**3. Discussion**

Earlier studies showed that astrocytes interact with each other by transferring low-molecular-weight compounds through gap junctions [17]. This process not only enables the long-distance transfer of energy substrates but is also important for the activation of several ATP-dependent reactions in two adjacent astrocytes. Calcium waves can propagate between astrocytes and form complex spatial-temporal patterns of Ca2+ activity [5]. However, whether astrocytes can regulate metabolic activity and autonomously provide a systematic response to stress conditions independently of neurons remains unclear.

The most important issue in investigating the collective actrocytic response is defining calcium activity characteristics that would reflect the network behavior. Our proposed approach to dynamic astrocytic network construction allows us to identify functional connections between astrocytes and determine the presence and changes of network activity. The developed algorithm represents the astrocytic network as an oriented graph, the vertices of which correspond to separate astrocytes, while the edges designate above-threshold correlations between astrocytic events. When the correlation between a pair of astrocytes is maximal for a significant time shift between calcium signals, it is attributed to the directional coupling. In turn, such causality allows us to define and estimate the rate of calcium wave propagation in primary astrocyte culture.

Selecting a threshold for the correlation value is crucial for identifying and tracking astrocytic networks. The choice is not apparent since even statistically independent random time series can yield nonzero correlations over finite time windows. Moreover, the characteristic level of spurious correlations would not be universal and depends on particular signals. To circumvent the problem, we defined the 'baseline' correlation level as the correlation value for the most distant astrocytes in the observation field in the control case, assuming that little or no actual interaction exists between them. The threshold chosen in this way is equally applicable to astrocyte cultures subject to external stimuli. In this case, changes in the network statistics provide insight into the modification of the astrocytic interaction network.

The developed algorithms are integrated into the custom-written software package, which performs complete analysis and data processing from the obtained microscope images to the dynamic network construction and can be a convenient tool for analyzing image series of cell metabolic activity. The approach currently applied to study the behavior of astrocytic cultures can further be used to analyze network activity in neuronal cultures and mixed neuron-glial cultures. More generally, the developed algorithms allow the processing of series of images obtained from arbitrary cell cultures with some intracellular chemical dynamics.

Our studies revealed that astrocytes exhibit comparatively low network activity under normal conditions in vitro. The number of long-distance connections and the level of correlations increase significantly in response to an increase in intercellular ATP concentration, which cannot be explained by simple ATP-mediated activation of calcium homeostasis, as the calculated correlations are insensitive to the changes in the base level of calcium activity and the frequency of calcium oscillations. This demonstrates that astrocytes can become organized into a functional dynamic network in response to external stimulation.

Ischemia modeling has a significant impact on network activity, manifested by the decrease in all values that characterize network connectivity. The results also highlight important changes in astrocyte responses to ATP stimulation after ischemic influence. We hypothesize that the depression of the ATP-stimulated network emergence in this case is due to adaptive astrocytic reactions. Several studies addressed the changes in the functional activity of neuronal networks in hypoxic and ischemic lesions. Earlier, we demonstrated that hypoxia leads to the dramatic suppression of network interactions between neural cells, up to complete disruption, that is manifested in the alterations of both the calcium and bioelectric activity, as recorded by multi-electrode matrices [19,20]. At the same time, little is known regarding the network activity of mono-astrocytic cultures. Here, we are the first to show that while the calcium oscillations persist in the post-ischemic period, the correlations between cells are almost completely lost. Importantly, 10 μM ATP stimulation in normal conditions increases the frequency and improves correlations between calcium oscillations in distant astrocytes, such that a large-scale connected functional network emerges. In the post-ischemic period, such a response to ATP is absent, which suggests deep functional impairment of the astrocytic network.

There are experimental data showing changes in gliotransmitter regulation after hypoxic influence. It has been established that ATP release in the brain stem, presumably carried out by astrocytes, helps maintain cellular respiration and counteract hypoxia. It has been demonstrated that acute systemic hypoxia (a 5-min reduction in oxygen concentration in the breathable air to 10%) causes the release of a key gliotransmitter (ATP) in the brain stem areas responsible for the formation of breathing rhythm. Blockade of ATP receptors in the same brain stem area alleviates hypoxia-induced respiratory depression [21].

Interestingly, blockade of the main type of astrocytic connexins Cx43, which should provide a metabolically consolidated response under stress, preserves network parameters in primary astrocyte cultures for at least 7 days after the modeled ischemia-like conditions. A substantial increase in cell viability in primary astrocyte cultures in ischemia modeling and blockade of gap junctions was also observed. Accumulated experimental data indicate that Cx43 expression in astrocytes increases under hypoxic influence, and Cx43 plays an important role in cell death and neuronal damage caused by cerebral ischemia [22,23]. It is assumed that ischemia/reperfusion leads to an increase in the concentration of extracellular Ca2+ ions, the release of inflammatory factors, and, as a result, the activation of astrocytic hemichannels [24]. Hemichannels consisting of Cx43 can also be activated by kinase p38 and proinflammatory cytokines released by activated microglia [25]. This leads to an uncontrolled release of ATP, glutamate, and calcium, leading to calcium overload and tissue excitotoxicity [8]. Our data on the preservation of cell viability and network parameters of astrocytic cultures in the remote posthypoxic period are consistent with a study demonstrating that the use of the Cx43 blocker Gap26 improves neurological function in animals and decreases the incidence of heart attack in an ischemia model in vivo [26]. Therefore, Cx43 could be a promising therapeutic target in the development of methods for brain ischemia protection. This is an exciting area for upcoming research.

The current study revealed the emergent property of astrocytes to functionally unite in a large-scale network, and the Cx43 inhibition in ischemic conditions may be considered a favorable factor. In this regard, it is essential to further investigate astrocytic interactions as a factor in brain adaptation to ischemic damage, especially changes in these adaptive properties under physiological astrogliosis.

#### **4. Materials and Methods**

#### *4.1. Ethics Statement*

All experimental procedures were approved by the Bioethics Committee of Lobachevsky University and carried out in accordance with Act 708n (23 082010) of the Russian Federation National Ministry of Public Health, which states the rules of laboratory practice for the care and use of laboratory animals, and Council Directive 2010/63 EU of the European Parliament (22 September 2010) on the protection of animals used for scientific purposes. Newborn C57BL/6 (P1-P3) mice were killed by cervical vertebra dislocation.
