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

Breathing cluster in complex neuron-astrocyte networks

Brain activities are featured by spatially distributed neural clusters of coherent firings and a spontaneous slow switching of the clusters between the coherent and incoherent states. Evidences from recent in vivo experiments suggest that astrocytes, a type of glial cell regarded previously as providing only structural and metabolic supports to neurons, participate actively in brain functions by regulating the neural firing activities, yet the underlying mechanism remains unknown. Here, introducing astrocyte as a reservoir of the glutamate released from the neuron synapses, we propose the model of the complex neuron-astrocyte network, and investigate the roles of astrocytes in regulating the cluster synchronization behaviors of networked chaotic neurons. It is found that a specific set of neurons on the network are synchronized and form a cluster, while the remaining neurons are kept as desynchronized. Moreover, during the course of network evolution, the cluster is switching between the synchrony and asynchrony states in an intermittent fashion, henceforth the phenomenon of "breathing cluster." By the method of symmetry-based analysis, we conduct a theoretical investigation on the synchronizability of the cluster. It is revealed that the contents of the cluster are determined by the network symmetry, while the breathing of the cluster is attributed to the interplay between the neural network and the astrocyte. The phenomenon of breathing cluster is demonstrated in different network models, including networks with different sizes, nodal dynamics, and coupling functions. The findings shed light on the cellular mechanism of astrocytes in regulating neural activities and give insights into the state-switching of the neocortex.

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.

Modulation of Astrocytes on Mode Selection of Neuron Firing Driven by Electromagnetic Induction

Both of astrocytes and electromagnetic induction are magnificent to modulate neuron firing by introducing feedback currents to membrane potential. An improved astro-neuron model considering both of the two factors is employed to investigate their different roles in modulation. The mixing mode, defined by combination of period bursting and depolarization blockage, characterizes the effect of astrocytes. Mixing mode and period bursting alternatively appear in parameter space with respect to the amplitude of feedback current on neuron from astrocyte modulation. However, magnetic flux obviously plays a role of neuron firing inhibition. It not only repels the mixing mode but also suppresses period bursting. The mixing mode becomes period bursting mode and even resting state when astrocytes are hyperexcitable. Abnormal activities of astrocytes are capable to induce depolarization blockage to compose the mixing mode together with bursting mode. But electromagnetic induction shows its strong ability of inhibition of neuron firing, which is also illustrated in the bifurcation diagram. Indeed, the combination of the two factors and appropriate choice of parameters show the great potential to control disorder of neuron firing like epilepsy.

Assessing the Effects of Opioids on Pathological Memory by a Computational Model

Introduction:

Opioids hijack learning and memory formation mechanisms of brain and induce a pathological memory in the hippocampus. This effect is mainly mediated by modifications in glutamatergic system. Speaking more precisely, Opioids presence in a synapse inhibits blockage of N-Methyl-D-Aspartate Receptor (NMDAR) by Mg²⁺, enhances conductance of NMDAR and thus, induces false Long-Term Potentiation (LTP).

Methods:

Based on experimental observations of different researchers, we developed a mathematical model for a pyramidal neuron of the hippocampus to study this false LTP. The model contains a spine of the pyramidal neuron with NMDAR, α-Amino-3-hydroxy-5-Methyl-4-isoxazole Propionic Acid Receptors (AMPARs), and Voltage-Gated Calcium Channels (VGCCs). The model also describes Calmodulin-dependent protein Kinase II (CaMKII) and AMPAR phosphorylation processes which are assumed to be the indicators of LTP induction in the synapse.

Results:

Simulation results indicate that the effect of inhibition of blockage of NMDARs by Mg²⁺ on the false LTP is not as crucial as the effect of NMDAR’s conductance modification by opioids. We also observed that activation of VGCCs has a dominant role in inducing pathological LTP.

Conclusion:

Our results confirm that preventing this pathological LTP is possible by three different mechanisms: 1. By decreasing NMDAR’s conductance; and 2. By attenuating VGCC’s mediated current; and 3. By enhancing glutamate clearance rate from the synapse.

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.

Glial responses to implanted electrodes in the brain

The use of implants that can electrically stimulate or record electrophysiological or neurochemical activity in nervous tissue is rapidly expanding. Despite remarkable results in clinical studies and increasing market approvals, the mechanisms underlying the therapeutic effects of neuroprosthetic and neuromodulation devices, as well as their side effects and reasons for their failure, remain poorly understood. A major assumption has been that the signal-generating neurons are the only important target cells of neural-interface technologies. However, recent evidence indicates that the supporting glial cells remodel the structure and function of neuronal networks and are an effector of stimulation-based therapy. Here, we reframe the traditional view of glia as a passive barrier, and discuss their role as an active determinant of the outcomes of device implantation. We also discuss the implications that this has on the development of bioelectronic medical devices.

A new bio-inspired stimulator to suppress hyper-synchronized neural firing in a cortical network

Hyper-synchronous neural oscillations are the character of several neurological diseases such as epilepsy. On the other hand, glial cells and particularly astrocytes can influence neural synchronization. Therefore, based on the recent researches, a new bio-inspired stimulator is proposed which basically is a dynamical model of the astrocyte biophysical model. The performance of the new stimulator is investigated on a large-scale, cortical network. Both excitatory and inhibitory synapses are also considered in the simulated spiking neural network. The simulation results show that the new stimulator has a good performance and is able to reduce recurrent abnormal excitability which in turn avoids the hyper-synchronous neural firing in the spiking neural network. In this way, the proposed stimulator has a demand controlled characteristic and is a good candidate for deep brain stimulation (DBS) technique to successfully suppress the neural hyper-synchronization.

A Digital Realization of Astrocyte and Neural Glial Interactions

The implementation of biological neural networks is a key objective of the neuromorphic research field. Astrocytes are the largest cell population in the brain. With the discovery of calcium wave propagation through astrocyte networks, now it is more evident that neuronal networks alone may not explain functionality of the strongest natural computer, the brain. Models of cortical function must now account for astrocyte activities as well as their relationships with neurons in encoding and manipulation of sensory information. From an engineering viewpoint, astrocytes provide feedback to both presynaptic and postsynaptic neurons to regulate their signaling behaviors. This paper presents a modified neural glial interaction model that allows a convenient digital implementation. This model can reproduce relevant biological astrocyte behaviors, which provide appropriate feedback control in regulating neuronal activities in the central nervous system (CNS). Accordingly, we investigate the feasibility of a digital implementation for a single astrocyte constructed by connecting a two coupled FitzHugh Nagumo (FHN) neuron model to an implementation of the proposed astrocyte model using neuron-astrocyte interactions. Hardware synthesis, physical implementation on FPGA, and theoretical analysis confirm that the proposed neuron astrocyte model, with significantly low hardware cost, can mimic biological behavior such as the regulation of postsynaptic neuron activity and the synaptic transmission mechanisms.

A digital neurmorphic circuit for a simplified model of astrocyte dynamics

Recent neurophysiologic findings have shown that astrocytes (the most abundant type of glial cells) are active partners in neural information processing and regulate the synaptic transmission dynamically. Motivated by these findings, in the present research, a digital neuromorphic circuit to implement the astrocyte dynamics is developed. To model the dynamics of the intracellular Ca(2+) waves produced by astrocytes, we utilize a simplified model which considers the main physiological pathways of neuron-astrocyte interactions. Next, a digital circuit for the astrocyte dynamic is proposed which is simulated using ModelSim and finally, it is implemented in hardware on the ZedBoard. The results of hardware synthesis, FPGA implementations are in agreement with MATLAB and ModelSim simulations and confirm that the proposed digital astrocyte is suitable for applications in reconfigurable neuromorphic devices which implement biologically brain circuits.

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.

Astrocyte-neuron interactions: from experimental research-based models to translational medicine

In this chapter, we review the principal astrocyte functions and the interactions between neurons and astrocytes. We then address how the experimentally observed functions have been verified in computational models and review recent experimental literature on astrocyte-neuron interactions. Benefits of computational neuroscience work are highlighted through selected studies with neurons and astrocytes by analyzing the existing models qualitatively and assessing the relevance of these models to experimental data. Common strategies to mathematical modeling and computer simulation in neuroscience are summarized for the nontechnical reader. The astrocyte-neuron interactions are then further illustrated by examples of some neurological and neurodegenerative diseases, where the miscommunication between glia and neurons is found to be increasingly important.

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.

Functional contributions of astrocytes in synchronization of a neuronal network model

In the present study, a biologically plausible neuronal population model is developed, which considers functional outcome of neuron-astrocyte interactions. Based on established neurophysiologic findings, astrocytes dynamically regulate the synaptic transmission of neuronal networks. The employed structure is based on the main physiological and anatomical features of the CA1 subfield of the hippocampus. Utilizing our model, we demonstrate that healthy astrocytes provide appropriate feedback control in regulating neural activity. In this way, the astrocytes compensate the increase of excitation coupling strength among neurons and stabilize the normal level of synchronized behavior. Next, malfunction of astrocytes in the regulatory feedback loop is investigated. In this way, pathologic astrocytes are no longer able to regulate and/or compensate the excessive increase of the excitation level. Consequently, disruption of astrocyte signaling initiates hypersynchronous firing of neurons. Our results suggest that diminishing of neuron-astrocyte cross-talk leads to an abnormal synchronized neuronal firing, which suggests that astrocytes could be a proximal target for the treatment of related disorders including epilepsy.