*2.1. ATP and Gap19 E*ff*ects on Functional Calcium Signaling in Astrocytes*

The starting point of the study was estimating the level of consolidated calcium activity of primary astrocytic cultures under normal conditions. This relied on the novel method of computational analysis of time-lapse calcium imaging as described in the materials and methods.

Astrocytes can easily exchange low-molecular-weight compounds (peptides up to 2 kDa, nucleotides, sugars) between adjacent cells through gap junctions that unite neighboring cells into a single functional conglomerate. However, such signals cannot propagate over long distances, as the speed of such passive transport is small and depends on the gradient of concentrations of low-molecular-weight substances in the cytoplasm of adjacent cells [17]. In this regard, an informative evaluation of functionally consolidated signals is given by remote in space and correlated in time calcium events in astrocytes. The correlation graph method showed a low-grade formation of functional networks between distant astrocytes in the "control" group of primary astrocyte cultures under normal conditions, characterized by a large number of disconnected subgraphs (Figure 1).

**Figure 1.** Representative examples of changes in correlation networks after ATP and connexin 43 blocker Gap19 application. (**A**) Control (PBS); (**B**) ATP (10 μM); (**C**) Gap19 (100 μM). (**1**)—before application; (**2**)—after application.

To examine the role of one of the most common types of connexins (connexins 43) in the consolidated astrocyte response, we used the selective blocker Gap19 at a concentration of 100 μM/mL. The application of Gap19 for 40 min did not affect the number of direct long-distance connections per astrocyte under normal conditions, which was 4.94 [3.94; 6.68] ("control" 3.95 [3.10; 4.47]). To validate the ability of astrocytes to become activated and produce a coordinated response to biochemical stimuli, we used ATP (10 μM), which led to a significant 3.5-fold increase in the average number of direct long-distant connections of an astrocyte (13.63 [3.61; 33.23]) over 10 min after ATP application (Figure 2).

**Figure 2.** Average number of direct long-distance connections of a single astrocyte. -—versus baseline, -—versus "Ischemia", *p* < 0.05, the Kolmogorov–Smirnov test.

Analysis of the main parameters of functional calcium activity in primary astrocyte cultures revealed that ATP addition did not cause significant changes in the percentage of cells that exhibited calcium activity. The percentage of oscillated cells in the "ATP" group was 61.47 [43.7; 70.9]% ("control" 69.5 [61.37; 79.33]%, Figure 3A). At the same time, significant changes in the frequency (before ATP addition 1.959 [1.605; 2.177] osc./min, after ATP addition 2.874 [1.884; 3.635] osc./min, Figure 3C) and duration (before ATP addition 13.449 [11.542; 15.135] s, after ATP addition 10.421 [9.611; 11.492] s) of calcium oscillations are shown (Figure 3B).

Studies on the characteristics of astrocyte connectivity showed that ATP application led to a significant increase in the mean values of the maximum correlation between pairs of average astrocyte calcium levels over time by 20% relative to the baseline (*p* < 0.05 the Kolmogorov–Smirnov test) (Figure 4). In the "ATP" group, an absolute change from 0.096 [0.094; 0.099] to 0.126 [0.105; 0.156] was identified. The application of Gap19 did not significantly change this parameter.

An analysis of network characteristics revealed that ATP application leads to a significant increase in the number of long-distant astrocytic connections that can be considered an emergence of complex interactions between astrocytes. The total number of connections per series increases from 732 [548; 796] to 2133 [515; 5134] (the Kolmogorov–Smirnov (KS) test). Such interactions cannot be considered a result of a simple increase in the frequency of calcium oscillations. At the same time, the number of correlated distant astrocytes was also increased.

The most important parameters that characterize network activity are the distribution of calcium signals between astrocytes in a culture, including the time of signal propagation and frequency characteristics of calcium oscillations. The application of ATP increased the number of high-frequency events and suppressed low-frequency events (Figure 5). To characterize the frequency of calcium events, we computed the power spectral density of the cell calcium intensity time series, and took the frequencies corresponding to the 10th and 90th signal energy percentiles as the characteristic lower and upper frequency bounds. These bounds were then averaged over the whole image field.

These findings indicate changes in the activity profile of the entire system in monoastrocytic culture. The low-frequency events are most likely associated with long-term metabolic changes and are fairly stable under normal conditions.

The study of the effects of connexin 43 blocker (Gap19) on the main parameters of network activity showed that despite the great physiological importance of this type of astrocytic connexin, significant changes were detected only in the speed of signal propagation between astrocytes under normal conditions (Figure 6). The percentage of cells that exhibited Ca2+ activity did not change significantly and was 83.1 [78.7; 88.4]% (Figure 3A). There were also no significant alterations in the duration (15.130 [12.634; 16.740] s) or frequency (1.792 [1.524; 1.975] osc./min) of Ca2+ events (Figure 3B,C).

**Figure 3.** Main parameters of functional calcium activity in primary astrocyte cultures in the context of ATP and Gap19 influence under normal conditions and 7 days after ischemia-like condition modeling. (**A**) Proportion of astrocytes exhibiting calcium activity; (**B**) Duration of Ca2+ oscillations, s.; (**C**) Number of Ca2+ oscillations per min. -—versus baseline (before application), *p* < 0.05, Wilcoxon rank-sum test.

**Figure 4.** Mean value of the correlation maximum on the shift between pairs of average astrocyte calcium levels over time. -—versus "Control", -—versus "Ischemia", *p* < 0.05, the Kolmogorov–Smirnov test.

**Figure 5.** Average low-frequency component of calcium intensity in primary astrocyte cultures after ATP and Gap19 addition. - ATP—versus baseline, *p* < 0.05, t-criteria (*p* = 0.004); -—versus "Control", *p* < 0.05, the Kolmogorov–Smirnov test (*p* = 0.005); -—versus "Ischemia", *p* < 0.05, t-criteria (*p* = 0.004).

**Figure 6.** The rate of signal delay between astrocytes. - Gap19—versus baseline, *p* < 0.05, t-criteria (*p* = 0.036); versus "Control", *p* < 0.05, the Kolmogorov–Smirnov test (*p* = 0.018). -—versus "Ischemia", *p* < 0.05, the Kolmogorov–Smirnov test (*p* = 0.006).

An analysis of network connectivity parameters did not reveal significant changes in the network characteristics of the astrocytic network under the selective blocker Gap19 application. Therefore, the role of connexin 43 in the formation of correlated calcium dynamics in primary astrocyte cultures under normal conditions is not significant.
