Applications and limitations of fitting of the operational model to determine relative efficacies of agonists

Proper determination of agonist efficacy is essential in the assessment of agonist selectivity and signalling bias. Agonist efficacy is a relative term that is dependent on the system in which it is measured, especially being dependent on receptor expression level. The operational model (OM) of functional receptor agonism is a useful means for the determination of agonist functional efficacy using the maximal response to agonist and ratio of agonist functional potency to its equilibrium dissociation constant (K-A) at the active state of the receptor. However, the functional efficacy parameter tau is interdependent on two other parameters of OM; agonist's K-A and the highest response that could be evoked in the system by any stimulus (E-MAX). Thus, fitting of OM to functional response data is a tricky process. In this work we analyse pitfalls of fitting OM to experimental data and propose a rigorous fitting procedure where K-A and E-MAX are derived from half-efficient concentration of agonist and apparent maximal responses obtained from a series of functional response curves. Subsequently, OM with fixed K-A and E-MAX is fitted to functional response data to obtain tau. The procedure was verified at M-2 and M-4 muscarinic receptors fused with the G(15) G-protein alpha-subunit. The procedure, however, is applicable to any receptor-effector system.