Classical methods for the estimation of antagonist affinity constants were developed under the assumption of one unique state for the receptor. The finding of receptor constitutive activity, which implies that at least two (one active and the other inactive) receptor states coexist at equilibrium, extended the concept of antagonism by distinguishing between neutral antagonists and inverse agonists. To account for the complexity introduced in the concept of antagonism, classical Schild and Cheng-Prusoff methods have been revisited within the two-state model of agonism. The resulting equations match the classical expressions for neutral antagonists but not for inverse agonists. It is suggested a revision of current routine procedures for antagonist affinity estimation.

706 -713, 2004). The former study allowed us to explain the mechanistic features associated with VFT recognition by agonists and antagonists integrating a negative allosteric interaction for agonist binding. The second study helped us to quantitatively describe the functional dynamics of transduction of the VFT occupation into functional response, confirming a putative positive cooperativity at the level of receptor coupling efficacy. This model will help both to better understand the functioning of these receptors and to characterize the mechanism of action of various types of allosteric modulators. Moreover, this model may be of general utility for oligomeric systems in which the ligand binding and effector domains correspond to distinct structural domains.The two main neurotransmitters, glutamate and GABA, activate not only ionotropic receptors but also G-proteincoupled receptors (GPCRs), called the metabotropic glutamate (mGlu) and GABA B receptors, respectively. These receptors belong to the class C of the large GPCR family (Pin et al., 2003) and play essential roles in the central nervous system by regulating fast excitatory and inhibitory transmission. As such, these receptors are the subject of intense research for the development of new drugs targeting the central nervous system.In addition to their sequence divergence with the other GPCRs, mGlu and GABA B receptors have peculiar structural characteristics. These receptors form constitutive dimers that are stabilized by a disulfide bridge in the case of mGlu receptors. Moreover, each protomer of a mGlu dimer is composed of three main structural domains: an extracellular Venus flytrap (VFT) domain where agonists bind, a transmembrane heptahelical domain (HD) responsible for G-protein activation, and a cysteine-rich domain (CRD) that interconnects the VFT and the HD both structurally and functionally (Rondard et al., 2006). These structural features make these receptors complex proteins and raise several issues regarding how agonist binding in the VFT leads to G-protein activation by the HD.Important information on the functioning of these proteins has been obtained from mutagenesis and structural studies

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.