A neuron–astrocyte transistor-like model for neuromorphic dressed neurons

doi:10.1016/j.neunet.2011.03.013

Neural Networks

Volume 24, Issue 7, September 2011, Pages 679-685

https://doi.org/10.1016/j.neunet.2011.03.013 Get rights and content

Abstract

Experimental evidences on the role of the synaptic glia as an active partner together with the bold synapse in neuronal signaling and dynamics of neural tissue strongly suggest to investigate on a more realistic neuron–glia model for better understanding human brain processing. Among the glial cells, the astrocytes play a crucial role in the tripartite synapsis, i.e. the dressed neuron. A well-known two-way astrocyte–neuron interaction can be found in the literature, completely revising the purely supportive role for the glia. The aim of this study is to provide a computationally efficient model for neuron–glia interaction. The neuron–glia interactions were simulated by implementing the Li–Rinzel model for an astrocyte and the Izhikevich model for a neuron. Assuming the dressed neuron dynamics similar to the nonlinear input–output characteristics of a bipolar junction transistor, we derived our computationally efficient model. This model may represent the fundamental computational unit for the development of real-time artificial neuron–glia networks opening new perspectives in pattern recognition systems and in brain neurophysiology.

Introduction

Traditionally, astrocytes have been considered to be non-excitable cells of the brain able to provide only structural and metabolic support to the neurons. However, in the last twenty years, this view has been changing. In fact, the large amount of experimental data characterizing the communication processes between astrocytes and astrocyte–neurons showed the possible role of glial cells in the dynamics of neural tissue. These recent results on the active functional role of the synaptic glia cells together with synapses in neuronal signaling (Fellin and Carmignoto, 2004, Newman, 2003, Nobile et al., 2003, Parpura et al., 1994, Parpura and Haydon, 2000) propose new approaches to applied neuroscience. Investigations on a neuron–glia alternative for the basis of human brain information processing are currently developing (Volman, Ben-Jacob, & Levine, 2007).

From a physiological point of view, astrocytes regulate the synaptic signaling current between two neurons modulating the amount of neurotransmitters into the synaptic cleft through inter- and intracellular calcium dynamics (Di Garbo et al., 2007, Newman, 2003, Parpura and Haydon, 2000, Volman et al., 2007). In detail, calcium dynamics is controlled by the interplay of calcium-induced calcium release, a nonlinear amplification method triggering the modulation of the pre-synaptic and post-synaptic neural activities and promoting depolarizing currents in neurons (De Pitta et al., 2009, Volman et al., 2007). The interplay of calcium-induced calcium release nonlinear amplification method is dependent on calcium channels opening to calcium stores such as the endoplasmic reticulum, and the action of active transporters that enable a reverse flux (De Pitta et al., 2009, De Pitta’ et al., 2008, Volman et al., 2007). The level of inositol 1, 4, 5-trisphosphate is directly controlled by signals impinging on the cell from its external environment. The elevation of the intracellular calcium level in astrocytes, promoted by the extracellular glutamate, triggers the release of glutamate from the astrocyte, modulating the pre-synaptic and post-synaptic depolarizing currents in neurons. Furthermore, inositol 1, 4, 5-trisphosphate dynamics are encoded by nonlinear amplitude and frequency modulation phenomena, while calcium oscillations are inherently frequency modulated (De Pitta’ et al., 2008).

Concerning derived nonlinear models, there are no extensive mathematical studies on dynamics of neuron–glia interactions, and the first systematic attempts to build a self-consistent model of the tripartite synapse in order to seize its dynamical and computational properties are under development (Allegrini et al., 2009, De Pitta’ et al., 2008, Di Garbo et al., 2007, Volman et al., 2007). Regarding single neurons, the most accurate biophysical model has been developed by Hodgkin and Huxley (Hodgkin & Huxley, 1952), following the so-called Hodgkin and Huxley Model (HHM). This model is able to exactly reproduce the shape of an action potential taking into account the involved ionic currents. The HHM is onerous to be implemented since it requires about 1200 FLOPs to simulate one millisecond of a single neuron activity. Several models attempt to reduce the mathematical complexity of such a neuron model, i.e. the Morris–Lecar model (Morris & Lecar, 1981) takes about 600 FLOPs, while the FitzHugh–Nagumo model (FitzHugh, 1961) takes about 72 FLOPs for one millisecond of neuron activity.

Izhikevich recently developed a simple model for an artificial neuron (Izhikevich, 2003, Izhikevich, 2004). This model is able to reproduce several functionalities of a biological neuron. It takes 13 FLOPs to emulate one millisecond of neuron activity. Regarding astrocytes, the Li–Rinzel (LR) model has been used to describe calcium dynamics (Li and Rinzel, 1994, Nadkarni and Jung, 2004). Considering a minimal neural network model made up of two coupled units, a neuron and an astrocyte, (the so-called “dressed” neuron), we can adopt the mathematical formulation for the neuron–glia signaling according to Nadkarni and Jung (Nadkarni and Jung, 2004, Nadkarni and Jung, 2003). These authors showed how the astrocyte is critical for the generation of firing activity of the neuron. More complete models, including plasma membrane calcium fluxes, suggest several differences compared to the model obtained by these authors (Di Garbo et al., 2007).

From an engineering point of view, this behavior resembles the functionalities of a Bipolar Junction Transistor (BJT), where the collector–emitter current can be viewed as being controlled by the base–emitter current. A transistor-like model for the neuron–astrocyte information processes could open new dramatic perspectives in neuroscience and neuroengineering, as well as in modern electronics. In this work we demonstrate how the dressed neuron signaling can be formalized through a transistor-like transfer function, starting from evidences in experimental data obtained by Nadkarni and Jung model (Nadkarni and Jung, 2004, Nadkarni and Jung, 2003). Future processing architectures can be organized around bi-dimensional grids of such an interacting artificial dressed neuron.

Section snippets

Experimental and biophysical models of tripartite synapses

The tripartite (three-part) synapse involves: a pre-synaptic neuron releasing neurotransmitters (glutamate) which activates or inhibits the activity of a post-synaptic neuron, the post-synaptic neuron and the astrocyte which protects cells by taking up glutamate to prevent overexcitation and secretes growth factors (Newman, 2003, Parpura et al., 1994, Parpura and Haydon, 2000, Volman et al., 2007). The astrocyte provides energy via glucose and modulates receptors function by locally released

Neuron–astrocyte transistor-like model

We implemented and simulated the Nadkarni and Jung expressions and the LR model for pre-synaptic current, $I_{n} (t)$ and the $r_{IP 3}$ data. We adopted the original parameters used in the LR model (Table 2). By varying $I_{n} (t)$ and $r_{IP 3}$ , two curves (Fig. 2) identify three separate zones where three different $I_{astro} (t)$ behaviors are defined (Fig. 3).

The two threshold curves are identified using a fitting procedure based on Least-Mean-Square Algorithm (LMS Algorithm) as follows: ${\begin{matrix} I_{t h_{1}} = z_{1} \cdot \sqrt[n_{1}]{r_{IP 3} - p_{1}} \\ I_{t h_{2}} = z_{2} \cdot r_{IP 3} - \end{matrix}$

Conclusions

In this article, we described the dressed neuron signaling through a nonlinear transistor-like transfer function. We derived the astrocytic current in function of both the pre-synaptic neuron current and the $r_{IP 3}$ of the astrocyte starting from computational data obtained implementing existing biophysical neuron–glia models (LR model). This work represents a computationally efficient model describing the synapse and astrocyte couplings. Through the model here proposed, indeed, it is possible to

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A neuron–astrocyte transistor-like model for neuromorphic dressed neurons

Abstract

Introduction

Section snippets

Experimental and biophysical models of tripartite synapses

Neuron–astrocyte transistor-like model

Conclusions

BioSystems

Biophysical Journal

Biophysical Journal

Trends in Neurosciences

FEBS Letters

The influence of the astrocyte field on neural dynamics and synchronization

Journal of Biological Physics

Glutamate regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes

Journal of Biological Physics

Coexistence of amplitude and frequency modulations in intracellular calcium dynamics

Physical Review E

Neuron-to-astrocyte signalling in the brain represents a distinct multifunctional unit

Neural Computation