(
A) Concentration–response curves of interactions between the orthosteric and allosteric ligands at the human M
4 mAChR in the pERK1/2 signaling assay. (
B–E) Quantification of data from (
A) to calculate (
B) the signaling efficacy (τ
A and τ
B), (
C) the transduction coupling coefficients (log (τ/K)) of each ligand, (
D) the functional cooperativity (αβ) between ligands, and (
E) the efficacy modulation (β) between ligands. All data are mean ± SEM of three or more independent experiments performed in duplicate or triplicate with the pharmacological parameters determined from a global fit of the data. The error in (
E) was propagated using the square root of the sum of the squares. Pharmacological parameters are reported in
Table 1.