Mechanistic analysis of the function of agonists and allosteric modulators: reconciling two-state and operational models

A 19F-qNMR-Guided Mathematical Model for G Protein-Coupled Receptor Signaling

G protein-coupled receptors (GPCRs) exhibit a wide range of pharmacological efficacies, yet the molecular mechanisms responsible for the differential efficacies in response to various ligands remain poorly understood. This lack of understanding has hindered the development of a solid foundation for establishing a mathematical model for signaling efficacy. However, recent progress has been made in delineating and quantifying receptor conformational states and associating function with these conformations. This progress has allowed us to construct a mathematical model for GPCR signaling efficacy that goes beyond the traditional ON/OFF binary switch model. In this study, we present a quantitative conformation-based mathematical model for GPCR signaling efficacy using the adenosine A2A receptor (A2AR) as a model system, under the guide of 19F quantitative nuclear magnetic resonance experiments. This model encompasses two signaling states, a fully activated state and a partially activated state, defined as being able to regulate the cognate Gα s nucleotide exchange with respective G protein recognition capacity. By quantifying the population distribution of each state, we can now in turn examine GPCR signaling efficacy. This advance provides a foundation for assessing GPCR signaling efficacy using a conformation-based mathematical model in response to ligand binding. SIGNIFICANCE STATEMENT: Mathematical models to describe signaling efficacy of GPCRs mostly suffer from considering only two states (ON/OFF). However, research indicates that a GPCR possesses multiple active-(like) states that can interact with Gαβγ independently, regulating varied nucleotide exchanges. With the guide of 19F-qNMR, the transitions among these states are quantified as a function of ligand and Gαβγ, serving as a foundation for a novel conformation-based mathematical signaling model.

Allosteric binding cooperativity in a kinetic context

Allosteric modulators are of prime interest in drug discovery. These drugs regulate the binding and function of endogenous ligands, with some advantages over orthosteric ligands. A typical pharmacological parameter in allosteric modulation is binding cooperativity. This property can yield unexpected but illuminating results when decomposed into its kinetic parameters. Using two reference models (the allosteric ternary complex receptor model and a heterodimer receptor model), a relationship has been derived for the cooperativity rate constant parameters. This relationship allows many combinations of the cooperativity kinetic parameters for a single binding cooperativity value obtained under equilibrium conditions. This assessment may help understand striking experimental results involving allosteric modulation and suggest further investigations in the field.

Therapeutic potential of allosteric modulators for the treatment of gastrointestinal motility disorders

Gastrointestinal motility is tightly regulated by the enteric nervous system (ENS). Disruption of coordinated enteric nervous system activity can result in dysmotility. Pharmacological treatment options for dysmotility include targeting of G protein-coupled receptors (GPCRs) expressed by neurons of the enteric nervous system. Current GPCR-targeting drugs for motility disorders bind to the highly conserved endogenous ligand-binding site and promote indiscriminate activation or inhibition of the target receptor throughout the body. This can be associated with significant side-effect liability and a loss of physiological tone. Allosteric modulators of GPCRs bind to a distinct site from the endogenous ligand, which is typically less conserved across multiple receptor subtypes and can modulate endogenous ligand signalling. Allosteric modulation of GPCRs that are important for enteric nervous system function may provide effective relief from motility disorders while limiting side-effects. This review will focus on how allosteric modulators of GPCRs may influence gastrointestinal motility, using 5-hydroxytryptamine (5-HT), acetylcholine (ACh) and opioid receptors as examples.

Involvement of the adenosine A1 receptor in the hypnotic effect of rosmarinic acid

Insomnia, the most common sleep disorder, is characterized by a longer sleep latency, greater sleep fragmentation, and consequent excessive daytime fatigue. Due to the various side effects of prescribed hypnotics, demand for new drugs is still high. Recent studies have suggested the adenosine receptor (AR) as a potential therapeutic target for insomnia, however, clinically useful hypnotics targeting AR are not yet available. In the present study, we evaluated the hypnotic effect of rosmarinic acid, a phenolic compound widely found in medicinal plants, through pentobarbital-induced sleep test, electroencephalography/electromyography (EEG/EMG), and immunohistochemistry in mice. The underlying mechanisms were assessed by pharmacological approach using 8-cyclopentyl-1,3-dipropylxanthine (DPCPX) and SCH5826, antagonists for A1R and A2AR, respectively. Receptor-binding assay and functional agonism were also performed. Our study provides a new evidence that rosmarinic acid has a direct binding activity (Ki = 14.21 ± 0.3 μM) and agonistic activity for A1R. We also found that rosmarinic acid significantly decreased sleep fragmentation and onset latency to NREM sleep, and these effects were abolished by DPCPX. The results from c-Fos immunostaining showed that rosmarinic acid decreased the neuronal activity in wake-promoting brain regions, such as the basal forebrain and the lateral hypothalamus, while increasing the neuronal activity in the ventrolateral preoptic nucleus, a sleep-promoting region; all these effects were significantly inhibited by DPCPX. Taken together, this study suggests that rosmarinic acid possesses novel activity as an A1R agonist and thereby exerts a hypnotic effect, and thus it may serve as a potential therapeutic agent for insomnia through targeting A1R.

Biased Allosteric Modulators: New Frontiers in GPCR Drug Discovery

G protein-coupled receptors (GPCRs) are the largest class of cell surface receptors in the genome and the most successful family of targets of FDA-approved drugs. New frontiers in GPCR drug discovery remain, however, as achieving receptor subtype selectivity and controlling off- and on-target side effects are not always possible with classic agonist and antagonist ligands. These challenges may be overcome by focusing development efforts on allosteric ligands that confer signaling bias. Biased allosteric modulators (BAMs) are an emerging class of GPCR ligands that engage less well-conserved regulatory motifs outside the orthosteric pocket and exert pathway-specific effects on receptor signaling. The unique ways that BAMs texturize receptor signaling present opportunities to fine-tune physiology and develop safer, more selective therapeutics. Here, we provide a conceptual framework for understanding the pharmacology of BAMs, explore their therapeutic potential, and discuss strategies for their discovery.

A mathematical model of parathyroid gland biology

Altered parathyroid gland biology in patients with chronic kidney disease (CKD) is a major contributor to chronic kidney disease-mineral bone disorder (CKD-MBD). This disorder is associated with an increased risk of bone disorders, vascular calcification, and cardiovascular events. Parathyroid hormone (PTH) secretion is primarily regulated by the ionized calcium concentration as well as the phosphate concentration in the extracellular fluid and vitamin D. The metabolic disturbances in patients with CKD lead to alterations in the parathyroid gland biology. A hallmark of CKD is secondary hyperparathyroidism, characterized by an increased production and release of PTH, reduced expression of calcium-sensing and vitamin D receptors on the surface of parathyroid cells, and hyperplasia and hypertrophy of these cells. These alterations happen on different timescales and influence each other, thereby triggering a cascade of negative and positive feedback loops in a highly complex manner. Due to this complexity, mathematical models are a useful tool to break down the patterns of the multidimensional cascade of processes enabling the detailed study of subsystems. Here, we introduce a comprehensive mathematical model that includes the major adaptive mechanisms governing the production, secretion, and degradation of PTH in patients with CKD on hemodialysis. Combined with models for medications targeting the parathyroid gland, it provides a ready-to-use tool to explore treatment strategies. While the model is of particular interest for use in hemodialysis patients with secondary hyperparathyroidism, it has the potential to be applicable to other clinical scenarios such as primary hyperparathyroidism or hypo- and hypercalcemia.

A Receptor Model With Binding Affinity, Activation Efficacy, and Signal Amplification Parameters for Complex Fractional Response Versus Occupancy Data

In quantitative pharmacology, multi-parameter receptor models are needed to account for the complex nonlinear relationship between fractional occupancy and response that can occur due to the intermixing of the effects of partial receptor activation and post-receptor signal amplification. Here, a general two-state receptor model and corresponding quantitative forms are proposed that unify three distinct processes, each characterized with its own parameter: 1) receptor binding, characterized by K_d, the equilibrium dissociation constant used for binding affinity; 2) receptor activation, characterized by an (intrinsic) efficacy parameter ε; and 3) post-activation signal transduction (amplification), characterized by a gain parameter γ. Constitutive activity is accommodated via an additional ε_R0 parameter quantifying the activation of the ligand-free receptor. Receptors can be active or inactive in both their ligand-free and ligand-bound states (two-state receptor theory), but ligand binding alters the likelihood of activation (induced fit). Because structural data now confirm that for most receptors in their active conformation, the small-molecule ligand-binding site is buried inside, straightforward binding to the active form (direct conformational selection) is unlikely. The proposed general equation has parameters that are more intuitive and better suited for optimization by nonlinear regression than those of the operational (Black and Leff) or del Castillo–Katz model. The model provides a unified framework for fitting complex data including a) fractional responses that do not match independently measured fractional occupancies, b) responses measured after partial irreversible inactivation of the “receptor reserve” (Furchgott method), c) fractional responses that are different along distinct downstream pathways (biased agonism), and d) responses with constitutive receptor activity. Furthermore, unlike previous models, the present one can be reduced back for special cases of its parameters to consecutively nested simplified forms that can be used on their own when adequate (e.g., ε_R0 = 0, no constitutive activity; γ = 1: E_max model for partial agonism; ε = 1: Clark equation).

Allosteric Modalities for Membrane-Bound Receptors: Insights from Drug Hunting for Brain Diseases

Medicinal chemists are accountable for embedding the appropriate drug target profile into the molecular architecture of a clinical candidate. An accurate characterization of the functional effects following binding of a drug to its biological target is a fundamental step in the discovery of new medicines, informing the translation of preclinical efficacy and safety observations into human trials. Membrane-bound proteins, particularly ion channels and G protein-coupled receptors (GPCRs), are biological targets prone to allosteric modulation. Investigations using allosteric drug candidates and chemical tools suggest that their functional effects may be tailored with a high degree of translational alignment, making them molecular tools to correct pathophysiological functional tone and enable personalized medicine when a causative target-to-disease link is known. We present select examples of functional molecular fine-tuning of allosterism and discuss consequences relevant to drug design.

A method for the quantification of biased signalling at constitutively active receptors

BACKGROUND AND PURPOSE

Biased agonism, the ability of an agonist to differentially activate one of several signal transduction pathways when acting at a given receptor, is an increasingly recognized phenomenon at many receptors. The Black and Leff operational model lacks a way to describe constitutive receptor activity and hence inverse agonism. Thus, it is impossible to analyse the biased signalling of inverse agonists using this model. In this theoretical work, we develop and illustrate methods for the analysis of biased inverse agonism.

EXPERIMENTAL APPROACH

Methods were derived for quantifying biased signalling in systems that demonstrate constitutive activity using the modified operational model proposed by Slack and Hall. The methods were illustrated using Monte Carlo simulations.

KEY RESULTS

The Monte Carlo simulations demonstrated that, with an appropriate experimental design, the model parameters are 'identifiable'. The method is consistent with methods based on the measurement of intrinsic relative activity (RA_i ) (ΔΔlogR or ΔΔlog(τ/K_a )) proposed by Ehlert and Kenakin and their co-workers but has some advantages. In particular, it allows the quantification of ligand bias independently of 'system bias' removing the requirement to normalize to a standard ligand.

CONCLUSIONS AND IMPLICATIONS

In systems with constitutive activity, the Slack and Hall model provides methods for quantifying the absolute bias of agonists and inverse agonists. This provides an alternative to methods based on RA_i and is complementary to the ΔΔlog(τ/K_a ) method of Kenakin et al. in systems where use of that method is inappropriate due to the presence of constitutive activity.

Quantifying the allosteric interactions within a G-protein-coupled receptor heterodimer

G-protein-coupled receptors are central to signal transduction and cell communication. The possibility that cells use receptor heteromerization to modulate individual receptor pathways is a surmise that cannot be precluded. Given the complexity of these processes, mathematical models contribute to understanding how receptors and their respective ligands regulate signaling. Here, a mathematical model is presented that quantifies the allosteric interactions within a receptor heterodimer. The model is based on the operational model of allosterism including constitutive receptor activity, which provides the pharmacological analysis of heteromerization with well-established and widely used modeling and fitting procedures.

Practical Strategies and Concepts in GPCR Allosteric Modulator Discovery: Recent Advances with Metabotropic Glutamate Receptors

Allosteric modulation of GPCRs has initiated a new era of basic and translational discovery, filled with therapeutic promise yet fraught with caveats. Allosteric ligands stabilize unique conformations of the GPCR that afford fundamentally new receptors, capable of novel pharmacology, unprecedented subtype selectivity, and unique signal bias. This review provides a comprehensive overview of the basics of GPCR allosteric pharmacology, medicinal chemistry, drug metabolism, and validated approaches to address each of the major challenges and caveats. Then, the review narrows focus to highlight recent advances in the discovery of allosteric ligands for metabotropic glutamate receptor subtypes 1-5 and 7 (mGlu1-5,7) highlighting key concepts ("molecular switches", signal bias, heterodimers) and practical solutions to enable the development of tool compounds and clinical candidates. The review closes with a section on late-breaking new advances with allosteric ligands for other GPCRs and emerging data for endogenous allosteric modulators.

Quantitative Measure of Receptor Agonist and Modulator Equi-Response and Equi-Occupancy Selectivity

G protein-coupled receptors (GPCRs) are an important class of drug targets. Quantitative analysis by global curve fitting of properly designed dose-dependent GPCR agonism and allosterism data permits the determination of all affinity and efficacy parameters based on a general operational model. We report here a quantitative and panoramic measure of receptor agonist and modulator equi-response and equi-occupancy selectivity calculated from these parameters. The selectivity values help to differentiate not only one agonist or modulator from another, but on-target from off-target receptor or functional pathway as well. Furthermore, in conjunction with target site free drug concentrations and endogenous agonist tones, the allosterism parameters and selectivity values may be used to predict in vivo efficacy and safety margins.

Exploring the active conformation of cyclohexane carboxylate positive allosteric modulators of the type 4 metabotropic glutamate receptor

The active conformation of a family of metabotropic glutamate receptor subtype 4 (mGlu4 ) positive allosteric modulators (PAMs) with the cyclohexane 1,2-dicarboxylic scaffold present in cis-2-(3,5-dichlorophenylcarbamoyl)cyclohexanecarboxylic acid (VU0155041) was investigated by testing structurally similar six-membered ring compounds that have a locked conformation. The norbornane and cyclohexane molecules designed as mGlu4 conformational probes and the enantiomers of the trans diastereomer were computationally characterized and tested in mGlu4 pharmacological assays. The results support a VU0155041 active conformation, with the chair cyclohexane having the aromatic amide substituent in an axial position and the carboxylate in an equatorial position. Moreover, the receptor displays enantiomeric discrimination of the chiral PAMs. The constructed pharmacophore characterized a highly constrained mGlu4 allosteric binding site, thus providing a step forward in structure-based drug design for mGlu4 PAMs.

Estimation of ligand affinity constants for receptor states in functional studies involving the allosteric modulation of G protein-coupled receptors: implications for ligand bias

INTRODUCTION

The affinity constants of a ligand for active and inactive states of a receptor ultimately determine its capacity to activate downstream signaling events. In this report, we describe a reverse-engineering strategy for estimating these microscopic constants.

METHODS

Our approach involves analyzing responses measured downstream in the signaling pathway of a G protein-coupled receptor under conditions of allosteric modulation and reduced receptor expression or partial receptor inactivation. The analysis also yields estimates of the isomerization constant of the unoccupied receptor, the sensitivity constant of the signaling pathway, and the more empirical parameters of the receptor population including the observed affinities and efficacies of allosteric and orthosteric ligands - including inverse agonists - and the efficacy of the unoccupied receptor (i.e., constitutive activity).

RESULTS AND DISCUSSION

We validate our approach with an analytical proof and by analysis of simulated data. We also use our method to analyze data from the literature. We show that the values of the microscopic constants of orthosteric and allosteric ligands are constant regardless of the allosteric interaction and the nature of the receptor-signaling pathway as long as the same active state mediates the response. Our analysis is useful for quantifying probe-dependent allosteric interactions and the selectivity of agonists for different signaling pathways. Knowing the isomerization constant and sensitivity constant of a signaling pathway in a given cell line or tissue preparation enables future investigators to estimate the affinity constants of agonists for receptor states simply through analysis of their concentration-response curves. Our approach also provides a means of validating in silico estimates of ligand affinity for crystal structures of active and inactive states of the receptor.