Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells

Computational Model of Complex Calcium Dynamics: Store Operated Ca2+ Channels and Mitochondrial Associated Membranes in Pancreatic Acinar Cells

This proposed model explores the intricate Ca2+ dynamics within the pancreatic acinar cells (PACs) by emphasizing the role of store-operated Ca2+ entry (SOCE) and the mitochondrial-associated membranes (MAMs) in the secretory region (apical) of the PACs. Traditionally, Ca2+ releases from the endoplasmic reticulum (ER) via calcium-induced calcium release (CICR). It has been shown to be important in regulating functions such as secretion of digestive enzymes in PACs. However, this model posits that upon the depletion of Ca2+ in the ER, the signaling protein stromal interaction molecule (STIM1) is activated. Activated STIM1, then facilitates the opening of Orai channels, allowing Ca2+ influx through the store-operated calcium channels (SOCCs). The model highlights the complexity of the Ca2+ dynamics, and the importance of SOCE and MAMs in the PACs Ca2+ homeostasis. The numerical and bifurcation analysis illustrate how changes in agonist concentrations can lead to the diverse Ca2+ oscillation patterns, such as thin to broader oscillations, sinusoidal patterns, and baseline fluctuations, driven by the feedback mechanisms involving Ca2+ and inositol 1,4,5 trisphosphate (IP3). This understanding could have broader implications for cellular physiology and the development of therapies targeting Ca2+ signaling pathways.

Ca2+ signals in pancreatic acinar cells in response to physiological stimulation in vivo

The exocrine pancreas secretes fluid and digestive enzymes in response to parasympathetic release of acetylcholine (ACh) via the vagus nerve and the gut hormone cholecystokinin (CCK). Both secretion of fluid and exocytosis of secretory granules containing enzymes and zymogens are dependent on an increase in the cytosolic [Ca²⁺ ] in acinar cells. It is thought that the specific spatiotemporal characteristics of the Ca²⁺ signals are fundamental for appropriate secretion and that these properties are disrupted in disease states in the pancreas. While extensive research has been performed to characterize Ca²⁺ signalling in acinar cells, this has exclusively been achieved in ex vivo preparations of exocrine cells, where it is difficult to mimic physiological conditions. Here we have developed a method to optically observe pancreatic acinar Ca²⁺ signals in vivo using a genetically expressed Ca²⁺ indicator and imaged with multi-photon microscopy in live animals. In vivo, acinar cells exhibited baseline activity in fasted animals, which was dependent on CCK1 receptors (CCK1Rs). Both stimulation of intrinsic nervous input and administration of systemic CCK induced oscillatory activity in a proportion of the cells, but the maximum frequencies were vastly different. Upon feeding, oscillatory activity was also observed, which was dependent on CCK1Rs. No evidence of a vago-vagal reflex mediating the effects of CCK was observed. Our in vivo method revealed the spatial and temporal profile of physiologically evoked Ca²⁺ signals, which will provide new insights into future studies of the mechanisms underlying exocrine physiology and that are disrupted in pathological conditions. KEY POINTS: In the exocrine pancreas, the spatiotemporal properties of Ca²⁺ signals are fundamentally important for the appropriate stimulation of secretion by the neurotransmitter acetylcholine and gut hormone cholecystokinin. These characteristics were previously defined in ex vivo studies. Here we report the spatiotemporal characteristics of Ca²⁺ signals in vivo in response to physiological stimulation in a mouse engineered to express a Ca²⁺ indicator in acinar cells. Specific Ca²⁺ 'signatures' probably important for stimulating secretion are evoked in vivo in fasted animals, by feeding, neural stimulation and cholecystokinin administration. The Ca²⁺ signals are probably the result of the direct action of ACh and CCK on acinar cells and not indirectly through a vago-vagal reflex.

Calcium imaging in intact mouse acinar cells in acute pancreas tissue slices

The physiology and pathophysiology of the exocrine pancreas are in close connection to changes in intra-cellular Ca²⁺ concentration. Most of our knowledge is based on in vitro experiments on acinar cells or acini enzymatically isolated from their surroundings, which can alter their structure, physiology, and limit our understanding. Due to these limitations, the acute pancreas tissue slice technique was introduced almost two decades ago as a complementary approach to assess the morphology and physiology of both the endocrine and exocrine pancreas in a more conserved in situ setting. In this study, we extend previous work to functional multicellular calcium imaging on acinar cells in tissue slices. The viability and morphological characteristics of acinar cells within the tissue slice were assessed using the LIVE/DEAD assay, transmission electron microscopy, and immunofluorescence imaging. The main aim of our study was to characterize the responses of acinar cells to stimulation with acetylcholine and compare them with responses to cerulein in pancreatic tissue slices, with special emphasis on inter-cellular and inter-acinar heterogeneity and coupling. To this end, calcium imaging was performed employing confocal microscopy during stimulation with a wide range of acetylcholine concentrations and selected concentrations of cerulein. We show that various calcium oscillation parameters depend monotonically on the stimulus concentration and that the activity is rather well synchronized within acini, but not between acini. The acute pancreas tissue slice represents a viable and reliable experimental approach for the evaluation of both intra- and inter-cellular signaling characteristics of acinar cell calcium dynamics. It can be utilized to assess many cells simultaneously with a high spatiotemporal resolution, thus providing an efficient and high-yield platform for future studies of normal acinar cell biology, pathophysiology, and screening pharmacological substances.

Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca²⁺ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP₃ with consequent abnormal release of Ca²⁺ from the endoplasmic reticulum (ER) through activation of IP₃ receptor (IP₃R) Ca²⁺ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP₃-mediated Ca²⁺ signaling. We investigate Ca²⁺ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca²⁺ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP₃R sensitivity to IP₃ for large doses. Our analysis also shows that the upstream production of IP₃ can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP₃ signaling.

A metabolic reaction-diffusion model for PKCα translocation via PIP2 hydrolysis in an endothelial cell

Hydrolysis of the phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2) at the cell membrane induces the release of inositol 1,4,5-trisphosphate (IP3) into the cytoplasm and diffusion of diacylglycerol (DAG) through the membrane, respectively. Release of IP3 subsequently increases Ca2+ levels in the cytoplasm, which results in activation of protein kinase C α (PKCα) by Ca2+ and DAG, and finally the translocation of PKCα from the cytoplasm to the membrane. In this study, we developed a metabolic reaction-diffusion framework to simulate PKCα translocation via PIP2 hydrolysis in an endothelial cell. A three-dimensional cell model, divided into membrane and cytoplasm domains, was reconstructed from confocal microscopy images. The associated metabolic reactions were divided into their corresponding domain; PIP2 hydrolysis at the membrane domain resulted in DAG diffusion at the membrane domain and IP3 release into the cytoplasm domain. In the cytoplasm domain, Ca2+ was released from the endoplasmic reticulum, and IP3, Ca2+, and PKCα diffused through the cytoplasm. PKCα bound Ca2+ at, and diffused through, the cytoplasm, and was finally activated by binding with DAG at the membrane. Using our model, we analyzed IP3 and DAG dynamics, Ca2+ waves, and PKCα translocation in response to a microscopic stimulus. We found a qualitative agreement between our simulation results and our experimental results obtained by live-cell imaging. Interestingly, our results suggest that PKCα translocation is dominated by DAG dynamics. This three-dimensional reaction-diffusion mathematical framework could be used to investigate the link between PKCα activation in a cell and cell function.

A mathematical model for the effects of amyloid beta on intracellular calcium

The accumulation of Alzheimer's disease (AD) associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium (Ca2+) levels by disrupting the intrinsic Ca2+ regulatory mechanism within cells. These disruptions can cause changes in homeostasis levels that can have detrimental effects on cell function and survival. Although studies have shown that Aβ can interfere with various Ca2+ fluxes, the complexity of these interactions remains elusive. We have constructed a mathematical model that simulates Ca2+ patterns under the influence of Aβ. Our simulations shows that Aβ can increase regions of mixed-mode oscillations leading to aberrant signals under various conditions. We investigate how Aβ affects individual flux contributions through inositol triphosphate (IP3) receptors, ryanodine receptors, and membrane pores. We demonstrate that controlling for the ryanodine receptor's maximal kinetic reaction rate may provide a biophysical way of managing aberrant Ca2+ signals. The influence of a dynamic model for IP3 production is also investigated under various conditions as well as the impact of changes in membrane potential. Our model is one of the first to investigate the effects of Aβ on a variety of cellular mechanisms providing a base modeling scheme from which further studies can draw on to better understand Ca2+ regulation in an AD environment.

Computational Model of Ca2+ Wave Propagation in Human Retinal Pigment Epithelial ARPE-19 Cells

Objective

Computational models of calcium (Ca²⁺) signaling have been constructed for several cell types. There are, however, no such models for retinal pigment epithelium (RPE). Our aim was to construct a Ca²⁺ signaling model for RPE based on our experimental data of mechanically induced Ca²⁺ wave in the in vitro model of RPE, the ARPE-19 monolayer.

Methods

We combined six essential Ca²⁺ signaling components into a model: stretch-sensitive Ca²⁺ channels (SSCCs), P₂Y₂ receptors, IP₃ receptors, ryanodine receptors, Ca²⁺ pumps, and gap junctions. The cells in our epithelial model are connected to each other to enable transport of signaling molecules. Parameterization was done by tuning the above model components so that the simulated Ca²⁺ waves reproduced our control experimental data and data where gap junctions were blocked.

Results

Our model was able to explain Ca²⁺ signaling in ARPE-19 cells, and the basic mechanism was found to be as follows: 1) Cells near the stimulus site are likely to conduct Ca²⁺ through plasma membrane SSCCs and gap junctions conduct the Ca²⁺ and IP³ between cells further away. 2) Most likely the stimulated cell secretes ligand to the extracellular space where the ligand diffusion mediates the Ca²⁺ signal so that the ligand concentration decreases with distance. 3) The phosphorylation of the IP₃ receptor defines the cell’s sensitivity to the extracellular ligand attenuating the Ca²⁺ signal in the distance.

Conclusions

The developed model was able to simulate an array of experimental data including drug effects. Furthermore, our simulations predict that suramin may interfere ligand binding on P₂Y₂ receptors or accelerate P₂Y₂ receptor phosphorylation, which may partially be the reason for Ca²⁺ wave attenuation by suramin. Being the first RPE Ca²⁺ signaling model created based on experimental data on ARPE-19 cell line, the model offers a platform for further modeling of native RPE functions.

Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling

Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.

Modelling the transition from simple to complex Ca²⁺ oscillations in pancreatic acinar cells

A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic acinar cells. This model is based on calcium-induced calcium release via inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) and includes calcium modulation of inositol (1,4,5) trisphosphate (IP3) levels through feedback regulation of degradation and production. In our model, the apical and the basal regions are separated by a region containing mitochondria, which is capable of restricting Ca2+ responses to the apical region. We were able to reproduce the observed oscillatory patterns, from baseline spikes to sinusoidal oscillations. The model predicts that calcium-dependent production and degradation of IP3 is a key mechanism for complex calcium oscillations in pancreatic acinar cells. A partial bifurcation analysis is performed which explores the dynamic behaviour of the model in both apical and basal regions.

Calcium and IP3 dynamics in cardiac myocytes: experimental and computational perspectives and approaches

Calcium plays a crucial role in excitation-contraction coupling (ECC), but it is also a pivotal second messenger activating Ca²⁺-dependent transcription factors in a process termed excitation-transcription coupling (ETC). Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor (IP₃R)-mediated Ca²⁺ release in the regulation of cytosolic and nuclear Ca²⁺ signals. IP₃ is generated by stimulation of plasma membrane receptors that couple to phospholipase C (PLC), liberating IP₃ from phosphatidylinositol 4,5-bisphosphate (PIP₂). An intriguing aspect of IP₃ signaling is the presence of the entire PIP₂-PLC-IP₃ signaling cascade as well as the presence of IP₃Rs at the inner and outer membranes of the nuclear envelope (NE) which functions as a Ca²⁺ store. The observation that the nucleus is surrounded by its own putative Ca²⁺ store raises the possibility that nuclear IP₃-dependent Ca²⁺ release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca²⁺ signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca²⁺ store; (ii) the nuclear pore complex is the major gateway for Ca²⁺ and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca²⁺ handling proteins including the Na⁺/Ca²⁺ exchanger (NCX)/GM1 complex, ryanodine receptors (RyRs), nicotinic acid adenine dinucleotide phosphate receptors (NAADPRs), Na⁺/K⁺ ATPase, and Na⁺/H⁺ exchanger. Thus, it appears that the nucleus represents a Ca²⁺ signaling domain equipped with its own ion channels and transporters that allow for complex local Ca²⁺ signals. Many experimental and modeling approaches have been used for the study of intracellular Ca²⁺ signaling but the key to the understanding of the dual role of Ca²⁺ mediating ECC and ECT lays in quantitative differences of local [Ca²⁺] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca²⁺ transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca²⁺ and IP₃ signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca²⁺ signals are required to translocate and activate Ca²⁺-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.

Comparison of models for IP3 receptor kinetics using stochastic simulations

Inositol 1,4,5-trisphosphate receptor (IP₃R) is a ubiquitous intracellular calcium (Ca²⁺) channel which has a major role in controlling Ca²⁺ levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP₃R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP₃R when modeling local Ca²⁺ transients in dendrites or overall Ca²⁺ dynamics in large neuronal models. The goal of this study was to evaluate existing IP₃R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson etal., 2003; Fraiman and Dawson, 2004; Doi etal., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP₃R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP₃R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP₃R with different concentrations of Ca²⁺ and IP₃ should be more carefully addressed when new models for IP₃R are developed.

Modelling the effect of specific inositol 1,4,5-trisphosphate receptor isoforms on cellular Ca2+ signals

BACKGROUND INFORMATION

Oscillations of cytosolic Ca2+ are well-known to rely on the regulatory properties of the InsP3R (inositol 1,4,5-trisphosphate receptor). Three isoforms of this channel have been identified. They differ in their regulatory properties by Ca2+ and InsP3. Experiments in different cell types clearly indicate that the relative amounts of each isoform affect the time course of Ca2+ changes after agonist stimulation. In the present study, we investigate whether different steady-state curves for the open probability of the InsP3Rs as a function of Ca2+ imply different dynamical behaviours when these receptors are present in a cellular environment. We therefore describe by a specific phenomenological model the three main types of curves that have been reported: (i) the classical bell-shaped curve, (ii) the bell-shaped curve that is shifted towards higher Ca2+ concentrations when InsP3 is increased, and (iii) a monotonous increasing function of cytosolic Ca2+.

RESULTS

We show that, although these types of curves can be ascribed to slight differences in the channel regulation by Ca2+ and InsP3, they can indicate important variations as to the receptor role in cellular Ca2+ control. Thus the receptor associated with the classical bell-shaped curve appears to be the most robust Ca2+ oscillator. If the steady-state curve is supposed to be a monotonous increasing function of cytosolic Ca2+, the modelled receptor cannot sustain Ca2+ oscillations in the absence of Ca2+ exchanges with the extracellular medium. When the bell-shaped curve is shifted towards higher Ca2+ concentrations with increasing InsP3 levels, the model predicts that the receptor is less robust to changes in density; this receptor, however, provides a finer control of the steady-state level of Ca2+ when varying the InsP3 concentration.

CONCLUSIONS

Our model allows us to propose an explanation for the experimental observations about the effect of selectively expressing or down-regulating InsP3R isoforms, as well as to make theoretical predictions.

BIFURCATION ANALYSIS OF CALCIUM OSCILLATIONS: TIME-SCALE SEPARATION, CANARDS, AND FREQUENCY LOWERING

The behavior of calcium oscillations near bifurcations is analyzed for three different models. For the model developed by Somogyi and Stucki [42], it is shown that the range of oscillations is bounded by supercritical and subcritical Hopf bifurcations. Near the latter, canard orbits arise, that is, quasi-harmonic oscillations with a very small amplitude grow very fast to become pulsed oscillations. The potential biological significance of this behavior is discussed. A time-scale analysis of this model is performed and an approximation formula for the oscillation period is derived. For two models that we presented earlier [30, 31], it is shown that a homoclinic bifurcation and an infinite period bifurcation, respectively, occur. These imply that the oscillation period can reach arbitrarily high values. This behavior is discussed in the light of frequency encoding, and the scaling laws of the oscillation period are given.

TEMPERATURE EFFECTS ON THE STOCHASTIC GATING OF THE IP3R CALCIUM RELEASE CHANNEL: A NUMERICAL SIMULATION STUDY

The importance of the kinetic study of endoplasmatic calcium ion channels in different intracellular processes is known today. Although there are few experimental reports on the temperature dependency of IP3R channel functions, we did not find any detailed theoretical study on this subject. For this purpose, we used a modified Gillespie algorithm to investigate the effect of temperature on the conditions affecting the open state of a single subunit of the De Young-Keizer (DYK) model. Population of the states was considered as the subject of fluctuation. Key features of the channel, such as bell-shaped dependency of open probability to the Calcium concentrations were modeled at different temperatures, too. The range of temperature variation was selected by regarding the experimental data on IP3R channel.

By increasing the temperature, we had the very slow time domains (t: 10-1 s ) and the much slower time domains (t: 100 s ) in addition to other time domains, which could be seen as new time categories in InsP3R studies, and so the results were reported in these time domains, as well.

We found out that increase in temperature declined the open probability in some concentrations of Ca 2+ and/or IP3. Also, by introducing the intensity graphs, broadening of the range of fluctuations and lowering of the order of frequency of fluctuations for the population of each state were observed due to the temperature increments.

The temperature effects on the activation and inactivation states of the channel were studied in the framework of the reaction paths. We did not find similar paths at different time domains; several paths observed which were totally different all together. These time-dependent reaction paths are also depending on the Ca 2+ and/or the IP3 concentrations. So, one can predict the most probable reaction paths at different concentrations and temperatures and also determine which kind of the path it is; a path for closing the channel or a path to open it.

Finally, the temperature effects on the calcium inhibited states were studied. We found out that calcium ion inhibitions were shifted to lower calcium concentration by increasing the temperature. The results suggests that inhibiting role of calcium is not only [ Ca 2+] and/or [IP3] dependent, but also temperature dependent.

Calcium oscillations

Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors.

The effect of intracellular calcium oscillations on fluid secretion in airway epithelium

Airway epithelium has been shown to elicit fluid secretion after a rise in intracellular calcium. This rise in intracellular calcium has been shown to display complex oscillations in many species after the binding of particular agonists to extracellular receptors. Fluid secreted by the airway epithelium is used to maintain the depth of the periciliary liquid (PCL) above the apical membrane of the epithelial cells lining the bronchial airways. Previous mathematical models have been published which separately consider the electrophysiology involved in regulating periciliary liquid depth, and the transmission of intracellular calcium waves in airway epithelial tissue. In this paper we present a mathematical model that combines these previous models and allows the effect of oscillations in intracellular calcium on fluid secretion by airway epithelial cells to be investigated. We show that an oscillatory calcium response produces different fluid secretion properties to that elicited by a tonic rise in intracellular calcium. These differences are shown to be due to saturation of the Ca(2+) activated ion channels.

Regulation of inositol 1,4,5-trisphosphate receptors by cAMP independent of cAMP-dependent protein kinase

In HEK cells stably expressing type 1 receptors for parathyroid hormone (PTH), PTH causes a sensitization of inositol 1,4,5-trisphosphate receptors (IP(3)R) to IP(3) that is entirely mediated by cAMP and requires cAMP to pass directly from type 6 adenylyl cyclase (AC6) to IP(3)R2. Using DT40 cells expressing single subtypes of mammalian IP(3)R, we demonstrate that high concentrations of cAMP similarly sensitize all IP(3)R isoforms to IP(3) by a mechanism that does not require cAMP-dependent protein kinase (PKA). IP(3) binding to IP(3)R2 is unaffected by cAMP, and sensitization is not mediated by the site through which ATP potentiates responses to IP(3). In single channel recordings from excised nuclear patches of cells expressing IP(3)R2, cAMP alone had no effect, but it increased the open probability of IP(3)R2 activated by a submaximal concentration of IP(3) alone or in combination with a maximally effective concentration of ATP. These results establish that cAMP itself increases the sensitivity of all IP(3)R subtypes to IP(3). For IP(3)R2, this sensitization results from cAMP binding to a novel site that increases the efficacy of IP(3). Using stably expressed short hairpin RNA to reduce expression of the G-protein, G alpha(s), we demonstrate that attenuation of AC activity by loss of G alpha(s) more substantially reduces sensitization of IP(3)R by PTH than does comparable direct inhibition of AC. This suggests that G alpha(s) may also specifically associate with each AC x IP(3)R complex. We conclude that all three subtypes of IP(3)R are regulated by cAMP independent of PKA. In HEK cells, where IP(3)R2 selectively associates with AC6, G alpha(s) also associates with the AC x IP(3)R signaling junction.

Spatiotemporal organization of Ca dynamics: a modeling-based approach

Calcium is a ubiquitous second messenger that mediates vital physiological responses such as fertilization, secretion, gene expression, or apoptosis. Given this variety of processes mediated by Ca(2+), these signals are highly organized both in time and space to ensure reliability and specificity. This review deals with the spatiotemporal organization of the Ca(2+) signaling pathway in electrically nonexcitable cells in which InsP(3) receptors are by far the most important Ca(2+) channels. We focus on the aspects of this highly regulated dynamical system for which an interplay between experiments and modeling is particularly fruitful. In particular, the importance of the relative densities of the different InsP(3) receptor subtypes will be discussed on the basis of a modeling approach linking the steady-state behaviors of these channels in electrophysiological experiments with their behavior in a cellular environment. Also, the interplay between InsP(3) metabolism and Ca(2+) oscillations will be considered. Finally, we discuss the relationships between stochastic openings of the Ca(2+) releasing channels at the microscopic level and the coordinated, regular behavior observed at the whole cell level on the basis of a combined experimental and modeling approach.

Multiple Ca2+ signaling pathways regulate intracellular Ca2+ activity in human cardiac fibroblasts

Ca(2+) signaling pathways are well studied in cardiac myocytes, but not in cardiac fibroblasts. The aim of the present study is to characterize Ca(2+) signaling pathways in cultured human cardiac fibroblasts using confocal scanning microscope and RT-PCR techniques. It was found that spontaneous intracellular Ca(2+) (Ca(i) (2+)) oscillations were present in about 29% of human cardiac fibroblasts, and the number of cells with Ca(i) (2+) oscillations was increased to 57.3% by application of 3% fetal bovine serum. Ca(i) (2+) oscillations were dependent on Ca(2+) entry. Ca(i) (2+) oscillations were abolished by the store-operated Ca(2+) (SOC) entry channel blocker La(3+), the phospholipase C inhibitor U-73122, and the inositol trisphosphate receptors (IP3Rs) inhibitor 2-aminoethoxydiphenyl borate, but not by ryanodine. The IP3R agonist thimerosal enhanced Ca(i) (2+) oscillations. Inhibition of plasma membrane Ca(2+) pump (PMCA) and Na(+)-Ca(2+) exchanger (NCX) also suppressed Ca(i) (2+) oscillations. In addition, the frequency of Ca(i) (2+) oscillations was reduced by nifedipine, and increased by Bay K8644 in cells with spontaneous Ca(2+) oscillations. RT-PCR revealed that mRNAs for IP3R1-3, SERCA1-3, Ca(V)1.2, NCX3, PMCA1,3,4, TRPC1,3,4,6, STIM1, and Orai1-3, were readily detectable, but not RyRs. Our results demonstrate for the first time that spontaneous Ca(i) (2+) oscillations are present in cultured human cardiac fibroblasts and are regulated by multiple Ca(2+) pathways, which are not identical to those of the well-studied contractile cardiomyocytes. This study provides a base for future investigations into how Ca(2+) signals regulate biological activity in human cardiac fibroblasts and cardiac remodeling under pathological conditions.

What can we learn from the irregularity of Ca2+ oscillations?

In most cells, Ca(2+) increases in response to external stimulation are organized in the form of oscillations and waves that sometimes propagate from one cell to another. Numerous experimental and theoretical studies reveal that this spatiotemporal organization contains a non-negligible level of stochasticity. In this study, we extend the previous work based on a statistical analysis of experimental Ca(2+) traces in isolated, hormone-stimulated hepatocytes and on stochastic simulations of Ca(2+) oscillations based on the Gillespie's algorithm. Comparison of the coefficients of variation in the periods of experimental and simulated Ca(2+) spikes provides information about the clustering and the specific subtypes of the Ca(2+) channels. In hepatocytes coupled by gap junctions, the global perfusion with a hormone leads to successive Ca(2+) responses, giving the appearance of an intercellular wave. Statistical analysis of experimental Ca(2+) oscillations in coupled hepatocytes confirms that this coordinated Ca(2+) spiking corresponds to a phase wave but suggests the existence of an additional coupling mechanism.

Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release

Airway epithelium has been shown to exhibit intracellular calcium waves after mechanical stimulation. Two classes of mechanism have been proposed to explain calcium wave propagation: diffusion through gap junctions of the intracellular messenger inositol 1,4,5-trisphosphate (IP3), and diffusion of paracrine extracellular messengers such as ATP. We have used single cell recordings of airway epithelium to parameterize a model of an airway epithelial cell. This was then incorporated into a spatial model of a cell culture where both mechanisms for calcium wave propagation are possible. It is shown that a decreasing return on the radius of Ca2+ wave propagation is achieved as the amount of ATP released from the stimulated cell increases. It is therefore shown that for a Ca2+ wave to propagate large distances, a significant fraction of the intracellular ATP pool would be required to be released. Further to this, the radial distribution of maximal calcium response from the stimulated cell does not produce the same flat profile of maximal calcium response seen in experiential studies. This suggests that an additional mechanism is important in Ca2+ wave propagation, such as regenerative release of ATP from cells downstream of the stimulated cell.

A mathematical model of calcium-induced fluid secretion in airway epithelium

Regulation of periciliary liquid (PCL) depth is of central importance to mucociliary clearance by the airway epithelium. Without adequate hydration mucociliary transport would cease, leading to build up of mucus in the airways, and impairing the clearance of any trapped inhaled particulates. Airway epithelial cells are known to release ATP under a number of stress conditions. Cell surface receptors bind ATP and trigger an intracellular calcium response which regulates the gating of specific ion channels on the apical and basolateral cell membranes. This shifts the electrochemical balance, resulting in the accumulation of Na(+) and Cl(-) in the periciliary liquid, and providing an osmotic driving force for water flux. In this study, we present a mathematical model of a single airway epithelial cell which describes the fluid secretion elicited after a rise in intracellular calcium. The model provides a basis to quantitatively analyse the influence of intracellular calcium signalling on fluid movement. The model demonstrates behaviour consistent with a number of experimental data on manipulating periciliary liquid volume and tonicity, and provides a quantitative basis for analysing the role of the different membrane ion channels in determining water flux following different physiological stimuli.

Regulation of inositol 1,4,5-trisphosphate-induced Ca2+ release by reversible phosphorylation and dephosphorylation

The inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) is a universal intracellular Ca2+-release channel. It is activated after cell stimulation and plays a crucial role in the initiation and propagation of the complex spatio-temporal Ca2+ signals that control cellular processes as different as fertilization, cell division, cell migration, differentiation, metabolism, muscle contraction, secretion, neuronal processing, and ultimately cell death. To achieve these various functions, often in a single cell, exquisite control of the Ca2+ release is needed. This review aims to highlight how protein kinases and protein phosphatases can interact with the IP3R or with associated proteins and so provide a large potential for fine tuning the Ca2+-release activity and for creating efficient Ca2+ signals in subcellular microdomains.

Inhibition of serine/threonine phosphatase enhances arachidonic acid-induced [Ca2+]i via protein kinase A

Arachidonic acid (AA) regulates intracellular calcium concentration ([Ca2+]i) in a variety of cell types including salivary cells. In the present study, the effects of serine/threonine phosphatases on AA-induced Ca(2+) signaling in mouse parotid acini were determined. Mice were euthanized with CO2. Treatment of acini with the serine/threonine phosphatase inhibitor calyculin A blocked both thapsigargin- and carbachol-induced Ca2+ entry but resulted in an enhancement of AA-induced Ca2+ release and entry. Effects were mimicked by the protein phosphatase-1 (PP1) inhibitor tautomycin but were inhibited by the PP2A inhibitor okadaic acid. The protein kinase A (PKA) inhibitor PKI(14-22) significantly attenuated AA-induced enhancement of Ca2+ release and entry in the presence of calyculin A, whereas it had no effect on calyculin A-induced inhibition of thapsigargin-induced Ca2+ responses. The ryanodine receptor (RyR) inhibitor, tetracaine, and StHt-31, a peptide known to competitively inhibit type II PKA regulatory subunit binding to PKA-anchoring protein (AKAP), abolished calyculin A enhancement of AA-induced Ca2+ release and entry. StHt-31 also abolished forskolin potentiation of 4-chloro-3-ethylphenol (4-CEP) and AA on Ca2+ release but had no effect on 8-(4-methoxyphenylthio)-2'-O-methyladenosine-3',5'-cAMP potentiation of 4-CEP responses. Results suggest that inhibition of PP1 results in an enhancement of AA-induced [Ca2+]i via PKA, AKAP, and RyRs.

Expression and characterization of LTx2, a neurotoxin from Lasiodora sp. effecting on calcium channels

Here, we described the expression and characterization of the recombinant toxin LTx2, which was previously isolated from the venomous cDNA library of a Brazilian spider, Lasiodora sp. (Mygalomorphae, Theraphosidae). The recombinant toxin found in the soluble and insoluble fractions was purified by reverse phase high-performance liquid chromatography (HPLC). Ca2+ imaging analysis revealed that the recombinant LTx2 acts on calcium channels of BC3H1 cells, blocking L-type calcium channels.

The type 2 inositol (1,4,5)-trisphosphate (InsP3) receptor determines the sensitivity of InsP3-induced Ca2+ release to ATP in pancreatic acinar cells

Calcium release through inositol (1,4,5)-trisphosphate receptors (InsP(3)R) is the primary signal driving digestive enzyme and fluid secretion from pancreatic acinar cells. The type 2 (InsP(3)R2) and type 3 (InsP(3)R3) InsP(3)R are the predominant isoforms expressed in acinar cells and are required for proper exocrine gland function. Both InsP(3)R2 and InsP(3)R3 are positively regulated by cytosolic ATP, but InsP(3)R2 is 10-fold more sensitive than InsP(3)R3 to this form of modulation. In this study, we examined the role of InsP(3)R2 in setting the sensitivity of InsP(3)-induced Ca(2+) release (IICR) to ATP in pancreatic acinar cells. IICR was measured in permeabilized acinar cells from wild-type (WT) and InsP(3)R2 knock-out (KO) mice. ATP augmented IICR from WT pancreatic cells with an EC(50) of 38 microm. However, the EC(50) was 10-fold higher in acinar cells isolated from InsP(3)R2-KO mice, indicating a role for InsP(3)R2 in setting the sensitivity of IICR to ATP. Consistent with this idea, heterologous expression of InsP(3)R2 in RinM5F cells, which natively express predominately InsP(3)R3, increased the sensitivity of IICR to ATP. Depletion of ATP attenuated agonist-induced Ca(2+) signaling in WT pancreatic acinar cells. This effect was more profound in acinar cells prepared from InsP(3)R2-KO mice. These data suggest that the sensitivity of IICR to ATP depletion is regulated by the particular complement of InsP(3)R expressed in an individual cell. The effects of metabolic stress on intracellular Ca(2+) signals can therefore be determined by the relative amount of InsP(3)R2 expressed in cells.

Calcium oscillations induced by ATP in human umbilical cord smooth muscle cells

Arterial smooth muscle cells exhibit vasomotion, related to oscillations in intracellular Ca(2+) concentration, but the origin and function of these has not yet been fully determined. We measured intracellular Ca(2+) using conventional fluorescent methods in primary cultured, human umbilical cord artery smooth muscle cells (HUCASMC). Spontaneous oscillations in Ca(2+) was found in only 1% of all cells but exogenous, micromolar concentrations of ATP could induce Ca(2+) oscillations in 70% of cells with the most common pattern being one of regular amplitude and frequency with a return to basal levels between each peak. The P2Y agonist, UTP, but not the P2X agonist alphabeta-methylene ATP, could also induce Ca(2+) oscillations. Once induced, these oscillations could not be blocked by G-protein, PLC, VGCC or TRP channel antagonists applied individually, but could be prevented when antagonists were applied together. In the presence of EGTA, micromolar concentrations of ATP induced an elevation in intracellular Ca(2+) but did not induce Ca(2+) oscillations. The oscillation frequency induced by ATP was affected by bath Ca(2+) concentration. Taken together, these data suggest that external Ca(2+) entry maintains the Ca(2+) oscillation induced by activation of P2Y receptors. Once induced, multiple mechanisms are involved to maintain the oscillation and the oscillation frequency is determined by the speed of Ca(2+) refilling. Chronic hypoxia enhanced the Ca(2+) response and altered the oscillation frequency. We suggest that these oscillations may play a role in the maintenance of umbilical blood flow during situations in which GPCR are activated.

Hybrid stochastic and deterministic simulations of calcium blips

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment

The effects of pharmacological interventions that modulate Ca(2+) homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca(2+)] in the cytosol, [Ca(2+)] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca(2+) stores and transmembrane ion fluxes via K(+) channels, Cl(-) channels, and voltage-operated Ca(2+) channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca(2+)] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.

Modelling calcium microdomains using homogenisation

Microdomains of calcium (i.e., areas on the nanometer scale that have qualitatively different calcium concentrations from that in the bulk cytosol) are known to be important in many situations. In cardiac cells, for instance, a calcium microdomain between the L-type channels and the ryanodine receptors, the so-called diadic cleft, is where the majority of the control of calcium release occurs. In other cell types that exhibit calcium oscillations and waves, the importance of microdomains in the vicinity of clusters of inositol trisphosphate receptors, or between the endoplasmic reticulum (ER) and other internal organelles or the plasma membrane, is clear. Given the limits of computational power, it is not currently realistic to model an entire cellular cytoplasm by incorporating detailed structural information about the ER throughout the entire cytoplasm. Hence, most models use a homogenised approach, assuming that both cytoplasm and ER coexist at each point of the domain. Conversely, microdomain models can be constructed, in which detailed structural information can be incorporated, but, until now, methods have not been developed for linking such a microdomain model to a model at the level of the entire cell. Using the homogenisation approach we developed in an earlier paper [Goel, P., Friedman, A., Sneyd, J., 2006. Homogenization of the cell cytoplasm: the calcium bidomain equations. SIAM J. Multiscale Modeling Simulation, in press] we show how a multiscale model of a calcium microdomain can be constructed. In this model a detailed model of the microdomain (in which the ER and the cytoplasm are separate compartments) is coupled to a homogenised model of the entire cell in a rigorous way. Our method is illustrated by a simple model of the diadic cleft of a cardiac half-sarcomere.

A kinetic Monte Carlo simulation study of inositol 1,4,5-trisphosphate receptor (IP3R) calcium release channel

Most of the previously theoretical studies about the stochastic nature of the IP3R calcium release channel gating use the chemical master equation (CME) approach. Because of the limitations of this approach we have used a stochastic simulation algorithm (SSA) presented by Gillespie. A single subunit of De Young-Keizer (DYK) model was simulated using Gillespie algorithm. The model has been considered in its complete form with eight states. We investigate the conditions which affect the open state of the model. Calcium concentrations were the subject of fluctuation in the previous works while in this study the population of the states is the subject of stochastic fluctuations. We found out that decreasing open probability is a function of Ca(2+) concentration in fast time domain, while in slow time domain it is a function of IP3 concentration. Studying the population of each state shows a time dependent reaction pattern in fast and medium time domains (10(-4) and 10(-3)s). In this pattern the state of X(010) has a determinative role in selecting the open state path. Also, intensity and frequency of fluctuations and Ca(2+) inhibitions have been studied. The results indicate that Gillespie algorithm can be a better choice for studying such systems, without using any approximation or elimination while having acceptable accuracy. In comparison with the chemical master equation, Gillespie algorithm is also provides a wide area for studying biological systems from other points of view.

Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level

Many essential physiological processes are controlled by calcium. To ensure reliability and specificity, calcium signals are highly organized in time and space in the form of oscillations and waves. Interesting findings have been obtained at various scales, ranging from the stochastic opening of a single calcium channel to the intercellular calcium wave spreading through an entire organ. A detailed understanding of calcium dynamics thus requires a link between observations at different scales. It appears that some regulations such as calcium-induced calcium release or PLC activation by calcium, as well as the weak diffusibility of calcium ions play a role at all levels of organization in most cell types. To comprehend how calcium waves spread from one cell to another, specific gap-junctional coupling and paracrine signaling must also be taken into account. On the basis of a pluridisciplinar approach ranging from physics to physiology, a unified description of calcium dynamics is emerging, which could help understanding how such a small ion can mediate so many vital functions in living systems.

Cholecystokinin and gastrin receptors

Cholecystokinin and gastrin receptors (CCK1R and CCK2R) are G protein-coupled receptors that have been the subject of intensive research in the last 10 years with corresponding advances in the understanding of their functioning and physiology. In this review, we first describe general properties of the receptors, such as the different signaling pathways used to exert short- and long-term effects and the structural data that explain their binding properties, activation, and regulation. We then focus on peripheral cholecystokinin receptors by describing their tissue distribution and physiological actions. Finally, pathophysiological peripheral actions of cholecystokinin receptors and their relevance in clinical disorders are reviewed.

Calcium oscillations and waves generated by multiple release mechanisms in pancreatic acinar cells

We explore the dynamic behavior of a model of calcium oscillations and wave propagation in the basal region of pancreatic acinar cells [Sneyd, J., et al., Biophys. J. 85: 1392-1405, 2003]. Since it is known that two principal calcium release pathways are involved, inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR), we study how the model behavior depends on the density of each receptor type. Calcium oscillations can be mediated either by IPR or RyR. Continuous increases in either RyR or IPR density can lead to the appearance and disappearance of oscillations multiple times, and the two receptor types interact via their common effect on cytoplasmic calcium concentration and the subsequent effect on the total amount of calcium inside the cell. Increases in agonist concentration can stimulate oscillations via the RyR by increasing calcium influx. Using a two time-scale approach, we explain these complex behaviors by treating the total amount of cellular calcium as a slow parameter. Oscillations are controlled by the shape of the slow manifold and where it intersects the nullcline of the slow variable. When calcium diffusion is included, the existence of traveling waves in the model equation is strongly dependent on the interplay between the total amount of calcium in the cell and membrane transport, a feature that can be experimentally tested. Our results help us understand the behavior of a model that includes both receptors in comparison to the properties of each receptor type in isolation.

A buffering SERCA pump in models of calcium dynamics

Many cells use oscillations in calcium concentration to transmit messages. The oscillations largely result from an influx of calcium into the cytosol from the endoplasmic reticulum (ER), followed by an efflux of calcium from the cytosol back into the ER. The sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump pumps calcium into the ER. It binds calcium on the cytosolic side and releases it on the ER side and in the delay between binding and release, calcium is buffered by the pump. We developed a model of a buffering SERCA pump and investigated whether including this in a model of calcium oscillations has any significant effects. We found that the oscillations produced when using the SERCA pump, which does not buffer calcium, have a larger amplitude and a slightly smaller period than when using the buffering SERCA pump. We show that the buffering SERCA pump shows adaptation to a stimulus, and we demonstrate that, by using a bidirectional SERCA pump, we are able to eliminate futile cycling of calcium between the cytosol and ER when the cell is at rest.

Adrenergic modulation of the type 1 IP3 receptors in the rat heart

Inositol 1,4,5-trisphosphate (IP3) receptors are calcium-releasing channels localized on the sarcoplasmic reticulum. IP3 receptors mediate the calcium mobilizing effect of a wide range of hormones, cytokines, and neurotransmitters and play an important role in variety of cell functions. The aim of this work was to study, how partial depletion of catecholamines affects the gene expression and protein levels of the type 1 IP3 receptors in rat heart. The type 1 IP3 receptor mRNA levels were studied in the left cardiac atrium and ventricle of rats treated with 6-hydroxydopamine (6-OHDA) in control and stressed conditions. The 6-OHDA produces anatomical and functional denervation resulting in decreased levels of noradrenaline and adrenaline. We also used corticoliberin (CRH) knockout mice, where secretion of adrenaline is significantly suppressed. Administration of 6-OHDA significantly decreases mRNA levels of the type 1 IP3 receptor in both, the left atrium and the left ventricle, while the gene expression of the sarcoplasmic reticular Ca2+-ATPase (SERCA 2) was unaffected. CRH knockout mice possess markedly lower levels of the type 1 IP3 receptor mRNA compared to wild-type mice in both, control and stressed conditions. These data point to the adrenergic modulation of the type 1 IP3 receptors in the rat hearts.

Models of the inositol trisphosphate receptor

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We review deterministic and stochastic mathematical models of the IPR, from the earliest ones of the 1970s and 1980s, to the most recent. The effects of IPR stochasticity on Ca2+ dynamics are briefly discussed.

Stabilizing role of calcium store-dependent plasma membrane calcium channels in action-potential firing and intracellular calcium oscillations

In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP3)-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP3-mediated intracellular calcium oscillator. The IP3 receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP3 and Ca2+. We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP3 concentrations, our integrated NRK cell model is at rest at -70 mV. For higher IP3 concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP3 concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near -20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes.

Atherosclerosis and calcium signalling in endothelial cells

The link between atherosclerosis and regions of disturbed flow and low wall shear stress is now firmly established, but the causal mechanisms underlying the link are not yet understood. It is now recognised that the endothelium is not simply a passive barrier between the blood and the vessel wall, but plays an active role in maintaining vascular homeostasis and participates in the onset of atherosclerosis. Calcium signalling is one of the principal intracellular signalling mechanisms by which endothelial cells (EC) respond to external stimuli, such as fluid shear stress and ligand binding. Previous studies have separately modelled mass transport of chemical species in the bloodstream and calcium dynamics in EC via the inositol trisphosphate (IP(3)) signalling pathway. We review existing models of these two phenomena, before going on to integrate the two components to provide an inclusive new model for the calcium response of the endothelium in an arbitrary vessel geometry. This enables the combined effects of fluid flow and biochemical stimulation on EC to be investigated and is the first time spatially varying, physiological fluid flow-related environmental factors have been combined with intracellular signalling in a mathematical model. Model results show that low endothelial calcium levels in the area of disturbed flow at an arterial widening may be one contributing factor to the onset of vascular disease.

The effect of residual on the stochastic gating of -regulated channel models

Single-channel models of intracellular Ca(2+) channels such as the inositol 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca(2+)-dependent transitions are mediated by a constant background [Ca(2+)] as opposed to a dynamic [Ca(2+)] representing the formation and collapse of a localized Ca(2+) domain. This assumption neglects the fact that Ca(2+) released by open intracellular Ca(2+) channels may influence subsequent gating through the processes of Ca(2+)-activation or -inactivation. We study the effect of such "residual Ca(2+)" from previous channel opening on the stochastic gating of minimal and realistic single-channel models coupled to a restricted cytoplasmic compartment. Using Monte Carlo simulation as well as analytical and numerical solution of a system of advection-reaction equations for the probability density of the domain [Ca(2+)] conditioned on the state of the channel, we determine how the steady-state open probability (p(open)) of single-channel models of Ca(2+)-regulated Ca(2+) channels depends on the time constant for Ca(2+) domain formation and collapse. As expected, p(open) for a minimal model including Ca(2+) activation increases as the domain time constant becomes large compared to the open and closed dwell times of the channel, that is, on average the channel is activated by residual Ca(2+) from previous openings. Interestingly, p(open) for a channel model that is inactivated by Ca(2+) also increases as a function of the domain time constant when the maximum domain [Ca(2+)] is fixed, because slow formation of the Ca(2+) domain attenuates Ca(2+)-mediated inactivation. Conversely, when the source amplitude of the channel is fixed, increasing the domain time constant leads to elevated domain [Ca(2+)] and decreased open probability. Consistent with these observations, a realistic De Young-Keizer-like IP(3)R model responds to residual Ca(2+) with a steady-state open probability that is a monotonic function of the domain time constant, though minimal models that include both Ca(2+)-activation and -inactivation show more complex behavior. We show how the probability density approach described here can be generalized for arbitrarily complex channel models and for any value of the domain time constant. In addition, we present a comparatively simple numerical procedure for estimating p(open) for models of Ca(2+)-regulated Ca(2+) channels in the limit of a very fast or very slow Ca(2+) domain. When the ordinary differential equation for the [Ca(2+)] in a restricted cytoplasmic compartment is replaced by a partial differential equation for the buffered diffusion of intracellular Ca(2+) in a homogeneous isotropic cytosol, we find the dependence of p(open) on the buffer time constant is qualitatively similar to the above-mentioned results.

Modelling of calcium handling in airway myocytes

Airway myocytes are the primary effectors of airway reactivity which modulates airway resistance and hence ventilation. Stimulation of airway myocytes results in an increase in the cytosolic Ca(2+) concentration ([Ca(2+)](i)) and the subsequent activation of the contractile apparatus. Many contractile agonists, including acetylcholine, induce [Ca(2+)](i) increase via Ca(2+) release from the sarcoplasmic reticulum through InsP(3) receptors. Several models have been developed to explain the characteristics of InsP(3)-induced [Ca(2+)](i) responses, in particular Ca(2+) oscillations. The article reviews the modelling of the major structures implicated in intracellular Ca(2+) handling, i.e., InsP(3) receptors, SERCAs, mitochondria and Ca(2+)-binding cytosolic proteins. We developed theoretical models specifically dedicated to the airway myocyte which include the major mechanisms responsible for intracellular Ca(2+) handling identified in these cells. These biocomputations pointed out the importance of the relative proportion of InsP(3) receptor isoforms and the respective role of the different mechanisms responsible for cytosolic Ca(2+) clearance in the pattern of [Ca(2+)](i) variations. We have developed a theoretical model of membrane conductances that predicts the variations in membrane potential and extracellular Ca(2+) influx. Stimulation of this model by simulated increase in [Ca(2+)](i) predicts membrane depolarisation, but not great enough to trigger a significant opening of voltage-dependant Ca(2+) channels. This may explain why airway contraction induced by cholinergic stimulation does not greatly depend on extracellular calcium. The development of such models of airway myocytes is important for the understanding of the cellular mechanisms of airway reactivity and their possible modulation by pharmacological agents.

Agonist activation of arachidonate-regulated Ca2+-selective (ARC) channels in murine parotid and pancreatic acinar cells

ARC channels (arachidonate-regulated Ca(2+)-selective channels) are a novel type of highly Ca(2+)-selective channel that are specifically activated by low concentrations of agonist-induced arachidonic acid. This activation occurs in the absence of any depletion of internal Ca(2+) stores (i.e. they are 'non-capacitative'). Previous studies in HEK293 cells have shown that these channels provide the predominant pathway for the entry of Ca(2+) seen at low agonist concentrations where oscillatory [Ca(2+)](i) signals are typically produced. In contrast, activation of the more widely studied store-operated Ca(2+) channels (e.g. CRAC channels) is only seen at higher agonist concentrations where sustained 'plateau-type'[Ca(2+)](i) responses are observed. We have now demonstrated the presence of ARC channels in both parotid and pancreatic acinar cells and shown that, again, they are specifically activated by the low concentrations of appropriate agonists (carbachol in the parotid, and both carbachol and cholecystokinin in the pancreas) that are associated with oscillatory [Ca(2+)](i) signals in these cells. Uncoupling the receptor-mediated activation of cytosolic phospholipase A(2) (cPLA(2)) with isotetrandrine reduces the activation of the ARC channels by carbachol and, correspondingly, markedly inhibits the [Ca(2+)](i) signals induced by low carbachol concentrations, whilst those signals seen at high agonist concentrations are essentially unaffected. Interestingly, in the pancreatic acinar cells, activation by cholecystokinin induces a current through the ARC channels that is only approximately 60% of that seen with carbachol. This is consistent with previous reports indicating that carbachol-induced [Ca(2+)](i) signals in these cells are much more dependent on Ca(2+) entry than are the cholecystokinin-induced responses.

Changes in IP3 receptor are associated with altered calcium response to cholecystokinin in diabetic rat pancreatic acini

OBJECTIVES

Pancreatic acini of diabetic rats release amylase less than normal acini on cholecystokinin (CCK) stimulation. Pancreatic enzyme secretion by CCK is closely related to the second messenger inositol 1,4,5-trisphosphate (IP3), which mobilizes intracellular calcium stores via the endoplasmic reticulum-located receptor IP3 (IP3R). Recently, we observed altered intracellular calcium response on CCK-8 stimulation in streptozotocin (STZ)- treated diabetic rat acini.

METHODS

To determine whether IP3R is involved in altered calcium response, we measured inositol phosphate (IP) formation and the expression and phosphorylation of type III IP3R protein in diabetic acini. Also, CCK receptor mRNA expression was examined to determine whether the changes in IP formation and IP3R protein phosphorylation in diabetic acini might result from the defect at the postreceptor level.

RESULTS

CCK-8-induced IP formation at all concentrations used was significantly reduced in diabetic acini, though IP formation was increased in a concentration-dependent manner. The expression of type III IP3R protein was significantly reduced in diabetic acini. Additionally, CCK-8-stimulated phosphorylation of type III IP3R protein was not observed in diabetic acini. However, the reduction of CCK receptor mRNA expression was not detected in diabetic acini.

CONCLUSION

Our results indicate that altered calcium response to CCK-8 in diabetic acini might be associated with a post-CCK receptor defect including the changes in IP formation, type III IP3R protein expression, and phosphorylation of type III IP3R protein.

InsP3 receptor type 2 and oscillatory and monophasic Ca2+ transients in rat adrenal chromaffin cells

Muscarinic receptor stimulation induced oscillatory and monophasic Ca(2+) transients in rat adrenal chromaffin cells in the absence of external Ca(2+). As this Ca(2+) mobilization may be mediated by InsP(3), we first explored types of InsP(3) receptors and their intracellular distribution in chromaffin cells. The InsP(3) receptor type 1 was not immunodetected in precipitates of adrenal medulla homogenates and in dissociated adrenal chromaffin cells, whereas an anti-type 3 mAb recognized a faint band with about 250 kDa, but no significant immunoreaction was visible in chromaffin cells. The anti-type 2 mAb strongly detected a band with about 220 kDa and the immunoreaction was observed perinuclearly and at the cell periphery. These results indicate that InsP(3) receptor type 2 is predominant in chromaffin cells. The oscillatory and monophasic Ca(2+) transients were reproduced in simulation based on a three-state kinetic model (shut, open, and inactivated states). Ca(2+) ions were found experimentally and theoretically to turn over rapidly between stores and the cytosol during stimulation. The results suggest that InsP(3) receptor type 2 is responsible for both oscillatory and monophasic Ca(2+) transients and that change in mode of Ca(2+) responses may be accounted for by the kinetic property of the type 2 receptor.

A comparison of three models of the inositol trisphosphate receptor

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We compare three mathematical models of the IPR, fitting each of them to the same data set to determine ranges for the parameter values. Each of the fits indicates that fast activation of the receptor, followed by slow inactivation, is an important feature of the model, and also that the speed of inositol trisphosphate IP3 binding cannot necessarily be assumed to be faster than Ca2+ activation. In addition, the model which assumed saturating binding rates of Ca2+ to the IPR demonstrated the best fit. However, lack of convergence in the fitting procedure indicates that responses to step increases of Ca2+ and IP3 provide insufficient data to determine the parameters unambiguously in any of the models.

Control of calcium oscillations by membrane fluxes

It is known that Ca(2+) influx plays an important role in the modulation of inositol trisphosphate-generated Ca(2+) oscillations, but controversy over the mechanisms underlying these effects exists. In addition, the effects of blocking membrane transport or reducing Ca(2+) entry vary from one cell type to another; in some cell types oscillations persist in the absence of Ca(2+) entry (although their frequency is affected), whereas in other cell types oscillations depend on Ca(2+) entry. We present theoretical and experimental evidence that membrane transport can control oscillations by controlling the total amount of Ca(2+) in the cell (the Ca(2+) load). Our model predicts that the cell can be balanced at a point where small changes in the Ca(2+) load can move the cell into or out of oscillatory regions, resulting in the appearance or disappearance of oscillations. Our theoretical predictions are verified by experimental results from HEK293 cells. We predict that the role of Ca(2+) influx during an oscillation is to replenish the Ca(2+) load of the cell. Despite this prediction, even during the peak of an oscillation the cell or the endoplasmic reticulum may not be measurably depleted of Ca(2+).

Crosstalk between cAMP and Ca2+ signaling in non-excitable cells

An impressive array of cytosolic calcium ([Ca2+](i)) signals exert control over a broad range of physiological processes. The specificity and fidelity of these [Ca2+](i) signals is encoded by the frequency, amplitude, and sub-cellular localization of the response. It is believed that the distinct characteristics of [Ca2+](i) signals underlies the differential activation of effectors and ultimately cellular events. This "shaping" of [Ca2+](i) signals can be achieved by the influence of additional signaling pathways modulating the molecular machinery responsible for generating [Ca2+](i) signals. There is a particularly rich source of potential sites of crosstalk between the cAMP and the [Ca2+](i) signaling pathways. This review will focus on the predominant molecular loci at which these classical signaling systems interact to impact the spatio-temporal pattern of [Ca2+](i) signaling in non-excitable cells.