Mathematical modeling of G protein-coupled receptor function: what can we learn from empirical and mechanistic models?

International Union of Basic and Clinical Pharmacology. CXI. Pharmacology, Signaling, and Physiology of Metabotropic Glutamate Receptors

Metabotropic glutamate (mGlu) receptors respond to glutamate, the major excitatory neurotransmitter in the mammalian brain, mediating a modulatory role that is critical for higher-order brain functions such as learning and memory. Since the first mGlu receptor was cloned in 1992, eight subtypes have been identified along with many isoforms and splice variants. The mGlu receptors are transmembrane-spanning proteins belonging to the class C G protein-coupled receptor family and represent attractive targets for a multitude of central nervous system disorders. Concerted drug discovery efforts over the past three decades have yielded a wealth of pharmacological tools including subtype-selective agents that competitively block or mimic the actions of glutamate or act allosterically via distinct sites to enhance or inhibit receptor activity. Herein, we review the physiologic and pathophysiological roles for individual mGlu receptor subtypes including the pleiotropic nature of intracellular signal transduction arising from each. We provide a comprehensive analysis of the in vitro and in vivo pharmacological properties of prototypical and commercially available orthosteric agonists and antagonists as well as allosteric modulators, including ligands that have entered clinical trials. Finally, we highlight emerging areas of research that hold promise to facilitate rational design of highly selective mGlu receptor-targeting therapeutics in the future. SIGNIFICANCE STATEMENT: The metabotropic glutamate receptors are attractive therapeutic targets for a range of psychiatric and neurological disorders. Over the past three decades, intense discovery efforts have yielded diverse pharmacological tools acting either competitively or allosterically, which have enabled dissection of fundamental biological process modulated by metabotropic glutamate receptors and established proof of concept for many therapeutic indications. We review metabotropic glutamate receptor molecular pharmacology and highlight emerging areas that are offering new avenues to selectively modulate neurotransmission.

Accuracy and Precision of the Receptorial Responsiveness Method (RRM) in the Quantification of A1 Adenosine Receptor Agonists

The receptorial responsiveness method (RRM) is a procedure that is based on a simple nonlinear regression while using a model with two variables (X, Y) and (at least) one parameter to be determined (c_x). The model of RRM describes the co-action of two agonists that consume the same response capacity (due to the use of the same postreceptorial signaling in a biological system). While using RRM, uniquely, an acute increase in the concentration of an agonist (near the receptors) can be quantified (as c_x), via evaluating E/c curves that were constructed with the same or another agonist in the same system. As this measurement is sensitive to the implementation of the curve fitting, the goal of the present study was to test RRM by combining different ways and setting options, namely: individual vs. global fitting, ordinary vs. robust fitting, and three weighting options (no weighting vs. weighting by 1/Y² vs. weighting by 1/SD²). During the testing, RRM was used to estimate the known concentrations of stable synthetic A₁ adenosine receptor agonists in isolated, paced guinea pig left atria. The estimates were then compared to the known agonist concentrations (to assess the accuracy of RRM); furthermore, the 95% confidence limits of the best-fit values were also considered (to evaluate the precision of RRM). It was found that, although the global fitting offered the most convenient way to perform RRM, the best estimates were provided by the individual fitting without any weighting, almost irrespective of the fact whether ordinary or robust fitting was chosen.

Mathematical modeling of the glucagon challenge test

A model for the homeostasis of glucose through the regulating hormones glucagon and insulin is described. It contains a subsystem that models the internalization of the glucagon receptor. Internalization is a mechanism in cell signaling, through which G-protein coupled receptors are taken from the surface of the cell to the endosome. The model is used to interpret data from a glucagon challenge test in which subjects have been under treatment with a novel glucagon receptor anti-sense drug which is aimed at reducing the number of receptors in the liver. It is shown how the receptor internalization results in tolerance of the blood glucose concentration to glucagon-induced hyperglycemia. We quantify the reduction of the number of receptors using the model and the data before and after treatment.

Pharmacological evidence for a metabotropic glutamate receptor heterodimer in neuronal cells

Metabotropic glutamate receptors (mGluRs) are mandatory dimers playing important roles in regulating CNS function. Although assumed to form exclusive homodimers, 16 possible heterodimeric mGluRs have been proposed but their existence in native cells remains elusive. Here, we set up two assays to specifically identify the pharmacological properties of rat mGlu heterodimers composed of mGlu2 and 4 subunits. We used either a heterodimer-specific conformational LRET-based biosensor or a system that guarantees the cell surface targeting of the heterodimer only. We identified mGlu2-4 specific pharmacological fingerprints that were also observed in a neuronal cell line and in lateral perforant path terminals naturally expressing mGlu2 and mGlu4. These results bring strong evidence for the existence of mGlu2-4 heterodimers in native cells. In addition to reporting a general approach to characterize heterodimeric mGluRs, our study opens new avenues to understanding the pathophysiological roles of mGlu heterodimers.

DOI:http://dx.doi.org/10.7554/eLife.25233.001

Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life

The term receptor reserve, first introduced and used in the traditional receptor theory, is an integrative measure of response-inducing ability of the interaction between an agonist and a receptor system (consisting of a receptor and its downstream signaling). The underlying phenomenon, i.e., stimulation of a submaximal fraction of receptors can apparently elicit the maximal effect (in certain cases), provides an opportunity to assess the receptor reserve. However, determining receptor reserve is challenging for agonists with short half-lives, such as adenosine. Although adenosine metabolism can be inhibited several ways (in order to prevent the rapid elimination of adenosine administered to construct concentration–effect (E/c) curves for the determination), the consequent accumulation of endogenous adenosine biases the results. To address this problem, we previously proposed a method, by means of which this bias can be mathematically corrected (utilizing a traditional receptor theory-independent approach). In the present investigation, we have offered in silico validation of this method by simulating E/c curves with the use of the operational model of agonism and then by evaluating them using our method. We have found that our method is suitable to reliably assess the receptor reserve for adenosine in our recently published experimental setting, suggesting that it may be capable for a qualitative determination of receptor reserve for rapidly eliminating agonists in general. In addition, we have disclosed a possible interference between FSCPX (8-cyclopentyl-N³-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N¹-propylxanthine), an irreversible A₁ adenosine receptor antagonist, and NBTI (S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine), a nucleoside transport inhibitor, i.e., FSCPX may blunt the effect of NBTI.