Abstract
The quantitative analysis of drug-receptor interactions developed by Gaddum and Schild is widely used for comparisons of agonist or antagonist effects. These approaches in mathematical forms do not use any information about the stoichiometry of the agonist-receptor interaction.
This means that the slope parameters (Hill coefficients) of dose-response curves are always considered to be equal 1. Simplification in the Gaddum equation often leads to an inaccurate estimation of the equilibrium dissociation constants of the competitive antagonists, which is the key characteristic of the receptor ligands.
In our previous study, we described a development and validation of a new mathematical model for mixture toxicity. This model can also be used in the situation where one compound in binary mixture has affinity toward a binding site but does not convert the receptor to its active form.
This corresponds to the combination of an agonist with a competitive antagonist. From our model, we derived a novel form of the Gaddum equation which contains the original hill coefficient of the agonist.
The improved equation could provide accurate estimation of the antagonist's dissociation constant (affinity) even in receptor binding assays where the slopes of the agonist dose-response curve differ from 1. In conclusion, this novel form of the Gaddum equation could improve hazard identification and dose-response assessment of chemical compounds.