From in silico astrocyte cell models to neuron-astrocyte network models: A review

Machine learning approach for recognition and morphological analysis of isolated astrocytes in phase contrast microscopy

Astrocytes are glycolytically active cells in the central nervous system playing a crucial role in various brain processes from homeostasis to neurotransmission. Astrocytes possess a complex branched morphology, frequently examined by fluorescent microscopy. However, staining and fixation may impact the properties of astrocytes, thereby affecting the accuracy of the experimental data of astrocytes dynamics and morphology. On the other hand, phase contrast microscopy can be used to study astrocytes morphology without affecting them, but the post-processing of the resulting low-contrast images is challenging. The main result of this work is a novel approach for recognition and morphological analysis of unstained astrocytes based on machine-learning recognition of microscopic images. We conducted a series of experiments involving the cultivation of isolated astrocytes from the rat brain cortex followed by microscopy. Using the proposed approach, we tracked the temporal evolution of the average total length of branches, branching, and area per astrocyte in our experiments. We believe that the proposed approach and the obtained experimental data will be of interest and benefit to the scientific communities in cell biology, biophysics, and machine learning.

Astrocytes: new evidence, new models, new roles

Astrocytes have been in the limelight of active research for about 3 decades now. Over this period, ideas about their function and role in the nervous system have evolved from simple assistance in energy supply and homeostasis maintenance to a complex informational and metabolic hub that integrates data on local neuronal activity, sensory and arousal context, and orchestrates many crucial processes in the brain. Rapid progress in experimental techniques and data analysis produces a growing body of data, which can be used as a foundation for formulation of new hypotheses, building new refined mathematical models, and ultimately should lead to a new level of understanding of the contribution of astrocytes to the cognitive tasks performed by the brain. Here, we highlight recent progress in astrocyte research, which we believe expands our understanding of how low-level signaling at a cellular level builds up to processes at the level of the whole brain and animal behavior. We start our review with revisiting data on the role of noradrenaline-mediated astrocytic signaling in locomotion, arousal, sensory integration, memory, and sleep. We then briefly review astrocyte contribution to the regulation of cerebral blood flow regulation, which is followed by a discussion of biophysical mechanisms underlying astrocyte effects on different brain processes. The experimental section is closed by an overview of recent experimental techniques available for modulation and visualization of astrocyte dynamics. We then evaluate how the new data can be potentially incorporated into the new mathematical models or where and how it already has been done. Finally, we discuss an interesting prospect that astrocytes may be key players in important processes such as the switching between sleep and wakefulness and the removal of toxic metabolites from the brain milieu.

Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models

When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena.

Parameter Inference for an Astrocyte Model using Machine Learning Approaches

Astrocytes are the largest subset of glial cells and perform structural, metabolic, and regulatory functions. They are directly involved in the communication at neuronal synapses and the maintenance of brain homeostasis. Several disorders, such as Alzheimer's, epilepsy, and schizophrenia, have been associated with astrocyte dysfunction. Computational models on various spatial levels have been proposed to aid in the understanding and research of astrocytes. The difficulty of computational astrocyte models is to fastly and precisely infer parameters. Physics informed neural networks (PINNs) use the underlying physics to infer parameters and, if necessary, dynamics that can not be observed. We have applied PINNs to estimate parameters for a computational model of an astrocytic compartment. The addition of two techniques helped with the gradient pathologies of the PINNS, the dynamic weighting of various loss components and the addition of Transformers. To overcome the issue that the neural network only learned the time dependence but did not know about eventual changes of the input stimulation to the astrocyte model, we followed an adaptation of PINNs from control theory (PINCs). In the end, we were able to infer parameters from artificial, noisy data, with stable results for the computational astrocyte model.

Information Encoding in Bursting Spiking Neural Network Modulated by Astrocytes

We investigated a mathematical model composed of a spiking neural network (SNN) interacting with astrocytes. We analysed how information content in the form of two-dimensional images can be represented by an SNN in the form of a spatiotemporal spiking pattern. The SNN includes excitatory and inhibitory neurons in some proportion, sustaining the excitation-inhibition balance of autonomous firing. The astrocytes accompanying each excitatory synapse provide a slow modulation of synaptic transmission strength. An information image was uploaded to the network in the form of excitatory stimulation pulses distributed in time reproducing the shape of the image. We found that astrocytic modulation prevented stimulation-induced SNN hyperexcitation and non-periodic bursting activity. Such homeostatic astrocytic regulation of neuronal activity makes it possible to restore the image supplied during stimulation and lost in the raster diagram of neuronal activity due to non-periodic neuronal firing. At a biological point, our model shows that astrocytes can act as an additional adaptive mechanism for regulating neural activity, which is crucial for sensory cortical representations.

Interplay between biochemical processes and network properties generates neuronal up and down states at the tripartite synapse

Neuronal up and down states have long been known to exist both in vitro and in vivo. A variety of functions and mechanisms have been proposed for their generation, but there has not been a clear connection between the functions and mechanisms. We explore the potential contribution of cellular-level biochemistry to the network-level mechanisms thought to underlie the generation of up and down states. We develop a neurochemical model of a single tripartite synapse, assumed to be within a network of similar tripartite synapses, to investigate possible function-mechanism links for the appearance of up and down states. We characterize the behavior of our model in different regions of parameter space and show that resource limitation at the tripartite synapse affects its ability to faithfully transmit input signals, leading to extinction-down states. Recovery of resources allows for "reignition" into up states. The tripartite synapse exhibits distinctive "regimes" of operation depending on whether ATP, neurotransmitter (glutamate), both, or neither, is limiting. Our model qualitatively matches the behavior of six disparate experimental systems, including both in vitro and in vivo models, without changing any model parameters except those related to the experimental conditions. We also explore the effects of varying different critical parameters within the model. Here we show that availability of energy, represented by ATP, and glutamate for neurotransmission at the cellular level are intimately related, and are capable of promoting state transitions at the network level as ignition and extinction phenomena. Our model is complementary to existing models of neuronal up and down states in that it focuses on cellular-level dynamics while still retaining essential network-level processes. Our model predicts the existence of a "final common pathway" of behavior at the tripartite synapse arising from scarcity of resources and may explain use dependence in the phenomenon of "local sleep." Ultimately, sleeplike behavior may be a fundamental property of networks of tripartite synapses.

Reinforcing Interdisciplinary Collaborations to Unravel the Astrocyte "Calcium Code"

In this review article, we present the major insights from and challenges faced in the acquisition, analysis and modeling of astrocyte calcium activity, aiming at bridging the gap between those fields to crack the complex astrocyte “Calcium Code”. We then propose strategies to reinforce interdisciplinary collaborative projects to unravel astrocyte function in health and disease.

Controlling synchronization of gamma oscillations by astrocytic modulation in a model hippocampal neural network

Recent in vitro and in vivo experiments demonstrate that astrocytes participate in the maintenance of cortical gamma oscillations and recognition memory. However, the mathematical understanding of the underlying dynamical mechanisms remains largely incomplete. Here we investigate how the interplay of slow modulatory astrocytic signaling with fast synaptic transmission controls coherent oscillations in the network of hippocampal interneurons that receive inputs from pyramidal cells. We show that the astrocytic regulation of signal transmission between neurons improves the firing synchrony and extends the region of coherent oscillations in the biologically relevant values of synaptic conductance. Astrocyte-mediated potentiation of inhibitory synaptic transmission markedly enhances the coherence of network oscillations over a broad range of model parameters. Astrocytic regulation of excitatory synaptic input improves the robustness of interneuron network gamma oscillations induced by physiologically relevant excitatory model drive. These findings suggest a mechanism, by which the astrocytes become involved in cognitive function and information processing through modulating fast neural network dynamics.

Brain energetics, mitochondria, and traumatic brain injury

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

Neuronal and Astrocytic Regulations in Schizophrenia: A Computational Modelling Study

According to the tripartite synapse model, astrocytes have a modulatory effect on neuronal signal transmission. More recently, astrocyte malfunction has been associated with psychiatric diseases such as schizophrenia. Several hypotheses have been proposed on the pathological mechanisms of astrocytes in schizophrenia. For example, post-mortem examinations have revealed a reduced astrocytic density in patients with schizophrenia. Another hypothesis suggests that disease symptoms are linked to an abnormality of glutamate transmission, which is also regulated by astrocytes (glutamate hypothesis of schizophrenia). Electrophysiological findings indicate a dispute over whether the disorder causes an increase or a decrease in neuronal and astrocytic activity. Moreover, there is no consensus as to which molecular pathways and network mechanisms are altered in schizophrenia. Computational models can aid the process in finding the underlying pathological malfunctions. The effect of astrocytes on the activity of neuron-astrocyte networks has been analysed with computational models. These can reproduce experimentally observed phenomena, such as astrocytic modulation of spike and burst signalling in neuron-astrocyte networks. Using an established computational neuron-astrocyte network model, we simulate experimental data of healthy and pathological networks by using different neuronal and astrocytic parameter configurations. In our simulations, the reduction of neuronal or astrocytic cell densities yields decreased glutamate levels and a statistically significant reduction in the network activity. Amplifications of the astrocytic ATP release toward postsynaptic terminals also reduced the network activity and resulted in temporarily increased glutamate levels. In contrast, reducing either the glutamate release or re-uptake in astrocytes resulted in higher network activities. Similarly, an increase in synaptic weights of excitatory or inhibitory neurons raises the excitability of individual cells and elevates the activation level of the network. To conclude, our simulations suggest that the impairment of both neurons and astrocytes disturbs the neuronal network activity in schizophrenia.

Negative Feedback Role of Astrocytes in Shaping Excitation in Brain Cell Co-cultures

Glial cells play an important role in maintaining neuronal homeostasis and may thus influence excitability in epileptogenesis. These cells in the brain have glutamate (Glu) transporters, which remove this neurotransmitter from the extracellular space. Lack of negative (-) feedback makes local neuronal circuits more excitable and potentially contributing to epileptogenic phenomena. In this study, the role of glial cells in providing (-) feedback is shown through different models of brain cells in culture imaged for intracellular calcium concentration [(Ca²⁺)_i]. Moreover, here we study the individual cells by putting them in categories. Neuronal networks with high and low (-) feedback were established by using anti-mitotics to deplete glial cells. Separate stimuli with very low subthreshold concentrations of Glu (250-750 nM) were added to cultures to test if the order of stimulations matter in regard to calcium dynamics outcomes. Additionally, KCl and ATP were used to stimulate glial cells. We found that for cultures high in (-) feedback, order of the stimulus was not important in predicting cellular responses and because of the complexity of networks in low (-) feedback cultures the order of stimulus matters. As an additional method for analysis, comparison of high (-) feedback cultures, and pure astrocytes was also considered. Glial cells in pure astrocyte cultures tend to be larger in size than glial cells in high (-) feedback cultures. The potential effect of (-) feedback at the blood brain barrier (BBB) was also considered for the inflammatory responses of nitric oxide (NO) production and [Ca²⁺]_i regulation using brain microvascular endothelial cells (BMVECs). The inflammatory and calcium signaling pathways both indicate the negative feedback role of astrocytes, poised between the BBB and structures deeper within the brain, where neuronal synapses are homeostatically maintained by glial uptake of neurotransmitters.

Ion dynamics at the energy-deprived tripartite synapse

The anatomical and functional organization of neurons and astrocytes at 'tripartite synapses' is essential for reliable neurotransmission, which critically depends on ATP. In low energy conditions, synaptic transmission fails, accompanied by a breakdown of ion gradients, changes in membrane potentials and cell swelling. The resulting cellular damage and cell death are causal to the often devastating consequences of an ischemic stroke. The severity of ischemic damage depends on the age and the brain region in which a stroke occurs, but the reasons for this differential vulnerability are far from understood. In the present study, we address this question by developing a comprehensive biophysical model of a glutamatergic synapse to identify key determinants of synaptic failure during energy deprivation. Our model is based on fundamental biophysical principles, includes dynamics of the most relevant ions, i.e., Na+, K+, Ca2+, Cl- and glutamate, and is calibrated with experimental data. It confirms the critical role of the Na+/K+-ATPase in maintaining ion gradients, membrane potentials and cell volumes. Our simulations demonstrate that the system exhibits two stable states, one physiological and one pathological. During energy deprivation, the physiological state may disappear, forcing a transit to the pathological state, which can be reverted when blocking voltage-gated Na+ and K+ channels. Our model predicts that the transition to the pathological state is favoured if the extracellular space fraction is small. A reduction in the extracellular space volume fraction, as, e.g. observed with ageing, will thus promote the brain's susceptibility to ischemic damage. Our work provides new insights into the brain's ability to recover from energy deprivation, with translational relevance for diagnosis and treatment of ischemic strokes.

Modeling Working Memory in a Spiking Neuron Network Accompanied by Astrocytes

We propose a novel biologically plausible computational model of working memory (WM) implemented by a spiking neuron network (SNN) interacting with a network of astrocytes. The SNN is modeled by synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons via chemicals diffused in the extracellular space. Calcium elevations occur in response to the increased concentration of the neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strength of the synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organized by the application of a cue pattern representing one from the memory set distorted by noise. We found that successful retrieval with the level of the correlation between the recalled pattern and ideal pattern exceeding 90% is possible for the multi-item WM task. Having analyzed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in the SNN leading to successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Modeling of Astrocyte Networks: Toward Realistic Topology and Dynamics

Neuronal firing and neuron-to-neuron synaptic wiring are currently widely described as orchestrated by astrocytes—elaborately ramified glial cells tiling the cortical and hippocampal space into non-overlapping domains, each covering hundreds of individual dendrites and hundreds thousands synapses. A key component to astrocytic signaling is the dynamics of cytosolic Ca²⁺ which displays multiscale spatiotemporal patterns from short confined elemental Ca²⁺ events (puffs) to Ca²⁺ waves expanding through many cells. Here, we synthesize the current understanding of astrocyte morphology, coupling local synaptic activity to astrocytic Ca²⁺ in perisynaptic astrocytic processes and morphology-defined mechanisms of Ca²⁺ regulation in a distributed model. To this end, we build simplified realistic data-driven spatial network templates and compile model equations as defined by local cell morphology. The input to the model is spatially uncorrelated stochastic synaptic activity. The proposed modeling approach is validated by statistics of simulated Ca²⁺ transients at a single cell level. In multicellular templates we observe regular sequences of cell entrainment in Ca²⁺ waves, as a result of interplay between stochastic input and morphology variability between individual astrocytes. Our approach adds spatial dimension to the existing astrocyte models by employment of realistic morphology while retaining enough flexibility and scalability to be embedded in multiscale heterocellular models of neural tissue. We conclude that the proposed approach provides a useful description of neuron-driven Ca²⁺-activity in the astrocyte syncytium.

Toward Closed-Loop Electrical Stimulation of Neuronal Systems: A Review

Biological neuronal cells communicate using neurochemistry and electrical signals. The same phenomena also allow us to probe and manipulate neuronal systems and communicate with them. Neuronal system malfunctions cause a multitude of symptoms and functional deficiencies that can be assessed and sometimes alleviated by electrical stimulation. Our working hypothesis is that real-time closed-loop full-duplex measurement and stimulation paradigms can provide more in-depth insight into neuronal networks and enhance our capability to control diseases of the nervous system. In this study, we review extracellular electrical stimulation methods used in in vivo, in vitro, and in silico neuroscience research and in the clinic (excluding methods mainly aimed at neuronal growth and other similar effects) and highlight the potential of closed-loop measurement and stimulation systems. A multitude of electrical stimulation and measurement-based methods are widely used in research and the clinic. Closed-loop methods have been proposed, and some are used in the clinic. However, closed-loop systems utilizing more complex measurement analysis and adaptive stimulation systems, such as artificial intelligence systems connected to biological neuronal systems, do not yet exist. Our review promotes the research and development of intelligent paradigms aimed at meaningful communications between neuronal and information and communications technology systems, "dialogical paradigms," which have the potential to take neuroscience and clinical methods to a new level.

Hydrogels for 3D Neural Tissue Models: Understanding Cell-Material Interactions at a Molecular Level

The development of 3D neural tissue analogs is of great interest to a range of biomedical engineering applications including tissue engineering of neural interfaces, treatment of neurodegenerative diseases and in vitro assessment of cell-material interactions. Despite continued efforts to develop synthetic or biosynthetic hydrogels which promote the development of complex neural networks in 3D, successful long-term 3D approaches have been restricted to the use of biologically derived constructs. In this study a poly (vinyl alcohol) biosynthetic hydrogel functionalized with gelatin and sericin (PVA-SG), was used to understand the interplay between cell-cell communication and cell-material interaction. This was used to probe critical short-term interactions that determine the success or failure of neural network growth and ultimately the development of a useful model. Complex primary ventral mesencephalic (VM) neural cells were encapsulated in PVA-SG hydrogels and critical molecular cues that demonstrate mechanosensory interaction were examined. Neuronal presence was constant over the 10 day culture, but the astrocyte population decreased in number. The lack of astrocytic support led to a reduction in neural process outgrowth from 24.0 ± 1.3 μm on Day 7 to 7.0 ± 0.1 μm on Day 10. Subsequently, purified astrocytes were studied in isolation to understand the reasons behind PVA-SG hydrogel inability to support neural network development. It was proposed that the spatially restrictive nature (or tight mesh size) of PVA-SG hydrogels limited the astrocytic actin polymerization together with a cytoplasmic-nuclear translocation of YAP over time, causing an alteration in their cell cycle. This was confirmed by the evaluation of p27^/Kip1 gene that was found to be upregulated by a twofold increase in expression at both Days 7 and 10 compared to Day 3, indicating the quiescent stage of the astrocytes in PVA-SG hydrogel. Cell migration was further studied by the quantification of MMP-2 production that was negligible compared to 2D controls, ranging from 2.7 ± 2.3% on Day 3 to 5.3 ± 2.9% on Day 10. This study demonstrates the importance of understanding astrocyte-material interactions at the molecular level, with the need to address spatial constraints in the 3D hydrogel environment. These findings will inform the design of future hydrogel constructs with greater capacity for remodeling by the cell population to create space for cell migration and neural process extension.

Advances in Astrocyte Computational Models: From Metabolic Reconstructions to Multi-omic Approaches

The growing importance of astrocytes in the field of neuroscience has led to a greater number of computational models devoted to the study of astrocytic functions and their metabolic interactions with neurons. The modeling of these interactions demands a combined understanding of brain physiology and the development of computational frameworks based on genomic-scale reconstructions, system biology, and dynamic models. These computational approaches have helped to highlight the neuroprotective mechanisms triggered by astrocytes and other glial cells, both under normal conditions and during neurodegenerative processes. In the present review, we evaluate some of the most relevant models of astrocyte metabolism, including genome-scale reconstructions and astrocyte-neuron interactions developed in the last few years. Additionally, we discuss novel strategies from the multi-omics perspective and computational models of other glial cell types that will increase our knowledge in brain metabolism and its association with neurodegenerative diseases.

Astrocytic Modulation of Neuronal Activity in the Suprachiasmatic Nucleus: Insights from Mathematical Modeling

The suprachiasmatic nucleus (SCN) of the hypothalamus consists of a highly heterogeneous neuronal population networked together to allow precise and robust circadian timekeeping in mammals. While the critical importance of SCN neurons in regulating circadian rhythms has been extensively studied, the roles of SCN astrocytes in circadian system function are not well understood. Recent experiments have demonstrated that SCN astrocytes are circadian oscillators with the same functional clock genes as SCN neurons. Astrocytes generate rhythmic outputs that are thought to modulate neuronal activity through pre- and postsynaptic interactions. In this study, we developed an in silico multicellular model of the SCN clock to investigate the impact of astrocytes in modulating neuronal activity and affecting key clock properties such as circadian rhythmicity, period, and synchronization. The model predicted that astrocytes could alter the rhythmic activity of neurons via bidirectional interactions at tripartite synapses. Specifically, astrocyte-regulated extracellular glutamate was predicted to increase neuropeptide signaling from neurons. Consistent with experimental results, we found that astrocytes could increase the circadian period and enhance neural synchronization according to their endogenous circadian period. The impact of astrocytic modulation of circadian rhythm amplitude, period, and synchronization was predicted to be strongest when astrocytes had periods between 0 and 2 h longer than neurons. Increasing the number of neurons coupled to the astrocyte also increased its impact on period modulation and synchrony. These computational results suggest that signals that modulate astrocytic rhythms or signaling (e.g., as a function of season, age, or treatment) could cause disruptions in circadian rhythm or serve as putative therapeutic targets.

The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks-e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called "seven pillars of aging" combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.

A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate

Recent research in neuroscience indicates the importance of tripartite synapses and gliotransmission mediated by astrocytes in neuronal system modulation. Although the astrocyte and neuronal network functions are interrelated, they are fundamentally different in their signaling patterns and, possibly, the time scales at which they operate. However, the exact nature of gliotransmission and the effect of the tripartite synapse function at the network level are currently elusive. In this paper, we propose a computational model of interactions between an astrocyte network and a neuron network, starting from tripartite synapses and spanning to a joint network level. Our model focuses on a two-dimensional setup emulating a mixed in vitro neuron-astrocyte cell culture. The model depicts astrocyte-released gliotransmitters exerting opposing effects on the neurons: increasing the release probability of the presynaptic neuron while hyperpolarizing the post-synaptic one at a longer time scale. We simulated the joint networks with various levels of astrocyte contributions and neuronal activity levels. Our results indicate that astrocytes prolong the burst duration of neurons, while restricting hyperactivity. Thus, in our model, the effect of astrocytes is homeostatic; the firing rate of the network stabilizes to an intermediate level independently of neuronal base activity. Our computational model highlights the plausible roles of astrocytes in interconnected astrocytic and neuronal networks. Our simulations support recent findings in neurons and astrocytes in vivo and in vitro suggesting that astrocytic networks provide a modulatory role in the bursting of the neuronal network.

High-order couplings in geometric complex networks of neurons

We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where traveling synchronization waves are observed from a first-neighbors-based coupling to evaluate the changes induced when higher-order dynamical interactions are included. We observe that the traveling-wave phenomenon gets enhanced by these interactions, allowing the activity to travel further in the system without generating pathological full synchronization states. This scheme could be a step toward a simple phenomenological modelization of neuroglial networks.

A Neuromorphic Digital Circuit for Neuronal Information Encoding Using Astrocytic Calcium Oscillations

Neurophysiological observations are clarifying how astrocytes can actively participate in information processing and how they can encode information through frequency and amplitude modulation of intracellular Ca²⁺ signals. Consequently, hardware realization of astrocytes is important for developing the next generation of bio-inspired computing systems. In this paper, astrocytic calcium oscillations and neuronal firing dynamics are presented by De Pittà and IF (Integrated & Fire) models, respectively. Considering highly nonlinear equations of the astrocyte model, linear approximation and single constant multiplication (SCM) techniques are employed for efficient hardware execution while maintaining the dynamic of the original models. This low-cost hardware architecture for the astrocyte model is able to show the essential features of different types of Ca²⁺ modulation such as amplitude modulation (AM), frequency modulation (FM), or both modes (AFM). To show good agreement between the results of original models simulated in MATLAB and the proposed digital circuits executed on FPGA, quantitative, and qualitative analyses including phase plane are done. This new neuromorphic circuit of astrocyte is able to successfully demonstrate AM/FM/AFM calcium signaling in its real operation on FPGA and has applications in self-repairing systems. It also can be employed as a subsystem for linking biological cells to artificial neuronal networks using astrocytic calcium oscillations in future research.

Simulation of calcium signaling in fine astrocytic processes: Effect of spatial properties on spontaneous activity

Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including the spatial organization of calcium channels IP3R, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on the spatial organization of the channels. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy and predicts that local variations of calcium indicators might contribute to the diversity of calcium signals observed in astrocytes. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability.

Astrocyte as Spatiotemporal Integrating Detector of Neuronal Activity

The functional role of astrocyte calcium signaling in brain information processing was intensely debated in recent decades. This interest was motivated by high resolution imaging techniques showing highly developed structure of distal astrocyte processes. Another point was the evidence of bi-directional astrocytic regulation of neuronal activity. To analyze the effects of interplay of calcium signals in processes and in soma mediating correlations between local signals and the cell-level response of the astrocyte we proposed spatially extended model of the astrocyte calcium dynamics. Specifically, we investigated how spatiotemporal properties of Ca²⁺ dynamics in spatially extended astrocyte model can coordinate (e.g., synchronize) networks of neurons and synapses.

The effect of glutamate-induced excitotoxicity on DNA methylation in astrocytes in a new in vitro neuron-astrocyte-endothelium co-culture system

Glutamate-induced excitotoxicity is a contributer to many neurological diseases. Astrocytes may represent a new target for treating glutamate-induced excitotoxicity. However, the in vitro culture system that mimics the in vivo microenvironment is lacking. This study aimed to establish a new in vitro co-culture system including neurons, astrocytes, and endothelial cells (NAE), and to investigate the effect of glutamate-induced excitotoxicity on DNA methylation in astrocytes. A NAE co-culture method was created using a Transwell chamber, in which neurons were seeded on the bottom of the lower chamber, endothelial cells were plated on the top membrane, and astrocytes were plated on the bottom membrane of the insert. Glutamate-induced toxicity was induced using glutamate and glycine, and examined using immunofluorescence and lactate dehydrogenase release assay. Global methylation in astrocytes was analyzed, and the expression of DNMT1 and DNMT3a was examined using Western blot analysis. Glutamate treatment induced less neuronal damage in the NAE system compared with the control group in which neurons and astrocytes were cultured alone. Global DNA methylation was increased and the expression of DNMT1 and DNMT3a in astrocytes was increased after glutamate treatment, which was blocked by application of the NMDAR inhibitor MK-801 and the DNMT inhibitor 5-azaC from the endothelial cells. The in vitro ANE culture system is effective for studying glutamate-induced excitotoxicity, and may be used for testing the passage of drugs across the blood-brain barrier. Inhibition of DNA methylation in astrocytes may be a new therapeutic strategy for treating glutamate-induced excitotoxicity.

Astrocyte calcium signaling: Interplay between structural and dynamical patterns

Inspired by calcium activity in astrocytes, which is different in the cell body and thick branches on the one hand and thin branchlets and leaflets on the other hand, we formulate a concept of spatially partitioned oscillators. These are inhomogeneous media with regions having different excitability properties, with a global dynamics governed by spatial configuration of such regions. Due to a high surface-to-volume ratio, calcium dynamics in astrocytic leaflets is dominated by transmembrane currents, while somatic calcium dynamics relies on exchange with intracellular stores, mediated by IP 3 , which is in turn synthesized in the space nearby the plasma membrane. Reciprocal coupling via diffusion of calcium and IP 3 between the two regions makes the spatial configuration an essential contributor to overall dynamics. Due to these features, the mechanisms governing the pattern formation of calcium dynamics differ from classical excitable systems with noise or from networks of clustered oscillators. We show how geometrical inhomogeneity can play an ordering role allowing for stable scenarios for calcium wave initiation and propagation.

Disentangling astroglial physiology with a realistic cell model in silico

Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. Our simulations suggest that currents generated by glutamate transporters or K+ channels have negligible distant effects on membrane voltage and that individual astrocytes can successfully handle extracellular K+ hotspots. We show how intracellular Ca2+ buffers affect Ca2+ waves and why the classical Ca2+ sparks-and-puffs mechanism is theoretically compatible with common readouts of astroglial Ca2+ imaging.

A New Computational Model for Astrocytes and Their Role in Biologically Realistic Neural Networks

Recent studies in neuroscience show that astrocytes alongside neurons participate in modulating synapses. It led to the new concept of “tripartite synapse”, which means that a synapse consists of three parts: presynaptic neuron, postsynaptic neuron, and neighboring astrocytes. However, it is still unclear what role is played by the astrocytes in the tripartite synapse. Detailed biocomputational modeling may help generate testable hypotheses. In this article, we aim to study the role of astrocytes in synaptic plasticity by exploring whether tripartite synapses are capable of improving the performance of a neural network. To achieve this goal, we developed a computational model of astrocytes based on the Izhikevich simple model of neurons. Next, two neural networks were implemented. The first network was only composed of neurons and had standard bipartite synapses. The second network included both neurons and astrocytes and had tripartite synapses. We used reinforcement learning and tested the networks on categorizing random stimuli. The results show that tripartite synapses are able to improve the performance of a neural network and lead to higher accuracy in a classification task. However, the bipartite network was more robust to noise. This research provides computational evidence to begin elucidating the possible beneficial role of astrocytes in synaptic plasticity and performance of a neural network.