New insight into isobolographic analysis for combinations of a full and partial agonist: Curved isoboles.

Receptor ligands in mixtures may produce effects that are greater than the effect predicted from their individual dose-response curves. The historical basis for predicting the mixture effect is based on Loewe's concept and its mathematical formulation. This concept considers compounds with constant relative potencies (parallel dose-response curves) and leads to linear additive isoboles. These lines serve as references for distinguishing additive from nonadditive interactions according to the positions of the experimental data on or outside of the lines. In this paper, we applied a highly relevant two-state model for a description of the receptor-ligand interaction in the construction of the isobologram. In our model we consider partial agonists that have dose-response curve slopes differing from one. With this theoretical basis, we demonstrated that a combination of compounds with different efficacies leads to curved isoboles. This model should overwrite Tallarida's flawed assumption about isobolographic analysis of partial agonists and enhance our understanding of how the partial agonists contribute to the overall mixture effect.