[Ca2+]i oscillations in sympathetic neurons: an experimental test of a theoretical model

Calcium oscillation on homogeneous and heterogeneous networks of ryanodine receptor

Calcium oscillation is an important calcium homeostasis, imbalance of which is the key mechanism of initiation and progression of many major diseases. The formation and maintenance of calcium homeostasis are closely related to the spatial distribution of calcium channels on endoplasmic reticulum, whose complex structure was unveiled by recent observations with superresolution imaging techniques. In the current paper, a theoretical framework is established by abstracting the spatial distribution of the calcium channels as a nonlinear biological complex network with calcium channels as nodes and Ca^{2+} as edges. A dynamical model for a ryanodine receptor (RyR) is adopted to investigate the effect of spatial distribution on calcium oscillation. The mean-field model can be well reproduced from the complete graph and dense Erdös-Rényi network. The synchronization of RyRs is found important to generate a global calcium oscillation. Below a critical density of the Erdös-Rényi or BaraBási-Albert network, the amplitude and interspike interval decrease rapidly with the end of disappearance of oscillation due to the desynchronization. The clique graph with a cluster structure cannot produce a global oscillation due to the failure of synchronization between clusters. A more realistic geometric network is constructed in a two-dimensional plane based on the experimental information about the RyR arrangement of clusters and the frequency distribution of cluster sizes. Different from the clique graph, the global oscillation can be generated with reasonable parameters on the geometric network. The simulation also suggests that existence of small clusters and rogue RyRs plays an important role in the maintenance of global calcium oscillation through keeping synchronization between large clusters. Such results support the heterogeneous distribution of RyRs with different-size clusters, which is helpful to understand recent observations with superresolution nanoscale imaging techniques. The current theoretical framework can also be extent to investigate other phenomena in calcium signal transduction.

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

Unraveling Aβ-Mediated Multi-Pathway Calcium Dynamics in Astrocytes: Implications for Alzheimer's Disease Treatment From Simulations

The accumulation of amyloid β peptide (Aβ) in the brain is hypothesized to be the major factor driving Alzheimer's disease (AD) pathogenesis. Mounting evidence suggests that astrocytes are the primary target of Aβ neurotoxicity. Aβ is known to interfere with multiple calcium fluxes, thus disrupting the calcium homeostasis regulation of astrocytes, which are likely to produce calcium oscillations. Ca²⁺ dyshomeostasis has been observed to precede the appearance of clinical symptoms of AD; however, it is experimentally very difficult to investigate the interactions of many mechanisms. Given that Ca²⁺ disruption is ubiquitously involved in AD progression, it is likely that focusing on Ca²⁺ dysregulation may serve as a potential therapeutic approach to preventing or treating AD, while current hypotheses concerning AD have so far failed to yield curable therapies. For this purpose, we derive and investigate a concise mathematical model for Aβ-mediated multi-pathway astrocytic intracellular Ca²⁺ dynamics. This model accounts for how Aβ affects various fluxes contributions through voltage-gated calcium channels, Aβ-formed channels and ryanodine receptors. Bifurcation analysis of Aβ level, which reflected the corresponding progression of the disease, revealed that Aβ significantly induced the increasing [Ca²⁺] _i and frequency of calcium oscillations. The influence of inositol 1,4,5-trisphosphate production (IP₃) is also investigated in the presence of Aβ as well as the impact of changes in resting membrane potential. In turn, the Ca²⁺ flux can be considerably changed by exerting specific interventions, such as ion channel blockers or receptor antagonists. By doing so, a "combination therapy" targeting multiple pathways simultaneously has finally been demonstrated to be more effective. This study helps to better understand the effect of Aβ, and our findings provide new insight into the treatment of AD.

Improved Computational Identification of Drug Response Using Optical Measurements of Human Stem Cell Derived Cardiomyocytes in Microphysiological Systems

Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) hold great potential for drug screening applications. However, their usefulness is limited by the relative immaturity of the cells' electrophysiological properties as compared to native cardiomyocytes in the adult human heart. In this work, we extend and improve on methodology to address this limitation, building on previously introduced computational procedures which predict drug effects for adult cells based on changes in optical measurements of action potentials and Ca2+ transients made in stem cell derived cardiac microtissues. This methodology quantifies ion channel changes through the inversion of data into a mathematical model, and maps this response to an adult phenotype through the assumption of functional invariance of fundamental intracellular and membrane channels during maturation. Here, we utilize an updated action potential model to represent both hiPSC-CMs and adult cardiomyocytes, apply an IC50-based model of dose-dependent drug effects, and introduce a continuation-based optimization algorithm for analysis of dose escalation measurements using five drugs with known effects. The improved methodology can identify drug induced changes more efficiently, and quantitate important metrics such as IC50 in line with published values. Consequently, the updated methodology is a step towards employing computational procedures to elucidate drug effects in adult cardiomyocytes for new drugs using stem cell-derived experimental tissues.

A Model of [Formula: see text] Dynamics in an Accurate Reconstruction of Parotid Acinar Cells

We have constructed a spatiotemporal model of [Formula: see text] dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. in J Theor Biol 419:383-393. https://doi.org/10.1016/j.jtbi.2016.04.030 , 2017b), which cannot generate realistic [Formula: see text] oscillations with the new data on IPR distribution, our new model reproduces the [Formula: see text] dynamics observed in parotid acinar cells. This model is then coupled with a fluid secretion model described in detail in a companion paper: A mathematical model of fluid transport in an accurate reconstruction of a parotid acinar cell (Vera-Sigüenza et al. in Bull Math Biol. https://doi.org/10.1007/s11538-018-0534-z , 2018b). Based on the new measurements of IPR distribution, we show that Class I models (where [Formula: see text] oscillations can occur at constant [[Formula: see text]]) can produce [Formula: see text] oscillations in parotid acinar cells, whereas Class II models (where [[Formula: see text]] needs to oscillate in order to produce [Formula: see text] oscillations) are unlikely to do so. In addition, we demonstrate that coupling fluid flow secretion with the [Formula: see text] signalling model changes the dynamics of the [Formula: see text] oscillations significantly, which indicates that [Formula: see text] dynamics and fluid flow cannot be accurately modelled independently. Further, we determine that an active propagation mechanism based on calcium-induced calcium release channels is needed to propagate the [Formula: see text] wave from the apical region to the basal region of the acinar cell.

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

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

Calcium dynamics in cardiac excitatory and non-excitatory cells and the role of gap junction

Calcium ions aid in the generation of action potential in myocytes and are responsible for the excitation-contraction coupling of heart. The heart muscle has specialized patches of cells, called excitatory cells (EC) such as the Sino-atrial node cells capable of auto-generation of action potential and cells which receive signals from the excitatory cells, called non-excitatory cells (NEC) such as cells of the ventricular and auricular walls. In order to understand cardiac calcium homeostasis, it is, therefore, important to study the calcium dynamics taking into account both types of cardiac cells. Here we have developed a model to capture the calcium dynamics in excitatory and non-excitatory cells taking into consideration the gap junction mediated calcium ion transfer from excitatory cell to non-excitatory cell. Our study revealed that the gap junctional coupling between excitatory and non-excitatory cells plays important role in the calcium dynamics. It is observed that any reduction in the functioning of gap junction may result in abnormal calcium oscillations in NEC, even when the calcium dynamics is normal in EC cell. Sensitivity of gap junction is observed to be independent of the pacing rate and hence a careful monitoring is required to maintain normal cardiomyocyte condition. It also highlights that sarcoplasmic reticulum may not be always able to control the amount of cytoplasmic calcium under the condition of calcium overload.

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.

Modeling calcium waves in an anatomically accurate three-dimensional parotid acinar cell

We construct a model of calcium waves in a three-dimensional anatomically accurate parotid acinar cell, constructed from experimental data. Gradients of inositol trisphosphate receptor (IPR) density are imposed, with the IPR density being greater closer to the lumen, which has a branched structure, and inositol trisphosphate (IP₃) is produced only at the basal membrane. We show (1) that IP₃ equilibrates so quickly across the cell that it can be assumed to be spatially homogeneous; (2) spatial separation of the sites of IP₃ action and IP₃ production does not preclude the formation of stable oscillatory Ca²⁺ waves. However, these waves are not waves in the mathematical sense of a traveling wave with fixed profile. They result instead from a time delay between the Ca²⁺ rise in the apical and basal regions; (3) the ryanodine receptors serve to reinforce the Ca²⁺ wave, but are not necessary for the wave to exist; (4) a spatially independent model is not sufficient to study saliva secretion, although a one-dimensional model might be sufficient. Our results here form the first stages of the construction of a multiscale and multicellular model of saliva secretion in an entire acinus.

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

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

Caffeine-induced Ca2+ oscillations in type I horizontal cells of the carp retina and the contribution of the store-operated Ca2+ entry pathway

The mechanisms of release, depletion, and refilling of endoplasmic reticulum (ER) Ca²⁺ were investigated in type I horizontal cells of the carp retina using a fluo-3-based Ca²⁺ imaging technique. Exogenous application of caffeine, a ryanodine receptor agonist, induced oscillatory intracellular free Ca²⁺ concentration ([Ca²⁺]_i) responses in a duration- and concentration-dependent manner. In Ca²⁺-free Ringer’s solution, [Ca²⁺]_i transients could also be induced by a brief caffeine application, whereas subsequent caffeine application induced no [Ca²⁺]_i increase, which implied that extracellular Ca²⁺ was required for ER refilling, confirming the necessity of a Ca²⁺ influx pathway for ER refilling. Depletion of ER Ca²⁺ by thapsigargin triggered a Ca²⁺ influx which could be blocked by the store-operated channel inhibitor 2-APB, which proved the existence of the store-operated Ca²⁺ entry pathway. Taken together, these results suggested that after being depleted by caffeine, the ER was replenished by Ca²⁺ influx via store-operated channels. These results reveal the fine modulation of ER Ca²⁺ signaling, and the activation of the store-operated Ca²⁺ entry pathway guarantees the replenishment of the ER so that the cell can be ready for response to the subsequent stimulus.

Mast cell-nerve cell interaction at acupoint: modeling mechanotransduction pathway induced by acupuncture

Mast cells are found abundant at sites of acupoints. Nerve cells share perivascular localization with mast cells. Acupuncture (mechanical stimuli) can activate mast cells to release adenosine triphosphate (ATP) which can activate nerve cells and modulates pain-processing pathways in response to acupuncture. In this paper, a mathematical model was constructed for describing intracellular Ca²⁺ signal and ATP release in a coupled mast cell and nerve cell system induced by mechanical stimuli. The results showed mechanical stimuli lead to a intracellular Ca²⁺ rise in the mast cell and ATP release, ATP diffuses in the extracellular space (ECS) and activates the nearby nerve cells, then induces electrical current in the nerve cell which spreads in the neural network. This study may facilitate our understanding of the mechanotransduction process induced by acupuncture and provide a methodology for quantitatively analyzing acupuncture treatment.

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.

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.

Real-Time dynamics of Ca2+, caspase-3/7, and morphological changes in retinal ganglion cell apoptosis under elevated pressure

Quantitative information on the dynamics of multiple molecular processes in individual live cells under controlled stress is central to the understanding of the cell behavior of interest and the establishment of reliable models. Here, the dynamics of the apoptosis regulator intracellular Ca(2+), apoptosis effector caspase-3/7, and morphological changes, as well as temporal correlation between them at the single cell level, are examined in retinal gangling cell line (differentiated RGC-5 cells) undergoing apoptosis at elevated hydrostatic pressure using a custom-designed imaging platform that allows long-term real-time simultaneous imaging of morphological and molecular-level physiological changes in large numbers of live cells (beyond the field-of-view of typical microscopy) under controlled hydrostatic pressure. This examination revealed intracellular Ca(2+) elevation with transient single or multiple peaks of less than 0.5 hour duration appearing at the early stages (typically less than 5 hours after the onset of 100 mmHg pressure) followed by gradual caspase-3/7 activation at late stages (typically later than 5 hours). The data reveal a strong temporal correlation between the Ca(2+) peak occurrence and morphological changes of neurite retraction and cell body shrinkage. This suggests that Ca(2+) elevation, through its impact on ion channel activity and water efflux, is likely responsible for the onset of apoptotic morphological changes. Moreover, the data show a significant cell-to-cell variation in the onset of caspase-3/7 activation, an inevitable consequence of the stochastic nature of the underlying biochemical reactions not captured by conventional assays based on population-averaged cellular responses. This real-time imaging study provides, for the first time, statistically significant data on simultaneous multiple molecular level changes to enable refinements and testing of models of the dynamics of mitochondria-mediated apoptosis. Further, the platform developed and the approach has direct significance to the study of a variety of signaling pathway phenomena.

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.

A design principle underlying the synchronization of oscillations in cellular systems

Biological oscillations are found ubiquitously in cells and are widely variable, with periods varying from milliseconds to months, and scales involving subcellular components to large groups of organisms. Interestingly, independent oscillators from different cells often show synchronization that is not the consequence of an external regulator. What is the underlying design principle of such synchronized oscillations, and can modeling show that the complex consequences arise from simple molecular or other interactions between oscillators? When biological oscillators are coupled with each other, we found that synchronization is induced when they are connected together through a positive feedback loop. Increasing the coupling strength of two independent oscillators shows a threshold beyond which synchronization occurs within a few cycles, and a second threshold where oscillation stops. The positive feedback loop can be composed of either double-positive (PP) or double-negative (NN) interactions between a node of each of the two oscillating networks. The different coupling structures have contrasting characteristics. In particular, PP coupling is advantageous with respect to stability of period and amplitude, when local oscillators are coupled with a short time delay, whereas NN coupling is advantageous for a long time delay. In addition, PP coupling results in more robust synchronized oscillations with respect to amplitude excursions but not period, with applied noise disturbances compared to NN coupling. However, PP coupling can induce a large fluctuation in the amplitude and period of the resulting synchronized oscillation depending on the coupling strength, whereas NN coupling ensures almost constant amplitude and period irrespective of the coupling strength. Intriguingly, we have also observed that artificial evolution of random digital oscillator circuits also follows this design principle. We conclude that a different coupling strategy might have been selected according to different evolutionary requirements.

Calcium oscillations in neurons

Oscillations in the cytosolic free Ca2+ concentration ([Ca2+]i) have been described in a variety of cells. In some cases, [Ca2+]i oscillations reflect cycles of membrane depolarization and voltage-dependent Ca2+ entry. In others, they are caused by periodic Ca2+ uptake and release by internal stores, with little immediate requirement for external Ca2+. A third type of [Ca2+]i oscillation is typified by caffeine-induced oscillations in sympathetic neurons. Here, the oscillations depend on the interplay between Ca2+ transport across the plasma membrane and transport by a caffeine-sensitive store. These oscillations can occur at a steady membrane potential and are blocked by ryanodine (1 microM), indicating that they do not result from voltage-dependent changes in Ca2+ entry but do require Ca(2+)-induced Ca2+ release. Entry of Ca2+ from the external medium is important during all phases of the oscillatory cycle except the rapid upstroke, which is dominated by Ca2+ release from an internal store. It is proposed that caffeine-induced [Ca2+]i oscillations are cyclic perturbations of [Ca2+]i caused by exchange of Ca2+ between the cytosol and the caffeine-sensitive store: net Ca2+ loss from the store increases [Ca2+]i transiently above its steady-state value ([Ca2+]ss), whereas net accumulation of Ca2+ by the store transiently depresses [Ca2+]i below [Ca2+]ss. The effects of rapid removal of Ca2+ and caffeine on the rate of change of [Ca2+]i (d[Ca2+]i/dt) provide estimates of the rates of net Ca2+ entry and (caffeine-sensitive) Ca2+ release and information on the way these rates vary during the oscillatory cycle.

Mechanisms of calcium sequestration during facilitation at active zones of an amphibian neuromuscular junction

The calcium transients (Delta[Ca(2+)](i)) at active zones of amphibian (Bufo marinus) motor-nerve terminals that accompany impulses, visualized using a low-affinity calcium indicator injected into the terminal, are described and the pathways of subsequent sequestration of the residual calcium determined, allowing development of a quantitative model of the sequestering processes. Blocking the endoplasmic reticulum calcium pump with thapsigargin did not affect Delta[Ca(2+)](i) for a single impulse but increased its amplitude during short trains. Blocking the uptake of calcium by mitochondria with CCCP had little effect on Delta[Ca(2+)](i) of a single impulse but greatly increased its amplitude during short trains. This present compartmental model is compatible with our previous Monte Carlo diffusion model of Ca(2+) sequestration during facilitation [Bennett, M.R., Farnell, L., Gibson, W.G., 2004. The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction. Biophys. J. 86(5), 2674-2690], with the single plasmalemma pump in that model now replaced by separate pumps for the plasmalemma and endoplasmic reticulum, as well as the introduction of a mitochondrial uniporter.

Models of the inositol trisphosphate receptor

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

Peripheral hot spots for local Ca2+ release after single action potentials in sympathetic ganglion neurons

Ca2+ release from the endoplasmic reticulum (ER) contributes to Ca2+ transients in frog sympathetic ganglion neurons. Here we use video-rate confocal fluo-4 fluorescence imaging to show that single action potentials reproducibly trigger rapidly rising Ca2+ transients at 1-3 local hot spots within the peripheral ER-rich layer in intact neurons in fresh ganglia and in the majority (74%) of cultured neurons. Hot spots were located near the nucleus or the axon hillock region. Other regions exhibited either slower and smaller signals or no response. Ca2+ signals spread into the cell at constant velocity across the ER in nonnuclear regions, indicating active propagation, but spread with a (time)1/2 dependence within the nucleus, consistent with diffusion. 26% of cultured cells exhibited uniform Ca2+ signals around the periphery, but hot spots were produced by loading the cytosol with EGTA or by bathing such cells in low-Ca2+ Ringer's solution. Peripheral hot spots for Ca2+ release within the perinuclear and axon hillock regions provide a mechanism for preferential initiation of nuclear and axonal Ca2+ signals by single action potentials in sympathetic ganglion neurons.

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.

Differential regulation of ER Ca2+ uptake and release rates accounts for multiple modes of Ca2+-induced Ca2+ release

The ER is a central element in Ca(2+) signaling, both as a modulator of cytoplasmic Ca(2+) concentration ([Ca(2+)](i)) and as a locus of Ca(2+)-regulated events. During surface membrane depolarization in excitable cells, the ER may either accumulate or release net Ca(2+), but the conditions of stimulation that determine which form of net Ca(2+) transport occurs are not well understood. The direction of net ER Ca(2+) transport depends on the relative rates of Ca(2+) uptake and release via distinct pathways that are differentially regulated by Ca(2+), so we investigated these rates and their sensitivity to Ca(2+) using sympathetic neurons as model cells. The rate of Ca(2+) uptake by SERCAs (J(SERCA)), measured as the t-BuBHQ-sensitive component of the total cytoplasmic Ca(2+) flux, increased monotonically with [Ca(2+)](i). Measurement of the rate of Ca(2+) release (J(Release)) during t-BuBHQ-induced [Ca(2+)](i) transients made it possible to characterize the Ca(2+) permeability of the ER ((~)P(ER)), describing the activity of all Ca(2+)-permeable channels that contribute to passive ER Ca(2+) release, including ryanodine-sensitive Ca(2+) release channels (RyRs) that are responsible for CICR. Simulations based on experimentally determined descriptions of J(SERCA), and of Ca(2+) extrusion across the plasma membrane (J(pm)) accounted for our previous finding that during weak depolarization, the ER accumulates Ca(2+), but at a rate that is attenuated by activation of a CICR pathway operating in parallel with SERCAs to regulate net ER Ca(2+) transport. Caffeine greatly increased the [Ca(2+)] sensitivity of ((~)P(ER)), accounting for the effects of caffeine on depolarization-evoked [Ca(2+)](i) elevations and caffeine-induced [Ca(2+)](i) oscillations. Extending the rate descriptions of J(SERCA), ((~)P(ER)), and J(pm) to higher [Ca(2+)](i) levels shows how the interplay between Ca(2+) transport systems with different Ca(2+) sensitivities accounts for the different modes of CICR over different ranges of [Ca(2+)](i) during stimulation.

The effect of calcium pump inhibitors on the response of intracellular calcium to caffeine in snail neurones

We have measured intracellular free calcium ([Ca(2+)]i) using Fura-2 or Ca(2+)-sensitive microelectrodes in voltage-clamped neurones of the snail, Helix aspersa. Caffeine-induced transient increases in [Ca(2+)]i were normally followed by a brief fall of [Ca(2+)]i below its pre-caffeine level. We investigated the cause of this undershoot by raising [Ca(2+)]i; and by inhibiting the plasma membrane or endoplasmic reticulum Ca ATPases (PMCA or SERCA respectively). When the cell membrane potential was decreased from -60 to -25mV, steady-state [Ca(2+)]i increased. The caffeine-induced transients were smaller while the undershoots were larger than in control conditions. When the PMCA was inhibited by high pH the steady-state [Ca(2+)]i increased by 100-400nM. The caffeine-induced [Ca(2+)]i increase and the subsequent undershoot both became larger. Injection of orthovanadate, which inhibits the PMCA and increases [Ca(2+)]i, did not block either effect of caffeine. But when the SERCA was inhibited by cyclopiazonic acid the undershoot disappeared. The phosphodiesterase inhibitor IBMX did not influence the undershoot. These results suggest that the undershoot is generated by the Ca(2+)] ATPase of the stores rather than that of the plasma membrane. Since the undershoot increased as [Ca(2+)]i increased, we conclude that at higher levels of [Ca(2+)]i the stores refill more rapidly.

Multiple modes of calcium-induced calcium release in sympathetic neurons I: attenuation of endoplasmic reticulum Ca2+ accumulation at low [Ca2+](i) during weak depolarization

Many cells express ryanodine receptors (RyRs) whose activation is thought to amplify depolarization-evoked elevations in cytoplasmic Ca2+ concentration [Ca2+](i) through a process of Ca2+ -induced Ca2+ release (CICR). In neurons, it is usually assumed that CICR triggers net Ca2+ release from an ER Ca2+ store. However, since net ER Ca 2+ transport depends on the relative rates of Ca2+ uptake and release via distinct pathways, weak activation of a CICR pathway during periods of ER Ca accumulation would have a totally different effect: attenuation of Ca2+ accumulation. Stronger CICR activation at higher [Ca2+](i) could further attenuate Ca2+ accumulation or trigger net Ca2+ release, depending on the quantitative properties of the underlying Ca2+ transporters. This and the companion study (Hongpaisan, J., N.B. Pivovarova, S.L. Colgrove, R.D. Leapman, and D.D. Friel, and S.B. Andrews. 2001. J. Gen. Physiol. 118:101-112) investigate which of these CICR "modes" operate during depolarization-induced Ca2+ entry in sympathetic neurons. The present study focuses on small [Ca2+](i) elevations (less than approximately 350 nM) evoked by weak depolarization. The following two approaches were used: (1) Ca2+ fluxes were estimated from simultaneous measurements of [Ca2+](i) and I(Ca) in fura-2-loaded cells (perforated patch conditions), and (2) total ER Ca concentrations ([Ca](ER)) were measured using X-ray microanalysis. Flux analysis revealed triggered net Ca2+ release during depolarization in the presence but not the absence of caffeine, and [Ca2+](i) responses were accelerated by SERCA inhibitors, implicating ER Ca2+ accumulation, which was confirmed by direct [Ca](ER) measurements. Ryanodine abolished caffeine-induced CICR and enhanced depolarization-induced ER Ca2+ accumulation, indicating that activation of the CICR pathway normally attenuates ER Ca2+ accumulation, which is a novel mechanism for accelerating evoked [Ca2+](i) responses. Theory shows how such a low gain mode of CICR can operate during weak stimulation and switch to net Ca2+ release at high [Ca2+](i), a transition demonstrated in the companion study. These results emphasize the importance of the relative rates of Ca2+ uptake and release in defining ER contributions to depolarization-induced Ca2+ signals.

Multiple modes of calcium-induced calcium release in sympathetic neurons II: a [Ca2+](i)- and location-dependent transition from endoplasmic reticulum Ca accumulation to net Ca release

CICR from an intracellular store, here directly characterized as the ER, usually refers to net Ca(2)+ release that amplifies evoked elevations in cytosolic free calcium [Ca2+](i). However, the companion paper (Albrecht, M.A., S.L. Colegrove, J. Hongpaisan, N.B. Pivovarova, S.B. Andrews, and D.D. Friel. 2001. J. Gen. Physiol. 118:83-100) shows that in sympathetic neurons, small [Ca2+](i) elevations evoked by weak depolarization stimulate ER Ca accumulation, but at a rate attenuated by activation of a ryanodine-sensitive CICR pathway. Here, we have measured depolarization-evoked changes in total ER Ca concentration ([Ca](ER)) as a function of [Ca2+](i), and found that progressively larger [Ca2+](i) elevations cause a graded transition from ER Ca accumulation to net release, consistent with the expression of multiple modes of CICR. [Ca](ER) is relatively high at rest (12.8 +/- 0.9 mmol/kg dry weight, mean +/- SEM) and is reduced by thapsigargin or ryanodine (5.5 +/- 0.7 and 4.7 +/- 1.1 mmol/kg, respectively). [Ca](ER) rises during weak depolarization (to 17.0 +/- 1.6 mmol/kg over 120s, [Ca2+](i) less than approximately 350 nM), changes little in response to stronger depolarization (12.1 +/- 1.1 mmol/kg, [Ca2+](i) approximately 700 nM), and declines (to 6.5 +/- 1.0 mmol/kg) with larger [Ca2+](i) elevations (>1 microM) evoked by the same depolarization when mitochondrial Ca2+ uptake is inhibited (FCCP). Thus, net ER Ca2+ transport exhibits a biphasic dependence on [Ca2+](i). With mitochondrial Ca2+ uptake enabled, [Ca](ER) rises after repolarization (to 16.6 +/- 1.8 mmol/kg at 15 min) as [Ca2+](i) falls within the permissive range for ER Ca accumulation over a period lengthened by mitochondrial Ca2+ release. Finally, although spatially averaged [Ca](ER) is unchanged during strong depolarization, net ER Ca2+ release still occurs, but only in the outermost approximately 5-microm cytoplasmic shell where [Ca2+](i) should reach its highest levels. Since mitochondrial Ca accumulation occurs preferentially in peripheral cytoplasm, as demonstrated here by electron energy loss Ca maps, the Ca content of ER and mitochondria exhibit reciprocal dependencies on proximity to sites of Ca2+ entry, possibly reflecting indirect mitochondrial regulation of ER Ca(2)+ transport.

Origin sites of calcium release and calcium oscillations in frog sympathetic neurons

In many neurons, Ca(2+) signaling depends on efflux of Ca(2+) from intracellular stores into the cytoplasm via caffeine-sensitive ryanodine receptors (RyRs) of the endoplasmic reticulum. We have used high-speed confocal microscopy to image depolarization- and caffeine-evoked increases in cytoplasmic Ca(2+) levels in individual cultured frog sympathetic neurons. Although caffeine-evoked Ca(2+) wave fronts propagated throughout the cell, in most cells the initial Ca(2+) release was from one or more discrete sites that were several micrometers wide and located at the cell edge, even in Ca(2+)-free external solution. During cell-wide cytoplasmic [Ca(2+)] oscillations triggered by continual caffeine application, the initial Ca(2+) release that began each Ca(2+) peak was from the same subcellular site or sites. The Ca(2+) wave fronts propagated with constant amplitude; the spread was mostly via calcium-induced calcium release. Propagation was faster around the cell periphery than radially inward. Local Ca(2+) levels within the cell body could increase or decrease independently of neighboring regions, suggesting independent action of spatially separate Ca(2+) stores. Confocal imaging of fluorescent analogs of ryanodine and thapsigargin, and of MitoTracker, showed potential structural correlates to the patterns of Ca(2+) release and propagation. High densities of RyRs were found in a ring around the cell periphery, mitochondria in a broader ring just inside the RyRs, and sarco-endoplasmic reticulum Ca(2+) ATPase pumps in hot spots at the cell edge. Discrete sites at the cell edge primed to release Ca(2+) from intracellular stores might preferentially convert Ca(2+) influx through a local area of plasma membrane into a cell-wide Ca(2+) increase.

Origin sites of calcium release and calcium oscillations in frog sympathetic neurons

In many neurons, Ca(2+) signaling depends on efflux of Ca(2+) from intracellular stores into the cytoplasm via caffeine-sensitive ryanodine receptors (RyRs) of the endoplasmic reticulum. We have used high-speed confocal microscopy to image depolarization- and caffeine-evoked increases in cytoplasmic Ca(2+) levels in individual cultured frog sympathetic neurons. Although caffeine-evoked Ca(2+) wave fronts propagated throughout the cell, in most cells the initial Ca(2+) release was from one or more discrete sites that were several micrometers wide and located at the cell edge, even in Ca(2+)-free external solution. During cell-wide cytoplasmic [Ca(2+)] oscillations triggered by continual caffeine application, the initial Ca(2+) release that began each Ca(2+) peak was from the same subcellular site or sites. The Ca(2+) wave fronts propagated with constant amplitude; the spread was mostly via calcium-induced calcium release. Propagation was faster around the cell periphery than radially inward. Local Ca(2+) levels within the cell body could increase or decrease independently of neighboring regions, suggesting independent action of spatially separate Ca(2+) stores. Confocal imaging of fluorescent analogs of ryanodine and thapsigargin, and of MitoTracker, showed potential structural correlates to the patterns of Ca(2+) release and propagation. High densities of RyRs were found in a ring around the cell periphery, mitochondria in a broader ring just inside the RyRs, and sarco-endoplasmic reticulum Ca(2+) ATPase pumps in hot spots at the cell edge. Discrete sites at the cell edge primed to release Ca(2+) from intracellular stores might preferentially convert Ca(2+) influx through a local area of plasma membrane into a cell-wide Ca(2+) increase.

Computational modeling of entorhinal cortex

Computational modeling provides a means for linking the physiological and anatomical characteristics of entorhinal cortex at a cellular level to the functional role of this region in behavior. We have developed detailed simulations of entorhinal cortical neurons and networks, with an emphasis on the role of acetylcholine in entorhinal cortical function. Computational modeling suggests that when acetylcholine levels are high, this sets appropriate dynamics for the storage of stimuli during performance of delayed matching tasks. In particular, acetylcholine activates a calcium-sensitive nonspecific cation current which provides an intrinsic cellular mechanism which could maintain neuronal activity across a delay period. Simulations demonstrate how this phenomena could underlie entorhinal cortex delay activity as described in previous unit recordings. Acetylcholine also induces theta rhythm oscillations which may be appropriate for timing of afferent input to be encoded in hippocampus and for extraction of individual stored sequences from multiple stored sequences. Lower levels of acetylcholine may allow sharp wave dynamics which can reactivate associations encoded in hippocampus and drive the formation of additional traces in hippocampus and entorhinal cortex during consolidation.

A four-compartment model for Ca2+ dynamics: an interpretation of Ca2+ decay after repetitive firing of intact nerve terminals

In the presynaptic nerve terminals of the bullfrog sympathetic ganglia, repetitive nerve firing evokes [Ca2+] transients that decay monotonically. An algorithm based on an eigenfunction expansion method was used for fitting these [Ca2+] decay records. The data were fitted by a linear combination of two to four exponential functions. A mathematical model with three intraterminal membrane-bound compartments was developed to describe the observed Ca2+ decay. The model predicts that the number of exponential functions, n, contained in the decay data corresponds to n-1 intraterminal Ca2+ stores that release Ca2+ during the decay. Moreover, when a store stops releasing or starts to release Ca2+, the decay data should be fitted by functions that contain one less exponential component for the former and one more for the latter than do the fitting functions for control data. Because of the current lack of a parameter by which quantitative comparisons can be made between two decay processes when at least one of them contained more than one exponential components, we defined a parameter, the overall rate (OR) of decay, as the trace of the coefficient matrix of the differential equation systems of our model. We used the mathematical properties of the model and of the OR to interpret effects of ryanodine and of a mitochondria uncoupler on Ca2+ decay. The results of the analysis were consistent with the ryanodine-sensitive store, mitochondria, and another, yet unidentified store release Ca2+ into the cytosol of the presynaptic nerve terminals during Ca2+ decay. Our model also predicts that mitochondrial Ca2+ buffering accounted for more than 86% of all the flux rates across various membranes combined and that there are type 3 and type 1 and/or type 2 ryanodine receptors in these terminals.

Modes of propagation of Ca(2+)-induced Ca2+ release in bullfrog sympathetic ganglion cells

How depolarization-induced Ca2+ entry or caffeine activates Ca(2+)-induced Ca2+ release (CICR) in the cytoplasm and nucleoplasm was studied by recording intracellular Ca2+ ([Ca2+]i) with a confocal microscope in cultured bullfrog sympathetic ganglion cells. The amplitude and propagation speed of voltage pulse-induced rises in [Ca2+]i were greater in the submembrane (< 5 microns depth) region than in the core region, and delayed and smaller, but significant, in the nucleus. Ryanodine and dantrolene reduced the rises in [Ca2+]i in both the cytoplasm and nucleus. A rapid application of high K+ solution induced global rises in [Ca2+]i in both the cytoplasm and nucleoplasm, which were decreased by dantrolene. Caffeine produced a slow, small rise in [Ca2+]i which grew into a global, regenerative rise both in the cytoplasm and nucleoplasm with some inward gradient in the cytoplasm. Each of the high [Ca2+]i phases during caffeine-induced [Ca2+]i oscillation began in the submembrane region, while low [Ca2+]i phases started in the core region. These results suggest that CICR activated by Ca2+ entry or caffeine occurs predominantly in the submembrane region causing an inwardly spreading Ca2+ wave or [Ca2+]i oscillations, and that the nuclear envelope can cause CICR in the nucleoplasm, which is delayed due to Ca2+ diffusion barrier at the nuclear pores.

Quantitative analysis of mitochondrial Ca2+ uptake and release pathways in sympathetic neurons. Reconstruction of the recovery after depolarization-evoked [Ca2+]i elevations

Rate equations for mitochondrial Ca2+ uptake and release and plasma membrane Ca2+ transport were determined from the measured fluxes in the preceding study and incorporated into a model of Ca2+ dynamics. It was asked if the measured fluxes are sufficient to account for the [Ca2+]i recovery kinetics after depolarization-evoked [Ca2+]i elevations. Ca2+ transport across the plasma membrane was described by a parallel extrusion/leak system, while the rates of mitochondrial Ca2+ uptake and release were represented using equations like those describing Ca2+ transport by isolated mitochondria. Taken together, these rate descriptions account very well for the time course of recovery after [Ca2+]i elevations evoked by weak and strong depolarization and their differential sensitivity to FCCP, CGP 37157, and [Na+]i. The model also leads to three general conclusions about mitochondrial Ca2+ transport in intact cells: (1) mitochondria are expected to accumulate Ca2+ even in response to stimuli that raise [Ca2+]i only slightly above resting levels; (2) there are two qualitatively different stimulus regimes that parallel the buffering and non-buffering modes of Ca2+ transport by isolated mitochondria that have been described previously; (3) the impact of mitochondrial Ca2+ transport on intracellular calcium dynamics is strongly influenced by nonmitochondrial Ca2+ transport; in particular, the magnitude of the prolonged [Ca2+]i elevation that occurs during the plateau phase of recovery is related to the Ca2+ set-point described in studies of isolated mitochondria, but is a property of mitochondrial Ca2+ transport in a cellular context. Finally, the model resolves the paradoxical finding that stimulus-induced [Ca2+]i elevations as small as approximately 300 nM increase intramitochondrial total Ca2+ concentration, but the steady [Ca2+]i elevations evoked by such stimuli are not influenced by FCCP.

Detection of salicylate and its hydroxylated adduct 2,3-dihydroxybenzoic acid in glutamate neurotoxicity and the effects of verapamil and ryanodine in rats

It has been suggested that salicylate hydroxylation can be used to detect hydroxyl radical formation in vivo. In the present study we investigated the effects of verapamil and or ryanodine on salicylate (SA) and its hydroxylated adduct; 2,3-dihydroxybenzoic acid (2,3-DHBA) levels in glutamate induced neurotoxicity of whole rat brains. To detect SA and 2,3-DHBA, an HPLC-EC/UV method was used. Retention time was found to be 3.9 min for 2,3-DHBA and 12.0 min for SA. Verapamil at 10(-5) and 10(-7) and ryanodine at 10(-5) M concentrations were found to have a significant decreasing effect on this degradation induced by glutamate. This was the highest dose for ryanodine tested. As an L-type voltage dependent calcium channel blocker, verapamil was found ineffective at 10(-4), 10(-6) and 10(-8) M concentrations. Surprisingly, none of the combined application groups (verapamil + ryanodine) was found effective on SA hydroxylation. As a result, ryanodine was effective only at the highest dose, while verapamil exerts its effect in a dose dependent fashion as reported before in the literature.

A database for cell signaling networks

We developed a data and knowledge base for cellular signal transduction in human cells, to make this rapidly growing information available. The database includes all the biological properties of cellular signal transduction, including biological reactions that transfer cellular signals and molecular attributes characterized by sequences, structures, and functions. Since the database is based on the object-oriented technique, highly flexible methods of data definition and modification are necessary to handle this diverse and complex biological information. The database includes attractive graphical representations of signaling cascades and the three-dimensional structure of molecules. The database is a novel application of ACEDB, which was the database originally developed to store the C. elegans genome. The database can be accessed through the Internet at http://geo.nihs.go.jp/csndb.html.

Caffeine-induced [Ca2+] oscillations in neurones of frog sympathetic ganglia

1. Single cell fluorimetry was used to monitor caffeine-induced oscillations of cytosolic [Ca2+] in frog sympathetic ganglion neurones in 2.0 mM K+ Ringer solution. 2. [Ca2+] oscillations decreased in frequency and exhibited three different amplitude patterns after the first large peak of [Ca2+]: (a) a series of big oscillations (BOs) of constant large amplitude (300-400 nM), (b) a series of much smaller oscillations (SOs) (40-60 nM), or (c) a series of decaying oscillations (DOs) of rapidly decreasing amplitude. 3. A model in which the oscillation amplitude was determined by the Ca2+ content of the endoplasmic reticulum (ER) whereas the oscillation frequency was controlled by how rapidly the cytosolic [Ca2+] reached the threshold for Ca2+-induced Ca2+ release (CICR) was able to simulate each observed pattern by varying the level of activity of the ER Ca2+ pump (SERCA), CICR and release-activated Ca2+ transport (RACT). A cumulative, cytosolic Ca2+-dependent inactivation of the plasma membrane (PM) Ca2+ influx or of the Ca2+-sensitive leak coefficient of the ryanodine receptors caused the oscillation frequency to decrease in the model. 4. Transitions between BOs and SOs and changes in [Ca2+] oscillations caused by ryanodine, thapsigargin, lanthanum and FCCP could also be simulated. 5. We conclude that RACT, SERCA, CICR and Ca2+-dependent PM Ca2+ influx are major mechanisms underlying [Ca2+] oscillations in these neurones.

Calcium transients evoked by action potentials in the somata of chick ciliary neurons

The effect of action potentials on the calcium concentration in the somata of chick ciliary neurons ([Ca2+]s) was determined by loading these with the calcium indicator calcium green-1. Following trains of 1-10 impulses (30 Hz) to the postganglionic nerve, the [Ca2+]s increased rapidly and then declined along a single exponential with a time constant of 0.70 +/- 0.04 s (fast phase). After trains of 20 or 50 impulses, the elevated [Ca2+]s declined as the sum of two exponentials, with time constants of 0.78 +/- 0.12 s (fast phase) and 4.0 +/- 0.4 s (moderate phase). After a 600-impulse postganglionic train of impulses, the elevated [Ca2+]s declined quickly over about 1 s, and then as the sum of two exponentials: that of the moderate phase and a slower component with a time constant of 109 +/- 16 s (slow phase). Similar time courses were observed following stimuli to the preganglionic nerve. Caffeine (3 mM) and ryanodine (20 microM) both sped the fast phase and slowed the moderate phase of [Ca2+]s decline. Carbonyl cyanide m-chlorophenyl hydrazone (CCCP, 2 microM) slowed the slow phase, without affecting the other phases of decline. These results are discussed in relation to identifying the mechanisms responsible for these different phases of Ca2+ removal.

Oscillating Ca2+-induced channel activity obtained in BLM with a mitochondrial membrane component

Oscillations in ion fluxes and membrane potential may be observed in cells and in mitochondria as well. We obtained Ca2+-induced oscillations in channel activity in black-lipid membranes reconstituted with hydrophobic components extracted from mitochondria. Mitoplasts prepared from purified rat liver mitochondria were extracted with ethanol followed by Folch extraction and further partial purification by silicic acid chromatography. Channel activity was measured in lipid bilayers formed from bovine brain lipids and 10% cardiolipin with addition of the purified fractions. The conductance with 10 mM Ca2+ was 100 pS or its multiples. Ca2+ gradients of 4: 1 induced oscillating channel activity for several hours, with initial open states of 40 s and closed states of 56 s; the open times gradually decreasing to 8.6 s. No channel activity was seen without added fractions. The channel activity was associated with a Ca2+-binding lipid, nonpolar, low-molecular-weight fraction that in gel electrophoresis was not stained with Coomassie Blue and did not contain carbohydrate-staining material. 1H-Nuclear magnetic resonance spectra of the substance showed the presence of aliphatic chains and carbonyls, but the detailed structure remains to be elucidated.

Glutamatergically induced pattern of Ca2+ driving potential as a mechanism of postsynaptic plasticity

Simulation studies were performed in a model of neuronal dendrite with Na+ and K+ channels and with ionotropic and metabotropic glutamate receptors. The ionotropic receptors were either N-methyl-D-aspartate (NMDA)-sensitive, voltage-dependent, and permeable to Ca2+, Na+, and K+, or non-NMDA-sensitive, voltage-independent, and permeable to Na+ and K+. The metabotropic receptors provided a catalytic effect on Ca2+-induced Ca2+ release from intracellular stores. Local intracellular concentration [Ca2+]i in the cytoplasm was changed because of exchange with the stores, axial diffusion, and transmembrane inward passive and outward pump fluxes. Tonic activation of ionotropic and metabotropic receptors in a particular range of intensities triggered the formation of spatially periodic [Ca2+]i hot and cold bands arising from an initial uniform state. The period and width of the bands were smaller at higher levels of tonic NMDA activation and higher metabotropically controlled rates of Ca2+-induced Ca2+ release. The bandwidths also depended on the dendrite diameter, the specific membrane, and cytoplasm resistivity. This activity-induced pattern led to long-term, spatially inhomogeneous change in local excitatory postsynaptic potentials (EPSPs) of NMDA synapses phasically activated with the same presynaptic intensity. The phasic EPSPs were potentiated if the synapse occurred in the hot band.

A realistic model of biphasic calcium transients in electrically nonexcitable cells

In many electrically nonexcitable cells, the release of calcium from internal stores is followed by a much slower phase in which the intracellular calcium concentration decreases gradually to a sustained value higher than the concentration before stimulation. This elevated calcium plateau has been shown to be the result of calcium influx. The model presented in this work describes a system consisting of a cytoplasmic calcium store and a plasma membrane calcium channel, both excitable by a membrane receptor; a fast cytoplasmic calcium buffer; and calcium pumps in both the calcium store and cellular membranes. Inherent difficulties in the numerical evaluation of the model, caused by very large calcium fluxes across the store membrane, were overcome by analytically separating the fast processes of calcium release from the slower processes of calcium cycling across the plasma membrane. This enabled the simulation of realistic biphasic calcium transients similar to those observed experimentally. The model predicted 1) a strong correlation between the rate of calcium cycling across the plasma membrane and the rate of calcium decay; and 2) a dependence on the level of cell excitation of the maximum rise in cytoplasmic calcium concentration, the level of the elevated calcium plateau, and the rate of calcium decay. Using the model, we simulated the washout of agonist from the bathing solution and the depletion of the calcium store by a pharmacological agent (such as thapsigargin) under several experimental conditions.

Release-activated Ca2+ transport in neurons of frog sympathetic ganglia

Frog sympathetic ganglion neurons exhibit a novel Ca2+ uptake mechanism, release-activated calcium transport or RACT, which is manifest in both cytosolic and store [Ca2+] signals as greatly accelerated Ca2+ uptake after Ca2+ release from internal stores. RACT is activated by Ca2+ release but not by Ca2+ entry and serves to selectively refill Ca2+ stores after release. RACT lowers cytosolic [Ca2+] with a rate constant about 1.6 times that of the SERCA pump with empty ER. RACT is thapsigargin-insensitive, was eliminated by ryanodine, but was not affected by blocking mitochondrial or plasma membrane Ca2+ transport. A Ca2+ flux model with RACT in the ER membrane reproduced the cytosolic and store [Ca2+] responses to all stimuli.

Ionic mechanisms of muscarinic depolarization in entorhinal cortex layer II neurons

The mechanisms underlying direct muscarinic depolarizing responses in the stellate cells (SCs) and non-SCs of medial entorhinal cortex layer II were investigated in tissue slices by intracellular recording and pressure-pulse applications of carbachol (CCh). Subthreshold CCh depolarizations were largely potentiated in amplitude and duration when paired with a short DC depolarization that triggered cell firing. During Na+ conductance block, CCh depolarizations were also potentiated by a brief DC depolarization that allowed Ca2+ influx and the potentiation was more robust in non-SCs than in SCs. Also, in non-SCs, CCh depolarizations could be accompanied by spikelike voltage oscillations at a slow frequency. In both SCs and non-SCs, the voltage-current (V-I) relations were similarly affected by CCh, which caused a shift to the left of the steady-state V-I relations over the entire voltage range and an increase in apparent slope input resistance at potentials positive to about -70 mV. CCh responses potentiated by Ca2+ influx demonstrated a selective increase in slope input resistance at potentials positive to about -75 mV in relation to the nonpotentiated responses. K+ conductance block with intracellular injection of Cs+ (3 M) and extracellular Ba2+ (1 mM) neither abolished CCh depolarizations nor resulted in any qualitatively distinct effect of CCh on the V-I relations. CCh depolarizations were also undiminished by block of the time-dependent inward rectifier Ih, with extracellular Cs . However, CCh depolarizations were abolished during Ca2+ conductance block with low-Ca2+ (0.5 mM) solutions containing Cd2+, Co2+, or Mn2+, as well as by intracellular Ca2+ chelation with bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid. Inhibition of the Na+-K+ ATPase with strophanthidin resulted in larger CCh depolarizations. On the other hand, when NaCl was replaced by N-methyl-D-glucamine, CCh depolarizations were largely diminished. CCh responses were blocked by 0.8 microM pirenzepine, whereas hexahydro-sila-difenidolhydrochloride,p-fluoroanalog (p-F-HHSiD) and himbacine were only effective antagonists at 5- to 10-fold larger concentrations. Our data are consistent with CCh depolarizations being mediated in both SCs and non-SCs by m1 receptor activation of a Ca2+-dependent cationic conductance largely permeable to Na+. Activation of this conductance is potentiated in a voltage-dependent manner by activity triggering Ca2+ influx. This property implements a Hebbian-like mechanism whereby muscarinic receptor activation may only be translated into substantial membrane depolarization if coupled to postsynaptic cell activity. Such a mechanism could be highly significant in light of the role of the entorhinal cortex in learning and memory as well as in pathologies such as temporal lobe epilepsy.

Repetitive Ca2+ spikes in a unicellular green alga

Cytosolic Ca2+ activity ([Ca2+]cy) and membrane potential were measured simultaneously in the unicellular green alga Eremosphaera viridis. Steady state [Ca2+]cy was about 160 nM. A 'light-off' stimulus induced a transient elevation of [Ca2+]cy ([Ca2+]cy spike) in parallel with a transient hyperpolarization of the plasma membrane. Caffeine and Sr2+, known to release Ca2+ from intracellular stores in animal cells, induced repetitive [Ca2+]cy spikes in Eremosphaera which were always accompanied by parallel repetitive transient hyperpolarizations. These transient hyperpolarizations could be used as an indicator for [Ca2+]cy spikes. Repetitive [Ca2+]cy spikes in Eremosphaera were similar to repetitive [Ca2+]cy spikes in excitable animal cells. The mechanisms underlying these [Ca2+]cy oscillations seem to be comparable in animal and plant cells.

Effect of beta-amyloid block of the fast-inactivating K+ channel on intracellular Ca2+ and excitability in a modeled neuron

beta-Amyloid peptide (A beta), one of the primary protein components of senile plaques found in Alzheimer disease, is believed to be toxic to neurons by a mechanism that may involve loss of intracellular calcium regulation. We have previously shown that A beta blocks the fast-inactivating potassium (A) current. In this work, we show, through the use of a mathematical model, that the A beta-mediated block of the A current could result in increased intracellular calcium levels and increased membrane excitability, both of which have been observed in vitro upon acute exposure to A beta. Simulation results are compared with experimental data from the literature; the simulations quantitatively capture the observed concentration dependence of the neuronal response and the level of increase in intracellular calcium.

Ryanodine receptor adaptation and Ca2+(-)induced Ca2+ release-dependent Ca2+ oscillations

A simplified mechanism that mimics "adaptation" of the ryanodine receptor (RyR) has been developed and its significance for Ca2+(-)induced Ca2+ release and Ca2+ oscillations investigated. For parameters that reproduce experimental data for the RyR from cardiac cells, adaptation of the RyR in combination with sarco/endoplasmic reticulum Ca2+ ATPase Ca2+ pumps in the internal stores can give rise to either low [Cai2+] steady states or Ca2+ oscillations coexisting with unphysiologically high [Cai2+] steady states. In this closed-cell-type model rapid, adaptation-dependent Ca2+ oscillations occur only in limited ranges of parameters. In the presence of Ca2+ influx and efflux from outside the cell (open-cell model) Ca2+ oscillations occur for a wide range of physiological parameter values and have a period that is determined by the rate of Ca2+ refilling of the stores. Although the rate of adaptation of the RyR has a role in determining the shape and the period of the Ca2+ spike, it is not essential for their existence. This is in marked contrast with what is observed for the inositol 1,4,5-trisphosphate receptor for which the biphasic activation and inhibition of its activity by Ca2+ are sufficient to produce oscillations. Results for this model are compared with those based on Ca2+(-)induced Ca2+ release alone in the bullfrog sympathetic neuron. This kinetic model should be suitable for analyzing phenomena associated with "Ca2+ sparks," including their merger into Ca2+ waves in cardiac myocytes.

Evidence for the existence of inositol (1,4,5)-trisphosphate- and ryanodine-sensitive pools in bovine endothelial cells. Ca2+ releases in cells with different basal level of intracellular Ca2+

In single bovine aortic endothelial (BAE) cells pre-loaded with Fura-2, Ca2+ transients in a Ca2+-free medium have been revealed, which evidently reflects Ca2+ release from intracellular stores. In cells with different levels of resting basal cytoplasmic Ca2+ ([Ca2+]i) from about 50 to 110 nM, a biphasic dependence of the Ca2+ transients on resting [Ca2+]i was shown and spontaneous Ca2+ oscillations were observed. At a [Ca2+]i level over 110 nM, a pronounced rise in Ca2+ transients occurred and only single transients were observed. Ryanodine (10 microM) produced a transient [Ca2+]i elevation, suggesting the presence of ryanodine receptors in intracellular store membranes. The results imply that both inositol 1,4,5-trisphosphate-sensitive Ca2+ release (IICR) and Ca2+-sensitive Ca2+ release (CICR) take place in BAE cells. Only IICR seems to be sufficient for generating baseline Ca2+ oscillations in BAE cells, whereas the ATP-induced (5-100 microM) Ca2+ response involves the CICR set in motion by an oscillatory IICR of high frequency. The completion of both the spontaneous and ATP-induced Ca2+ transients was associated with a [Ca2+]i decrease to a level below the initial resting [Ca2+]i (undershoot). Its depth biphasically depended on the resting [Ca2+]i from 50 to 110 nM, suggesting that the lack of a Ca2+ leak from inositol 1,4,5-trisphosphate-sensitive stores is responsible for the undershoot in this range. The Ca2+ leak is concluded to play a key role in the initiation and termination of regenerative IICR both in spontaneous oscillations and in ATP-induced transients.