Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release

The finding and researching algorithm for potentially oscillating enzymatic systems

Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations' own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case - oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.

Long-Time Phase Correlations Reveal Regulation of Beating Cardiomyocytes

Spontaneous contractions of cardiomyocytes are driven by calcium oscillations due to the activity of ionic calcium channels and pumps. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that, in addition to the short-time (1-2 Hz), beat-to-beat variability, there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes. Our theoretical model relates these long-time correlations to cellular regulation that restores the frequency to its average, homeostatic value in response to stochastic perturbations.

A Computational Model for the Cold Response Pathway in Plants

Understanding the mechanism by which plants respond to cold stress and strengthen their tolerance to low temperatures is an important and challenging task in plant sciences. Experiments have established that the first step in the perception and transduction of the cold stress signal consists of a transient influx of Ca²⁺. This Ca²⁺ influx triggers the activation of a cascade of phosphorylation-dephosphorylation reactions that eventually affects the expression of C-repeat-binding factors (CBFs, notably CBF3), which were shown in many plants to control resistance to cold stress by regulating the expression of cold-regulated (COR) genes. Based on experimental observations mostly made on Arabidopsis thaliana, we build a computational model for the cold response pathway in plants, from the transduction of the cold signal via the transient influx of Ca²⁺ to the activation of the phosphorylation cascade leading to CBF3 expression. We explore the dynamics of this regulatory network by means of numerical simulations and compare the results with experimental observations on the dynamics of the cold response, both for the wild type and for mutants. The simulations show how, in response to cold stress, a brief Ca²⁺ influx, which is over in minutes, is transduced along the successive steps of the network to trigger the expression of cold response genes such as CBF3 within hours. Sometimes, instead of a single Ca²⁺ spike the decrease in temperature brings about a train of high-frequency Ca²⁺ oscillations. The model is applied to both types of Ca²⁺ signaling. We determine the dynamics of the network in response to a series of identical cold stresses, to account for the observation of desensitization and resensitization. The analysis of the model predicts the possibility of an oscillatory expression of CBF3 originating from the negative feedback exerted by ZAT12, a factor itself controlled by CBF3. Finally, we extend the model to incorporate the circadian control of CBF3 expression, to account for the gating of the response to cold stress by the plant circadian clock.

Cardiomyocyte Calcium Ion Oscillations-Lessons From Physics

We review a theoretical, coarse-grained description for cardiomyocytes calcium dynamics that is motivated by experiments on RyR channel dynamics and provides an analogy to other spontaneously oscillating systems. We show how a minimal model, that focuses on calcium channel and pump dynamics and kinetics, results in a single, easily understood equation for spontaneous calcium oscillations (the Van-der-Pol equation). We analyze experiments on isolated RyR channels to quantify how the channel dynamics depends both on the local calcium concentration, as well as its temporal behavior (“adaptation”). Our oscillator model analytically predicts the conditions for spontaneous oscillations, their frequency and amplitude, and how each of those scale with the small number of relevant parameters related to calcium channel and pump activity. The minimal model is easily extended to include the effects of noise and external pacing (electrical or mechanical). We show how our simple oscillator predicts and explains the experimental observations of synchronization, “bursting” and reduction of apparent noise in the beating dynamics of paced cells. Thus, our analogy and theoretical approach provides robust predictions for the beating dynamics, and their biochemical and mechanical modulation.

Physics of Spontaneous Calcium Oscillations in Cardiac Cells and Their Entrainment

Mechanical contraction in muscle cells requires Ca to allow myosin binding to actin. Beating cardiomyocytes contain internal Ca stores whose cytoplasmic concentration oscillates. Our theory explains observed single channel dynamics as well as cellular oscillations in spontaneously beating cardiomyocytes. The Ca dependence of channel activity responsible for Ca release includes positive feedback with a delayed response. We use this to predict a dynamical equation for global calcium oscillations with only a few physically relevant parameters. The theory accounts for the observed entrainment of beating to an oscillatory electric or mechanical field.

Effect of 2,5-dimethylphenol on Ca(2+) movement and viability in PC3 human prostate cancer cells

The phenolic compound 2,5-dimethylphenol is a natural product. 2,5-Dimethylphenol has been shown to affect rat hepatic and pulmonary microsomal metabolism. However, the effect of 2,5-dimethylphenol on Ca(2+ )signaling and cyotoxicity has never been explored in any culture cells. This study explored the effect of 2,5-dimethylphenol on cytosolic free Ca(2+ )levels ([Ca(2+)]i) and cell viability in PC3 human prostate cancer cells. 2,5-Dimethylphenol at concentrations between 500 μM and 1000 μM evoked [Ca(2+)]i rises in a concentration-dependent manner. This Ca(2+ )signal was inhibited by approximately half by the removal of extracellular Ca(2+). 2,5-Dimethylphenol-induced Ca(2+ )influx was confirmed by Mn(2+)-induced quench of fura-2 fluorescence. Pretreatment with the protein kinase C (PKC) inhibitor GF109203X, nifedipine or the store-operated Ca(2+ )entry inhibitors (econazole or SKF96365) inhibited 2,5-dimethylphenol-induced Ca(2+ )signal in Ca(2+)-containing medium by ∼30%. Treatment with the endoplasmic reticulum Ca(2+ )pump inhibitor thapsigargin in Ca(2+)-free medium abolished 2,5-dimethylphenol-induced [Ca(2+)]i rises. Conversely, treatment with 2,5-dimethylphenol abolished thapsigargin-induced [Ca(2+)]i rises. Inhibition of phospholipase C (PLC) with U73122 reduced 2,5-dimethylphenol-evoked [Ca(2+)]i rises by ∼80%. 2,5-Dimethylphenol killed cells at concentrations of 350-1000 μM in a concentration-dependent fashion. Chelation of cytosolic Ca(2+ )with 1,2-bis(2-aminophenoxy)ethane-N, N, N', N'-tetraacetic acid/AM (BAPTA/AM) did not prevent 2,5-dimethylphenol's cytotoxicity. Together, in PC3 cells, 2,5-dimethylphenol induced [Ca(2+)]i rises that involved Ca(2+ )entry through PKC-regulated store-operated Ca(2+ )channels and PLC-dependent Ca(2+ )release from the endoplasmic reticulum. 2,5-Dimethylphenol induced cytotoxicity in a Ca(2+)-independent manner.

The free energy cost of accurate biochemical oscillations

Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study three different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. In all the systems studied, we find that the phase diffusion constant depends on the free energy dissipation per period following the same inverse relation parameterized by system specific constants. This relationship and its range of validity are shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this general relationship and testable predictions are also presented.

Robust concentration and frequency control in oscillatory homeostats

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

Mathematical modeling of calcium waves induced by mechanical stimulation in keratinocytes

Recent studies have shown that the behavior of calcium in the epidermis is closely related to the conditions of the skin, especially the differentiation of the epidermal keratinocytes and the permeability barrier function, and therefore a correct understanding of the calcium dynamics is important in explaining epidermal homeostasis. Here we report on experimental observations of in vitro calcium waves in keratinocytes induced by mechanical stimulation, and present a mathematical model that can describe the experimentally observed wave behavior that includes finite-range wave propagation and a ring-shaped pattern. A mechanism of the ring formation hypothesized by our model may be related to similar calcium propagation patterns observed during the wound healing process in the epidermis. We discuss a possible extension of our model that may serve as a tool for investigating the mechanisms of various skin diseases.

Systematic computation of nonlinear cellular and molecular dynamics with low-power CytoMimetic circuits: a simulation study

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented.

Calcium wave propagation in networks of endothelial cells: model-based theoretical and experimental study

In this paper, we present a combined theoretical and experimental study of the propagation of calcium signals in multicellular structures composed of human endothelial cells. We consider multicellular structures composed of a single chain of cells as well as a chain of cells with a side branch, namely a “T” structure. In the experiments, we investigate the result of applying mechano-stimulation to induce signaling in the form of calcium waves along the chain and the effect of single and dual stimulation of the multicellular structure. The experimental results provide evidence of an effect of architecture on the propagation of calcium waves. Simulations based on a model of calcium-induced calcium release and cell-to-cell diffusion through gap junctions shows that the propagation of calcium waves is dependent upon the competition between intracellular calcium regulation and architecture-dependent intercellular diffusion.

Calcium wave signal has been found in a wide variety of cell types. Over the last years, a large number of calcium experiments have shown that calcium signal is not only an intracellular regulator but is also able to be transmitted to surrounding cells as intercellular signal. This paper focuses on the development of an approach with complementary integration of theoretical and experimental methods for studying the multi-level interactions in multicellular architectures and their effect on collective cell dynamic behavior. We describe new types of higher-order (across structure) behaviors arising from lower-order (within cells) phenomena, and make predictions concerning the mechanisms underlying the dynamics of multicellular biological systems. The theoretical approach describes numerically the dynamics of non-linear behavior of calcium-based signaling in model networks of cells. Microengineered, geometrically constrained networks of human umbilical vein endothelial cells (HUVEC) serve as platforms to arbitrate the theoretical predictions in terms of the effect of network topology on the spatiotemporal characteristics of emerging calcium signals.

Intercellular synchronization of diffusively coupled Ca(2+) oscillators

We examine the synchrony in the dynamics of localized [Ca(2 + )](i) oscillations among a group of cells exhibiting such complex Ca(2 + ) oscillations, connected in the form of long chain, via diffusing coupling where cytosolic Ca(2 + ) and inositol 1,4,5-triphosphate are coupling molecules. Based on our numerical results, we could able to identify three regimes, namely desynchronized, transition and synchronized regimes in the (T - k(e)) (time period-coupling constant) and (A - k(e)) (amplitude-coupling constant) spaces which are supported by phase plots (Δϕ verses time) and recurrence plots, respectively. We further show the increase of synchronization among the cells as the number of coupling molecules increases in the (T - k(e)) and (A - k(e)) spaces.

Fundamental properties of Ca2+ signals

BACKGROUND

Ca2+ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca2+ concentration. Recent investigations changed basic ideas on the dynamic character of Ca2+ signals and challenge traditional ideas on information transmission.

SCOPE OF REVIEW

We present recent findings on key characteristics of the cytosolic Ca2+ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca2+ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca2+ concentration to ideas about information transmission by stochastic signals.

MAJOR CONCLUSIONS

We demonstrate the importance of the hierarchal arrangement of Ca2+ release sites on the emergence of cellular Ca2+ spikes. Stochastic Ca2+ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties.

GENERAL SIGNIFICANCE

Robust and reliable signal transduction pathways that entail Ca2+ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2+ dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling.

A model for Ca2+ waves in networks of glial cells incorporating both intercellular and extracellular communication pathways

Networks of glial cells, and in particular astrocytes, are capable of sustaining calcium (Ca(2+)) waves both in vivo and in vitro. Experimentally, it has been shown that there are two separate modes of communication: the first by the passage of an agent (inositol 1,4,5-triphosphate, IP(3)) through gap junctions (GJs) joining cells; the second by the diffusion of an extracellular agent (adenosine triphosphate, ATP) that binds to receptors on the cells. In both cases, the outcome is the release of Ca(2+) from internal stores in the glial cells. These two modes of communication are not mutually exclusive, but probably work in conjunction in many cases. We present a model of a two-dimensional network of glial cells that incorporates regenerative intercellular (GJ) and extracellular (ATP) pathways. In the extreme cases of only one type of pathway, the results are in agreement with previous models. Adding an extracellular pathway to the GJ model increased the extent and duration of the Ca(2+) wave, but did not significantly change the speed of propagation. Conversely, adding GJs to the extracellular model did increase the wave speed. The model was modified to apply to the retina by extending it to include both astrocytes and Müller cells, with GJs the dominant coupling between astrocytes and ATP responsible for most of the remaining communication. It was found that both pathways are necessary to account for experimental results.

A mathematical model of spontaneous calcium(II) oscillations in astrocytes

Astrocytes exhibit oscillations and waves of Ca2+ ions within their cytosol and it appears that this behavior helps facilitate the astrocyte's interaction with its environment, including its neighboring neurons. Often changes in the oscillatory behavior are initiated by an external stimulus such as glutamate, recently however, it has been observed that oscillations are also initiated spontaneously. We propose here a mathematical model of how spontaneous Ca2+ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment.

Spiral calcium waves: implications for signalling

Spiral patterns of intracellular Ca2+ release demonstrate a direct relationship between increasing wavefront curvature and increasing propagation velocity. An equally important phenomenon is the annihilation of colliding Ca2+ waves, which reveals an underlying refractory period during which further Ca2+ release is temporarily inhibited. Treatment of intracellular Ca2+ release as an excitable medium accounts for both observations. This theoretical framework is analogous to the more familiar concept of electrical excitability in neuronal membranes. In this analogy, the inositol 1,4,5-trisphosphate receptor ion channel plays a role analogous to that of Na+ channels while Ca(2+)-induced Ca2+ release provides the mechanism for excitation. Furthermore, Ca(2+)-ATPases play a role similar to that of the K+ channels in neuronal excitation, that is, they return the system to rest. We demonstrated that overexpression of a sarco/endoplasmic reticulum Ca(2+)-ATPase increases the frequency of Ca2+ wave activity. More recent experiments reveal a strong dependence of the propagation velocity on wavelength as predicted by the dispersion relation of excitability. This important result accounts for an observed correlation between wave frequency and spatial dominance of Ca2+ foci and suggests a new mechanism for the encoding of signal information.

Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms

Intracellular Ca(2+) oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca(2+)-induced Ca(2+) release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca(2+) oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca(2+) spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca(2+) oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca(2+)-release channel on a unique intracellular store at high cytosolic Ca(2+) concentrations, (ii) taking into account the Ca(2+)-activated degradation of inositol 1,4,5-trisphosphate (IP(3)), or (iii) considering explicity the evolution of the Ca(2+) concentration in two different pools, one sensitive and the other one insensitive to IP(3). Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP(3) into account shows chaotic behaviour.

Cytosolic inositol 1,4,5-trisphosphate dynamics during intracellular calcium oscillations in living cells

We developed genetically encoded fluorescent inositol 1,4,5-trisphosphate (IP₃) sensors that do not severely interfere with intracellular Ca²⁺ dynamics and used them to monitor the spatiotemporal dynamics of both cytosolic IP₃ and Ca²⁺ in single HeLa cells after stimulation of exogenously expressed metabotropic glutamate receptor 5a or endogenous histamine receptors. IP₃ started to increase at a relatively constant rate before the pacemaker Ca²⁺ rise, and the subsequent abrupt Ca²⁺ rise was not accompanied by any acceleration in the rate of increase in IP₃. Cytosolic [IP₃] did not return to its basal level during the intervals between Ca²⁺ spikes, and IP₃ gradually accumulated in the cytosol with a little or no fluctuations during cytosolic Ca²⁺ oscillations. These results indicate that the Ca²⁺-induced regenerative IP₃ production is not a driving force of the upstroke of Ca²⁺ spikes and that the apparent IP₃ sensitivity for Ca²⁺ spike generation progressively decreases during Ca²⁺ oscillations.

Purinergic signalling and intercellular Ca2+ wave propagation in the organ of Corti

Extracellular ATP is a key neuromodulator of visual and auditory sensory epithelia. In the rat cochlea, pharmacological dissection indicates that ATP, acting through a highly sensitive purinergic/IP(3)-mediated signaling pathway with (little or) no involvement of ryanodine receptors, is the principal paracrine mediator implicated in the propagation of calcium waves through supporting and epithelial cells. Measurement of sensitivity to UTP and other purinergic agonists implicate P2Y(2) and P2Y(4) as the main P2Y receptor isoforms involved in these responses. Ca2+ waves, elicited under highly reproducible conditions by carefully controlling dose (1 microM) and timing of focal agonist application (0.2s), extended over radial distance greater than 160 microm from the source, identical to those activated by damaging single outer hair cells. Altogether, these results indicate that intercellular calcium waves are a robust phenomenon that confers a significant ability for cell-cell communication in the mammalian cochlea. Further ongoing research will reveal the roles that such Ca2+ waves play in the inner ear.

oscillations in a model of energy-dependent uptake by the endoplasmic reticulum

Active Ca2+ transport in living cells necessitates controlled supply of metabolic energy. Direct coupling between sarco/endoplasmic reticulum (ER) Ca2+ ATPases (SERCA) and intracellular energy-generation sites has been well established experimentally. On the basis of these experimental findings we propose a pump-driven model to investigate complex dynamic properties of a cell system. The model describes the pump process both by the Ca2+ ATPase itself and by a suitable description of the glycolysis. The associated set of differential equations shows a rich behavior, the solutions ranging from simple periodic oscillations to complex patterns such as bursting and spiking. Recent experimental results on calcium oscillations in Xenopus laevis oocytes and on dynamic patterns of intracellular Ca2+ concentrations in electrically non-excitable cells are well described by corresponding theoretical results derived within the proposed model. The simulation results are further compared to spontaneous [Ca2+] oscillations in primitive endodermal cells.

Egg activation events are regulated by the duration of a sustained [Ca2+]cyt signal in the mouse

Although the dynamics of oscillations of cytosolic Ca2+ concentration ([Ca2+]cyt) play important roles in early mammalian development, the impact of the duration when [Ca2+]cyt is elevated is not known. To determine the sensitivity of fertilization-associated responses [i.e., cortical granule exocytosis, resumption of the cell cycle, Ca2+/calmodulin-dependent protein kinase II (CaMKII) activity, recruitment of maternal mRNAs] and developmental competence of the parthenotes to the duration of a [Ca2+]cyt transient, unfertilized mouse eggs were subjected to a prolonged [Ca2+]cyt change for 15, 25, or 50 min by means of repetitive Ca2+ electropermeabilization at 2-min intervals. The initiation and completion of fertilization-associated responses are correlated with the duration of time in which the [Ca2+]cyt is elevated, with the exception that autonomous CaMKII activity is down-regulated with prolonged elevated [Ca2+]cyt. Activated eggs from 25- or 50-min treatments readily develop to the blastocyst stage with no sign of apoptosis or necrosis and some implant. Ca2+ influx into unfertilized eggs causes neither Ca2+ release from intracellular stores nor rapid removal of cytosolic Ca2+. Thus, the total Ca2+ signal input appears to be an important regulatory parameter that ensures completion of fertilization-associated events and oocytes have a surprising degree of tolerance for a prolonged change in [Ca2+]cyt.

UNLOCKING THE SECRETS OF CELL SIGNALING

My scientific life has been spent trying to understand how cells communicate with each other. This interest in cell signaling began with studies on the control of fluid secretion by an insect salivary gland, and the subsequent quest led to the discovery of inositol trisphosphate (IP3) and its role in calcium signaling, which effectively divided my scientific career into two distinct parts. The first part was primarily experimental and culminated in the discovery of IP3, which set the agenda for the second half during which I have enjoyed exploring the many functions of this remarkably versatile signaling system. It has been particularly exciting to find out how this IP3/Ca2+ signaling pathway has been adapted to control processes as diverse as fertilization, proliferation, cell contraction, secretion, and information processing in neuronal cells.

A potential role of modulating inositol 1,4,5-trisphosphate receptor desensitization and recovery rates in regulating ovulation

Regulation of the human menstrual cycle is a frequency dependent process controlled in part by the pulsatile release of gonadotropin releasing hormone (GnRH) from the hypothalamus. The binding of GnRH to gonadotroph cells in the pituitary stimulates inositol 1,4,5-trisphosphate (IP3) mediated release of calcium from the endoplasmic reticulum, resulting in calcium oscillations and the secretion of luteinizing hormone (LH). A sudden increase in serum LH concentrations known as the LH surge triggers ovulation. Here we model the intracellular calcium dynamics of gonadotroph cells by adapting the model of Li and Rinzel (J. Theor. Biol. 166 (1994) 461) to include the desensitization of IP3 receptors to IP3. Allowing the resensitization rate of these receptors to vary over the course of the cycle suffices to explain the LH surge in both the normal menstrual cycle, and in the treatment of Kallmann's syndrome (a condition where endogenous production of GnRH is absent).

Modeling the dependence of the period of intracellular Ca2+ waves on SERCA expression

Contrary to intuitive expectations, overexpression of sarco-endoplasmic reticulum (ER) Ca(2+) ATPases (SERCAs) in Xenopus oocytes leads to a decrease in the period and an increase in the amplitude of intracellular Ca(2+) waves. Here we examine these experimental findings by modeling Ca(2+) release using a modified Othmer-Tang-model. An increase in the period and a reduction in the amplitude of Ca(2+) wave activity are obtained when increases in SERCA density are simulated while keeping all other parameters of the model constant. However, Ca(2+) wave period can be reduced and the wave amplitude and velocity can be significantly increased when an increase in the luminal ER Ca(2+) concentration due to SERCA overexpression is incorporated into the model. Increased luminal Ca(2+) occurs because increased SERCA activity lowers cytosolic Ca(2+), which is partially replenished by Ca(2+) influx across the plasma membrane. These simulations are supported by experimental data demonstrating higher luminal Ca(2+) levels, decreased periods, increased amplitude, and increased velocity of Ca(2+) waves in response to increased SERCA density.

Invited review: significance of spatial and temporal heterogeneity of calcium transients in smooth muscle

The multiplicity of mechanisms involved in regulation of intracellular Ca(2+) concentration ([Ca(2+)](i)) in smooth muscle results in both intra- and intercellular heterogeneities in [Ca(2+)](i). Heterogeneity in [Ca(2+)](i) regulation is reflected by the presence of spontaneous, localized [Ca(2+)](i) transients (Ca(2+) sparks) representing Ca(2+) release through ryanodine receptor (RyR) channels. Ca(2+) sparks display variable spatial Ca(2+) distributions with every occurrence within and across cellular regions. Individual sparks are often grouped, and fusion of sparks produces large local elevations in [Ca(2+)](i) that occasionally trigger propagating [Ca(2+)](i) waves. Ca(2+) sparks may modulate membrane potential and thus smooth muscle contractility. Sparks may also be the target of other regulatory factors in smooth muscle. Agonists induce propagating [Ca(2+)](i) oscillations that originate from foci with high spark incidence and also represent Ca(2+) release through RyR channels. With increasing agonist concentration, the peak of regional [Ca(2+)](i) oscillations remains relatively constant, whereas both frequency and propagation velocity increase. In contrast, the global cellular response appears as a concentration-dependent increase in peak as well as mean cellular [Ca(2+)](i), representing a spatial and temporal integration of the oscillations. The significance of agonist-induced [Ca(2+)](i) oscillations lies in the establishment of a global [Ca(2+)](i) level for slower Ca(2+)-dependent physiological processes.

Reversible vacuolation of T-tubules in skeletal muscle: mechanisms and implications for cell biology

The majority of investigations of the transverse tubules (T-system) of skeletal muscle have been devoted to their role in excitation-contraction coupling, with particular reference to contact with the sarcoplasmic reticulum and the mechanism of Ca2- release. By contrast, this review is concerned with structural and functional aspects of the vacuolation of T-tubules. It covers experimental procedures used in reversible vacuolation induced by the efflux-influx of glycerol and other small nonelectrolytes, sugars, and ions. The characteristics of the phenomenon, associated alterations in muscle function, and the swelling of analogous structures in nonmuscle cells are considered. Possible functions of reversible vacuolation in water balance, transport, membrane repair, muscle pathology, and fatigue are considered, and the potential application of reversible vacuolation in the transfection of skeletal muscle is discussed. In relation to the possible mechanisms involved in reversible vacuolation, particular attention is given to the dynamic and structural aspects of the opening and closing of T-tubules, the origin of vacuolar membranes, and the localized character of tubular swelling.

Extracting information from cDNA arrays

High-density DNA arrays allow measurements of gene expression levels (messenger RNA abundance) for thousands of genes simultaneously. We analyze arrays with spotted cDNA used in monitoring of expression profiles. A dilution series of a mouse liver probe is deployed to quantify the reproducibility of expression measurements. Saturation effects limit the accessible signal range at high intensities. Additive noise and outshining from neighboring spots dominate at low intensities. For repeated measurements on the same filter and filter-to-filter comparisons correlation coefficients of 0.98 are found. Next we consider the clustering of gene expression time series from stimulated human fibroblasts which aims at finding co-regulated genes. We analyze how preprocessing, the distance measure, and the clustering algorithm affect the resulting clusters. Finally we discuss algorithms for the identification of transcription factor binding sites from clusters of co-regulated genes. (c) 2001 American Institute of Physics.

Robustness of the bistable behavior of a biological signaling feedback loop

Biological signaling networks comprised of cellular components including signaling proteins and small molecule messengers control the many cell function in responses to various extracellular and intracellular signals including hormone and neurotransmitter inputs, and genetic events. Many signaling pathways have motifs familiar to electronics and control theory design. Feedback loops are among the most common of these. Using experimentally derived parameters, we modeled a positive feedback loop in signaling pathways used by growth factors to trigger cell proliferation. This feedback loop is bistable under physiological conditions, although the system can move to a monostable state as well. We find that bistability persists under a wide range of regulatory conditions, even when core enzymes in the feedback loop deviate from physiological values. We did not observe any other phenomena in the core feedback loop, but the addition of a delayed inhibitory feedback was able to generate oscillations under rather extreme parameter conditions. Such oscillations may not be of physiological relevance. We propose that the kinetic properties of this feedback loop have evolved to support bistability and flexibility in going between bistable and monostable modes, while simultaneously being very refractory to oscillatory states. (c) 2001 American Institute of Physics.

Excitable calcium wave propagation in the presence of localized stores

We study the propagation of calcium waves in the presence of a discrete distribution of calcium stores. Calcium-induced calcium release coupled to diffusion can be used to produce a criterion for wave propagation across connected clusters of stores. The velocity of the resulting wave and its relationship to the frequency of the excitatory stimulus can then be described using percolation theory. Simulations show a homogeneous and a fractal regime and are in agreement with both experiments and theory.

Coupled intra- and extracellular Ca2+ dynamics in recurrent seizure-like events

We considered the evolution of Ca2+ oscillation dynamics in recurrent seizure-like events. Dynamic system behaviour was characterized in the state space reconstructed from intra- and extracellular [Ca2+] fluctuations simultaneously measured in cultured rat hippocampal slices under low-[Mg2+] conditions. When associated in the seizure-like event, these fluctuations occurred on a restricted set, the attractor, embedded in the full state space with less than five degrees of freedom. Instantaneous relative phase differences indicated field potential-driven phase jumps locked onto seizure-like events. To account for recurrent dynamics, calculations were performed on different extensions of a model for Ca2+ oscillation. These identified bidirectional, asymmetrical coupling of extracellular with intracellular (cytosolic, Ca2+ store, mitochondrial) Ca2+ dynamics as critical in its development.

Ruled by waves? Intracellular and intercellular calcium signalling

The field of calcium signalling has evolved rapidly the last 20 years. Physiologists had worked with cytosolic Ca2+ as the coupler of excitation and contraction of muscles and as a secretory signal in exocrine glands and in the synapses of the brain for several decades before the discovery of cellular calcium as a second messenger. Development of powerful techniques for measuring the concentration of cytosolic free calcium ions in cell suspensions and later in single cells and even in different cellular compartments, has resulted in an upsurge in the knowledge of the cellular machinery involved in intracellular calcium signalling. However, the focus on intracellular mechanisms might have led this field of study away from physiology. During the last few years there is an increasing evidence for an important role of calcium also as an intercellular signal. Via gap junctions calcium is able to co-ordinate cell populations and even organs like the liver. Here we will give an overview of the general mechanisms of intracellular calcium signalling, and then review the recent data on intercellular calcium signals. A functional coupling of cells in different tissues and organs by the way of calcium might be an important mechanism for controlling and synchronizing physiological responses

Impact of mitochondrial Ca2+ cycling on pattern formation and stability

Energization of mitochondria significantly alters the pattern of Ca2+ wave activity mediated by activation of the inositol (1,4,5) trisphosphate (IP3) receptor (IP3R) in Xenopus oocytes. The number of pulsatile foci is reduced and spiral Ca2+ waves are no longer observed. Rather, target patterns of Ca2+ release predominate, and when fragmented, fail to form spirals. Ca2+ wave velocity, amplitude, decay time, and periodicity are also increased. We have simulated these experimental findings by supplementing an existing mathematical model with a differential equation for mitochondrial Ca2+ uptake and release. Our calculations show that mitochondrial Ca2+ efflux plays a critical role in pattern formation by prolonging the recovery time of IP3Rs from a refractory state. We also show that under conditions of high energization of mitochondria, the Ca2+ dynamics can become bistable with a second stable stationary state of high resting Ca2+ concentration.

Spatial characteristics to calcium signalling; the calcium wave as a basic unit in plant cell calcium signalling

Many signals that modify plant cell growth and development initiate changes in cytoplasmic Ca2+. The subsequent movement of Ca2+in the cytoplasm is thought to take place via waves of free Ca2+. These waves may be initiated at defined regions of the cell and movement requires release from a reticulated endoplasmic reticulum and the vacuole. The mechanism of wave propagation is outlined and the possible basis of repetitive reticulum wave formation, Ca2+oscillations and capacitative Ca2+signalling is discussed. Evidence for the presence of Ca2+waves in plant cells is outlined, and from studies on raphides it is suggested that the capabilities for capacitative Ca2+signalling are also present. The paper finishes with an outline of the possible interrelation between Ca2+waves and organelles and describes the intercellular movement of Ca2+waves and the relevance of such information communication to plant development.

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

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

Effects on the hepatocyte [Ca2+]i oscillator of inhibition of the plasma membrane Ca2+ pump by carboxyeosin or glucagon-(19-29)

Single rat hepatocytes, microinjected with the Ca(2+)-sensitive photoprotein aequorin, respond to agonists acting through the phosphoinositide signalling pathway by the generation of oscillations in cytosolic free Ca2+ concentration ([Ca2+]i). The duration of [Ca2+]i transients generated is characteristic of the receptor species activated; the variability results in differences in the rate of fall of [Ca2+]i from its peak. It is conceivable that the plasma membrane Ca(2+)-ATPase (PM Ca2+ pump) may have an important role in the mechanism underlying agonist specificity. It has recently been shown that an esterified form of carboxyeosin, an inhibitor of the red cell PM Ca2+ pump, is suitable for use in whole cell studies. Glucagon-(19-29) (mini-glucagon) inhibits the Ca2+ pump in liver plasma membranes, mediated by Gs. We show here that carboxyeosin and mini-glucagon inhibit Ca2+ efflux from populations of intact rat hepatocytes. We show that carboxyeosin and mini-glucagon enhance the frequency of oscillations induced by Ca(2+)-mobilizing agonists in single hepatocytes, but do not affect the duration of individual transients. Furthermore, we demonstrate that inhibition of the hepatocyte PM Ca2+ pump enables the continued generation of [Ca2+]i oscillations for a prolonged period following the removal of extracellular Ca2+.

Interneuron-specific Ca2+ responses linked to metabotropic and ionotropic glutamate receptors in rat hippocampal slices

Glutamate-mediated regulation of intracellular Ca2+ levels was examined in different populations of CA1 interneurons, using confocal microscopy and the Ca2+ indicator fluo 3-AM in rat hippocampal slices. Interneurons in basal [stratum oriens/alveus (OA)] and apical [strata radiatum and lacunosum-moleculare (R/LM)] dendritic layers responded heterogeneously to glutamate. In control medium, OA interneurons responded mostly with oscillatory Ca2+ responses, which consisted of a large Ca2+ transient and successive smaller elevations. R/LM interneurons responded mostly with biphasic responses, characterized by an initial large transient and a secondary prolonged elevation. Other interneurons in both R/LM and OA responded with transient elevations in Ca2+ levels. Ionotropic glutamate receptor antagonists (+/-)2-amino-5-phosphonopentanoic acid and 6-cyano-7-nitro-quinoxaline-2,3-dione reduced peak Ca2+ responses in OA and R/LM cells, and blocked biphasic responses in R/LM interneurons. The metabotropic glutamate receptor antagonist (RS)-alpha-methyl-4-carboxyphenylglycine reduced peak Ca2+ responses only in OA interneurons, and prevented oscillatory responses. In low Ca2+ medium, peak responses were reduced in R/LM but not in OA interneurons, and oscillatory responses were absent. Combination of ionotropic and metabotropic receptor antagonists blocked all glutamate-evoked Ca2+ responses. Activation of different types of glutamate receptors may thus produce heterogeneous Ca2+ signals in subpopulations of CA1 interneurons. Ionotropic receptors may generate biphasic responses in interneurons in apical dendritic layers, whereas combined activation of metabotropic and ionotropic receptors may trigger oscillatory responses in interneurons of basal dendritic layers. These heterogeneous Ca2+ responses indicate that glutamate-mediated Ca2+ processes and second messenger systems differ in subpopulations of hippocampal interneurons and suggest possible postsynaptic functional specialization of interneurons.

[Ca2+]i oscillations and [Ca2+]i waves in rat megakaryocytes

ATP activated [Ca2+]i oscillations were measured in single rat megakaryocytes using fluorescence ratio microscopy. With increasing ATP concentration the duration of the [Ca2+]i oscillations increased, however, there was considerable variation from cell to cell in the absolute value of the peak [Ca2+]i and the frequency and duration of the oscillations. This variation depended, in part, on the level of Fura-2 loading suggesting that megakaryocytes are sensitive to buffering of [Ca2+]i by Fura-2. Agents, that increase the level of intracellular cGMP (sodium nitroprusside and 8-pCPT-cGMP) or cAMP (prostacyclin, IBMX, forskolin and 8-bromo-cAMP) inhibited [Ca2+]i oscillations. Despite the large cell to cell variation in the patterns of [Ca2+]i oscillations, reapplication of the agents that elevated cAMP or cGMP inhibited the oscillations similarly. Using video rate fluorescence ratio imaging we found that the agonist-induced [Ca2+]i oscillations were the result of a well-defined [Ca2+]i wave, which spread across the cell with an average speed of about 35 microns/s, during the rising phase of each oscillatory spike. After reaching a peak, [Ca2+]i decreased uniformly across the whole cell during the falling phase of the spike. Analysis of the temperature dependence of [Ca2+]i waves showed that the rate of [Ca2+]i decay exhibited a strong temperature dependence (Q10 approximately 4), whereas, the rate of rise exhibited a weak temperature dependence (Q10 approximately 1.3), suggesting, that the rate limiting process for [Ca2+]i wave propagation in rat megakaryocytes is the rate of [Ca2+]i diffusion.

Arachidonic acid-induced calcium signalling in human airway smooth muscle cells

The spatiotemporal distribution of Ca2+ signals evoked by arachidonic acid (AA) was investigated in human bronchial smooth muscle cells (SMC), using the single cell video imaging technique and Fura-2 as a fluorescent dye. Baseline Ca2+ levels were markedly heterogeneous in one and the same cell; the local Ca2 concentration laid between 90 +/- 11 and 215 +/- 18 nM (n = 15). AA (2 mM) induced propagating Ca2+ waves, travelling at a mean velocity of 18 +/- 3 microns/sec (n = 7). Ca2+ signals originated at discrete trigger zones, whose kinetic properties differed from those of neighbouring regions. Ca2+ in the trigger zones rose in two phases, with rates of 9.5 +/- 0.8 and 88 +/- 6 nM/sec (n = 17). A single cell frequently exhibited more than one trigger zones. In some cells, the wave did not reach all regions; such inert zones separated functionally the cell in independently active regions. Some regions presented Ca2+ signals that did not spread to the rest of the cell, forming isolated foci. The spatiotemporal variability of Ca2+ signals evoked by AA could result from the heterogeneity of Ca2+ homeostatic processes.

Modeling the interrelations between the calcium oscillations and ER membrane potential oscillations

A refined electrochemical model accounting for intracellular calcium oscillations and their interrelations with oscillations of the potential difference across the membrane of the endoplasmic reticulum (ER) or other intracellular calcium stores is established. The ATP dependent uptake of Ca2+ from the cytosol into the ER, the Ca2+ release from the ER through channels following a calcium-induced calcium release mechanism, and a potential-dependent Ca2+ leak flux out of the ER are included in the model and described by plausible rate laws. The binding of calcium to specific proteins such as calmodulin is taken into account. The quasi-electroneutrality condition allows us to express the transmembrane potential in terms of the concentrations of cytosolic calcium and free binding sites on proteins, which are the two independent variables of the model. We include monovalent ions in the model, because they make up a considerable portion in the balance of electroneutrality. As the permeability of the endoplasmic membrane for these ions is much higher than that for calcium ions, we assume the former to be in Nernst equilibrium. A stability analysis of the steady-state solutions (which are unique or multiple depending on parameter values) is carried out and the Hopf bifurcation leading from stable steady states to self-sustained oscillations is analysed with the help of appropriate mathematical techniques. The oscillations obtained by numerical integration exhibit the typical spike-like shape found in experiments and reasonable values of frequency and amplitude. The model describes the process of switching between stationary and pulsatile regimes as well as changes in oscillation frequency upon parameter changes. It turns out that calcium oscillations can arise without a permanent influx of calcium into the cell, when a calcium-buffering system such as calmodulin is included.

Ca2+ oscillations and intercellular Ca2+ waves in ATP-stimulated articular chondrocytes

Cytosolic Ca2+ oscillations are known to occur in many cell types stimulated with agonists linked to the phosphoinositide signaling pathway. Trains of repetitive short-lasting Ca2+ spikes could be induced in articular chondrocytes by extracellular ATP, an agonist potently effective in stimulating cartilage resorption. The mechanism of these Ca2+ oscillations was studied by computerized video imaging on primary cultures of articular chondrocytes. Few cycles of oscillatory activity could be evoked in the absence of extracellular Ca2+, while, for oscillations to be sustained, Ca2+ influx was required. Thapsigargin irreversibly blocked Ca2+ oscillations, thus demonstrating the crucial involvement of intracellular stores in triggering the rhythmic activity. Apart from activating intracellular Ca2+ release, extracellular ATP also induced a noncapacitive Ca2+ influx in these cells. This ATP-mediated influx modulates both the oscillation frequency and intracellular stores refilling. In monolayers of confluent cells, Ca2+ oscillations spread from cell to cell in the form of intercellular waves. Propagating waves could also be observed in the absence of extracellular Ca2+, demonstrating that Ca2+ itself is not required for signal coordination. These results demonstrate that complex spatiotemporal pathways of Ca2+ oscillations and intercellular Ca2+ waves could be activated in articular chondrocytes during degenerative diseases.

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

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

Caffeine- and histamine-induced oscillations of K(Ca) current in single smooth muscle cells of rabbit cerebral artery

In the present experiment, we characterized the intracellular Ca2+ oscillations induced by caffeine (1mM) or histamine (1-3microM) in voltage-clamped single smooth muscle cells of rabbit cerebral (basilar) artery. Superfusion of caffeine or histamine induced periodic oscillations of large whole-cell K+ current with fairly uniform amplitudes and intervals. The oscillatory K+ current was abolished by inclusion of ethylenebis(oxonitrilo)tetraacetate (EGTA, 5mM) in the pipette solution. Caffeine- and histamine-induced periodic activation of the large-conductance Ca2+-activated K+ [K(Ca)] channel was recorded in the cell-attached patch mode. These results suggest that the oscillations of K+ current are carried by the K(Ca) channel and reflect the oscillations of intracellular Ca2+ concentration ([Ca2+]i). Ryanodine (1-10microM) abolished both caffeine- and histamine-induced oscillations. Caffeine-induced oscillations were abolished by the sarcoplasmic reticulum Ca2+-adenosine 5'-triphosphatase (Ca2+-ATPase) inhibitor, cyclopiazonic acid (10microM), and a high concentration of caffeine (10mM). Inclusion of heparin (3mg/ml) in the pipette solution blocked histamine-induced oscillations, but did not block caffeine-induced oscillations. By the removal of extracellular Ca2+, but not by the addition of verapamil and Cd2+, the caffeine-induced oscillations were abolished. Increasing Ca2+ influx rate increased the frequencies of caffeine-induced oscillations. Spontaneous oscillations were also observed in cells that were not superfused with agonists, and had similar characteristics to the caffeine-induced oscillations. From the above results, it is concluded, that in smooth muscle cells of the rabbit cerebral (basilar) artery, ryanodine-sensitive Ca2+-induced Ca2+ release pools play key roles in the generation of caffeine- and histamine-induced intracellular Ca2+ oscillations.

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

[Ca2+]i oscillations have been described in a variety of cells. This study focuses on caffeine-induced [Ca2+]i oscillations in sympathetic neurons. Previous work has shown that these oscillations require Ca2+ entry from the extracellular medium and Ca(2+)-induced Ca2+ release from a caffeine- and ryanodine-sensitive store. The aim of the study was to understand the mechanism responsible for the oscillations. As a starting point, [Ca2+]i relaxations were examined after membrane depolarization and exposure to caffeine. For both stimuli, post-stimulus relaxations could be described by the sum of two decaying exponential functions, consistent with a one-pool system in which Ca2+ transport between compartments is regulated by linear Ca2+ pumps and leaks. After modifying the store to include a [Ca2+]i-sensitive leak, the model also exhibits oscillations such as those observed experimentally. The model was tested by comparing measured and predicted net Ca2+ fluxes during the oscillatory cycle. Three independent fluxes were measured, describing the rates of 1) Ca2+ entry across the plasma membrane, 2) Ca2+ release by the internal store, and 3) Ca2+ extrusion across the plasma membrane and uptake by the internal store. Starting with estimates of the model parameters deduced from post-stimulus relaxations and the rapid upstroke, a set of parameter values was found that provides a good description of [Ca2+]i throughout the oscillatory cycle. With the same parameter values, there was also good agreement between the measured and simulated net fluxes. Thus, a one-pool model with a single [Ca2+]i-sensitive Ca2+ permeability is adequate to account for many of the quantitative properties of steady-state [Ca2+]i oscillations in sympathetic neurons. Inactivation of the intracellular Ca2+ permeability, cooperative nonlinear Ca2+ uptake and extrusion mechanisms, and functional links between plasma membrane Ca2+ transport and the internal store are not required.

Chaos in intracellular Ca2+ oscillations in a new model for non-excitable cells

A new model for intracellular Ca2+ oscillations is presented. The new model reinterprets two previous models, the ICC and CICR mechanisms, and incorporates the bell-shaped dependence of Ca2+ release on cytosolic [Ca2+]. Complex oscillations and chaos are found with this new model, confirming experimental observations of complex oscillations. A rich bifurcation sequence is found for the model as the stimulation due to agonist (R) is varied, including a period doubling route to chaos and a period-adding sequence of mixed-mode states.

Thapsigargin induces cytoplasmic free Ca2+ oscillations in mouse oocytes

The mechanisms of calcium signalling in mammalian oocytes during maturation and fertilization are controversial. In this study we measured intracellular free Ca2+ concentrations ([Ca2+]i) with the photoprotein aequorin microinjected into immature mouse oocytes. Immature mouse oocytes typically produced [Ca2+]i responses to muscarinic acetylcholine (ACh) stimulation with two types of component. The first component consisted of a broad transient rise in [Ca2+]i lasting about 1 min. The second component consisted of pulsatile oscillations which could occur before, during or after the broad transient, but typically occurred on the rising phase of the broad transient, with a duration of about 5 s. Removal of external Ca2+ ([Ca2+]o) abolished the Ca2+ responses to ACh. Exposure of oocytes to the specific microsomal Ca(2+)-ATPase inhibitors thapsigargin (TG) and cyclopiazonic acid unexpectedly produced sustained oscillations in [Ca2+]i which were sensitive to the concentration of Ca2+ in the external milieu. The frequency of these oscillations was slow, and ceased, sometimes after several cycles, when Ca2+o was removed. Raised [Ca2+]o significantly increased the frequency in cells oscillating to TG and stimulated nonoscillating cells to begin oscillating. The majority of responsive oocytes which did not produce oscillations to ACh alone (70%), did so after TG treatment. Detailed data analysis indicated that these oscillations were identical to those generated by TG alone, with a similar sensitivity to changes in [Ca2+]o. Exposure of oocytes to ryanodine did not inhibit oscillatory behaviour. These results suggest that immature mouse oocytes possess a store which is insensitive to both TG and ryanodine and is capable of supporting [Ca2+]i oscillations.

PDGF-BB triggered cytoplasmic calcium responses in cells with endogenous or stably transfected PDGF beta-receptors

Platelet-derived growth factor-BB (PDGF-BB) triggered signal transduction was investigated in human foreskin fibroblasts with endogenous PDGF beta-receptors, and porcine aortic endothelial (PAE) cells with stably transfected PDGF beta-receptors. Immunoprecipitation and immunoblotting showed that PDGF induced dose-dependent autophosphorylation of PDGF beta-receptor, and the PLC-gamma associates with autophosphorylated PDGF beta-receptors and becomes phosphorylated. Activation of PLC-gamma is known to induce fluctuations of the concentration of cytoplasmic calcium ([Ca2+]i). Microfluorometry and digital imaging were employed for measurements of the concentration of [Ca2+]i. In both cell types the growth factor induced four types of [Ca2+]i responses; no rise, a small and sluggish monophasic rise, a biphasic rise with an initial transient peak followed by a sustain elevation, and finally regular oscillations. The frequencies and amplitudes of the oscillatory responses were independent of agonist concentration after stimulation with PDGF-BB. Latency, the period from application of stimulus to the first [Ca2+]i peak, was reduced at higher concentrations of agonist. Also, the proportion of responding cells increased with higher concentrations of ligand. Oscillations of [Ca2+]i were elicited at submaximal concentrations of agonist. In PAE cells PDGF-BB triggered a single [Ca2+]i peak in absence of external Ca2+. Ligand-induced oscillations and sustained increases of [Ca2+]i were counteracted by the inorganic Ca2+ channel blocker Ce3+. These results show that similar types of [Ca2+]i responses occur in different cell types independently of whether the PDGF beta-receptors are expressed endogeneously or after transfection. Potentially, the different [Ca2+]i responses have distinct physiological consequences.