Classes and mechanisms of calcium waves

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.

Live-cell imaging of rapid calcium dynamics using fluorescent, genetically-encoded GCaMP probes with Aspergillus fumigatus

Calcium signalling plays a fundamental role in fungal intracellular signalling. Previous approaches (fluorescent dyes, bioluminescent aequorin, genetically encoded cameleon probes) with imaging rapid subcellular changes in cytosolic free calcium ([Ca²⁺]_c) in fungal cells have produced inconsistent results. Recent data obtained with new fluorescent, genetically encoded GCaMP probes, that are very bright, have resolved this problem. Here, exposing conidia or conidial germlings to high external Ca²⁺, as an example of an external stressor, induced very dramatic, rapid and dynamic [Ca²⁺]_c changes with localized [Ca²⁺]_c transients and waves. Considerable heterogeneity in the timing of Ca²⁺ responses of different spores/germlings within the cell population was observed.

Optimal pulse length of insonification for Piezo1 activation and intracellular calcium response

Ultrasound (US) neuromodulation, especially sonogenetics, has been demonstrated with potential applications in noninvasive and targeted treatment of various neurological disorders. Despite the growing interest, the mechanism for US neuromodulation remains elusive, and the optimal condition for eliciting a neural response with minimal adverse effect has not been identified. Here, we investigate the Piezo1 activation and intracellular calcium response elicited by acoustical streaming induced shear stress under various US exposure conditions. We find that Piezo1 activation and resultant intracellular calcium response depend critically on shear stress amplitude and pulse length of the stimulation. Under the same insonification acoustic energy, we further identify an optical pulse length that leads to maximum cell deformation, Piezo1 activation, and calcium response with minimal injury, confirmed by numerical modeling of Piezo1 channel gating dynamics. Our results provide insight into the mechanism of ultrasonic activation of Piezo1 and highlight the importance of optimizing US exposure conditions in sonogenetics applications.

The role of the cytoskeleton in germ plasm aggregation and compaction in the zebrafish embryo

The transmission of genetic information from one generation to another is crucial for survival of animal species. This is accomplished by the induction of primordial germ cells (PGCs) that will eventually establish the germline. In some animals the germline is induced by signals in gastrula, whereas in others it is specified by inheritance of maternal determinants, known as germ plasm. In zebrafish, aggregation and compaction of maternally derived germ plasm during the first several embryonic cell cycles is essential for generation of PGCs. These processes are controlled by cellular functions associated with the cellular division apparatus. Ribonucleoparticles containing germ plasm components are bound to both the ends of astral microtubules and a dynamic F-actin network through a mechanism integrated with that which drives the cell division program. In this chapter we discuss the role that modifications of the cell division apparatus, including the cytoskeleton and cytoskeleton-associated proteins, play in the regulation of zebrafish germ plasm assembly.

Cytoplasmic Calcium Buffering: An Integrative Crosstalk

Calcium (Ca²⁺) buffering is part of an integrative crosstalk between different mechanisms and elements involved in the control of free Ca²⁺ ions persistence in the cytoplasm and hence, in the Ca²⁺-dependence of many intracellular processes. Alterations of Ca²⁺ homeostasis and signaling from systemic to subcellular levels also play a pivotal role in the pathogenesis of many diseases.Compared with Ca²⁺ sequestration towards intracellular Ca²⁺ stores, Ca²⁺ buffering is a rapid process occurring in a subsecond scale. Any molecule (or binding site) with the ability to bind Ca²⁺ ions could be considered, at least in principle, as a buffer. However, the term Ca²⁺ buffer is applied only to a small subset of Ca²⁺ binding proteins containing acidic side-chain residues.Ca²⁺ buffering in the cytoplasm mainly relies on mobile and immobile or fixed buffers controlling the diffusion of free Ca²⁺ ions inside the cytosol both temporally and spatially. Mobility of buffers depends on their molecular weight, but other parameters as their concentration, affinity for Ca²⁺ or Ca²⁺ binding and dissociation kinetics next to their diffusional mobility also contribute to make Ca²⁺ signaling one of the most complex signaling activities of the cell.The crosstalk between all the elements involved in the intracellular Ca²⁺ dynamics is a process of extreme complexity due to the diversity of structural and molecular elements involved but permit a highly regulated spatiotemporal control of the signal mediated by Ca²⁺ ions. The basis of modeling tools to study Ca²⁺ dynamics are also presented.

Extracellular histones induce calcium signals in the endothelium of resistance-sized mesenteric arteries and cause loss of endothelium-dependent dilation

Histone proteins are elevated in the circulation after traumatic injury owing to cellular lysis and release from neutrophils. Elevated circulating histones in trauma contribute to coagulopathy and mortality through a mechanism suspected to involve endothelial cell (EC) dysfunction. However, the functional consequences of histone exposure on intact blood vessels are unknown. Here, we sought to understand the effects of clinically relevant concentrations of histones on the endothelium in intact, resistance-sized, mesenteric arteries (MAs). EC Ca2+ was measured with high spatial and temporal resolution in MAs from mice selectively expressing the EC-specific, genetically encoded ratiometric Ca2+ indicator, Cx40-GCaMP-GR, and vessel diameter was measured by edge detection. Application of purified histone protein directly to the endothelium of en face mouse and human MA preparations produced large Ca2+ signals that spread within and between ECs. Surprisingly, luminal application of histones had no effect on the diameter of pressurized arteries. Instead, after prolonged exposure (30 min), it reduced dilations to endothelium-dependent vasodilators and ultimately caused death of ~25% of ECs, as evidenced by markedly elevated cytosolic Ca2+ levels (793 ± 75 nM) and uptake of propidium iodide. Removal of extracellular Ca2+ but not depletion of intracellular Ca2+ stores prevented histone-induced Ca2+ signals. Histone-induced signals were not suppressed by transient receptor potential vanilloid 4 (TRPV4) channel inhibition (100 nM GSK2193874) or genetic ablation of TRPV4 channels or Toll-like receptor receptors. These data demonstrate that histones are robust activators of noncanonical EC Ca2+ signaling, which cause vascular dysfunction through loss of endothelium-dependent dilation in resistance-sized MAs. NEW & NOTEWORTHY We describe the first use of the endothelial cell (EC)-specific, ratiometric, genetically encoded Ca2+ indicator, Cx40-GCaMP-GR, to study the effect of histone proteins on EC Ca2+ signaling. We found that histones induce an influx of Ca2+ in ECs that does not cause vasodilation but instead causes Ca2+ overload, EC death, and vascular dysfunction in the form of lost endothelium-dependent dilation.

Integration of intracellular signaling: Biological analogues of wires, processors and memories organized by a centrosome 3D reference system

BACKGROUND

Myriads of signaling pathways in a single cell function to achieve the highest spatio-temporal integration. Data are accumulating on the role of electromechanical soliton-like waves in signal transduction processes. Theoretical studies strongly suggest feasibility of both classical and quantum computing involving microtubules.

AIM

A theoretical study of the role of the complex composed of the plasma membrane and the microtubule-based cytoskeleton as a system that transmits, stores and processes information.

METHODS

Theoretical analysis presented here refers to (i) the Penrose-Hameroff theory of consciousness (Orchestrated Objective Reduction; Orch OR), (ii) the description of the centrosome as a reference system for construction of the 3D map of the cell proposed by Regolini, (iii) the Heimburg-Jackson model of the nerve pulse propagation along axons' lipid bilayer as soliton-like electro-mechanical waves.

RESULTS AND CONCLUSION

The ideas presented in this paper provide a qualitative model for the decision-making processes in a living cell undergoing a differentiation process.

OUTLOOK

This paper paves the way for the real-time live-cell observation of information processing by microtubule-based cytoskeleton and cell fate decision making.

Slow calcium waves mediate furrow microtubule reorganization and germ plasm compaction in the early zebrafish embryo

Zebrafish germ plasm ribonucleoparticles (RNPs) become recruited to furrows of early zebrafish embryos through their association with astral microtubules ends. During the initiation of cytokinesis, microtubules are remodeled into a furrow microtubule array (FMA), which is thought to be analogous to the mammalian midbody involved in membrane abscission. During furrow maturation, RNPs and FMA tubules transition from their original distribution along the furrow to enrichments at the furrow distal ends, which facilitates germ plasm mass compaction. We show that nebel mutants exhibit reduced furrow-associated slow calcium waves (SCWs), caused at least in part by defective enrichment of calcium stores. RNP and FMA distal enrichment mirrors the medial-to-distal polarity of SCWs, and inhibition of calcium release or downstream mediators such as Calmodulin affects RNP and FMA distal enrichment. Blastomeres with reduced or lacking SCWs, such as early blastomeres in nebel mutants and wild-type blastomeres at later stages, exhibit medially bundling microtubules similar to midbodies in other cell types. Our data indicate that SCWs provide medial-to-distal directionality along the furrow to facilitate germ plasm RNP enrichment at the furrow ends.

Dynamics and mechanisms of intracellular calcium waves elicited by tandem bubble-induced jetting flow

One of the earliest events in cellular mechanotransduction is often an increase in intracellular calcium concentration associated with intracellular calcium waves (ICWs) in various physiologic or pathophysiologic processes. Although cavitation-induced calcium responses are believed to be important for modulating downstream bioeffects such as cell injury and mechanotransduction in ultrasound therapy, the fundamental mechanisms of these responses have not been elucidated. In this study, we investigated mechanistically the ICWs elicited in single HeLa cells by the tandem bubble-induced jetting flow in a microfluidic system. We identified two distinct (fast and slow) types of ICWs at varying degrees of flow shear stress-induced membrane deformation, as determined by different bubble standoff distances. We showed that ICWs were initiated by an extracellular calcium influx across the cell membrane nearest to the jetting flow, either primarily through poration sites for fast ICWs or opening of mechanosensitive ion channels for slow ICWs, which then propagated in the cytosol via a reaction-diffusion process from the endoplasmic reticulum. The speed of ICW (CICW ) was found to correlate strongly with the severity of cell injury, with CICW in the range of 33 μm/s to 93 μm/s for fast ICWs and 1.4 μm/s to 12 μm/s for slow ICWs. Finally, we demonstrated that micrometer-sized beads attached to the cell membrane integrin could trigger ICWs under mild cavitation conditions without collateral injury. The relation between the characteristics of ICW and cell injury, and potential strategies to mitigate cavitation-induced injury while evoking an intracellular calcium response, may be particularly useful for exploiting ultrasound-stimulated mechanotransduction applications in the future.

Fertilization in Starfish and Sea Urchin: Roles of Actin

Marine animals relying on "external fertilization" provide advantageous opportunities to study the mechanisms of gamete activation and fusion, as well as the subsequent embryonic development. Owing to the large number of eggs that are easily available and handled, starfish and sea urchins have been chosen as favorable animal models in this line of research for over 150 years. Indeed, much of our knowledge on fertilization came from studies in the echinoderms. Fertilization involves mutual stimulation between eggs and sperm, which leads to morphological, biochemical, and physiological changes on both sides to ensure successful gamete fusion. In this chapter, we review the roles of actin in the fertilization of starfish and sea urchin eggs. As fertilization is essentially an event that takes place on the egg surface, it has been predicted that suboolemmal actin filaments would make significant contributions to sperm entry. A growing body of evidence from starfish and sea urchin eggs suggests that the prompt reorganization of the actin pools around the time of fertilization plays crucial regulatory roles not only in guiding sperm entry but also in modulating intracellular Ca²⁺ signaling and egg activation.

Calcium spikes, waves and oscillations in a large, patterned epithelial tissue

While calcium signaling in excitable cells, such as muscle or neurons, is extensively characterized, calcium signaling in epithelial tissues is little understood. Specifically, the range of intercellular calcium signaling patterns elicited by tightly coupled epithelial cells and their function in the regulation of epithelial characteristics are little explored. We found that in Drosophila imaginal discs, a widely studied epithelial model organ, complex spatiotemporal calcium dynamics occur. We describe patterns that include intercellular waves traversing large tissue domains in striking oscillatory patterns as well as spikes confined to local domains of neighboring cells. The spatiotemporal characteristics of intercellular waves and oscillations arise as emergent properties of calcium mobilization within a sheet of gap-junction coupled cells and are influenced by cell size and environmental history. While the in vivo function of spikes, waves and oscillations requires further characterization, our genetic experiments suggest that core calcium signaling components guide actomyosin organization. Our study thus suggests a possible role for calcium signaling in epithelia but importantly, introduces a model epithelium enabling the dissection of cellular mechanisms supporting the initiation, transmission and regeneration of long-range intercellular calcium waves and the emergence of oscillations in a highly coupled multicellular sheet.

Intercellular ultrafast Ca(2+) wave in vascular smooth muscle cells: numerical and experimental study

Vascular smooth muscle cells exhibit intercellular Ca²⁺ waves in response to local mechanical or KCl stimulation. Recently, a new type of intercellular Ca²⁺ wave was observed in vitro in a linear arrangement of smooth muscle cells. The intercellular wave was denominated ultrafast Ca²⁺ wave and it was suggested to be the result of the interplay between membrane potential and Ca²⁺ dynamics which depended on influx of extracellular Ca²⁺, cell membrane depolarization and its intercel- lular propagation. In the present study we measured experimentally the conduction velocity of the membrane depolarization and performed simulations of the ultrafast Ca²⁺ wave along coupled smooth muscle cells. Numerical results reproduced a wide spectrum of experimental observations, including Ca²⁺ wave velocity, electrotonic membrane depolarization along the network, effects of inhibitors and independence of the Ca²⁺ wave speed on the intracellular stores. The numerical data also provided new physiological insights suggesting ranges of crucial model parameters that may be altered experimentally and that could significantly affect wave kinetics allowing the modulation of the wave characteristics experimentally. Numerical and experimental results supported the hypothesis that the propagation of membrane depolarization acts as an intercellular messenger mediating intercellular ultrafast Ca²⁺ waves in smooth muscle cells.

The cell's self-generated "electrome": The biophysical essence of the immaterial dimension of Life?

In the classical “mind-body” wording, “body” is usually associated with the “mass aspect” of living entities and “mind” with the “immaterial” one. Thoughts, consciousness and soul are classified as immaterial. A most challenging question emerges: Can something that is truly immaterial, thus that in the wording of physics has no mass, exist at all? Many will answer: “No, impossible.” My answer is that it is very well possible, that no esoteric mechanisms need to be invoked, but that this possibility is inherent to 2 well established but undervalued physiological mechanisms. The first one is electrical in nature. In analogy with “genome,” “proteome” etc. “electrome” (a novel term) stands for the totality of all ionic currents of any living entity, from the cellular to the organismal level. Cellular electricity is truly vital. Death of any cell ensues at the very moment that it irreversibly (excluding regeneration) loses its ability to realize its electrical dimension. The second mechanism involves communication activity that is invariably executed by sender-receiver entities that incessantly handle information. Information itself is immaterial (= no mass). Both mechanisms are instrumental to the functioning of all cells, in particular to their still enigmatic cognitive memory system. Ionic/electrical currents associated with the cytoskeleton likely play a key role but have been largely overlooked. This paper aims at initiating a discussion platform from which students with different backgrounds but all interested in the immaterial dimension of life could engage in elaborating an integrating vocabulary and in initiating experimental approaches.

ATP as a Messenger in Astrocyte-Neuronal Communication

Astrocytes are activated during both excitatory and inhibitory synaptic transmission and respond with intracellular Ca2+i elevations. Ca2+i oscillations and waves in astrocytes now appear to represent the glial arm of a dynamic neuronal-glial signaling process. Advances within the last year have shown that stimuli that elevate Ca2+i in astrocytes have the potential to modulate synaptic function. Recent studies have shown that astrocytic calcium waves, initially believed to depend on the integrity of functional gap junction channels for the passage of intercellular signals, are actually mediated by release of ATP and subsequent activation of purinergic receptors on neighboring cells. ATP release is in turn regulated by the expression of gap junction proteins, establishing a novel dimension between gap junctions and extracellular-mediated signaling events. The role of ATP and its breakdown product, adenosine, on synaptic transmission are discussed.

Initiation of metamorphosis and control of ecdysteroid biosynthesis in insects: The interplay of absence of Juvenile hormone, PTTH, and Ca(2+)-homeostasis

The paradigm saying that release of the brain neuropeptide big prothoracicotropic hormone (PTTH) initiates metamorphosis by activating the Torso-receptor/ERK pathway in larval prothoracic glands (PGs) is widely accepted nowadays. Upon ligand-receptor interaction Ca(2+) enters the PG cells and acts as a secondary messenger. Ecdysteroidogenesis results, later followed by apoptosis. Yet, some data do not fit in this model. In some species decapitated animals can still molt, even repeatedly, and metamorphose. PTTH does not universally occur in all insect species. PGs may also have other functions; PGs as counterpart of the vertebrate thymus? There are also small PTTHs. Finally, PTTH remains abundantly present in adults and plays a role in control of ecdysteroidogenesis (=sex steroid production) in gonads. This is currently documented only in males. This urges a rethinking of the PTTH-PG paradigm. The key question is: Why does PTTH-induced Ca(2+) entry only result in ecdysteroidogenesis and apoptosis in specific cells/tissues, namely the PGs and gonads? Indeed, numerous other neuropeptides also use Ca(2+) as secondary messenger. The recent rediscovery that in both invertebrates and vertebrates at least some isoforms of Ca(2+)-ATPase need the presence of an endogenous farnesol/juvenile hormone(JH)-like sesquiterpenoid for keeping cytosolic [Ca(2+)]i below the limit of apoptosis-induction, triggered the idea that it is not primarily PTTH, but rather the drop to zero of the JH titer that acts as the primordial initiator of metamorphosis by increasing [Ca(2+)]i. PTTH likely potentiates this effect but only in cells expressing Torso. PTTH: an evolutionarily ancient gonadotropin?

The essence of female-male physiological dimorphism: differential Ca2+-homeostasis enabled by the interplay between farnesol-like endogenous sesquiterpenoids and sex-steroids? The Calcigender paradigm

Ca(2+) is the most omnipresent pollutant on earth, in higher concentrations a real threat to all living cells. When [Ca(2+)]i rises above 100 nM (=resting level), excess Ca(2+) needs to be confined in the SER and mitochondria, or extruded by the different Ca(2+)-ATPases. The evolutionary origin of eggs and sperm cells has a crucial, yet often overlooked link with Ca(2+)-homeostasis. Because there is no goal whatsoever in evolution, gametes did neither originate "with the purpose" of generating a progeny nor of increasing fitness by introducing meiosis. The explanation may simply be that females "invented the trick" to extrude eggs from their body as an escape strategy for getting rid of toxic excess Ca(2+) resulting from a sex-hormone driven increased influx into particular cells and tissues. The production of Ca(2+)-rich milk, seminal fluid in males and all secreted proteins by eukaryotic cells may be similarly explained. This view necessitates an upgrade of the role of the RER-Golgi system in extruding Ca(2+). In the context of insect metamorphosis, it has recently been (re)discovered that (some isoforms of) Ca(2+)-ATPases act as membrane receptors for some types of lipophilic ligands, in particular for endogenous farnesol-like sesquiterpenoids (FLS) and, perhaps, for some steroid hormones as well. A novel paradigm, tentatively named "Calcigender" emerges. Its essence is: gender-specific physiotypes ensue from differential Ca(2+)-homeostasis enabled by genetic differences, farnesol/FLS and sex hormones. Apparently the body of reproducing females gets temporarily more poisoned by Ca(2+) than the male one, a selective benefit rather than a disadvantage.

Basis for a neuronal version of Grover's quantum algorithm

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N^1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca²⁺ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca²⁺-induced Ca²⁺ release and the search (or signaling) velocity of Ca²⁺ wave propagation. As chemical processes, such as the duration of Ca²⁺ mobilization, become rate-limiting over interstore distances, Ca²⁺ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca²⁺ diffusion coefficient, D^1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca²⁺ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.

Calcium signaling in extraembryonic domains during early teleost development

It is becoming recognized that the extraembryonic domains of developing vertebrates, that is, those that make no cellular contribution to the embryo proper, act as important signaling centers that induce and pattern the germ layers and help establish the key embryonic axes. In the embryos of teleost fish, in particular, significant progress has been made in understanding how signaling activity in extraembryonic domains, such as the enveloping layer, the yolk syncytial layer, and the yolk cell, might help regulate development via a combination of inductive interactions, cellular dynamics, and localized gene expression. Ca(2+) signaling in a variety of forms that include propagating waves and standing gradients is a feature found in all three teleostean extraembryonic domains. This leads us to propose that in addition to their other well-characterized signaling activities, extraembryonic domains are well suited (due to their relative stability and continuity) to act as Ca(2+) signaling centers and conduits.

The essence of insect metamorphosis and aging: electrical rewiring of cells driven by the principles of juvenile hormone-dependent Ca(2+)-homeostasis

In holometabolous insects the fall to zero of the titer of Juvenile Hormone ends its still poorly understood "status quo" mode of action in larvae. Concurrently it initiates metamorphosis of which the programmed cell death of all internal tissues that actively secrete proteins, such as the fat body, midgut, salivary glands, prothoracic glands, etc. is the most drastic aspect. These tissues have a very well developed rough endoplasmic reticulum, a known storage site of intracellular Ca(2+). A persistent high [Ca(2+)]i is toxic, lethal and causal to apoptosis. Metamorphosis becomes a logical phenomenon if analyzed from: (1) the causal link between calcium toxicity and apoptosis; (2) the largely overlooked fact that at least some isoforms of Ca(2+)-ATPases have a binding site for farnesol-like endogenous sesquiterpenoids (FRS). The Ca(2+)-ATPase blocker thapsigargin, like JH a sesquiterpenoid derivative, illustrates how absence of JH might work. The Ca(2+)-homeostasis system is concurrently extremely well conserved in evolution and highly variable, enabling tissue-, developmental-, and species specificity. As long as JH succeeds in keeping [Ca(2+)]i low by keeping the Ca(2+)-ATPases pumping, it acts as "the status quo" hormone. When it disappears, its various inhibitory effects are lifted. The electrical wiring system of cells, in particular in the regenerating tissues, is subject to change during metamorphosis. The possibility is discussed that in vertebrates an endogenous farnesol-like sesquiterpenoid, probably farnesol itself, acts as a functional, but hitherto completely overlooked Juvenile anti-aging "Inbrome", a novel concept in signaling.

Ultrafast Ca2+ wave in cultured vascular smooth muscle cells aligned on a micropatterned surface

Communication between vascular smooth muscle cells (SMCs) allows control of their contraction and so regulation of blood flow. The contractile state of SMCs is regulated by cytosolic Ca2+ concentration ([Ca2+]i) which propagates as Ca2+ waves over a significant distance along the vessel. We have characterized an intercellular ultrafast Ca2+ wave observed in cultured A7r5 cell line and in primary cultured SMCs (pSMCs) from rat mesenteric arteries. This wave, induced by local mechanical or local KCl stimulation, had a velocity around 15 mm/s. Combining of precise alignment of cells with fast Ca2+ imaging and intracellular membrane potential recording, allowed us to analyze rapid [Ca2+]i dynamics and membrane potential events along the network of cells. The rate of [Ca2+]i increase along the network decreased with distance from the stimulation site. Gap junctions or voltage-operated Ca2+ channels (VOCCs) inhibition suppressed the ultrafast Ca2+ wave. Mechanical stimulation induced a membrane depolarization that propagated and that decayed exponentially with distance. Our results demonstrate that an electrotonic spread of membrane depolarization drives a rapid Ca2+ entry from the external medium through VOCCs, modeled as an ultrafast Ca2+ wave. This wave may trigger and drive slower Ca2+ waves observed ex vivo and in vivo.

Characterization of Ca(2+) signaling in the external yolk syncytial layer during the late blastula and early gastrula periods of zebrafish development

Preferential loading of the complementary bioluminescent (f-aequorin) and fluorescent (Calcium Green-1 dextran) Ca(2+) reporters into the yolk syncytial layer (YSL) of zebrafish embryos, revealed the generation of stochastic patterns of fast, short-range, and slow, long-range Ca(2+) waves that propagate exclusively through the external YSL (E-YSL). Starting abruptly just after doming (~4.5h post-fertilization: hpf), and ending at the shield stage (~6.0hpf) these distinct classes of waves propagated at mean velocities of ~50 and ~4μm/s, respectively. Although the number and pattern of these waves varied between embryos, their initiation site and arcs of propagation displayed a distinct dorsal bias, suggesting an association with the formation and maintenance of the nascent dorsal-ventral axis. Wave initiation coincided with a characteristic clustering of YSL nuclei (YSN), and their associated perinuclear ER, in the E-YSL. Furthermore, the inter-YSN distance (IND) appeared to be critical such that Ca(2+) wave propagation occurred only when this was <~8μm; an IND >~8μm was coincidental with wave termination at shield stage. Treatment with the IP3R antagonist, 2-APB, the Ca(2+) buffer, 5,5'-dibromo BAPTA, and the SERCA-pump inhibitor, thapsigargin, resulted in a significant disruption of the E-YSL Ca(2+) waves, whereas exposure to the RyR antagonists, ryanodine and dantrolene, had no significant effect. These findings led us to propose that the E-YSL Ca(2+) waves are generated mainly via Ca(2+) release from IP3Rs located in the perinuclear ER, and that the clustering of the YSN is an essential step in providing a CICR pathway required for wave propagation. This article is part of a Special Issue entitled: 12th European Symposium on Calcium.

Intracellular signaling by diffusion: can waves of hydrogen peroxide transmit intracellular information in plant cells?

Amplitude- and frequency-modulated waves of Ca(2+) ions transmit information inside cells. Reactive Oxygen Species (ROS), specifically hydrogen peroxide, have been proposed to have a similar role in plant cells. We consider the feasibility of such an intracellular communication system in view of the physical and biochemical conditions in plant cells. As model system, we use a H(2)O(2) signal originating at the plasma membrane (PM) and spreading through the cytosol. We consider two maximally simple types of signals, isolated pulses and harmonic oscillations. First we consider the basic limits on such signals as regards signal origin, frequency, amplitude, and distance. Then we establish the impact of ROS-removing enzymes on the ability of H(2)O(2) to transmit signals. Finally, we consider to what extent cytoplasmic streaming distorts signals. This modeling allows us to predict the conditions under which diffusion-mediated signaling is possible. We show that purely diffusive transmission of intracellular information by H(2)O(2) over a distance of 1 μm (typical distance between organelles, which may function as relay stations) is possible at frequencies well above 1 Hz, which is the highest frequency observed experimentally. This allows both frequency and amplitude modulation of the signal. Signaling over a distance of 10 μm (typical distance between the PM and the nucleus) may be possible, but requires high signal amplitudes or, equivalently, a very low detection threshold. Furthermore, at this longer distance a high rate of enzymatic degradation is required to make signaling at frequencies above 0.1 Hz possible. In either case, cytoplasmic streaming does not seriously disturb signals. We conclude that although purely diffusion-mediated signaling without relaying stations is theoretically possible, it is unlikely to work in practice, since it requires a much faster enzymatic degradation and a much lower cellular background concentration of H(2)O(2) than observed experimentally.

Ancient Chinese medicine and mechanistic evidence of acupuncture physiology

Acupuncture has been widely used in China for three millennia as an art of healing. Yet, its physiology is not yet understood. The current interest in acupuncture started in 1971. Soon afterward, extensive research led to the concept of neural signaling with possible involvement of opioid peptides, glutamate, adenosine and identifying responsive parts in the central nervous system. In the last decade scientists began investigating the subject with anatomical and molecular imaging. It was found that mechanical movements of the needle, ignored in the past, appear to be central to the method and intracellular calcium ions may play a pivotal role. In this review, we trace the technique of clinical treatment from the first written record about 2,200 years ago to the modern time. The ancient texts have been used to introduce the concepts of yin, yang, qi, de qi, and meridians, the traditional foundation of acupuncture. We explore the sequence of the physiological process, from the turning of the needle, the mechanical wave activation of calcium ion channel to beta-endorphin secretion. By using modern terminology to re-interpret the ancient texts, we have found that the 2nd century b.c. physiologists were meticulous investigators and their explanation fits well with the mechanistic model derived from magnetic resonance imaging (MRI) and confocal microscopy. In conclusion, the ancient model appears to have withstood the test of time surprisingly well confirming the popular axiom that the old wine is better than the new.

Overcoming macrophage-mediated axonal dieback following CNS injury

Trauma to the adult CNS initiates multiple processes including primary and secondary axotomy, inflammation, and glial scar formation that have devastating effects on neuronal regeneration. After spinal cord injury, the infiltration of phagocytic macrophages coincides with long-distance axonal retraction from the initial site of injury, a deleterious phenomenon known as axonal dieback. We have previously shown that activated macrophages directly induce long-distance retraction of dystrophic axons in an in vitro model of the glial scar. We hypothesized that treatments that are primarily thought to increase neuronal regeneration following spinal cord injury may in fact derive a portion of their beneficial effects from inhibition of macrophage-mediated axonal retraction. We analyzed the effects of protease inhibition, substrate modification, and neuronal preconditioning on macrophage-axon interactions using our established in vitro model. General inhibition of matrix metalloproteinases and specific inhibition of MMP-9 prevented macrophage-induced axonal retraction despite significant physical interactions between the two cell types, whereas inhibition of MMP-2 had no effect. Chondroitinase ABC-mediated digestion of the aggrecan substrate also prevented macrophage-induced axonal retraction in the presence of extensive macrophage-axon interactions. The use of a conditioning lesion to stimulate intrinsic neuronal growth potential in the absence of substrate modification likewise prevented macrophage-induced axonal retraction in vitro and in vivo following spinal cord injury. These data provide valuable insight into the cellular and molecular mechanisms underlying macrophage-mediated axonal retraction and demonstrate modifications that can alleviate the detrimental effects of this unfavorable phenomenon on the postlesion CNS.

Transition of spiral calcium waves between multiple stable patterns can be triggered by a single calcium spark in a fire-diffuse-fire model

Spiral patterns have been found in various nonequilibrium systems. The Ca(2+)-induced Ca(2+) release system in single cardiac cells is unique for highly discrete reaction elements, each giving rise to a Ca(2+) spark upon excitation. We imaged the spiral Ca(2+) waves in isolated cardiac cells and numerically studied the effect of system excitability on spiral patterns using a two-dimensional fire-diffuse-fire model. We found that under certain conditions, the system was able to display multiple stable patterns of spiral waves, each exhibiting different periods and distinct routines of spiral tips. Transition between these different patterns could be triggered by an internal fluctuation in the form of a single Ca(2+) spark.

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Calcium ions (Ca(2+)) are an important second messenger in eucaryotic cells. They are involved in numerous physiological processes which are triggered by calcium signals in the form of local release events, temporal oscillations, or reaction-diffusion waves. The diffusive spread of calcium signals in the cytosol is strongly affected by calcium-binding proteins (buffers). In addition, the cytosol contains a large number of inert molecules and molecular structures which make it a crowded environment. Here, we investigate the effects of such excluded volumes on calcium diffusion in the presence of different kinds of buffers. We find that the contributions in slowing down Ca(2+) diffusion coming from buffering and molecular crowding are not additive, i.e., the reduction in Ca(2+) diffusivity due to crowding and buffering together is not the sum of each single contribution. In the presence of Ca(2+) gradients and high affinity mobile buffers the effective diffusion coefficient of Ca(2+) can be reduced by up to 60% in highly crowded environments. This suggests that molecular crowding may significantly affect the shape of Ca(2+) microdomains and wave propagation in cell types with high excluded volume fractions.

Glutamate regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes

Recent years have witnessed an increasing interest in neuron-glia communication. This interest stems from the realization that glia participate in cognitive functions and information processing and are involved in many brain disorders and neurodegenerative diseases. An important process in neuron-glia communications is astrocyte encoding of synaptic information transfer-the modulation of intracellular calcium (Ca(2+)) dynamics in astrocytes in response to synaptic activity. Here, we derive and investigate a concise mathematical model for glutamate-induced astrocytic intracellular Ca(2+) dynamics that captures the essential biochemical features of the regulatory pathway of inositol 1,4,5-trisphosphate (IP(3)). Starting from the well-known two-variable (intracellular Ca(2+) and inactive IP(3) receptors) Li-Rinzel model for calcium-induced calcium release, we incorporate the regulation of IP(3) production and phosphorylation. Doing so, we extend it to a three-variable model (which we refer to as the ChI model) that could account for Ca(2+) oscillations with endogenous IP(3) metabolism. This ChI model is then further extended into the G-ChI model to include regulation of IP(3) production by external glutamate signals. Compared with previous similar models, our three-variable models include a more realistic description of IP(3) production and degradation pathways, lumping together their essential nonlinearities within a concise formulation. Using bifurcation analysis and time simulations, we demonstrate the existence of new putative dynamical features. The cross-couplings between IP(3) and Ca(2+) pathways endow the system with self-consistent oscillatory properties and favor mixed frequency-amplitude encoding modes over pure amplitude-modulation ones. These and additional results of our model are in general agreement with available experimental data and may have important implications for the role of astrocytes in the synaptic transfer of information.

Long-range axonal calcium sweep induces axon retraction

Axon guidance molecules trigger a cascade of local signal in growth cones and evoke various morphologic responses, including axon attraction, repulsion, elongation, and retraction. However, little is known about whether subcellular compartments, other than axonal growth cones, control axon outgrowth. We found that in isolated dentate granule cells, local application of glutamate to the somatodendritic areas, but not the axon itself, induced rapid axon retraction, during which a calcium wave propagated from the somata to the axon terminals. The calcium wave and axon retraction were both inhibited by blockade of voltage-sensitive calcium channels and intracellular calcium dynamics. A combination of perisomatic application of calcium ionophore and depolarizing current injection induced axonal calcium sweep and axon retraction. Thus, perisomatic environments can modulate axon behavior through long-range intracellular communication.

Calcium and signal transduction

Cell signaling is an essential process in which a variety of external signals, defined as first messengers, are translated inside the cells into specific responses, which are mediated by a less numerous group of second messengers. The exchange of signals became a necessity when the transition from monocellular to pluricellular life brought with it the division of labor among the cells of the organisms: unicellular organisms do not depend on the mutual exchange of signals, as they essentially only compete with each other for nutrients. Calcium (Ca²⁺) was selected during evolution as second messenger, because its chemistry made it a much more flexible ligand than the other abundant cations in the primordial environment (Na⁺, K⁺, Mg²⁺ ). Ca²⁺ can accept binding sites of irregular geometries and is thus ideally suited to be a carrier of biological information. The Ca²⁺ signal has properties that set it apart from those of all other biological messengers: they will be reviewed in this contribution. Among them, the ambivalent character of the Ca²⁺ signal is the most important: while essential to the viability of the cells, it can also easily become a conveyor of doom.

Calcium waves and development

Those calcium oscillations which go deep into cells take the form of 'fast' calcium waves. In fully active cells at room temperature, these move at 15-30 microns/s and are propagated by a reaction-diffusion mechanism governed by the Luther equation in which calcium ions are the only propagators and calcium-induced calcium release is the only reaction. However, they may be initiated by a second mode of Ca(2+)-induced Ca2+ release within the lumen of the endoplasmic reticulum (ER). In sea urchin fertilization, this second mode of Ca(2+)-induced Ca2+ release is in turn begun by calcium entering the sperm and thence the ER. Subsurface calcium waves include an important class of surface contraction waves which move at 0.3-3 microns/s and are called 'slow' waves. Their prototype is the 0.5 micron/s wave which accompanies and controls cytokinesis in large eggs. Slow waves may be propagated by mechanical tension rather than by diffusion. Recent work with Dictyostelium transfected with apoaequorin has provided the first views of free calcium patterns within a developing, multicellular organism. During most or all of development, those regions which will differentiate into stalk or stalk-like cells (as opposed to spores) exhibit frequent calcium pulses. These pulses are believed to be fast calcium waves and to feed back on these regions so as to favour non-spore differentiation.

Calcium signalling in cardiac muscle cells

In heart cells, several distinct kinds of transient spatial patterns of cytoplasmic calcium ion concentration ([Ca2+]i) can be observed: (1) [Ca2+]i waves, in which regions of spontaneously increased [Ca2+]i propagate at high velocity (100 microns/s) through the cell; (2) Ca2+ 'sparks', which are spontaneous, non-propagating changes in [Ca2+]i that are localized in small (approximately 2 microns) subcellular regions; and (3) evoked [Ca2+]i transients that are elicited by electrical depolarization, in association with normal excitation-contraction (E-C) coupling. In confocal [Ca2+]i images, evoked [Ca2+]i transients appear to be nearly spatially uniform throughout the cell, except during their rising phase or during small depolarizations. In contrast to [Ca2+]i waves and spontaneous Ca2+ sparks, evoked [Ca2+]i transients are triggered by L-type Ca2+ channel current and they are 'controlled', in the sense that stopping the L-type Ca2+ current stops them. Despite their different characteristics, all three types of Ca2+ transient involve Ca(2+)-induced release of Ca2+ from the sarcoplasmic reticulum. Here, we address the question of how the autocatalytic process of Ca(2+)-induced Ca2+ release, which can easily be understood to underlie spontaneous regenerative ('uncontrolled'), propagating [Ca2+]i waves, might be 'harnessed', under other circumstances, to produce controlled changes in [Ca2+]i, as during normal excitation-contraction coupling, or changes in [Ca2+]i that do not propagate. We discuss our observations of Ca2+ waves, Ca2+ sparks and normal Ca2+ transients in heart cells and review our results on the 'gain' of Ca(2+)-induced Ca2+ release. We discuss a model involving Ca2+ microdomains beneath L-type Ca2+ channels, and clusters of Ca(2+)-activated Ca2+ release channels in the sarcoplasmic reticulum which may form the basis of the answer to this question.

Calcium puffs in Xenopus oocytes

The second messenger inositol 1,4,5-trisphosphate (InsP3) functions in large part by liberating calcium ions from intracellular stores. This release process is highly non-linear and shows a regenerative characteristic that allows production of all-or-none calcium spikes which propagate as waves. However, at low concentrations of InsP3 an additional mode of calcium liberation is seen in Xenopus oocytes, transient 'puffs' of cytosolic calcium that last for a few hundred milliseconds and are restricted to within a few micrometres. Puffs are generally of similar size and the amount of calcium released (about 3 x 10(-18) mol) suggests that they arise through the concerted opening of several InsP3-gated calcium release channels. Puff sites are present at a density of about one per 30 microns 2 in the animal hemisphere of the oocyte. Each site functions autonomously, producing puffs at largely random intervals. We conclude that calcium puffs represent 'quantal' units of InsP3-evoked calcium liberation, which may result from local regenerative feedback by cytosolic calcium ions at functionally discrete release sites.

Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level

Many essential physiological processes are controlled by calcium. To ensure reliability and specificity, calcium signals are highly organized in time and space in the form of oscillations and waves. Interesting findings have been obtained at various scales, ranging from the stochastic opening of a single calcium channel to the intercellular calcium wave spreading through an entire organ. A detailed understanding of calcium dynamics thus requires a link between observations at different scales. It appears that some regulations such as calcium-induced calcium release or PLC activation by calcium, as well as the weak diffusibility of calcium ions play a role at all levels of organization in most cell types. To comprehend how calcium waves spread from one cell to another, specific gap-junctional coupling and paracrine signaling must also be taken into account. On the basis of a pluridisciplinar approach ranging from physics to physiology, a unified description of calcium dynamics is emerging, which could help understanding how such a small ion can mediate so many vital functions in living systems.

Dynamic and static calcium gradients inside large snail (Helix aspersa) neurones detected with calcium-sensitive microelectrodes

We have used quartz Ca²⁺-sensitive microelectrodes (CASMs) in large voltage-clamped snail neurones to investigate the inward spread of Ca²⁺ after a brief depolarisation. Both steady state and [Ca²⁺]_i transients changed with depth of penetration. When the CASM tip was within 20 μm of the far side of the cell the [Ca²⁺]_i transient time to peak was 4.4 ± 0.5 s, rising to 14.7 ± 0.7 s at a distance of 80 μm. We estimate that the Ca²⁺ transients travelled centripetally at an average speed of 6 μm² s⁻¹ and decreased in size by half over a distance of about 45 μm. Cyclopiazonic acid had little effect on the size and time to peak of Ca²⁺ transients but slowed their recovery significantly. This suggests that the endoplasmic reticulum curtails rather than reinforces the transients. Injecting the calcium buffer BAPTA made the Ca²⁺ transients more uniform in size and increased their times to peak and rates of recovery near the membrane. We have developed a computational model for the transients, which includes diffusion, uptake and Ca²⁺ extrusion. Good fits were obtained with a rather large apparent diffusion coefficient of about 90 ± 20 μm² s⁻¹.This may assist fast recovery by extrusion.

The asymptotic behavior of solutions of the buffered bistable system

In this paper, we study a model for calcium buffering with bistable nonlinearity. We present some results on the stability of equilibrium states and show that there exists a threshold phenomenon in our model. In comparing with the model without buffers, we see that stationary buffers cannot destroy the asymptotic stability of the associated equilibrium states and the threshold phenomenon. Moreover, we also investigate the propagation property of solutions with initial data being a disturbance of one of the stable states which is confined to a half-line. We show that the more stable state will eventually dominate the whole dynamics and that the speed of this propagation (or invading process) is positive.

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

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

A common biomechanical model for the formation of stationary cell domains and propagating waves in the developing organisms

Many important morphogenetic processes that take place in the development of an animal start from the segregation of a homogeneous layer of cells into a different number of the domains of columnar and flattened cells. In many cases, waves of cell shape transformation travel throughout embryonic tissues. A biomechanical model is presented which embraces both kinds of event. The model is based on the idea of interplay between short- and long-range factors. While the former promote the spreading of a given cell state along a cell row in the recalculation direction, long-range factors are associated with self-generated tensions which, after exceeding a certain threshold, induce active cell extension and hence the rise of tangential pressure. Different kinds of biologically realistic stationary structures, as well as various kinds of the running waves, can be modelled under different parameter values. Moreover, the current model can be coupled with the previous one (Beloussov and Grabovsky, Comput. Methods Biomech. Biomed. Eng., 6: 53-63 (2003)) permitting a common causal chain to be created, moving from the state of an initial homogeneous cell layer towards the complicated shapes of embryonic rudiments.

Long-range oscillatory Ca2+waves in rat spinal dorsal horn

Synchronous activity of large populations of neurons shapes neuronal networks during development. However, re-emergence of such activity at later stages of development could severely disrupt the orderly processing of sensory information, e.g. in the spinal dorsal horn. We used Ca2+ imaging in spinal cord slices of neonatal and young rats to assess under which conditions synchronous activity occurs in dorsal horn. No spontaneous synchronous Ca2+ transients were detected. However, increasing neuronal excitability by application of 4-aminopyridine after pretreatment of the slice with blockers of (RS)-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate, gamma-aminobutyric acid (GABA)(A) and glycine receptors evoked repetitive Ca2+ waves in dorsal horn. These waves spread mediolaterally with a speed of 1.0 +/- 0.1 mm/s and affected virtually every dorsal horn neuron. The Ca2+ waves were associated with large depolarizing shifts of the membrane potential of participating neurons and were most likely synaptically mediated because they were abolished by blockade of action potentials or N-methyl-D-aspartate (NMDA) receptors. They were most pronounced in the superficial dorsal horn and absent from the ventral horn. A significant proportion of the Ca2+ waves spread to the contralateral dorsal horn. This seemed to be enabled by disinhibition as primary afferent-induced dorsal horn excitation crossed the midline only when GABA(A) and glycine receptors were blocked. Interestingly, the Ca2+ waves occurred under conditions where AMPA/kainate receptors were blocked. Thus, superficial dorsal horn NMDA receptors are able to sustain synchronous neuronal excitation in the absence of functional AMPA/kainate receptors.

A proton-led model of fast calcium waves

Fast (10-30 microm/s) calcium waves can be propagated through all nucleated eukaryotic cells that have been tested as well as certain cell-free extracts. In a widely used model, they are propagated by a reaction-diffusion cycle in which calcium ions diffuse along the outside of endoplasmic reticula and induce their own release from calsequestrin or calreticulin molecules stored within the reticulum's lumen. Here we propose a new tandem wave model in which they are also propagated by a reaction-diffusion cycle within a reticulum's lumen. In this cycle, increases in luminal [H(+)] induce proton release from luminal calsequestrin or calreticulin. The released protons diffuse ahead to where they release more protons from these luminal storage proteins. What might be called proton induced proton release. They also raise luminal electropositivity. The resultant luminal waves are coordinated with extrareticular ones by movements of calcium and hydrogen ions through the reticular membrane. This model makes five testable predictions which include the autorelease of protons in solutions of calsequestrins or calreticulins as well as waves of increased [H(+)], of increased [Ca(2+)] and of more positive voltage within the reticula of whole cells. Moreover, under some conditions, such luminal waves should cross regions without cytosolic ones.

Disposition of calcium release units in agarose gel for an optimal propagation of Ca2+ signals

Clusters of calcium-loaded sarcoplasmic reticulum (SR) vesicles in agarose gel were previously shown to behave as an excitable medium that propagates calcium waves. In a 3D-hexagonal disposition, the distance between neighboring spheres (which may stand for SR vesicles) is constant and the relationship between distance and vesicular protein concentration is expected to be nonlinear. To obtain a distribution of SR vesicles at different protein concentrations as homogeneous as possible, liquid agarose gels were carefully stirred. Electron micrographs, however, did not confirm the expected relationship between inter-SR vesicle distance and vesicular protein concentration. Light micrographs, to the contrary, resulted in a protein concentration-dependent disposition of clusters of SR vesicles, which is described by a linear function. Stable calcium waves in agarose gel occurred at SR vesicle protein concentrations between 7 and 16 g/l. At lower protein concentrations, local calcium oscillations or abortive waves were observed. The velocities of calcium waves were optimum at approximately 12 g/l and amounted to nearly 60 microm/s. The corresponding distance of neighboring calcium release units was calculated to be approximately 4 microm. The results further show that calcium signaling in the described reaction-diffusion system is optimal in a relatively small range of diffusion lengths. A change by +/-2 microm resulted in a reduction of the propagation velocity by 40%. It would appear that 1), the distance between calcium release units (clusters of ryanodine receptors in cells) is a sensitive parameter concerning propagation of Ca2+ signals; and 2), a dysfunction of the reaction-diffusion system in living cells, however, might have a negative effect on the spreading of intracellular calcium signals, thus on the cell's function.

Intercellular calcium signalling in cultured renal epithelia: a theoretical study of synchronization mode and pacemaker activity

We investigate a two-dimensional lattice model representation of intercellular Ca2+ signalling in a population of epithelial cells coupled by gap junctions. The model is based on and compared with Ca2+ imaging data from globally bradykinin-stimulated MDCK-I (Madin-Darby canine kidney)-I cell layers. We study large-scale synchronization of relevance to our laboratory experiments. The system is found to express a wealth of dynamics, including quasiperiodic, chaotic and multiply-periodic behaviour for intermediate couplings. We take a particular interest in understanding the role of "pacemaker cells" in the synchronization process. It has been hypothesized that a few highly hormone-sensitive cells control the collective frequency of oscillation, which is close to the natural frequencies (without coupling) of these cells. The model behaviour is consistent with the conjectures of the pacemaker cell hypothesis near the critical coupling where the cells lock onto a single frequency. However, the simulations predict that the frequency in globally connected systems decreases with increasing coupling. It is found that a pacemaker is not defined by its natural frequency alone, but that other intrinsic or local factors must be considered. Inclusion of partly sensitized cells that do not oscillate autonomously in the cell layer increases the coupling necessary for global synchronization. For not excessively high coupling, these cells oscillate irregularly and with distinctive lower frequencies. In summary, the present study shows that the frequency of synchronized oscillations is not dictated by one or few fast-responding cells. The collective frequency is the result of a two-way communication between the phase-advanced pacemaker and its environment.

Sheet excitability and nonlinear wave propagation

In the Xenopus laevis oocyte, calcium ion channels are clustered in a thin shell. Motivated by this morphology, we study a general class of reaction-diffusion systems that include most of the well-known models that support wave propagation but restricting excitability to a "sheet" of codimension 1. We find waves that undergo propagation failure with increasing diffusion coefficient and a scaling regime in which the wave speed is independent of it.

Local calcium signaling in neurons

Transient rises in the cytoplasmic concentration of calcium ions serve as second messenger signals that control many neuronal functions. Selective triggering of these functions is achieved through spatial localization of calcium signals. Several qualitatively different forms of local calcium signaling can be distinguished by the location of open calcium channels as well as by the distance between these channels and the calcium binding proteins that serve as the molecular targets of calcium action. Local calcium signaling is especially prominent at presynaptic active zones and postsynaptic densities, structures that are distinguished by highly organized macromolecular arrays that yield precise spatial arrangements of calcium signaling proteins. Similar forms of local calcium signaling may be employed throughout the nervous system, though much remains to be learned about the molecular underpinnings of these events.