Giant glial cell: new insight through mechanism-based modeling

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

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

Astrocytic modulation on neuronal electric mode selection induced by magnetic field effect

Astrocytes as well as electromagnetic induction have been primarily considered as main factors in regulating neuronal firing patterns in the recent decade. In this work, an improved neuron-astrocyte model in consideration of the modulation of astrocytes and the electromagnetic induction is employed to explore the extend to which both of the factors affect the firing modes of the neurons. The "alternation mode", defined as the alternative of neural normal spiking mode with the high-frequency bursting-like mode, clearly shows the functions of astrocytes on neurons. Moreover, the firing pattern of the neuron becomes more abnormal when astrocytes are hyper-excitable, the reason why the abnormal coupling of the astrocyte leads to the "alternation mode" of the neuron have been studied. In addition, the effect of electromagnetic induction manifests nonlinear characteristic towards neurons, complex firing modes of neurons are observed in the weaker field and a switching mode consists with quiescent and spiking mode appears when there is a higher stronger field. This approved model can reveal the normal or abnormal electric activities of neuron considered electromagnetic induction induced by the degree of excitability of the astrocyte. These results can provide potential understanding about the effects of astrocyte on neuronal activity when the coupling of electromagnetic field is considered.

Modeling of Astrocyte Networks: Toward Realistic Topology and Dynamics

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

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

The idea that astrocytes may be active partners in synaptic information processing has recently emerged from abundant experimental reports. Because of their spatial proximity to neurons and their bidirectional communication with them, astrocytes are now considered as an important third element of the synapse. Astrocytes integrate and process synaptic information and by doing so generate cytosolic calcium signals that are believed to reflect neuronal transmitter release. Moreover, they regulate neuronal information transmission by releasing gliotransmitters into the synaptic cleft affecting both pre- and postsynaptic receptors. Concurrent with the first experimental reports of the astrocytic impact on neural network dynamics, computational models describing astrocytic functions have been developed. In this review, we give an overview over the published computational models of astrocytic functions, from single-cell dynamics to the tripartite synapse level and network models of astrocytes and neurons.

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.

Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms

Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation ('depolarisation block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K( + )]₀ causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K( + )](o) conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin-Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K( + )]₀-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.

Dynamical patterns of calcium signaling in a functional model of neuron-astrocyte networks

We propose a functional mathematical model for neuron-astrocyte networks. The model incorporates elements of the tripartite synapse and the spatial branching structure of coupled astrocytes. We consider glutamate-induced calcium signaling as a specific mode of excitability and transmission in astrocytic-neuronal networks. We reproduce local and global dynamical patterns observed experimentally.