Two roles of Ca2+ in agonist stimulated Ca2+ oscillations

IP3RPEP6, a novel peptide inhibitor of IP3 receptor channels that does not affect connexin-43 hemichannels

AIM

Inositol 1,4,5-trisphosphate receptors (IP3 Rs) are intracellular Ca2+ -release channels with crucial roles in cell function. Current IP3 R inhibitors suffer from off-target effects and poor selectivity towards the three distinct IP3 R subtypes. We developed a novel peptide inhibitor of IP3 Rs and determined its effect on connexin-43 (Cx43) hemichannels, which are co-activated by IP3 R stimulation.

METHODS

IP3RPEP6 was developed by in silico molecular docking studies and characterized by on-nucleus patch-clamp experiments of IP3 R2 channels and carbachol-induced IP3 -mediated Ca2+ responses in IP3 R1, 2 or 3 expressing cells, triple IP3 R KO cells and astrocytes. Cx43 hemichannels were studied by patch-clamp and ATP-release approaches, and by inhibition with Gap19 peptide. IP3RPEP6 interactions with IP3 Rs were verified by co-immunoprecipitation and affinity pull-down assays.

RESULTS

IP3RPEP6 concentration-dependently reduced the open probability of IP3 R2 channels and competitively inhibited IP3 Rs in an IC50 order of IP3 R2 (~3.9 μM) < IP3 R3 (~4.3 μM) < IP3 R1 (~9.0 μM), without affecting Cx43 hemichannels or ryanodine receptors. IP3RPEP6 co-immunoprecipitated with IP3 R2 but not with IP3 R1; interaction with IP3 R3 varied between cell types. The IC50 of IP3RPEP6 inhibition of carbachol-induced Ca2+ responses decreased with increasing cellular Cx43 expression. Moreover, Gap19-inhibition of Cx43 hemichannels significantly reduced the amplitude of the IP3 -Ca2+ responses and strongly increased the EC50 of these responses. Finally, we identified palmitoyl-8G-IP3RPEP6 as a membrane-permeable IP3RPEP6 version allowing extracellular application of the IP3 R-inhibiting peptide.

CONCLUSION

IP3RPEP6 inhibits IP3 R2/R3 at concentrations that have limited effects on IP3 R1. IP3 R activation triggers hemichannel opening, which strongly affects the amplitude and concentration-dependence of IP3 -triggered Ca2+ responses.

On the Ca2＋ elevation in vascular endothelial cells due to inositol trisphosphate-sensitive store receptors activation: A data-driven modeling approach

Agonist-induced Ca2+ signaling is essential for the regulation of many vital functions in endothelial cells (ECs). A broad range of stimuli elevate the cytosolic Ca2＋ concentration by promoting a pathway mediated by inositol 1,4,5 trisphosphate (IP3) which causes Ca2＋ release from intracellular stores. Despite its importance, there are very few studies focusing on the quantification of such dynamics in the vascular endothelium. Here, by using data from isolated ECs, we established a minimalistic modeling framework able to quantitatively capture the main features (averaged over a cell population) of the cytosolic Ca2＋ response to different IP3 stimulation levels. A suitable description of Ca2＋-regulatory function of inositol 1,4,5 trisphosphate receptors (IP3Rs) and corresponding parameter space are identified by comparing the different model variants against experimental mean population data. The same approach is used to numerically assess the relevance of cytosolic Ca2＋ buffering, as well as Ca2＋ store IP3-sensitivity in the overall cell dynamics. The variability in the dynamics' features observed across the population can be explained (at least in part) through variation of certain model parameters (such as buffering capacity or Ca2＋ store sensitivity to IP3). The results, in terms of experimental fitting and validation, support the proposed minimalistic model as a reference framework for the quantification of the EC Ca2＋ dynamics induced by IP3Rs activation.

Genomic divergence during artificial selection by feed conversion ratio in Pekin ducks

Pekin ducks are world-famous for its fast growth and have become the majority of breeds rearing in duck industry. Feed conversion ratio (FCR) is an important trait in Pekin ducks breeding and production, and the underlying biological processes are complex. To gain an insight to the possible biological mechanism underlying the FCR in Pekin ducks, an artificial selection population (S) and a natural population (Z7) were used in this study. The FCR of S line decreased from 2.184 ± 0.057 in the first generation to 1.886 ± 0.063 in the eighth generation, which displays significantly low FCR (p = 0.0032) than that of the Z7 line (2.23 ± 0.046). Then, 9 samples from eighth generation of S line and 10 samples from Z7 were used for whole-genome resequencing. Analyses of F_ST, θπ and XP-EHH revealed 450, 479 and 356 candidate genes, which involved in 1,955, 1,933 and 1,964 candidate divergent regions (CDRs), respectively. And the integration of three approaches resulted in 30 overlapping genes. Functional analysis of 30 candidate genes revealed that variants of KCNQ1 and ADCY7, which were involved in the pancreatic secretion signal pathway, could be important molecular markers for high feed conversion efficiency in S line breeding.

Structure-function relationships of the disease-linked A218T oxytocin receptor variant

Various single nucleotide polymorphisms (SNPs) in the oxytocin receptor (OXTR) gene have been associated with behavioral traits, autism spectrum disorder (ASD) and other diseases. The non-synonymous SNP rs4686302 results in the OXTR variant A218T and has been linked to core characteristics of ASD, trait empathy and preterm birth. However, the molecular and intracellular mechanisms underlying those associations are still elusive. Here, we uncovered the molecular and intracellular consequences of this mutation that may affect the psychological or behavioral outcome of oxytocin (OXT)-treatment regimens in clinical studies, and provide a mechanistic explanation for an altered receptor function. We created two monoclonal HEK293 cell lines, stably expressing either the wild-type or A218T OXTR. We detected an increased OXTR protein stability, accompanied by a shift in Ca²⁺ dynamics and reduced MAPK pathway activation in the A218T cells. Combined whole-genome and RNA sequencing analyses in OXT-treated cells revealed 7823 differentially regulated genes in A218T compared to wild-type cells, including 429 genes being associated with ASD. Furthermore, computational modeling provided a molecular basis for the observed change in OXTR stability suggesting that the OXTR mutation affects downstream events by altering receptor activation and signaling, in agreement with our in vitro results. In summary, our study provides the cellular mechanism that links the OXTR rs4686302 SNP with genetic dysregulations associated with aspects of ASD.

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).

A Model for the Acrosome Reaction in Mammalian Sperm

The acrosome reaction is a complex, calcium-dependent reaction that results in an exocytotic event required for successful fertilization of the egg. It has long been thought that the acrosome reaction occurs upon sperm binding to the zona pellucida, a viscoelastic layer surrounding the oocyte. Recent studies have suggested that the reaction may even occur before the sperm encounters the zona, perhaps mediated by progesterone or some other agonist. It has been particularly difficult to understand differences between progesterone-induced and zona-induced reactions experimentally and whether one substance is the more biologically relevant trigger. Until this present work, there has been little effort to mathematically model the acrosome reaction in sperm as a whole. Instead, attention has been paid to modeling portions of the pathways involved in other cell types. Here we present a base model for the acrosome reaction which characterizes the known biochemical reactions and behaviors of the system. Our model allows us to analyze several pathways that may act as a stabilizing mechanism for avoiding sustained oscillatory calcium responses often observed in other cell types. Such an oscillatory regime might otherwise prevent acrosomal exocytosis and therefore inhibit fertilization. Results indicate that the acrosome reaction may rely upon multiple redundant mechanisms to avoid entering an oscillatory state and instead maintain a high resting level of calcium, known to be required for successful acrosomal exocytosis and, ultimately, fertilization of the oocyte.

The Phase Lag between Agonist-Induced Oscillatory Ca2+ and IP3 Signals Does Not Imply Causality (December 2015)

Activated phospholipase C (PLC*) generates 1,4,5-triphosphate (IP₃) and diacylglycerol (DAG) from phosphatidyl inositol (PIP₂). The DAG remains in the plasma membrane and co-activates conventional protein kinase C (PKC) with Ca²⁺. We have developed a mathematical model for the activation of the Ca²⁺-dependent PKC and its negative feedback on phospholipase C (PLC) and coupled it to the De Young-Keizer model for IP₃ mediated Ca²⁺ oscillations. The model describes the cascade of reactions for the translocation of PKC to plasma membrane, and simulates activation of Ca²⁺ and diacylglycerol (DAG) oscillations. The model demonstrates that oscillations in Ca²⁺ and DAG are possible with or without a positive Ca²⁺ feedback on phospholipase C consistent with experiment. In many experimental studies, the timing of the peaks of the Ca²⁺ and IP₃ oscillations have been used to suggest causality, i.e. that the IP₃ oscillations cause the Ca²⁺ oscillations. The model is used to explore this question. To this end, the positive and negative feedback between Ca²⁺ and IP₃ production are modulated, resulting in changes to the phase lag between the peaks in [Ca²⁺]_cyt and [IP]_cyt. The model simulates a possible experimental protocol that can be used to differentiate whether or not the positive feedback of Ca²⁺ on PLC is needed for the oscillations.

Neurovascular coupling: a parallel implementation

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular K⁺ and the smooth muscle cell (SMC) Ca²⁺ pathway termed a neurovascular unit (NVU). Luminal agonists acting on P2Y receptors on the endothelial cell (EC) surface provide a flux of inositol trisphosphate (IP₃) into the endothelial cytosol. This concentration of IP₃ is transported via gap junctions between EC and SMC providing a source of sarcoplasmic derived Ca²⁺ in the SMC. The model is able to relate a neuronal input signal to the corresponding vessel reaction (contraction or dilation). A tissue slice consisting of blocks, each of which contain an NVU is connected to a space filling H-tree, simulating a perfusing arterial tree (vasculature) The model couples the NVUs to the vascular tree via a stretch mediated Ca²⁺ channel on both the EC and SMC. The SMC is induced to oscillate by increasing an agonist flux in the EC and hence increased IP₃ induced Ca²⁺ from the SMC stores with the resulting calcium-induced calcium release (CICR) oscillation inhibiting NVC thereby relating blood flow to vessel contraction and dilation following neuronal activation. The coupling between the vasculature and the set of NVUs is relatively weak for the case with agonist induced where only the Ca²⁺ in cells inside the activated area becomes oscillatory however, the radii of vessels both inside and outside the activated area oscillate (albeit small for those outside). In addition the oscillation profile differs between coupled and decoupled states with the time required to refill the cytosol with decreasing Ca²⁺ and increasing frequency with coupling. The solution algorithm is shown to have excellent weak and strong scaling. Results have been generated for tissue slices containing up to 4096 blocks.

Immobilized IL-8 Triggers Phagocytosis and Dynamic Changes in Membrane Microtopology in Human Neutrophils

The interaction of leukocytes with surface bound ligands can be limited by the location of the molecules relative to the surface topology of the cell. In this report, we examine the dynamic response of neutrophils to IL-8-fractalkine chimera immobilized on bead surfaces, taking into account changes in receptor occupancy resulting from changes in surface topography. As a readout for receptor signaling, we observe the dynamics of calcium release in neutrophils following contact with the IL-8 coated surface. After a delay that depended on the initial area of contact and the surface density of IL-8, the cell began to phagocytose the IL-8 coated bead. This appeared to be a pre-requisite for release of calcium, which typically followed shortly after the initiation of phagocytosis. In separate experiments, effective kinetic coefficients for the formation of bonds between immobilized IL-8 and receptors on the cell surface were determined. Using these coefficients, we were able to estimate the number of bound receptors in the nascent contact zone. Kinetic modeling of the signaling response predicted that cell spreading and a concomitant increase in the density of occupied receptors would be required for the experimentally observed calcium dynamics. Postulating that there is an increase in receptor occupancy resulting from smoothing of the cell surface as it is stretched over the bead enabled us to obtain model predictions consistent with experimental observations. This study reveals the likely importance of membrane microtopology as a rate-limiting property and potential means of regulation of cell responses stimulated by two-dimensional surface interactions.

Neurovascular coupling and the influence of luminal agonists via the endothelium

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular K(+) and the smooth muscle cell Ca(2+) pathway. Luminal agonists acting on P2Y receptors on the endothelial cell surface provide a flux of IP3 into the endothelial cytosol. This concentration of IP3 is transported via gap junctions between endothelial and smooth muscle cells providing a source of sacroplasmic derived Ca(2+) in the smooth muscle cell. The model is able to relate a neuronal input signal to the corresponding vessel reaction. Results indicate that blood flow mediated IP3 production via the agonist ATP has a substantial effect on the contraction/dilation dynamics of the SMC. The resulting variation in cytosolic Ca(2+) can enhance and inhibit the flow of blood to the cortical tissue. IP3 coupling between endothelial and smooth muscle cells seems to be important in the dynamics of the smooth muscle cell. The VOCC channels are, due to the hyperpolarisation from K(+) SMC efflux, almost entirely closed and do not seem to play a significant role during neuronal activity. The current model shows that astrocytic Ca(2+) is not necessary for neurovascular coupling to occur in contrast to a number of experiments outlining the importance of astrocytic Ca(2+) in NVC, however this Ca(2+) pathway is not the only one mediating NVC. Importantly agonists in flowing blood have a significant influence on the endothelial and smooth muscle cell dynamics.

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 spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness

Spontaneous calcium (Ca2+) oscillations (SCOs) in astrocytes might be a crucial signaling for the multipurpose role of this type of cell in several brain functions. To interpret experimental data of astrocytic SCOs, which has been largely observed in the last decade, several groups have attempted to accommodate biophysical models that were developed in the past for Ca2+ signaling in other cell types. In most of the cases, only predictive strategies were used to estimate specific parameters of these modified models from actual experiments. In this study, we discuss the most remarkable models used to describe Ca2+ signaling in astrocytes. At the same time, we aim to revise the particulars of applying these models to interpret epifluorescent time series obtained from large regions of interest. Specially, we developed a detailed model for global Ca2+ signaling in the somata of astrocytes. In order to estimate some of the parameters in our model, we propose a deductive reasoning strategy, i.e., a statistical inference method that results from combining a filtering technique and a maximum likelihood principle. By means of computer simulations, we evaluate the accuracy of this estimation's strategy. Finally, we use the new model, in combination with a recent experimental findings by our group, to estimate the degree of cluster coupling inside the soma during the genesis of global Ca2+ events.

Connexin 43 hemichannels contribute to cytoplasmic Ca2+ oscillations by providing a bimodal Ca2+-dependent Ca2+ entry pathway

Many cellular functions are driven by changes in the intracellular Ca(2+) concentration ([Ca(2+)](i)) that are highly organized in time and space. Ca(2+) oscillations are particularly important in this respect and are based on positive and negative [Ca(2+)](i) feedback on inositol 1,4,5-trisphosphate receptors (InsP(3)Rs). Connexin hemichannels are Ca(2+)-permeable plasma membrane channels that are also controlled by [Ca(2+)](i). We aimed to investigate how hemichannels may contribute to Ca(2+) oscillations. Madin-Darby canine kidney cells expressing connexin-32 (Cx32) and Cx43 were exposed to bradykinin (BK) or ATP to induce Ca(2+) oscillations. BK-induced oscillations were rapidly (minutes) and reversibly inhibited by the connexin-mimetic peptides (32)Gap27/(43)Gap26, whereas ATP-induced oscillations were unaffected. Furthermore, these peptides inhibited the BK-triggered release of calcein, a hemichannel-permeable dye. BK-induced oscillations, but not those induced by ATP, were dependent on extracellular Ca(2+). Alleviating the negative feedback of [Ca(2+)](i) on InsP(3)Rs using cytochrome c inhibited BK- and ATP-induced oscillations. Cx32 and Cx43 hemichannels are activated by <500 nm [Ca(2+)](i) but inhibited by higher concentrations and CT9 peptide (last 9 amino acids of the Cx43 C terminus) removes this high [Ca(2+)](i) inhibition. Unlike interfering with the bell-shaped dependence of InsP(3)Rs to [Ca(2+)](i), CT9 peptide prevented BK-induced oscillations but not those triggered by ATP. Collectively, these data indicate that connexin hemichannels contribute to BK-induced oscillations by allowing Ca(2+) entry during the rising phase of the Ca(2+) spikes and by providing an OFF mechanism during the falling phase of the spikes. Hemichannels were not sufficient to ignite oscillations by themselves; however, their contribution was crucial as hemichannel inhibition stopped the oscillations.

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.

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.

Highly cooperative dependence of sarco/endoplasmic reticulum calcium ATPase SERCA2a pump activity on cytosolic calcium in living cells

Sarco/endoplasmic reticulum (SR/ER) Ca(2+)-ATPase (SERCA) is an intracellular Ca(2+) pump localized on the SR/ER membrane. The role of SERCA in refilling intracellular Ca(2+) stores is pivotal for maintaining intracellular Ca(2+) homeostasis, and disturbed SERCA activity causes many disease phenotypes, including heart failure, diabetes, cancer, and Alzheimer disease. Although SERCA activity has been described using a simple enzyme activity equation, the dynamics of SERCA activity in living cells is still unknown. To monitor SERCA activity in living cells, we constructed an enhanced CFP (ECFP)- and FlAsH-tagged SERCA2a, designated F-L577, which retains the ATP-dependent Ca(2+) pump activity. The FRET efficiency between ECFP and FlAsH of F-L577 is dependent on the conformational state of the molecule. ER luminal Ca(2+) imaging confirmed that the FRET signal changes directly reflect the Ca(2+) pump activity. Dual imaging of cytosolic Ca(2+) and the FRET signals of F-L577 in intact COS7 cells revealed that SERCA2a activity is coincident with the oscillatory cytosolic Ca(2+) concentration changes evoked by ATP stimulation. The Ca(2+) pump activity of SERCA2a in intact cells can be expressed by the Hill equation with an apparent affinity for Ca(2+) of 0.41 ± 0.0095 μm and a Hill coefficient of 5.7 ± 0.73. These results indicate that in the cellular environment the Ca(2+) dependence of ATPase activation is highly cooperative and that SERCA2a acts as a rapid switch to refill Ca(2+) stores in living cells for shaping the intracellular Ca(2+) dynamics. F-L577 will be useful for future studies on Ca(2+) signaling involving SERCA2a activity.

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.

A model of CatSper channel mediated calcium dynamics in mammalian spermatozoa

CatSpers are calcium (Ca(2+)) channels that are located along the principal piece of mammalian sperm flagella and are directly linked to sperm motility and hyperactivation. It has been observed that Ca(2+) entry through CatSper channels triggers a tail to head Ca(2+) propagation in mouse sperm, as well as a sustained increase of Ca(2+) in the head. Here, we develop a mathematical model to investigate this propagation and sustained increase in the head. A 1-d reaction-diffusion model tracking intracellular Ca(2+) with flux terms for the CatSper channels, a leak flux, and plasma membrane Ca(2+) clearance mechanism is studied. Results of this simple model exhibit tail to head Ca(2+) propagation, but no sustained increase in the head. Therefore, in this model, a simple plasma membrane pump-leak system with diffusion in the cytosol cannot account for these experimentally observed results. It has been proposed that Ca(2+) influx from the CatSper channels induce additional Ca(2+) release from an internal store. We test this hypothesis by examining the possible role of Ca(2+) release from the redundant nuclear envelope (RNE), an inositol 1,4,5-trisphosphate (IP(3)) gated Ca(2+) store in the neck. The simple model is extended to include an equation for IP(3) synthesis, degradation, and diffusion, as well as flux terms for Ca(2+) in the RNE. When IP(3) and the RNE are accounted for, the results of the model exhibit a tail to head Ca(2+) propagation as well as a sustained increase of Ca(2+) in the head.

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y(6) receptors activated by the ubiquitous signaling nucleotide uridine 5'-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5'-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

Cross-talk between signaling pathways can generate robust oscillations in calcium and cAMP

Background

To control and manipulate cellular signaling, we need to understand cellular strategies for information transfer, integration, and decision-making. A key feature of signal transduction is the generation of only a few intracellular messengers by many extracellular stimuli.

Methodology/Principal Findings

Here we model molecular cross-talk between two classic second messengers, cyclic AMP (cAMP) and calcium, and show that the dynamical complexity of the response of both messengers increases substantially through their interaction. In our model of a non-excitable cell, both cAMP and calcium concentrations can oscillate. If mutually inhibitory, cross-talk between the two second messengers can increase the range of agonist concentrations for which oscillations occur. If mutually activating, cross-talk decreases the oscillation range, but can generate ‘bursting’ oscillations of calcium and may enable better filtering of noise.

Conclusion

We postulate that this increased dynamical complexity allows the cell to encode more information, particularly if both second messengers encode signals. In their native environments, it is unlikely that cells are exposed to one stimulus at a time, and cross-talk may help generate sufficiently complex responses to allow the cell to discriminate between different combinations and concentrations of extracellular agonists.

A dual receptor crosstalk model of G-protein-coupled signal transduction

Macrophage cells that are stimulated by two different ligands that bind to G-protein-coupled receptors (GPCRs) usually respond as if the stimulus effects are additive, but for a minority of ligand combinations the response is synergistic. The G-protein-coupled receptor system integrates signaling cues from the environment to actuate cell morphology, gene expression, ion homeostasis, and other physiological states. We analyze the effects of the two signaling molecules complement factors 5a (C5a) and uridine diphosphate (UDP) on the intracellular second messenger calcium to elucidate the principles that govern the processing of multiple signals by GPCRs. We have developed a formal hypothesis, in the form of a kinetic model, for the mechanism of action of this GPCR signal transduction system using data obtained from RAW264.7 macrophage cells. Bayesian statistical methods are employed to represent uncertainty in both data and model parameters and formally tie the model to experimental data. When the model is also used as a tool in the design of experiments, it predicts a synergistic region in the calcium peak height dose response that results when cells are simultaneously stimulated by C5a and UDP. An analysis of the model reveals a potential mechanism for crosstalk between the Galphai-coupled C5a receptor and the Galphaq-coupled UDP receptor signaling systems that results in synergistic calcium release.

Computational modeling of paroxysmal depolarization shifts in neurons induced by the glutamate release from astrocytes

Recent experimental studies have shown that astrocytes respond to external stimuli with a transient increase of the intracellular calcium concentration or can exhibit self-sustained spontaneous activity. Both evoked and spontaneous astrocytic calcium oscillations are accompanied by exocytosis of glutamate caged in astrocytes leading to paroxysmal depolarization shifts (PDS) in neighboring neurons. Here, we present a simple mathematical model of the interaction between astrocytes and neurons that is able to numerically reproduce the experimental results concerning the initiation of the PDS. The timing of glutamate release from the astrocyte is studied by means of a combined modeling of a vesicle cycle and the dynamics of SNARE-proteins. The neuronal slow inward currents (SICs), induced by the astrocytic glutamate and leading to PDS, are modeled via the activation of presynaptic glutamate receptors. The dependence of the bidirectional communication between neurons and astrocytes on the concentration of glutamate transporters is analyzed, as well. Our numerical results are in line with experimental findings showing that astrocyte can induce synchronous PDSs in neighboring neurons, resulting in a transient synchronous spiking activity.

A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations

In some cell types, oscillations in the concentration of free intracellular calcium ([Ca2+]) are accompanied by oscillations in the concentration of inositol 1,4,5-trisphosphate ([IP3]). However, in most cell types it is still an open question as to whether oscillations in [IP3] are necessary for Ca2+ oscillations in vivo, or whether they merely follow passively. Using a wide range of models, we show that the response to an artificially applied pulse of IP3 can be used to distinguish between these two cases. Hence, we show that muscarinic receptor-mediated, long-period Ca2+ oscillations in pancreatic acinar cells depend on [IP3] oscillations, whereas short-period Ca2+ oscillations in airway smooth muscle do not.

Glutamate-induced glutamate release: a proposed mechanism for calcium bursting in astrocytes

Here we present a new model for the generation of complex calcium-bursting patterns in astrocytes, a type of brain cell recently implicated in a variety of neural functions including memory formation. The model involves two positive feedback processes, in which the key feedback species are calcium ion and glutamate. The latter is the most abundant excitatory neurotransmitter in the brain and has been shown to be involved in bidirectional communication between astrocytes and nearby neurons. The glutamate feedback process considered here is shown to be critical for the generation of complex bursting oscillations in the astrocytes and to, perhaps, code for information which may be passed from neuron to neuron via the astrocyte. These processes may be involved in memory storage and formation as well as in mechanisms which lead to dynamical diseases such as epilepsy.

Ca2+-Dependent Induction of Intracellular Ca2+ Oscillation in Hippocampal Astrocytes During Metabotropic Glutamate Receptor Activation

We have investigated whether the intracellular calcium concentration ([Ca(2+)](i)) oscillations induced in astrocytes using the metabotropic glutamate-receptor agonist, (1S,3R)-1-aminocyclopentane-1,3-dicarboxylic acid (t-ACPD) are Ca(2+)-dependent, using three different Ca(2+) indicators with different affinities for Ca(2+). When rat hippocampal cells in culture were loaded with fura-2 (K(d): 145 nM), two-thirds of the cells showed obvious oscillatory increase in [Ca (2+)](i) during t-ACPD-administration. Those cells were identified as astrocytes by immuno-histochemistry in our previous paper. In cells loaded with fura-2FF (K(d): 25,000 nM), a similar percentage of t-ACPD-responsive cells showed oscillatory [Ca(2+)](i) changes. However, in cells loaded with quin-2 (K(d): 60 nM), t-ACPD induced no oscillatory responses, but some cells showed a small transient increase in the [Ca(2+)](i). The same small transient [Ca(2+)](i) increase was seen in cells loaded with both fura-2FF and BAPTA, a Ca(2+) chelator (K(d): 135 nM). These findings indicate the involvement of [Ca(2+)](i)-dependent regulatory mechanisms in the induction of the t-ACPD-induced oscillatory change in the [Ca(2+)](i) in astrocytes.

Dopamine receptor-mediated Ca(2+) signaling in striatal medium spiny neurons

Inositol 1,4,5-trisphosphate (InsP(3)) and cAMP are the two second messengers that play an important role in neuronal signaling. Here, we investigated the interactions of InsP(3)- and cAMP-mediated signaling pathways activated by dopamine in striatal medium spiny neurons (MSN). We found that in approximately 40% of the MSN, application of dopamine elicited robust repetitive Ca(2+) transients (oscillations). In pharmacological experiments with specific agonists and antagonists, we found that the observed Ca(2+) oscillations were triggered by activation of D1 class dopamine receptors (DARs). We further demonstrated that activation of phospholipase C was required for induction of dopamine-induced Ca(2+) oscillations and that maintenance of dopamine-evoked Ca(2+) oscillations required both Ca(2+) influx and Ca(2+) mobilization from internal Ca(2+) stores. In "priming" experiments with a type 2 5-hydroxytryptamine receptor agonist, we have shown a likely role for calcyon in coupling D1 class DARs with Ca(2+) oscillations in MSN. In experiments with the DAR-specific agonist SKF83959, we discovered that phospholipase C activation alone could not account for dopamine-induced Ca(2+) oscillations. We further demonstrated that direct activation of protein kinase A by 8-bromo-cAMP or inhibition of protein phosphatase-1 (PP1) or calcineurin (PP2B) resulted in elevation of basal Ca(2+) levels in MSN, but not in Ca(2+) oscillations. In experiments with competitive peptides, we have shown an importance of type 1 InsP(3) receptor association with PP1alpha and with AKAP9.protein kinase A for dopamine-induced Ca(2+) oscillations. In experiments with MSN from DARPP-32 knock-out mice, we demonstrated a regulatory role of DARPP-32 in dopamine-induced Ca(2+) oscillations. Our results indicate that, following D1 class DAR activation, InsP(3) and cAMP signaling pathways converge on the type 1 InsP(3) receptor, resulting in Ca(2+) oscillations in MSN.

A wave of IP3 production accompanies the fertilization Ca2+ wave in the egg of the frog, Xenopus laevis: theoretical and experimental support

The fertilization Ca2+ wave in Xenopus laevis is a single, large wave of elevated free Ca2+ that is initiated at the point of sperm-egg fusion and traverses the entire width of the egg. This Ca2+ wave involves an increase in inositol-1,4,5-trisphosphate (IP3) resulting from the interaction of the sperm and egg, which then results in the activation of the endoplasmic reticulum Ca2+ release machinery. The extraordinarily large size of this cell (1.2 mm diameter) together with the small surface region of sperm-receptor activation makes special demands on the IP3-dependent Ca2+ mobilizing machinery. We propose a detailed model of the fertilization Ca2+ wave in Xenopus eggs that requires an accompanying wave of IP3 production. While the Ca2+ wave is initiated by a localized increase of IP3 near the site of sperm-egg fusion, the Ca2+ wave propagates via IP3 production correlated with the Ca2+ wave-possibly via Ca(2+)-mediated PLC activation. Such a Ca(2+)-mediated IP(3) production wave has not been required previously to explain the fertilization Ca2+ wave in eggs; we argue this is necessary to explain the observed IP3 dynamics in Xenopus eggs. To test our hypothesis, we have measured the IP3 levels from 20 nl "sips" of the egg cortex during wave propagation. We were unable to detect the low IP3 levels in unfertilized eggs, but after fertilization, [IP3] ranged from 175 to 430 nM at the sperm entry point and from 120 to 700 nM 90 degrees away once the Ca2+ wave passed that region about 2 min after fertilization. Prior to the Ca2+ wave reaching that region the IP3 levels were undetectable. Since significant IP3 could not diffuse to this region from the sperm entry point within 2 min, this observation is consistent with a regenerative wave of IP3 production.

Calcium signaling components of oscillating invertebrate neurons in vitro

We have studied the Ca(2+) dynamics of bursting-spiking neurons in the lobster stomatogastric ganglion. Neurons in this ganglion undergo spontaneous oscillations in membrane voltage with a period of 1-10 s in situ. We found that neurons isolated from the ganglion and filled with the fluorescent calcium indicator Fluo-4 show simultaneous changes of membrane potential and cytoplasmic Ca(2+) concentration ([Ca(2+)](I)). These Ca(2+) signals are highly heterogeneous both in terms of amplitude and time constants. They showed variable spatial distributions with the soma exhibiting low and slow signals, and a region in the process with large and fast signals. Ca(2+) transients in the processes are dependent on external Ca(2+) and can be blocked by Co(2+), but not other, more specific Ca(2+) current blockers. Rather, nifedipine a known Ca(2+) current blocker, affects the distribution of the Ca(2+) signal, which suggests a specific localization of Ca(2+) channels. Although the signal is not absolutely dependent on action potentials, it is greatly reduced when action potentials are blocked by tetrodotoxin. Termination of the signal depends only slightly on Ca(2+) buffering mechanisms such as mitochondria, Ca(2+)/Na(+) and Ca(2+)/H(+) exchangers. We also demonstrate the presence of caffeine-sensitive internal stores in stomatogastric ganglion cells. The store distribution is different but overlaps with the voltage-dependent distribution. The maximal caffeine-activated Ca(2+) signal is in the soma and it is smaller in the processes. Unlike the voltage-activated Ca(2+) signal this signal is not blocked by Co(2+). Nevertheless, the two types of signal interact during caffeine application. This unique spatial separation of two Ca(2+) sources may have important functional implication.

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Analysis of Mn(2+)/Ca(2+) influx and release during Ca(2+) oscillations in mouse eggs injected with sperm extract

Repetitive Ca(2+) release from the endoplasmic reticulum (ER) is necessary for activation of mammalian eggs. Influx and release of Mn(2+) and Ca(2+) during Ca(2+) oscillations induced by injection of sperm extract (SE) into mouse eggs were investigated by Mn(2+)-quenching of intracellular Fura-2 after adding Mn(2+) to external medium. Mn(2+)/Ca(2+) influx was detected at the resting state. A marked Mn(2+)/Ca(2+) influx occurred during the first Ca(2+) release upon SE injection, and persistently facilitated Mn(2+)/Ca(2+) influx was observed during steady Ca(2+) oscillations. As intracellular Mn(2+) concentration ([Mn(2+)](i)) increased progressively, periodic [Mn(2+)](i) rises appeared, corresponding to each Ca(2+)transient but taking a slower time course. A numerical simulation based on continuous Mn(2+)/Ca(2+) influx-extrusion across the plasma membrane and release-uptake across the ER membrane in a competitive manner mimicked well the Mn(2+) oscillations calculated from experimental data, strongly suggesting that repetitive Mn(2+) release develops after Mn(2+) entry and uptake into the ER. In other experiments, a marked Mn(2+) influx occurred upon Mn(2+) addition to Ca(2+)-free medium after depletion of the ER using an ER Ca(2+) pump inhibitor plus repeated injection of inositol 1,4,5-trisphosphate (InsP(3)). No significant increase in Mn(2+) influx was induced by injection of SE, InsP(3), or Ca(2+), when Ca(2+) release was prevented by pre-injection of an antibody against the InsP(3) receptor. We concluded that Ca(2+) influx is activated during the initial large Ca(2+)release possibly by a capacitative mechanism and kept facilitated during steady Ca(2+) oscillations. The finding that repetitive Mn(2+) release is caused by continuous Mn(2+) entry suggests that continuous Ca(2+) influx may play a critical role in refilling the ER and, thereby, maintaining Ca(2+)oscillations in mammalian fertilization.

An image-based model of calcium waves in differentiated neuroblastoma cells

Calcium waves produced by bradykinin-induced inositol-1,4, 5-trisphosphate (InsP(3))-mediated release from endoplasmic reticulum (ER) have been imaged in N1E-115 neuroblastoma cells. A model of this process was built using the "virtual cell," a general computational system for integrating experimental image, biochemical, and electrophysiological data. The model geometry was based on a cell for which the calcium wave had been experimentally recorded. The distributions of the relevant cellular components [InsP(3) receptor (InsP(3)R)], sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pumps, bradykinin receptors, and ER] were based on 3D confocal immunofluorescence images. Wherever possible, known biochemical and electrophysiological data were used to constrain the model. The simulation closely matched the spatial and temporal characteristics of the experimental calcium wave. Predictions on different patterns of calcium signals after InsP(3) uncaging or for different cell geometries were confirmed experimentally, thus helping to validate the model. Models in which the spatial distributions of key components are altered suggest that initiation of the wave in the center of the neurite derives from an interplay of soma-biased ER distribution and InsP(3) generation biased toward the neurite. Simulations demonstrate that mobile buffers (like the indicator fura-2) significantly delay initiation and lower the amplitude of the wave. Analysis of the role played by calcium diffusion indicated that the speed of the wave is only slightly dependent on the ability of calcium to diffuse to and activate neighboring InsP(3) receptor sites.

The physiologic concentration of inositol 1,4,5-trisphosphate in the oocytes of Xenopus laevis

To measure the concentration of inositol 1,4,5-trisphosphate ([IP3]) in small regions of single Xenopus oocytes, a biological detector cell was combined with capillary electrophoresis. This method is 10, 000 times more sensitive than all existing assays enabling subcellular measurement of [IP3] in Xenopus oocytes. Upon addition of lysophosphatidic acid to an oocyte, [IP3] increased from 40 to 650 nM within 2 min. IP3 concentrations as high as 1.8 microM were measured after activation with lysophosphatidic acid, suggesting that the physiologic concentration of IP3 ranges from the tens of nanomolar to a few micromolar in Xenopus oocytes. Since the IP3 receptor in Xenopus oocytes is nearly identical to the type I receptor of mammalian cells, the range of [IP3] in most mammalian cells is likely to be similar to that in the oocyte. By selecting or engineering the appropriate detector cell, this strategy should be applicable to cyclic adenosine diphosphate ribose and nicotinic acid adenine dinucleotide phosphate, and to the discovery of new Ca2+-releasing second messengers.

Physiological features of visceral smooth muscle cells, with special reference to receptors and ion channels

Visceral smooth muscle cells (VSMC) play an essential role, through changes in their contraction-relaxation cycle, in the maintenance of homeostasis in biological systems. The features of these cells differ markedly by tissue and by species; moreover, there are often regional differences within a given tissue. The biophysical features used to investigate ion channels in VSMC have progressed from the original extracellular recording methods (large electrode, single or double sucrose gap methods), to the intracellular (microelectrode) recording method, and then to methods for recording from membrane fractions (patch-clamp, including cell-attached patch-clamp, methods). Remarkable advances are now being made thanks to the application of these more modern biophysical procedures and to the development of techniques in molecular biology. Even so, we still have much to learn about the physiological features of these channels and about their contribution to the activity of both cell and tissue. In this review, we take a detailed look at ion channels in VSMC and at receptor-operated ion channels in particular; we look at their interaction with the contraction-relaxation cycle in individual VSMC and especially at the way in which their activity is related to Ca2+ movements and Ca2+ homeostasis in the cell. In sections II and III, we discuss research findings mainly derived from the use of the microelectrode, although we also introduce work done using the patch-clamp procedure. These sections cover work on the electrical activity of VSMC membranes (sect. II) and on neuromuscular transmission (sect. III). In sections IV and V, we discuss work done, using the patch-clamp procedure, on individual ion channels (Na+, Ca2+, K+, and Cl-; sect. IV) and on various types of receptor-operated ion channels (with or without coupled GTP-binding proteins and voltage dependent and independent; sect. V). In sect. VI, we look at work done on the role of Ca2+ in VSMC using the patch-clamp procedure, biochemical procedures, measurements of Ca2+ transients, and Ca2+ sensitivity of contractile proteins of VSMC. We discuss the way in which Ca2+ mobilization occurs after membrane activation (Ca2+ influx and efflux through the surface membrane, Ca2+ release from and uptake into the sarcoplasmic reticulum, and dynamic changes in Ca2+ within the cytosol). In this article, we make only limited reference to vascular smooth muscle research, since we reviewed the features of ion channels in vascular tissues only recently.

Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca2+ oscillations

Inositol 1,4,5-trisphosphate (Ins-1,4,5-P3) is responsible for Ca2+ mobilization in response to external stimulation in many cell types. The latter phenomenon often occurs as repetitive Ca2+ spikes. In this study, the effect of the two Ins-1,4,5-P3 metabolizing enzymes (Ins-1,4,5-P3 3-kinase and 5-phosphatase) on the temporal pattern of Ca2+ oscillations has been investigated. On the basis of the well-documented Ins-1,4,5-P3 3-kinase stimulation by the Ca2+/calmodulin complex and of the experimentally-determined kinetic characteristics of these enzymes, we predict that 5-phosphatase primarily controls the levels of Ins-1,4,5-P3 and, thereby, the occurrence and frequency of Ca2+ oscillations. Consequently, the model reproduces the experimental observation performed in Chinese hamster ovary cells that 5-phosphatase overexpression has a much more pronounced effect on the pattern of Ca2+ oscillations than 3-kinase overexpression. We also investigated, in more detail, under which conditions a similar effect could be observed in other cell types expressing various Ins-1,4,5-P3 3-kinase activities.

Calcium, BOBs, QEDs, microdomains and a cellular decision: control of mitotic cell division in sand dollar blastomeres

The role of Ca2+ in controlling cell processes (e.g. mitosis) presents an enigma in its ubiquity and selectivity. Intracellular free Ca2+ (Ca2+i) is an essential regulator of specific biochemical and physiological aspects of mitosis (e.g. nuclear envelope breakdown (NEB)). Changes in Ca2+i concentrations during mitosis in second cell-cycle sand dollar (Echinaracnius parma) blastomeres were imaged as Ca(2+)-dependent luminescence of the photoprotein aequorin with multi-spectral analytical video microscopy. Photons of this luminescence were seen as bright observable blobs (BOBs). Spatiotemporal patterns of BOBs were followed through one or more cell cycles to detect directly changes in Ca2+i, and were seen to change in a characteristic fashion prior to NEB, the onset of anaphase chromosome movement, and during cytokinesis. These patterns were observed from one cell cycle to the next in a single cell, from cell to cell, and from egg batch to egg batch. In both mitosis and synaptic transmission increases in Ca2+i concentration occurs in discrete, short-lived, highly localized pulses we name quantum emission domains (QEDs) within regions we named microdomains. Signal and statistical optical analyses of spatiotemporal BOB patterns show that many BOBs are linked by constant displacements in space-time (velocity). Linked BOBs are thus nonrandom and are classified as QEDS. Analyses of QED patterns demonstrated that the calcium signals required for NEB are nonrandom, and are evoked by an agent(s) generated proximal to a Ca2+i-QED; models of waves, diffusible agonists and Ca(2+)-activated Ca2+ release do not fit pre-NEB cell data. Spatial and temporal resolution of this multispectral approach significantly exceeds that reported for other methods, and avoids the perturbations associated with many fluorescent Ca2+ reporters that interfere with cells being studied (Ca(2+)-buffering, UV toxicity, etc.). Spatiotemporal patterns of Ca2+i-QED can control so many different processes, i.e. specific frequencies used to control particular processes. Predictive and structured patterns of calcium signals (e.g. a language expressed in Ca2+) may selectively regulate specific Ca(2+)-dependent cellular processes.

Reversible desensitization of inositol trisphosphate-induced calcium release provides a mechanism for repetitive calcium spikes

Repetitive transient increases in cytosolic calcium concentration (calcium spikes or calcium oscillations) are a common mode of signal transduction in receptor-mediated cell activation. Repetitive calcium spikes are initiated by phospholipase C-mediated production of inositol 1,4,5-trisphosphate (InsP3) and are thought to be generated by a positive feedback mechanism in which calcium potentiates its own release, a negative feedback mechanism by which calcium release is terminated, and a slow recovery process that defines the time interval between calcium spikes. The molecular mechanisms that terminate each calcium spike and define the spike frequency are not yet known. Here we show, in intact rat basophilic leukemia cells, that calcium responses induced by InsP3 are diminished for a period of 30-60 s following an InsP3-induced calcium spike. The sensitivity of calcium release for InsP3 was probed by UV laser-mediated photorelease of InsP3, and calcium responses were monitored by fluorescence calcium imaging. A maximal loss in sensitivity (desensitization) was observed for InsP3 increases that resulted in a near maximal calcium spike and was expressed as an 80-100% reduction in the calcium response to an equal amount of InsP3, released 10 s after the first UV pulse. When the amount of released InsP3 in the second pulse was increased 2-3-fold, desensitization was overcome and a second calcium response of equal amplitude to the first was produced. A power dependence of 3.2 was measured between the amount of released InsP3 and the amplitude of the triggered calcium response, explaining how a small decrease in InsP3 sensitivity can lead to a nearly complete reduction in the calcium response. Desensitization was abolished by the addition of the calcium buffers BAPTA and EGTA and could be induced by microinjection of calcium, suggesting that it is a calcium-dependent process. Half-maximal desensitization was observed at a free calcium concentration of 290 nM and increased with a power of 3.7 with peak calcium concentration. These studies suggest that reversible desensitization of InsP3-induced calcium release serves as a "saw-tooth" parameter that controls the termination of each spike and the frequency of calcium spikes.

Reversible phosphorylation as a controlling factor for sustaining calcium oscillations in HeLa cells: Involvement of calmodulin-dependent kinase II and a calyculin A-inhibitable phosphatase

The role of reversible phosphorylation in histamine-induced Ca2+ oscillations in HeLa cells has been investigated by using various activators and inhibitors of protein kinases and phosphatases. Electroporation was employed to introduce impermeable materials into single cells, which proved to be a useful and convenient tool. Of the kinases examined, cAMP-dependent kinase, protein kinase C, and calmodulin-dependent kinase II (CaMK II), only CaMK II was essential. When added during oscillations, both W-7, a calmodulin antagonist, and KN-62, a specific CaMK II inhibitor, caused one large Ca2+ spike before halting the process. Introduction of the Ca2+/calmodulin-independent catalytic domain of CaMK II into the cells forestalled their response to histamine. These results show that intracellular Ca2+ cannot oscillate when CaMK II is locked in either the inactive or the stimulated state. External Ca2+ electroporated into cells preloaded with the catalytic domains was quickly removed (but not when the cells were pretreated with the endoplasmic reticulum Ca(2+)-ATPase inhibitor, tapsigargin), indicating that the ATP-driven Ca2+ pump was somehow activated by CaMK II. Protein phosphatase inhibitors calyculin A and okadaic acid abolished ongoing oscillations and, when added at low concentrations, prolonged the interspike interval. Immunoprecipitation experiments with 32P(i)-labeled cells provided the first evidence that inositol 1,4,5-trisphosphate receptor (IP3R) was phosphorylated by CaMK II in vivo. The extent of phosphorylation was increased in the presence of histamine, significantly enhanced by calyculin A, and greatly reduced by W-7. Our observations are consistent with the concept that repetitive phosphorylation-dephosphorylation cycles regulating IP3R and Ca2+ pumps are a controlling factor for sustained Ca2+ oscillations in HeLa, and possibly other, cells.

Effect of Ca2+ influx on intracellular free Ca2+ responses in antigen-stimulated RBL-2H3 cells

We undertake a quantitative investigation of changes in intracellular free Ca2+ concentration ([Ca2+]i) in antigen-stimulated rat basophilic leukemia (RBL-2H3) cells, which include contributions of both Ca2+ store release and Ca2+ influx from the medium. Following Keizer and De Young (J. Keizer and G. De Young. Biophys. J. 61: 649-660, 1992), we develop a highly constrained mathematical model for [Ca2+]i oscillations in RBL-2H3 cells, which includes activation of the inositol trisphosphate receptor (IP3R) by inositol 1,4,5-trisphospate, indirect Ca2+ activation of the IP3R via Ca2+ -dependent activity of phospholipase C-gamma, slow inhibition of the IP3R by cytosolic Ca2+, refilling of Ca2+ stores by a Ca2+ -ATPase (SERCA)-type pump, and a simple representation of the dependence of plasma membrane (PM) fluxes on experimental conditions. Using this full (open cell) model, we simulate [Ca2+]i responses for protocols in which antigen concentration and external Ca2+ are manipulated and compare out calculations with experimental data. In protocol A, cells are stimulated in the presence of external Ca2+, in protocols B and C, cells are stimulated in the absence of external Ca2+, with external Ca2+ later reapplied in protocol C. We are able to reproduce quantitatively the important features of all three protocols, including the dose response of protocol B, the [Ca2+]i response to thapsigargin, and lag time results, and we provide qualitative explanations for the responses derived from our calculations. We also develop a simplified (closed cell) version of the model in which PM fluxes are neglected and total free Ca2+ concentration ([Ca2+]T) is a slowly varying parameter. This permits us to explain in a simple graphical fashion how PM fluxes may influence [Ca2+]i responses in RBH-2H3 cells through modulation of [Ca2+]T.

Extracellular calcium concentration controls the frequency of intracellular calcium spiking independently of inositol 1,4,5-trisphosphate production in HeLa cells

Stimulation of single HeLa cells with histamine evoked repetitive increases of the intracellular calcium ion concentration (Ca2+ spikes). The frequency of Ca2+ spiking increased as the extracellular hormone concentration was elevated. In addition, the frequency of Ca2+ spiking could be accelerated by increasing the extracellular Ca2+ concentration ([Ca2+]0) in the presence of a constant hormone concentration. The range of [Ca2+]0 over which the spiking frequency could be titrated was nominally-zero to 10mM, being half-maximally effective at approx. 1 and 2.5mM for 37 and 22 degrees C respectively. The effect of [Ca2+]0 on inositol phosphates production was also examined. Changes of [Ca2+]0 over a range which had been found to affect the frequency of Ca2+ spiking did not have any effect on the rate of myo-inositol 1,4,5-trisphosphate (InsP3) production, although an increase in inositol phosphates production was observed as [Ca2+]0 was increased from zero to values giving less than half-maximal Ca2+ spike frequency. These data suggest that at low Ca2+ spike frequency, Ca2+-stimulated activation of phospholipase C may contribute to Ca2+ spiking in HeLa cells, but under some conditions the availability of Ca2+ to the intracellular stores, rather than changes in the rate of InsP3 production, determines the Ca2+ spike frequency.

Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations

Recent research dealing with experiments and theoretical models of Ca2+ excitability of the endoplasmic reticulum (ER) membrane induced by inositol 1,4,5-trisphosphate (IP3) is reviewed. Ca2+ excitability refers to the ability of a small increment of cytoplasmic Ca2+ concentration ([Ca2+]i) to trigger a large [Ca2+]i pulse or oscillations. Such nonlinear regenerative behavior is conferred by the existence of IP3 channels and Ca(2+)-ATPase transporters on the ER membrane, which extends throughout the cytoplasm. Ca2+ excitability resembles the plasma membrane electrical excitability of neurons and other cells: it is driven by the ionic concentration gradient across the ER membrane (higher Ca2+ concentration inside the ER); each [Ca2+]i spike partially consumes the prestored energy that is reestablished through ATP-dependent active transport; and [Ca2+]i, the excitation variable, controls the nonlinear dynamic release rate of ER Ca2+. This review focuses on the kinetic models based on these features and on experiments dealing with the kinetic properties of [Ca2+]i-dependent gating of the IP3 receptor channel. We summarize evidence in favor of two roles for [Ca2+]i in gating the channel's opening: activation at a rapid time scale and inactivation on a slower time scale. Exploiting an analogy to the well-known Hodgkin-Huxley model for neuronal electrical excitability, we show how Ca2+ excitability of the ER membrane can be explained by these gating properties combined with the ER Ca2+ pump activity. The theory's ability to predict is illustrated by comparing calculated with experimental [Ca2+]i responses for pituitary gonadotrophs under various stimulus conditions.

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.

GnRH-induced cytosolic calcium oscillations in pituitary gonadotrophs: phase resetting by membrane depolarization

Cultured rat pituitary gonadotrophs under whole-cell voltage clamp conditions respond to the hypothalamic hormone GnRH with synchronized oscillatory changes in both cytosolic Ca2+ concentration ([Ca2+]i) and [Ca2+]i-activated, apamin-sensitive K+ current (IK(Ca)). We found, and report here for the first time, that in GnRH-stimulated cells a brief depolarizing pulse can elicit a transient [Ca2+]i rise similar to the endogenous cycle. Furthermore, Ca2+ entry during a single depolarizing pulse was found to shift the phase of subsequent endogenous [Ca2+]i oscillations, which thereafter continue to occur at their previous frequency before the pulse. Application of two consecutive depolarizing pulses showed that the size of the [Ca2+]i rise evoked by the second pulse depended on the time lapsed between two consecutive pulses, indicating that each endogenous or evoked [Ca2+]i rise cycle leaves the Ca2+ release mechanism of the gonadotroph in a refractory state. Recovery from this condition can be described by an exponential function of the time lapsed between the pulses (time constant of ca. 1 s). We propose that the underlying mechanism in both refractoriness after endogenous cycles and phase resetting by a brief pulse of Ca2+ entry involves the InsP3 receptor-channel molecule presumed to be located on the cytosolic aspect of the endoplasmic reticulum membrane.

InsP3-induced Ca2+ excitability of the endoplasmic reticulum

Oscillations in intracellular Ca2+ can be induced by a variety of cellular signalling processes (Woods et al., 1986; Berridge 1988; Jacob et al., 1988) and appear to play a role in secretion (Stojilković et al., 1994), fertilization (Miyazaki et al., 1993), and smooth muscle contraction (Iino and Tsukioka, 1994). Recently, great progress has been made in understanding the mechanisms involved in a particular class of Ca2+ oscillation, associated with the second messenger inositol 1,4,5-trisphosphate (InsP3) (Berridge, 1993). Working in concert with intracellular Ca2+, InsP3 controls Ca2+ release via the InsP3 receptor in the endoplasmic reticulum (ER) (Berridge and Irvine, 1989). The IP3 receptor is regulated by its coagonists InsP3 and Ca2+, which both activate and inhibit Ca2+ release (Finch et al., 1991; Bezprozvanny et al., 1991; De Young and Keizer, 1992). These processes, together with the periodic activation of Ca2+ uptake into the ER, have been identified as key features in the mechanism of InsP3-induced Ca2+ oscillations in pituitary gonadotrophs (Li et al., 1994), Xenopus laevis oocytes (Lechleiter and Clapham, 1992; Atri et al., 1993), and other cell types (Keizer and De Young, 1993). Earlier discussions and models of InsP3-induced Ca2+ oscillations focused on the nature and number of internal releasable pools of Ca2+ (Goldbeter et al., 1990; Swillens and Mercan, 1990; Somogyi and Stucki, 1991), the importance of oscillations in InsP3 (Meyer and Stryer, 1988), and other issues not based on detailed experimental findings in specific cells types.