Dynamic image recognition in a spiking neuron network supplied by astrocytes

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Citation: Stasenko, S.V.; Kazantsev

V.B. Dynamic image recognition in a

spiking neuron network supplied by

astrocytes. Preprints 2022,1, 0.

https://doi.org/

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Article

Dynamic image recognition in a spiking neuron network

supplied by astrocytes

Sergey V. Stasenko 1* , and Victor B. Kazantsev 1

1Moscow Institute of Physics and Technology

*Correspondence: stasenko@neuro.nnov.ru

Abstract:

Mathematical model of spiking neuron network (SNN) supplied by astrocytes is investigated.

The astrocytes are speciﬁc type of brain cells which are not electrically excitable but inducing chemical

modulations of neuronal ﬁring. We analyzed how the astrocytes inﬂuence on images encoded in the

form of dynamic spiking pattern of the SNN. Serving at much slower time scale the astrocytic network

interacting with the spiking neurons can remarkably enhance the image recognition quality. Spiking

dynamics was affected by noise distorting the information image. We demonstrated that the activation

of astrocyte can signiﬁcantly suppress noise inﬂuence improving dynamic image representation by the

SNN.

Keywords: spiking neural network; neuron-glial interactions; astrocyte

1. Introduction

The construction of biologically relevant models of brain information processing still

remains one of the key tasks of modern mathematical neuroscience. In neurobiology, key mech-

anisms of information processing concern synaptic transmission between the brain network

neurons. Synaptic plasticity, e.g. adaptive changes in the connection strengths, is believed to be

the main instrument of implementation learning and memory in the neuron networks. Follow-

ing the neurobiological studies many mathematical models targeted to describe experimental

results and, hence, to imitate brain functions have been proposed. However, it is still remain

a challenge on how at network level brain circuits can generate so ﬁnely tuned and effective

information representation and processing.

In recent two decades neurobiological experiments have revealed that neurons and neu-

ronal networks are not alone in the brain universe. It was found that glial cells, particularly

astrocytes, known before as just “supporting” cells providing mostly metabolic functions, can

also participate in information processing by means of chemical regulations of neuronal activity

and synaptic transmission [

–

]. Inclusion of the third player, e.g. astrocytes, in the classical

“presynapse-postsynapse” signal transmission scheme led to the concept of a tripartite synapse

[

]. Astrocytes through calcium-dependent release of neuroactive chemicals (for example,

glutamate) affect the pre- and postsynaptic compartments of the synapse. When spikes are

generated by a presynaptic neuron, a neurotransmitter (for example, glutamate) is released

from the presynaptic terminal. By diffusion part of the chemicals leave synaptic cleft and bind

to metabotropic glutamate receptors (mGluRs) on the astrocyte, which may be located near

the presynaptic terminal. Activation of metabotropic glutamate receptors G-mediated leads

to the formation of inositol-1,4,5-triphosphate (IP

). This process after a cascade of molecular

transformations inside the astrocyte leads to the release of

Ca2+

into the cytoplasm. It induces

the release of the neuroactive chemicals called gliatransmitters (for example, glutamate, adeno-

sine triphosphate (ATP), D-serine, GABA) back to the extrasynaptic space. Next, they bind

to pre- or postsynaptic receptors resulting ﬁnally in modulation of the efﬁciency of synaptic

transmission completing the feedback loop [6].

arXiv:2210.01419v1 [q-bio.NC] 4 Oct 2022

2 of 11

Many mathematical models were then proposed to explore the functional role of astrocytes

in neuronal dynamics. They include model of the “dressed neuron,” which describes the

astrocyte- mediated changes in neural excitability [

], model of the astrocyte serving as a

frequency selective “gate keeper” [

], model of the astrocyte regulating presynaptic functions

[

] and many others. In particular, it was demonstrated that gliotransmitters can effectively

con trol presynaptic facilitation and depression. The model of the tripartite synapse has recently

been employed to demonstrate the functions of astrocytes in the coordination of neuronal

network signaling, in particular, spike-timing-dependent plasticity and learning [

–

]. In

models of astrocytic networks, communication between astrocytes has been described as

Ca2+

wave propagation and synchronization of

Ca2+

waves [

]. However, due to a variety of

potential actions, that may be speciﬁc for brain regions and neuronal sub-types, the functional

roles of astrocytes in network dynamics are still a subject of debate.

Role of astrocytes as collaborators of spiking neuron networks (SNN) in implementing

learning and memory functions have been intensivly discussed in recent computational models

[

–

]. Speciﬁcally, it was demonstrated that the astrocytes serving at much slower time scale

can help SNN to distinguish highly overlapping images. Here we present another SNN model

accompanied by the astrocytes that can signiﬁcantly enhance recognition of information images

encoded in the form of dynamical spiking patterns stored by the SNN.

2. The model

2.1. Mathematical model of single neuron

The SNN’s individual neuron is described by the Hodgkin-Huxley model [

] deter-

mined that the squid axon curries three major currents: voltage-gated persistent

K+

current,

, with four activation gates (resulting in the term

in the equation below, where

is the

activation variable for

K+

), voltage-gated transient

Na+

current,

INa

, with three activation

gates and one inactivation gate (term

m3h

below), and Ohmic leak current,

, which is carried

mostly by

Cl−

ions. The complete set (Eq.

(1)

) of space-clamped Hodgkin-Huxley equations is

C˙

V=Iinj −

INa

z }| {

gNam3h(V−VNa)−

z }| {

gKn4(V−VK)−

z }| {

gL(V−VL)

n=αn(V)(1−n)−βn(V)n

m=αm(V)(1−m)−βm(V)m

h=αh(V)(1−h)−βh(V)h, (1)

where:

Iinj =Istim +Inoise +Isyn (2)

αn(V) = 0.01(V+55)

1−exp[−(V+55)/10]

βn(V) = 1.125exp[−(V+65)/80]

αm(V) = 0.1(V+40)

1−exp[−(V+40)/10]

βm(V) = 4exp[−(V+65)/18]

αh(V) = 0.07exp[−(V+65)/20]

βn(V) = 1

1+exp[−(V+35)/10]

Shifted Nernst equilibrium potentials for

INa

and

are

VNa =50 mV

VK=−77 mV

and

VL=−54.4 mV

, respectively. Typical values of maximal conductances for

INa

and

3 of 11

are

gNa =36 mS/cm2

gK=120 mS/cm2

and

gL=0.3 mS/cm2

, respectively. The functions

α(V)

and

β(V)

describe the transition rates between open and closed states of the channels.

C=1 ¯F/cm2

is the membrane capacitance and

Iinj

(Eq.

(2)

) is the applied current which

consists from three parts: Istim,Inoise and Isyn.

2.2. Applied currents

Images applied to the SNN were encoded as matrices

of size

n×k

and values from 0

to 1 for each pixel, where 0 is the absence of color, and

and

are the corresponding image

sizes (length and width). Next, the matrix

was transformed into an

l×

1 vector

, where

l=n×k

and corresponds to the neuron index in the neural network. Thus, the stimulation

current, Istim, will be written in the following form:

Istim =S×AS, (3)

where ASis the amplitude of stimulus taken here for illustration with value 5.3 nA.

The synaptic current,

Isyn

, is modeled using conductance-based approach as following

form:

Isyn =gj(Vj−V), (4)

where:

gj=

−gj

τj

(5)

In our model index

is used for excitatory (exc) and inhibitory (inh) synapses. Reversal

potentials for synaptic currents are equal

0 mV

and

−80 mV

for excitatory and inhibitory

synapses, respectively.

τj

is the time relaxation equaled

5 ms

and

10 ms

for excitatory and

inhibitory synapses, respectively. Excitatory (inhibitory) synapses will increase the excitatory

(inhibitory) conductance in the postsynaptic cell whenever a presynaptic action potential

arrives:

gj←gj+wj, (6)

where

- synaptic weight equaled

3 nS

and

77 nS

for excitatory and inhibitory synapses,

respectively.

Besides the synaptic input, each neuron receives a noisy thalamic input (

Inoise

). The noisy

thalamic input is set in a random way for all neurons in the range from 0 to Anoise.

Each spike in the neuron model induces the release of neurotransmitter. To describe the

neuron to astrocyte cross-talk, here we only focus on the excitatory neurons releasing glutamate.

Following earlier experimental and modeling studies, we assumed that the glutamate-mediate

exchange was the key mechanism to induce coherent neuronal excitations [

]. The role of

GABAergic neurons in our network is to support the excitation and inhibition balance avoiding

hyperexcitation states.

For simplicity, we take a phenomenological model of released glutamate dynamics. In the

mean ﬁeld approximation average concentration of synaptic glutamate concentration for each

excitatory synapses, Xe, was described by this equations:

Xe(t) = Xe(ts)exp(−t/τX), if ts<t<ts+1,

Xe(ts−0) + 1, if t=ts,(7)

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Citation:Stasenko,S.V.;KazantsevV.B.Dynamicimagerecognitioninaspikingneuronnetworksuppliedbyastrocytes.Preprints2022,1,0.https://doi.org/Publisher'sNote:MDPIstaysneutralwithregardtojurisdictionalclaimsinpublishedmapsandinstitutionalafl-iations.Copyright:©2022bytheauthors.SubmittedtoPreprintsforposs...

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Dynamic image recognition in a spiking neuron network supplied by astrocytes

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