Concentration addition as a classic null model for toxicology and pharmacology is based on Loewe's mathematical formulation and the linearity of the isoboles. Novel mathematical models, however, propose curved isoboles in certain conditions. This article aims to test the hypothesis of the curvature of isoboles in experimental measurements. With the assumption of linear isoboles, a partial agonist acts as an antagonist above its maximal effect level. The isoboles automatically convert to a positive slope. For curved isoboles, a partial agonist acts as an antagonist at higher effect levels than its maximal effect alone. The discrepancies between effect levels were studied with an estrogen receptor binding assay (BMAEREluc/ERα) using a mixture of 17β-estradiol and fulvestrant as a partial agonist. A mixture of 17β-estradiol and fulvestrant acts as a partial agonist and causes the diminishing of the effect level of 17β-estradiol at a significantly higher level than the maximal effect of their partial-agonistic dose-response curve. Measured, elevated effect levels were well predicted by the mathematical model. Nonlinear isoboles may change our understanding and definition of synergism or antagonism and prompt further attention in receptor theory.

The Laboratory of Environmental Biotechnology Institute of Microbiology of the Czech Academy of Sciences Vídeňská 1083 Prague 142 20 Czech Republic

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