Dynamics of a minimal neural model consisting of an astrocyte, a neuron, and an interneuron

Dynamic modeling of astrocyte-neuron interactions under the influence of Aβ deposition

β-amyloid (Aβ) protein accumulation is recognized as a key factor in Alzheimer's disease (AD) pathogenesis. Its effects on astrocyte function appear primarily as disturbances to intracellular calcium signaling, which, in turn, affects neuronal excitability. We propose an innovative neuron-astrocyte interaction model to examine how Aβ accumulation influences astrocyte calcium oscillation and neuronal excitability, emphasizing its significance in AD pathogenesis. This comprehensive model describes not only the response of the astrocyte to presynaptic neuron stimulation but also the release of the downstream signaling glutamate and its consequential feedback on neurons. Our research concentrates on changes within two prominent pathways affected by Aβ: the creation of Aβ astrocyte membrane pores and the enhanced sensitivity of ryanodine receptors. By incorporating these adjustments into our astrocyte model, we can reproduce previous experimental findings regarding aberrant astrocyte calcium activity and neural behavior associated with Aβ from a neural computational viewpoint. Within a specified range of Aβ influence, our numerical analysis reveals that astrocyte cytoplasmic calcium rises, calcium oscillation frequency increases, and the time to the first calcium peak shortens, indicating the disrupted astrocyte calcium signaling. Simultaneously, the neuronal firing rate and cytosolic calcium concentration increase while the threshold current for initiating repetitive firing diminishes, implying heightened neuronal excitability. Given that increased neuronal excitability commonly occurs in early AD patients and correlates with cognitive decline, our findings may highlight the importance of Aβ accumulation in AD pathogenesis and provide a theoretical basis for identifying neuronal markers in the early stages of the disease.

An investigation into the effective role of astrocyte in the hippocampus pattern separation process: A computational modeling study

A physiologically realistic three layer neuron-astrocyte network model is used to evaluate the biological mechanism in pattern separation. The innovative feature of the model is the use of a combination of three elements: neuron, interneuron and astrocyte. In the input layer, a pyramidal neuron receives input patterns from stimulus current, while in the middle layer there are two pyramidal neurons coupled with two inhibitory interneurons and an astrocyte. Finally, in the third layer, a pyramidal neuron produces the output of the model by integrating the output of two neurons from the middle layer resulting from inhibitory and excitatory connections among neurons, interneurons and the astrocyte. Results of computer simulations show that the neuron-astrocyte network within the hippocampal dentate gyrus can generate diverse, complex and different output patterns to given inputs. It is concluded that astrocytes within the dentate gyrus play an important role in the pattern separation process.

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.

Astrocytic Kir4.1 channels and gap junctions account for spontaneous epileptic seizure

Experimental recordings in hippocampal slices indicate that astrocytic dysfunction may cause neuronal hyper-excitation or seizures. Considering that astrocytes play important roles in mediating local uptake and spatial buffering of K⁺ in the extracellular space of the cortical circuit, we constructed a novel model of an astrocyte-neuron network module consisting of a single compartment neuron and 4 surrounding connected astrocytes and including extracellular potassium dynamics. Next, we developed a new model function for the astrocyte gap junctions, connecting two astrocyte-neuron network modules. The function form and parameters of the gap junction were based on nonlinear regression fitting of a set of experimental data published in previous studies. Moreover, we have created numerical simulations using the above single astrocyte-neuron network module and the coupled astrocyte-neuron network modules. Our model validates previous experimental observations that both Kir4.1 channels and gap junctions play important roles in regulating the concentration of extracellular potassium. In addition, we also observe that changes in Kir4.1 channel conductance and gap junction strength induce spontaneous epileptic activity in the absence of external stimuli.

Astrocytes are critical regulators of normal physiological activity in the central nervous system, and one of their key functions is removing extracellular K⁺. In recent years, numerous biological studies have shown that astrocytic Kir4.1 channels and gap junctions between astrocytes act as major K⁺ clearance mechanisms. Dysfunction of either of these regulatory mechanisms may cause generation of K⁺-induced seizures. However, it is unclear how and to what extent these two K⁺-regulating processes lead to spontaneous epileptic activity. These questions were addressed in the present study by constructing novel single astrocyte-neuron network models and a coupled astrocyte-neuron module network connected by an astrocyte gap junction based on existing experimental observations and previous theoretical reports. Simulation results first verified that either down-regulation of astrocytic Kir4.1 channels or a decrease of the gap junction strength between astrocytes causes neuropathological hyper-excitability and spontaneous epileptic activity. These results imply that dysfunctional astrocytes should be considered as targets for therapeutic strategies in epilepsy.

Computational simulation: astrocyte-induced depolarization of neighboring neurons mediates synchronous UP states in a neural network

Although recent reports have suggested that synchronous neuronal UP states are mediated by astrocytic activity, the mechanism responsible for this remains unknown. Astrocytic glutamate release synchronously depolarizes adjacent neurons, while synaptic transmissions are blocked. The purpose of this study was to confirm that astrocytic depolarization, propagated through synaptic connections, can lead to synchronous neuronal UP states. We applied astrocytic currents to local neurons in a neural network consisting of model cortical neurons. Our results show that astrocytic depolarization may generate synchronous UP states for hundreds of milliseconds in neurons even if they do not directly receive glutamate release from the activated astrocyte.

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.

Computational model of neuron-astrocyte interactions during focal seizure generation

Empirical research in the last decade revealed that astrocytes can respond to neurotransmitters with Ca²⁺ elevations and generate feedback signals to neurons which modulate synaptic transmission and neuronal excitability. This discovery changed our basic understanding of brain function and provided new perspectives for how astrocytes can participate not only to information processing, but also to the genesis of brain disorders, such as epilepsy. Epilepsy is a neurological disorder characterized by recurrent seizures that can arise focally at restricted areas and propagate throughout the brain. Studies in brain slice models suggest that astrocytes contribute to epileptiform activity by increasing neuronal excitability through a Ca²⁺-dependent release of glutamate. The underlying mechanism remains, however, unclear. In this study, we implemented a parsimonious network model of neurons and astrocytes. The model consists of excitatory and inhibitory neurons described by Izhikevich's neuron dynamics. The experimentally observed Ca²⁺ change in astrocytes in response to neuronal activity was modeled with linear equations. We considered that glutamate is released from astrocytes above certain intracellular Ca²⁺ concentrations thus providing a non-linear positive feedback signal to neurons. Propagating seizure-like ictal discharges (IDs) were reliably evoked in our computational model by repeatedly exciting a small area of the network, which replicates experimental results in a slice model of focal ID in entorhinal cortex. We found that the threshold of focal ID generation was lowered when an excitatory feedback-loop between astrocytes and neurons was included. Simulations show that astrocytes can contribute to ID generation by directly affecting the excitatory/inhibitory balance of the neuronal network. Our model can be used to obtain mechanistic insights into the distinct contributions of the different signaling pathways to the generation and propagation of focal IDs.

P2X7 receptor-mediated calcium dynamics in HEK293 cells: experimental characterization and modelling approach

The P2X7 receptor (P2X7R) induces ionotropic Ca²⁺ signalling in different cell types. It plays an important role in the immune response and in the nervous system. Here, the mechanisms underlying intracellular Ca²⁺ variations evoked by 3'-O-(4-benzoyl)benzoyl-ATP (BzATP), a potent agonist of the P2X7R, in transfected HEK293 cells, are investigated both experimentally and theoretically. We propose a minimal model of P2X7R that is capable of reproducing, qualitatively and quantitatively, the experimental data. This approach was also adopted for the P2X7R variant, which lacks the entire C-terminus tail (trP2X7R). Then we introduce a biophysical model describing the Ca²⁺ dynamics in HEK293. Our model gives an account of the ionotropic Ca²⁺ influx evoked by BzATP on the basis of the kinetics model of P2X7R. To explain the complex Ca²⁺ responses evoked by BzATP, the model predicted that an impairment in Ca²⁺ extrusion flux through the plasma membrane is a key factor for Ca²⁺ homeostasis in HEK293 cells.

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.

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.

Effects of transmitters and amyloid-beta peptide on calcium signals in rat cortical astrocytes: Fura-2AM measurements and stochastic model simulations

Background

To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25–35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals.

Methodology/Principal Findings

Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25–35. A25–35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25–35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements.

Conclusions/Significance

Nanomolar A25–35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25–35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system.

Astrocytes and human cognition: modeling information integration and modulation of neuronal activity

Recent research focusing on the participation of astrocytes in glutamatergic tripartite synapses has revealed mechanisms that support cognitive functions common to human and other mammalian species, such as learning, perception, conscious integration, memory formation/retrieval and the control of voluntary behavior. Astrocytes can modulate neuronal activity by means of release of glutamate, d-serine, adenosine triphosphate and other signaling molecules, contributing to sustain, reinforce or depress pre- and post-synaptic membranes. We review molecular mechanisms present in tripartite synapses and model the cognitive role of astrocytes. Single protoplasmic astrocytes operate as a "Local Hub", integrating information patterns from neuronal and glial populations. Two mechanisms, here modeled as the "domino" and "carousel" effects, contribute to the formation of intercellular calcium waves. As waves propagate through gap junctions and reach other types of astrocytes (interlaminar, polarized, fibrous and varicose projection), the active astroglial network functions as a "Master Hub" that integrates results of distributed processing from several brain areas and supports conscious states. Response of this network would define the effect exerted on neuronal plasticity (membrane potentiation or depression), behavior and psychosomatic processes. Theoretical results of our modeling can contribute to the development of new experimental research programs to test cognitive functions of astrocytes.