Two-State Models and the Analysis of the Allosteric Effect of Gallamine at the M 2 Muscarinic Receptor Frederick J. Ehlert and Michael T. Griffin Department of Pharmacology, School of Medicine, University of California, Irvine, California (F.J.E.); and Department of Physical Sciences, Chapman University, Orange, California (M.T.G.) Received January 22, 2008; accepted February 26, 2008 ABSTRACT We measured the influence of gallamine on the functional re- sponses and binding properties of selected agonists at the M 2 muscarinic receptor and analyzed the data within the context of the allosteric ternary complex model. Our analysis showed that gallamine modified agonist affinity without influencing efficacy. To explain this behavior, we investigated the allosteric ternary complex model at a deeper level of analysis to assess alloster- ism in terms of the differential affinity of gallamine for ground and active states of the receptor. Our simulations showed that two-state models based on a single orthosteric site for the agonist linked to an allosteric site for gallamine could not ac- count for affinity-only modulation, even if multiple conforma- tions of ground and active states were considered. We also expanded the tandem two-site model (J Biol Chem 275:18836 – 18844, 2000) within the context of the allosteric ternary com- plex model and analyzed the resulting hybrid model at the level of receptor states. This model posits that the agonist first binds to a relay site and then shuttles to the activation site to turn on the receptor. If it is assumed that allosterism occurs at the relay site and not the activation site, then this model can account for affinity-only modulation in a manner consistent with the allo- steric ternary complex model. A variety of drugs have been shown to modulate the bind- ing of ligands allosterically to the primary recognition site (orthosteric site) of muscarinic receptors (Stockton et al., 1983; Birdsall and Lazareno, 2005). Allosterism is often an- alyzed within the context of the allosteric ternary complex model as shown in Fig. 1b, which illustrates that both ortho- steric and allosteric ligands bind to their respective sites on the same receptor with dissociation constants of K X and K A , respectively (Stockton et al., 1983; Ehlert, 1988a). When both ligands are bound to the receptor, their observed dissociation constants (K obs ) are modified by the factor , which is a measure of the cooperativity between the binding of the two ligands. By considering that the ternary complex (XRA) might have an altered intrinsic efficacy (ε') compared to that of the binary (XR) complex (ε), it is possible to measure allosteric modulation of intrinsic efficacy in functional exper- iments (Ehlert, 1988a, 2005). We can also consider the allosteric model at a deeper level of analysis and examine how the allosteric ligand changes the affinity and intrinsic efficacy of the orthosteric ligand- receptor complex. The two-state allosteric model described mathematically in Fig. 1c and schematically in Fig. 2a is the simplest way to address this question. If the orthosteric and allosteric ligands exhibit the same preference for the ground and active states, then the interaction is positively coopera- tive ( 1), whereas if the ligands exhibit the opposite selectivity, the interaction is negatively cooperative (0  1). Predictions from this model include a correlation between the quality (negative or positive) and magnitude of the coop- erativity and the intrinsic efficacy of the orthosteric ligand- receptor complex. In addition, if the orthosteric ligand lacks sufficient intrinsic efficacy to activate the receptor com- pletely at 100% occupancy in both the absence and presence of the allosteric modulator, the modulation in affinity occurs with a simultaneous modulation in the proportion of recep- tors in the active state at 100% receptor occupancy (i.e., efficacy modulation). Heteromeric GABA A receptor subtypes exhibit many of the predictions of the two-state allosteric model with regard to benzodiazepines and other allosteric modulators (Ehlert et al., 1983; Levitan et al., 1988; Sigel and Baur, 1988). This work was supported by a National Institutes of Health Grant GM 69829 (to F.J.E.). Article, publication date, and citation information can be found at http://jpet.aspetjournals.org. doi:10.1124/jpet.108.136960. ABBREVIATIONS: BM5, N-methyl-N- (1-methyl-4-pyrrolidino-2-butynyl) acetamide; CHO, Chinese hamster ovary; hM 2 , human M 2 muscarinic receptor; 4-DAMP mustard, N-(2-chloroethyl)-4-piperidinyl diphenyl acetate; AC-42, 4-n-butyl-1-[4-(2-methylphenyl)-4-oxo-1-butyl]-piperidine); DMEM, Dulbecco’s modified Eagle’s medium; EC 50 , concentration of agonist eliciting half-maximal response; KRB, Krebs-Ringer bicarbonate; McN-A-343, [4-[[N-(3-chlorophenyl)carbamoyl]oxy]-2-butynyl]trimethylammonium; NMS, N-methylscopolamine. 0022-3565/08/3253-1039–1060$20.00 THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS Vol. 325, No. 3 Copyright © 2008 by The American Society for Pharmacology and Experimental Therapeutics 136960/3335355 JPET 325:1039–1060, 2008 Printed in U.S.A. 1039 at ASPET Journals on February 11, 2018 jpet.aspetjournals.org Downloaded from