A mathematical model for astrocytes mediated LTP at single hippocampal synapses

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.

Trans-Anethole Alleviates Trimethyltin Chloride-Induced Impairments in Long-Term Potentiation

Trans-anethole is an aromatic compound that has been studied for its anti-inflammation, anticonvulsant, antinociceptive, and anticancer effects. A recent report found that trans-anethole exerted neuroprotective effects on the brain via multiple pathways. Since noxious stimuli may both induce neuronal cell injury and affect synaptic functions (e.g., synaptic transmission or plasticity), it is important to understand whether the neuroprotective effect of trans-anethole extends to synaptic plasticity. Here, the effects of trimethyltin (TMT), which is a neurotoxic organotin compound, was investigated using the field recording method on hippocampal slice of mice. The influence of trans-anethole on long-term potentiation (LTP) was also studied for both NMDA receptor-dependent and NMDA receptor–independent cases. The action of trans-anethole on TMT-induced LTP impairment was examined, too. These results revealed that trans-anethole enhances NMDA receptor-dependent and -independent LTP and alleviates TMT-induced LTP impairment. These results suggest that trans-anethole modulates hippocampal LTP induction, prompting us to speculate that it may be helpful for improving cognitive impairment arising from neurodegenerative diseases, including Alzheimer’s disease.

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.

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.

A Computational Study on Synaptic Plasticity Regulation and Information Processing in Neuron-Astrocyte Networks

Postsynaptic ionotropic receptors critically shape synaptic currents and underpin their activity-dependent plasticity. In recent years, regulation of expression of these receptors by slow inward and outward currents mediated by gliotransmitter release from astrocytes has come under scrutiny as a potentially important mechanism for the regulation of synaptic information transfer. In this study, we consider a model of astrocyte-regulated synapses to investigate this hypothesis at the level of layered networks of interacting neurons and astrocytes. Our simulations hint that gliotransmission sustains the transfer function across layers, although it decorrelates the neuronal activity from the signal pattern. Overall, our results make clear how astrocytes could transform neuronal activity by inducing a lowfrequency modulation of postsynaptic activity.

Astrocyte as Spatiotemporal Integrating Detector of Neuronal Activity

The functional role of astrocyte calcium signaling in brain information processing was intensely debated in recent decades. This interest was motivated by high resolution imaging techniques showing highly developed structure of distal astrocyte processes. Another point was the evidence of bi-directional astrocytic regulation of neuronal activity. To analyze the effects of interplay of calcium signals in processes and in soma mediating correlations between local signals and the cell-level response of the astrocyte we proposed spatially extended model of the astrocyte calcium dynamics. Specifically, we investigated how spatiotemporal properties of Ca²⁺ dynamics in spatially extended astrocyte model can coordinate (e.g., synchronize) networks of neurons and synapses.

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.

Computational modeling of opioid-induced synaptic plasticity in hippocampus

According to a broad range of research, opioids consumption can lead to pathological memory formation. Experimental observations suggested that hippocampal glutamatergic synapses play an indispensable role in forming such a pathological memory. It has been suggested that memory formation at the synaptic level is developed through LTP induction. Here, we attempt to computationally indicate how morphine induces pathological LTP at hippocampal CA3-CA1 synapses. Then, based on simulations, we will suggest how one can prevent this type of pathological LTP. To this purpose, a detailed computational model is presented, which consists of one pyramidal neuron and one interneuron both from CA3, one CA1 pyramidal neuron, and one astrocyte. Based on experimental findings morphine affects the hippocampal neurons in three primary ways: 1) disinhibitory mechanism of interneurons in CA3, 2) enhancement of NMDARs current by μ Opioid Receptor (μOR) activation and 3) by attenuation of astrocytic glutamate reuptake ability. By utilizing these effects, simulations were implemented. Our results indicate that morphine can induce LTP by all aforementioned possible mechanisms. Based on our simulation results, attenuation of pathologic LTP achieved mainly by stimulation of astrocytic glutamate transporters, down-regulation of the astrocytic metabotropic glutamate receptors (mGlurs) or by applying NMDAR’s antagonist. Based on our observations, we suggest that astrocyte has a dominant role in forming addiction-related memories. This finding may help researchers in exploring drug actions for preventing relapse.

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.

Mechanisms of heterosynaptic metaplasticity

Synaptic plasticity is fundamental to the neural processes underlying learning and memory. Interestingly, synaptic plasticity itself can be dynamically regulated by prior activity, in a process termed 'metaplasticity', which can be expressed both homosynaptically and heterosynaptically. Here, we focus on heterosynaptic metaplasticity, particularly long-range interactions between synapses spread across dendritic compartments, and review evidence for intracellular versus intercellular signalling pathways leading to this effect. Of particular interest is our previously reported finding that priming stimulation in stratum oriens of area CA1 in the hippocampal slice heterosynaptically inhibits subsequent long-term potentiation and facilitates long-term depression in stratum radiatum. As we have excluded the most likely intracellular signalling pathways that might mediate this long-range heterosynaptic effect, we consider the hypothesis that intercellular communication may be critically involved. This hypothesis is supported by the finding that extracellular ATP hydrolysis, and activation of adenosine A2 receptors are required to induce the metaplastic state. Moreover, delivery of the priming stimulation in stratum oriens elicited astrocytic calcium responses in stratum radiatum. Both the astrocytic responses and the metaplasticity were blocked by gap junction inhibitors. Taken together, these findings support a novel intercellular communication system, possibly involving astrocytes, being required for this type of heterosynaptic metaplasticity.

A possible role of astrocytes in contextual memory retrieval: An analysis obtained using a quantitative framework

The hippocampus is central to our understanding of memory formation and retrieval. Its CA1 region is known for encoding contextual memory. Here, using a computational approach, which embeds existing physiological data, we propose a particular role of astrocytes in contextual memory retrieval. We provide a quantitative framework under which the astrocyte modulates the firing of a context-associated CA1 pyramidal neurons, resulting in a prominent tuning of neurons to a delta rhythm. Using the very framework, we further studied astrocytic function in the modulation of neuronal firing under pathological conditions, i.e., during astrocytic induction of epileptiform discharge in CA1 pyramidal neurons. Thus, we provide a quantitative framework that would aid understanding of the Schaffer collateral-CA1 tripartite synapse in health and disease.

Novel Spiking Neuron-Astrocyte Networks based on nonlinear transistor-like models of tripartite synapses

In this paper a novel and efficient computational implementation of a Spiking Neuron-Astrocyte Network (SNAN) is reported. Neurons are modeled according to the Izhikevich formulation and the neuron-astrocyte interactions are intended as tripartite synapsis and modeled with the previously proposed nonlinear transistor-like model. Concerning the learning rules, the original spike-timing dependent plasticity is used for the neural part of the SNAN whereas an ad-hoc rule is proposed for the astrocyte part. SNAN performances are compared with a standard spiking neural network (SNN) and evaluated using the polychronization concept, i.e., number of co-existing groups that spontaneously generate patterns of polychronous activity. The astrocyte-neuron ratio is the biologically inspired value of 1.5. The proposed SNAN shows higher number of polychronous groups than SNN, remarkably achieved for the whole duration of simulation (24 hours).

A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity

In this paper, we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca(2 + ) dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been modeled. As an application, this model clearly shows synaptic potentiation in the hippocampal region, i.e., astrocyte Ca(2 + ) mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea and Araque (Science 317, 1083-1086, 2007); Henneberger et al. (Nature 463, 232-236, 2010); Navarrete et al. (PLoS Biol. 10, e1001259, 2012)).