1)The Emax is the maximal response of the system, Bottom is the baseline level of response, X is the agonist concentration, and n is the transducer slope. The parameter LogR is the transduction coefficient; LogR is a composite parameter that incorporates both the affinity and efficacy of the agonist into single parameter values (48). Except where indicated, U69,593 is used as the reference compound. Other partial agonists were fit to Eq. 2:Response = Bottom +EmaxBottom1+(1+10(XLogKA)10(X+LogRReference+LogRAiTest))n(2) The parameter definitions in Eq. 2 are identical to Eq. 1. Two additional parameters are included in Eq. 2: The LogKA is the agonist equilibrium affinity constant and the LogRAiTest is the difference in LogR values between the reference and test agonist. The LogRAiTest value of each test compound was used to produce bias factors by subtracting Δlog(τ/KA)assay of each agonist accordingly in two assays to generate ΔΔlog(τ/KA)assay1−assay2 as expressed in Eq. 3:Bias factor=10ΔΔlog(τ/KA)assay1-assay2=10(10Δlog(τ/KA)assay110Δlog(τ/KA)assay2)(3)Triazole 1.1 is more efficacious than U69,593 in the [35S]GTPγS binding assays with striatal membrane and the inhibition of cAMP accumulation assays in primary striatal neurons. For this reason, triazole 1.1 was used to determine the maximum response in the system. To produce a complete picture of the effects observed, the bias factor was also produced from nonlinear regression using the three-parameter dose-response equation, as a function of the Emax and EC50, using the equation indicated in Eq. 4:Bias factor =10ΔΔlog(Emax/EC50)assay1-assay2=10(10Δlog(Emax/EC50)assay110Δlog(Emax/EC50)assay2)(4)Statistical tests are noted in the figure legends. Student’s t test indicates an unpaired two-tailed analysis for at least three of independent experiments performed in multiple replicates.

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