Development of operational models of receptor activation including constitutive receptor activity and their use to determine the efficacy of the chemokine CCL17 at the CC chemokine receptor CCR4

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.

Quantitative receptor model for responses that are left- or right-shifted versus occupancy (are more or less concentration sensitive): the SABRE approach

Simple one-to three-parameter models routinely used to fit typical dose-response curves and calculate EC50 values using the Hill or Clark equation cannot provide the full picture connecting measured response to receptor occupancy, which can be quite complex due to the interplay between partial agonism and (pathway-dependent) signal amplification. The recently introduced SABRE quantitative receptor model is the first one that explicitly includes a parameter for signal amplification (γ) in addition to those for binding affinity (K d), receptor-activation efficacy (ε), constitutive activity (ε R0), and steepness of response (Hill slope, n). It can provide a unified framework to fit complex cases, where fractional response and occupancy do not match, as well as simple ones, where parameters constrained to specific values can be used (e.g., ε R0 = 0, γ = 1, or n = 1). Here, it is shown for the first time that SABRE can fit not only typical cases where response curves are left-shifted compared to occupancy (κ = K d/EC50 > 1) due to signal amplification (γ > 1), but also less common ones where they are right-shifted (i.e., less concentration-sensitive; κ = K d/EC50 < 1) by modeling them as apparent signal attenuation/loss (γ < 1). Illustrations are provided with μ-opioid receptor (MOPr) data from three different experiments with one left- and one right-shifted response (G protein activation and β-arrestin2 recruitment, respectively; EC50,Gprt < K d < EC50,βArr). For such cases of diverging pathways with differently shifted responses, partial agonists can cause very weak responses in the less concentration-sensitive pathway without having to be biased ligands due to the combination of low ligand efficacy and signal attenuation/loss-an illustration with SABRE-fitted oliceridine data is included.

Skipping a pillar does not make for strong foundations: Pharmacokinetic-pharmacodynamic reasoning behind the shape of dose-response relationships in oncology

Dose-response analysis is often applied to the quantification of drug-effect especially for slowly responding disease end points where a comparison is made across dose levels after a particular period of treatment. It has long been recognized that exposure - response is more appropriate than dose-response. However, trials necessarily are designed as dose-response experiments. Second, a wide range of functional forms are used to express relationships between dose and response. These considerations are also important for clinical development because pharmacokinetic (PK; and variability) plus pharmacokinetic-pharmacodynamic modeling may allow one to anticipate the shape of the dose-response curve and so the trial design. Here, we describe how the location and steepness of the dose response is determined by the PKs of the compound being tested and its exposure-response relationship in terms of potency (location), efficacy (maximum effect) and Hill coefficient (steepness). Thus, the location (50% effective dose [ED50 ]) is dependent not only on the potency (half-maximal effective concentration) but also the compound's PKs. Similarly, the steepness of the dose response is shown to be a function of the half-life of the drug. It is also shown that the shape of relationship varies dependent on the assumed time course of the disease. This is important in the context of drug-discovery where the in vivo potencies of compounds are compared as well as when considering an analysis of summary data (for example, model-based meta-analysis) for clinical decision making.

Phosphoproteomic mapping of CCR5 and ACKR2 signaling properties

ACKR2 is an atypical chemokine receptor which is structurally uncoupled from G proteins and is unable to activate signaling pathways used by conventional chemokine receptors to promote cell migration. Nonetheless, ACKR2 regulates inflammatory and immune responses by shaping chemokine gradients in tissues via scavenging inflammatory chemokines. To investigate the signaling pathways downstream to ACKR2, a quantitative SILAC-based phosphoproteomic analysis coupled with a systems biology approach with network analysis, was carried out on a HEK293 cell model expressing either ACKR2 or its conventional counterpart CCR5. The model was stimulated with the common agonist CCL3L1 for short (3 min) and long (30 min) durations. As expected, many of the identified proteins are known to participate in conventional signal transduction pathways and in the regulation of cytoskeleton dynamics. However, our analyses revealed unique phosphorylation and network signatures, suggesting roles for ACKR2 other than its scavenger activity. In conclusion, the mapping of phosphorylation events at a holistic level indicated that conventional and atypical chemokine receptors differ in signaling properties. This provides an unprecedented level of detail in chemokine receptor signaling and identifying potential targets for the regulation of ACKR2 and CCR5 function.

Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments

Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.

Systematic Assessment of Chemokine Signaling at Chemokine Receptors CCR4, CCR7 and CCR10

Chemokines interact with chemokine receptors in a promiscuous network, such that each receptor can be activated by multiple chemokines. Moreover, different chemokines have been reported to preferentially activate different signalling pathways via the same receptor, a phenomenon known as biased agonism. The human CC chemokine receptors (CCRs) CCR4, CCR7 and CCR10 play important roles in T cell trafficking and have been reported to display biased agonism. To systematically characterize these effects, we analysed G protein- and β-arrestin-mediated signal transduction resulting from stimulation of these receptors by each of their cognate chemokine ligands within the same cellular background. Although the chemokines did not elicit ligand-biased agonism, the three receptors exhibited different arrays of signaling outcomes. Stimulation of CCR4 by either CC chemokine ligand 17 (CCL17) or CCL22 induced β-arrestin recruitment but not G protein-mediated signaling, suggesting that CCR4 has the potential to act as a scavenger receptor. At CCR7, both CCL19 and CCL21 stimulated G protein signaling and β-arrestin recruitment, with CCL19 consistently displaying higher potency. At CCR10, CCL27 and CCL28(4-108) stimulated both G protein signaling and β-arrestin recruitment, whereas CCL28(1-108) was inactive, suggesting that CCL28(4-108) is the biologically relevant form of this chemokine. These comparisons emphasize the intrinsic abilities of different receptors to couple with different downstream signaling pathways. Comparison of these results with previous studies indicates that differential agonism at these receptors may be highly dependent on the cellular context.

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.

Direct evidence that the GPCR CysLTR2 mutant causative of uveal melanoma is constitutively active with highly biased signaling

Uveal melanoma is the most common eye cancer in adults and is clinically and genetically distinct from skin cutaneous melanoma. In a subset of cases, the oncogenic driver is an activating mutation in CYSLTR2, the gene encoding the G protein-coupled receptor cysteinyl-leukotriene receptor 2 (CysLTR2). The mutant CYSLTR2 encodes for the CysLTR2-L129Q receptor, with the substitution of Leu to Gln at position 129 (3.43). The ability of CysLTR2-L129Q to cause malignant transformation has been hypothesized to result from constitutive activity, but how the receptor could escape desensitization is unknown. Here, we characterize the functional properties of CysLTR2-L129Q. We show that CysLTR2-L129Q is a constitutively active mutant that strongly drives Gq/11 signaling pathways. However, CysLTR2-L129Q only poorly recruits β-arrestin. Using a modified Slack-Hall operational model, we quantified the constitutive activity for both pathways and conclude that CysLTR2-L129Q displays profound signaling bias for Gq/11 signaling pathways while escaping β-arrestin-mediated downregulation. CYSLTR2 is the first known example of a G protein-coupled receptor driver oncogene that encodes a highly biased constitutively active mutant receptor. These results provide new insights into the mechanism of CysLTR2-L129Q oncoprotein signaling and suggest CYSLTR2 as a promising potential therapeutic target in uveal melanoma.

A single unified model for fitting simple to complex receptor response data

The fitting of complex receptor-response data where fractional response and occupancy do not match is challenging. They encompass important cases including (a) the presence of "receptor reserve" and/or partial agonism, (b) multiple responses assessed at different vantage points along a pathway, (c) responses that are different along diverging downstream pathways (biased agonism), and (d) constitutive activity. For these, simple models such as the well-known Clark or Hill equations cannot be used. Those that can, such as the operational (Black&Leff) model, do not provide a unified approach, have multiple nonintuitive parameters that are challenging to fit in well-defined manner, have difficulties incorporating binding data, and cannot be reduced or connected to simpler forms. We have recently introduced a quantitative receptor model (SABRE) that includes parameters for Signal Amplification (γ), Binding affinity (Kd), Receptor activation Efficacy (ε), and constitutive activity (εR0). It provides a single equation to fit complex cases within a full two-state framework with the possibility of incorporating receptor occupancy data (i.e., experimental Kds). Simpler cases can be fit by using consecutively reduced forms obtained by constraining parameters to specific values, e.g., εR0 = 0: no constitutive activity, γ = 1: no amplification (Emax-type fitting), and ε = 1: no partial agonism (Clark equation). Here, a Hill-type extension is introduced (n ≠ 1), and simulated and experimental receptor-response data from simple to increasingly complex cases are fitted within the unified framework of SABRE with differently constrained parameters.

Analyzing kinetic signaling data for G-protein-coupled receptors

In classical pharmacology, bioassay data are fit to general equations (e.g. the dose response equation) to determine empirical drug parameters (e.g. EC50 and Emax), which are then used to calculate chemical parameters such as affinity and efficacy. Here we used a similar approach for kinetic, time course signaling data, to allow empirical and chemical definition of signaling by G-protein-coupled receptors in kinetic terms. Experimental data are analyzed using general time course equations (model-free approach) and mechanistic model equations (mechanistic approach) in the commonly-used curve-fitting program, GraphPad Prism. A literature survey indicated signaling time course data usually conform to one of four curve shapes: the straight line, association exponential curve, rise-and-fall to zero curve, and rise-and-fall to steady-state curve. In the model-free approach, the initial rate of signaling is quantified and this is done by curve-fitting to the whole time course, avoiding the need to select the linear part of the curve. It is shown that the four shapes are consistent with a mechanistic model of signaling, based on enzyme kinetics, with the shape defined by the regulation of signaling mechanisms (e.g. receptor desensitization, signal degradation). Signaling efficacy is the initial rate of signaling by agonist-occupied receptor (kτ), simply the rate of signal generation before it becomes affected by regulation mechanisms, measurable using the model-free analysis. Regulation of signaling parameters such as the receptor desensitization rate constant can be estimated if the mechanism is known. This study extends the empirical and mechanistic approach used in classical pharmacology to kinetic signaling data, facilitating optimization of new therapeutics in kinetic terms.

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).

Kinetic and system bias as drivers of metabotropic glutamate receptor 5 allosteric modulator pharmacology

Allosteric modulators of the metabotropic glutamate receptor subtype 5 (mGlu₅) have been proposed as potential therapies for various CNS disorders. These ligands bind to sites distinct from the orthosteric (or endogenous) ligand, often with improved subtype selectivity and spatio-temporal control over receptor responses. We recently revealed that mGlu₅ allosteric agonists and positive allosteric modulators exhibit biased agonism and/or modulation. To establish whether negative allosteric modulators (NAMs) engender similar bias, we rigorously characterized the pharmacology of eight diverse mGlu₅ NAMs. Radioligand inhibition binding studies revealed novel modes of interaction with mGlu₅ for select NAMs, with biphasic or incomplete inhibition of the radiolabeled NAM, [³H]methoxy-PEPy. We assessed mGlu₅-mediated intracellular Ca²⁺ (iCa²⁺) mobilization and inositol phosphate (IP₁) accumulation in HEK293A cells stably expressing low levels of mGlu₅ (HEK293A-rat mGlu₅-low) and mouse embryonic cortical neurons. The apparent affinity of acetylenic NAMs, MPEP, MTEP and dipraglurant, was dependent on the signaling pathway measured, agonist used, and cell type (HEK293A-rat mGlu₅-low versus mouse cortical neurons). In contrast, the acetylenic partial NAM, M-5MPEP, and structurally distinct NAMs (VU0366248, VU0366058, fenobam), had similar affinity estimates irrespective of the assay or cellular background. Biased modulation was evident for VU0366248 in mouse cortical neurons where it was a NAM for DHPG-mediated iCa²⁺ mobilization, but neutral with DHPG in IP₁ accumulation assays. Overall, this study highlights the inherent complexity in mGlu₅ NAM pharmacology that we hypothesize may influence interpretation when translating into preclinical models and beyond in the design and development of novel therapeutics for neuropsychiatric and neurological disorders.

An evaluation of the operational model when applied to quantify functional selectivity

BACKGROUND AND PURPOSE

Functional selectivity describes the ability of ligands to differentially regulate multiple signalling pathways when coupled to a single receptor, and the operational model is commonly used to analyse these data. Here, we assess the mathematical properties of the operational model and evaluate the outcomes of fixing parameters on model performance.

EXPERIMENTAL APPROACH

The operational model was evaluated using both a mathematical identifiability analysis and simulation.

KEY RESULTS

Mathematical analysis revealed that the parameters R0 and KE were not independently identifiable which can be solved by considering their ratio, τ. The ratio parameter, τ, was often imprecisely estimated when only functional assay data were available and generally only the transduction coefficient R ( τKA) could be estimated precisely. The general operational model (that includes baseline and the Hill coefficient) required either the parameters Em or KA to be fixed. The normalization process largely cancelled out the mean error of the calculated Δlog (R) caused by fixing these parameters. From this analysis, it was determined that we can avoid the need for a full agonist ligand to be included in an experiment to determine Δlog (R).

CONCLUSION AND IMPLICATIONS

This analysis has provided a ready-to-use understanding of current methods for quantifying functional selectivity. It showed that current methods are generally tolerant to fixing parameters. A new method was proposed that removes the need for including a high efficacy ligand in any given experiment, which allows application to large-scale screening to identify compounds with desirable features of functional selectivity.

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.

Modelling and simulation of biased agonism dynamics at a G protein-coupled receptor

Theoretical models of G protein-coupled receptor (GPCR) concentration-response relationships often assume an agonist producing a single functional response via a single active state of the receptor. These models have largely been analysed assuming steady-state conditions. There is now much experimental evidence to suggest that many GPCRs can exist in multiple receptor conformations and elicit numerous functional responses, with ligands having the potential to activate different signalling pathways to varying extents-a concept referred to as biased agonism, functional selectivity or pluri-dimensional efficacy. Moreover, recent experimental results indicate a clear possibility for time-dependent bias, whereby an agonist's bias with respect to different pathways may vary dynamically. Efforts towards understanding the implications of temporal bias by characterising and quantifying ligand effects on multiple pathways will clearly be aided by extending current equilibrium binding and biased activation models to include G protein activation dynamics. Here, we present a new model of time-dependent biased agonism, based on ordinary differential equations for multiple cubic ternary complex activation models with G protein cycle dynamics. This model allows simulation and analysis of multi-pathway activation bias dynamics at a single receptor for the first time, at the level of active G protein (αGTP), towards the analysis of dynamic functional responses. The model is generally applicable to systems with NG G proteins and N* active receptor states. Numerical simulations for NG=N*=2 reveal new insights into the effects of system parameters (including cooperativities, and ligand and receptor concentrations) on bias dynamics, highlighting new phenomena including the dynamic inter-conversion of bias direction. Further, we fit this model to 'wet' experimental data for two competing G proteins (Gi and Gs) that become activated upon stimulation of the adenosine A1 receptor with adenosine derivative compounds. Finally, we show that our model can qualitatively describe the temporal dynamics of this competing G protein activation.

Kinetic operational models of agonism for G-protein-coupled receptors

The application of kinetics to research and therapeutic development of G-protein-coupled receptors has become increasingly valuable. Pharmacological models provide the foundation of pharmacology, providing concepts and measurable parameters such as efficacy and potency that have underlain decades of successful drug discovery. Currently there are few pharmacological models that incorporate kinetic activity in such a way as to yield experimentally-accessible drug parameters. In this study, a kinetic model of pharmacological response was developed that provides a kinetic descriptor of efficacy (the transduction rate constant, k_τ) and allows measurement of receptor-ligand binding kinetics from functional data. The model assumes: (1) receptor interacts with a precursor of the response ("Transduction potential") and converts it to the response. (2) The response can decay. Familiar response vs time plots emerge, depending on whether transduction potential is depleted and/or response decays. These are the straight line, the "association" exponential curve, and the rise-and-fall curve. Convenient, familiar methods are described for measuring the model parameters and files are provided for the curve-fitting program Prism (GraphPad Software) that can be used as a guide. The efficacy parameter k_τ is straightforward to measure and accounts for receptor reserve; all that is required is measurement of response over time at a maximally-stimulating concentration of agonist. The modular nature of the model framework allows it to be extended. Here this is done to incorporate antagonist-receptor binding kinetics and slow agonist-receptor equilibration. In principle, the modular framework can incorporate other cellular processes, such as receptor desensitization. The kinetic response model described here can be applied to measure kinetic pharmacological parameters than can be used to advance the understanding of GPCR pharmacology and optimize new and improved therapeutics.

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.

A three-parameter two-state model of receptor function that incorporates affinity, efficacy, and signal amplification

A generalized model of receptor function is proposed that relies on the essential assumptions of the minimal two-state receptor theory (i.e., ligand binding followed by receptor activation), but uses a different parametrization and allows nonlinear response (transduction) for possible signal amplification. For the most general case, three parameters are used: Kd, the classic equilibrium dissociation constant to characterize binding affinity; ε, an intrinsic efficacy to characterize the ability of the bound ligand to activate the receptor (ranging from 0 for an antagonist to 1 for a full agonist); and γ, a gain (amplification) parameter to characterize the nonlinearity of postactivation signal transduction (ranging from 1 for no amplification to infinity). The obtained equation, E/Emax=εγLεγ+1-εL+Kd, resembles that of the operational (Black and Leff) or minimal two-state (del Castillo-Katz) models, E/Emax=τLτ+1L+Kd, with εγ playing a role somewhat similar to that of the τ efficacy parameter of those models, but has several advantages. Its parameters are more intuitive as they are conceptually clearly related to the different steps of binding, activation, and signal transduction (amplification), and they are also better suited for optimization by nonlinear regression. It allows fitting of complex data where receptor binding and response are measured separately and the fractional occupancy and response are mismatched. Unlike the previous models, it is a true generalized model as simplified forms can be reproduced with special cases of its parameters. Such simplified forms can be used on their own to characterize partial agonism, competing partial and full agonists, or signal amplification.

2,8-Diazaspiro[4.5]decan-8-yl)pyrimidin-4-amine potent CCR4 antagonists capable of inducing receptor endocytosis

A number of potent 2,8-diazaspiro[4.5]decan-8-yl)pyrimidin-4-amine CCR4 antagonists binding to the extracellular allosteric site were synthesised. (R)-N-(2,4-Dichlorobenzyl)-2-(2-(pyrrolidin-2-ylmethyl)-2,8-diazaspiro[4.5]decan-8-yl)pyrimidin-4-amine (R)-(18a) has high affinity in both the [(125)I]-TARC binding assay with a pKi of 8.8, and the [(35)S]-GTPγS functional assay with a pIC50 of 8.1, and high activity in the human whole blood actin polymerisation assay (pA2 = 6.7). The most potent antagonists were also investigated for their ability to induce endocytosis of CCR4 and were found to internalise about 60% of the cell surface receptors, a property which is not commonly shared by small molecule antagonists of chemokine receptors.

Pharmacological properties of acid N-thiazolylamide FFA2 agonists

FFA2 is a receptor for short-chain fatty acids. Propionate (C3) and 4-chloro-α-(1-methylethyl)-N-2-thiazolyl-benzeneacetamide (4-CMTB), the prototypical synthetic FFA2 agonist, evoke calcium mobilization in neutrophils and inhibit lipolysis in adipocytes via this G-protein-coupled receptor. 4-CMTB contains an N-thiazolylamide motif but no acid group, and 4-CMTB and C3 bind to different sites on FFA2 and show allosteric cooperativity. Recently, FFA2 agonists have been described that contain both N-thiazolylamide and carboxylate groups, reminiscent of bitopic ligands. These are thought to engage the carboxylate-binding site on FFA2, but preliminary evidence suggests they do not bind to the same site as 4-CMTB even though both contain N-thiazolylamide. Here, we describe the characterization of four FFA2 ligands containing both N-thiazolylamide and carboxylate. (R)-3-benzyl-4-((4-(2-chlorophenyl)thiazol-2-yl)(methyl)amino)-4-oxobutanoic acid (compound 14) exhibits allosteric agonism with 4-CMTB but not C3. Three other compounds agonize FFA2 in [³⁵S]GTPγS-incorporation or cAMP assays but behave as inverse agonists in yeast-based gene-reporter assays, showing orthosteric antagonism of C3 responses but allosteric antagonism of 4-CMTB responses. Thus, the bitopic-like FFA2 ligands engage the orthosteric site but do not compete at the site of 4-CMTB binding on an FFA2 receptor molecule. Compound 14 activates FFA2 on human neutrophils and mouse adipocytes, but appears not to inhibit lipolysis upon treatment of human primary adipocytes in spite of the presence of a functional FFA2 receptor in these cells. Hence, these new ligands may reveal differences in coupling of FFA2 between human and rodent adipose tissues.

Lead identification and structure-activity relationships of heteroarylpyrazole arylsulfonamides as allosteric CC-chemokine receptor 4 (CCR4) antagonists

A knowledge-based library of aryl 2,3-dichlorophenylsulfonamides was synthesised and screened as human CCR4 antagonists, in order to identify a suitable hit for the start of a lead-optimisation programme. X-ray diffraction studies were used to identify the pyrazole ring as a moiety that could bring about intramolecular hydrogen bonding with the sulfonamide NH and provide a clip or orthogonal conformation that was believed to be the preferred active conformation. Replacement of the core phenyl ring with a pyridine, and replacement of the 2,3-dichlorobenzenesulfonamide with 5-chlorothiophenesulfonamide provided compound 33 which has excellent physicochemical properties and represents a good starting point for a lead optimisation programme. Electronic structure calculations indicated that the preference for the clip or orthogonal conformation found in the small molecule crystal structures of 7 and 14 was in agreement with the order of potency in the biological assay.

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

Two-state and operational models of both agonism and allosterism are compared to identify and characterize common pharmacological parameters. To account for the receptor-dependent basal response, constitutive receptor activity is considered in the operational models. By arranging two-state models as the fraction of active receptors and operational models as the fractional response relative to the maximum effect of the system, a one-by-one correspondence between parameters is found. The comparative analysis allows a better understanding of complex allosteric interactions. In particular, the inclusion of constitutive receptor activity in the operational model of allosterism allows the characterization of modulators able to lower the basal response of the system; that is, allosteric modulators with negative intrinsic efficacy. Theoretical simulations and overall goodness of fit of the models to simulated data suggest that it is feasible to apply the models to experimental data and constitute one step forward in receptor theory formalism.

Internalization of the chemokine receptor CCR4 can be evoked by orthosteric and allosteric receptor antagonists

The chemokine receptor CCR4 has at least two natural agonist ligands, MDC (CCL22) and TARC (CCL17) which bind to the same orthosteric site with a similar affinity. Both ligands are known to evoke chemotaxis of CCR4-bearing T cells and also elicit CCR4 receptor internalization. A series of small molecule allosteric antagonists have been described which displace the agonist ligand, and inhibit chemotaxis. The aim of this study was to determine which cellular coupling pathways are involved in internalization, and if antagonists binding to the CCR4 receptor could themselves evoke receptor internalization. CCL22 binding coupled CCR4 efficiently to β-arrestin and stimulated GTPγS binding however CCL17 did not couple to β-arrestin and only partially stimulated GTPγS binding. CCL22 potently induced internalization of almost all cell surface CCR4, while CCL17 showed only weak effects. We describe four small molecule antagonists that were demonstrated to bind to two distinct allosteric sites on the CCR4 receptor, and while both classes inhibited agonist ligand binding and chemotaxis, one of the allosteric sites also evoked receptor internalization. Furthermore, we also characterize an N-terminally truncated version of CCL22 which acts as a competitive antagonist at the orthosteric site, and surprisingly also evokes receptor internalization without demonstrating any agonist activity. Collectively this study demonstrates that orthosteric and allosteric antagonists of the CCR4 receptor are capable of evoking receptor internalization, providing a novel strategy for drug discovery against this class of target.

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

Empirical and mechanistic models differ in their approaches to the analysis of pharmacological effect. Whereas the parameters of the former are not physical constants those of the latter embody the nature, often complex, of biology. Empirical models are exclusively used for curve fitting, merely to characterize the shape of the E/[A] curves. Mechanistic models, on the contrary, enable the examination of mechanistic hypotheses by parameter simulation. Regretfully, the many parameters that mechanistic models may include can represent a great difficulty for curve fitting, representing, thus, a challenge for computational method development. In the present study some empirical and mechanistic models are shown and the connections, which may appear in a number of cases between them, are analyzed from the curves they yield. It may be concluded that systematic and careful curve shape analysis can be extremely useful for the understanding of receptor function, ligand classification and drug discovery, thus providing a common language for the communication between pharmacologists and medicinal chemists.

Antagonism of human CC-chemokine receptor 4 can be achieved through three distinct binding sites on the receptor

Chemokine receptor antagonists appear to access two distinct binding sites on different members of this receptor family. One class of CCR4 antagonists has been suggested to bind to a site accessible from the cytoplasm while a second class did not bind to this site. In this report, we demonstrate that antagonists representing a variety of structural classes bind to two distinct allosteric sites on CCR4. The effects of pairs of low-molecular weight and/or chemokine CCR4 antagonists were evaluated on CCL17- and CCL22-induced responses of human CCR4⁺ T cells. This provided an initial grouping of the antagonists into sets which appeared to bind to distinct binding sites. Binding studies were then performed with radioligands from each set to confirm these groupings. Some novel receptor theory was developed to allow the interpretation of the effects of the antagonist combinations. The theory indicates that, generally, the concentration-ratio of a pair of competing allosteric modulators is maximally the sum of their individual effects while that of two modulators acting at different sites is likely to be greater than their sum. The low-molecular weight antagonists could be grouped into two sets on the basis of the functional and binding experiments. The antagonistic chemokines formed a third set whose behaviour was consistent with that of simple competitive antagonists. These studies indicate that there are two allosteric regulatory sites on CCR4.

The chemokine receptor CCR1 is constitutively active, which leads to G protein-independent, β-arrestin-mediated internalization

Activation of G protein-coupled receptors by their associated ligands has been extensively studied, and increasing structural information about the molecular mechanisms underlying ligand-dependent receptor activation is beginning to emerge with the recent expansion in GPCR crystal structures. However, some GPCRs are also able to adopt active conformations in the absence of agonist binding that result in the initiation of signal transduction and receptor down-modulation. In this report, we show that the CC-type chemokine receptor 1 (CCR1) exhibits significant constitutive activity leading to a variety of cellular responses. CCR1 expression is sufficient to induce inhibition of cAMP formation, increased F-actin content, and basal migration of human and murine leukocytes. The constitutive activity leads to basal phosphorylation of the receptor, recruitment of β-arrestin-2, and subsequent receptor internalization. CCR1 concurrently engages Gαi and β-arrestin-2 in a multiprotein complex, which may be accommodated by homo-oligomerization or receptor clustering. The data suggest the presence of two functional states for CCR1; whereas receptor coupled to Gαi functions as a canonical GPCR, albeit with high constitutive activity, the CCR1·β-arrestin-2 complex is required for G protein-independent constitutive receptor internalization. The pertussis toxin-insensitive uptake of chemokine by the receptor suggests that the CCR1·β-arrestin-2 complex may be related to a potential scavenging function of the receptor, which may be important for maintenance of chemokine gradients and receptor responsiveness in complex fields of chemokines during inflammation.

Synthesis and structure-activity relationships of indazole arylsulfonamides as allosteric CC-chemokine receptor 4 (CCR4) antagonists

A series of indazole arylsulfonamides were synthesized and examined as human CCR4 antagonists. Methoxy- or hydroxyl-containing groups were the more potent indazole C4 substituents. Only small groups were tolerated at C5, C6, or C7, with the C6 analogues being preferred. The most potent N3-substituent was 5-chlorothiophene-2-sulfonamide. N1 meta-substituted benzyl groups possessing an α-amino-3-[(methylamino)acyl]-group were the most potent N1-substituents. Strongly basic amino groups had low oral absorption in vivo. Less basic analogues, such as morpholines, had good oral absorption; however, they also had high clearance. The most potent compound with high absorption in two species was analogue 6 (GSK2239633A), which was selected for further development. Aryl sulfonamide antagonists bind to CCR4 at an intracellular allosteric site denoted site II. X-ray diffraction studies on two indazole sulfonamide fragments suggested the presence of an important intramolecular interaction in the active conformation.

Allosteric transition: a comparison of two models

Introduction

Two recent models are in use for analysis of allosteric drug action at receptor sites remote from orthosteric binding sites. One is an allosteric two-state mechanical model derived in 2000 by David Hall. The other is an extended operational model developed in 2007 by Arthur Christopoulos’s group. The models are valid in pharmacology, enzymology, transportology as well as several other fields of biology involving allosteric concentration effects.

Results

I show here that Hall’s model for interactions between an orthoster, an alloster, and a receptive unit is the best choice of model both for simulation and analysis of allosteric concentration-responses at equilibrium or steady-state.

Conclusions

As detailed knowledge of receptors systems becomes available, systems with several pathways and states and/ or more than two binding sites should be analysed by extended forms of the Hall model rather than for instance a Hill type exponentiation of terms as introduced in non-mechanistic (operational) model approaches; yielding semi-quantitative estimates of actual system parameters based on Hill’s unlikely simultaneity model for G protein-coupled receptors.

Application of receptor theory to allosteric modulation of receptors

In this chapter, three topics are considered. The allosteric two-state model (ATSM) is compared with explicit multiconformational models. This demonstrates that the ATSM encapsulates the common behaviors of any model with at least two active and two inactive conformations: the "states" of the model represent ensembles of active and inactive conformations. A matrix representation of multiconformational models is introduced to provide a compact notation for models with arbitrarily large numbers of conformations. Allosteric modulation is further explored in the context of an operational model of receptor activity which includes constitutive receptor activity. Fitting this model allows the apparent affinity, intrinsic efficacy, and cooperativity constants of a pair of allosteric ligands to be determined. It is also demonstrated that, within certain limits, it is possible to estimate the parameters of the ATSM. Finally, a novel operational model is developed that may allow the analysis of protean ligands. This model requires a nonlinear stimulus function and two parameters to define the efficacy of a ligand. Expressions describing competitive and allosteric interactions under this model are developed and the results of applying null analyses to the data are determined.