Critical re-evaluation of the slope factor of the operational model of agonism: Do not exponentiate operational efficacy

Although being a relative term, agonist efficacy is a cornerstone in the proper assessment of agonist selectivity and signalling bias. The 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. Functional analysis of OMA demonstrates that the slope factor implemented by Black and Leff affects relationships among parameters of the OMA. Fitting of the OMA with Black & Leff slope factor to concentration-response curves theoretical model-based data resulted in wrong estimates of operational efficacy and affinity. In contrast, fitting the OMA modified by the Hill coefficient to the same data resulted in correct estimates of operational efficacy and affinity. Therefore, OMA modified by the Hill coefficient should be preferred over the Black & Leff equation for ranking of agonism and subsequent analysis, like quantification of signalling bias, when concentration-response curves differ in the slope factor and mechanism of action is known. Otherwise. Black & Leff equation should be used with extreme caution acknowledging potential pitfalls.