Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design

✅ 全文

模拟炎症环境中G蛋白偶联受体的信号传导改变以推进药物设计

作者 Arne Thies; Vikram Sunkara; Sourav Ray; Hanna Wulkow; Melih Ö. Celik; Fatih Yergöz; Christof Schütte; Christoph Stein; Marcus Weber; Stefanie Winkelmann 期刊 Scientific Reports 发表日期 2023 ISSN 2045-2322 DOI 10.1038/s41598-023-27699-w 类型原创研究 (Original Research)

📄 中文摘要 Chinese Abstract

中文

G蛋白偶联受体（GPCR）是最大的细胞膜受体家族，也是重要的药物靶点，参与多种疾病过程，包括疼痛、成瘾和炎症。μ-阿片受体（MOR）是一种关键的GPCR，介导镇痛作用，但在健康组织中激活时会引起呼吸抑制等不良反应。此前，作者开发了NFEPP，一种新型MOR激动剂，旨在选择性激活炎症组织特有的酸性环境中的受体，从而潜在地避免在健康组织（pH 7.4）中的副作用。虽然早期工作模拟了细胞外配体-受体相互作用，但本研究将分析扩展至细胞内信号通路——特别是G蛋白激活和钙通道调节——在健康和炎症条件下（不同pH和自由基浓度）的表现。

📋 英文结构化总结 English Structured Summary

全文整理

Background:

G-protein coupled receptors (GPCRs) are the largest class of cell membrane receptors and major drug targets, involved in numerous disorders including pain, addiction, and inflammation. The μ-opioid receptor (MOR) is a key GPCR that mediates analgesia but also causes adverse effects like respiratory depression when activated in healthy tissues. Previously, the authors developed NFEPP, a novel MOR agonist designed to selectively activate receptors in acidic environments typical of inflamed tissue, thereby potentially avoiding side effects in healthy tissues (pH 7.4). While earlier work modeled extracellular ligand–receptor interactions, this study extends the analysis to intracellular signaling pathways—specifically G-protein activation and calcium channel modulation—under both healthy and inflamed conditions (varying pH and radical concentrations).

Methods:

The authors developed a stochastic biochemical reaction network model encompassing the full MOR signaling cascade: ligand binding, receptor activation, G-protein dissociation into α and βγ subunits, inhibition of plasma membrane calcium channels by βγ subunits, receptor internalization, recycling, and degradation. The model includes 11 reactions with associated propensity functions and is governed by the chemical master equation. It was validated using in vitro experimental data from FRET assays measuring G-protein subunit dissociation and patch-clamp recordings of calcium currents in sensory neurons. Parameter estimation combined literature-based initial values with fitting to experimental data; ligand binding rates (k₁) were adjusted for different pH levels and ligands (NFEPP vs fentanyl), while other rate constants were assumed constant across conditions due to intracellular pH homeostasis.

Results:

Simulations showed that NFEPP exhibits markedly reduced binding affinity and calcium channel inhibition at normal physiological pH (7.4) compared to acidic pH (6.5), whereas fentanyl’s activity remains high at both pH levels. This confirms NFEPP’s pH-dependent selectivity for inflamed tissue. In the presence of reactive oxygen species (radicals), constitutive G-protein activation increased, but ligand binding affinity decreased. However, the impact of low pH on overall GPCR function was found to be more significant than that of radicals. The stochastic model revealed non-linear relationships between ligand binding rates and calcium current inhibition, explaining the differential efficacy of NFEPP versus fentanyl in pathological versus healthy environments.

Data Summary:

Key quantitative findings include: for fentanyl, k₁ = 2.5 × 10⁻² s⁻¹ at pH 7.4 and 1.25 × 10⁻² s⁻¹ at pH 6.5; for NFEPP, k₁ = 5 × 10⁻⁴ s⁻¹ at pH 7.4 and 2.5 × 10⁻³ s⁻¹ at pH 6.5—demonstrating a 50-fold difference in binding rate for NFEPP between healthy and inflamed pH. Simulations used 20 MORs and 40 G-proteins per compartment. FRET data showed significantly less G-protein dissociation with NFEPP at pH 7.4 versus other conditions. Calcium channel inhibition was substantially lower for NFEPP at pH 7.4 compared to fentanyl, aligning with its reduced side-effect profile.

Conclusions:

The study demonstrates that low extracellular pH—not radical concentration—is the dominant factor altering GPCR signaling in inflamed tissue. The stochastic model successfully captures the environment-dependent behavior of opioid ligands, showing that NFEPP’s design principle (preferential activation at acidic pH) translates into selective intracellular signaling and reduced off-target effects. These findings support the feasibility of designing pathology-activated drugs that act only at disease sites, minimizing systemic side effects.

Practical Significance:

This work advances rational drug design for safer analgesics by providing a validated computational framework to predict how GPCR-targeting drugs behave under disease-specific physiological conditions. The approach can be applied to develop other "smart" therapeutics that activate only in pathological microenvironments (e.g., tumors, inflamed joints), improving therapeutic indices and patient safety.

📋 中文结构化总结 Chinese Structured Summary

中文

背景:

方法:

作者开发了一个随机生化反应网络模型，涵盖完整的MOR信号级联：配体结合、受体激活、G蛋白解离为α和βγ亚基、βγ亚基对质膜钙通道的抑制、受体内化、再循环和降解。该模型包含11个反应及其相应的倾向函数，由化学主方程控制。使用FRET实验测量的G蛋白亚基解离数据和感觉神经元钙电流的膜钳记录数据进行体外实验验证。参数估计结合了基于文献的初始值和实验数据拟合；配体结合速率（k₁）针对不同pH水平和配体（NFEPP与芬太尼）进行调整，而其他速率常数由于细胞内pH稳态假设在不同条件下保持不变。

结果:

模拟显示，NFEPP在正常生理pH（7.4）下表现出显著降低的结合亲和力和钙通道抑制，而在酸性pH（6.5）下则较高，而芬太尼在两种pH水平下均保持高活性。这证实了NFEPP对炎症组织的pH依赖性选择性。在活性氧（自由基）存在下，组成性G蛋白激活增加，但配体结合亲和力降低。然而，低pH对整体GPCR功能的影响被发现比自由基更为显著。随机模型揭示了配体结合速率与钙电流抑制之间的非线性关系，解释了NFEPP与芬太尼在病理与健康环境中疗效差异的原因。

数据总结:

关键定量结果包括：芬太尼在pH 7.4时k₁ = 2.5 × 10⁻² s⁻¹，在pH 6.5时k₁ = 1.25 × 10⁻² s⁻¹；NFEPP在pH 7.4时k₁ = 5 × 10⁻⁴ s⁻¹，在pH 6.5时k₁ = 2.5 × 10⁻³ s⁻¹——显示NFEPP在健康与炎症pH之间的结合速率存在50倍差异。模拟使用每个区室20个MOR和40个G蛋白。FRET数据显示，在pH 7.4下NFEPP的G蛋白解离显著少于其他条件。NFEPP在pH 7.4下的钙通道抑制显著低于芬太尼，与其降低的副作用特征一致。

结论:

研究表明，低细胞外pH——而非自由基浓度——是改变炎症组织中GPCR信号传导的主导因素。随机模型成功捕获了阿片类配体的环境依赖性行为，表明NFEPP的设计原理（在酸性pH下优先激活）转化为选择性细胞内信号传导和减少的脱靶效应。这些发现支持了设计仅在疾病部位激活的病理激活药物的可行性，从而最小化全身副作用。

实际意义:

这项工作通过提供一个经过验证的计算框架来预测GPCR靶向药物在疾病特异性生理条件下的行为，推进了更安全的镇痛药的理性设计。该方法可用于开发其他仅在病理微环境（如肿瘤、炎症关节）中激活的"智能"治疗药物，提高治疗指数和患者安全性。

📖 英文全文 English Full Text

pmc Sci Rep Sci Rep 1579 scirep Scientific Reports 2045-2322 Nature Publishing Group PMC9837128 PMC9837128.1 9837128 9837128 36635362 10.1038/s41598-023-27699-w 27699 1 Article Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design Thies Arne 2 Sunkara Vikram 1 Ray Sourav 1 Wulkow Hanna 1 Celik M. Özgür 3 Yergöz Fatih 3 Schütte Christof 1 2 Stein Christoph 3 Weber Marcus 1 http://orcid.org/0000-0002-0114-7819 Winkelmann Stefanie winkelmann@zib.de 1 1 grid.425649.8 0000 0001 1010 926X Zuse Institute Berlin, 14195 Berlin, Germany 2 grid.14095.39 0000 0000 9116 4836 Institut für Mathematik und Informatik, Freie Universität Berlin, 14195 Berlin, Germany 3 grid.6363.0 0000 0001 2218 4662 Institute of Experimental Anaesthesiology, Charité Universitätsmedizin, Corporate Member of Freie Universität and Humboldt Universität Berlin, 12200 Berlin, Germany 12 1 2023 2023 13 425018 607 3 5 2022 5 1 2023 12 01 2023 14 01 2023 14 01 2023 © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. Subject terms Cell biology Computational biology and bioinformatics Drug discovery Systems biology Mathematics and computing http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft 390685689 477/19-1 Stein Christoph Collaborative research center 1114 Project C03 Zuse-Institut Berlin (4269) Open Access funding enabled and organized by Projekt DEAL. pmc-status-qastatus 0 pmc-status-live yes pmc-status-embargo no pmc-status-released yes pmc-prop-open-access yes pmc-prop-olf no pmc-prop-manuscript no pmc-prop-legally-suppressed no pmc-prop-has-pdf yes pmc-prop-has-supplement yes pmc-prop-pdf-only no pmc-prop-suppress-copyright no pmc-prop-is-real-version no pmc-prop-is-scanned-article no pmc-prop-preprint no pmc-prop-in-epmc yes pmc-license-ref CC BY issue-copyright-statement © The Author(s) 2023 Introduction The family of G-protein coupled receptors (GPCRs) represents the largest class of receptors in the human genome and some of the most common drug targets. Located on the cell membrane, they transduce extracellular signals into key physiological effects. Natural GPCR ligands include neurotransmitters, chemokines, hormones, odours or photons. GPCRs are involved in a large number of disorders, such as diabetes, high blood pressure, depression, addiction, pain, arthritis, Parkinson’s and many others 1 . A prominent member of this family is the \documentclass[12pt]{minimal}

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\begin{document}$$\mu$$\end{document} μ -opioid receptor (MOR). It binds endogenous opioid peptides (e.g. endorphins, enkephalins) as well as exogenous drugs (e.g. morphine, fentanyl), and its activation results in the modulation of intracellular G-proteins and second messengers (e.g. cAMP, ion channels). MOR plays major roles in analgesia (inhibition of pain), addiction, bowel movement, arousal, respiration and other physiological functions 2 . Recent works of our group 3 led to the development of the novel analgesic compound N -(3-fluoro-1-phenethylpiperidin-4-yl)- N -phenylpropionamide (NFEPP) which activates the MOR preferentially at acidic extracellular pH-levels, as given in injured tissues 2 . This is of utmost interest because it may preclude the adverse effects of conventional MOR agonists like fentanyl which include constipation, sedation and apnea. These adverse effects are mediated mostly in the brain and the gut, i.e. in healthy tissues (pH 7.4). Since the generation of pain can be effectively inhibited by blocking the electrical excitation of sensory neurons at the site of the injury (i.e. the origin of nociceptive stimulation), this gives rise to the hope that NFEPP might have less or even no adverse effects, which could already be corroborated in animal studies 3 – 6 . Up to now, the effects of NFEPP and fentanyl were mathematically analysed at the level of their binding rates at relevant amino acid residues accessible from the extracellular side of MOR 3 , 7 . To get a more complete picture, we herein present a model of the intracellular second messenger pathways relevant to pain and analgesia. The mechanism underlying the analgesic effect of MOR activation in nociceptive neurons is mainly due to a stabilisation or even lowering of the plasma membrane potential beneath the threshold value required to elicit an action potential 2 , 8 . This effect is mediated via intracellular inhibitory G-proteins, which dissociate into \documentclass[12pt]{minimal}

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\begin{document}$$\beta \gamma$$\end{document} β γ -subunits after formation of a receptor–ligand complex 9 . Among other actions, the \documentclass[12pt]{minimal}

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\begin{document}$$\beta \gamma$$\end{document} β γ -subunits bind to calcium channels in the plasma membrane. This leads to closure of the channels, thereby lowering the amount of positive calcium-ion influx and reducing cellular excitability 2 , 8 , 10 , 11 . In this paper, we model this pathway to analyse the in vitro effects of fentanyl and NFEPP on the number of closed membrane calcium channels and activated (i.e. dissociated) G-protein complexes at different pH-levels in cultured cells and sensory neurons to investigate basic mechanisms underlying opioid analgesia. We propose a reaction network that connects the receptor–ligand interactions to the G-protein cycle, and further to the signalling cycle of calcium channel opening and closing (see Fig. 1 for an illustration). After careful parametrization and validation of the model using Förster resonance energy transfer (FRET) data from corresponding in vitro experiments, the stochastic reaction process was simulated for different values of the receptor–ligand binding rate, comparing the mean inhibition of calcium currents resulting from these numerical simulations to additional data from in vitro patch clamp experiments. By numerical simulation of the reaction network, we observe that the binding rate has a non-linear effect onto the mean amplitude of deactivated calcium channels, which explains the different effects of NFEPP and fentanyl in inflamed versus healthy environments. It is important to note that our approach differs from others that have investigated signalling pathways from receptor to the nucleus or to intracellular second messengers (not to the plasma membrane) 12 , 13 . In contrast to those studies, we choose a stochastic approach because it delivers more information than deterministic alternatives. Aside from pH, other inflammatory mediators play important roles. For example, reactive oxygen species (radicals) can modulate the function of GPCRs 14 – 17 . In order to understand the interplay between pH and additional radicals for the signalling, we modelled different scenarios and performed in vitro experiments. In the precense of radicals, G-protein activation can be initiated in the absence of an opioid ligand (so-called constitutive G-protein activation). Motivated by this observation, we included the reaction of constitutive G-protein dissociation in our network. Altogether, the resulting model allows to study two different inflammatory conditions: influence of pH, and influence of radicals. With regard to (a), lower pH value changes the protonation state of amino acid residues and opioid ligands, and we investigate whether this affects the binding rates and subsequent modulation of calcium channels. Concerning (b), we study whether an increased concentration of radicals may have an effect on the binding affinity of ligands and/or increase the probability for constitutive G-protein dissociation. A crucial advantage of the model is that it also permits to analyse the combined effects of (1) and (2), and our results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Unlike in our previous work, we here studied these effects at the systems biology instead of molecular level: results from reaction network simulation are integrated with data from in vitro experiments in order to analyse the consequences of environment-dependent ligand binding rates onto the downstream signalling, i.e. calcium channel inhibition. Figure 1 Overview of the reaction network. Biochemical reaction network for the \documentclass[12pt]{minimal}

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\begin{document}$$\mu$$\end{document} μ -opioid receptor signalling pathway, connecting the receptor cycle to the G-protein cycle and further to the signal cycle of membrane calcium channel modulation, see “ The reaction network ” for an explanation. The focal point of this study is the analysis of the impact that the rates for ligand-induced receptor activation (blue) and for constitutive G-protein activation (orange) have onto the overall dynamics. The values of the rate constants \documentclass[12pt]{minimal}

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\begin{document}$$k_j$$\end{document} k j can be found in Table 2 . Models and methods In this section we introduce a probabilistic model for the signalling pathway from receptor activation over the G-protein cycle to the calcium channel inhibition. We explain the in vitro experiments which were performed to validate the modelling results and estimate the parameter values. Moreover, we motivate our choice of parameter values and specify the numerical approach used for solving the system. The reaction network The biochemical reaction network under consideration consists of the following reactions (see Table 1 for an overview and Fig. 1 for an illustration). A ligand L attaches to a receptor R in the membrane, resulting in a receptor–ligand complex RL (reaction \documentclass[12pt]{minimal}

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\begin{document}$${\mathcal {R}}_1$$\end{document} R 1 ). This binding process is dependent on the concentration of protons (i.e. pH) in the microenvironment of the receptor. The protonation of both the ligand and certain residues in the receptor are important determinants for receptor activation, likely due to the pH-dependent formation of hydrogen bonds and/or salt bridges between ligand and receptor 18 , 19 . This receptor–ligand complex RL activates a trimeric G-protein complex which leads to exchange of GDP by GTP and subsequent dissociation into \documentclass[12pt]{minimal}

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\begin{document}$$f_j:{\mathbb {N}}_0^{11} \rightarrow [0,\infty )$$\end{document} f j : N 0 11 → [ 0 , ∞ ) , which can be found in the right column of Table 1 . The temporal evolution of the system is described by the Markov jump process \documentclass[12pt]{minimal}

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\begin{document}$$\begin{aligned} \frac{d}{dt} p({\varvec{x}},t) = \sum _{j=1}^{11} \left[ f_j({\varvec{x}}-\varvec{\nu }_j)p({\varvec{x}}-\varvec{\nu }_j,t) - f_j({\varvec{x}})p({\varvec{x}},t) \right] . \end{aligned}$$\end{document} d dt p ( x , t ) = ∑ j = 1 11 f j ( x - ν j ) p ( x - ν j , t ) - f j ( x ) p ( x , t ) . The reaction rate equation characterising the corresponding deterministic reaction system is given by the ordinary differential equation (ODE) 2 \documentclass[12pt]{minimal}

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\begin{document}$${\varvec{C}}(t)=\frac{1}{V}{\varvec{X}}(t)$$\end{document} C ( t ) = 1 V X ( t ) , where V is the system’s volume. It is well-known that the volume-rescaled Markov jump process \documentclass[12pt]{minimal}

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\begin{document}$$V\rightarrow \infty$$\end{document} V → ∞ 22 . Stochastic vs deterministic approach The stochastic approach has several advantages over the deterministic one. At first, ODEs are an approximation assuming that the higher moments are trivially given by powers of the first moment. Stochastic modelling is exact in the sense that it takes into account all higher moments. Furthermore, the stochastic approach is closer to reality because it assumes a finite set (discrete number) of molecules, while ODEs consider concentrations and only work as approximations for large particle numbers. So the stochastic model is better suited for modelling a small compartment like an axon terminal with a small number of MORs and G-proteins. For our analysis, we will consider comparatively small numbers of molecules for all species (concretely, 20 MORs and 40 G-proteins, see Table 3 ), such that the stochastic approach is indispensable. Last but not least, a stochastic model delivers more information than ODEs. E.g., it enabled us to analyse the variances of the trajectories or the probability distribution of certain variables like the number of ligand–receptor binding events, which will be done in “ Isolated impact of pH value ”. In many situations, however, the ODE model provides a valid approximation of the rescaled first moment of the stochastic process, \documentclass[12pt]{minimal}

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\begin{document}$$k_1,\ldots ,k_{10}$$\end{document} k 1 , … , k 10 based on experimental data. Laboratory in vitro experiments In order to validate our model, we performed laboratory experiments measuring G-protein activation and membrane calcium currents in vitro. To determine initial G-protein activation (as reflected by the exchange rate of GDP for GTP), the [ \documentclass[12pt]{minimal}

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\begin{document}$$\gamma$$\end{document} γ S binding assay was used. Because these experiments require genetic alteration (by transfection) of cells, we performed these measurements in commonly used human embryonic kidney (HEK293) cells. In addition, we extracted data produced by FRET experiments 3 . These experiments measure ligand-induced G-protein subunit dissociation (which follows G-protein activation). The FRET experiments were used to fit the reaction rates. To mimic the mechanisms underlying in vivo opioid analgesia, we examined calcium currents in sensory neurons harvested from rodents using a patch-clamp protocol (see Supplementary Information for methodological details). The experimental results are shown in Figs. 2 and 5 a below, and described in more detail in “ Isolated impact of pH value ”. Figure 2 In vitro experiments: G-protein activation. Time course of ligand-induced G-protein subunit dissociation measured by FRET in HEK293 cells. FRET efficiency is depicted as percentage of initial intensities, corrected for photobleaching 3 . A higher number of dissociated G-protein subunits (stronger G-protein activation) is represented by more negative values. One can directly see that the blue “curve” (NFEPP at pH 7.4) shows lower numbers of dissociated subunits (weaker G-protein activation) compared to the other scenarios. The dashed line indicates the time point \documentclass[12pt]{minimal}

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\begin{document}$$t=20$$\end{document} t = 20 s where the ligand was added. Parameter estimation Our model includes eleven previously unknown parameters \documentclass[12pt]{minimal}

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\begin{document}$$k_1,\ldots ,k_{11}$$\end{document} k 1 , … , k 11 . The determination of appropriate values for these parameters included two main steps: a rough selection of values based on literature, followed by more precise standard parameter estimation. In Ray et al. 7 , it has been shown by means of molecular dynamics (MD) simulations that the ligand binding affinity varies for different ligands and pH values. The protonation of both the ligand and certain residues in the receptor are important determinants for receptor activation, likely due to the pH-dependent formation of hydrogen bonds and/or salt bridges between ligand and receptor 18 , 19 . We used the relative changes of the rate constant as determined in Ray et al. 7 and chose the following different values of \documentclass[12pt]{minimal}

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\begin{document}$$k_1=2.5\times 10^{-3}\,\text {s}^{-1}$$\end{document} k 1 = 2.5 × 10 - 3 s - 1 for NFEPP/pH 6.5, and \documentclass[12pt]{minimal}

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\begin{document}$$k_1=5\times 10^{-4}\,\text {s}^{-1}$$\end{document} k 1 = 5 × 10 - 4 s - 1 for NFEPP/pH 7.4. As the in vitro experiments used for the parameter estimation were performed in the absence of radicals, the rate \documentclass[12pt]{minimal}

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\begin{document}$${\mathcal {R}}_{11}$$\end{document} R 11 , was set to zero, because constitutive activation probably does not play an important role in healthy tissue. The parameters \documentclass[12pt]{minimal}

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\begin{document}$$k_2,\ldots ,k_{10}$$\end{document} k 2 , … , k 10 of the other intracellular reactions were assumed to depend only mildly (if at all) on the ligand/pH combination in the cellular environment; for each of these parameters a single value has been chosen, independent of ligand and pH. This is a reasonable assumption because we chose an intracellular pH value of 7.4 based on well-known mechanisms of cellular homeostasis: although transient (several minutes) changes of intracellular pH may occur with tissue acidosis, intracellular buffer systems and ion pumps in the plasma membrane will rapidly restore physiological pH to ensure cell viability 23 . Since most previous studies examined situations of longer-lasting inflammation (up to several days) 3 – 6 , we look at this situation, as well. Using results from Zamponi et al. 24 , we started by setting the rate constant \documentclass[12pt]{minimal}

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\begin{document}$$k_5=5\times 10^{-2}\,\text {s}^{-1}$$\end{document} k 5 = 5 × 10 - 2 s - 1 and proceeded to arrange the other values relative to it according to what is known in the literature. Comparing previous work 24 , 25 it can be deduced that \documentclass[12pt]{minimal}

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\begin{document}$$k_1$$\end{document} k 1 see text. It has been tested that, for these parameter values, the residual distance between data and stochastic model is very close to the residual distance for the ODE model. Figure 3 Experimental in vitro data and optimally fitted ODE model. Dots represent the time course of ligand-induced G-protein subunit dissociation measured by FRET in HEK293 cells. FRET values were transformed into concentration of undissociated G-proteins by a scaling factor. Lines indicate the best-fit of the ODE model to the data (using optimal parameters). For methodological details, see Spahn et al. 3 . Numerical simulations of the reaction network Simulations of the stochastic reaction network were performed using Python 3. For each combination of rate constants, 500 Monte Carlo simulations were carried out and the arithmetic mean was calculated in order to estimate the percentage of closed calcium channels plotted in Figs. 4 and 8 . The initial state numbers of receptors, G-proteins and calcium channels were chosen at a ratio of 1:2:4 (see Table 3 ). These numbers are only a rough estimate since the exact stoichiometry of binding events in relation to the number of activated second messengers is currently not fully understood at the experimental level 30 , 31 . However, these numbers should suffice to get some first impressions of the properties of the reaction network. As a time horizon for each simulation 1200 s were chosen. The results are presented in “ Results ”. In order to find the steady state of the dynamics under pure constitutive activation (i.e., ignoring the ligand-induced activation of receptors given by reaction \documentclass[12pt]{minimal}

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\begin{document}$$k_{11}$$\end{document} k 11 for constitutive G-protein activation, we determined the long-term average number a of closed calcium channels under these conditions. This long-term mean a (rounded to natural numbers) of closed calcium channels was then used to determine the initial state for the dynamics including receptor activation (see Table 3 for the results). To check for normal distribution of the mean, the 500 runs were divided into batches of 50 and the respective means then tested. Anderson–Darling test indicated normal distribution with \documentclass[12pt]{minimal}

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\begin{document}$$k_{11}=5\times 10^{-5}$$\end{document} k 11 = 5 × 10 - 5 (“ Combined impact of pH value and increased radical concentration ”). Results We already demonstrated that the reaction network model introduced in “ Models and methods ” allows to explain the time course of G-protein subunit dissociation correctly for different ligands and pH values. Based on this validation step, the model was used to analyse the impact (a) of different extracellular pH values correlating to those occurring in injured tissues in vivo 2 in combination with a conventional or a pH-dependent opioid ligand (fentanyl or NFEPP, respectively) (see “ Isolated impact of pH value ”), and (b) of radicals (see “ Combined impact of pH value and increased radical concentration ”) onto the overall signalling pathway. Based on our parameter fitting results, the changing pH value was modelled via varying the rate constant \documentclass[12pt]{minimal}

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\begin{document}$$44 \%$$\end{document} 44 % of all calcium channels), while for NFEPP/pH 7.4 the amplitude is significantly reduced to approximately \documentclass[12pt]{minimal}

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# 在炎症环境中模拟G蛋白偶联受体的信号传导改变以推进药物设计

我们先前报道了原型阿片类镇痛药NFEPP的成功设计、合成与测试，该药物不会引发不良反应。NFEPP的设计过程基于G蛋白偶联受体（GPCR）与配体之间胞外相互作用的数学建模，其核心认识是GPCR在病理条件下的功能与在健康条件下有所不同。我们现在提出了一个额外的、新颖的GPCR功能随机模型，该模型包含了G蛋白亚基的胞内解离以及质膜钙通道的调控，并考虑了这些过程对炎症组织和健康组织参数（pH值、自由基）的依赖性。该模型已针对不同pH值和自由基浓度下配体NFEPP和芬太尼的体外实验数据进行了验证。我们观察到，与较低pH值相比，NFEPP在正常pH值下的结合亲和力和钙通道抑制作用显著降低，而芬太尼的效果则相反。随着自由基浓度的增加，我们发现G蛋白的组成型激活增强，但配体结合亲和力降低。综合评估这些不同的效应，结果表明，与自由基相比，低pH值是炎症环境中整体GPCR功能的更为重要的决定因素。未来的药物设计工作应考虑这一点。

## 引言

G蛋白偶联受体（GPCR）家族是人类基因组中最大的一类受体，也是最常见的药物靶点之一。它们位于细胞膜上，将细胞外信号转导为关键的生理效应。天然的GPCR配体包括神经递质、趋化因子、激素、气味分子或光子。GPCR参与多种疾病，如糖尿病、高血压、抑郁症、成瘾、疼痛、关节炎、帕金森病等¹。该家族的一个突出成员是μ-阿片受体（MOR）。它结合内源性阿片肽（如内啡肽、脑啡肽）以及外源性药物（如吗啡、芬太尼），其激活导致胞内G蛋白和第二信使（如cAMP、离子通道）的调控。MOR在镇痛（疼痛抑制）、成瘾、肠道运动、觉醒、呼吸及其他生理功能中发挥重要作用²。

我们团队近期的工作³导致了一种新型镇痛化合物N-(3-氟-1-苯乙基哌啶-4-基)-N-苯基丙酰胺（NFEPP）的开发，该化合物优先在酸性细胞外pH水平下激活MOR，而酸性环境正是受伤组织的特征²。这一点极为重要，因为它可能避免传统MOR激动剂（如芬太尼）的不良反应，包括便秘、镇静和呼吸暂停。这些不良反应主要发生在脑和肠道中，即健康组织（pH 7.4）中。由于疼痛的产生可以通过在损伤部位（即伤害性刺激的起源处）阻断感觉神经元的电兴奋来有效抑制，因此人们寄希望于NFEPP可能具有更少甚至没有不良反应，这一点已在动物研究中得到证实³⁻⁶。

到目前为止，NFEPP和芬太尼的效应已在MOR胞外侧可及氨基酸残基的结合速率水平上进行了数学分析³,⁷。为了获得更完整的图景，我们在此呈现了与疼痛和镇痛相关的胞内第二信使通路的模型。MOR激活在伤害性神经元中产生镇痛效应的机制主要是通过稳定甚至降低膜电位至产生动作电位所需的阈值以下²,⁸。这一效应通过胞内抑制性G蛋白介导，G蛋白在受体-配体复合物形成后解离为α-和βγ-亚基⁹。其中，βγ-亚基与质膜上的钙通道结合。这导致通道关闭，从而减少钙离子的正向内流并降低细胞兴奋性²,⁸,¹⁰,¹¹。在本文中，我们对这一通路进行建模，以分析芬太元和NFEPP在不同pH水平下对培养细胞和感觉神经元中闭合膜钙通道数量和激活（即解离）G蛋白复合物体外效应，从而研究阿片类药物镇痛的基本机制。

我们提出了一个将受体-配体相互作用与G蛋白循环连接起来，并进一步与钙通道开闭信号循环连接的反应网络（见图1说明）。在用相应体外实验的Förster共振能量转移（FRET）数据对模型进行仔细参数化和验证后，针对不同受体-配体结合速率值模拟了随机反应过程，并将这些数值模拟产生的钙电流平均抑制与体外膜片钳实验的额外数据进行比较。通过对反应网络的数值模拟，我们观察到结合速率对失活钙通道平均幅度具有非线性效应，这解释了NFEPP和芬太尼在炎症环境与健康环境中效应的差异。

重要的是要注意，我们的方法不同于那些研究从受体到细胞核或到胞内第二信使（而非质膜）的信号通路的研究¹²,¹³。与这些研究不同，我们选择随机方法，因为它比确定性替代方案提供更多信息。

除pH值外，其他炎症介质也发挥重要作用。例如，活性氧（自由基）可以调节GPCR的功能¹⁴⁻¹⁷。为了理解pH值与额外自由基之间的信号传导相互作用，我们模拟了不同场景并进行了体外实验。在自由基存在下，G蛋白激活可以在没有阿片类药物配体的情况下启动（即所谓的G蛋白组成型激活）。受此观察的启发，我们在网络中加入了G蛋白组成型解离反应。

总而言之，所得到的模型允许研究两种不同的炎症条件：pH值的影响和自由基的影响。关于（a），较低的pH值会改变氨基酸残基和阿片类药物配子的质子化状态，我们研究这是否影响结合速率和随后的钙通道调控。关于（b），我们研究自由基浓度的增加是否可能影响配体的结合亲和力和/或增加G蛋白组成型解离的概率。

该模型的一个关键优势是它还允许分析（1）和（2）的综合效应，我们的结果表明，与自由基相比，低pH值是炎症环境中整体GPCR功能的更为重要的决定因素。与我们之前的工作不同，我们在这里在系统生物学而非分子水平上研究了这些效应：反应网络模拟的结果与体外实验数据相结合，以分析环境依赖性配体结合速率对下游信号传导（即钙通道抑制）的影响。

## 模型与方法

在本节中，我们介绍从受体激活到G蛋白循环再到钙通道抑制的信号通路的概率模型。我们解释了为验证建模结果和估计参数值而进行的体外实验。此外，我们论证了参数值的选择动机，并指定了用于求解系统的数值方法。

### 反应网络

所考虑的生物化学反应网络由以下反应组成（见表1概述和图1说明）。配体L与膜中的受体R结合，产生受体-配体复合物RL（反应R₁）。这一结合过程取决于受体微环境中质子（即pH值）的浓度。配体和受体中某些残基的质子化是受体激活的重要决定因素，可能是由于配体和受体之间氢键和/或盐桥的pH依赖性形成¹⁸,¹⁹。该受体-配体复合物RL激活三聚体G蛋白复合物，导致GDP被GTP交换，随后解离为α-和βγ-亚基（反应R₂）。这些亚基激活不同的信号通路。随着GTP的水解，出现另一个反应伙伴M（如抑制蛋白）（反应R₃），它启动受体-配体复合物的内化（反应R₄）。βγ-亚基通过与质膜钙通道结合来抑制它（反应R₅）（在其他论文²⁰中，这被称为将钙通道从"愿意"状态切换到"不情愿"状态）。在βγ-亚基从钙通道解离后，三聚体G蛋白复合物重新形成，钙通道打开（反应R₆）。内化的受体RL_w要么被循环回细胞膜（反应R₇），要么被降解（反应R₈）。反应伙伴M本身可以被降解（反应R₉）。配体L在与受体结合之前可能消失，例如通过与其它细胞外成分的非特异性结合或被降解（反应R₁₀），或者在胞内被降解（反应R₇和R₈）。G蛋白的组成型激活由反应R₁₁给出，我们简单地使用没有配体的R₂。也就是说，我们将组成型结合反应建模为一个净反应，首先进行GTP和GDP的交换，然后βγ-亚基从GPCR复合物上解离。

### 随机方法与确定性方法的比较

随机方法比确定性方法有几个优势。首先，常微分方程（ODE）是一个近似，假设高阶矩由第一矩的幂简单给出。随机建模是精确的，因为它考虑了所有高阶矩。此外，随机方法更接近现实，因为它假设有限集合（离散数量）的分子，而ODE考虑浓度，仅在大粒子数时才作为近似有效。因此，随机模型更适合模拟像轴突末端这样具有少量MOR和G蛋白的小区室。对于我们的分析，我们将考虑所有物种相对较少的分子数量（具体而言，20个MOR和40个G蛋白，见表3），因此随机方法是不可或缺的。最后但同样重要的是，随机模型比ODE提供更多信息。例如，它使我们能够分析轨迹的方差或某些变量的概率分布，如配体-受体结合事件的数量，这将在"pH值的孤立影响"一节中完成。然而，在许多情况下，ODE模型提供了随机过程的重新缩放一阶矩C(t)≈E(X(t))/V的有效近似，这里也是如此。这一事实将在"参数估计"一节中被利用，其中将使用较简单的ODE模型而非随机模型来基于实验数据估计反应速率k₁,…,k₁₀。

### 实验室体外实验

为了验证我们的模型，我们进行了体外实验，测量G蛋白激活和膜钙电流。为了确定初始G蛋白激活（反映为GDP被GTP的交换速率），使用了[³⁵S]-GTPγS结合实验。由于这些实验需要细胞的基因改造（通过转染），我们在常用的人胚胎肾（HEK293）细胞中进行了这些测量。此外，我们提取了FRET实验产生的数据³。这些实验测量配体诱导的G蛋白亚基解离（在G蛋白激活之后）。FRET实验用于拟合反应速率。为了模拟体内阿片类药物镇痛的机制，我们使用膜片钳方案检查了从啮齿动物提取的感觉神经元中的钙电流（方法学细节见补充信息）。实验结果如图2和5a所示，并在"pH值的孤立影响"一节中更详细地描述。

### 参数估计

我们的模型包括十一个先前未知的参数k₁,…,k₁₁。确定这些参数的适当值包括两个主要步骤：基于文献粗略选择值，然后进行更精确的参数估计。

在Ray等人⁷中，已经通过分子动力学（MD）模拟表明，不同配体和pH值的配体结合亲和力各不相同。配体和受体中某些残基的质子化是受体激活的重要决定因素，可能是由于配体和受体之间氢键和/或盐桥的pH依赖性形成¹⁸,¹⁹。我们使用了Ray等人⁷中确定的速率常数的相对变化，并为不同配体/pH组合选择以下不同的k₁值：芬太尼/pH 6.5时k₁=1.25×10⁻² s⁻¹，芬太尼/pH 7.4时k₁=2.5×10⁻² s⁻¹，NFEPP/pH 6.5时k₁=2.5×10⁻³ s⁻¹，NFEPP/pH 7.4时k₁=5×10⁻⁴ s⁻¹。

由于用于参数估计的体外实验在无自由基条件下进行，负责组成型G蛋白激活R₁₁的速率k₁₁被设为零，因为组成型激活在健康组织中可能不起重要作用。

假设其它胞内反应的参数k₂,…,k₁₀仅轻微（如果有的话）依赖于细胞环境中的配体/pH组合；为每个参数选择单一值，与配体和pH无关。这是一个合理的假设，因为我们基于众所周知的细胞稳态机制选择了7.4的胞内pH值：尽管组织酸中毒可能发生短暂的（数分钟）胞内pH变化，但胞内缓冲系统和质膜中的离子泵将迅速恢复生理pH以确保细胞活力²³。由于大多数先前研究检查了持续时间更长的炎症状态（长达数天）³⁻⁶，我们也考察了这种情况。

使用Zamponi等人²⁴的结果，我们首先将βγ-亚基与钙通道之间中心结合反应的速率常数k₅设为5×10⁻² s⁻¹，然后根据文献中已知的知识相对于它排列其它值。比较先前的工作²⁴,²⁵，可以推断R₅的时间尺度比R₂和R₃短一个数量级（R₂略快于R₃），因此我们选择k₂和k₅分别为k₅的五分之一和十分之一。假设反应R₄、R₆、R₉的速率常数与R₂和R₃的速率常数具有相同的数量级（R₆略快）。内化配体-受体复合物的循环和降解要慢得多，在分钟级别（Williams等人²⁶中的图1），这导致内化受体R₇和R₈反应的速率常数k₇和k₈相对较小。由于非特异性结合和其它事件导致的配体胞外衰变（反应R₁₀）被设定为在钙通道抑制上显示出第一效应的值。

在基于可用信息完成粗略参数值选择这一初始步骤后，我们使用体外实验FRET数据（见下文图2）通过标准参数估计技术微调了参数k₁,…,k₁₀，该数据由四种情况的G蛋白激活的四个单独时间序列组成：芬太尼/pH 6.5、芬太尼/pH 7.4、NFEPP/pH 6.5和NFEPP/pH 7.4。

实验数据首先通过确定偏移时间（添加相应配体的时间点）和将模型中未解离G蛋白的数量映射到测量FRET信号的线性缩放变换进行预处理。然后，通过最优地调整参数k₂,…,k₁₀，最小化ODE模型解与实验数据之间的残差距离，从先前选择的初始值开始（表2第二列"预选"）。这里，残差是ODE解与数据之间的均方距离的总和，对所有四个时间序列求和。最小化是在软件PREDICI²⁹的框架内使用标准参数估计技术²⁷,²⁸完成的。

所得参数值如表2第三列"参数估计"所示。这些k₂,…,k₁₀的值，一次性对所有四种配体/pH组合进行了最优调整，被固定。在最后一步中，针对每种配体/pH组合，通过最小化每个单一时间序列的残差函数（固定k₂,…,k₁₀），微调参数k₁。

一些最优参数值与预选值存在轻微偏差，但与文献没有观察到强烈对比；事实上，更仔细的检查显示，基于模型的模拟与实验之间的均方偏差通过微调参数显著减少。得到的最佳拟合如图3所示。

### 反应网络的数值模拟

随机反应网络的模拟使用Python 3进行。对于每种速率常数组合，进行了500次蒙特卡洛模拟，并计算算术平均值，以估计图4和8中绘制的闭合钙通道百分比。受体、G蛋白和钙通道的初始状态数量选择为1:2:4的比例（见表3）。这些数字只是一个粗略估计，因为结合事件相对于激活第二信使数量的确切化学计量目前在实验水平上尚未完全理解³⁰,³¹。然而，这些数字应该足以获得反应网络特性的第一印象。每次模拟选择1200秒的时间范围。结果在"结果"一节中呈现。

为了找到纯组成型激活下动力学的稳态（即忽略由反应R₁给出的受体配体诱导激活），进行了没有配体的模拟（或等价地，k₁=0）。给定组成型G蛋白激活的非零速率常数k₁₁，我们确定了这些条件下闭合钙通道的长期平均数量a。然后使用该闭合钙通道的长期均值a（四舍五入为自然数）来确定包括受体激活的动力学的初始状态（见表3结果）。

为了检查均值的正态分布，将500次运行分成50批，然后检验各自的均值。Anderson-Darling检验以P≤0.05指示正态分布，因此图中显示了t分布的95%置信区间。

## 结果

我们已经证明，"模型与方法"一节中引入的反应网络模型能够正确解释不同配体和pH值下G蛋白亚基解离的时间进程。基于这一验证步骤，该模型被用于分析（a）与体内受伤组织中发生的不同细胞外pH值结合常规或pH依赖性阿片类药物配体（芬太尼或NFEPP）的影响（见"pH值的孤立影响"），以及（b）自由基对整个信号通路的影响（见"pH值与增加的自由基浓度的综合影响"）。

根据我们的参数拟合结果，变化的pH值通过改变配体-受体结合的速率常数k₁来建模。另一方面，假设额外的自由基降低阿片类药物的结合速率k₁，同时增加组成型激活的速率k₁₁ ¹⁷,³²。

### pH值的孤立影响

对于以下分析，我们将速率常数k₁₁设为零。我们的目标是分析受体配体诱导激活的变化速率k₁>0（由结合反应R₁: L+R→RL给出）对闭合钙通道Ca_off数量的影响。我们检查了配体芬太尼和NFEPP与变化的pH水平的组合（见方程(3)中各自的速率值k₁）。所有反应网络模拟中其它反应的速率保持不变，基于胞内pH保持在7.4的假设（见表2）。

图4a表示不同配体结合速率k₁下闭合钙通道平均数量的演变。对于除NFEPP/pH 7.4之外的所有配体和pH对，我们观察到闭合钙通道的幅度相似（约所有钙通道的44%），而对于NFEPP/pH 7.4，幅度显著降低至约29%（但请注意，在总共80个通道中最多只能关闭40个，因为只有40个G蛋白，因此最大钙通道抑制为50%）。在图4b中，显示了闭合钙通道数量随时间的方差。我们可以观察到，NFEPP在正常pH值下的方差显著大于所有其它场景。这些信息将用于支持以下结论：钙通道抑制的降低不是由于轨迹的均匀下降。

### 体外实验结果

通过膜片钳实验测量了芬太尼或NFEPP在pH 6.5和pH 7.4下对大鼠感觉神经元中电压诱导钙电流的最大抑制。结果与图4a中模拟的场景相当，在低pH下芬太尼和NFEPP都有效抑制钙电流，而在正常pH下NFEPP的效果显著低于芬太尼（图5a）。图2显示了用于数据拟合的实验。

### 非线性行为和随机效应

鉴于我们的模型与体外结果非常吻合，我们现在寻求获得关于钙通道抑制幅度与结合速率k₁之间依赖性的更多信息。因此我们将两者相互绘制；结果如图5b所示。我们看到钙通道抑制幅度的非线性行为，在k₁<2×10⁻³ s⁻¹时急剧下降，钙通道响应迅速下降。

为了研究随机效应，我们计算了在模拟运行的时间间隔[0,1200 s]内配体与受体之间结合事件数量的概率分布（见图6）。随着k₁的降低（见相应配体/pH对的方程(3)），分布向较低值移动并获得更宽的范围。非线性也体现在从(c)到(d)的移动与其它移动相比更大。

### pH值与增加的自由基浓度的综合影响

我们接下来研究了变化pH值与上升自由基水平相结合对信号传导的影响。

#### 体外实验结果

活性氧可以通过向样品中添加H₂O₂在体外实验中产生（见补充信息）。我们的实验数据支持增加的自由基（H₂O₂）浓度与增加的G蛋白组成型激活相关，见图7。这意味着我们可以通过改变随机模型中组成型激活的速率k₁₁来包括自由基的可能影响。

根据文献，增加的自由基浓度促进受体中二硫键（DSB）的形成¹⁴,³³。假设我们体外实验中观察到的组成型激活源于DSB形成，因为添加二硫苏糖醇（DTT）——一种破坏DSB的还原剂——逆转了最高浓度（1 mM）H₂O₂对基础G蛋白激活的效应（图7）。更多最近的报告进一步支持DSB形成影响GPCR的功能¹⁵,¹⁶，并且有证据表明MOR的组成型活性与半胱氨酸残基的可及性增强相关³⁴（这对DSB形成至关重要）。

自由基形成DSB也被其它研究小组研究过，考虑了对GPCR配体激活的影响（在我们的模型中指结合速率k₁）。例如，Zhang等人³²描述了去除MOR胞外部分DSB后配体结合降低。Wheatley等人¹⁷的综述文章提到，在打破胞外DSB后，CXC趋化因子受体4的激动剂亲和力降低，血管紧张素II 1型受体的组成型活性增加。在文献中提到的所有例子中，由于原始DSB构型的变化导致的受体结构变化降低了特异性设计配体的结合亲和力。

关于我们的模型，这些结果表明，在研究包括增加的自由基浓度的炎症组织时，应降低配体激活速率k₁的值。

#### 相应改变随机模型

随着炎症的进展，现在对k₁有两个影响，一个来自pH值，一个来自自由基。为了分析综合效应，考虑到额外DSB形成的影响，方程(3)中给出的k₁值在炎症场景（pH 6.5，额外自由基）中降低至80%。具体值见表4。

至于组成型激活，我们的体外实验表明，我们可以通过增加相应的速率常数k₁₁来包括额外自由基的影响。包含自由基场景的现有实验数据不允许直接参数估计k₁₁。我们在存在自由基的情况下选择值k₁₁=5×10⁻⁵，在健康组织场景中诱导大约5个闭合钙通道的基础水平，与其它模型参数值相比，这似乎是一个合理的值。在没有自由基的场景中，我们如前所述设k₁₁=0。