Sensing and refilling calcium stores in an excitable cell

Dynamic mechanism of multiple bursting patterns in a whole-cell multiscale model with calcium oscillations

The dynamic mechanism of a whole-cell model containing electrical signalling and two-compartment Ca2+ signalling in gonadotrophs is investigated. The transition from spiking to bursting by Hopf bifurcation of the fast subsystem about the slow variable is detected via the suitable parameters. When the timescale of K+ gating variable is changed, the relaxation oscillation with locally small fluctuation, chaotic bursting and mixed-mode bursting (MMB) are revealed through chaos. In addition, the bifurcation of [Ca2+]i with regard to [IP3] is analysed, showing periodic solutions, torus, period doubling solutions and chaos. Finally, hyperpolarizations and torus canard-like behaviours of the full system under a set of specific parameters are elucidated.

Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis

The reproductive neuroendocrine axis, or hypothalamo-pituitary-gonadal (HPG) axis, is a paragon of complex biological system involving numerous cell types, spread over several anatomical levels communicating through entangled endocrine feedback loops. The HPG axis exhibits remarkable dynamic behaviors on multiple time and space scales, which are an inexhaustible source of studies for mathematical and computational biology. In this review, we will describe a variety of modeling approaches of the HPG axis from a cellular endocrinology viewpoint. We will in particular investigate the questions raised by some of the most striking features of the HPG axis: (i) the pulsatile secretion of hypothalamic and pituitary hormones, and its counterpart, the cell signaling induced by frequency-encoded hormonal signals, and (ii) the dual, gametogenic and glandular function of the gonads, which relies on the tight control of the somatic cell populations ensuring the proper maturation and timely release of the germ cells.

A computational model for gonadotropin releasing cells in the teleost fish medaka

Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca²⁺ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na⁺ currents (I_Na), high-voltage activated Ca²⁺ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I_Ca. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I_Na, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I_Na and I_Ca, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I_Ca-based APs. We put a particular focus on how the big conductance K⁺ current (I_BK) modulates the AP shape. Interestingly, we find that I_BK can prolong AP duration in models that fire I_Ca-based APs, while it consistently shortens the duration of the predominantly I_Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I_Na-mediated APs.

Excitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. Since one type of ion channels is permeable to Ca²⁺ ions, there is typically an influx of Ca²⁺ during an AP. Pituitary cells therefore use AP firing to regulate their cytosolic Ca²⁺ concentration, which in turn controls their hormone secretion rate. The amount of Ca²⁺ that enters during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Pituitary APs are generally mediated by a combination of Ca²⁺ channels and Na⁺ channels, and the relative contributions of from the two vary between cell types, animal species and biological conditions. Previous computer models have predominantly been adapted to data from pituitary cells which tend to fire Ca²⁺-based APs. Here we develop a new model, adapted to data from pituitary cells in the fish medaka, which APs that are predominantly Na⁺-based, and compare its dynamical properties to the previous models that fire Ca²⁺-based APs.

Common and diverse elements of ion channels and receptors underlying electrical activity in endocrine pituitary cells

The pituitary gland contains six types of endocrine cells defined by hormones they secrete: corticotrophs, melanotrophs, gonadotrophs, thyrotrophs, somatotrophs, and lactotrophs. All these cell types are electrically excitable, and voltage-gated calcium influx is the major trigger for their hormone secretion. Along with hormone intracellular content, G-protein-coupled receptor and ion channel expression can also be considered as defining cell type identity. While many aspects of the developmental and activity dependent regulation of hormone and G-protein-coupled receptor expression have been elucidated, much less is known about the regulation of the ion channels needed for excitation-secretion coupling in these cells. We compare the spontaneous and receptor-controlled patterns of electrical signaling among endocrine pituitary cell types, including insights gained from mathematical modeling. We argue that a common set of ionic currents unites these cells, while differential expression of another subset of ionic currents could underlie cell type-specific patterns. We demonstrate these ideas using a generic mathematical model, showing that it reproduces many observed features of pituitary electrical signaling. Mapping these observations to the developmental lineage suggests possible modes of regulation that may give rise to mature pituitary cell types.

Modeling the diversity of spontaneous and agonist-induced electrical activity in anterior pituitary corticotrophs

Pituitary corticotrophs fire action potentials spontaneously and in response to stimulation with corticotropin-releasing hormone (CRH) and arginine vasopressin (AVP), and such electrical activity is critical for calcium signaling and calcium-dependent adrenocorticotropic hormone secretion. These cells typically fire tall, sharp action potentials when spontaneously active, but a variety of other spontaneous patterns have also been reported, including various modes of bursting. There is variability in reports of the fraction of corticotrophs that are electrically active, as well as their patterns of activity, and the sources of this variation are not well understood. The ionic mechanisms responsible for CRH- and AVP-triggered electrical activity in corticotrophs are also poorly characterized. We use electrophysiological measurements and mathematical modeling to investigate possible sources of variability in patterns of spontaneous and agonist-induced corticotroph electrical activity. In the model, variation in as few as two parameters can give rise to many of the types of patterns observed in electrophysiological recordings of corticotrophs. We compare the known mechanisms for CRH, AVP, and glucocorticoid actions and find that different ionic mechanisms can contribute in different but complementary ways to generate the complex time courses of CRH and AVP responses. In summary, our modeling suggests that corticotrophs have several mechanisms at their disposal to achieve their primary function of pacemaking depolarization and increased electrical activity in response to CRH and AVP.NEW & NOTEWORTHY We and others recently demonstrated that the electrical activity and calcium dynamics of corticotrophs are strikingly diverse, both spontaneously and in response to the agonists CRH and AVP. Here we demonstrate this diversity with electrophysiological measurements and use mathematical modeling to investigate its possible sources. We compare the known mechanisms of agonist-induced activity in the model, showing how the context of ionic conductances dictates the effects of agonists even when their target is fixed.

Estimating the biophysical properties of neurons with intracellular calcium dynamics

We investigate the dynamics of a conductance-based neuron model coupled to a model of intracellular calcium uptake and release by the endoplasmic reticulum. The intracellular calcium dynamics occur on a time scale that is orders of magnitude slower than voltage spiking behavior. Coupling these mechanisms sets the stage for the appearance of chaotic dynamics, which we observe within certain ranges of model parameter values. We then explore the question of whether one can, using observed voltage data alone, estimate the states and parameters of the voltage plus calcium (V+Ca) dynamics model. We find the answer is negative. Indeed, we show that voltage plus another observed quantity must be known to allow the estimation to be accurate. We show that observing both the voltage time course V(t) and the intracellular Ca time course will permit accurate estimation, and from the estimated model state, accurate prediction after observations are completed. This sets the stage for how one will be able to use a more detailed model of V+Ca dynamics in neuron activity in the analysis of experimental data on individual neurons as well as functional networks in which the nodes (neurons) have these biophysical properties.

Coordination of calcium signals by pituitary endocrine cells in situ

The pulsatile secretion of hormones from the mammalian pituitary gland drives a wide range of homeostatic responses by dynamically altering the functional set-point of effector tissues. To accomplish this, endocrine cell populations residing within the intact pituitary display large-scale changes in coordinated calcium-spiking activity in response to various hypothalamic and peripheral inputs. Although the pituitary gland is structurally compartmentalized into specific and intermingled endocrine cell networks, providing a clear morphological basis for such coordinated activity, the mechanisms which facilitate the timely propagation of information between cells in situ remain largely unexplored. Therefore, the aim of the current review is to highlight the range of signalling modalities known to be employed by endocrine cells to coordinate intracellular calcium rises, and discuss how these mechanisms are integrated at the population level to orchestrate cell function and tissue output.

Molecular mechanisms of pituitary endocrine cell calcium handling

Endocrine pituitary cells express numerous voltage-gated Na(+), Ca(2+), K(+), and Cl(-) channels and several ligand-gated channels, and they fire action potentials spontaneously. Depending on the cell type, this electrical activity can generate localized or global Ca(2+) signals, the latter reaching the threshold for stimulus-secretion coupling. These cells also express numerous G-protein-coupled receptors, which can stimulate or silence electrical activity and Ca(2+) influx through voltage-gated Ca(2+) channels and hormone release. Receptors positively coupled to the adenylyl cyclase signaling pathway stimulate electrical activity with cAMP, which activates hyperpolarization-activated cyclic nucleotide-regulated channels directly, or by cAMP-dependent kinase-mediated phosphorylation of K(+), Na(+), Ca(2+), and/or non-selective cation-conducting channels. Receptors that are negatively coupled to adenylyl cyclase signaling pathways inhibit spontaneous electrical activity and accompanied Ca(2+) transients predominantly through the activation of inwardly rectifying K(+) channels and the inhibition of voltage-gated Ca(2+) channels. The Ca(2+)-mobilizing receptors activate inositol trisphosphate-gated Ca(2+) channels in the endoplasmic reticulum, leading to Ca(2+) release in an oscillatory or non-oscillatory manner, depending on the cell type. This Ca(2+) release causes a cell type-specific modulation of electrical activity and intracellular Ca(2+) handling.

Ion channels and signaling in the pituitary gland

Endocrine pituitary cells are neuronlike; they express numerous voltage-gated sodium, calcium, potassium, and chloride channels and fire action potentials spontaneously, accompanied by a rise in intracellular calcium. In some cells, spontaneous electrical activity is sufficient to drive the intracellular calcium concentration above the threshold for stimulus-secretion and stimulus-transcription coupling. In others, the function of these action potentials is to maintain the cells in a responsive state with cytosolic calcium near, but below, the threshold level. Some pituitary cells also express gap junction channels, which could be used for intercellular Ca(2+) signaling in these cells. Endocrine cells also express extracellular ligand-gated ion channels, and their activation by hypothalamic and intrapituitary hormones leads to amplification of the pacemaking activity and facilitation of calcium influx and hormone release. These cells also express numerous G protein-coupled receptors, which can stimulate or silence electrical activity and action potential-dependent calcium influx and hormone release. Other members of this receptor family can activate calcium channels in the endoplasmic reticulum, leading to a cell type-specific modulation of electrical activity. This review summarizes recent findings in this field and our current understanding of the complex relationship between voltage-gated ion channels, ligand-gated ion channels, gap junction channels, and G protein-coupled receptors in pituitary cells.

Use of virtual cell in studies of cellular dynamics

The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems. In this chapter, we discuss modeling capabilities of VCell and demonstrate representative examples of the models published by the VCell users.

An integrated model of electrical spiking, bursting, and calcium oscillations in GnRH neurons

The plasma membrane electrical activities of neurons that secrete gonadotropin-releasing hormone (GnRH) have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities. The goal of this article is to develop a single model that accounts for the previously modeled experimental results and some more recent results that have not been accounted for. The latter includes two types of membrane potential bursting mechanisms and their associated cytosolic calcium oscillations. One bursting mechanism has not been reported in experiments and is thus regarded as a model prediction. Although the model is mainly based on data collected in immortalized GnRH cell lines, it is capable of explaining some properties of GnRH neurons observed in several other preparations including mature GnRH neurons in hypothalamic slices. We present a spatial model that incorporates a detailed description of calcium dynamics in a three-dimensional cell body with the ion channels evenly distributed on the cell surface. A phenomenological reduction of the spatial model into a simplified form is also presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities in the pulsatile release of GnRH.

Multiple roles of Gi/o protein-coupled receptors in control of action potential secretion coupling in pituitary lactotrophs

G(i/o) protein-coupled receptors, signaling through G protein-dependent and protein-independent pathways, have prominent effects on secretion by modulating calcium signaling and regulating the size of the releasable secretory pool, the rates of exocytosis and endocytosis, and de novo synthesis. Pituitary cells fire action potentials spontaneously, and the associated calcium influx is sufficient to maintain prolactin (PRL) release but not gonadotropin release at high and steady levels for many hours. Such secretion, termed intrinsic, spontaneous, or basal, reflects fusion of secretory vesicles triggered by the cell type-specific pattern of action potentials. In lactotrophs, activation of endothelin ET(A) and dopamine D(2) receptors causes inhibition of spontaneous electrical activity and basal adenylyl cyclase activity accompanied with inhibition of basal PRL release. Agonist-induced inhibition of cAMP production and firing of action potentials is abolished in cells with blocked pertussis toxin (PTX)-sensitive G(i/o) signaling pathway. However, agonist-induced inhibition of PRL release is only partially relieved in such treated cells, indicating that both receptors also inhibit exocytosis downstream of cAMP/calcium signaling. The PTX-insensitive step in agonist-induced inhibition of PRL release is not affected by inhibition of phosphoinositide 3-kinase and glycogen synthase kinase-3 but is partially rescued by downregulation of the G(z)alpha expression. Thus, ET(A) and D(2) receptors inhibit basal PRL release not only by blocking electrical activity but also by desensitizing calcium-secretion coupling.

Correlation analysis a tool for comparing relaxation-type models to experimental data

We describe a new technique for comparing mathematical models to the biological systems that are described. This technique is appropriate for systems that produce relaxation oscillations or bursting oscillations, and takes advantage of noise that is inherent to all biological systems. Both types of oscillations are composed of active phases of activity followed by silent phases, repeating periodically. The presence of noise adds variability to the durations of the different phases. The central idea of the technique is that the active phase duration may be correlated with either/both the previous or next silent phase duration, and the resulting correlation pattern provides information about the dynamic structure of the system. Correlation patterns can easily be determined by making scatter plots and applying correlation analysis to the cluster of data points. This could be done both with experimental data and with model simulation data. If the model correlation pattern is in general agreement with the experimental data, then this adds support for the validity of the model. Otherwise, the model must be corrected. While this tool is only one test of many required to validate a mathematical model, it is easy to implement and is noninvasive.

Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations

Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.

A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons

Cultured gonadotropin-releasing hormone (GnRH) neurons have been shown to express GnRH receptors. GnRH binding to its receptors activates three types of G-proteins at increasing doses. These G-proteins selectively activate or inhibit GnRH secretion by regulating the intracellular levels of Ca2+ and cAMP. Based on these recent observations, we build a model in which GnRH plays the roles of a feedback regulator and a diffusible synchronizing agent. We show that this GnRH-regulated GnRH-release mechanism is sufficient for generating pulsatile GnRH release. The model reproduces the observed effects of some key drugs that disturb the GnRH pulse generator in specific ways. Simulations of 100 heterogeneous neurons revealed that the synchronization mediated by a common pool of diffusible GnRH is robust. The population can generate synchronized pulsatile signals even when all the individual GnRH neurons oscillate at different amplitudes and peak at different times. These results suggest that the positive and negative effects of the autocrine regulation by GnRH on GnRH neurons are sufficient and robust in generating GnRH pulses.

Roles of purinergic P2X receptors as pacemaking channels and modulators of calcium-mobilizing pathway in pituitary gonadotrophs

Anterior pituitary cells release ATP and express several subtypes of purinergic P2 receptors, but their biophysical properties and roles in spontaneous and receptor-controlled electrical activity have not been characterized. Here we focused on extracellular ATP actions in gonadotrophs from embryonic, neonatal, and adult rats. In cells from all three age groups, the Ca2+-mobilizing agonist GnRH induced oscillatory, hyperpolarizing, nondesensitizing, and slow deactivating currents. In contrast, ATP induced nonoscillatory, depolarizing, slowly desensitizing, and rapidly deactivating current, indicating that these cells express cation-conducting P2X channels but not Ca2+-mobilizing P2Y receptors. The amplitudes of P2X current response and the rates of receptor desensitization were dependent on ATP concentration. The biophysical and pharmacological properties of P2X currents were consistent with the expression of P2X2 subtype of channels in these cells. ATP-induced rapid depolarization of gonadotrophs lead to initiation of firing in quiescent cells, an increase in the frequency of action potentials in spontaneously active cells, and a transient stimulation of LH release. ATP also influenced GnRH-induced current and membrane potential oscillations and LH release in an extracellular Ca2+-dependent manner. These inositol 1,4,5-triphosphate-dependent oscillations were facilitated, slowed, or stopped, depending of ATP concentration, the time of its application, and the level of Ca2+ content in intracellular stores. These results indicate that, in gonadotrophs, P2X receptors could operate as pacemaking channels and modulators of GnRH-controlled electrical activity and secretion.

Modeling and analysis of calcium signaling events leading to long-term depression in cerebellar Purkinje cells

Modeling and simulation of the calcium signaling events that precede long-term depression of synaptic activity in cerebellar Purkinje cells are performed using the Virtual Cell biological modeling framework. It is found that the unusually high density and low sensitivity of inositol-1,4,5-trisphosphate receptors (IP3R) are critical to the ability of the cell to generate and localize a calcium spike in a single dendritic spine. The results also demonstrate the model's capability to simulate the supralinear calcium spike observed experimentally during coincident activation of the parallel and climbing fibers. The sensitivity of the calcium spikes to certain biological and geometrical effects is investigated as well as the mechanisms that underlie the cell's ability to generate the supralinear spike. The sensitivity of calcium release rates from the IP3R to calcium concentrations, as well as IP3 concentrations, allows the calcium spike to form. The diffusion barrier caused by the small radius of the spine neck is shown to be important, as a threshold radius is observed above which a spike cannot be formed. Additionally, the calcium buffer capacity and diffusion rates from the spine are found to be important parameters in shaping the calcium spike.

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

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

Role of Ca2+ store in AMPA-triggered Ca2+ dynamics in retinal horizontal cells

Fura-2 fluorescent calcium imaging was applied to measure [Ca(2+)](i) in freshly dissociated horizontal cells of carp retina, and a model containing endoplasmic reticulum (ER) membrane processes and plasma membrane processes was constructed for quantitative analyses of the AMPA-triggered calcium dynamics. A transient increase followed by a sustained steady level of [Ca(2+)](i) was observed when 100 microM AMPA was applied, while the initial transient increase of [Ca(2+)](i) was suppressed by exogenously applied ryanodine. The model analyses results suggest that the AMPA-triggered calcium dynamics involves a number of cytoplasmic and endoplasmic processes that interact with each other. It also suggests that calcium store is an important part contributing to the transient calcium signal.

Control of calcium oscillations by membrane fluxes

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

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.

Dependence of pituitary hormone secretion on the pattern of spontaneous voltage-gated calcium influx. Cell type-specific action potential secretion coupling

In excitable cells, voltage-gated calcium influx provides an effective mechanism for the activation of exocytosis. In this study, we demonstrate that although rat anterior pituitary lactotrophs, somatotrophs, and gonadotrophs exhibited spontaneous and extracellular calcium-dependent electrical activity, voltage-gated calcium influx triggered secretion only in lactotrophs and somatotrophs. The lack of action potential-driven secretion in gonadotrophs was not due to the proportion of spontaneously firing cells or spike frequency. Gonadotrophs exhibited calcium signals during prolonged depolarization comparable with signals observed in somatotrophs and lactotrophs. The secretory vesicles in all three cell types also had a similar sensitivity to voltage-gated calcium influx. However, the pattern of action potential calcium influx differed among three cell types. Spontaneous activity in gonadotrophs was characterized by high amplitude, sharp spikes that had a limited capacity to promote calcium influx, whereas lactotrophs and somatotrophs fired plateau-bursting action potentials that generated high amplitude calcium signals. Furthermore, a shift in the pattern of firing from sharp spikes to plateau-like spikes in gonadotrophs triggered luteinizing hormone secretion. These results indicate that the cell type-specific action potential secretion coupling in pituitary cells is determined by the capacity of their plasma membrane oscillator to generate threshold calcium signals.

Mitochondrial modulation of intracellular Ca(2+) signaling

IP3-mediated Ca(2+) release plays a fundamental role in many cell signaling processes and has been the subject of numerous modeling studies. Only recently has the important role that mitochondria play in the dynamics of intracellular Ca(2+) signaling begun to be considered in experimental work and in computational models. Mitochondria sequester large amounts of Ca(2+) and thus have a modulatory effect on intracellular Ca(2+) signaling, and mitochondrial uptake of Ca(2+), in turn, has a regulatory effect on mitochondrial function. Here we integrate a well-established model of IP3-mediated Ca(2+) signaling with a detailed model of mitochondrial Ca(2+) handling and metabolic function. The incorporation of mitochondria results in oscillations in a bistable formulation of the IP3 model, and increasing metabolic substrate decreases the frequency of these oscillations consistent with the literature. Ca(2+) spikes from the cytosol are communicated into mitochondria and are shown to induce realistic metabolic changes. The model has been formulated using a modular approach that is easy to modify and should serve as a useful basis for the investigation of questions regarding the interaction of these two systems.

Regularization mechanisms of spiking-bursting neurons

An essential question raised after the observation of highly variable bursting activity in individual neurons of Central Pattern Generators (CPGs) is how an assembly of such cells can cooperatively act to produce regular signals to motor systems. It is well known that some neurons in the lobster stomatogastric ganglion have a highly irregular spiking-bursting behavior when they are synaptically isolated from any connection in the CPG. Experimental recordings show that periodic stimuli on a single neuron can regulate its firing activity. Other evidence demonstrates that specific chemical and/or electrical synapses among neurons also induce the regularization of the rhythms. In this paper we present a modeling study in which a slow subcellular dynamics, the exchange of calcium between an intracellular store and the cytoplasm, is responsible for the origin and control of the irregular spiking-bursting activity. We show this in simulations of single cells under periodic driving and in minimal networks where the cooperative activity can induce regularization. While often neglected in the description of realistic neuron models, subcellular processes with slow dynamics may play an important role in information processing and short-term memory of spiking-bursting neurons.

Identification of membrane calcium channels essential for cytoplasmic and nuclear calcium elevations induced by vascular endothelial growth factor in human endothelial cells

Vascular endothelial growth factor (VEGF) is mitogenic for endothelial cells and has been shown to induce angiogenesis and endothelial cell migration through stimulation of endothelial tyrosine-kinase receptors. Here, using confocal microscopy and the patch-clamp technique on endothelial cells, membrane permeability to calcium as well as cytoplasmic and nuclear free calcium levels have been investigated in the first stages of tyrosine-kinase receptor activation by VEGF. VEGF (0.5nM) as well as inositol trisphosphate (IP3) induced an activation of membrane calcium-permeable channels exhibiting a similar low conductance in the range of 10 pS. The VEGF-triggered activation of these calcium channels, mediated by IP3 and involving the intracellular calcium stores, results in an increase in both cytoplasmic and nuclear calcium levels in endothelial cells, potentially modulating gene expression. Finally, the effect of Ni2+, a calcium channel blocker, on endothelial cell proliferation has been studied. The results show that inhibition of extracellular calcium influx significantly inhibits VEGF-induced cell proliferation. In the process of cell stimulation by VEGF, and possibly by other growth factors, activation of calcium channels could then be a key step in calcium-regulated gene expression and cell activation. These results suggest that the use of calcium channel blockers could be a novel way of prevention or reversion of VEGF-induced tumoral angiogenesis.

CRH-induced electrical activity and calcium signalling in pituitary corticotrophs

Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to the agonist corticotropin releasing hormone (CRH). There is indirect evidence suggesting that the agonist, by way of complex intracellular mechanisms, modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. We have previously constructed a Hodgkin-Huxley-type model of this process, which indicated that an increase in the L-type Ca2+ current is sufficient to generate repetitive action potentials (LeBeau et al. (1997). Biophys. J.73, 1263-1275). CRH is also believed to inhibit an inwardly rectifying K+ current. In this paper, we have found that a CRH-induced inhibition of the inwardly rectifying K+ current increases the model action potential firing frequency, [Ca2+]i transients and membrane excitability. This dual modulatory action of CRH on inward rectifier and voltage-gated Ca2+ channels better describes the observed CRH-induced effects. This structural alteration to the model along with parameter changes bring the model firing frequency in line with experimental data. We also show that the model exhibits experimentally observed bursting behaviour, where the depolarization spike is followed by small oscillations in the membrane potential.

Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators

Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit.

Confocal laser scanning microscopy of calcium dynamics in living cells

Confocal laser scanning microscopy (CLSM) is widely used to monitor intracellular calcium levels in living cells loaded with calcium-sensitive fluorophores. This review examines the basic advantages and limitations of CLSM in in vivo imaging analyses of calcium dynamics. The benefits of utilizing ratioed images and dextran-conjugated fluorophores are addressed, and practical aspects of handling confocal datasets are outlined. After considering some relatively new microscopical methods that can be used in conjunction with conventional CLSM, possible future applications of confocal techniques in analyses of intracellular calcium dynamics are discussed.

Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+ oscillators

We have developed a mathematical model of arterial vasomotion in which irregular rhythmic activity is generated by the nonlinear interaction of intracellular and membrane oscillators that depend on cyclic release of Ca2+ from internal stores and cyclic influx of extracellular Ca2+, respectively. Four key control variables were selected on the basis of the pharmacological characteristics of histamine-induced vasomotion in rabbit ear arteries: Ca2+ concentration in the cytosol, Ca2+ concentration in ryanodine-sensitive stores, cell membrane potential, and the open state probability of Ca2+-activated K+ channels. Although not represented by independent dynamic variables, the model also incorporates Na+/Ca2+ exchange, the Na+-K+-ATPase, Cl- fluxes, and Ca2+ efflux via the extrusion ATPase. Simulations reproduce a wide spectrum of experimental observations, including 1) the effects of interventions that modulate the functionality of Ca2+ stores and membrane ion channels, 2) paradoxes such as the apparently unpredictable dual action of Ca2+ antagonists and low extracellular Na+ concentration, which can abolish vasomotion or promote the appearance of large-amplitude oscillations, and 3) period-doubling, quasiperiodic, and intermittent routes to chaos. Nonlinearity is essential to explain these diverse patterns of experimental vascular response.

A current activated on depletion of intracellular Ca2+ stores can regulate exocytosis in adrenal chromaffin cells

Exocytosis in excitable cells is strongly coupled to Ca2+ entry through voltage-gated channels but can be evoked by activation of membrane receptors that release Ca2+ from inositol 1,4, 5-trisphosphate-sensitive internal stores. In many cell types, depletion of Ca2+ stores activates Ca2+ influx across the plasma membrane, a process known as capacitative or store-operated Ca2+ entry. This influx is mediated by a number of voltage-independent, Ca2+-selective currents. In addition to replenishing Ca2+ stores, these currents are hypothesized to play an important role in agonist-evoked secretion in nonexcitable cells, although this has not been confirmed experimentally. The existence and physiological function of such currents in excitable cells is not known. Using the capacitance detection technique to monitor exocytosis, we provide direct experimental evidence that a similar mechanism exists in bovine adrenal chromaffin cells. Depletion of intracellular Ca2+ stores with thapsigargin, a SERCA pump inhibitor, or with BAPTA, an exogenous Ca2+ chelator, activates a small-amplitude, voltage-independent current that is carried by Ca2+ and Na+ ions. Ca2+ entry through this pathway is sufficient to stimulate exocytosis at negative membrane potentials. In addition, depolarization-evoked exocytosis is markedly facilitated on activation of the current. These data suggest that excitable cells possess a store-operated Ca2+ influx mechanism that may both directly trigger exocytosis and modulate excitation-secretion coupling.

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

The properties of inositol 1,4,5-trisphosphate (IP3)-dependent intracellular calcium oscillations in pancreatic acinar cells depend crucially on the agonist used to stimulate them. Acetylcholine or carbachol (CCh) cause high-frequency (10-12-s period) calcium oscillations that are superimposed on a raised baseline, while cholecystokinin (CCK) causes long-period (>100-s period) baseline spiking. We show that physiological concentrations of CCK induce rapid phosphorylation of the IP3 receptor, which is not true of physiological concentrations of CCh. Based on this and other experimental data, we construct a mathematical model of agonist-specific intracellular calcium oscillations in pancreatic acinar cells. Model simulations agree with previous experimental work on the rates of activation and inactivation of the IP3 receptor by calcium (DuFour, J.-F., I.M. Arias, and T.J. Turner. 1997. J. Biol. Chem. 272:2675-2681), and reproduce both short-period, raised baseline oscillations, and long-period baseline spiking. The steady state open probability curve of the model IP3 receptor is an increasing function of calcium concentration, as found for type-III IP3 receptors by Hagar et al. (Hagar, R.E., A.D. Burgstahler, M.H. Nathanson, and B.E. Ehrlich. 1998. Nature. 396:81-84). We use the model to predict the effect of the removal of external calcium, and this prediction is confirmed experimentally. We also predict that, for type-III IP3 receptors, the steady state open probability curve will shift to lower calcium concentrations as the background IP3 concentration increases. We conclude that the differences between CCh- and CCK-induced calcium oscillations in pancreatic acinar cells can be explained by two principal mechanisms: (a) CCK causes more phosphorylation of the IP3 receptor than does CCh, and the phosphorylated receptor cannot pass calcium current; and (b) the rate of calcium ATPase pumping and the rate of calcium influx from the outside the cell are greater in the presence of CCh than in the presence of CCK.

A current activated on depletion of intracellular Ca2+ stores can regulate exocytosis in adrenal chromaffin cells

Exocytosis in excitable cells is strongly coupled to Ca2+ entry through voltage-gated channels but can be evoked by activation of membrane receptors that release Ca2+ from inositol 1,4, 5-trisphosphate-sensitive internal stores. In many cell types, depletion of Ca2+ stores activates Ca2+ influx across the plasma membrane, a process known as capacitative or store-operated Ca2+ entry. This influx is mediated by a number of voltage-independent, Ca2+-selective currents. In addition to replenishing Ca2+ stores, these currents are hypothesized to play an important role in agonist-evoked secretion in nonexcitable cells, although this has not been confirmed experimentally. The existence and physiological function of such currents in excitable cells is not known. Using the capacitance detection technique to monitor exocytosis, we provide direct experimental evidence that a similar mechanism exists in bovine adrenal chromaffin cells. Depletion of intracellular Ca2+ stores with thapsigargin, a SERCA pump inhibitor, or with BAPTA, an exogenous Ca2+ chelator, activates a small-amplitude, voltage-independent current that is carried by Ca2+ and Na+ ions. Ca2+ entry through this pathway is sufficient to stimulate exocytosis at negative membrane potentials. In addition, depolarization-evoked exocytosis is markedly facilitated on activation of the current. These data suggest that excitable cells possess a store-operated Ca2+ influx mechanism that may both directly trigger exocytosis and modulate excitation-secretion coupling.

Competitive calcium binding: implications for dendritic calcium signaling

Action potentials evoke calcium transients in dendrites of neocortical pyramidal neurons with time constants of < 100 ms at physiological temperature. This time period may not be sufficient for inflowing calcium ions to equilibrate with all present Ca2+-binding molecules. We therefore explored nonequilibrium dynamics of Ca2+ binding to numerous Ca2+ reaction partners within a dendritelike compartment using numerical simulations. After a brief Ca2+ influx, the reaction partner with the fastest Ca2+ binding kinetics initially binds more Ca2+ than predicted from chemical equilibrium, while companion reaction partners bind less. This difference is consolidated and may result in bypassing of slow reaction partners if a Ca2+ clearance mechanism is active. On the other hand, slower reaction partners effectively bind Ca2+ during repetitive calcium current pulses or during slower Ca2+ influx. Nonequilibrium Ca2+ distribution can further be enhanced through strategic placement of the reaction partners within the compartment. Using the Ca2+ buffer EGTA as a competitor of fluo-3, we demonstrate competitive Ca2+ binding within dendrites experimentally. Nonequilibrium calcium dynamics is proposed as a potential mechanism for differential and conditional activation of intradendritic targets.

Calcium

Ca2+ is involved in an intriguing variety of different biological events. The rapid development of techniques such as region- or organelle-directed fluorescent probes and laser scanning confocal microscopy for studying cellular biological events at a molecular level provides us with a rich daily intake of new results. While detailed three-dimensional structures of many intracellular and extracellular Ca2+-binding proteins have become available, structural information on key membrane proteins is still lacking. An integrated picture of the molecular events behind the multifunctional roles of Ca2+ in biological systems is still pending.

The regulation of gonadotropin-releasing hormone-induced calcium signals in male rat gonadotrophs by testosterone is mediated by dihydrotestosterone

The biological effects of testosterone (T) may be mediated directly by T or indirectly by its metabolites, dihydrotestosterone (DHT) and estradiol. The present study examined whether the metabolism of T is involved in the regulation of GnRH-induced Ca2+ signaling at the pituitary. In gonadotrophs from castrated rats, a significantly greater percentage of gonadotrophs demonstrated oscillatory Ca2+ responses to 100 nM GnRH than cells from intact rats (72% vs. 24%; P < 0.05). This increase was prevented by the administration of T propionate (0.1 mg/kg x day), DHT benzoate (2 mg/kg x day,), estradiol benzoate (EB; 5 microg/kg x day), or the combination of the above doses of DHT benzoate and EB. In all cases the proportion of gonadotrophs from the steroid-treated rats having oscillatory Ca2+ responses to 100 nM GnRH was between 21-25% (P > 0.05, compared with intact rats). To assess the importance of T metabolism, intact male rats were treated with the aromatase inhibitor letrozole (1 mg/kg x day), the 5alpha-reductase inhibitor finasteride (50 mg/kg x day), or their respective vehicles for 7 days. Letrozole had no effect on GnRH-induced Ca2+ signals, serum LH concentrations, or ventral prostate or testes weight. Finasteride treatment, however, mimicked the effects of castration, with significantly more gonadotrophs exhibiting Ca2+ oscillations in response to 100 nM GnRH than gonadotrophs from the vehicle-treated group (71% vs. 20% respectively; P < 0.05). Finasteride also caused a significant (P < 0.05) decrease in prostatic weight and DHT concentration, but had no significant effect on either prostatic T or serum LH concentrations. These findings suggest that in the intact male rat, the effects of T on GnRH-induced Ca2+ signaling are preferentially mediated via DHT. The results of this study also show that in the absence of androgens, estradiol may regulate GnRH-induced Ca2+ signaling in the male rat pituitary.

Ca2+ entry into PC12 cells initiated by ryanodine receptors or inositol 1,4,5-trisphosphate receptors

Capacitative Ca2+ entry (CCE) is a universal mechanism for refilling intracellular Ca2+ stores in electrically non-excitable cells. The situation in excitable cells is less clear, however, since they may rely on other entry mechanisms for Ca2+-store refilling. In the present study we investigated CCE in intact PC12 cells, using acetylcholine to bring about activation of InsP3 receptors (InsP3Rs), caffeine to activate ryanodine receptors (RyRs) and thapsigargin to inhibit sarco/endoplasmic reticulum Ca2+-ATPase pumps. We found that depletion of the InsP3-, caffeine- or thapsigargin-sensitive stores promoted Ca2+ entry, suggesting that stimulation of either InsP3Rs or RyRs can activate CCE. The CCE pathways activated by InsP3Rs, RyRs and thapsigargin appeared to be independent at least in part, since their effects were found to be additive. However, CCE triggered by caffeine, acetylcholine or thapsigargin progressively diminished with time. The decay of CCE caused by one agent also inhibited subsequent responses to the others, suggesting that some component of the CCE pathway is common to all intracellular Ca2+ stores. The magnitude of CCE stimulated by InsP3Rs or RyRs was related to the size of the stores; the InsP3-sensitive store was smaller than the RyR-sensitive store and triggered a smaller entry component. However, both stores filled with a similar half time (about 1 min), and both could be filled more rapidly by depolarization-induced Ca2+ entry through voltage-operated channels. A significant basal Ca2+ influx was apparent in PC12 cells. The basal entry component may be under the control of the InsP3-sensitive Ca2+ store, since short incubations in Ca2+-free medium depleted this store.