Activation of store-operated calcium entry in airway smooth muscle cells: insight from a mathematical model

A dynamical model of TGF-β activation in asthmatic airways

Excessive activation of the regulatory cytokine transforming growth factor $\beta $ (TGF-$\beta $) via contraction of airway smooth muscle (ASM) is associated with the development of asthma. In this study, we develop an ordinary differential equation model that describes the change in density of the key airway wall constituents, ASM and extracellular matrix (ECM), and their interplay with subcellular signalling pathways leading to the activation of TGF-$\beta $. We identify bistable parameter regimes where there are two positive steady states, corresponding to either reduced or elevated TGF-$\beta $ concentration, with the latter leading additionally to increased ASM and ECM density. We associate the former with a healthy homeostatic state and the latter with a diseased (asthmatic) state. We demonstrate that external stimuli, inducing TGF-$\beta $ activation via ASM contraction (mimicking an asthmatic exacerbation), can perturb the system irreversibly from the healthy state to the diseased one. We show that the properties of the stimuli, such as their frequency or strength, and the clearance of surplus active TGF-$\beta $, are important in determining the long-term dynamics and the development of disease. Finally, we demonstrate the utility of this model in investigating temporal responses to bronchial thermoplasty, a therapeutic intervention in which ASM is ablated by applying thermal energy to the airway wall. The model predicts the parameter-dependent threshold damage required to obtain irreversible reduction in ASM content, suggesting that certain asthma phenotypes are more likely to benefit from this intervention.

Inherent differences of small airway contraction and Ca2+ oscillations in airway smooth muscle cells between BALB/c and C57BL/6 mouse strains

BALB/c and C57BL/6 mouse strains are widely used as animal model in studies of respiratory diseases, such as asthma. Asthma is characterized by airway hyperresponsiveness, which is eventually resulted from the excessive airway smooth muscle (ASM) contraction mediated by Ca²⁺ oscillations in ASM cells. It is reported that BALB/c mice have inherently higher airway responsiveness, but show no different contractive response of tracheal ring as compared to C57BL/6 mice. However, whether the different airway responsiveness is due to the different extents of small airway contraction, and what's underlying mechanism remains unknown. Here, we assess agonist-induced small airway contraction and Ca²⁺ oscillations in ASM cells between BALB/c and C57BL/6 mice by using precision-cut lung slices (PCLS). We found that BALB/c mice showed an intrinsically stronger extent of small airway narrowing and faster Ca²⁺ oscillations in ASM cells in response to agonists. These differences were associated with a higher magnitude of Ca²⁺ influx via store-operated Ca²⁺ entry (SOCE), as a result of increased expression of SOCE components (STIM1, Orai1) in the ASM cells of small airway of BALB/c mice. An established mathematical model and experimental results suggested that the increased SOC current could result in increased agonist-induced Ca²⁺ oscillations. Therefore, the inherently higher SOC underlies the increased Ca²⁺ oscillation frequency in ASM cells and stronger small airway contraction in BALB/c mice, thus higher airway responsiveness in BALB/c than C57BL/6 mouse strain.

Exercise Reduces Airway Smooth Muscle Contraction in Asthmatic Rats via Inhibition of IL-4 Secretion and Store-Operated Ca2+ Entry Pathway

PURPOSE

Increased evidence has shown that aerobic exercise reduces airway hyperresponsiveness in asthmatic individuals. However, the underlying mechanisms of action remain elusive. This study aimed to investigate the effect of exercise on airway smooth muscle (ASM) contractile function in asthmatic rats, and uncover the possible involvement of interleukin 4 (IL-4) and the store-operated Ca²⁺ entry (SOCE) pathway.

METHODS

In this study, chicken ovalbumin was used to induce asthma in male Sprague-Dawley rats. The exercise group received moderate-intensity aerobic exercise training for 4 weeks. IL-4 concentrations in bronchoalveolar lavage fluid (BALF) samples were evaluated by enzyme linked immunosorbent assay. The contractile function of the ASM was investigated using tracheal ring tension experiments and intracellular Ca²⁺ imaging techniques. Western blot analysis was used to evaluate expression levels of calcium-release activated calcium (CRAC) channel protein (Orai) and stromal interaction molecule 1 (STIM1) in ASM.

RESULTS

Our data showed that the carbachol-stimulated, SOCE-mediated contraction of rat ASM was significantly increased in asthmatic rats, which could be abolished by exercise. Pharmacological studies revealed that GSK5498A and BTP-2, selective blockers of CRAC channels significantly inhibited SOCE-induced ASM contraction. In addition, exercise inhibited the up-regulation of IL-4 in BALF as well as STIM1 and Orai expression in the ASM of asthmatic rats. In line with these observations, we demonstrated that pretreatment of the ASM with IL-4 up-regulated the expression level of STIM1, Orai1 and Orai2, thereby promoting SOCE-mediated ASM contraction.

CONCLUSIONS

The data in this study reveal that aerobic exercise may improve the ASM contractile function in asthmatic rats by inhibiting IL-4 secretion and by down-regulating the expression of STIM1, Orai1 and Orai2, thus decreasing excessive SOCE-mediated ASM contraction in asthmatic rats.

Characterizing spontaneous Ca2+ local transients in OPCs using computational modeling

Spontaneous Ca2+ local transients (SCaLTs) in isolated oligodendrocyte precursor cells are largely regulated by the following fluxes: store-operated Ca2+ entry (SOCE), Na+/Ca2+ exchange, Ca2+ pumping through Ca2+-ATPases, and Ca2+-induced Ca2+-release through ryanodine receptors and inositol-trisphosphate receptors. However, the relative contributions of these fluxes in mediating fast spiking and the slow baseline oscillations seen in SCaLTs remain incompletely understood. Here, we developed a stochastic spatiotemporal computational model to simulate SCaLTs in a homogeneous medium with ionic flow between the extracellular, cytoplasmic, and endoplasmic-reticulum compartments. By simulating the model and plotting both the histograms of SCaLTs obtained experimentally and from the model as well as the standard deviation of inter-SCaLT intervals against inter-SCaLT interval averages of multiple model and experimental realizations, we revealed the following: (1) SCaLTs exhibit very similar characteristics between the two data sets, (2) they are mostly random, (3) they encode information in their frequency, and (4) their slow baseline oscillations could be due to the stochastic slow clustering of inositol-trisphosphate receptors (modeled as an Ornstein-Uhlenbeck noise process). Bifurcation analysis of a deterministic temporal version of the model showed that the contribution of fluxes to SCaLTs depends on the parameter regime and that the combination of excitability, stochasticity, and mixed-mode oscillations are responsible for irregular spiking and doublets in SCaLTs. Additionally, our results demonstrated that blocking each flux reduces SCaLTs' frequency and that the reverse (forward) mode of Na+/Ca2+ exchange decreases (increases) SCaLTs. Taken together, these results provide a quantitative framework for SCaLT formation in oligodendrocyte precursor cells.

Mathematical Analysis of Membrane Transporters Dynamics: A Calcium Fluxes Case Study

A tight control of intracellular [Ca[Formula: see text]] is essential for the survival and normal function of cells. In this study we investigate key mechanistic steps by which calcium is regulated and calcium oscillations could occur using in silico modeling of membrane transporters. To do so we give a deterministic description of intracellular Ca[Formula: see text] dynamics using nonlinear dynamics in order to understand Ca[Formula: see text] signaling. We first present the ordinary differential equations (ODEs) system for cell calcium kinetics and make a preliminary work on Sobol indices. We then describe and analyze complex transporters action. Besides, we analyze the whole system. We finally perform numerical simulations and compare our results to real data.

A mathematical model to quantify RYR Ca2+ leak and associated heat production in resting human skeletal muscle fibers

Cycling of Ca2+ between the sarcoplasmic reticulum (SR) and myoplasm is an important component of skeletal muscle resting metabolism. As part of this cycle, Ca2+ leaks from the SR into the myoplasm and is pumped back into the SR using ATP, which leads to the consumption of O2 and generation of heat. Ca2+ may leak through release channels or ryanodine receptors (RYRs). RYR Ca2+ leak can be monitored in a skinned fiber preparation in which leaked Ca2+ is pumped into the t-system and measured with a fluorescent dye. However, accurate quantification faces a number of hurdles. To overcome them, we developed a mathematical model of Ca2+ movement in these preparations. The model incorporated Ca2+ pumps that move Ca2+ from the myoplasm to the SR and from the junctional space (JS) to the t-system, Ca2+ buffering by EGTA in the JS and myoplasm and by buffers in the SR, and Ca2+ leaks from the SR into the JS and myoplasm and from the t-system into the myoplasm. The model accurately simulated Ca2+ uptake into the t-system, the relationship between myoplasmic [Ca2+] and steady-state t-system [Ca2+], and the effect of blocking RYR Ca2+ leak on t-system Ca2+ uptake. The magnitude of the leak through the RYRs would contribute ∼5% of the resting heat production of human muscle. In normal resting fibers, RYR Ca2+ leak makes a small contribution to resting metabolism. RYR-focused pathologies have the potential to increase RYR Ca2+ leak and the RYR leak component of resting metabolism.

High-affinity P2Y2 and low-affinity P2X7 receptor interaction modulates ATP-mediated calcium signaling in murine osteoblasts

The P2 purinergic receptor family implicated in many physiological processes, including neurotransmission, mechanical adaptation and inflammation, consists of ATP-gated non-specific cation channels P2XRs and G-protein coupled receptors P2YRs. Different cells, including bone forming osteoblasts, express multiple P2 receptors; however, how P2X and P2Y receptors interact in generating cellular responses to various doses of [ATP] remains poorly understood. Using primary bone marrow and compact bone derived osteoblasts and BMP2-expressing C2C12 osteoblastic cells, we demonstrated conserved features in the P2-mediated Ca2+ responses to ATP, including a transition of Ca2+ response signatures from transient at low [ATP] to oscillatory at moderate [ATP], and back to transient at high [ATP], and a non-monotonic changes in the response magnitudes which exhibited two troughs at 10-4 and 10-2 M [ATP]. We identified P2Y2 and P2X7 receptors as predominantly contributing to these responses and constructed a mathematical model of P2Y2R-induced inositol trisphosphate (IP3) mediated Ca2+ release coupled to a Markov model of P2X7R dynamics to study this system. Model predictions were validated using parental and CRISPR/Cas9-generated P2Y2 and P2Y7 knockouts in osteoblastic C2C12-BMP cells. Activation of P2Y2 by progressively increasing [ATP] induced a transition from transient to oscillatory to transient Ca2+ responses due to the biphasic nature of IP3Rs and the interaction of SERCA pumps with IP3Rs. At high [ATP], activation of P2X7R modulated the response magnitudes through an interplay between the biphasic nature of IP3Rs and the desensitization kinetics of P2X7Rs. Moreover, we found that P2Y2 activity may alter the kinetics of P2X7 towards favouring naïve state activation. Finally, we demonstrated the functional consequences of lacking P2Y2 or P2X7 in osteoblast mechanotransduction. This study thus provides important insights into the biophysical mechanisms underlying ATP-dependent Ca2+ response signatures, which are important in mediating bone mechanoadaptation.

Three-Dimensional Model of Sub-Plasmalemmal Ca2+ Microdomains Evoked by the Interplay Between ORAI1 and InsP3 Receptors

Ca²⁺ signaling plays an essential role in T cell activation, which is a key step to start an adaptive immune response. During the transition from a quiescent to a fully activated state, Ca²⁺ microdomains characterized by reduced spatial and temporal extents are observed in the junctions between the plasma membrane (PM) and the endoplasmic reticulum (ER). Such Ca²⁺ responses can also occur in response to T cell adhesion to other cells or extracellular matrix proteins in otherwise unstimulated T cells. These non-TCR/CD3-dependent Ca²⁺ microdomains rely on d-myo-inositol 1,4,5-trisphosphate (IP₃) signaling and subsequent store operated Ca²⁺ entry (SOCE) via the ORAI/STIM system. The detailed molecular mechanism of adhesion-dependent Ca²⁺ microdomain formation remains to be fully elucidated. We used mathematical modeling to investigate the spatiotemporal characteristics of T cell Ca²⁺ microdomains and their molecular regulators. We developed a reaction-diffusion model using COMSOL Multiphysics to describe the evolution of cytosolic and ER Ca²⁺ concentrations in a three-dimensional ER-PM junction. Equations are based on a previously proposed realistic description of the junction, which is extended to take into account IP₃ receptors (IP₃R) that are located next to the junction. The first model only considered the ORAI channels and the SERCA pumps. Taking into account the existence of preformed clusters of ORAI1 and STIM2, ORAI1 slightly opens in conditions of a full ER. These simulated Ca²⁺ microdomains are too small as compared to those observed in unstimulated T cells. When considering the opening of the IP₃Rs located near the junction, the local depletion of ER Ca²⁺ allows for larger Ca²⁺ fluxes through the ORAI1 channels and hence larger local Ca²⁺ concentrations. Computational results moreover show that Ca²⁺ diffusion in the ER has a major impact on the Ca²⁺ changes in the junction, by affecting the local Ca²⁺ gradients in the sub-PM ER. Besides pointing out the likely involvement of the spontaneous openings of IP₃Rs in the activation of SOCE in conditions of T cell adhesion prior to full activation, the model provides a tool to investigate how Ca²⁺ microdomains extent and interact in response to T cell receptor activation.

Understanding doxorubicin associated calcium remodeling during triple-negative breast cancer treatment: an in silico study

Aim:

Triple-negative breast cancer (TNBC) is the most malignant subtype of breast cancer with high heterogeneity, rapid progression, and paucity of treatment options. The most effective chemotherapeutic drug used to treat TNBC is doxorubicin (Doxo) which is an anthracycline antibiotic. However, Doxo treatment alters cytosolic calcium dynamics leading to drug-resistance condition. The aim of this study is to capture the alterations in the activity of various calcium channels and pumps during Doxo treatment and their consequences on cytosolic calcium dynamics that ultimately result in drug resistance.

Methods:

In the present study, a mathematical model is proposed to capture the complex dynamical landscape of intracellular calcium during Doxo treatment. This study provides an insight into Doxo remodeling of calcium dynamics and associated drug-resistance effect. The model was first analyzed analytically and then explored through numerical simulation using techniques like global sensitivity analysis, parameter recalibration, etc.

Results:

The model is used to predict the potential combination therapy for Doxo that can overcome Doxo associated drug resistance. The results show targeting the dysregulated Ca²⁺ channels and pumps might provide efficient chemotherapy in TNBC. It was also observed that the indispensability of calcium influx rate is paramount in the Doxo drug resistance. Finally, three drugs were identified from existing literature that could be used as a combination therapy along with Doxo.

Conclusions:

The investigation highlights the importance of integrating the calcium signaling of various calcium regulating compounds for their effective anti-tumor effects deliverance along with chemotherapeutic agents. The results from this study might provide a new direction to the experimental biologists to explore different combination therapies with Doxo to enhance its anti-tumor effect.

Reciprocal Correlations of Inflammatory and Calcium Signaling in Asthma Pathogenesis

Asthma is a chronic disease characterized by airway hyperresponsiveness, which can be caused by exposure to an allergen, spasmogen, or be induced by exercise. Despite its prevalence, the exact mechanisms by which the airway becomes hyperresponsive in asthma are not fully understood. There is evidence that myosin light-chain kinase is overexpressed, with a concomitant downregulation of myosin light-chain phosphatase in the airway smooth muscle, leading to sustained contraction. Additionally, the sarco/endoplasmic reticulum ATPase may be affected by inflammatory cytokines, such as IL-4, IL-5, IL-13, and TNF-α, which are all associated with asthmatic airway inflammation. IL-13 and TNF-α seem to promote sodium/calcium exchanger 1 overexpression as well. Anyhow, the exact mechanisms beyond these dysregulations need to be clarified. Of note, multiple studies show an association between asthma and the ORMLD3 gene, opening new perspectives to future potential gene therapies. Currently, several treatments are available for asthma, although many of them have systemic side effects, or are not effective in patients with severe asthma. Furthering our knowledge on the molecular and pathophysiological mechanisms of asthma plays a pivotal role for the development of new and more targeted treatments for patients who cannot totally benefit from the current therapies.

Cell shape regulates subcellular organelle location to control early Ca2+ signal dynamics in vascular smooth muscle cells

The shape of the cell is connected to its function; however, we do not fully understand underlying mechanisms by which global shape regulates a cell's functional capabilities. Using theory, experiments and simulation, we investigated how physiologically relevant cell shape changes affect subcellular organization, and consequently intracellular signaling, to control information flow needed for phenotypic function. Vascular smooth muscle cells going from a proliferative and motile circular shape to a contractile fusiform shape show changes in the location of the sarcoplasmic reticulum, inter-organelle distances, and differential distribution of receptors in the plasma membrane. These factors together lead to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca2+ dynamics in the cytoplasm, and the nucleus resulting in phenotypic changes, as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell shape affects subcellular organization to modulate signaling that enables phenotypic changes.

A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes

Multiple cellular organelles tightly orchestrate intracellular calcium (Ca²⁺) dynamics to regulate cellular activities and maintain homeostasis. The interplay between the endoplasmic reticulum (ER), a major store of intracellular Ca²⁺, and mitochondria, an important source of adenosine triphosphate (ATP), has been the subject of much research, as their dysfunction has been linked with metabolic diseases. Interestingly, throughout the cell’s cytosolic domain, these two organelles share common microdomains called mitochondria-associated ER membranes (MAMs), where their membranes are in close apposition. The role of MAMs is critical for intracellular Ca²⁺ dynamics as they provide hubs for direct Ca²⁺ exchange between the organelles. A recent experimental study reported correlation between obesity and MAM formation in mouse liver cells, and obesity-related cellular changes that are closely associated with the regulation of Ca²⁺ dynamics. We constructed a mathematical model to study the effects of MAM Ca²⁺ dynamics on global Ca²⁺ activities. Through a series of model simulations, we investigated cellular mechanisms underlying the altered Ca²⁺ dynamics in the cells under obesity. We predict that, as the dosage of stimulus gradually increases, liver cells from obese mice will reach the state of saturated cytosolic Ca²⁺ concentration at a lower stimulus concentration, compared to cells from healthy mice.

It is well known that intracellular Ca²⁺ oscillations carry encoded signals in their amplitude and frequency to regulate various cellular processes, and accumulating evidence supports the importance of the interplay between the ER and mitochondria in cellular Ca²⁺ homeostasis. Miscommunications between the organelles may be involved in the development of metabolic diseases. Based on a recent experimental study that spotlighted a correlation between obesity and physical interactions of the ER and mitochondria in mouse hepatic cells, we constructed a mathematical model as a tool to probe the effects of the cellular changes linked with obesity on global cellular Ca²⁺ dynamics. Our model successfully reproduced the experimental study that observed a positive correlation between an increase in ER-mitochondrial junctions and the magnitude of mitochondrial Ca²⁺ responses. We postulate that hepatic cells from lean animals exhibit Ca²⁺ oscillations that are more robust under higher concentrations of stimulus, compared to cells from obese animals.

A mathematical and computational model of the calcium dynamics in Caenorhabditis elegans ASH sensory neuron

We propose a mathematical and computational model that captures the stimulus-generated Ca²⁺ transients in the C. elegans ASH sensory neuron. The rationale is to develop a tool that will enable a cross-talk between modeling and experiments, using modeling results to guide targeted experimental efforts. The model is built based on biophysical events and molecular cascades known to unfold as part of neurons' Ca²⁺ homeostasis mechanism, as well as on Ca²⁺ signaling events. The state of ion channels is described by their probability of being activated or inactivated, and the remaining molecular states are based on biochemically defined kinetic equations or known biochemical motifs. We estimate the parameters of the model using experimental data of hyperosmotic stimulus-evoked Ca²⁺ transients detected with a FRET sensor in young and aged worms, unstressed and exposed to oxidative stress. We use a hybrid optimization method composed of a multi-objective genetic algorithm and nonlinear least-squares to estimate the model parameters. We first obtain the model parameters for young unstressed worms. Next, we use these values of the parameters as a starting point to identify the model parameters for stressed and aged worms. We show that the model, in combination with experimental data, corroborates literature results. In addition, we demonstrate that our model can be used to predict ASH response to complex combinations of stimulation pulses. The proposed model includes for the first time the ASH Ca²⁺ dynamics observed during both "on" and "off" responses. This mathematical and computational effort is the first to propose a dynamic model of the Ca²⁺ transients' mechanism in C. elegans neurons, based on biochemical pathways of the cell's Ca²⁺ homeostasis machinery. We believe that the proposed model can be used to further elucidate the Ca²⁺ dynamics of a key C. elegans neuron, to guide future experiments on C. elegans neurobiology, and to pave the way for the development of more mathematical models for neuronal Ca²⁺ dynamics.

Orosomucoid-like 3 (ORMDL3) upregulates airway smooth muscle proliferation, contraction, and Ca2+ oscillations in asthma

BACKGROUND

Airway hyperresponsiveness is a major feature of asthma attributed predominantly to an extrinsic immune/inflammatory response increasing airway smooth muscle (ASM) contractility.

OBJECTIVE

We investigated whether increased ASM expression of orosomucoid-like 3 (ORMDL3), a gene on chromosome 17q21 highly linked to asthma, induced increased ASM proliferation and contractility in vitro and influenced airway contractility and calcium flux in ASM in precision-cut lung slices (PCLSs) from wild-type and hORMDL3Zp3-Cre mice (which express increased levels of human ORMDL3 [hORMDL3]).

METHODS

Levels of ASM proliferation and contraction were assessed in ASM cells transfected with ORMDL3 in vitro. In addition, airway contractility and calcium oscillations were quantitated in ASM cells in PCLSs derived from naive wild-type and naive hORMDL3Zp3-Cre mice, which do not have a blood supply.

RESULTS

Increased ASM expression of ORMDL3 in vitro resulted in increased ASM proliferation and contractility. PCLSs derived from naive hORMDL3Zp3-Cre mice, which do not have airway inflammation, exhibit increased airway contractility with increased calcium oscillations in ASM cells. Increased ASM ORMDL3 expression increases levels of ASM sarcoplasmic reticulum Ca2+ ATPase 2b (SERCA2b), which increases ASM proliferation and contractility.

CONCLUSION

Overall, these studies provide evidence that an intrinsic increase in ORMDL3 expression in ASM can induce increased ASM proliferation and contractility, which might contribute to increased airway hyperresponsiveness in the absence of airway inflammation in asthmatic patients.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: Insights into ER refilling and the spatial signature of Ca2+ signals

The spatial organisation of Orai channels and SERCA pumps within ER-PM junctions is important for enhancing the versatility and specificity of sub-cellular Ca²⁺ signals generated during store operated Ca²⁺ entry (SOCE). In this paper, we present a novel three dimensional spatio-temporal model describing Ca²⁺ dynamics in the ER-PM junction and sub-PM ER during SOCE. We investigate the role of Orai channel and SERCA pump location to provide insights into how these components shape the Ca²⁺ signals generated and affect ER refilling. We find that the organisation of Orai channels within the ER-PM junction controls the amplitude and shape of the Ca²⁺ profile but does not enhance ER refilling. The model shows that ER refilling is only weakly affected by the location of SERCA2b pumps within the ER-PM junction and that the placement of SERCA2a pumps within the ER-PM junction has much greater control over ER refilling.

Diversity of Evoked Astrocyte Ca2+ Dynamics Quantified through Experimental Measurements and Mathematical Modeling

Astrocytes are a major cell type in the mammalian brain. They are not electrically excitable, but generate prominent Ca²⁺ signals related to a wide variety of critical functions. The mechanisms driving these Ca²⁺ events remain incompletely understood. In this study, we integrate Ca²⁺ imaging, quantitative data analysis, and mechanistic computational modeling to study the spatial and temporal heterogeneity of cortical astrocyte Ca²⁺ transients evoked by focal application of ATP in mouse brain slices. Based on experimental results, we tune a single-compartment mathematical model of IP₃-dependent Ca²⁺ responses in astrocytes and use that model to study response heterogeneity. Using information from the experimental data and the underlying bifurcation structure of our mathematical model, we categorize all astrocyte Ca²⁺ responses into four general types based on their temporal characteristics: Single-Peak, Multi-Peak, Plateau, and Long-Lasting responses. We find that the distribution of experimentally-recorded response types depends on the location within an astrocyte, with somatic responses dominated by Single-Peak (SP) responses and large and small processes generating more Multi-Peak responses. On the other hand, response kinetics differ more between cells and trials than with location within a given astrocyte. We use the computational model to elucidate possible sources of Ca²⁺ response variability: (1) temporal dynamics of IP₃, and (2) relative flux rates through Ca²⁺ channels and pumps. Our model also predicts the effects of blocking Ca²⁺ channels/pumps; for example, blocking store-operated Ca²⁺ (SOC) channels in the model eliminates Plateau and Long-Lasting responses (consistent with previous experimental observations). Finally, we propose that observed differences in response type distributions between astrocyte somas and processes can be attributed to systematic differences in IP₃ rise durations and Ca²⁺ flux rates.

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

A mathematical model of calcium dynamics in HSY cells

Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations.

The relative contributions of store-operated and voltage-gated Ca2+ channels to the control of Ca2+ oscillations in airway smooth muscle

KEY POINTS

Agonist-dependent oscillations in the concentration of free cytosolic calcium are a vital mechanism for the control of airway smooth muscle contraction and thus are a critical factor in airway hyper-responsiveness. Using a mathematical model, closely tied to experimental work, we show that the oscillations in membrane potential accompanying the calcium oscillations have no significant effect on the properties of the calcium oscillations. In addition, the model shows that calcium entry through store-operated calcium channels is critical for calcium oscillations, but calcium entry through voltage-gated channels has much less effect. The model predicts that voltage-gated channels are less important than store-operated channels in the control of airway smooth muscle tone.

ABSTRACT

Airway smooth muscle contraction is typically the key mechanism underlying airway hyper-responsiveness, and the strength of muscle contraction is determined by the frequency of oscillations of intracellular calcium (Ca²⁺ ) concentration. In airway smooth muscle cells, these Ca²⁺ oscillations are caused by cyclic Ca²⁺ release from the sarcoplasmic reticulum, although Ca²⁺ influx via plasma membrane channels is also necessary to sustain the oscillations over longer times. To assess the relative contributions of store-operated and voltage-gated Ca²⁺ channels to this Ca²⁺ influx, we generated a comprehensive mathematical model, based on experimental Ca²⁺ measurements in mouse precision-cut lung slices, to simulate Ca²⁺ oscillations and changes in membrane potential. Agonist-induced Ca²⁺ oscillations are accompanied by oscillations in membrane potential, although the membrane potential oscillations are too small to generate large Ca²⁺ currents through voltage-gated Ca²⁺ channels, and thus have little effect on the Ca²⁺ oscillations. Ca²⁺ entry through voltage-gated channels only becomes important when the cell is depolarized (e.g. by a high external K⁺ concentration). As a result, agonist-induced Ca²⁺ oscillations are critically dependent on Ca²⁺ entry through store-operated channels but do not depend strongly on Ca²⁺ entry though voltage-gated channels.

Store-Operated Ca2+ Entry in Oocytes Modulate the Dynamics of IP3 -Dependent Ca2+ Release From Oscillatory to Tonic

Ca²⁺ signaling is ubiquitous and mediates various cellular functions encoded in its spatial, temporal, and amplitude features. Here, we investigate the role of store-operated Ca²⁺ entry (SOCE) in regulating the temporal dynamics of Ca²⁺ signals in Xenopus oocytes, which can be either oscillatory or tonic. Oscillatory Ca²⁺ release from intracellular stores is typically observed at physiological agonist concentration. When Ca²⁺ release leads to Ca²⁺ store depletion, this triggers the activation of SOCE that translates into a low-amplitude tonic Ca²⁺ signal. SOCE has also been implicated in fueling Ca²⁺ oscillations when activated at low levels. Here, we show that sustained SOCE activation in the presence of IP₃ to gate IP₃ receptors (IP₃ R) results in a pump-leak steady state across the endoplasmic reticulum (ER) membrane that inhibits Ca²⁺ oscillations and produces a tonic Ca²⁺ signal. Tonic signaling downstream of SOCE activation relies on focal Ca²⁺ entry through SOCE ER-plasma membrane (PM) junctions, Ca²⁺ uptake into the ER, followed by release through open IP₃ Rs at distant sites, a process we refer to as "Ca²⁺ teleporting." Therefore, sustained SOCE activation in the presence of an IP₃ -dependent "leak" pathway at the ER membrane results in a switch from oscillatory to tonic Ca²⁺ signaling. J. Cell. Physiol. 232: 1095-1103, 2017. © 2016 Wiley Periodicals, Inc.

Store-operated calcium entry is required for sustained contraction and Ca2+ oscillations of airway smooth muscle

KEY POINTS

Airway hyper-responsiveness in asthma is driven by excessive contraction of airway smooth muscle cells (ASMCs). Agonist-induced Ca²⁺ oscillations underlie this contraction of ASMCs and the magnitude of this contraction is proportional to the Ca²⁺ oscillation frequency. Sustained contraction and Ca²⁺ oscillations require an influx of extracellular Ca²⁺ , although the mechanisms and pathways mediating this Ca²⁺ influx during agonist-induced ASMC contraction are not well defined. By inhibiting store-operated calcium entry (SOCE) or voltage-gated Ca²⁺ channels (VGCCs), we show that SOCE, rather than Ca²⁺ influx via VGCCs, provides the major Ca²⁺ entry pathway into ASMCs to sustain ASMCs contraction and Ca²⁺ oscillations. SOCE may therefore serve as a potential target for new bronchodilators to reduce airway hyper-responsiveness in asthma.

ABSTRACT

Asthma is characterized by airway hyper-responsiveness: the excessive contraction of airway smooth muscle. The extent of this airway contraction is proportional to the frequency of Ca²⁺ oscillations within airway smooth muscle cells (ASMCs). Sustained Ca²⁺ oscillations require a Ca²⁺ influx to replenish Ca²⁺ losses across the plasma membrane. Our previous studies implied store-operated calcium entry (SOCE) as the major pathway for this Ca²⁺ influx. In the present study, we explore this hypothesis, by examining the effects of SOCE inhibitors (GSK7975A and GSK5498A) as well as L-type voltage-gated Ca²⁺ channel inhibitors (nifedipine and nimodipine) on airway contraction and Ca²⁺ oscillations and SOCE-mediated Ca²⁺ influx in ASMCs within mouse precision-cut lung slices. We found that both GSK7975A and GSK5498A were able to fully relax methacholine-induced airway contraction by abolishing the Ca²⁺ oscillations, in a manner similar to that observed in zero extracellular Ca²⁺ ([Ca²⁺ ]_e ). In addition, GSK7975A and GSK5498A inhibited increases in intracellular Ca²⁺ ([Ca²⁺ ]_i ) in ASMCs with depleted Ca²⁺ -stores in response to increased [Ca²⁺ ]_e , demonstrating a response consistent with the inhibition of SOCE. However, GSK7975A and GSK5498A did not reduce Ca²⁺ release via IP₃ receptors stimulated with IP₃ released from caged-IP₃ . By contrast, nifedipine and nimodipine only partially reduced airway contraction, Ca²⁺ oscillation frequency and SOCE-mediated Ca²⁺ influx. These data suggest that SOCE is the major Ca²⁺ influx pathway for ASMCs with respect to sustaining agonist-induced airway contraction and the underlying Ca²⁺ oscillations. The mechanisms of SOCE may therefore form novel targets for new bronchodilators.

Ryanodine receptor sensitization results in abnormal calcium signaling in airway smooth muscle cells

Intracellular Ca(2+) dynamics of airway smooth muscle cells (ASMCs) are believed to play a major role in airway hyperresponsiveness and remodeling in asthma. Prior studies have underscored a prominent role for inositol 1,4,5-triphosphate (IP3) receptors in normal agonist-induced Ca(2+) oscillations, whereas ryanodine receptors (RyRs) appear to remain closed during such Ca(2+) oscillations, which mediate ASMC contraction. Nevertheless, RyRs have been hypothesized to play a role in hyperresponsive Ca(2+) signaling. This could be explained by RyRs being "sensitized" to open more frequently by certain compounds. We investigate the implications of RyR sensitization on Ca(2+) dynamics in ASMC using a combination of mathematical modeling and experiments with mouse precision-cut lung slices. Caffeine is used to increase the sensitivity of RyRs to cytosolic Ca(2+) concentration ([Ca(2+)]i) and sarcoplasmic reticulum Ca(2+) ([Ca(2+)]SR). In ASMCs, high caffeine concentrations (>10 mM) induce a sustained elevation of [Ca(2+)]i. Our mathematical model accounts for this by the activation of store-operated Ca(2+) entry that results from a large increase in the RyR sensitivity to [Ca(2+)]SR and the associated Ca(2+) release, which leads to a reduction of [Ca(2+)]SR. Importantly, our model also predicts that: (1) moderate RyR sensitization induces slow Ca(2+) oscillations, a result experimentally confirmed with low concentrations of caffeine; and (2) high RyR sensitization suppresses fast, agonist-induced Ca(2+) oscillations by inducing substantial store-operated Ca(2+) entry and elevated [Ca(2+)]i. These results suggest that RyR sensitization could play a role in ASMC proliferation (by inducing slow Ca(2+) oscillations) and in airway hyperresponsiveness (by inducing greater mean [Ca(2+)]i for similar levels of contractile agonist).

Lentiviral shRNA against KCa3.1 inhibits allergic response in allergic rhinitis and suppresses mast cell activity via PI3K/AKT signaling pathway

Calcium-activated potassium ion channel-3.1 (KCa3.1) plays a pivotal role in the potassium-calcium exchange involved in atopy. This study aimed to explore the impact of lentiviral-mediated shRNA silencing KCa3.1 on allergic response in a murine allergic rhinitis (AR) model. The BALB/c mice were divided into four groups: untreated AR group, negative control AR group, lentiviral KCa3.1-shRNA treated AR group and normal control group. Concentrations of ovalbumin (OVA)-specific IgE, histamine and leukotrienes C4 (LTC4) in serum, and IL-4, IL-9 and IL-17 in nasal lavage fluid (NLF) were analyzed. Goblet cells and mast cells were counted. KCa3.1 positive cells were counted after immunolabelling by immunofluorescence method. KCa3.1, Mucin 5AC (MUC5AC), and tryptase mRNA levels were determined using real-time polymerase chain reaction. Furthermore, P815 cell line was used to explore the role and mechanism of lentiviral KCa3.1-shRNA on mast cells. The results showed that LV-KCa3.1-shRNA intervention effectively attenuated allergic responses in LV-KCa3.1-shRNA treated mice. LV-KCa3.1-shRNA intervention effectively suppressed KCa3.1 levels and phosphorylation of AKT in P815 cells, leading to the downregulation of tryptase, IL-6 and IL-8 levels. LV-KCa3.1-shRNA intervention effectively attenuated the allergic responses in AR and suppressed mast cell activity by inhibiting PI3K/AKT signaling pathway.

Caffeine-induced Ca(2+) oscillations in type I horizontal cell of carp retina: a mathematical model

Oscillations in intracellular free Ca(2+) concentration ([Ca(2+)]i) have been observed in a variety of cell types. In the present study, we constructed a mathematical model to simulate the caffeine-induced [Ca(2+)]i oscillations based on experimental data obtained from isolated type I horizontal cell of carp retina. The results of model analysis confirm the notion that the caffeine-induced [Ca(2+)]i oscillations involve a number of cytoplasmic and endoplasmic Ca(2+) processes that interact with each other. Using this model, we evaluated the importance of store-operated channel (SOC) in caffeine-induced [Ca(2+)]i oscillations. The model suggests that store-operated Ca(2+) entry (SOCE) is elicited upon depletion of the endoplasmic reticulum (ER). When the SOC conductance is set to 0, caffeine-induced [Ca(2+)]i oscillations are abolished, which agrees with the experimental observation that [Ca(2+)]i oscillations were abolished when SOC was blocked pharmacologically, verifying that SOC is necessary for sustained [Ca(2+)]i oscillations.

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells

The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.

The inositol trisphosphate receptor () is one of the most important cellular components responsible for calcium oscillations. Over the past decade, two major questions about the have arisen. Firstly, what fundamental properties of the allow it to perform its function? Secondly, although calcium oscillations are caused by the stochastic properties of small numbers of is it possible for a deterministic model to be a reliable predictor of calcium dynamics? Using airway smooth muscle cells as an example, we show that calcium dynamics can be accurately modeled using simplified models, and, secondly, that deterministic models are qualitatively accurate predictors of calcium dynamics. These results are important for the study of calcium dynamics in many cell types.

Ca2+ handling and sensitivity in airway smooth muscle: emerging concepts for mechanistic understanding and therapeutic targeting

Free calcium ions within the cytosol serve as a key secondary messenger system for a diverse range of cellular processes. Dysregulation of cytosolic Ca(2+) handling in airway smooth muscle (ASM) has been implicated in asthma, and it has been hypothesised that this leads, at least in part, to associated changes in both the architecture and function of the lung. Significant research is therefore directed towards furthering our understanding of the mechanisms which control ASM cytosolic calcium, in addition to those regulating the sensitivity of its downstream effector targets to calcium. Key aspects of the recent developments in this field were discussed at the 8th Young Investigators' Symposium on Smooth Muscle (2013, Groningen, The Netherlands), and are outlined in this review.

Modeling the intracellular organization of calcium signaling

Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.