Computational Models for Calcium-Mediated Astrocyte Functions

Astrocyte-mediated neuronal irregularities and dynamics: the complexity of the tripartite synapse

Despite significant advancements in recent decades, gaining a comprehensive understanding of brain computations remains a significant challenge in neuroscience. Using computational models is crucial for unraveling this complex phenomenon and is equally indispensable for studying neurological disorders. This endeavor has created many neuronal models that capture brain dynamics at various scales and complexities. However, most existing models do not account for the potential influence of glial cells, particularly astrocytes, on neuronal physiology. This gap persists even with the emerging evidence indicating their critical role in regulating neural network activity, plasticity, and even neurological pathologies. To address this gap, some works proposed models that include neuron-glia interactions. Also, while some literature focuses on sophisticated models of neuron-glia interactions that mimic the complexity of physiological phenomena, there are also existing works that propose simplified models of neural-glial ensembles. Building upon these efforts, we aimed to contribute further to the field by proposing a simplified tripartite synapse model that encompasses the presynaptic neuron, postsynaptic neuron, and astrocyte. We defined the tripartite synapse model based on the Adaptive Exponential Integrate-and-Fire neuron model and a simplified scheme of the astrocyte model previously proposed by Postnov. Through our simulations, we demonstrated how astrocytes can influence neuronal firing behavior by sequentially activating and deactivating different pathways within the tripartite synapse. This modulation by astrocytes can shape neuronal behavior and introduce irregularities in the firing patterns of both presynaptic and postsynaptic neurons through the introduction of new pathways and configurations of relevant parameters.

Aβ-mediated synaptic glutamate dynamics and calcium dynamics in astrocytes associated with Alzheimer's disease

The accumulation of amyloid β peptide A β is assumed to be one of the main causes of Alzheimer's disease AD . There is increasing evidence that astrocytes are the primary targets of Aβ. Aβ can cause abnormal synaptic glutamate, aberrant extrasynaptic glutamate, and astrocytic calcium dysregulation through astrocyte glutamate transporters facing the synaptic cleft (GLT-syn), astrocyte glutamate transporters facing the extrasynaptic space (GLT-ess), metabotropic glutamate receptors in astrocytes (mGluR), N-methyl-D-aspartate receptors in astrocytes (NMDAR), and glutamatergic gliotransmitter release (Glio-Rel). However, it is difficult to experimentally identify the extent to which each pathway affects synaptic glutamate, extrasynaptic glutamate, and astrocytic calcium signaling. Motivated by these findings, this work established a concise mathematical model of astrocyteCa 2 + dynamics, including the above Aβ-mediated glutamate-related multiple pathways. The model results presented the extent to which five mechanisms acted upon by Aβ affect synaptic glutamate, extrasynaptic glutamate, and astrocytic intracellularCa 2 + signals. We found that GLT-syn is the main pathway through which Aβ affects synaptic glutamate. GLT-ess and Glio-Rel are the main pathways through which A β affects extrasynaptic glutamate. GLT-syn, mGluR, and NMDAR are the main pathways through which Aβ affects astrocytic intracellularCa 2 + signals. Additionally, we discovered a strong, monotonically increasing relationship between the mean glutamate concentration and the meanCa 2 + oscillation amplitude (or frequency). Our results may have therapeutic implications for slowing cell death induced by the combination of glutamate imbalance andCa 2 + dysregulation in AD.

Dynamical modeling and analysis of epileptic discharges transition caused by glutamate release with metabolism processes regulation from astrocyte

Glutamate (Glu) is a crucial excitatory neurotransmitter in the central nervous system that transmits brain information by activating excitatory receptors on neuronal membranes. Physiological studies have demonstrated that abnormal Glu metabolism in astrocytes is closely related to the pathogenesis of epilepsy. The astrocyte metabolism processes mainly involve the Glu uptake through astrocyte EAAT2, the Glu-glutamine (Gln) conversion, and the Glu release. However, the relationship between these Glu metabolism processes and epileptic discharges remains unclear. In this paper, we propose a novel neuron-astrocyte model by integrating the dynamical modeling of astrocyte Glu metabolism processes, which include Glu metabolism in astrocytes consisting of the Glu uptake, Glu-Gln conversion, Glu diffusion, and the resulting Glu release as well as Glu-mediated bidirectional communication between neuron and astrocyte. Furthermore, the influences of astrocyte multiple Glu metabolism processes on the Glu release and dynamics transition of neuronal epileptic discharges are verified through numerical experiments and dynamical analyses from various nonlinear dynamics perspectives, such as time series, phase plane trajectories, interspike intervals, and bifurcation diagrams. Our results suggest that the downregulation expression of EAAT2 uptake, the slowdown of the Glu-Gln conversion rate, and excessively elevated Glu equilibrium concentration in astrocytes can cause an increase in Glu released from astrocytes, which results in the aggravation of epileptic seizures. Meanwhile, neuronal epileptic discharge states transition from bursting to mixed-mode spiking and tonic firing induced by the combination of these abnormal metabolism processes. This study provides a theoretical foundation and dynamical analysis methodology for further exploring the dynamics evolution and physiopathological mechanisms of epilepsy.

Numerical Simulations and Bifurcation of Ca2+ Oscillatory Behaviour in the Connection of Neurons and Astrocytes

Extensive research has demonstrated that astrocytes actively participate in the regulation of synaptic communication. To examine the dynamic behavior of the model, a neuron-astrocyte model has been solved, and a bifurcation analysis has been performed. This paper uses the equilibrium point, stability theory, and the center manifold theorem to theoretically investigate the dynamical analysis of Ca2+ oscillations in the cytosol. The connections at tripartite synapses between the cells have been modeled using IP3 and 2-AG. A mathematical model is used to depict the overall framework of bifurcation and induced Ca2+ dynamics. The differences in the presence and disappearance of Ca2+ oscillations are partially explained by two subcritical Hopf bifurcation points, according to the results. Communication between the cells occurs through the oscillations of Ca2+ concentration. Furthermore, numerical simulations are conducted to confirm the efficacy of the suggested approach. Thus, our findings imply that neuron-astrocyte crosstalk plays a fundamental role in generating a variety of neuronal activities, thereby improving the brain's capacity for information processing.

Computational modeling of the relationship between morphological heterogeneity and functional responses in mouse hippocampal astrocytes

Recent studies indicate that astrocytes show heterogeneity in morphology and physiological function. They integrate synaptic signals and release calcium in reaction to active neurons. These calcium signals are not yet fully understood as they are highly dependent on the cell's morphology, which can vary across and within brain regions. We found structural heterogeneity among mouse hippocampal CA1 astrocytes based on geometric features, clustering 741 cells into six classes. Of those, we selected 84 cells and reconstructed their morphology based on confocal microscope images and converted them into multi-compartment models with a high detailedness. We applied a computational biophysical model simulating the intracellular ion and IP3 signaling and diffusion in those 3D cell geometries. The cells were stimulated with three different glutamate stimuli. Calcium mainly oscillated in the stimulated and the neighboring compartment but not in the soma. Significant differences were found in the peak width, mean prominence, and mean peak amplitude of the calcium signal when comparing the signals in the stimulated and neighboring compartments. Overall, this study highlights the influence of the complex morphology of astrocytes on intracellular ionic signaling.

Neuron-Glial Interactions: Implications for Plasticity, Behavior, and Cognition

The traditional view of glial cells as mere supportive tissue has shifted, due to advances in technology and theoretical conceptualization, to include a diversity of other functions, such as regulation of complex behaviors. Astrocytes, the most abundant glial cells in the central nervous system (CNS), have been shown to modulate synaptic functions through gliotransmitter-mediated neurotransmitter reuptake, influencing neuronal signaling and behavioral functions. Contemporary studies further highlight astrocytes' involvement in complex cognitive functions. For instance, inhibiting astrocytes in the hippocampus can lead to memory deficits, suggesting their integral role in memory processes. Moreover, astrocytic calcium activity and astrocyte-neuron metabolic coupling have been linked to changes in synaptic strength and learning. Microglia, another type of glial cell, also extend beyond their supportive roles, contributing to learning and memory processes, with microglial reductions impacting these functions in a developmentally dependent manner. Oligodendrocytes, traditionally thought to have limited roles postdevelopment, are now recognized for their activity-dependent modulation of myelination and plasticity, thus influencing behavioral responses. Recent advancements in technology and computational modeling have expanded our understanding of glial functions, particularly how astrocytes influence neuronal circuits and behaviors. This review underscores the importance of glial cells in CNS functions and the need for further research to unravel the complexities of neuron-glia interactions, the impact of these interactions on brain functions, and potential implications for neurological diseases.

Computational modeling of neuron-glia signaling interactions to unravel cellular and neural circuit functioning

Glial cells have been shown to be vital for various brain functions, including homeostasis, information processing, and cognition. Over the past 30 years, various signaling interactions between neuronal and glial cells have been shown to underlie these functions. This review summarizes the interactions, particularly between neurons and astrocytes, which are types of glial cells. Some of the interactions remain controversial in part due to the nature of experimental methods and preparations used. Based on the accumulated data, computational models of the neuron-astrocyte interactions have been developed to explain the complex functions of astrocytes in neural circuits and to test conflicting hypotheses. This review presents the most significant recent models, modeling methods and simulation tools for neuron-astrocyte interactions. In the future, we will especially need more experimental research on awake animals in vivo and new computational models of neuron-glia interactions to advance our understanding of cellular dynamics and the functioning of neural circuits in different brain regions.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

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.

CellRemorph: A Toolkit for Transforming, Selecting, and Slicing 3D Cell Structures on the Road to Morphologically Detailed Astrocyte Simulations

Understanding functions of astrocytes can be greatly enhanced by building and simulating computational models that capture their morphological details. Novel computational tools enable utilization of existing morphological data of astrocytes and building models that have appropriate level of details for specific simulation purposes. In addition to analyzing existing computational tools for constructing, transforming, and assessing astrocyte morphologies, we present here the CellRemorph toolkit implemented as an add-on for Blender, a 3D modeling platform increasingly recognized for its utility for manipulating 3D biological data. To our knowledge, CellRemorph is the first toolkit for transforming astrocyte morphologies from polygonal surface meshes into adjustable surface point clouds and vice versa, precisely selecting nanoprocesses, and slicing morphologies into segments with equal surface areas or volumes. CellRemorph is an open-source toolkit under the GNU General Public License and easily accessible via an intuitive graphical user interface. CellRemorph will be a valuable addition to other Blender add-ons, providing novel functionality that facilitates the creation of realistic astrocyte morphologies for different types of morphologically detailed simulations elucidating the role of astrocytes both in health and disease.

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.

The Structure and Function of Glial Networks: Beyond the Neuronal Connections

Glial cells, consisting of astrocytes, oligodendrocyte lineage cells, and microglia, account for >50% of the total number of cells in the mammalian brain. They play key roles in the modulation of various brain activities under physiological and pathological conditions. Although the typical morphological features and characteristic functions of these cells are well described, the organization of interconnections of the different glial cell populations and their impact on the healthy and diseased brain is not completely understood. Understanding these processes remains a profound challenge. Accumulating evidence suggests that glial cells can form highly complex interconnections with each other. The astroglial network has been well described. Oligodendrocytes and microglia may also contribute to the formation of glial networks under various circumstances. In this review, we discuss the structure and function of glial networks and their pathological relevance to central nervous system diseases. We also highlight opportunities for future research on the glial connectome.

A perspective on astrocyte regulation of neural circuit function and animal behavior

Studies over the past two decades have demonstrated that astrocytes are tightly associated with neurons and play pivotal roles in neural circuit development, operation, and adaptation in health and disease. Nevertheless, precisely how astrocytes integrate diverse neuronal signals, modulate neural circuit structure and function at multiple temporal and spatial scales, and influence animal behavior or disease through aberrant excitation and molecular output remains unclear. This Perspective discusses how new and state-of-the-art approaches, including fluorescence indicators, opto- and chemogenetic actuators, genetic targeting tools, quantitative behavioral assays, and computational methods, might help resolve these longstanding questions. It also addresses complicating factors in interpreting astrocytes' role in neural circuit regulation and animal behavior, such as their heterogeneity, metabolism, and inter-glial communication. Research on these questions should provide a deeper mechanistic understanding of astrocyte-neuron assemblies' role in neural circuit function, complex behaviors, and disease.

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.

Experimental and computational analyses of calcium dynamics in 22q11.2 deletion model astrocytes

Methods for deriving mechanistic information from intracellular calcium dynamics have largely been applied to neuronal data despite the knowledge of roles of glial cells in behavior, cognition, and psychiatric disorders. Using calcium imaging, computer vision, and Bayesian kinetic inference (BKI), we analyzed calcium dynamics in primary astrocytes derived from control or Df1/⁺ mice, a model of 22q11.2 deletion (DiGeorge syndrome). Inference of the highest-likelihood molecular kinetic characteristics of intracellular calcium dynamics identified changes in the activity of the sarcoendoplasmic reticulum calcium ATPase (SERCA). Application of a SERCA inhibitor to wild-type astrocytes reproduced the differences detected in Df1/⁺ astrocytes. Our work reveals the molecular changes driving the calcium kinetics in astrocytes from a 22q11.2 deletion model. BKI can be useful for mechanistically dissecting calcium dynamics in glial cells and formulating and testing hypotheses about underlying molecular mechanisms.

Controlling the spontaneous firing behavior of a neuron with astrocyte

Mounting evidence in recent years suggests that astrocytes, a sub-type of glial cells, not only serve metabolic and structural support for neurons and synapses but also play critical roles in the regulation of proper functioning of the nervous system. In this work, we investigate the effect of astrocytes on the spontaneous firing activity of a neuron through a combined model that includes a neuron-astrocyte pair. First, we show that an astrocyte may provide a kind of multistability in neuron dynamics by inducing different firing modes such as random and bursty spiking. Then, we identify the underlying mechanism of this behavior and search for the astrocytic factors that may have regulatory roles in different firing regimes. More specifically, we explore how an astrocyte can participate in the occurrence and control of spontaneous irregular spiking activity of a neuron in random spiking mode. Additionally, we systematically investigate the bursty firing regime dynamics of the neuron under the variation of biophysical facts related to the intracellular environment of the astrocyte. It is found that an astrocyte coupled to a neuron can provide a control mechanism for both spontaneous firing irregularity and burst firing statistics, i.e., burst regularity and size.

Neuron-Glia Interactions and Brain Circuits

Recent evidence suggests that glial cells take an active role in a number of brain functions that were previously attributed solely to neurons. For example, astrocytes, one type of glial cells, have been shown to promote coordinated activation of neuronal networks, modulate sensory-evoked neuronal network activity, and influence brain state transitions during development. This reinforces the idea that astrocytes not only provide the "housekeeping" for the neurons, but that they also play a vital role in supporting and expanding the functions of brain circuits and networks. Despite this accumulated knowledge, the field of computational neuroscience has mostly focused on modeling neuronal functions, ignoring the glial cells and the interactions they have with the neurons. In this chapter, we introduce the biology of neuron-glia interactions, summarize the existing computational models and tools, and emphasize the glial properties that may be important in modeling brain functions in the future.

Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration

In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. We found that astrocytes possess a variety of complex dynamical modes, including chaos and multistability, that can further provide different modulations of neuronal circuits, enhancing their plasticity and flexibility.

Neurosurgery at the crossroads of immunology and nanotechnology. New reality in the COVID-19 pandemic

Neurosurgery as one of the most technologically demanding medical fields rapidly adapts the newest developments from multiple scientific disciplines for treating brain tumors. Despite half a century of clinical trials, survival for brain primary tumors such as glioblastoma (GBM), the most common primary brain cancer, or rare ones including primary central nervous system lymphoma (PCNSL), is dismal. Cancer therapy and research have currently shifted toward targeted approaches, and personalized therapies. The orchestration of novel and effective blood-brain barrier (BBB) drug delivery approaches, targeting of cancer cells and regulating tumor microenvironment including the immune system are the key themes of this review. As the global pandemic due to SARS-CoV-2 virus continues, neurosurgery and neuro-oncology must wrestle with the issues related to treatment-related immune dysfunction. The selection of chemotherapeutic treatments, even rare cases of hypersensitivity reactions (HSRs) that occur among immunocompromised people, and number of vaccinations they have to get are emerging as a new chapter for modern Nano neurosurgery.

Unraveling Aβ-Mediated Multi-Pathway Calcium Dynamics in Astrocytes: Implications for Alzheimer's Disease Treatment From Simulations

The accumulation of amyloid β peptide (Aβ) in the brain is hypothesized to be the major factor driving Alzheimer's disease (AD) pathogenesis. Mounting evidence suggests that astrocytes are the primary target of Aβ neurotoxicity. Aβ is known to interfere with multiple calcium fluxes, thus disrupting the calcium homeostasis regulation of astrocytes, which are likely to produce calcium oscillations. Ca²⁺ dyshomeostasis has been observed to precede the appearance of clinical symptoms of AD; however, it is experimentally very difficult to investigate the interactions of many mechanisms. Given that Ca²⁺ disruption is ubiquitously involved in AD progression, it is likely that focusing on Ca²⁺ dysregulation may serve as a potential therapeutic approach to preventing or treating AD, while current hypotheses concerning AD have so far failed to yield curable therapies. For this purpose, we derive and investigate a concise mathematical model for Aβ-mediated multi-pathway astrocytic intracellular Ca²⁺ dynamics. This model accounts for how Aβ affects various fluxes contributions through voltage-gated calcium channels, Aβ-formed channels and ryanodine receptors. Bifurcation analysis of Aβ level, which reflected the corresponding progression of the disease, revealed that Aβ significantly induced the increasing [Ca²⁺] _i and frequency of calcium oscillations. The influence of inositol 1,4,5-trisphosphate production (IP₃) is also investigated in the presence of Aβ as well as the impact of changes in resting membrane potential. In turn, the Ca²⁺ flux can be considerably changed by exerting specific interventions, such as ion channel blockers or receptor antagonists. By doing so, a "combination therapy" targeting multiple pathways simultaneously has finally been demonstrated to be more effective. This study helps to better understand the effect of Aβ, and our findings provide new insight into the treatment of AD.

Polyphenols and Stem Cells for Neuroregeneration in Parkinson's Disease and Amyotrophic Lateral Sclerosis

Parkinson's disease (PD) and Amyotrophic lateral sclerosis (ALS) are neurological disorders, pathologically characterized by chronic degeneration of dopaminergic neurons and motor neurons respectively. There is still no cure or effective treatment against the disease progression and most of the treatments are symptomatic. The present review offers an overview of the different factors involved in the pathogenesis of these diseases. Subsequently, we focused on the recent advanced studies of dietary polyphenols and stem cell therapies, which have made it possible to slow down the progression of neurodegeneration. To date, stem cells and different polyphenols have been used for the directional induction of neural stem cells into dopaminergic neurons and motor neurons. We have also discussed their involvement in the modulation of different signal transduction pathways and growth factor levels in various in vivo and in vitro studies. Likewise stem cells, polyphenols also exhibit the potential of neuroprotection by their anti-apoptotic, anti-inflammatory, anti-oxidant properties regulating the growth factors levels and molecular signaling events. Overall this review provides a detailed insight into recent strategies that promise the use of polyphenol with stem cell therapy for the possible treatment of PD and ALS.

Emulation of Astrocyte Induced Neural Phase Synchrony in Spin-Orbit Torque Oscillator Neurons

Astrocytes play a central role in inducing concerted phase synchronized neural-wave patterns inside the brain. In this article, we demonstrate that injected radio-frequency signal in underlying heavy metal layer of spin-orbit torque oscillator neurons mimic the neuron phase synchronization effect realized by glial cells. Potential application of such phase coupling effects is illustrated in the context of a temporal "binding problem." We also present the design of a coupled neuron-synapse-astrocyte network enabled by compact neuromimetic devices by combining the concepts of local spike-timing dependent plasticity and astrocyte induced neural phase synchrony.

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.

A Computational Study of Astrocytic GABA Release at the Glutamatergic Synapse: EAAT-2 and GAT-3 Coupled Dynamics

Neurotransmitter dynamics within neuronal synapses can be controlled by astrocytes and reflect key contributors to neuronal activity. In particular, Glutamate (Glu) released by activated neurons is predominantly removed from the synaptic space by perisynaptic astrocytic transporters EAAT-2 (GLT-1). In previous work, we showed that the time course of Glu transport is affected by ionic concentration gradients either side of the astrocytic membrane and has the propensity for influencing postsynaptic neuronal excitability. Experimental findings co-localize GABA transporters GAT-3 with EAAT-2 on the perisynaptic astrocytic membrane. While these transporters are unlikely to facilitate the uptake of synaptic GABA, this paper presents simulation results which demonstrate the coupling of EAAT-2 and GAT-3, giving rise to the ionic-dependent reversed transport of GAT-3. The resulting efflux of GABA from the astrocyte to the synaptic space reflects an important astrocytic mechanism for modulation of hyperexcitability. Key results also illustrate an astrocytic-mediated modulation of synaptic neuronal excitation by released GABA at the glutamatergic synapse.

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.

Astrocyte-mediated spike-timing-dependent long-term depression modulates synaptic properties in the developing cortex

Astrocytes have been shown to modulate synaptic transmission and plasticity in specific cortical synapses, but our understanding of the underlying molecular and cellular mechanisms remains limited. Here we present a new biophysicochemical model of a somatosensory cortical layer 4 to layer 2/3 synapse to study the role of astrocytes in spike-timing-dependent long-term depression (t-LTD) in vivo. By applying the synapse model and electrophysiological data recorded from rodent somatosensory cortex, we show that a signal from a postsynaptic neuron, orchestrated by endocannabinoids, astrocytic calcium signaling, and presynaptic N-methyl-D-aspartate receptors coupled with calcineurin signaling, induces t-LTD which is sensitive to the temporal difference between post- and presynaptic firing. We predict for the first time the dynamics of astrocyte-mediated molecular mechanisms underlying t-LTD and link complex biochemical networks at presynaptic, postsynaptic, and astrocytic sites to the time window of t-LTD induction. During t-LTD a single astrocyte acts as a delay factor for fast neuronal activity and integrates fast neuronal sensory processing with slow non-neuronal processing to modulate synaptic properties in the brain. Our results suggest that astrocytes play a critical role in synaptic computation during postnatal development and are of paramount importance in guiding the development of brain circuit functions, learning and memory.

A Computational Model to Investigate GABA-Activated Astrocyte Modulation of Neuronal Excitation

Gamma-aminobutyric acid (GABA) is critical for proper neural network function and can activate astrocytes to induce neuronal excitability; however, the mechanism by which astrocytes transform inhibitory signaling to excitatory enhancement remains unclear. Computational modeling can be a powerful tool to provide further understanding of how GABA-activated astrocytes modulate neuronal excitation. In the present study, we implemented a biophysical neuronal network model to investigate the effects of astrocytes on excitatory pre- and postsynaptic terminals following exposure to increasing concentrations of external GABA. The model completely describes the effects of GABA on astrocytes and excitatory presynaptic terminals within the framework of glutamatergic gliotransmission according to neurophysiological findings. Utilizing this model, our results show that astrocytes can rapidly respond to incoming GABA by inducing Ca²⁺ oscillations and subsequent gliotransmitter glutamate release. Elevation in GABA concentrations not only naturally decreases neuronal spikes but also enhances astrocytic glutamate release, which leads to an increase in astrocyte-mediated presynaptic release and postsynaptic slow inward currents. Neuronal excitation induced by GABA-activated astrocytes partly counteracts the inhibitory effect of GABA. Overall, the model helps to increase knowledge regarding the involvement of astrocytes in neuronal regulation using simulated bath perfusion of GABA, which may be useful for exploring the effects of GABA-type antiepileptic drugs.

GPCR mediated control of calcium dynamics: A systems perspective

G-protein coupled receptor (GPCR) mediated calcium (Ca²⁺)-signaling transduction remains crucial in designing drugs for various complex diseases including neurodegeneration, chronic heart failure as well as respiratory diseases. Although there are several reviews detailing various aspects of Ca²⁺-signaling such as the role of IP₃ receptors and Ca²⁺-induced-Ca²⁺-release, none of them provide an integrated view of the mathematical descriptions of GPCR signal transduction and investigations on dose-response curves. This article is the first study in reviewing the network structures underlying GPCR signal transduction that control downstream [Ca_c²⁺]-oscillations. The central theme of this paper is to present the biochemical pathways, as well as molecular mechanisms underlying the GPCR-mediated Ca²⁺-dynamics in order to facilitate a better understanding of how agonist concentration is encoded in Ca²⁺-signals for G_αq, G_αs, and G_αi/o signaling pathways. Moreover, we present the GPCR targeting drugs that are relevant for treating cardiac, respiratory, and neuro-diseases. The current paper presents the ODE formulation for various models along with the detailed schematics of signaling networks. To provide a systems perspective, we present the network motifs that can provide readers an insight into the complex and intriguing science of agonist-mediated Ca²⁺-dynamics. One of the features of this review is to pinpoint the interplay between positive and negative feedback loops that are involved in controlling intracellular [Ca_c²⁺]-oscillations. Furthermore, we review several examples of dose-response curves obtained from [Ca_c²⁺]-spiking for various GPCR pathways. This paper is expected to be useful for pharmacologists and computational biologists for designing clinical applications of GPCR targeting drugs through modulation of Ca²⁺-dynamics.

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.

Astroglial Isopotentiality and Calcium-Associated Biomagnetic Field Effects on Cortical Neuronal Coupling

Synaptic neurotransmission is necessary but does not sufficiently explain superior cognitive faculties. Growing evidence has shown that neuron-astroglial chemical crosstalk plays a critical role in the processing of information, computation, and memory. In addition to chemical and electrical communication among neurons and between neurons and astrocytes, other nonsynaptic mechanisms called ephaptic interactions can contribute to the neuronal synchronization from different brain regions involved in the processing of information. New research on brain astrocytes has clearly shown that the membrane potential of these cells remains very stable among neighboring and distant astrocytes due to the marked bioelectric coupling between them through gap junctions. This finding raises the possibility that the neocortical astroglial network exerts a guiding template modulating the excitability and synchronization of trillions of neurons by astroglial Ca²⁺-associated bioelectromagnetic interactions. We propose that bioelectric and biomagnetic fields of the astroglial network equalize extracellular local field potentials (LFPs) and associated local magnetic field potentials (LMFPs) in the cortical layers of the brain areas involved in the processing of information, contributing to the adequate and coherent integration of external and internal signals. This article reviews the current knowledge of ephaptic interactions in the cerebral cortex and proposes that the isopotentiality of cortical astrocytes is a prerequisite for the maintenance of the bioelectromagnetic crosstalk between neurons and astrocytes in the neocortex.

A roadmap to integrate astrocytes into Systems Neuroscience

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease.

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.

Biophysical Psychiatry-How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders

The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a "biophysical psychiatry," an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.

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.

Improving CNS Delivery to Brain Metastases by Blood-Tumor Barrier Disruption

Brain metastases encompass nearly 80% of all intracranial tumors. A late stage diagnosis confers a poor prognosis, with patients typically surviving less than 2 years. Poor survival can be equated to limited effective treatment modalities. One reason for the failure rates is the presence of the blood-brain barrier (BBB) and blood-tumor barrier (BTB) that limit the access of potentially effective chemotherapeutics to metastatic lesions. Strategies to overcome these barriers include new small molecule entities capable of crossing into the brain parenchyma, novel formulations of existing chemotherapies, and disruptive techniques. Here, we review BBB physiology and BTB pathophysiology. Additionally, we review the limitations of routinely practiced therapies and three current methods being explored for BBB/BTB disruption for improved delivery of chemotherapy to brain tumors.

A mathematical model for the effects of amyloid beta on intracellular calcium

The accumulation of Alzheimer's disease (AD) associated Amyloid beta (Aβ) oligomers can trigger aberrant intracellular calcium (Ca2+) levels by disrupting the intrinsic Ca2+ regulatory mechanism within cells. These disruptions can cause changes in homeostasis levels that can have detrimental effects on cell function and survival. Although studies have shown that Aβ can interfere with various Ca2+ fluxes, the complexity of these interactions remains elusive. We have constructed a mathematical model that simulates Ca2+ patterns under the influence of Aβ. Our simulations shows that Aβ can increase regions of mixed-mode oscillations leading to aberrant signals under various conditions. We investigate how Aβ affects individual flux contributions through inositol triphosphate (IP3) receptors, ryanodine receptors, and membrane pores. We demonstrate that controlling for the ryanodine receptor's maximal kinetic reaction rate may provide a biophysical way of managing aberrant Ca2+ signals. The influence of a dynamic model for IP3 production is also investigated under various conditions as well as the impact of changes in membrane potential. Our model is one of the first to investigate the effects of Aβ on a variety of cellular mechanisms providing a base modeling scheme from which further studies can draw on to better understand Ca2+ regulation in an AD environment.

Challenges in Reproducibility, Replicability, and Comparability of Computational Models and Tools for Neuronal and Glial Networks, Cells, and Subcellular Structures

The possibility to replicate and reproduce published research results is one of the biggest challenges in all areas of science. In computational neuroscience, there are thousands of models available. However, it is rarely possible to reimplement the models based on the information in the original publication, let alone rerun the models just because the model implementations have not been made publicly available. We evaluate and discuss the comparability of a versatile choice of simulation tools: tools for biochemical reactions and spiking neuronal networks, and relatively new tools for growth in cell cultures. The replicability and reproducibility issues are considered for computational models that are equally diverse, including the models for intracellular signal transduction of neurons and glial cells, in addition to single glial cells, neuron-glia interactions, and selected examples of spiking neuronal networks. We also address the comparability of the simulation results with one another to comprehend if the studied models can be used to answer similar research questions. In addition to presenting the challenges in reproducibility and replicability of published results in computational neuroscience, we highlight the need for developing recommendations and good practices for publishing simulation tools and computational models. Model validation and flexible model description must be an integral part of the tool used to simulate and develop computational models. Constant improvement on experimental techniques and recording protocols leads to increasing knowledge about the biophysical mechanisms in neural systems. This poses new challenges for computational neuroscience: extended or completely new computational methods and models may be required. Careful evaluation and categorization of the existing models and tools provide a foundation for these future needs, for constructing multiscale models or extending the models to incorporate additional or more detailed biophysical mechanisms. Improving the quality of publications in computational neuroscience, enabling progressive building of advanced computational models and tools, can be achieved only through adopting publishing standards which underline replicability and reproducibility of research results.