Analysis of equilibrium binding of an orthosteric tracer and two allosteric modulators

Allosteric ligands bind to receptors at sites that are distinct from those endogenous agonists and orthosteric pharmacological agents interact with. Both an allosteric and orthosteric ligand bind simultaneously to the receptor to form a ternary complex, where each ligand influences binding affinity of the other to the receptor, either positively or negatively. Allosteric modulators are an intensively studied group of receptor ligands because of their potentially greater selectivity over orthosteric ligands, with the possibility of fine tuning of the effects of endogenous neurotransmitters and hormones. The affinity of an unlabelled allosteric ligand is commonly estimated by measuring its effects on binding of a radio-labelled orthosteric tracer. This scenario is complicated by many folds when one studies the kinetics of interactions of two allosteric agents, added simultaneously, on binding of an orthosteric tracer. In this paper, we provide, for the first time, theoretical basis for analysis of such complex interactions. We have expanded our analysis to include the possibility of having two allosteric modulators interact with the same or different sites on the receptor. An added value of our analysis is to provide a tool to distinguish between the two situations. Finally, we also modelled binding of two molecules of one allosteric modulator to one receptor.