Bidirectional coupling between astrocytes and neurons mediates learning and dynamic coordination in the brain: a multiple modeling approach

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.

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution. However, these metastable dynamical patterns were easily stabilized in the presence of small variations in coupling strength. Metastable rotating waves and their pinning in the presence of asymmetry in the direction of coupling and the disappearance of metastable dynamical patterns due to asymmetry in the output function of a neuron were also examined. Further, in a two-dimensional array of neurons with nearest-neighbor coupling, intrinsically one-dimensional patterns were dominant in transients, and self-excitation in these neurons affected the metastable dynamical patterns.

The hallmarks of Parkinson's disease

Since the discovery of dopamine as a neurotransmitter in the 1950s, Parkinson's disease (PD) research has generated a rich and complex body of knowledge, revealing PD to be an age-related multifactorial disease, influenced by both genetic and environmental factors. The tremendous complexity of the disease is increased by a nonlinear progression of the pathogenesis between molecular, cellular and organic systems. In this minireview, we explore the complexity of PD and propose a systems-based approach, organizing the available information around cellular disease hallmarks. We encourage our peers to adopt this cell-based view with the aim of improving communication in interdisciplinary research endeavors targeting the molecular events, modulatory cell-to-cell signaling pathways and emerging clinical phenotypes related to PD.

Enaction and Psychology

The enactive approach to cognitive science aims to provide an account of the mind that is both naturalistic and nonreductive. Psychological activity is viewed not as occurring within the individual organism but in the engagement between the motivated autonomous agent and their context (including their social context). The approach has been developing within the fields of philosophy, artificial life, and computational biology for the past two decades and is now growing within the domain of psychology more generally. In this short paper we outline the conceptual framework of the enactive approach. Illustrative research questions and methods for investigation are also broached, including some existing examples from theoretical, behavioral, and computational modeling research. It is suggested that an enactive psychology provides the basis for the conceptual framework of the enactive approach.

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.

Outline of a general theory of behavior and brain coordination

Much evidence suggests that dynamic laws of neurobehavioral coordination are sui generis: they deal with collective properties that are repeatable from one system to another and emerge from microscopic dynamics but may not (even in principle) be deducible from them. Nevertheless, it is useful to try to understand the relationship between different levels while all the time respecting the autonomy of each. We report a program of research that uses the theoretical concepts of coordination dynamics and quantitative measurements of simple, well-defined experimental model systems to explicitly relate neural and behavioral levels of description in human beings. Our approach is both top-down and bottom-up and aims at ending up in the same place: top-down to derive behavioral patterns from neural fields, and bottom-up to generate neural field patterns from bidirectional coupling between astrocytes and neurons. Much progress can be made by recognizing that the two approaches--reductionism and emergentism--are complementary. A key to understanding is to couch the coordination of very different things--from molecules to thoughts--in the common language of coordination dynamics.

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).

Bi-directional astrocytic regulation of neuronal activity within a network

The concept of a tripartite synapse holds that astrocytes can affect both the pre- and post-synaptic compartments through the Ca²⁺-dependent release of gliotransmitters. Because astrocytic Ca²⁺ transients usually last for a few seconds, we assumed that astrocytic regulation of synaptic transmission may also occur on the scale of seconds. Here, we considered the basic physiological functions of tripartite synapses and investigated astrocytic regulation at the level of neural network activity. The firing dynamics of individual neurons in a spontaneous firing network was described by the Hodgkin–Huxley model. The neurons received excitatory synaptic input driven by the Poisson spike train with variable frequency. The mean field concentration of the released neurotransmitter was used to describe the presynaptic dynamics. The amplitudes of the excitatory postsynaptic currents (PSCs) obeyed the gamma distribution law. In our model, astrocytes depressed the presynaptic release and enhanced the PSCs. As a result, low frequency synaptic input was suppressed while high frequency input was amplified. The analysis of the neuron spiking frequency as an indicator of network activity revealed that tripartite synaptic transmission dramatically changed the local network operation compared to bipartite synapses. Specifically, the astrocytes supported homeostatic regulation of the network activity by increasing or decreasing firing of the neurons. Thus, the astrocyte activation may modulate a transition of neural network into bistable regime of activity with two stable firing levels and spontaneous transitions between them.

The computational power of astrocyte mediated synaptic plasticity

Research in the last two decades has made clear that astrocytes play a crucial role in the brain beyond their functions in energy metabolism and homeostasis. Many studies have shown that astrocytes can dynamically modulate neuronal excitability and synaptic plasticity, and might participate in higher brain functions like learning and memory. With the plethora of astrocyte mediated signaling processes described in the literature today, the current challenge is to identify, which of these processes happen under what physiological condition, and how this shapes information processing and, ultimately, behavior. To answer these questions will require a combination of advanced physiological, genetical, and behavioral experiments. Additionally, mathematical modeling will prove crucial for testing predictions on the possible functions of astrocytes in neuronal networks, and to generate novel ideas as to how astrocytes can contribute to the complexity of the brain. Here, we aim to provide an outline of how astrocytes can interact with neurons. We do this by reviewing recent experimental literature on astrocyte-neuron interactions, discussing the dynamic effects of astrocytes on neuronal excitability and short- and long-term synaptic plasticity. Finally, we will outline the potential computational functions that astrocyte-neuron interactions can serve in the brain. We will discuss how astrocytes could govern metaplasticity in the brain, how they might organize the clustering of synaptic inputs, and how they could function as memory elements for neuronal activity. We conclude that astrocytes can enhance the computational power of neuronal networks in previously unexpected ways.

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.

A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking

Over the past decades, our view of astrocytes has switched from passive support cells to active processing elements in the brain. The current view is that astrocytes shape neuronal communication and also play an important role in many neurodegenerative diseases. Despite the growing awareness of the importance of astrocytes, the exact mechanisms underlying neuron-astrocyte communication and the physiological consequences of astrocytic-neuronal interactions remain largely unclear. In this work, we define a modeling framework that will permit to address unanswered questions regarding the role of astrocytes. Our computational model of a detailed glutamatergic synapse facilitates the analysis of neural system responses to various stimuli and conditions that are otherwise difficult to obtain experimentally, in particular the readouts at the sub-cellular level. In this paper, we extend a detailed glutamatergic synaptic model, to include astrocytic glutamate transporters. We demonstrate how these glial transporters, responsible for the majority of glutamate uptake, modulate synaptic transmission mediated by ionotropic AMPA and NMDA receptors at glutamatergic synapses. Furthermore, we investigate how these local signaling effects at the synaptic level are translated into varying spatio-temporal patterns of neuron firing. Paired pulse stimulation results reveal that the effect of astrocytic glutamate uptake is more apparent when the input inter-spike interval is sufficiently long to allow the receptors to recover from desensitization. These results suggest an important functional role of astrocytes in spike timing dependent processes and demand further investigation of the molecular basis of certain neurological diseases specifically related to alterations in astrocytic glutamate uptake, such as epilepsy.

Self-repair in a bidirectionally coupled astrocyte-neuron (AN) system based on retrograde signaling

In this paper we demonstrate that retrograde signaling via astrocytes may underpin self-repair in the brain. Faults manifest themselves in silent or near silent neurons caused by low transmission probability (PR) synapses; the enhancement of the transmission PR of a healthy neighboring synapse by retrograde signaling can enhance the transmission PR of the "faulty" synapse (repair). Our model of self-repair is based on recent research showing that retrograde signaling via astrocytes can increase the PR of neurotransmitter release at damaged or low transmission PR synapses. The model demonstrates that astrocytes are capable of bidirectional communication with neurons which leads to modulation of synaptic activity, and that indirect signaling through retrograde messengers such as endocannabinoids leads to modulation of synaptic transmission PR. Although our model operates at the level of cells, it provides a new research direction on brain-like self-repair which can be extended to networks of astrocytes and neurons. It also provides a biologically inspired basis for developing highly adaptive, distributed computing systems that can, at fine levels of granularity, fault detect, diagnose and self-repair autonomously, without the traditional constraint of a central fault detect/repair unit.