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

Cooperative Gating of a K+ Channel by Unmodified Biological Anionic Lipids Viewed by Solid-State NMR Spectroscopy

Lipids adhere to membrane proteins to stimulate or suppress molecular and ionic transport and signal transduction. Yet, the molecular details of lipid-protein interaction and their functional impact are poorly characterized. Here we combine NMR, coarse-grained molecular dynamics (CGMD), and functional assays to reveal classic cooperativity in the binding and subsequent activation of a bacterial inward rectifier potassium (Kir) channel by phosphatidylglycerol (PG), a common component of many membranes. Past studies of lipid activation of Kir channels focused primarily on phosphatidylinositol bisphosphate, a relatively rare signaling lipid that is tightly regulated in space and time. We use solid-state NMR to quantify the binding of unmodified 13C-PG to the K+ channel KirBac1.1 in liposomes. This specific lipid-protein interaction has a dissociation constant (Kd) of ∼7 mol percentage PG (ΧPG) with positive cooperativity (n = 3.8) and approaches saturation near 20% ΧPG. Liposomal flux assays show that K+ flux also increases with PG in a cooperative manner with an EC50 of ∼20% ΧPG, within the physiological range. Further quantitative fitting of these data reveals that PG acts as a partial (80%) agonist with fivefold K+ flux amplification. Comparisons of NMR chemical shift perturbation and CGMD simulations at different ΧPG confirm the direct interaction of PG with key residues, several of which would not be accessible to lipid headgroups in the closed state of the channel. Allosteric regulation by a common lipid is directly relevant to the activation mechanisms of several human ion channels. This study highlights the role of concentration-dependent lipid-protein interactions and tightly controlled protein allostery in the activation and regulation of ion channels.

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.

Zafirlukast Is a Promising Scaffold for Selectively Inhibiting TNFR1 Signaling

Tumor necrosis factor (TNF) plays an important role in the pathogenesis of inflammatory and autoimmune diseases such as rheumatoid arthritis and Crohn's disease. The biological effects of TNF are mediated by binding to TNF receptors, TNF receptor 1 (TNFR1), or TNF receptor 2 (TNFR2), and this coupling makes TNFR1-specific inhibition by small-molecule therapies essential to avoid deleterious side effects. Recently, we engineered a time-resolved fluorescence resonance energy transfer biosensor for high-throughput screening of small molecules that modulate TNFR1 conformational states and identified zafirlukast as a compound that inhibits receptor activation, albeit at low potency. Here, we synthesized 16 analogues of zafirlukast and tested their potency and specificity for TNFR1 signaling. Using cell-based functional assays, we identified three analogues with significantly improved efficacy and potency, each of which induces a conformational change in the receptor (as measured by fluorescence resonance energy transfer (FRET) in cells). The best analogue decreased NF-κB activation by 2.2-fold, IκBα efficiency by 3.3-fold, and relative potency by two orders of magnitude. Importantly, we showed that the analogues do not block TNF binding to TNFR1 and that binding to the receptor's extracellular domain is strongly cooperative. Despite these improvements, the best candidate's maximum inhibition of NF-κB is only 63%, leaving room for further improvements to the zafirlukast scaffold to achieve full inhibition and prove its potential as a therapeutic lead. Interestingly, while we find that the analogues also bind to TNFR2 in vitro, they do not inhibit TNFR2 function in cells or cause any conformational changes upon binding. Thus, these lead compounds should also be used as reagents to study conformational-dependent activation of TNF receptors.

Quantification of receptor binding from response data obtained at different receptor levels: a simple individual sigmoid fitting and a unified SABRE approach

Methods that allow quantification of receptor binding (occupancy) by measuring response (effect) data only are of interest as they can be used to allow characterization of binding properties (e.g., dissociation constant, K_d) without having to perform explicit ligand binding experiments that require different setups (e.g., use of labeled ligands). However, since response depends not just on the binding affinity-determined receptor occupancy, but also on receptor activation, which is affected by ligand efficacy (plus constitutive activity, if present), and downstream pathway amplification, this requires the acquisition and fitting of multiple concentration-response data. Here, two alternative methods, which both are straightforward to implement using nonlinear regression software, are described to fit such multiple responses measured at different receptor levels that can be obtained, for example, by partial irreversible receptor inactivation (i.e., Furchgott method) or different expression levels. One is a simple method via straightforward fitting of each response with sigmoid functions and estimation of K_d from the obtained E_max and EC₅₀ values as K_d = (E_max·EC'₅₀ - E'_max·EC₅₀)/(E_max - E'_max). This is less error-prone than the original Furchgott method of double-reciprocal fit and simpler than alternatives that require concentration interpolations, thus, should allow more widespread use of this so-far underutilized approach to estimate binding properties. Relative efficacies can then be compared using E_max·K_d/EC₅₀ values. The other is a complex method that uses the SABRE receptor model to obtain a unified fit of the multiple concentration-response curves with a single set of parameters that include binding affinity K_d, efficacy ε, amplification γ, and Hill coefficient n. Illustrations with simulated and experimental data are presented including with activity data of three muscarinic agonists measured in rabbit myocardium.

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.

Functional anatomy of the full-length CXCR4-CXCL12 complex systematically dissected by quantitative model-guided mutagenesis

Because of their prominent roles in development, cancer, and HIV, the chemokine receptor CXCR4 and its ligand CXCL12 have been the subject of numerous structural and functional studies, but the determinants of ligand binding, selectivity, and signaling are still poorly understood. Here, building on our latest structural model, we used a systematic mutagenesis strategy to dissect the functional anatomy of the CXCR4-CXCL12 complex. Key charge swap mutagenesis experiments provided evidence for pairwise interactions between oppositely charged residues in the receptor and chemokine, confirming the accuracy of the predicted orientation of the chemokine relative to the receptor and providing insight into ligand selectivity. Progressive deletion of N-terminal residues revealed an unexpected contribution of the receptor N terminus to chemokine signaling. This finding challenges a longstanding "two-site" hypothesis about the essential features of the receptor-chemokine interaction in which the N terminus contributes only to binding affinity. Our results suggest that although the interaction of the chemokine N terminus with the receptor-binding pocket is the key driver of signaling, the signaling amplitude depends on the extent to which the receptor N terminus binds the chemokine. Together with systematic characterization of other epitopes, these data enable us to propose an experimentally consistent structural model for how CXCL12 binds CXCR4 and initiates signal transmission through the receptor transmembrane domain.

An Advanced In Silico Modelling of the Interaction between FSCPX, an Irreversible A1 Adenosine Receptor Antagonist, and NBTI, a Nucleoside Transport Inhibitor, in the Guinea Pig Atrium

In earlier studies, we generated concentration-response (E/c) curves with CPA (N6-cyclopentyladenosine; a selective A1 adenosine receptor agonist) or adenosine, in the presence or absence of S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine (NBTI, a selective nucleoside transport inhibitor), and with or without a pretreatment with 8-cyclopentyl-N3-[3-(4-(fluorosulfonyl)-benzoyloxy)propyl]-N1-propylxanthine (FSCPX, a chemical known as a selective, irreversible A1 adenosine receptor antagonist), in isolated, paced guinea pig left atria. Meanwhile, we observed a paradoxical phenomenon, i.e. the co-treatment with FSCPX and NBTI appeared to enhance the direct negative inotropic response to adenosine. In the present in silico study, we aimed to reproduce eight of these E/c curves. Four models (and two additional variants of the last model) were constructed, each one representing a set of assumptions, in order to find the model exhibiting the best fit to the ex vivo data, and to gain insight into the paradoxical phenomenon in question. We have obtained in silico evidence for an interference between effects of FSCPX and NBTI upon our ex vivo experimental setting. Regarding the mechanism of this interference, in silico evidence has been gained for the assumption that FSCPX inhibits the effect of NBTI on the level of endogenous (but not exogenous) adenosine. As an explanation, it may be hypothesized that FSCPX inhibits an enzyme participating in the interstitial adenosine formation. In addition, our results suggest that NBTI does not stop the inward adenosine flux in the guinea pig atrium completely.

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).

Pharmacology education: Reflections and challenges

Pharmacology is one of the cornerstones in health sciences curricula as well as research-oriented biomedical programs in higher education. New educational insights and scientific developments in teaching and learning, as well as exciting discoveries in pharmacology research, must prompt pharmacology teachers to regularly rethink and adjust their teaching. Reflecting on pharmacology education, this paper touches upon some educational issues that might inspire readers of this journal who are involved in pharmacology teaching.

Design, Synthesis, and Evaluation of Novel Immunomodulatory Small Molecules Targeting the CD40⁻CD154 Costimulatory Protein-Protein Interaction

We report the design, synthesis, and testing of novel small-molecule compounds targeting the CD40⁻CD154 (CD40L) costimulatory interaction for immunomodulatory purposes. This protein-protein interaction (PPI) is a TNF-superfamily (TNFSF) costimulatory interaction that is an important therapeutic target since it plays crucial roles in the activation of T cell responses, and there is resurgent interest in its modulation with several biologics in development. However, this interaction, just as all other PPIs, is difficult to target by small molecules. Following up on our previous work, we have now identified novel compounds such as DRI-C21091 or DRI-C21095 that show activity (IC50) in the high nanomolar to low micromolar range in the binding inhibition assay and more than thirty-fold selectivity versus other TNFSF PPIs including OX40⁻OX40L, BAFFR-BAFF, and TNF-R1-TNFα. Protein thermal shift (differential scanning fluorimetry) assays indicate CD154 and not CD40 as the binding partner. Activity has also been confirmed in cell assays and in a mouse model (alloantigen-induced T cell expansion in a draining lymph node). Our results expand the chemical space of identified small-molecule CD40⁻CD154 costimulatory inhibitors and provide lead structures that have the potential to be developed as orally bioavailable immunomodulatory therapeutics that are safer and less immunogenic than corresponding biologics.

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.

Toward Small-Molecule Inhibition of Protein-Protein Interactions: General Aspects and Recent Progress in Targeting Costimulatory and Coinhibitory (Immune Checkpoint) Interactions

Protein-Protein Interactions (PPIs) that are part of the costimulatory and coinhibitory (immune checkpoint) signaling are critical for adequate T cell response and are important therapeutic targets for immunomodulation. Biologics targeting them have already achieved considerable clinical success in the treatment of autoimmune diseases or transplant recipients (e.g., abatacept, belatacept, and belimumab) as well as cancer (e.g., ipilimumab, nivolumab, pembrolizumab, atezolizumab, durvalumab, and avelumab). In view of such progress, there have been only relatively limited efforts toward developing small-molecule PPI inhibitors (SMPPIIs) targeting these cosignaling interactions, possibly because they, as all other PPIs, are difficult to target by small molecules and were not considered druggable. Nevertheless, substantial progress has been achieved during the last decade. SMPPIIs proving the feasibility of such approaches have been identified through various strategies for a number of cosignaling interactions including CD40-CD40L, OX40-OX40L, BAFFR-BAFF, CD80-CD28, and PD-1-PD-L1s. Here, after an overview of the general aspects and challenges of SMPPII-focused drug discovery, we review them briefly together with relevant structural, immune-signaling, physicochemical, and medicinal chemistry aspects. While so far only a few of these SMPPIIs have shown activity in animal models (DRI-C21045 for CD40-D40L, KR33426 for BAFFR-BAFF) or reached clinical development (RhuDex for CD80-CD28, CA-170 for PD-1-PD-L1), there is proof-of-principle evidence for the feasibility of such approaches in immunomodulation. They can result in products that are easier to develop/ manufacture and are less likely to be immunogenic or encounter postmarket safety events than corresponding biologics, and, contrary to them, can even become orally bioavailable.

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.