Functional modeling of astrocytes in epilepsy: a feedback system perspective

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.

The important role of glial transmitters released by astrocytes in Alzheimer's disease: A perspective from dynamical modeling

This paper aims to establish a coupling model of neuronal populations and astrocytes and, on this basis, explore the possible mechanism of electroencephalography (EEG) slowing in Alzheimer's disease (AD) from the viewpoint of dynamical modeling. First and foremost, excitatory and inhibitory time constants are shown to induce the early symptoms of AD. The corresponding dynamic nature is mainly due to changes in the amplitude and frequency of the oscillatory behavior. However, there are also a few cases that can be attributed to the change of the oscillation mode caused by the limit cycle bifurcation and birhythmicity. Then, an improved neural mass model influenced by astrocytes is proposed, considering the important effects of glutamate and adenosine triphosphate (ATP) released by astrocytes on the synaptic transmission process reported in experiments. The results show that a dysfunctional astrocyte disrupts the physiological state, causing three typical EEG slowing phenomena reported clinically: the decreased dominant frequency, the decreased rhythmic activity in the α band, and the increased rhythmic activity in the δ+θ band. In addition, astrocytes may control AD when the effect of ATP on synaptic connections is greater than that of glutamate. The control rate depends on the ratio of the effect of glutamate on excitatory and inhibitory synaptic connections. These modeling results can not only reproduce some experimental and clinical results, but, more importantly, may offer a prediction of some underlying phenomena, helping to inspire the disease mechanisms and therapeutic methods of targeting astrocytes.

Computational Models for Calcium-Mediated Astrocyte Functions

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

DESYNCHRONIZATION OF TWO COUPLED LIMIT-CYCLE OSCILLATORS USING AN ASTROCYTE-INSPIRED CONTROLLER

Astrocytes have potential to break synchrony between neurons. Authors' recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an efficient controller, parameters of controller are tuned through an optimization algorithm. The proposed bio-inspired controller takes advantages of three important properties: (1) the controller desynchronizes the oscillators without any undesirable effects (e.g. stopping, annihilating or starting divergent oscillations); (2) it consumes little effort to preserve the desirable desynchronized state; and (3) the controller is robust with respect to parameters' variations. Simulation results reveal the ability of the proposed controller.

Information transmission in a neuron-astrocyte coupled model

A coupled model containing two neurons and one astrocyte is constructed by integrating Hodgkin-Huxley neuronal model and Li-Rinzel calcium model. Based on this hybrid model, information transmission between neurons is studied numerically. Our results show that when the successive spikes are produced in neuron 1 (N1), the bursting-like spikes (BLSs) occur in two neurons simultaneously during the spikes being transferred to neuron 2 (N2). The existence of the astrocyte and a higher expression level of mGluRs facilitate the occurrence of BLSs, but the rate of occurrence is not sensitive to the parameters. Furthermore, time delay τ occurs during the information transmission, and τ is almost independent of the effect of the astrocyte. Additionally, we found that low coupling strength may result in the distortion of the information, and this distortion is also proven to be almost independent of the astrocyte.

A phase plane analysis of neuron-astrocyte interactions

Intensive experimental studies have shown that astrocytes are active partners in modulation of synaptic transmission. In the present research, we study neuron-astrocyte signaling using a biologically inspired model of one neuron synapsing one astrocyte. In this model, the firing dynamics of the neuron is described by the Morris-Lecar model and the Ca(2+) dynamics of a single astrocyte explained by a functional model introduced by Postnov and colleagues. Using the coupled neuron-astrocyte model and based on the results of the phase plane analyses, it is demonstrated that the astrocyte is able to activate the silent neuron or change the neuron spiking frequency through bidirectional communication. This suggests that astrocyte feedback signaling is capable of modulating spike transmission frequency by changing neuron spiking frequency. This effect is described by a saddle-node on invariant circle bifurcation in the coupled neuron-astrocyte model. In this way, our results suggest that the neuron-astrocyte crosstalk has a fundamental role in producing diverse neuronal activities and therefore enhances the information processing capabilities of the brain.

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

Based on recent findings, astrocytes, a subtype of glial cells, dynamically regulate the synaptic transmission of neuronal networks. In this research, a biologically inspired neuronal network model is constructed by connecting two Morris-Lecar neuron models. In this minimal network model, neuron-astrocyte interactions are considered in a functional-based procedure. Utilizing the developed model and according to the theoretical analysis carried out in the article, it is confirmed that, the astrocyte increases the threshold value of synchronization and provides appropriate feedback control in regulating the neural activities. Therefore, the healthy astrocyte has the potential to desynchronize the synchrony between two coupled neurons. Next, we investigate malfunction of the astrocyte in the regulatory feedback loop. Mathematically, we verify that pathologic astrocyte is no longer able to increase the synchronization threshold and therefore, it cannot compensate excessive increase in the excitation level. The main reason behind this is the fact that healthy astrocyte can optimally increase the input current of the individual neurons, while the so-called pathological astrocyte is unable to modify correctly the amount of this current. Consequently, disruptions of the signaling function of astrocyte initiate the hypersynchronous firing of neurons. In other words, reduction in neuron-astrocyte cross-talk will lead to synchronized firing of neurons. Therefore, our results propose that the astrocyte could have a key role in stabilizing neural activity.