We show how equilibrium binding curves of receptor heterodimers and homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric coupling between receptor monomers.Guanine nucleotide-binding protein (G protein) coupled receptors (GPCRs) are the largest family of signaling proteins in the mammalian genome and targets for therapeutic drugs (1, 2). When GPCRs are activated by extracellular agonists, they interact with heterotrimeric G proteins to regulate downstream second messenger and protein kinase cascades; notably, cyclic-adenosine monophosphate (cAMP), inositol 1,4,5-triphosphate (IP 3 ), and diacylglycerol (DAG). For example, agonist binding to the β 2 -adrenergic receptor (β 2 AR) stimulates adenylate cyclase (AC) and generates cAMP. Agonist binding to the β 2 AR leads to conformational changes in the 7-transmembrane receptor that destabilize the nucleotidebinding pocket of the G-protein α s -subunit to release GDP, prior to GTP binding and activation of G proteins. G-protein binding to the 7-transmembrane receptor, in turn, changes the affinity of ligand binding (3).Equilibrium receptor-occupancy models are used by pharmacologists to quantify changes in ligand affinity and efficacy, and various modes of activation of GPCRs (4-8). Allosteric modulators of GPCRs are of therapeutic interest due to their potential for greater specificity than agonist and antagonist orthosteric ligands (9). Indeed, allosteric modulators hold promise for treating numerous CNS disorders, including schizophrenia (10, 11).Evidence for clustering of GPCRs has been obtained using various experimental methods, including radioligand binding, coimmunoprecipitation, and fluorescence resonance energy transfer microscopy (FRET) (12-14). Indeed, some GPCRs are obligate dimers (e.g., the GABA B receptor and taste receptors for sweet and umami responses) (15-17). The physical interactions between monomeric units of GPCR oligomers are likely to be important determinants in the mechanism of receptor activation (18)(19)(20). It is widely believed that dimerization and higher-order complexing diversifies GPCR signaling (21-23). Although mathematical analysis has provided specific insights into the complexity of allosteric interactions of receptor oligomers (24, 25), a deeper theoretical understanding of oligomeric signaling could lead to further opportunities for pharmacological intervention. This paper introduces a novel theoretical framework for understanding allostery and thermodynamic constraints in oligomeric receptor models that are composed of any num- ber of identical monomers. The framework allows equilibrium occupancy measures (i.e., binding curves) of receptor homodimers to be expressed in terms of the properties of constituent monomers, without appro...