Failure of neuron network coherence induced by SARS-CoV-2-infected astrocytes Sergey V. Stasenko1 Alexander E. Hramov23 and Victor B. Kazantsev124

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Failure of neuron network coherence induced by

SARS-CoV-2-infected astrocytes

Sergey V. Stasenko1,*, Alexander E. Hramov2,3, and Victor B. Kazantsev1,2,4

1Laboratory of advanced methods for high-dimensional data analysis, Lobachevsky university, Nizhniy

Novgorod,603022, Russia

2Neuroscience and Cognitive Technology Lab, Innopolis University, Innopolis, 420500, Russia

3Department of New Cardiological Informational Technologies, Saratov State Medical University, Saratov, 410012,

Russia

4Laboratory for Neuromodeling, Neuroscience Research Institute, Samara State Medical University, Samara,

443099, Russia

*stasenko@neuro.nnov.ru

ABSTRACT

Coherent activations of brain neuron networks underlay many physiological functions associated with various behavioral

states. These synchronous ﬂuctuations in the electrical activity of the brain are also referred to as brain rhythms. At the

cellular level, the rhythmicity can be induced by various mechanisms of intrinsic oscillations in neurons or network circulation of

excitation between synaptically coupled neurons. One of the speciﬁc mechanisms concerns the activity of brain astrocytes

that accompany neurons and can coherently modulate synaptic contacts of neighboring neurons, synchronizing their activity.

Recent studies have shown that coronavirus infection (Covid-19), entering the central nervous system and infecting astrocytes,

causes various metabolic disorders. Speciﬁcally, Covid-19 can depress the synthesis of astrocytic glutamate and GABA. It

is also known that in the postcovid state, patients may suffer from symptoms of anxiety and impaired cognitive functions,

which may be a consequence of disturbed brain rhythms. We propose a mathematical model of a spiking neural network

accompanied by astrocytes capable to generate quasi-synchronous rhythmic bursting discharges. The model predicts that

if the astrocytes are infected, and the release of glutamate is depressed, then normal burst rhythmicity suffers dramatically.

Interestingly, in some cases, the failure of network coherence may be intermittent with intervals of normal rhythmicity, or the

synchronization can completely disappears.

Introduction

The synchronization of the neural network activity at the cellular and network levels gives rise to rhythmic voltage ﬂuctuations

traveling across brain regions, known as neuronal oscillations or brain waves

1,2

. Modulation of neural oscillations is provided

by the dynamic interplay between neuronal connectivity patterns, cellular membrane properties, intrinsic circuitry, speed of

axonal conduction, and synaptic delays

3–6

. The neural oscillations ﬂuctuate between two main states, known as “up states”

and “down states”

. The network coherence providing by the up state in spatially organized cortical neural ensembles play

a crucial role for several sensory and motor processes, as well as for cognitive ﬂexibility (i.e., attention, memory), thereby

playing a fundamental role in the brain’s basic functions

8,9

. Furthermore, different network dynamics (from slow to ultra-fast

oscillations) can change according to the behavioral state, with some frequency bands being associated with sleep, while other

frequencies predominate during arousal or conscious states10–12.

Besides purely neuronal mechanisms, many recent studies revealed the essential contributions made by astrocytes to many

physiological brain functions,including synaptogenesis

, metabolic coupling

, nitrosative regulation of synaptic release

15–17

synaptic transmission

, network oscillations

, and plasticity

20,21

. Astrocytes can play a signiﬁcant role in the processing of

synaptic information through impact on pre- and post-synaptic neurons. This fact leads to the concept of a tripartite synapse

22,23

A part of the neurotransmitter released from the presynaptic terminals (i.e., glutamate) can diffuse out of the synaptic cleft and

bind to metabotropic glutamate receptors (mGluRs) on the astrocytic processes that are located near the neuronal synaptic

compartments. The neurotransmitter activates G-protein mediated signaling cascades that result in phospholipase C (PLC)

activation and insitol-1,4,5-trisphosphaste (IP3) production. The IP3 binds to IP3-receptors in the intracellular stores and

triggers

Ca2+

release into the cytoplasm. Such an increase in intracellular

Ca2+

can trigger the release of gliotransmitters

[e.g., glutamate, adenosine triphosphate (ATP), D-serine, and GABA] into the extracellular space. A gliotransmitter can affect

both the pre- and post-synaptic parts of the neuron. By binding to presynaptic receptors, it can either potentiate or depress

presynaptic release probability. One of the key pathways in the tripartite synapse is mediated by glutamate released by the

arXiv:2210.01014v1 [q-bio.NC] 3 Oct 2022

astrocyte

25–27

. Such glutamate can potentially target presynaptic NMDA receptors, which increase the release probability

or presynaptic mGluRs, which decrease it

. Presynaptic kainate receptors exhibit a more complex modulation of synaptic

transmission through both metabotropic and ionotropic effects

30,31

. Based on experiment facts, many computational models

have been proposed taking into account neuron to astrocyte interactions to describe the interneuronal communication

32–38

Many experimental works are shown that astrocytes can coordinate the neuronal network activations

38–41

. Because astrocyte is

affected by a large number of synapses, the gliatransmission should also contribute to the effect of neuronal synchronization.

Particularly, it was demonstrated in a hippocampal network, where calcium elevations in astrocytes and subsequent glutamate

release led to the synchronous excitation of clusters of pyramidal neurons42,43.

Coronavirus COVID-19 has become a global challenge of the modern world, stimulating intensive research in many related

areas of science. Along with the development of vaccines, a fundamentally important global task is to investigate Covid-19

effects on different systems of human organisms. Recent studies have shown that coronavirus infection, entering the central

nervous system and infecting astrocytes, causes various metabolic disorders, one of which is a decrease in the synthesis of

astrocytic glutamate and GABA

. It is also known that in the postcovid state, patients may suffer from symptoms of anxiety and

impaired cognitive functions, which may be a consequence of disturbed brain rhythms. In this paper, we propose a mathematical

model of impact SARS-CoV-2-infected astrocyte on the ability to synchronize neural networks and produce brain rhythms. We

show that depending on the degree of disturbance in the synthesis of gliatransmitters neuronal network synchronization can be

partially or completely suppressed.

Results

First, let us consider how the astrocytes induced the appearance of quasi-synchronous bursting dynamics. If no astrocytic

feedback is activated, e.g.,

γY=0

, the network showed asynchronous spontaneous ﬁring due to uncorrelated noisy component

of applied current,

Iext

stimulated all neurons (not shown in the ﬁgures). When the feedback is activated,

γY>0

, the model

starts to generate population burst discharges as illustrated in Fig. 3. Similar to previous modeling studies

38–41 t

he astrocytes

started to coordinate neuronal activity, inducing a certain level of coherence in the network ﬁring. On the one hand, each

astrocyte was activated integrating neuronal activity in its neighboring space. On the other hand, when astrocyte was activated

it facilitated synchronously the activation of accompanying neurons within a certain area. In a result, neurons generated

quasi-synchronous high-frequency burst discharges (Fig. 3). These discharges were synchronized with peaks of extracellular

glutamate concentration associated with the astrocytes activations. It should be noted that population burst dynamics is typical

for living networks formed in dissociated cortical (or hippocampal) neuronal culture models in vitro

45–47

. In such biological

models normal bursting indicates normal activity. In different pathological conditions (hypoxic–ischemic injury, alpha or theta

coma or electrocerebral inactivity48) bursting fails what indicates the decrease of functional coherence in the network ﬁring.

Next, we activated the virus pathological action in the model by increasing

γvirus >0

. Figure 4illustrates how network

activity changed in this case. The raster plot shows that normal bursting were interrupted by the intervals of asynchronous

uncorrelated ﬁring. Corresponﬁng graphs of glutamate concentration in the right panels indicate that in these intervals the

astrocytes were partly (lower peaks) or completely (no peaks) inhibited. After this intervals bursts were spontaneously

recovered to normal sequences. So that, the result of SARS-CoV-2-infection at network level provokes to the failure of

normal synchronization at network level while each neuron in the network works ﬁne and each synaptic connections stay well

functioning. Note, that for low values of

γvirus

associated with a “light” infection cases the intervals of uncorrelated ﬁring are

quite shot indicating a kind intermittent behavior between long lasting normal synchronous (e.g. “laminar”) stages and rather

shot pathological asynchronous (e.g. “turbulent”) breaks.

The next prediction of the model concerns a gradual character of the infection inﬂuence. It means that higher level of

SARS-CoV-2 concentration in the organism will result in stronger pathological response. In terms of our model the increase of

γvirus

leads to the increase of intervals of “pathological” ﬁring (Fig. 5). One can note that the number of normal bursts withing

the same sample window signiﬁcantly descrease. In terms of neuro- and gliatransmitter concentrations (right panels of Fig.

5) we also noticed the decrease of functionality not only of all astrocytes but also neurons. Some of them become depressed

because of lack of sufﬁcient amount glutamate to support normal excitatory transmission. So that, the higher SARS-CoV-2

concentration is exposed, then more astrocytes are infected and, hence, more “explicit” pathological synchrony breaks appear at

the level of network ﬁring.

As one may expect now, further increase of

γvirus

completely inhibited the synchronization. It is illustrated in Fig. 6.

Correspondingly, all astrocytes failed to realease any glutamate. Note, however, that overall network ﬁring still preserves

sustained by activations of excitatory neurons with relatively strong glutamatergic synapses. To quantify the gradual character

of the network dysfunction due to SARS-CoV-2 infection we calculated the quantity reﬂecting the average burst frequency

versus γvirus (Fig. 7). The graph represents monotonically descreading function vanishing at γvirus →1.

2/12

Discussion

We proposed a spiking neuron network model of synaptically coupled neurons accompanied of SARS-CoV-2-infected astrocytes.

The model accounts for astrocyte activation depending on the integrative level of neuronal ﬁring and the astrocyte to neuron

feedback that is based on released gliatransmitter (glutamate) that facilitates group ﬁring of neurons within the astrocyte territory.

We found that the astrocyte disfunction and failure of gliatransmitter release that was the consequence of SARS-CoV-2-infection

lead to failure of network synchronization. We have also illustrated that normal dynamics can be restored spontaneously,

interspersed with intervals of pathological arousal.

At present, cognitive dysfunctions are reported as one of the most dangerous consequences of SARS-CoV-2 infection in

post covid states. At the cognitive level, normal brain functioning can be associated with certain functional networks, where a

particular function is associated with long-range correlations between different neuronal groups. Failure of such correlations

may indicate the appearance of particular cognitive dysfunctions.

At the cellular level, functional synchronization is provided by coherent ﬁring patterns of underlying spiking neuronal

circuits. Following in vitro biological models of neuronal cultures where the appearance of population bursts provides functional

synchronization, our mathematical model predicted that infected astrocytes might be responsible for failure of functional

synchronization and consequent cognitive dysfunctions.

Methods

Mathematical model of single neuron

To describe the dynamics of a single neuron, we take Izhikevich’s model

. It represents a compromise between computational

complexity and biophysical plausibility. Despite its computational simplicity, this model can reproduce a large number of

phenomena occurring in real neurons. The Izhikevich model is given in the form of a differential equations system (1):

(CmdVm

dt =k(Vm−Vr)(Vm−Vt)−Um+Iext +Isyn,

dUm

dt =a(b(Vm−Vr)−Um).(1)

If Vm≥Vpeak , than

(Vm=c,

Um=Um+d,(2)

where

a,b,c,d,k,Cm

are the different parameters of the neuron.

is the potential difference on the inside and outside of the

membrane, and

is a "recovery variable" describing the process of activation and deactivation of potassium and sodium

membrane channels, respectively. As a result, we have negative feedback concerning the dynamics of the potential

on the

cell membrane. The resting potential value in the model lies in the range from –70 to –60 mV. Its value is determined by the

parameter

, which describes the sensitivity of the recovery variable to subthreshold potential ﬂuctuations on the neuronal cell

membrane. The parameter

sets the characteristic time scale of the change in the recovery variable

. The

Vpeak

value limits

the spike amplitude. Parameters

and

specify the values of

and

after spike generation.

Iext

is the externally applied

current. The neuron model is in an excitable mode and will demonstrate the generation of spikes in response to an applied

current.

Isyn

is the sum of synaptic currents from all neurons with which this neuron is connected. Synaptic currents were

calculated as follows:

Isyn =∑yi jwi j,(3)

so that

Isyn

represents the weighted sum of all synaptic currents of postsynaptic neurons with

wi j

denoting the weights for

glutamatergic and GABAergic synapses between neurons. For excitatory and inhibitory contacts, the weights have positive

and negative signs, respectively. Variables

yi j

denote the output signal (synaptic neurotransmitter) from the

th neuron to the

th neuron which involved in generation of

Isyn

. In our model, the number of synaptic connections is

N2×p

, where

is the

number of neurons,

is the probability of communication between two random neurons and equal 0.1 (

10%

of connections).

Each synaptic weight was set randomly for all connections in the range from 20 to 60. If a spike is generated on the presynaptic

neuron, a jump in the synaptic current occurs on the postsynaptic one, which further decays exponentially. As a result, synaptic

neurotransmitter concentration, yi j, was calculated as follows:

yi j(t) = yi j(ti)exp(−t/τy)if,ts<t<ts+1,

yi j(ts−0) + 1 if,t=ts,(4)

3/12

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FailureofneuronnetworkcoherenceinducedbySARS-CoV-2-infectedastrocytesSergeyV.Stasenko1,*,AlexanderE.Hramov2,3,andVictorB.Kazantsev1,2,41Laboratoryofadvancedmethodsforhigh-dimensionaldataanalysis,Lobachevskyuniversity,NizhniyNovgorod,603022,Russia2NeuroscienceandCognitiveTechnologyLab,InnopolisUniver...

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Failure of neuron network coherence induced by SARS-CoV-2-infected astrocytes Sergey V. Stasenko1 Alexander E. Hramov23 and Victor B. Kazantsev124

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