*4.9. Construction of a Dynamic Astrocytic Network*

The approach for reconstruction of an astrocytic network is based on calculating the Pearson correlation coefficient between filtered signals of each cell pair:

$$\rho\_{ij} = \frac{\sum\_{k=-1}^{n} \mathbb{1}\_{k}^{i} \mathbb{1}\_{k}^{j}}{\sqrt{\sum\_{k=-1}^{n} \left(\mathbb{1}\_{k}^{i}\right)^{2} \sum\_{k=-1}^{n} \left(\mathbb{1}\_{k}^{j}\right)^{2}}},\tag{1}$$

$$
\dot{\mathbf{x}}\_k^j = \mathbf{x}\_k^j - \langle \mathbf{x}\_s^j \rangle\_{k-w,k} \tag{2}
$$

*xi k* —calcium signal of i-th cell at time *k*,

*x*ˇ*i k* —calcium signal minus moving average with window size *w*,

*xi <sup>s</sup>k*−*w*,*k*—average of signal in range [*<sup>k</sup>* <sup>−</sup> *<sup>w</sup>*, *<sup>k</sup>*].

The astrocytic network is represented as an undirected graph, where vertices correspond to cells, and edges are drawn between the cells for which the correlation coefficient exceeds a certain threshold. Cellular signals are characterized by two main quantities: the level of intracellular calcium and the size of a calcium event inside the cell. Both are used to construct the network. Furthermore, the propagation of calcium signals between cells leads to detectable time delays in calcium elevations (Supplementary Material Movie 1) and in certain cases allows for assignment of a directed edge. Different time delays were probed to choose the one for which the correlation between a pair of cells would be maximal (Supplementary Material 2).

A threshold was set to reject spurious correlations between cell calcium signals that would be caused by coincidence rather than actual interaction. The choice of the threshold was based on the following. Since the direct interaction between astrocytes is local, the mutual influence should decrease with distance. Therefore, the baseline level of correlations can be estimated from values that are found for remote astrocytes. Given the typical size of an astrocyte up to 40 μm, we referred to the correlation level between cells separated by at least 100 μm as the baseline [31].

The implementation of this approach is illustrated in Figure 8A,B, which shows a typical relationship between the level of correlation and the distance in pairs of astrocytes in the control experiment. Adjacent cells are marked in red. Three indicative groups of points are highlighted in the figure. For the nearby and directly interacting astrocytes (distance between central points < 40 μm), the correlation coefficient can reach 0.9. For distant astrocytes (distance > 300 μm), the correlation does not exceed 0.3. We used this value as a threshold to distinguish a significant correlation between pairs of astrocytes. The third group of points is represented by pairs of astrocytes located at distances ranging from 40 to 300 μm with cross-correlation values exceeding 0.3. These properties are interpreted as the result of an indirect dynamic interaction between astrocytes and almost do not occur in the control group.

The correlation astrocytic network is constructed as follows: the vertices of the graph are mapped to astrocytes, and the presence of a significant level of correlation between pairs of astrocytes (correlation greater than 0.3) is indicated by an edge connecting the corresponding vertices. A characteristic example of the obtained network for the control group is presented in Figure 8C. Such networks typically display a sufficiently large number of small local groups.

**Figure 8.** The distance–correlation relationship between pairs of neighboring (red) and distant (blue) astrocytes in the control state (**A**) and after applying ATP; (**B**) An example of a correlation network of astrocytes with a threshold ρ > 0.3 for the control state (**C**) and after applying ATP (**D**)**.**

#### *4.10. Dynamic Astrocytic Network Analysis*

The impact of external factors on astrocytic culture can lead to changes in the correlation and dynamic properties of the system. As a result of exposure to ATP, the point cloud expands and shows higher correlation values at long distances (Figure 8A,B). This reflects an increase in the connectivity of the dynamical astrocytic network. While the original graph would contain several disconnected subgraphs, the resulting correlation astrocytic network manifests the so-called giant component, a connected subgraph of the size of the order of the entire network, due to the emerging large number of long-range functional connections (Figure 8D).

Network analysis focuses on the following key features: the number of functional connections between astrocyte pairs, the average number of connections between astrocytes, the average propagation speed of delays between signals, the average correlation level of network cells, and the frequency of cell signals, as described in detail in Supplementary Material 2.

#### *4.11. Statistical Analysis*

The astrocytic responses to various biochemical stimuli were investigated using statistical analysis. Astrocyte cultures were divided into different groups. The control group was designated as representing a normal state of astrocytic activity.

The influence of external factors on the astrocyte state was determined by comparing feature samples of the control and case groups by the one-sided two-sample Kolmogorov–Smirnov test. This is a nonparametric test that quantifies the distance between the empirical distribution functions of two samples [32]. The computed features of some groups violate the normality assumption for parametric tests. The normality of distributions is tested by applying the Kolmogorov–Smirnov test (KS test) (*p* < 0.05 for some groups, but not for all). To overcome this, a two-sample KS test was applied. Determination of the distribution shift direction was provided by a one-sided KS test. To assess whether group mean ranks differ, the Wilcoxon rank-sum test was applied to the data. A t-test was performed to compare group values with the initial baseline.

Statistical significance was determined using stats module of SciPy library [33]. The one-sided two-sample KS test is performed by the ks\_2samp function. The Wilcoxon rank-sum test is performed by the Mann-Whitney function. Differences between groups were considered statistically significant if *p* < 0.05.

Descriptive statistics of each feature per group are represented as "M [Q1; Q3]", where M—median, Q1—first quartile (quantile 0.25), and Q3—third quartile (quantile 0.75) of the group samples.
