A quantitative model of purinergic junctional transmission of calcium waves in astrocyte networks

A model of neurovascular coupling and its application to cortical spreading depolarization

Cortical spreading depolarization (CSD) is a neuropathological condition involving propagating waves of neuronal silence, and is related to multiple diseases, such as migraine aura, traumatic brain injury (TBI), stroke, and cardiac arrest, as well as poor outcome of patients. While CSDs of different severity share similar roots on the ion exchange level, they can lead to different vascular responses (namely spreading hyperemia and spreading ischemia). In this paper, we propose a mathematical model relating neuronal activities to predict vascular changes as measured with near-infrared spectroscopy (NIRS) and fMRI recordings, and apply it to the extreme case of CSD, where sustained near-complete neuronal depolarization is seen. We utilize three serially connected models (namely, ion exchange, neurovascular coupling, and hemodynamic model) which are described by differential equations. Propagating waves of ion concentrations, as well as the associated vasodynamics and hemodynamics, are simulated by solving these equations. Our proposed model predicts vasodynamics and hemodynamics that agree both qualitatively and quantitatively with experimental literature. Mathematical modeling and simulation offer a powerful tool to help understand the underlying mechanisms of CSD and help interpret the data. In addition, it helps develop novel monitoring techniques prior to data collection. Our simulated results strongly suggest that fMRI is unable to reliably distinguish between spreading hyperemia and spreading ischemia, while NIRS signals are substantially distinct in the two cases.

Analysis of Network Models with Neuron-Astrocyte Interactions

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula: see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula: see text] concentrations, and the Ca[Formula: see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula: see text] in the ER, variation of cytoplasmic Ca[Formula: see text] transient peak in ECs, the resting cytoplasmic Ca[Formula: see text] concentration, the effect of removing ATP from the plasma on Ca[Formula: see text] homeostasis, and the saturation of cytoplasmic Ca[Formula: see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula: see text] kinetics.

Amyloid pathology disrupts gliotransmitter release in astrocytes

Accumulation of amyloid-beta (Aβ) is associated with synaptic dysfunction and destabilization of astrocytic calcium homeostasis. A growing body of evidence support astrocytes as active modulators of synaptic transmission via calcium-mediated gliotransmission. However, the details of mechanisms linking Aβ signaling, astrocytic calcium dynamics, and gliotransmission are not known. We developed a biophysical model that describes calcium signaling and the ensuing gliotransmitter release from a single astrocytic process when stimulated by glutamate release from hippocampal neurons. The model accurately captures the temporal dynamics of microdomain calcium signaling and glutamate release via both kiss-and-run and full-fusion exocytosis. We investigate the roles of two crucial calcium regulating machineries affected by Aβ: plasma-membrane calcium pumps (PMCA) and metabotropic glutamate receptors (mGluRs). When we implemented these Aβ-affected molecular changes in our astrocyte model, it led to an increase in the rate and synchrony of calcium events. Our model also reproduces several previous findings of Aβ associated aberrant calcium activity, such as increased intracellular calcium level and increased spontaneous calcium activity, and synchronous calcium events. The study establishes a causal link between previous observations of hyperactive astrocytes in Alzheimer’s disease (AD) and Aβ-induced modifications in mGluR and PMCA functions. Analogous to neurotransmitter release, gliotransmitter exocytosis closely tracks calcium changes in astrocyte processes, thereby guaranteeing tight control of synaptic signaling by astrocytes. However, the downstream effects of AD-related calcium changes in astrocytes on gliotransmitter release are not known. Our results show that enhanced rate of exocytosis resulting from modified calcium signaling in astrocytes leads to a rapid depletion of docked vesicles that disrupts the crucial temporal correspondence between a calcium event and vesicular release. We propose that the loss of temporal correspondence between calcium events and gliotransmission in astrocytes pathologically alters astrocytic modulation of synaptic transmission in the presence of Aβ accumulation.

Signaling by astrocytes is critical to information processing at synapses, and its aberration plays a central role in neurological diseases, especially Alzheimer’s disease (AD). A complete characterization of calcium signaling and the resulting pattern of gliotransmitter release from fine astrocytic processes are not accessible to current experimental tools. We developed a biophysical model that can quantitatively describe signaling by astrocytes in response to a wide range of synaptic activity. We show that AD-related molecular alterations disrupt the concurrence of calcium and gliotransmitter release events, a characterizing feature that enables astrocytes to influence synaptic signaling.

A norepinephrine-dependent glial calcium wave travels in the spinal cord upon acoustovestibular stimuli

Although calcium waves have been widely observed in glial cells, their occurrence in vivo during behavior remains less understood. Here, we investigated the recruitment of glial cells in the hindbrain and spinal cord after acousto-vestibular (AV) stimuli triggering escape responses using in vivo population calcium imaging in larval zebrafish. We observed that gap-junction-coupled spinal glial network exhibits large and homogenous calcium increases that rose in the rostral spinal cord and propagated bi-directionally toward the spinal cord and toward the hindbrain. Spinal glial calcium waves were driven by the recruitment of neurons and in particular, of noradrenergic signaling acting through α-adrenergic receptors. Noradrenergic neurons of the medulla-oblongata (NE-MO) were revealed in the vicinity of where the calcium wave started. NE-MO were recruited upon AV stimulation and sent dense axonal projections in the rostro-lateral spinal cord, suggesting these cells could trigger the glial wave to propagate down the spinal cord. Altogether, our results revealed that a simple AV stimulation is sufficient to recruit noradrenergic neurons in the brainstem that trigger in the rostral spinal cord two massive glial calcium waves, one traveling caudally in the spinal cord and another rostrally into the hindbrain.

Astrocytes in stress accumulate lipid droplets

When the brain is in a pathological state, the content of lipid droplets (LDs), the lipid storage organelles, is increased, particularly in glial cells, but rarely in neurons. The biology and mechanisms leading to LD accumulation in astrocytes, glial cells with key homeostatic functions, are poorly understood. We imaged fluorescently labeled LDs by microscopy in isolated and brain tissue rat astrocytes and in glia-like cells in Drosophila brain to determine the (sub)cellular localization, mobility, and content of LDs under various stress conditions characteristic for brain pathologies. LDs exhibited confined mobility proximal to mitochondria and endoplasmic reticulum that was attenuated by metabolic stress and by increased intracellular Ca²⁺ , likely to enhance the LD-organelle interaction imaged by electron microscopy. When de novo biogenesis of LDs was attenuated by inhibition of DGAT1 and DGAT2 enzymes, the astrocyte cell number was reduced by ~40%, suggesting that in astrocytes LD turnover is important for cell survival and/or proliferative cycle. Exposure to noradrenaline, a brain stress response system neuromodulator, and metabolic and hypoxic stress strongly facilitated LD accumulation in astrocytes. The observed response of stressed astrocytes may be viewed as a support for energy provision, but also to be neuroprotective against the stress-induced lipotoxicity.

Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca²⁺ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP₃ with consequent abnormal release of Ca²⁺ from the endoplasmic reticulum (ER) through activation of IP₃ receptor (IP₃R) Ca²⁺ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP₃-mediated Ca²⁺ signaling. We investigate Ca²⁺ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca²⁺ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP₃R sensitivity to IP₃ for large doses. Our analysis also shows that the upstream production of IP₃ can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP₃ signaling.

Computational analysis of NIRS and BOLD signal from neurovascular coupling with three neuron-system feedforward inhibition network

Several neurological disorders occur due to hypoxic condition in brain arising from impairment of cerebral functionality, which can be controlled by neural stimulation driven vasoactive response mediated through biological response in astrocyte, a phenomenon known as neurovascular coupling. Brain can adjust with the problem of hypoxic condition by causing vasodilation with the help of this mechanism. To deduce the mechanism behind vasodilation of blood vessel caused by neuronal stimulus, current study articulates a mathematical model involving neuronal system feedforward inhibition network model (FFI) with two other functional components of neurovascular coupling, i.e. astrocyte and smooth muscle cell lining blood vessel. This study includes the neural inhibition network system where glutamatergic pyramidal neuron and GABAergic interneuron act antagonistically with each other. The proposed model successfully includes the implication of the inhibition system to design mathematical model for neurovascular coupling. Result of the proposed model shows that the increase in neuronal stimulus from 20 to 60 µA/cm² has the ability to increase the vasodilatory activity of blood tissue vasculature. Oxygenation level and hemodynamic response due to input synaptic stimulation has been calculated by regional cerebral oxygenation level (rS0₂) and blood oxygen level dependent (BOLD) imaging signal which supports vasodilation of blood vessel with increase in synaptic input stimulus.

Coronary Smooth Muscle Cell Calcium Dynamics: Effects of Bifurcation Angle on Atheroprone Conditions

This work investigates the effect of arterial bifurcation angulation on atherosclerosis development through in-silico simulations of coupled cell dynamics. The computational model presented here combines cellular pathways, fluid dynamics, and physiologically-realistic vessel geometries as observed in the human vasculature. The coupled cells model includes endothelial cells (ECs) and smooth muscle cells (SMCs) with ion dynamics, hetero and homotypic coupling, as well as electro-diffusive coupling. Three arterial bifurcation surface models were used in the coupled cells simulations. All three simulations showed propagating waves of Ca²⁺ in both the SMC and EC layers, following the introduction of a luminal agonist, in this case ATP. Immediately following the introduction of ATP concentration Ca²⁺ waves propagate from the area of high ATP toward the areas of low ATP concentration, forming complex patterns where waves interact with eachother, collide and fade. These dynamic phenomena are repeated with a series of waves of slower velocity. The underlying motivation of this research was to examine the macro-scale phenomena, given that the characteristic length scales of atherosclerotic plaques are much larger than a single cell. The micro-scale dynamics were modeled on macro-scale arterial bifurcation surfaces containing over one million cells. The results of the simulations presented here suggest that susceptibility to atherosclerosis development depends on the bifurcation angulation. In conjunction with findings reported in the literature, the simulation results demonstrate that arterial bifurcations containing wider angles have a more prominent influence on the coupled cells pathways associated with the development of atherosclerosis, by means of disturbed flow and lower SMC Ca²⁺ concentrations. The discussion of the results considers the findings of this research within the context of the potential link between information transport through frequency encoding of Ca²⁺ wave dynamics and development of atheroprone conditions.

Three-dimensional model of intracellular and intercellular Ca2+ waves propagation in endothelial cells

Intracellular and intercellular Ca²⁺ waves play key roles in cellular functions, and focal stimulation triggers Ca²⁺ wave propagation from stimulation points to neighboring cells, involving localized metabolism reactions and specific diffusion processes. Among these, inositol 1,4,5-trisphosphate (IP₃) is produced at membranes and diffuses into the cytoplasm to release Ca²⁺ from endoplasmic reticulum (ER). In this study, we developed a three-dimensional (3D) simulation model for intercellular and intracellular Ca²⁺ waves in endothelial cells (ECs). 3D model of 2 cells was reconstructed from confocal microscopic images and was connected via gap junctions. Cells have membrane and cytoplasm domains, and metabolic reactions were divided into each domain. Finally, the intracellular and intercellular Ca²⁺ wave propagations were induced using microscopic stimulation and were compared between numerical simulations and experiments. The experiments showed that initial sharp increases in intracellular Ca²⁺ occurred approximately 0.3 s after application of stimuli. In addition, Ca²⁺ wave speeds remained constant in cells, with intracellular and intercellular speeds of approximately 35 and 15 μm/s, respectively. Simulations indicated initial increases in Ca²⁺ concentrations at points of stimulation, and these were then propagated across stimulated and neighboring cells. In particular, initial rapid increases in intracellular Ca²⁺ were delayed and subsequent intracellular and intercellular Ca²⁺ wave speeds were approximately 25 and 12 μm/s, respectively. Simulation results were in agreement with those from cell culture experiments, indicating the utility of our 3D model for investigations of intracellular and intercellular messaging in ECs.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of "entrainment," which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed.

3D time-varying simulations of Ca2+ dynamics in arterial coupled cells: A massively parallel implementation

Preferential locations of atherosclerotic plaque are strongly associated with the areas of low wall shear stress and disturbed haemodynamic characteristics such as flow detachment, flow recirculation and oscillatory flow. The areas of low wall shear stress are also associated with the reduced production of adenosine triphosphate in the endothelial layer, as well as the resulting reduced production of inositol trisphosphate (IP³ ). The subsequent variation in Ca²⁺ signalling and nitric oxide synthesis could lead to the impairment of the atheroprotective function played by nitric oxide. In previous studies, it has been suggested that the reduced IP³ and Ca²⁺ signalling can explain the correlation of atherosclerosis with induced low WSS and disturbed flow characteristics. The massively parallel implementation described in this article provides insight into the dynamics of coupled smooth muscle cells and endothelial cells mapped onto the surface of an idealised arterial bifurcation. We show that variations in coupling parameters, which model normal and pathological conditions, provide vastly different smooth muscle cell Ca²⁺ dynamics and wave propagation profiles. The extensibility of the coupled cells model and scalability of the implementation provide a solid framework for in silico investigations of the interaction between complex cellular chemistry and the macro-scale processes determined by fluid dynamics. © 2016 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

Time-dependent uptake and trafficking of vesicles capturing extracellular S100B in cultured rat astrocytes

Astrocytes, the most heterogeneous glial cells in the central nervous system, contribute to brain homeostasis, by regulating a myriad of functions, including the clearance of extracellular debris. When cells are damaged, cytoplasmic proteins may exit into the extracellular space. One such protein is S100B, which may exert toxic effects on neighboring cells unless it is removed from the extracellular space, but the mechanisms of this clearance are poorly understood. By using time-lapse confocal microscopy and fluorescently labeled S100B (S100B-Alexa⁴⁸⁸ ) and fluorescent dextran (Dextran⁵⁴⁶ ), a fluid phase uptake marker, we examined the uptake of fluorescently labeled S100B-Alexa⁴⁸⁸ from extracellular space and monitored trafficking of vesicles that internalized S100B-Alexa⁴⁸⁸ . Initially, S100B-Alexa⁴⁸⁸ and Dextran⁵⁴⁶ internalized with distinct rates into different endocytotic vesicles; S100B-Alexa⁴⁸⁸ internalized into smaller vesicles than Dextran⁵⁴⁶ . At a later stage, S100B-Alexa⁴⁸⁸ -positive vesicles substantially co-localized with Dextran⁵⁴⁶ -positive endolysosomes and with acidic LysoTracker-positive vesicles. Cell treatment with anti-receptor for advanced glycation end products (RAGE) antibody, which binds to RAGE, a 'scavenger receptor', partially inhibited uptake of S100B-Alexa⁴⁸⁸ , but not of Dextran⁵⁴⁶ . The dynamin inhibitor dynole 34-2 inhibited internalization of both fluorescent probes. Directional mobility of S100B-Alexa⁴⁸⁸ -positive vesicles increased over time and was inhibited by ATP stimulation, an agent that increases cytosolic free calcium concentration ([Ca²⁺ ]_i ). We conclude that astrocytes exhibit RAGE- and dynamin-dependent vesicular mechanism to efficiently remove S100B from the extracellular space. If a similar process occurs in vivo, astroglia may mitigate the toxic effects of extracellular S100B by this process under pathophysiologic conditions. This study reveals the vesicular clearance mechanism of extracellular S100B in astrocytes. Initially, fluorescent S100B internalizes into smaller endocytotic vesicles than dextran molecules. At a later stage, both probes co-localize within endolysosomes. S100B internalization is both dynamin- and RAGE-dependent, whereas dextran internalization is dependent on dynamin. Vesicle internalization likely mitigates the toxic effects of extracellular S100B and other waste products.

A mechanistic model of a PDGFRα(+) cell

A novel platelet-derived growth factor receptor alpha-positive cell (PDGFRα(+)) has recently been identified as part of the purinergic inhibitory neural control mechanism in the gastrointestinal (GI) tract. The mechanism through which PDGFRα(+) cells mediate GI muscle relaxation has been found to be associated with the purine receptors P2Y1 and apamin-sensitive SK3 channels that are highly expressed in these cells. This study aims to develop a mechanistic model elucidating a proposed mechanism through which PDGFRα(+) cells contribute to purinergic inhibitory neuromuscular transmission. In accordance with recent experimental findings, the model describes how the binding of neurotransmitters, released from enteric neurons, triggers the release of Ca(2+) from the endoplasmic reticulum in the PDGFRα(+) cells, and how this subsequently leads to large amplitude transient outward currents, which in turn hyperpolarize the cell. The model has been validated against experimental recordings and good agreement was found under normal and pharmacologically-altered conditions. This model demonstrates the feasibility of the proposed mechanism and provides a basis for understanding the mechanism underlying purinergic control of colonic motility.

Modelling cell cycle synchronisation in networks of coupled radial glial cells

Radial glial cells play a crucial role in the embryonic mammalian brain. Their proliferation is thought to be controlled, in part, by ATP mediated calcium signals. It has been hypothesised that these signals act to locally synchronise cell cycles, so that clusters of cells proliferate together, shedding daughter cells in uniform sheets. In this paper we investigate this cell cycle synchronisation by taking an ordinary differential equation model that couples the dynamics of intracellular calcium and the cell cycle and extend it to populations of cells coupled via extracellular ATP signals. Through bifurcation analysis we show that although ATP mediated calcium release can lead to cell cycle synchronisation, a number of other asynchronous oscillatory solutions including torus solutions dominate the parameter space and cell cycle synchronisation is far from guaranteed. Despite this, numerical results indicate that the transient and not the asymptotic behaviour of the system is important in accounting for cell cycle synchronisation. In particular, quiescent cells can be entrained on to the cell cycle via ATP mediated calcium signals initiated by a driving cell and crucially will cycle in near synchrony with the driving cell for the duration of neurogenesis. This behaviour is highly sensitive to the timing of ATP release, with release at the G1/S phase transition of the cell cycle far more likely to lead to near synchrony than release during mid G1 phase. This result, which suggests that ATP release timing is critical to radial glia cell cycle synchronisation, may help us to understand normal and pathological brain development.

Modeling the functional network of primary intercellular Ca2+ wave propagation in astrocytes and its application to study drug effects

We introduce a simple procedure of multivariate signal analysis to uncover the functional connectivity among cells composing a living tissue and describe how to apply it for extracting insight on the effect of drugs in the tissue. The procedure is based on the covariance matrix of time resolved activity signals. By determining the time-lag that maximizes covariance, one derives the weight of the corresponding connection between cells. Introducing simple constraints, it is possible to conclude whether pairs of cells are functionally connected and in which direction. After testing the method against synthetic data we apply it to study intercellular propagation of Ca(2+) waves in astrocytes following an external stimulus, with the aim of uncovering the functional cellular connectivity network. Our method proves to be particularly suited for this type of networking signal propagation where signals are pulse-like and have short time-delays, and is shown to be superior to standard methods, namely a multivariate Granger algorithm. Finally, based on the statistical analysis of the connection weight distribution, we propose simple measures for assessing the impact of drugs on the functional connectivity between cells.

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

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

Mathematical approaches to modeling of cortical spreading depression

Migraine with aura (MwA) is a debilitating disease that afflicts about 25%-30% of migraine sufferers. During MwA, a visual illusion propagates in the visual field, then disappears, and is followed by a sustained headache. MwA was conjectured by Lashley to be related to some neurological phenomenon. A few years later, Leão observed electrophysiological waves in the brain that are now known as cortical spreading depression (CSD). CSD waves were soon conjectured to be the neurological phenomenon underlying MwA that had been suggested by Lashley. However, the confirmation of the link between MwA and CSD was not made until 2001 by Hadjikhani et al. [Proc. Natl. Acad. Sci. U.S.A. 98, 4687-4692 (2001)] using functional MRI techniques. Despite the fact that CSD has been studied continuously since its discovery in 1944, our detailed understandings of the interactions between the mechanisms underlying CSD waves have remained elusive. The connection between MwA and CSD makes the understanding of CSD even more compelling and urgent. In addition to all of the information gleaned from the many experimental studies on CSD since its discovery, mathematical modeling studies provide a general and in some sense more precise alternative method for exploring a variety of mechanisms, which may be important to develop a comprehensive picture of the diverse mechanisms leading to CSD wave instigation and propagation. Some of the mechanisms that are believed to be important include ion diffusion, membrane ionic currents, osmotic effects, spatial buffering, neurotransmitter substances, gap junctions, metabolic pumps, and synaptic connections. Discrete and continuum models of CSD consist of coupled nonlinear differential equations for the ion concentrations. In this review of the current quantitative understanding of CSD, we focus on these modeling paradigms and various mechanisms that are felt to be important for CSD.

A positive feedback cell signaling nucleation model of astrocyte dynamics

We constructed a model of calcium signaling in astrocyte neural glial cells that incorporates a positive feedback nucleation mechanism, whereby small microdomain increases in local calcium can stochastically produce global cellular and intercellular network scale dynamics. The model is able to simultaneously capture dynamic spatial and temporal heterogeneities associated with intracellular calcium transients in individual cells and intercellular calcium waves (ICW) in spatially realistic networks of astrocytes, i.e., networks where the positions of cells were taken from real in vitro experimental data of spontaneously forming sparse networks, as opposed to artificially constructed grid networks or other non-realistic geometries. This is the first work we are aware of where an intracellular model of calcium signaling that reproduces intracellular dynamics inherently accounts for intercellular network dynamics. These results suggest that a nucleation type mechanism should be further investigated experimentally in order to test its contribution to calcium signaling in astrocytes and in other cells more broadly. It may also be of interest in engineered neuromimetic network systems that attempt to emulate biological signaling and information processing properties in synthetic hardwired neuromorphometric circuits or coded algorithms.

Modeling the contributions of Ca2+ flows to spontaneous Ca2+ oscillations and cortical spreading depression-triggered Ca2+ waves in astrocyte networks

Astrocytes participate in brain functions through Ca(2+) signals, including Ca(2+) waves and Ca(2+) oscillations. Currently the mechanisms of Ca(2+) signals in astrocytes are not fully clear. Here, we present a computational model to specify the relative contributions of different Ca(2+) flows between the extracellular space, the cytoplasm and the endoplasmic reticulum of astrocytes to the generation of spontaneous Ca(2+) oscillations (CASs) and cortical spreading depression (CSD)-triggered Ca(2+) waves (CSDCWs) in a one-dimensional astrocyte network. This model shows that CASs depend primarily on Ca(2+) released from internal stores of astrocytes, and CSDCWs depend mainly on voltage-gated Ca(2+) influx. It predicts that voltage-gated Ca(2+) influx is able to generate Ca(2+) waves during the process of CSD even after depleting internal Ca(2+) stores. Furthermore, the model investigates the interactions between CASs and CSDCWs and shows that the pass of CSDCWs suppresses CASs, whereas CASs do not prevent the generation of CSDCWs. This work quantitatively analyzes the generation of astrocytic Ca(2+) signals and indicates different mechanisms underlying CSDCWs and non-CSDCWs. Research on the different types of Ca(2+) signals might help to understand the ways by which astrocytes participate in information processing in brain functions.

Intercellular Ca(2+) waves: mechanisms and function

Intercellular calcium (Ca(2+)) waves (ICWs) represent the propagation of increases in intracellular Ca(2+) through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca(2+) from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs.

IFN-γ-induced increase in the mobility of MHC class II compartments in astrocytes depends on intermediate filaments

Background

In immune-mediated diseases of the central nervous system, astrocytes exposed to interferon-γ (IFN-γ) can express major histocompatibility complex (MHC) class II molecules and antigens on their surface. MHC class II molecules are thought to be delivered to the cell surface by membrane-bound vesicles. However, the characteristics and dynamics of this vesicular traffic are unclear, particularly in reactive astrocytes, which overexpress intermediate filament (IF) proteins that may affect trafficking. The aim of this study was to determine the mobility of MHC class II vesicles in wild-type (WT) astrocytes and in astrocytes devoid of IFs.

Methods

The identity of MHC class II compartments in WT and IF-deficient astrocytes 48 h after IFN-γ activation was determined immunocytochemically by using confocal microscopy. Time-lapse confocal imaging and Alexa Fluor⁵⁴⁶-dextran labeling of late endosomes/lysosomes in IFN-γ treated cells was used to characterize the motion of MHC class II vesicles. The mobility of vesicles was analyzed using ParticleTR software.

Results

Confocal imaging of primary cultures of WT and IF-deficient astrocytes revealed IFN-γ induced MHC class II expression in late endosomes/lysosomes, which were specifically labeled with Alexa Fluor⁵⁴⁶-conjugated dextran. Live imaging revealed faster movement of dextran-positive vesicles in IFN-γ-treated than in untreated astrocytes. Vesicle mobility was lower in IFN-γ-treated IF-deficient astrocytes than in WT astrocytes. Thus, the IFN-γ-induced increase in the mobility of MHC class II compartments is IF-dependent.

Conclusions

Since reactivity of astrocytes is a hallmark of many CNS pathologies, it is likely that the up-regulation of IFs under such conditions allows a faster and therefore a more efficient delivery of MHC class II molecules to the cell surface. In vivo, such regulatory mechanisms may enable antigen-presenting reactive astrocytes to respond rapidly and in a controlled manner to CNS inflammation.

Amyotrophic lateral sclerosis immunoglobulins G enhance the mobility of Lysotracker-labelled vesicles in cultured rat astrocytes

AIM

We examined the effect of purified immunoglobulins G (IgG) from patients with amyotrophic lateral sclerosis (ALS) on the mobility and exocytotic release from Lysotracker-stained vesicles in cultured rat astrocytes.

METHODS

Time-lapse confocal images were acquired, and vesicle mobility was analysed before and after the application of ALS IgG. The vesicle counts were obtained to assess cargo exocytosis from stained organelles.

RESULTS

At rest, when mobility was monitored for 2 min in bath with Ca(2+), two vesicle populations were discovered: (1) non-mobile vesicles (6.1%) with total track length (TL) < 1 μm, averaging at 0.33 ± 0.01 μm (n = 1305) and (2) mobile vesicles (93.9%) with TL > 1 μm, averaging at 3.03 ± 0.01 μm (n = 20,200). ALS IgG (0.1 mg mL(-1)) from 12 of 13 patients increased the TL of mobile vesicles by approx. 24% and maximal displacement (MD) by approx. 26% within 4 min, while the IgG from control group did not alter the vesicle mobility. The mobility enhancement by ALS IgG was reduced in extracellular solution devoid of Ca(2+), indicating that ALS IgG vesicle mobility enhancement involves changes in Ca(2+) homeostasis. To examine whether enhanced mobility relates to elevated Ca(2+) activity, cells were stimulated by 1 mm ATP, a cytosolic Ca(2+) increasing agent, in the presence (2 mm) and in the absence of extracellular Ca(2+). ATP stimulation triggered an increase in TL by approx. 7% and 12% and a decrease in MD by approx. 11% and 1%, within 4 min respectively. Interestingly, none of the stimuli triggered the release of vesicle cargo.

CONCLUSION

Amyotrophic lateral sclerosis-IgG-enhanced vesicle mobility in astrocytes engages changes in calcium homeostasis.

Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes

Bifurcation mechanisms underlying calcium oscillations in the network of astrocytes are investigated. Network model includes the dynamics of intracellular calcium concentration and intercellular diffusion of inositol 1,4,5-trisphosphate through gap junctions. Bifurcation analysis of underlying nonlinear dynamical system is presented. Parameter regions and principle bifurcation boundaries have been delineated and described. We show how variations of the diffusion rate can lead to generation of network calcium oscillations in originally nonoscillating cells. Different scenarios of regular activity and its transitions to chaotic dynamics have been obtained. Then, the bifurcations have been associated with statistical characteristics of calcium signals showing that different bifurcation scenarios yield qualitative changes in experimentally measurable quantities of the astrocyte activity, e.g., statistics of calcium spikes.

A framework for simulating and estimating the state and functional topology of complex dynamic geometric networks

We introduce a framework for simulating signal propagation in geometric networks (networks that can be mapped to geometric graphs in some space) and developing algorithms that estimate (i.e., map) the state and functional topology of complex dynamic geometric networks. Within the framework, we define the key features typically present in such networks and of particular relevance to biological cellular neural networks: dynamics, signaling, observation, and control. The framework is particularly well suited for estimating functional connectivity in cellular neural networks from experimentally observable data and has been implemented using graphics processing unit high-performance computing. Computationally, the framework can simulate cellular network signaling close to or faster than real time. We further propose a standard test set of networks to measure performance and compare different mapping algorithms.

Astrocytes in Alzheimer's disease

The circuitry of the human brain is formed by neuronal networks embedded into astroglial syncytia. The astrocytes perform numerous functions, providing for the overall brain homeostasis, assisting in neurogenesis, determining the micro-architecture of the grey matter, and defending the brain through evolutionary conserved astrogliosis programs. Astroglial cells are engaged in neurological diseases by determining the progression and outcome of neuropathological process. Astrocytes are specifically involved in various neurodegenerative diseases, including Alzheimer's disease, amyotrophic lateral sclerosis, Parkinson's disease, and various forms of dementia. Recent evidence suggest that early stages of neurodegenerative processes are associated with atrophy of astroglia, which causes disruptions in synaptic connectivity, disbalance in neurotransmitter homeostasis, and neuronal death through increased excitotoxicity. At the later stages, astrocytes become activated and contribute to the neuroinflammatory component of neurodegeneration.

Intermediate filaments attenuate stimulation-dependent mobility of endosomes/lysosomes in astrocytes

Intermediate filament (IF) proteins upregulation is a hallmark of astrocyte activation and reactive gliosis, but its pathophysiological implications remain incompletely understood. A recently reported association between IFs and directional mobility of peptidergic vesicles allows us to hypothesize that IFs affect vesicle dynamics and exocytosis-mediated astrocyte communication with neighboring cells. Here, we ask whether the trafficking of recycling vesicles (i.e., those fused to and then retrieved from the plasma membrane) and endosomes/lysosomes depends on IFs. Recycling vesicles were labeled by antibodies against vesicle glutamate transporter 1 (VGLUT1) and atrial natriuretic peptide (ANP), respectively, and by lysotracker, which labels endosomes/lysosomes. Quantitative fluorescence microscopy was used to monitor the mobility of labeled vesicles in astrocytes, derived from either wild-type (WT) mice or mice deficient in glial fibrillary acidic protein and vimentin (GFAP(-/-)Vim(-/-)), the latter lacking astrocyte IFs. Stimulation with ionomycin or ATP enhanced the mobility of VGLUT1-positive vesicles and reduced the mobility of ANP-positive vesicles in WT astrocytes. In GFAP(-/-)Vim(-/-) astrocytes, both vesicle types responded to stimulation, but the relative increase in mobility of VGLUT1-positive vesicles was more prominent compared with nonstimulated cells, whereas the stimulation-dependent attenuation of ANP-positive vesicles mobility was reduced compared with nonstimulated cells. The mobility of endosomes/lysosomes decreased following stimulation in WT astrocytes. However, in GFAP(-/-)Vim(-/-) astrocytes, a small increase in the mobility of endosomes/lysosomes was observed. These findings show that astrocyte IFs differentially affect the stimulation-dependent mobility of vesicles. We propose that upregulation of IFs in pathologic states may alter the function of astrocytes by deregulating vesicle trafficking.

Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow

An optical flow gradient algorithm was applied to spontaneously forming networks of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution. Optical flow estimates the direction and speed of motion of objects in an image between subsequent frames in a recorded digital sequence of images (i.e., a movie). Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling patterns. We begin by briefly reviewing the mathematics of the optical flow algorithm, and then describe how to solve for the displacement vectors and how to measure their reliability. We then compare computed flow vectors with manually estimated vectors for the progression of a calcium signal recorded from representative astrocyte cultures. Finally, we applied the algorithm to preparations of primary astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in order to illustrate the capability of the algorithm for capturing different types of spatiotemporal calcium activity. We discuss the imaging requirements, parameter selection and threshold selection for reliable measurements, and offer perspectives on uses of the vector data.

Concurrent observations of astrocytic Ca(2+) activity and multisite extracellular potentials from an intact cerebral cortex

In basic neuroscience, the attention has been recently focused on the role played by the protoplasmic astrocytes in modulating the activity of nearby neurons or else on assisting a long-term/sustained communication between these neurons and the surrounding microvasculature. However, to understand the physiological mechanisms underlying such a multiscale interactions in space and time, novel methodologies are required. This paper reports about an experimental setting and a procedure that was developed to obtain concurrently two-photon astrocytic Ca(2+) imaging and multisite large-scale extracellular potentials as recorded by a silicon-based probe. Solutions to several technical drawbacks (e.g. removal of photoelectric artifacts, the establishment of safety ranges for microinjection) are provided which are intrinsic to the technology and procedure utilized. Through the use of SR101 to stain protoplasmic astrocytes, it was possible to combine functional information represented by the Ca(2+) activity in individual astrocytes and the LFPs with geometrical descriptors of the astrocytic/vessel networks.

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.

Dynamical patterns of calcium signaling in a functional model of neuron-astrocyte networks

We propose a functional mathematical model for neuron-astrocyte networks. The model incorporates elements of the tripartite synapse and the spatial branching structure of coupled astrocytes. We consider glutamate-induced calcium signaling as a specific mode of excitability and transmission in astrocytic-neuronal networks. We reproduce local and global dynamical patterns observed experimentally.

Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release

Airway epithelium has been shown to exhibit intracellular calcium waves after mechanical stimulation. Two classes of mechanism have been proposed to explain calcium wave propagation: diffusion through gap junctions of the intracellular messenger inositol 1,4,5-trisphosphate (IP3), and diffusion of paracrine extracellular messengers such as ATP. We have used single cell recordings of airway epithelium to parameterize a model of an airway epithelial cell. This was then incorporated into a spatial model of a cell culture where both mechanisms for calcium wave propagation are possible. It is shown that a decreasing return on the radius of Ca2+ wave propagation is achieved as the amount of ATP released from the stimulated cell increases. It is therefore shown that for a Ca2+ wave to propagate large distances, a significant fraction of the intracellular ATP pool would be required to be released. Further to this, the radial distribution of maximal calcium response from the stimulated cell does not produce the same flat profile of maximal calcium response seen in experiential studies. This suggests that an additional mechanism is important in Ca2+ wave propagation, such as regenerative release of ATP from cells downstream of the stimulated cell.

P2X7 regenerative-loop potentiation of glutamate synaptic transmission by microglia and astrocytes

P2X7 purinergic receptors have been implicated in chronic neuropathic and neuroinflammatory pain as well as in depression. These receptors are predominantly found in the central nervous system on microglial cells and on glutamatergic nerve terminals. Here, we develop hypotheses concerning mechanisms by which transient high-frequency impulse firing in glutamatergic terminals, such as occurs in nociceptor terminals accompanying neuropathic/neuroinflammatory pain, can lead to long-lasting changes in neural network function that is mediated by surrounding glial cells. The hypothesis consists of two parts. In the first, glutamate released by low-frequency (2Hz) terminal action potentials is insufficient to generate postsynaptic action potentials, but these are generated by brief high-frequency input bursts. Glutamate released by these bursts is partly removed by transporters on the enveloping astrocyte processes and also excites AMPA receptors on these processes, which then release ATP. This ATP is partly metabolised to adenosine, which acts on presynaptic A1 receptors to inhibit glutamate release. The remaining ATP acts on the presynaptic P2X7 receptors to facilitate glutamate release by both the high-frequency burst of action potentials as well as by a continuous low-frequency (2Hz) action potential firing that occurs in the absence of a neuropathic/neuroinflammatory insult. The positive feedback of terminal glutamate release, triggering astrocyte ATP release and leading to further glutamate release through activation of P2X7 receptors, is then sufficient to allow the normal low-frequency (2Hz) action potentials to now elicit postsynaptic action potentials after the insult is removed. In the second part of this model, the high concentration of ATP derived from astrocytes at the terminal attracts microglia by chemotaxis. The P2X7 receptors on these microglia are then engaged, resulting in microglia secreting the cytokine TNFalpha. This acts on postsynaptic TNF-R1 receptors to increase the number of AMPA receptors there, thus enhancing the efficacy of synaptic transmission. The TNFalpha also acts on presynaptic TNF-R1 to increase the amount of glutamate released by each nerve terminal impulse. Experimental tests can be made of this hypothesis that P2X7 receptors on the presynaptic terminal and those on the microglia synergistically act to ensure feedback pathways that reset to a high level the efficacy of synaptic transmission, thus ensuring chronic neuropathic/neuroinflammatory pain even when the initial insult has subsided.

Regulated exocytosis and vesicle trafficking in astrocytes

Astrocytes are increasingly viewed as crucial cells supporting and integrating brain functions. It is thought that the release of gliotransmitters into the extracellular space by regulated exocytosis supports a significant part of communication between astrocytes and neurons. Prior to exocytosis, the membrane-bound vesicles are transported through the astrocyte cytoplasm. Our recent studies have revealed new insights into vesicle trafficking in the cytoplasm of astrocytes and are reviewed in this article. The prefusion mobility of fluorescently labeled peptidergic vesicles was studied in cultured rat and mouse astrocytes. Vesicle delivery to the plasma membrane involved an interaction with the cytoskeleton, in particular with microtubules and actin filaments. Interestingly, vesicle mobility in mouse astrocytes deficient in intermediate filaments show impaired directionality of peptidergic vesicle mobility. To explore whether stimuli that increase the concentration of free calcium ions in the cytoplasm triggered vesicular ATP release from astrocytes, human embryonic kidney-293T cells transfected with a P2X(3) receptor were used as sniffers to detect ATP release. Glutamate stimulation of astrocytes was followed by an increase in the incidence of small, transient, inward currents in sniffer cells, reminiscent of postsynaptic quantal events observed at synapses. Some of the membrane-bound vesicles are retrieved from the plasma membrane to be recycled back into the cytosol. Trafficking velocity of postfusion (recycling) atrial natriuretic peptide vesicles was one order of magnitude slower in comparison to the mobility of prefusion vesicles. However, transport of all vesicle types studied required an intact cytoskeleton.

Spontaneous calcium signals induced by gap junctions in a network model of astrocytes

The dynamics of a network model of astrocytes coupled by gap junctions is investigated. Calcium dynamics of the single cell is described by the biophysical model comprising the set of three nonlinear differential equations. Intercellular dynamics is provided by the diffusion of inositol 1,4,5-trisphosphate (IP3) through gap junctions between neighboring astrocytes. It is found that the diffusion induces the appearance of spontaneous activity patterns in the network. Stability of the network steady state is analyzed. It is proved that the increase of the diffusion coefficient above a certain critical value yields the generation of low-amplitude subthreshold oscillatory signals in a certain frequency range. It is shown that such spontaneous oscillations can facilitate calcium pulse generation and provide a certain time scale in astrocyte signaling.

A quantitative model of cortical spreading depression due to purinergic and gap-junction transmission in astrocyte networks

Spreading depression (SD), a propagating wave of electrical silence in the cortex and archicortex, involves depolarization of neurons and astrocytes for approximately 1 min, due principally to a large increase in extracellular K+. SD is accompanied by large increases in extracellular ATP and is blocked by glutamate N-methyl-D-aspartate receptor antagonists. As a principal means of transmission between astrocytes is through their release of ATP, we have investigated if a model in which SD is driven by the effects of astrocyte waves of ATP interacting with waves of glutamate release from neurons and astrocytes can give a quantitative account of experimental observations on SD. We show that the characteristics of SD and the accompanying extracellular ionic changes can be accommodated by such a model-whether astrocyte transmission is principally through the release of ATP, as in archicortex (hippocampus) and spinal cord, or via gap junctions, as in the neocortex. Furthermore, these models give quantitative accounts of the effects on the characteristics of SD of agents toxic for astrocytes and of gap-junction blockers. Finally, an additional series of critical tests of the model is suggested.

Diffusion modeling of ATP signaling suggests a partially regenerative mechanism underlies astrocyte intercellular calcium waves

Network signaling through astrocyte syncytiums putatively contribute to the regulation of a number of both physiological and pathophysiological processes in the mammalian central nervous system. As such, an understanding of the underlying mechanisms is critical to determining any roles played by signaling through astrocyte networks. Astrocyte signaling is primarily mediated by the propagation of intercellular calcium waves (ICW) in the sense that paracrine signaling results in measurable intracellular calcium transients. Although the molecular mechanisms are relatively well known, there is conflicting data regarding the mechanism by which the signal propagates through the network. Experimentally there is evidence for both a point source signaling model in which adenosine triphosphate (ATP) is released by an initially activated astrocyte only, and a regenerative signaling model in which downstream astrocytes release ATP. We modeled both conditions as a simple lumped parameter phenomenological diffusion model and show that the only possible mechanism that can accurately reproduce experimentally measured results is a dual signaling mechanism that incorporates elements of both proposed signaling models. Specifically, we were able to accurately simulate experimentally measured in vitroICW dynamics by assuming a point source signaling model with a downstream regenerative component. These results suggest that seemingly conflicting data in the literature are actually complimentary, and represents a highly efficient and robustly engineered signaling mechanism.

ATP signalling in epilepsy

This paper focuses on a role for ATP neurotransmission and gliotransmission in the pathophysiology of epileptic seizures. ATP along with gap junctions propagates the glial calcium wave, which is an extraneuronal signalling pathway in the central nervous system. Recently astrocyte intercellular calcium waves have been shown to underlie seizures, and conventional antiepileptic drugs have been shown to attenuate these calcium waves. Blocking ATP-mediated gliotransmission, therefore, represents a potential target for antiepileptic drugs. Furthermore, while knowledge of an antiepileptic role for adenosine is not new, a recent study showed that adenosine accumulates from the hydrolysis of accumulated ATP released by astrocytes and is believed to inhibit distant synapses by acting on adenosine receptors. Such a mechanism is consistent with a surround-inhibitory mechanism whose failure would predispose to seizures. Other potential roles for ATP signalling in the initiation and spread of epileptiform discharges may involve synaptic plasticity and coordination of synaptic networks. We conclude by making speculations about future developments.

Stimulation inhibits the mobility of recycling peptidergic vesicles in astrocytes

Astrocytes are increasingly viewed as playing many roles in the integration of brain function. These cells store among other gliotransmitters also neuroactive peptides in membrane bound vesicles, the trafficking and release of which, may be changed in altered conditions, therefore affecting the physiological status of neurons. In general, peptidergic membrane-bound secretory vesicles fuse with the plasma membrane in the process of exocytosis. Some of them are retrieved from the plasma membrane to be recycled back into the cytosol. The mobility of retrieving vesicles in astrocytes was not studied yet, however, understanding the mechanisms of such trafficking would highlight the communication paths between astrocytes and neurons. We labeled vesicles with antibodies against the vesicle atrial natriuretic peptide (ANP), which is stored inside secretory vesicles. ANP-vesicles in astrocytes have been proposed to enter Ca2+-dependent secretion and here we show that they are associated with synaptotagmin IV (SytIV), a regulator of exocytosis in astrocytes. Moreover, the results show that recycling ANP-vesicles are to a significant extent acidic. Their velocity (0.06+/-0.001 microm/s) is one order of magnitude lower than the velocity of vesicles trafficking to the plasma membrane (Potokar et al. (2005) Biochem Biophys Res Commun 329:678-683; Potokar et al. (2007) Traffic 8:12-20). Interestingly, ionomycin or ATP application further attenuated ANP-vesicle mobility to 0.02+/-0.002 and to 0.03+/-0.001 microm/s, respectively. In summary, the mobility of recycling peptidergic vesicles appears to be slower than the vesicle traffic to the plasma membrane and it requires an intact cytoskeleton. Physiological implications of attenuated traffic of ANP-vesicles are considered in the discussion.

Purinergic junctional transmission and propagation of calcium waves in cultured spinal cord microglial networks

In order to elucidate the mechanisms of purinergic transmission of calcium (Ca(2 + )) waves between microglial cells, we have employed micro-photolithographic methods to form discrete patterns of microglia that allow quantitative measurements of Ca(2 + ) wave propagation. Microglia were confined to lanes 20-100 [Formula: see text] wide and Ca(2 + ) waves propagated from a point of mechanical stimulation, with a diminution in amplitude, for about 120 [Formula: see text]. The number of cells participating in propagation also decreased over this distance. Ca(2 + ) waves could propagate across a cell-free lane from one microglia lane to another if this distance of separation was less than about 60 [Formula: see text], indicating that propagation involved diffusion of a chemical transmitter. This transmitter was identified as ATP since all Ca(2 + ) wave propagation was blocked by the purinoceptor antagonist suramin, which blocks P2Y(2) and P2Y(12) at relatively low concentrations. Antibodies to P2Y(12) showed these at very high density compared with P2Y(2), indicating a role for P2Y(12) receptors. These observations were quantitatively accounted for by a model in which the main determinants are the diffusion of ATP released from a stimulated microglial cell and differences in the dissociation constant of the purinoceptors on the microglial cells.

Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells

The cellular mechanisms that couple activity of glutamatergic synapses with changes in blood flow, measured by a variety of techniques including the BOLD signal, have not previously been modelled. Here we provide such a model, that successfully accounts for the main observed changes in blood flow in both visual cortex and somatosensory cortex following their stimulation by high-contrast drifting grating or by single whisker stimulation, respectively. Coupling from glutamatergic synapses to smooth muscle cells of arterioles is effected by astrocytes releasing epoxyeicosatrienoic acids (EETs) onto them, following glutamate stimulation of the astrocyte. Coupling of EETs to the smooth muscle of arterioles is by means of potassium channels in their membranes, leading to hyperpolarization, relaxation and hence an increase in blood flow. This model predicts a linear increase in blood flow with increasing numbers of activated astrocytes, but a non-linear increase with increasing glutamate release.