Control of calcium oscillations by membrane fluxes

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

Intracellular Calcium Dynamics in Primary Human Adrenocortical Cells Deciphered with a Novel Pipeline

INTRODUCTION

The fluctuations of the intracellular Ca2+ concentration ([Ca2+]i) are key physiological signals for cell function under normal conditions and can undergo profound alterations in disease states, as high blood pressure due to endocrine disorders like primary aldosteronism (PA). However, when assessing such fluctuations several parameters in the Ca2+ signal dynamics need to be considered, which renders their assessment challenging.

AIM

Aim to develop an observer-independent custom-made pipeline to analyze Ca2+ dynamics in terms of frequency and peak parameters, as amplitude, full width at half maximum (FWHM) and area under the curve (AUC).

METHODS

We applied a custom-made methodology to aldosterone-producing adenoma (APA) and APA adjacent cells (AAC) and found this pipeline to be suitable for monitoring and processing a wide-range of [Ca2+]i events in these cell types delivering reproducible results.

CONCLUSION

The designed pipeline can provide a useful tool for [Ca2+]i signal analysis that allows comparisons of Ca2+ dynamics not only in PA, but in other cell phenotypes that are relevant for the regulation of blood pressure.

An integrate-and-fire approach to Ca2+ signaling. Part II: Cumulative refractoriness

Inositol 1,4,5-trisphosphate-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. The agonist concentration stimulating Ca2+ signals is encoded in the frequency of a Ca2+ concentration spike sequence. When a cell is stimulated, the interspike intervals (ISIs) often show a distinct transient during which they gradually increase, a system property we refer to as cumulative refractoriness. We extend a previously published stochastic model to include the Ca2+ concentration in the intracellular Ca2+ store as a slow adaptation variable. This model can reproduce both stationary and transient statistics of experimentally observed ISI sequences. We derive approximate expressions for the mean and coefficient of variation of the stationary ISIs. We also consider the response to the onset of a constant stimulus and estimate the length of the transient and the strength of the adaptation of the ISI. We show that the adaptation sets the coefficient of variation in agreement with current ideas derived from experiments. Moreover, we explain why, despite a pronounced transient behavior, ISI correlations can be weak, as often observed in experiments. Finally, we fit our model to reproduce the transient statistics of experimentally observed ISI sequences in stimulated HEK cells. The fitted model is able to qualitatively reproduce the relationship between the stationary interval correlations and the number of transient intervals, as well as the strength of the ISI adaptation. We also find positive correlations in the experimental sequence that cannot be explained by our model.

Omnitemporal choreographies of all five STIM/Orai and IP3Rs underlie the complexity of mammalian Ca2+ signaling

Stromal-interaction molecules (STIM1/2) sense endoplasmic reticulum (ER) Ca²⁺ depletion and activate Orai channels. However, the choreography of interactions between native STIM/Orai proteins under physiological agonist stimulation is unknown. We show that the five STIM1/2 and Orai1/2/3 proteins are non-redundant and function together to ensure the graded diversity of mammalian Ca²⁺ signaling. Physiological Ca²⁺ signaling requires functional interactions between STIM1/2, Orai1/2/3, and IP₃Rs, ensuring that receptor-mediated Ca²⁺ release is tailored to Ca²⁺ entry and nuclear factor of activated T cells (NFAT) activation. The N-terminal Ca²⁺-binding ER-luminal domains of unactivated STIM1/2 inhibit IP₃R-evoked Ca²⁺ release. A gradual increase in agonist intensity and STIM1/2 activation relieves IP₃R inhibition. Concomitantly, activated STIM1/2 C termini differentially interact with Orai1/2/3 as agonist intensity increases. Thus, coordinated and omnitemporal functions of all five STIM/Orai and IP₃Rs translate the strength of agonist stimulation to precise levels of Ca²⁺ signaling and NFAT induction, ensuring the fidelity of complex mammalian Ca²⁺ signaling.

Ca2+ oscillations in rat carotid body type 1 cells in normoxia and hypoxia

We studied the mechanisms by which carotid body glomus (type 1) cells produce spontaneous Ca²⁺ oscillations in normoxia and hypoxia. In cells perfused with normoxic solution at 37°C, we observed relatively uniform, low-frequency Ca²⁺ oscillations in >60% of cells, with each cell showing its own intrinsic frequency and amplitude. The mean frequency and amplitude of Ca²⁺ oscillations were 0.6 ± 0.1 Hz and 180 ± 42 nM, respectively. The duration of each Ca²⁺ oscillation ranged from 14 to 26 s (mean of ∼20 s). Inhibition of inositol (1,4,5)-trisphosphate receptor and store-operated Ca²⁺ entry (SOCE) using 2-APB abolished Ca²⁺ oscillations. Inhibition of endoplasmic reticulum Ca²⁺-ATPase (SERCA) using thapsigargin abolished Ca²⁺ oscillations. ML-9, an inhibitor of STIM1 translocation, also strongly reduced Ca²⁺ oscillations. Inhibitors of L- and T-type Ca²⁺ channels (Ca_v; verapamil>nifedipine>TTA-P2) markedly reduced the frequency of Ca²⁺ oscillations. Thus, Ca²⁺ oscillations observed in normoxia were caused by cyclical Ca²⁺ fluxes at the ER, which was supported by Ca²⁺ influx via Ca²⁺ channels. Hypoxia (2-5% O₂) increased the frequency and amplitude of Ca²⁺ oscillations, and Ca_v inhibitors (verapamil>nifedipine>>TTA-P2) reduced these effects of hypoxia. Our study shows that Ca²⁺ oscillations represent the basic Ca²⁺ signaling mechanism in normoxia and hypoxia in CB glomus cells.

A Statistical View on Calcium Oscillations

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics

Upon inositol trisphosphate (IP₃) stimulation of non-excitable cells, including vascular endothelial cells, calcium (Ca²⁺) shuttling between the endoplasmic reticulum (ER) and mitochondria, facilitated by complexes called Mitochondria-Associated ER Membranes (MAMs), is known to play an important role in the occurrence of cytosolic Ca²⁺ concentration ([Ca²⁺]_Cyt) oscillations. A mathematical compartmental closed-cell model of Ca²⁺ dynamics was developed that accounts for ER-mitochondria Ca²⁺ microdomains as the µd compartment (besides the cytosol, ER and mitochondria), Ca²⁺ influx to/efflux from each compartment and Ca²⁺ buffering. Varying the distribution of functional receptors in MAMs vs. the rest of ER/mitochondrial membranes, a parameter called the channel connectivity coefficient (to the µd), allowed for generation of [Ca²⁺]_Cytoscillations driven by distinct mechanisms at various levels of IP₃ stimulation. Oscillations could be initiated by the transient opening of IP₃ receptors facing either the cytosol or the µd, and subsequent refilling of the respective compartment by Ca²⁺ efflux from the ER and/or the mitochondria. Only under conditions where the µd became the oscillation-driving compartment, silencing the Mitochondrial Ca²⁺ Uniporter led to oscillation inhibition. Thus, the model predicts that alternative mechanisms can yield [Ca²⁺]_Cyt oscillations in non-excitable cells, and, under certain conditions, the ER-mitochondria µd can play a regulatory role.

Estradiol-Mediated Axogenesis of Hypothalamic Neurons Requires ERK1/2 and Ryanodine Receptors-Dependent Intracellular Ca2+ Rise in Male Rats

17β-estradiol (E2) induces axonal growth through extracellular signal-regulated kinase 1 and 2 (ERK1/2)-MAPK cascade in hypothalamic neurons of male rat embryos in vitro, but the mechanism that initiates these events is poorly understood. This study reports the intracellular Ca²⁺ increase that participates in the activation of ERK1/2 and axogenesis induced by E2. Hypothalamic neuron cultures were established from 16-day-old male rat embryos and fed with astroglia-conditioned media for 48 h. E2-induced ERK phosphorylation was completely abolished by a ryanodine receptor (RyR) inhibitor (ryanodine) and partially attenuated by an L-type voltage-gated Ca²⁺ channel (L-VGCC) blocker (nifedipine), an inositol-1,4,5-trisphosphate receptor (IP₃R) inhibitor (2-APB), and a phospholipase C (PLC) inhibitor (U-73122). We also conducted Ca²⁺ imaging recording using primary cultured neurons. The results show that E2 rapidly induces an increase in cytosolic Ca²⁺, which often occurs in repetitive Ca²⁺ oscillations. This response was not observed in the absence of extracellular Ca²⁺ or with inhibitory ryanodine and was markedly reduced by nifedipine. E2-induced axonal growth was completely inhibited by ryanodine. In summary, the results suggest that Ca²⁺ mobilization from extracellular space as well as from the endoplasmic reticulum is necessary for E2-induced ERK1/2 activation and axogenesis. Understanding the mechanisms of brain estrogenic actions might contribute to develop novel estrogen-based therapies for neurodegenerative diseases.

Coding and decoding of oscillatory Ca2+ signals

About 30 years after their first observation, Ca²⁺ oscillations are now recognised as a universal mechanism of signal transduction. These oscillations are driven by periodic cycles of release and uptake of Ca²⁺ between the cytoplasm and the endoplasmic reticulum. Their frequency often increases with the level of stimulation, which can be decoded by some molecules. However, it is becoming increasingly evident that the widespread core oscillatory mechanism is modulated in many ways, depending on the cell type and on the physiological conditions. Interplay with inositol 1,4,5-trisphosphate metabolism and with other Ca²⁺ stores as the extracellular medium or mitochondria can much affect the properties of these oscillations. In many cases, these finely tuned characteristics of Ca²⁺ oscillations impact the physiological response that is triggered by the signal. Moreover, oscillations are intrinsically irregular. This randomness can also be exploited by the cell. In this review, we discuss evidences of these additional manifestations of the versatility of Ca²⁺ signalling.

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

Ca2+ signalling in mouse urethral smooth muscle in situ: role of Ca2+ stores and Ca2+ influx mechanisms

KEY POINTS

Contraction of urethral smooth muscle cells (USMCs) contributes to urinary continence. Ca2+ signalling in USMCs was investigated in intact urethral muscles using a genetically encoded Ca2+ sensor, GCaMP3, expressed selectively in USMCs. USMCs were spontaneously active in situ, firing intracellular Ca2+ waves that were asynchronous at different sites within cells and between adjacent cells. Spontaneous Ca2+ waves in USMCs were myogenic but enhanced by adrenergic or purinergic agonists and decreased by nitric oxide. Ca2+ waves arose from inositol trisphosphate type 1 receptors and ryanodine receptors, and Ca2+ influx by store-operated calcium entry was required to maintain Ca2+ release events. Ca2+ release and development of Ca2+ waves appear to be the primary source of Ca2+ for excitation-contraction coupling in the mouse urethra, and no evidence was found that voltage-dependent Ca2+ entry via L-type or T-type channels was required for responses to α adrenergic responses.

ABSTRACT

Urethral smooth muscle cells (USMCs) generate myogenic tone and contribute to urinary continence. Currently, little is known about Ca2+ signalling in USMCs in situ, and therefore little is known about the source(s) of Ca2+ required for excitation-contraction coupling. We characterized Ca2+ signalling in USMCs within intact urethral muscles using a genetically encoded Ca2+ sensor, GCaMP3, expressed selectively in USMCs. USMCs fired spontaneous intracellular Ca2+ waves that did not propagate cell-to-cell across muscle bundles. Ca2+ waves increased dramatically in response to the α1 adrenoceptor agonist phenylephrine (10 μm) and to ATP (10 μm). Ca2+ waves were inhibited by the nitric oxide donor DEA NONOate (10 μm). Ca2+ influx and release from sarcoplasmic reticulum stores contributed to Ca2+ waves, as Ca2+ free bathing solution and blocking the sarcoplasmic Ca2+ -ATPase abolished activity. Intracellular Ca2+ release involved cooperation between ryanadine receptors and inositol trisphosphate receptors, as tetracaine and ryanodine (100 μm) and xestospongin C (1 μm) reduced Ca2+ waves. Ca2+ waves were insensitive to L-type Ca2+ channel modulators nifedipine (1 μm), nicardipine (1 μm), isradipine (1 μm) and FPL 64176 (1 μm), and were unaffected by the T-type Ca2+ channel antagonists NNC-550396 (1 μm) and TTA-A2 (1 μm). Ca2+ waves were reduced by the store operated Ca2+ entry blocker SKF 96365 (10 μm) and by an Orai antagonist, GSK-7975A (1 μm). The latter also reduced urethral contractions induced by phenylephrine, suggesting that Orai can function effectively as a receptor-operated channel. In conclusion, Ca2+ waves in mouse USMCs are a source of Ca2+ for excitation-contraction coupling in urethral muscles.

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.

Wave failure at strong coupling in intracellular Ca^{2+} signaling system with clustered channels

As an important intracellular signal, Ca^{2+} ions control diverse cellular functions. In this paper, we discuss the Ca^{2+} signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate (IP_{3}) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large Ca^{2+} diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological Ca^{2+} signaling systems.

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.

Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations

Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.

Rhythmic behavior is omnipresent in biology and has many crucial functions. In cells the activation levels and abundances of signaling molecules such as NF-κB, p53, EGFR or calcium repeatedly increase and decrease in response to stimuli. Such a dynamic behavior can also be observed monitoring the concentrations of mRNAs and proteins in the circadian clock and the cell cycle. Period and amplitude which are the time span between peaks and the peak height, respectively, as well as their variabilities are important features of oscillations. The circadian period is very stable allowing for proper time keeping, whereas in calcium signaling the period is very variable encoding different stimulation strengths. Our goal is to examine the origin of differences in sensitivities of periods and amplitudes using a computational approach. We use prototype oscillators and demonstrate that they can be used to derive general principles that explain the degree of robustness in period and amplitude for a set of commonly used models of cellular oscillators. Our findings imply that the robustness of oscillating systems can be influenced by feedback type and kinetic properties to which special attention should be paid when designing mathematical models of cellular rhythms.

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.

Nuclear pores enable sustained perinuclear calcium oscillations

Background

Calcium signalling relies on the flux of calcium ions across membranes yet how signals in different compartments are related remains unclear. In particular, similar calcium signals on both sides of the nuclear envelope have been reported and attributed to passive diffusion through nuclear pores. However, observed differing cytosolic and nucleosolic calcium signatures suggest that the signalling machinery in these compartments can act independently.

Results

We adapt the fire-diffuse-fire model to investigate the generation of perinuclear calcium oscillations. We demonstrate that autonomous spatio-temporal calcium patterns are still possible in the presence of nuclear and cytosolic coupling via nuclear pores. The presence or absence of this autonomy is dependent upon the strength of the coupling and the maximum firing rate of an individual calcium channel. In all cases, coupling through the nuclear pores enables robust signalling with respect to changes in the diffusion constant.

Conclusions

We show that contradictory interpretations of experimental data with respect to the autonomy of nuclear calcium oscillations can be reconciled within one model, with different observations being a consequence of varying nuclear pore permeabilities for calcium and refractory conditions of channels. Furthermore, our results provide an explanation for why calcium oscillations on both sides of the nuclear envelope may be beneficial for sustained perinuclear signaling.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0289-9) contains supplementary material, which is available to authorized users.

Cellular Architecture Regulates Collective Calcium Signaling and Cell Contractility

A key feature of multicellular systems is the ability of cells to function collectively in response to external stimuli. However, the mechanisms of intercellular cell signaling and their functional implications in diverse vascular structures are poorly understood. Using a combination of computational modeling and plasma lithography micropatterning, we investigate the roles of structural arrangement of endothelial cells in collective calcium signaling and cell contractility. Under histamine stimulation, endothelial cells in self-assembled and microengineered networks, but not individual cells and monolayers, exhibit calcium oscillations. Micropatterning, pharmacological inhibition, and computational modeling reveal that the calcium oscillation depends on the number of neighboring cells coupled via gap junctional intercellular communication, providing a mechanistic basis of the architecture-dependent calcium signaling. Furthermore, the calcium oscillation attenuates the histamine-induced cytoskeletal reorganization and cell contraction, resulting in differential cell responses in an architecture-dependent manner. Taken together, our results suggest that endothelial cells can sense and respond to chemical stimuli according to the vascular architecture via collective calcium signaling.

Sodium-calcium exchanger and R-type Ca(2+) channels mediate spontaneous [Ca(2+)]i oscillations in magnocellular neurones of the rat supraoptic nucleus

Isolated supraoptic neurones generate spontaneous [Ca(2+)]i oscillations in isolated conditions. Here we report in depth analysis of the contribution of plasmalemmal ion channels (Ca(2+), Na(+)), Na(+)/Ca(2+) exchanger (NCX), intracellular Ca(2+) release channels (InsP3Rs and RyRs), Ca(2+) storage organelles, plasma membrane Ca(2+) pump and intracellular signal transduction cascades into spontaneous Ca(2+) activity. While removal of extracellular Ca(2+) or incubation with non-specific voltage-gated Ca(2+) channel (VGCC) blocker Cd(2+) suppressed the oscillations, neither Ni(2+) nor TTA-P2, the T-type VGCC blockers, had an effect. Inhibitors of VGCC nicardipine, ω-conotoxin GVIA, ω-conotoxin MVIIC, ω-agatoxin IVA (for L-, N-, P and P/Q-type channels, respectively) did not affect [Ca(2+)]i oscillations. In contrast, a specific R-type VGCC blocker SNX-482 attenuated [Ca(2+)]i oscillations. Incubation with TTX had no effect, whereas removal of the extracellular Na(+) or application of an inhibitor of the reverse operation mode of Na(+)/Ca(2+) exchanger KB-R7943 blocked the oscillations. The mitochondrial uncoupler CCCP irreversibly blocked spontaneous [Ca(2+)]i activity. Exposure of neurones to Ca(2+) mobilisers (thapsigargin, cyclopiazonic acid, caffeine and ryanodine); 4-aminopyridine (A-type K(+) current blocker); phospholipase C and adenylyl cyclase pathways blockers U-73122, Rp-cAMP, SQ-22536 and H-89 had no effect. Oscillations were blocked by GABA, but not by glutamate, apamin or dynorphin. In conclusion, spontaneous oscillations in magnocellular neurones are mediated by a concerted action of R-type Ca(2+) channels and the NCX fluctuating between forward and reverse modes.

Routes of Ca2+ Shuttling during Ca2+ Oscillations: FOCUS ON THE ROLE OF MITOCHONDRIAL Ca2+ HANDLING AND CYTOSOLIC Ca2+ BUFFERS

In some cell types, Ca²⁺ oscillations are strictly dependent on Ca²⁺ influx across the plasma membrane, whereas in others, oscillations also persist in the absence of Ca²⁺ influx. We observed that, in primary mesothelial cells, the plasmalemmal Ca²⁺ influx played a pivotal role. However, when the Ca²⁺ transport across the plasma membrane by the “lanthanum insulation method” was blocked prior to the induction of the serum-induced Ca²⁺ oscillations, mitochondrial Ca²⁺ transport was found to be able to substitute for the plasmalemmal Ca²⁺ exchange function, thus rendering the oscillations independent of extracellular Ca²⁺. However, in a physiological situation, the Ca²⁺-buffering capacity of mitochondria was found not to be essential for Ca²⁺ oscillations. Moreover, brief spontaneous Ca²⁺ changes were observed in the mitochondrial Ca²⁺ concentration without apparent changes in the cytosolic Ca²⁺ concentration, indicating the presence of a mitochondrial autonomous Ca²⁺ signaling mechanism. In the presence of calretinin, a Ca²⁺-buffering protein, the amplitude of cytosolic spikes during oscillations was decreased, and the amount of Ca²⁺ ions taken up by mitochondria was reduced. Thus, the increased calretinin expression observed in mesothelioma cells and in certain colon cancer might be correlated to the increased resistance of these tumor cells to proapoptotic/pronecrotic signals. We identified and characterized (experimentally and by modeling) three Ca²⁺ shuttling pathways in primary mesothelial cells during Ca²⁺ oscillations: Ca²⁺ shuttled between (i) the endoplasmic reticulum (ER) and mitochondria, (ii) the ER and the extracellular space, and (iii) the ER and cytoplasmic Ca²⁺ buffers.

The role of IP3 receptor channel clustering in Ca2+ wave propagation during oocyte maturation

During oocyte maturation, the calcium-signaling machinery undergoes a dramatic remodeling resulting in distinctly different calcium-release patterns on all organizational scales from puffs to waves. The dynamics of the Ca(2+) release wave in mature as compared to immature oocytes are defined by a slower propagation speed and longer duration of the high Ca(2+) plateau. In this chapter, we use computational modeling to identify the changes in the signaling machinery, which contribute most significantly to the alterations observed in Ca(2+) wave propagation during Xenopus oocyte maturation. In addition to loss of store-operated calcium entry and internalization of plasma membrane pumps, we propose that spatial reorganization of the IP3 receptors in the plane of the ER membrane is a key factor for the observed signaling changes in Ca(2+) wave propagation.

Robust concentration and frequency control in oscillatory homeostats

Homeostatic and adaptive control mechanisms are essential for keeping organisms structurally and functionally stable. Integral feedback is a control theoretic concept which has long been known to keep a controlled variable A robustly (i.e. perturbation-independent) at a given set-point A(set) by feeding the integrated error back into the process that generates A. The classical concept of homeostasis as robust regulation within narrow limits is often considered as unsatisfactory and even incompatible with many biological systems which show sustained oscillations, such as circadian rhythms and oscillatory calcium signaling. Nevertheless, there are many similarities between the biological processes which participate in oscillatory mechanisms and classical homeostatic (non-oscillatory) mechanisms. We have investigated whether biological oscillators can show robust homeostatic and adaptive behaviors, and this paper is an attempt to extend the homeostatic concept to include oscillatory conditions. Based on our previously published kinetic conditions on how to generate biochemical models with robust homeostasis we found two properties, which appear to be of general interest concerning oscillatory and homeostatic controlled biological systems. The first one is the ability of these oscillators ("oscillatory homeostats") to keep the average level of a controlled variable at a defined set-point by involving compensatory changes in frequency and/or amplitude. The second property is the ability to keep the period/frequency of the oscillator tuned within a certain well-defined range. In this paper we highlight mechanisms that lead to these two properties. The biological applications of these findings are discussed using three examples, the homeostatic aspects during oscillatory calcium and p53 signaling, and the involvement of circadian rhythms in homeostatic regulation.

Calcium signalling in Cajal-like interstitial cells of the lower urinary tract

Interstitial cells of Cajal (ICC) serve several critical physiological roles in visceral smooth muscle organs, including acting as electrical pacemakers to modulate phasic contractile activity and as intermediaries in motor neurotransmission. The major roles of ICC have been described in the gastrointestinal tract, however, ICC-like cells (ICC-LC) can also be found in other visceral organs, including those of the lower urinary tract (LUT), where they provide similar functions, acting as electrical pacemakers and as intermediary cells involved in the modulation of neurotransmission to adjacent smooth muscle cells. The physiological functions of ICC-LC, in particular their role as pacemakers, relies on their ability to generate transient and propagating intracellular Ca(2+) events. The role of ICC-LC as pacemakers and neuromodulators in the LUT is increasingly apparent and the study of their intracellular Ca(2+) dynamics will provide a better understanding of their role in LUT excitability.

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.

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.

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.

Are Orai1 and Orai3 channels more important than calcium influx for cell proliferation?

Transformed and tumoral cells share the characteristic of being able to proliferate even when external calcium concentration is very low. We have investigated whether Human Embryonic Kidney 293 cells, human hepatoma cell Huh-7 and HeLa cells were able to proliferate when kept 72h in complete culture medium without external calcium. Our data showed that cell proliferation rate was similar over a range of external calcium concentration (2μM to 1.8mM). Incubation in the absence of external calcium for 72h had no significant effect on endoplasmic reticulum (ER) Ca(2+) contents but resulted in a significant decrease in cytosolic free calcium concentration in all 3 cell types. Cell proliferation rates were dependent on Orai1 and Orai3 expression levels in HEK293 and HeLa cells. Silencing Orai1 or Orai3 resulted in a 50% reduction in cell proliferation rate. Flow cytometry analysis showed that Orai3 induced a small but significant increase in cell number in G2/M phase. RO-3306, a cdk-1 inhibitor, induced a 90% arrest in G2/M reversible in less than 15min. Our data showed that progression through G2/M phase after release from RO-3306-induced cell cycle arrest was slower in both Orai1 and Orai3 knock-downs. Overexpressing Orai1, Orai3 and the dominant negative non-permeant mutants E106Q-Orai1 and E81Q-Orai3 induced a 50% increase in cell proliferation rate in HEK293 cells. Our data clearly demonstrated that Orai1 and Orai3 proteins are more important than calcium influx to control cell proliferation in some cell lines and that this process is probably independent of ICRAC and Iarc.

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

Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.

Membrane associated complexes in calcium dynamics modelling

Mitochondria not only govern energy production, but are also involved in crucial cellular signalling processes. They are one of the most important organelles determining the Ca(2+) regulatory pathway in the cell. Several mathematical models explaining these mechanisms were constructed, but only few of them describe interplay between calcium concentrations in endoplasmic reticulum (ER), cytoplasm and mitochondria. Experiments measuring calcium concentrations in mitochondria and ER suggested the existence of cytosolic microdomains with locally elevated calcium concentration in the nearest vicinity of the outer mitochondrial membrane. These intermediate physical connections between ER and mitochondria are called MAM (mitochondria-associated ER membrane) complexes. We propose a model with a direct calcium flow from ER to mitochondria, which may be justified by the existence of MAMs, and perform detailed numerical analysis of the effect of this flow on the type and shape of calcium oscillations. The model is partially based on the Marhl et al model. We have numerically found that the stable oscillations exist for a considerable set of parameter values. However, for some parameter sets the oscillations disappear and the trajectories of the model tend to a steady state with very high calcium level in mitochondria. This can be interpreted as an early step in an apoptotic pathway.

Store-operated calcium entry could prevent continuous spiking of membrane potential to sustain normal intracellular calcium oscillations and normal potential bursting in pancreatic β-cells

We propose a dynamical store-operated calcium entry (SOCE) model to analyze the complex role of SOCE in modulating calcium oscillations and electrical activity in pancreatic β-cells and provide a new mathematical insight. Using this model, we simulate the SOCE role in a number of cases with different SOCE conductances. When the SOCE conductance is set to 0 or very small (5 pS), our numerical simulation conforms to the experimental observation that endoplasmic reticulum (ER) calcium can sustain normal calcium oscillations and the depletion of ER calcium transforms the normal calcium oscillations into a sustained calcium increase with oscillations of much higher frequency and much smaller amplitude, and transforms the normal membrane potential oscillations to a pattern of continuous spiking. When the SOCE conductance is increased to 20 pS and the ER calcium is depleted, our numerical simulation conforms to the other experimental observation that the normal calcium and potential oscillations are sustained and augmented a little bit. Moreover, the oscillation frequency is increased a very little bit. A further increase of the conductance to 35 pS slows down the oscillation a little bit. This numerical evidence suggests that a sufficiently large SOCE can prevent the continuous spiking of membrane potential to sustain the normal calcium oscillations and the normal membrane potential bursting. A careful examination of our simulated dynamics of the ATP/ADP ratio, the ATP-sensitive outward K(+) current, and the voltage-gated inward Ca(2+) current reveals that intracellular periodic Ca(2+) peaks perhaps resulted from SOCE might play a role in stabilizing the membrane potential at its resting level (avoiding the continuous spiking) for a certain period of time by accelerating ATP consumption, reducing the ratio ATP/ADP, opening the ATP-sensitive potassium channel, and repolarizing the membrane potential.

Modeling the contributions of Ca2+ flows to spontaneous Ca2+ oscillations and cortical spreading depression-triggered Ca2+ waves in astrocyte networks

Astrocytes participate in brain functions through Ca(2+) signals, including Ca(2+) waves and Ca(2+) oscillations. Currently the mechanisms of Ca(2+) signals in astrocytes are not fully clear. Here, we present a computational model to specify the relative contributions of different Ca(2+) flows between the extracellular space, the cytoplasm and the endoplasmic reticulum of astrocytes to the generation of spontaneous Ca(2+) oscillations (CASs) and cortical spreading depression (CSD)-triggered Ca(2+) waves (CSDCWs) in a one-dimensional astrocyte network. This model shows that CASs depend primarily on Ca(2+) released from internal stores of astrocytes, and CSDCWs depend mainly on voltage-gated Ca(2+) influx. It predicts that voltage-gated Ca(2+) influx is able to generate Ca(2+) waves during the process of CSD even after depleting internal Ca(2+) stores. Furthermore, the model investigates the interactions between CASs and CSDCWs and shows that the pass of CSDCWs suppresses CASs, whereas CASs do not prevent the generation of CSDCWs. This work quantitatively analyzes the generation of astrocytic Ca(2+) signals and indicates different mechanisms underlying CSDCWs and non-CSDCWs. Research on the different types of Ca(2+) signals might help to understand the ways by which astrocytes participate in information processing in brain functions.

Multilevel complexity of calcium signaling: Modeling angiogenesis

Intracellular calcium signaling is a universal, evolutionary conserved and versatile regulator of cell biochemistry. The complexity of calcium signaling and related cell machinery can be investigated by the use of experimental strategies, as well as by computational approaches. Vascular endothelium is a fascinating model to study the specific properties and roles of calcium signals at multiple biological levels. During the past 20 years, live cell imaging, patch clamp and other techniques have allowed us to detect and interfere with calcium signaling in endothelial cells (ECs), providing a huge amount of information on the regulation of vascularization (angiogenesis) in normal and tumoral tissues. These data range from the spatiotemporal dynamics of calcium within different cell microcompartments to those in entire multicellular and organized EC networks. Beside experimental strategies, in silico endothelial models, specifically designed for simulating calcium signaling, are contributing to our knowledge of vascular physiology and pathology. They help to investigate and predict the quantitative features of proangiogenic events moving through subcellular, cellular and supracellular levels. This review focuses on some recent developments of computational approaches for proangiogenic endothelial calcium signaling. In particular, we discuss the creation of hybrid simulation environments, which combine and integrate discrete Cellular Potts Models. They are able to capture the phenomenological mechanisms of cell morphological reorganization, migration, and intercellular adhesion, with single-cell spatiotemporal models, based on reaction-diffusion equations that describe the agonist-induced intracellular calcium events.

A multi-scale approach to airway hyperresponsiveness: from molecule to organ

Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca²⁺ signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Localized activation of proteins in a free intracellular space: dependence of cellular morphologies and reaction schemes

Localized activation of proteins in a cell is crucial for the segregation of cellular functions leading, for example, to the development of polarized cells and chemotaxis. If there is a physical diffusion barrier, localized activation of proteins will emerge. In case of no physical barrier, however, it is not clear to what extent the protein activation is localized within a three dimensional intracellular space. In the previous report we showed a simulation result of localized activation of Ca(2+)/calmodulin-dependent kinase II (CaMKII) within a dendritic spine of a neuron, and this localization was enhanced by the diffusion of calmodulin. However, a dendritic spine will act as a physical diffusion barrier. Here, we report that the localization of activated proteins is seen in more simplified morphology with no diffusion barrier. Furthermore, this localization was seen with a simple reaction scheme. In case that a Ca(2+) source was located at the center of the spherical cell with diameter of 20μm, which is the extreme case without any physical diffusion barrier, the simulation results showed localized activation of a protein around the Ca(2+) source. This localized activation was also enhanced by the diffusion of calmodulin. These localizations were not blurred with time within the tested time range. The reason for the increase in the localization by the diffusion of calmodulin was the replenishment of free calmodulin from surrounding regions. These simulation results indicate that the localized activation of proteins emerges in biological cells without any physical diffusion barrier, and the replenishment of proteins by diffusion can act as an enhancer of localized activation of downstream proteins.

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.

Activation and regulation of store-operated calcium entry

The process of store-operated Ca²⁺ entry (SOCE), whereby Ca²⁺ influx across the plasma membrane is activated in response to depletion of intracellular Ca²⁺ stores in the endoplasmic reticulum (ER), has been under investigation for greater than 25 years; however, only in the past 5 years have we come to understand this mechanism at the molecular level. A surge of recent experimentation indicates that STIM molecules function as Ca²⁺ sensors within the ER that, upon Ca²⁺ store depletion, rearrange to sites very near to the plasma membrane. At these plasma membrane-ER junctions, STIM interacts with and activates SOCE channels of the Orai family. The molecular and biophysical data that have led to these findings are discussed in this review, as are several controversies within this rapidly expanding field.

The physiological function of store-operated calcium entry

Store-operated Ca(2+) entry is a process whereby the depletion of intracellular Ca(2+) stores signals the opening of plasma membrane Ca(2+) channels. It has long been thought that the main function of store-operated Ca(2+) entry was the replenishment of intracellular Ca(2+) stores following their discharge during intracellular Ca(2+) signaling. Recent results, however, suggest that the primary function of these channels may be to provide direct Ca(2+) signals to recipients localized to spatially restricted areas close to the sites of Ca(2+) entry in order to initiate specific signaling pathways.

Rational method in the repetitive calcium oscillation measurement in wild type human epithelial kidney cells

Cells stimulated with physiological stimuli usually exhibit oscillations in cytosolic Ca(2+) concentration ([Ca(2+)](i)), a signal playing central roles in regulation of various cellular processes. For explicating their unknown mechanisms, studies are commonly conducted in single cells from several cell lines, in particular the human epithelial kidney (HEK293) cell line. However, [Ca(2+)](i) oscillating responses to agonists in vitro are found difficult to be induced and varied with different types of cells and agonists. This study shows that treatment of the wild type HEK293 cells with low concentrations of carbachol (1-10 μM), an agonist of the muscarinic receptor, resulted in non-oscillated but sustained [Ca(2+)](i) increase by loading the cells with 1 μM fura2/AM. However, repetitive and long lasting [Ca(2+)](i) oscillations could be induced in 31.1% of the tested cells loaded with 0.1 μM fura2/AM. Additionally, the occurrence of the typical Ca(2+) spikes further increased to 47.2% and 60.7% when the Ca(2+) concentration in the bathing medium was decreased from 1.8 mM to 1.5 mM and the medium temperature was set to 35 ± 1°C from 22 ± 2°C. Therefore, this study provides a useful approach for measuring [Ca(2+)](i) oscillatory response to relevant physiological stimulation in a wild type cell line through the adjustments of the concentrations adopted for the Ca(2+) indicator and extracellular medium Ca(2+) and of the temperature set for the experiment.

Understanding anomalous delays in a model of intracellular calcium dynamics

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al., "A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations," Proc. Natl. Acad. Sci. U.S.A. 103, 1675-1680 (2006)] that the mechanisms underlying the generation and control of such oscillations can be determined by means of a simple experiment, whereby a single exogenous pulse of inositol trisphosphate (IP(3)) is applied to the cell. However, more detailed mathematical investigations [M. Domijan et al., "Dynamical probing of the mechanisms underlying calcium oscillations," J. Nonlinear Sci. 16, 483-506 (2006)] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of models that make different assumptions about the mechanisms underlying the calcium oscillations. In particular, we show how recently developed canard theory for singularly perturbed systems with three or more slow variables [M. Wechselberger, "A propos de canards (Apropos canards)," Preprint, 2010] applies to these calcium models and how the presence of a curve of folded singularities and corresponding canards can result in anomalous delays in the response of these models to a pulse of IP(3).

A mathematical analysis of agonist- and KCl-induced Ca(2+) oscillations in mouse airway smooth muscle cells

Airway hyperresponsiveness is a major characteristic of asthma and is generally ascribed to excessive airway narrowing associated with the contraction of airway smooth muscle cells (ASMCs). ASMC contraction is initiated by a rise in intracellular calcium concentration ([Ca(2+)](i)), observed as oscillatory Ca(2+) waves that can be induced by either agonist or high extracellular K(+) (KCl). In this work, we present a model of oscillatory Ca(2+) waves based on experimental data that incorporate both the inositol trisphosphate receptor and the ryanodine receptor. We then combined this Ca(2+) model and our modified actin-myosin cross-bridge model to investigate the role and contribution of oscillatory Ca(2+) waves to contractile force generation in mouse ASMCs. The model predicts that: 1), the difference in behavior of agonist- and KCl-induced Ca(2+) waves results principally from the fact that the sarcoplasmic reticulum is depleted during agonist-induced oscillations, but is overfilled during KCl-induced oscillations; 2), regardless of the order in which agonist and KCl are added into the cell, the resulting [Ca(2+)](i) oscillations will always be the short-period, agonist-induced-like oscillations; and 3), both the inositol trisphosphate receptor and the ryanodine receptor densities are higher toward one end of the cell. In addition, our results indicate that oscillatory Ca(2+) waves generate less contraction than whole-cell Ca(2+) oscillations induced by the same agonist concentration. This is due to the spatial inhomogeneity of the receptor distributions.

Designing dynamical output feedback controllers for store-operated Ca²+ entry

Store-operated calcium entry (SOCE) has been proposed as the main process controlling Ca²+ entry in non-excitable cells. Although recent breakthroughs in experimental studies of SOCE have been made, its mathematical modeling has not been developed. In the present work, SOCE is viewed as a feedback control system subject to an extracellular agonist disturbance and an extracellular calcium input. We then design a dynamic output feedback controller to reject the disturbance and track Ca²+ resting levels in the cytosol and the endoplasmic reticulum (ER). The constructed feedback control system is validated by published experimental data and its global asymptotic stability is proved by using the LaSalle's invariance principle. We then simulate the dynamic responses of STIM1 and Orai1, two major components in the operation of the store-operated channels, to the depletion of Ca²+ in the ER with thapsigargin, which show that: (1) Upon the depletion of Ca²+ in the ER, the concentrations of activated STIM1 and STIM1-Orai1 cluster are elevated gradually, indicating that STIM1 is accumulating in the ER-PM junctions and that the cytosolic portion of the active STIM1 is binding to Orai1 and driving the opening of CRAC channels for Ca²+ entry; (2) after the extracellular Ca²+ addition, the concentrations of both STIM1 and STIM1-Orai1 cluster decrease but still much higher than the original levels. We also simulate the system responses to the agonist disturbance, which show that, when a sequence of periodic agonist pulses is applied, the system returns to its equilibrium after each pulse. This indicates that the designed feedback controller can reject the disturbance and track the equilibrium.

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.

Ca2+-activated K channels in parotid acinar cells: The functional basis for the hyperpolarized activation of BK channels

Fluid secretion relies on a close interplay between Ca(2+)-activated Cl and K channels. Salivary acinar cells contain both large conductance, BK, and intermediate conductance, IK1, K channels. Physiological fluid secretion occurs with only modest (<500 nM) increases in intracellular Ca(2+) levels but BK channels in many cell types and in heterologous expression systems require very high concentrations for significant activation. We report here our efforts to understand this apparent contradiction. We determined the Ca(2+) dependence of IK1 and BK channels in mouse parotid acinar cells. IK1 channels activated with an apparent Ca(2+) affinity of about 350 nM and a Hill coefficient near 3. Native parotid BK channels activated at similar Ca(2+) levels unlike the BK channels in other cell types. Since the parotid BK channel is encoded by an uncommon splice variant, we examined this clone in a heterologous expression system. In contrast to the native parotid channel, activation of this expressed "parSlo" channel required very high levels of Ca(2+). In order to understand the functional basis for the special properties of the native channels, we analyzed the parotid BK channel in the context of the Horrigan-Aldrich model of BK channel gating. We found that the shifted activation of parotid BK channels resulted from a hyperpolarizing shift of the voltage dependence of voltage sensor activation and channel opening and included a large change in the coupling of these two processes.

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.