Modeling Working Memory in a Spiking Neuron Network Accompanied by Astrocytes

Abstract

We propose a novel biologically plausible computational model of working memory (WM) implemented by a spiking neuron network (SNN) interacting with a network of astrocytes. The SNN is modeled by synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons via chemicals diffused in the extracellular space. Calcium elevations occur in response to the increased concentration of the neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strength of the synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organized by the application of a cue pattern representing one from the memory set distorted by noise. We found that successful retrieval with the level of the correlation between the recalled pattern and ideal pattern exceeding 90% is possible for the multi-item WM task. Having analyzed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in the SNN leading to successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Keywords: astrocyte; delayed activity; neuron-astrocyte interaction; spiking neural network; working memory.

Figure 1

A neuron-astrocyte network topology. The neuron-astrocyte network consists of two interacting layers: a neural network layer and an astrocytic layer. The neuronal network with dimension W × H (79 × 79) consists of synaptically coupled excitatory neurons modeled by the Izhikevich neuron. Neurons in the network are connected randomly. The astrocytic network consists of diffusely connected astrocytes with dimension M × N (26 × 26). Blue lines show connections between elements in each layer. We consider the bidirectional interaction between the neuronal and astrocytic layers. Each astrocyte is interconnected with a neuronal ensemble of N_a = 16 neurons with dimensions 4 × 4 (red lines) with overlapping in one row (violet lines). The input signal is fed to the neural network.

Figure 2

Time course of a training and test protocol in the multi-item WM paradigm used. During training the samples were loaded sequentially by applying external inputs of 200 ms durations with 100 ms inter-item intervals. After a 700 ms training stimulus was applied, we tested the maintenance of the memory by applying matching and non-matching items of 150 ms durations and 250 ms inter-item intervals.

Figure 3

Model of neuron-astrocyte interaction. (A) Spike train and (B) concentration of the neurotransmitter, G(t), of the stimulus-specific neuron. (C,D) Same as in (A,B) but for an unspecific neuron. (E) Intracellular concentration of Ca²⁺ and IP₃ in a stimulus-specific astrocyte. Black bars at the top indicate periods when each of the stimuli (training stimulus—sample, nonmatching test items—nonmatch, test cue—match) were presented. In response to the presynaptic spike train (A,C), the neurotransmitter, glutamate, G releases (B,D) into extracellular space and the concentration of IP₃ increases in the astrocyte (E, blue line) inducing the elevation of intracellular Ca²⁺ (E, red line).

Figure 4

Delayed matching to sample WM task. (A) One trial of the task simulated in the network. Spike raster of the neuronal network showing sample-selective delay activity. Neurons belonging to the stimulus-specific population are indicated by blue color. Black bars at the top indicate periods when each of the stimuli (training stimulus—sample, nonmatching test items—non-match, test cue—match) were presented. (B,C) The averaged firing rate of the stimulus-specific and unspecific neurons over time, respectively (20 ms bins).

Figure 5

Snapshots of the training (A–C) and testing (D,E) of the neuron-astrocyte network in the single-item working memory task. (A) Training sample. (B) Response of the neuronal network to the sample. The values of the membrane potentials are shown. (C) Intracellular Ca²⁺ concentrations in the astrocytic layer. (D) Testing item with 20% salt and pepper noise. (E) Cued recall in the neuronal network. The averaged firing rate on the test time interval for each neuron is shown.

Figure 6

Neuron-astrocyte network simulation with four loaded memory items. (A,C,E) Spike train and (B,D,F) concentration of the neurotransmitter, G(t), of three neurons belonging to different stimulus-specific populations. (A,B) Stimulus-specific neuron to sample 0. (C,D) Stimulus-specific neuron to sample 2. (E,F) Neuron unspecific to all samples. Black bars at the top indicate periods when each of the stimuli (training stimulus—sample, non-matching test items—nm, match cue—m) were presented.

Figure 7

Multi-item WM in the neuron-astrocyte network. (A) Spike raster of the neuronal network with four training patterns. Neurons are colored according to their pattern selectivity. Pattern overlapping in neuronal populations is 35.2% on average for four patterns. Black bars indicate periods when each of the stimuli were presented. (B,C) The averaged firing rate of the stimulus-specific and unspecific neurons over time, respectively (20 ms bins). (D) Correlation of filtered items. The different colors correspond to the correlations with different ideal samples. The dotted line shows the correlation of the testing item (for 20% noise level in test). Black bars at the top indicate periods when each of the stimuli (training stimulus—sample, non-matching test items—nm, match cue—m) were presented.

Figure 8

Snapshots of the training (A,B,C,F,G,H) and testing (D,E,I,J) of the neuron-astrocyte network in the multi-item working memory task. We used the following training set consisting of four samples: 0,1,2,3. (A,F) The example of the first and last training samples, respectively. (B,G) The response of the neuronal network to samples. The values of the membrane potentials are shown. (C,H) The intracellular Ca²⁺ concentrations in the astrocytic layer. (D,I) The testing items with 20% salt and pepper noise. (E,J) The cued recalls in the neuronal network. The firing rate averaged on the test time interval for each neuron is shown.

Figure 9

Correlation between recalled pattern (see section 3.5) and ideal item in a multi-item WM task performed by the neuron-astrocyte network. The correlation averaged over four patterns is shown. (A) Noise-resistance of the model. Dependence of correlation on the noise level in training and testing. The correlation difference between cued recall pattern and noisy input is shown. (B,C) The influence of the neuron-astrocytic interaction structure. (B) Dependence of correlation on the number of spiking neurons required for the calcium elevation in the astrocyte, F_act, and on the number of spiking neurons required for the emergence of astrocyte-induced enhancement synaptic transmission, F_astro. (C) Dependence of correlation on noise level in training samples and on the parameter, F_act. F_astro = 0.5. For (B,C) noise level in cue is 20%.

Figure 10

Influence of synaptic connectivities architecture in the neural network on the correlation of recalled pattern in the multi-item WM task performed by the neuron-astrocyte network. The correlation averaged over four patterns is shown. (A) Dependence of correlation on the number of output synaptic connections for each neuron, N_out, and synaptic weight, η. λ = 5. (B) Dependence of correlation on the number of output synaptic connections for each neuron, N_out, and synaptic connection distribution parameter, λ Equation (4). η = 0.025.

Figure 11

Capacity of the multi-item WM in the neuron-astrocyte network. Capacity as a function of the sample number in training. The number of images with a correlation of recalled pattern higher than 90% is shown.

Figure 12

Capacity of the multi-item WM in the neuron-astrocyte network in the case of non-overlapping neuronal populations obtained analytically. Capacity as a function of the sample number in the training sequence.

Figure 13

Concept of WM operation in the spiking neuron network model accompanied by astrocytes.