Recent studies in neuroscience show that astrocytes alongside neurons participate in modulating synapses. It led to the new concept of “tripartite synapse”, which means that a synapse consists of three parts: presynaptic neuron, postsynaptic neuron, and neighboring astrocytes. However, it is still unclear what role is played by the astrocytes in the tripartite synapse. Detailed biocomputational modeling may help generate testable hypotheses. In this article, we aim to study the role of astrocytes in synaptic plasticity by exploring whether tripartite synapses are capable of improving the performance of a neural network. To achieve this goal, we developed a computational model of astrocytes based on the Izhikevich simple model of neurons. Next, two neural networks were implemented. The first network was only composed of neurons and had standard bipartite synapses. The second network included both neurons and astrocytes and had tripartite synapses. We used reinforcement learning and tested the networks on categorizing random stimuli. The results show that tripartite synapses are able to improve the performance of a neural network and lead to higher accuracy in a classification task. However, the bipartite network was more robust to noise. This research provides computational evidence to begin elucidating the possible beneficial role of astrocytes in synaptic plasticity and performance of a neural network.
Neurons and glia cells are building blocks of the human brain. Neurons are defined based on their ability to produce action potentials; the other cells in the human brain, which do not support this ability, are called glia cells [
These findings are important because glia cells are up to 50 times more numerous than neurons [
Given the mounting evidence that astrocytes contribute to neural computation, a follow–up question is what roles do astrocytes play in neural computation? One intriguing possibility is that astrocytes could contribute to learning and memory [
Many computational neuroscience models of astrocytes have been proposed to account for the many differences between neurons and astrocytes [
Note that many existing astrocyte models do not account for one or both these characteristics. For example, some existing models are not presenting a linear I–V curve in astrocytes [
This research aimed to study the role of astrocytes in the performance of neural networks. More specifically, we intended to test whether astrocytes are capable of improving the performance of a spiking neural network. The reminder of this article is organized as follows. First, Section
Although astrocytes recently received much attention in neurophysiology [
The Izhikevich model is a computationally efficient, biologically plausible, model of neurons that allows for real-time simulation of networks of spiking neurons on a desktop PC [
Parameter values used to model neurons and astrocytes based on the Izhikevich simple model of neurons. The neuron parameters represent a pyramidal neuron in neocortex [
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Neuron | 100 | -60 | -40 | 0.7 | 0.03 | -2 | -50 | 100 | 35 |
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Astrocyte | 6 | -70 | | | | | -50 | 100 | 35 |
The Izhikevich model of neurons is flexible in modeling different types of neurons. However, the Izhikevich model has never been used to model astrocytes, and no parameter values were previously available. As shown in Figure
The current/voltage relationship (IV curve) for a biological astrocyte (a) Pannasch et al. [
Biological astrocyte
Astrocyte model
Figure
Membrane potential of the astrocyte model by injecting the current of I=4mA from t=100ms to t=1000ms.
This section proposed a new biologically realistic astrocyte model that accurately represent the linear IV relationship and does not spike. Given that the natural shape of the IV relationship in the Izhikevich model is nonlinear, the reader may wonder why we chose not to use a linear equation to model astrocytes instead of Izhikevich neuron’s equations. Our choice was motivated by the fact that the Izhikevich model is popular and well-defined. Hence, the proposed model allows for modeling astrocytes simply by modifying the values of the parameters of available neurons. This makes the inclusion of astrocytes convenient in neural networks using the Izhikevich model, as astrocytes can be modeled as just another type of neurons.
The change in the membrane potential is studied by simulating the injection of the current of
Section
To study how astrocytes affect synaptic plasticity and the network’s overall performance, we implemented two networks: the first network contained neurons and bipartite synapses (Section
The architecture of the bipartite network. This model consists of 10 presynaptic neurons, 2 postsynaptic neurons, and 20 plastic synapses.
In the tripartite network, astrocytes were modeled as proposed in Section
Simplified signaling pathways in a tripartite synapse. The astrocyte receives
To model the signaling pathways of
Architecture of the tripartite network. Astrocytes are shown as stars. The neurotransmitter associated with each synapse is indicated on top of each line. G stands for glutamate and k stands for
Synaptic plasticity can be presented in terms of different learning models. In this research, we used the reinforcement learning algorithm described by [
To calculate
Obtained Reward is
Parameter values used to implement reinforcement learning.
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To test for the learning ability of the bipartite and tripartite networks, a simple classification experiment was designed. To generate classification stimuli, the input layer of the networks was used as a 1–dimensional input grid with Gaussian filters. Specifically, each input neuron was located at coordinate 5, 15, 25,..., 95 in a arbitrary 1D space. The location of the neuron was the mean of the Gaussian filter, and all Gaussian filters had a standard deviation of 30. In each simulated trial, the location of one of the input neurons was randomly selected and a current of 70 mV was injected through the Gaussian filter. Because the Gaussian filters overlap, surrounding neurons also received current, but to a lesser extend based on the Gaussian filter. The exact timing of the injected current (and trial) is shown in Algorithm
All plastic connections were initially random, and the network needed to learn to associate the first 5 presynaptic neurons with the first postsynaptic neuron and the last five presynaptic neurons with the second postsynaptic neuron using reinforcement learning. For example, if the first presynaptic neuron had received the most current and the winner was the first postsynaptic neuron, positive feedback was provided (in the form of dopamine release). In contrast, if the seventh presynaptic neuron had received the most current and the first postsynaptic neuron was the winner, negative feedback was provided (in the form of a dip in dopamine).
The simulation methodology is described in Algorithm
In this section, first, we present the results of implementing one single synapse. Next, the classification results of the bipartite and tripartite networks are provided.
The result of implementing a bipartite synapse, which consist of presynaptic and postsynaptic neurons, is presented in Figure
Behavior of neurons in a bipartite synapse (a) and tripartite synapse (b). The top and bottom panels show spikes in the presynaptic and postsynaptic neurons (respectively), while the middle panels show the input to the postsynaptic neuron.
Bipartite synapse
Tripartite synapse
Classification accuracy for the tripartite (top) and bipartite (bottom) networks in a non-noisy condition.
Next, a small amount of noise,
Accuracy in the classification task for the tripartite (circle) and bipartite (square) networks in noisy conditions.
Noise =
Noise =
Noise =
The results presented in this section provide an answer to the question that was first asked: Are astrocytes capable of enhancing the performance of a neural network? The answer is ‘yes’ (in the noiseless environment), although this result clearly does not mean that the tripartite network always work better than the bipartite network. To be more specific, our goal here was not to show that tripartite networks had an advantage over bipartite networks for all parameter values in all conditions. We only tried to show that astrocytes can be considered as a candidate for improving the performance of a neural network in specific conditions, and the role of astrocytes in improving the performance of a neural network is plausible. Further, we showed that the effect of astrocytes is to increase the length of activation (or number of spikes) in postsynaptic neurons.
In this research we tried to answer the following questions:
The answer is yes, the computational result in this research suggest that there are conditions in which astrocytes improve synaptic plasticity and the performance of a neural network.
This research opens up possibilities for many future directions. First, by having a simple biologically realistic dynamical model of astrocytes, different theories about the roles of astrocytes can be tested more easily. For example, research in physiology shows that the number of astrocytes increases in neurodegenerative diseases [
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This research was supported, in part, by Grant no. 2R01MH063760 from the National Institute of Mental Health to Sébastien Hélie. Some of this work has been presented in the Mathematical and Computational Cognitive Science weekly colloquium in the Department of Psychological Sciences at Purdue University by Zahra Sajedinia.