A critical re-evaluation of the slope factor of the operational model of agonism: When to exponentiate operational efficacy.

Agonist efficacy denoting the "strength" of agonist action is a cornerstone in the proper assessment of agonist selectivity and signalling bias. The simulation models are very accurate but complex and hard to fit experimental data. The parsimonious operational model of agonism (OMA) has become successful in the determination of agonist efficacies and ranking them. In 1983, Black and Leff introduced the slope factor to the OMA to make it more flexible and allow for fitting steep as well as flat concentration-response curves. First, we performed a functional analysis to indicate the potential pitfalls of the OMA. Namely, exponentiation of operational efficacy may break relationships among the OMA parameters. The fitting of the Black & Leff equation to the theoretical curves of several models of functional responses and the experimental data confirmed the fickleness of the exponentiation of operational efficacy affecting estimates of operational efficacy as well as other OMA parameters. In contrast, fitting The OMA based on the Hill equation to the same data led to better estimates of model parameters. In conclusion, Hill equation-based OMA should be preferred over the Black & Leff equation when functional-response curves differ in the slope factor. Otherwise, the Black & Leff equation should be used with extreme caution acknowledging potential pitfalls.