Old and new ways to calculate the affinity of agonists and antagonists interacting with G-protein-coupled monomeric and dimeric receptors: The receptor–dimer cooperativity index

Abstract

Almost all existing models that explain heptahelical G-protein-coupled receptor (GPCR) operation are based on the occurrence of monomeric receptor species. However, an increasing number of studies show that many G-protein-coupled heptahelical membrane receptors (HMR) are expressed in the plasma membrane as dimers. We here review the approaches for fitting ligand binding data that are based on the existence of receptor monomers and also the new ones based on the existence of receptor dimers. The reasons for equivocal interpretations of the fitting of data to receptor dimers, assuming they are monomers, are also discussed. A recently devised model for receptor dimers provides a new approach for fitting data that eventually gives more accurate and physiological relevant parameters. Fitting data using the new procedure gives not only the equilibrium dissociation constants for high- and low-affinity binding to receptor dimers but also a “cooperativity index” that reflects the molecular communication within the dimer. A comprehensive way to fit binding data from saturation isotherms and from competition assays to a dimer receptor model is reported and compared with the traditional way of fitting data. The new procedure can be applied to any receptor forming dimers; from receptor tyrosine kinases to intracellular receptors (e.g., estrogen receptor) and in general for ligand binding to proteins forming dimers.

Introduction

Colquhoun (1973) and Thron (1973) pioneered some studies that led to the subsequent development of models for neurotransmitter and/or hormone receptors (De Lean et al., 1980, Costa and Herz, 1989, Costa et al., 1992, Lefkowitz et al., 1993, Onaran et al., 1993, Samama et al., 1993, Samama et al., 1994, Leff, 1995, Tuèek and Proška, 1995, Franco et al., 1996, Weiss et al., 1996a, Weiss et al., 1996b, Weiss et al., 1996c, Hall, 2000, Lorenzen et al., 2002). The main aim of any of those models was to explain the behaviour of G protein-coupled receptors (GPCR), also known as 7 transmembrane or heptaspanning/heptahelical membrane receptors (HMR) because they contain 7 alpha helices that traverse the membrane of the cell or the endoplasmic reticulum. HMR are a superfamily of receptors with enormous current and future therapeutic potential. The majority of the models devised for HMR comes from the noncooperative 3-state mechanism proposed 50 years ago by del Castillo and Katz (1957) to explain the behaviour of nicotinic acetylcholine receptors, which are ligand-gated ion channels but not HMR (Fig. 1A). Those authors postulated that when acetylcholine binds to the receptor, a conformational change is produced in the receptor that converts into a selective ion channel. This is a sequential model correlating a closed channel in absence of the neurotransmitter but progressing in the presence of the neurotransmitter to an intermediate closed state and afterwards to an open channel. A summary of all the models that assume that receptors are monomeric is shown in Fig. 1.

One of the most useful models for HMR is the “two-state model of receptor activation,” (Leff, 1995) which postulates that there are at least 2 conformational forms that are in equilibrium: R and R^⁎ (Fig. 1B). One of the conformational forms is capable of signalling, and it is considered the “active” molecule. The other conformational state is considered to be the inactive state of the receptor. The model considers an orthosteric center where the agonist binds and subsequently displaces the equilibrium towards the active state. If binding of natural or synthetic compounds to this orthosteric or competitive center displaces the equilibrium to the active state, the compounds are considered as agonists. Other compounds binding to the orthosteric center competing with agonists but unable to affect the equilibrium are considered (neutral) antagonists. Occurrence of equilibrium between the active and the inactive form in the absence of ligands explains the so-called constitutive activity due to the existing, usually low proportion of active molecules in the plasma membrane, which therefore produces a basal (constitutive) signalling in the absence of agonists. There are compounds that displace the equilibrium towards the inactive form, subsequently decreasing the constitutive activity. These compounds are known as inverse agonists or negative antagonists. Many compounds previously thought to be neutral antagonists are in fact inverse agonists (Franco et al., 2005 and references therein).

Other more complex models include the occurrence of allosteric sites to explain the allosteric regulation performed by molecules structurally different from the agonist. Thus, the “ternary complex model” proposed by De Lean et al. (1980; Fig. 1C) includes an allosteric or regulatory site where G proteins can bind. The binding of G proteins to this allosteric center modulates the operation of the HMR and in particular the effect of agonists. G proteins do not compete with agonists or antagonists for the orthosteric center and therefore are noncompetitive modulators. They may modify the value of the dissociation constant (K_D) of the agonist but not the total amount of receptors (R_Total). The “ternary complex model of allosteric modulation” is a generalization of the “ternary complex model” in which the allosteric modulation is not restricted to G proteins and includes different compounds, which may have pharmacological activity, acting on allosteric sites (see Tuèek and Proška, 1995, Lazareno et al., 1998 and references therein). Samama et al. (1993) expanded this model and developed the “extended ternary complex model” (Fig. 1D), which included different affinity states (R and R^⁎) for the receptor uncoupled to the G protein. As in the two-state model, R is the unproductive form, and R^⁎ is the active form. In this model it is assumed that the G protein binds to a specific and allosteric site in R^⁎. The G protein, acting as an allosteric modulator, modifies the agonist binding and/or affects the equilibrium between R and R^⁎. Since the allosteric modulator (in this case the G protein) does not compete with orthosteric compounds, maximum binding is not affected but K_D is. The “cubic ternary complex model” (Weiss et al., 1996a, Weiss et al., 1996b, Weiss et al., 1996c; Fig. 1E) expands the “extended ternary complex model”, allowing the binding of G to R and R^⁎. This combines the “ternary complex model” (Fig. 1C) and the “two-state model of receptor activation” (Fig. 1B). More recently the “allosteric two-state model” developed by Hall (2000) generalizes the “cubic ternary complex model” of Weiss et al., 1996a, Weiss et al., 1996b, Weiss et al., 1996c. This model is similar to the “cubic ternary complex model,” since the allosteric modulation is not restricted to G protein and includes different compounds. More complex models, including the “quaternary complex model” of allosteric interactions, have been proposed assuming similar principles as those described above (Christopoulos & Kenakin, 2002).

None of these models is however able to satisfactorily explain the binding characteristics of receptors displaying biphasic binding isotherms (e.g., nonlinear Scatchard plots), such as, profiles of agonist binding to the orthosteric center with Hill coefficients different from 1 (Roy et al., 1973, Limbird et al., 1975, Mattera et al., 1985, Sinkins et al., 1993, Sinkins and Wells, 1993, Wreggett and Wells, 1995, Chidiac, 1998, Lazareno et al., 1998, Franco et al., 2000, Jordan et al., 2003, Trankle et al., 2003, Suzuki et al., 2004, Albizu et al., 2006). This in fact indicates the occurrence of homotropic cooperativity. Models postulating the coexistence of orthosteric and allosteric centers in the same receptor molecule as that devised by Hall (2000) allow explaining heterotropic cooperativity exerted by allosteric modulators but not homotropic cooperativity, which is quite common for many HMR. As defined for enzymes, this is just the conceptual difference between cooperativity (homotropic cooperativity) and allosteric modulation, leading to heterotropic cooperativity exerted by the agonist binding to an orthosteric center and an effector different from the agonist binding to an allosteric center (see Hall, 2000).

To overcome the problem derived from the occurrence of biphasic binding isotherms, the most commonly used approach is based on the addition of 2 isotherms corresponding to the binding to 2 different receptor forms (or sites; Fig. 1F). For instance, one of the receptors would be coupled to a G protein and would display high affinity, whereas the other receptor would be uncoupled from any G protein and would display low-affinity binding for agonists. These 2 different forms of the receptor, which have different affinity for agonists, have to be independent and cannot be in equilibrium. For this reason the model is usually known as the two-independent-site model (see Casadó et al., 1990; Fig. 1F). Addition of binding to a low-affinity receptor site and to a high-affinity site would explain biphasic binding isotherms. Although this approach has been very useful and is continuously used in cases of complex binding, it could only be considered meaningful if the 2 states with high- and low-affinity for ligands were totally independent, that is if they were not in equilibrium or if they could not interconvert. It is then interesting to note that the models described in the Fig. 1B–G are based on an equilibrium between R and R^⁎ and therefore they would only explain biphasic binding isotherms if the concentration of G protein (or the allosteric modulator) would be lower or similar to that of the receptor, which does not occur under physiological conditions (Neubig, 1994). Another possibility would be to consider that R and G are in equilibrium but assuming low and rapid equilibria involving the agonist, R and G proteins; this is unlikely since the binding protocols fix the concentration of R and G and therefore the radioligand binding would be monophasic irrespective of whether the equilibria between the different components of the system are rapid or slow. In addition it has been observed that agonists induce changes in the proportions of the so-called “high” and “low” affinity sites, which strongly suggests that these 2 states cannot exist separately but they are interconnected (Wong et al., 1986, Casadó et al., 1991). Taken together these circumstances make the approach of the 2 independent sites useful but equivocal since all models and the experimental evidence points towards a “dependence” of the different forms of the receptor, that is the existence of equilibrium between the forms. On the other hand, the two-independent-site model is only useful to handle concave-upward Scatchard plots, such as negative cooperativity. In fact this approach cannot explain positive cooperativity, which is not as common as negative cooperativity among HMR but it does occur such as the examples reported by Mattera et al. (1985) for agonist binding to muscarinic receptors, and Jordan et al. (2003) and Tomassini et al. (2003) for agonist binding to mu and delta opioid receptors. Sinkins et al. (1993) and Sinkins and Wells (1993) demonstrated the occurrence of positive cooperativity in the agonist binding to histamine receptors and concluded that their results could not be explained by the occurrence of 2 independent receptor sites or by the ligand-regulated equilibrium between 2 sites. Lazareno et al. (1998) arrived at a similar conclusion that, working with muscarinic receptors, observed positive homotropic, neutral or negative cooperativity, depending on the receptor subtype and on the ligand used in the binding assays. Mattera et al. (1985) did propose the occurrence of a multivalent receptor molecule, such as having more than 1 center for the binding of agonists or that the actual active receptor present in the plasma membrane possesses some kind of oligomeric characteristic. At that time it was not yet evident that HMR were capable of dimerize/oligomerize and therefore we proposed an alternative model of heptaspanning receptor operation based on intermolecular receptor–receptor, receptor–protein, and receptor–lipid interactions. The “cluster-arranged cooperative model” (Franco et al., 1996; Fig. 2A) was the first formulated model able to explain biphasic binding isotherms for agonist binding to heptaspanning monomeric receptors in cases of negative cooperativity.

We were aware of the requirement for receptor–protein and receptor–lipid interactions to achieve the conformational changes to be transmitted to the different receptor molecules, considered as monomers, and that would account for both negative and positive cooperativity. According to the apparent negative cooperativity in the ligand binding to adenosine A₁ receptors and to the fact that agonists are able to cluster the receptors, it was assumed that receptors within the cluster (or microdomain) display a decreased affinity. A relevant feature in this model was the assumption that each agonist molecule that binds to the receptor is able to infinitesimally modify the affinity of subsequent agonist molecules interacting with the “empty” receptors in the cluster. It was proven that this agonist-induced global change in the affinity explains a negative cooperativity in the binding of adenosine to A₁ receptors but the model could also explain positive cooperativity (Franco et al., 1996).

Based on functional evidence, it was proposed that HMR would form dimers. Electrophoretic mobility and coimmunoprecipitation assays gave the first indication of dimer formation. Biophysical techniques such as BRET, FRET, or force atomic microscopy were then developed to demonstrate that dimers are formed by direct interaction of 2 heptaspanning membrane receptors and that they occurred in living cells. Given now the almost universal occurrence of heptaspanning membrane receptors as dimers (see Bouvier, 2001, Devi, 2001, Rios et al., 2001, Agnati et al., 2003, Franco et al., 2003, Terrillon and Bouvier, 2004, Agnati et al., 2005, Franco et al., 2005, Prinster et al., 2005, Milligan, 2006 for extensive review), the understanding of ligand–receptor interactions and subsequent activation processes must be revised. HMR may eventually form higher-order oligomers and the actual stoichiometry is not known. It should be, however, noted that models based on trimers, tetramers, etc., would be more complex, but also they would be of little added value in terms of fitting radioligand binding data. In fact the experimental error, inherent in this type of experiments of ligand binding, and the limited number of data points would not give sufficient improvement, and the F test would refuse a model with higher number of parameters. Therefore, we think that both a dimer-based model is very useful and a trimer- or tetramer-based model would not give in practice more than 2 “reliable” macroscopic dissociation equilibrium constants.

To explain ligand binding and activation mechanisms of HMR, their dimeric structure must be taken into account and the interpretation of biphasic binding isotherms using a receptor dimer model is more straightforward. We have recently introduced the two-state receptor dimer model (Fig. 2B) in which cooperativity is naturally explained by assuming that binding of the first ligand to the dimer modifies the equilibrium parameters of binding of the second ligand molecule to the dimer (Franco et al., 2005, Franco et al., 2006). The “two-state dimer receptor model” is based on the possibility that conformational changes in one of the molecules in the dimer are transmitted to the second molecule. This implies communication (cross-talk) is possible between the 2 subunits of the receptor dimer. The model is an extension of the “two-state model of receptor activation” but considering dimeric structures able to bind 1 molecule to the orthosteric centre in each monomer. Negative or positive cooperativity is naturally explained by assuming that binding of the first ligand modifies (negatively or positively) the equilibrium parameters defining the binding of the second ligand molecule. The analysis of the binding of agonists, inverse agonists, or antagonists to receptors by the two-state dimer receptor model can explain the reported behaviour of HMR, thus contributing to better understand the operation of these receptors of great therapeutic potential. This two-state dimer model can be useful for investigating other types of receptors, such as nicotinic acetylcholine receptors, which have several identical binding sites (Edelstein et al., 1996). Furthermore, the model predicts other features (e.g., dual effects for a given compound) of HMR — a tool that could be useful for improving current therapeutic strategies that target this type of receptors.

It should be noted that also recently Durroux (2005) has introduced 2 different models in which receptor dimers are taken into account. In one of the models describing ligand–receptor interactions, receptors oscillate between 2 dimeric states: the R∼R state in which protomers are independent from one another and the R–R state in which protomers are able to establish a cross-talk (Fig. 2C). The second model describes ligand–receptor interactions in a scenario in which receptors oscillate between a monomeric state and a dimeric state in which protomers are able to cross-talk (Fig. 2D). This switch from a monomeric receptor to a receptor dimer, or vice versa, has been observed for only few HMR (Gomes et al., 2001, Rios et al., 2001) in which the ligand affects the monomer–dimer conversion. Future studies will permit to know whether this conversion is possible and if so, which is the proportion of receptors able to convert from monomers to dimers or vice versa. The current view, however, is that the majority of HMR are present as constitutive dimers on the cell surface (Bouvier, 2001, Agnati et al., 2003, Canals et al., 2003). Interestingly, the first of the models described by Durroux (2005; Fig. 2C) would lead to the same type of equations as those provided by our model (Fig. 2B; Franco et al., 2005, Franco et al., 2006).