Approaches to Study Gap Junctional Coupling

Astrocytes and oligodendrocytes are main players in the brain to ensure ion and neurotransmitter homeostasis, metabolic supply, and fast action potential propagation in axons. These functions are fostered by the formation of large syncytia in which mainly astrocytes and oligodendrocytes are directly coupled. Panglial networks constitute on connexin-based gap junctions in the membranes of neighboring cells that allow the passage of ions, metabolites, and currents. However, these networks are not uniform but exhibit a brain region-dependent heterogeneous connectivity influencing electrical communication and intercellular ion spread. Here, we describe different approaches to analyze gap junctional communication in acute tissue slices that can be implemented easily in most electrophysiology and imaging laboratories. These approaches include paired recordings, determination of syncytial isopotentiality, tracer coupling followed by analysis of network topography, and wide field imaging of ion sensitive dyes. These approaches are capable to reveal cellular heterogeneity causing electrical isolation of functional circuits, reduced ion-transfer between different cell types, and anisotropy of tracer coupling. With a selective or combinatory use of these methods, the results will shed light on cellular properties of glial cells and their contribution to neuronal function.

Another approach for a priori identification of astrocytes is the utilization of reporter mice, such as GFAP-eGFP mice (Nolte et al., 2001). However, the transcript labels only a subset of astrocytes (Nimmerjahn et al., 2004) and, moreover, the transcript is also weakly expressed by NG2 glia (Matthias et al., 2003). Alternatively, ALDH1L1-eGFP mice can be used to identify astrocytes (Heintz, 2004;Yang et al., 2011). These reporter mice exhibit a more accurate labeling pattern of astrocyte populations (Cahoy et al., 2008). Aside this, reporter mice are available to a priori identify other glia, such as oligodendrocytes (PLP-GFP mice; Fuss et al., 2000) or NG2 glia (NG2-eYFP mice; Karram et al., 2008). It is worth mentioning that all these reporter mice are suitable to be combined with imaging of ion-sensitive dyes (Moshrefi-Ravasdjani et al., 2017).

Patch Clamp-Based Approaches
Electrophysiological methods are commonly used to detect gap junctional coupling of cells. In 1966, the first evidence that astrocytes are intercellularly coupled was provided by an electrophysiological study of amphibian optic nerve by Kuffler et al. (1966). In their report, an elegant triplesharp-electrode recording mode was used to reveal a "lowresistance connection" between neuroglia, which we know now as the gap junctional coupling of fibrous astrocytes in optic nerves. This electrophysiological method was continually used until the 1980s for glial physiology study. For example, Kettenmann and Ransom used it to record cultured astrocytes and oligodendrocytes, confirming that gap junctions were indeed the molecular identities for the functional coupling of these glial subtypes (Kettenmann and Ransom, 1988;Ransom and Kettenmann, 1990).
The advent of patch-clamp in the 1990s ushered electrophysiological studies into a new era. Since the patchclamp system is able for simultaneous current injection and membrane potential recording, now only two electrodes are used for paired recording. Here, we will limit our discussion to this advanced paired recording mode and its application to analyze the functional connectivity of neighboring astrocytes.
Until now, this technique has been used by several research laboratories for study of gap junctional coupling in native astrocytes in brain slices and freshly isolated astrocytes Meme et al., 2009;Xu et al., 2010Xu et al., , 2014Ma et al., 2016;Zhong et al., 2016;Kiyoshi et al., 2018). These studies demonstrated the paired recording mode as a highly sensitive method for revealing the functional coupling of astrocytes in situ and in pairs of freshly dissociated astrocytes. To address the electrical role of gap junctional coupling for astrocyte syncytium, a single electrode method was developed in 2016 with details described in the following "Astrocyte Syncytial Isopotentiality" section. Together with computational modeling, this method allows for monitoring dynamical changes in the coupling strength of an astrocyte syncytium Kiyoshi et al., 2018). Another way to assess gap junctional coupling is to add a tracer to the internal solution of patch pipettes and to visualize gap junction-coupled cells. In the following section, we will first discuss the rationale, application, advantage, and limitation of the commonly used paired recording model and the newly developed syncytial isopotentiality measurement. Thereafter, we will highlight, how the addition of gap junction-permeable tracers to the pipette solution can be used to visualize cell-tocell coupling and to subsequently analyze the topography of tracer-coupled networks.

Paired Recording Mode
The rationale behind the design of the paired recording model lies in the basic properties of gap junction channels. Gap junctions are large aqueous pores, 8-16 Å, filled with electrolytes that make them ideal electrical conductors for the flow of ionic currents between coupled cells (Weber et al., 2004). In the adjacent cells, the easiness of the ionic current flow is determined by the number of gap junctions aggregated on the plaques in the interface of the adjacent cells, or the intercellular gap junctional resistance (R gap ). Accordingly, the paired recording mode is designed to examine the R gap through the passing of injected currents in one of the two coupled cells and to measure subsequently the size of remaining transjunctional voltage arriving at the second cell (Figures 2A,B; Bennett, 1966;Bennett et al., 1991;Ma et al., 2016). There are unique characteristics associated with paired recordings. It is known that the gap junctions formed by different Cxs differ in their permeability properties for endogenous compounds, therefore, differentially regulate the intercellular transfer of metabolites, i.e., glucose, and signaling molecules, such as ATP, glutamate, and IP 3 (Goldberg et al., 1999(Goldberg et al., , 2002Niessen et al., 2000). It is also known that Cxs vary in pore size and conductivity (∼30 to ∼300 pS) (Hille, 2001). However, the Cxs ubiquitously exhibit high selectivity to the major intracellular monovalent cation K + and Na + in the order of K + > Na + (Wang and Veenstra, 1997), and these ions are charge carriers that mediate current flow between coupled cells. Thus, independent of Cx isoforms, transjunctional voltage measurements stand out as an universal readout of gap junctional coupling (Veenstra et al., 1995;Veenstra, 1996). Additionally, paired recordings are featured by their high detection sensitivity conferred by the FIGURE 2 | Analysis of electrical coupling. (A) Paired recording of two neighboring astrocytes from hippocampal CA1 region. (B) In whole-cell current-clamp mode, the current steps, shown in the inset, were alternately delivered to one of the cells in a pair, termed the stimulated cell (C stim ), and that induced membrane potential changes in the C stim meanwhile induced transjunctional voltages (V transjunc ) in the coupled neighbor. (C) A pair of freshly dissociated hippocampal astrocytes, identified by their SR101 staining, was recorded with K + free/Na + containing electrode solution. state-of-the-art electronic engineering technology of the patchclamp amplifier, allowing detection of the ionic currents at the picoampere scale.
Experimentally, two adjacent astrocytes are sequentially recorded in whole-cell mode (Figures 2A,B). Subsequently, the current can be alternately injected into one of the recorded cells, defined as the stimulated cell (C stim .), whereas the transjunctional voltage is recorded in the neighboring recipient cell (C reci .). Although the R gap can be calculated from the basic membrane properties and the current-induced membrane voltages, the coupling strength is commonly expressed as the coupling coefficient (CC)-the ratio of voltages measured from the C reci ./C stim . The higher a CC value, the stronger the cell-tocell coupling (Bennett, 1966;Bennett et al., 1991;Ma et al., 2016).
A major advantage of paired recordings is their high sensitivity, which is determined by the open probability that is universally high among gap junctions in the range of 0.6-0.9; whereas the sensitivity of tracer coupling is mostly determined by the pore selectivity that varies among gap junctions (Nielsen et al., 2012). Consequently, in simultaneous transjunctional voltage and dye coupling measurements, it is common to see measurable transjunctional voltages in an absence of detectable dye coupling (Murphy et al., 1983;Ransom and Kettenmann, 1990;Sontheimer et al., 1991;Xu et al., 2010). An example that paired recordings have a higher sensitivity was shown in a study carried out in hippocampal astrocytes in situ (Xu et al., 2010). Incubation of brain slices with a gap junction inhibitor, meclofenamic acid (MFA, 100 µM), was able to inhibit astrocyte gap junctional coupling by 99% . Interestingly, in the presence of 100 µM MFA, the cross-diffusion of two tracers, Lucifer Yellow (LY) and biocytin, separately loaded into two recording electrodes, were completely inhibited, whereas the transjunctional voltages remained intact (Xu et al., 2010). In the barrel cortex, the Cx43 expression was found to be enriched within the barrels, but largely absent in the interbarrel space (septa), and this was associated with a restricted dye coupling inside the barrels (Houades et al., 2006). To examine whether such segregated dye coupling indeed indicates a complete absence of gap junctional of astrocytes between barrels and their surrounding septa, the paired recording was carried out between a pair of astrocytes, one inside another outside of the barrel. The results showed that in the transjunctional voltage measurement, astrocytes do communicate inside and outside of the barrels and, therefore, are gap junctional coupled into a syncytium . Therefore, the existence of gap junctional coupling can be more sensitively inspected by this method.
Nevertheless, there are also technical challenges and limitations. First of all, still, only a handful of experimenters successfully employed paired recordings in their research. The technical complexity of paired recordings to monitor junctional coupling has limited more researchers to take advantage of this powerful tool in their glial physiology study. The second obstacle that impedes the application of paired recordings is the low R M of astrocytes at an estimated level of 6.4 M (Du et al., 2015). As a result, the "leaky" membrane shunts most of the injected currents, making it impossible to estimate the current passing through gap junctions resulting in erroneous CC calculation . To make the matters worse, astrocytes are coupled into a syncytial network; each astrocyte is typically directly coupled to 7-9 nearest neighbors across the brain (Xu et al., 2010;Ma et al., 2016;Kiyoshi et al., 2018). Consequently, the injected currents to one of the recorded astrocytes should be redistributed into coupled astrocytes at unknown ratios (in a parallel electrical circuit) (Cotrina et al., 1998). Therefore, the leaking membrane and syncytial coupling make it next to impossible to calculate the actual CC in brain slice recordings. Consequently, rather low CC values in the range from 1.6% to 5.1% were reported from hippocampal astrocytes in situ (Meme et al., 2009;Xu et al., 2010).
To solve this problem, the innovative use of paired recordings was applied to freshly dissociated pairs of astrocytes to avoid extensive coupling. To circumvent the shunt of injected currents through abundantly expressed membrane K + channels, the physiological K + content in the electrode solution was substituted equimolarly by Na + ; hence, the electrode Na + equilibrating with the recorded pair of astrocytes will not leak through the membrane K + channels, and measured currents will therefore better reflect junctional coupling (Figures 2C,D). Under these conditions, a strong coupling CC of 94% was revealed. Based on this CC, there was an estimate of 2.000 gap junctions aggregated at the interface of two neighboring astrocytes, and a calculated R gap at 4.3 M , which is even lower than the astrocytic R M of 6.4 M (Du et al., 2015). These results together indicate that the electrical barrier between astrocytes is nearly absent. Recently, ultrastructural details of astrocyte-astrocyte contacts have been revealed that explain how such a low inter-astrocytic resistance could be biophysically achieved .
In summary, the rationale for paired recordings is based on an uniform feature of high open probability of gap junction channels for two intracellular monovalent cations, K + and Na + . Therefore, it offers a rather universal readout to study the functional gap junctional coupling at high sensitivity. For brain slice studies, however, the paired recordings are most valuable for inspecting the existence of functional gap junctional coupling, but are of limited value for quantitative analysis of the CC between astrocytes due to the low R M and syncytial coupling. Combinatory use of freshly dissociated pairs of astrocytes and non-physiological Na + or Cs + electrode solution is a powerful alternative to circumvent the above obstacles.

Astrocyte Syncytial Isopotentiality
As mentioned above, the R gap between astrocytes is even lower than astrocytes' R M , suggesting that two neighboring astrocytes are able to constantly equalize their membrane potentials and therefore electrically behave as one cell. By extension, the gap junction coupled astrocytes should then be able to balance their membrane potentials to comparable levels so that a syncytial isopotentiality could be achieved. In fact, this possibility was postulated in the past (Muller, 1996) and was discussed by Richard Orkand and his colleagues to be a necessity for the operation of K + spatial buffering in the brain (personal communication with Dr. Serguei Skatchkov). This syncytial isopotentiality was experimentally demonstrated in 2016 , and a system-wide existence of this feature in the astrocyte networks was confirmed soon after that (Huang et al., 2018;Kiyoshi et al., 2018;. The rationale for the methodological design is based on a basic feature of astrocytes. Physiologically, an astrocyte behaves as a perfect K + electrode (Kuffler et al., 1966;Ransom and Goldring, 1973). Therefore, one can experimentally substitute the intracellular K + concentration ([K + ] i ) through dialysis of the recorded cell with electrode solution containing equimolar (i.e. 140 mM) Na + (or Cs + ) . This, in turn, alters the V M of the recorded astrocyte from K + equilibrium potential (E K , -80 mV) to Na + equilibrium potential (E Na , ∼ 0 mV) according to the prediction from the Goldman-Hodgkin-Katz (GHK) equation. In single freshly dissociated astrocytes, the V M indeed shifts to ∼ 0 mV ( Figure 3A) . However, should the R gap be sufficiently low, the associated syncytium can then instantaneously act to compensate for the loss of physiological membrane potential (V M ) in the recorded cell, and the level of the compensation should be determined by the coupling strength and the number of directly nearest coupled neighbors Kiyoshi et al., 2018).
Experimentally, the syncytial isopotentiality can be detected by the substitution of endogenous K + by a 140 mM Na + /K +free electrode solution ([Na + ] P ) (Figures 3A,B) and recording the astrocyte in current-clamp mode. The breakthrough of the membrane patch shifted the V M immediately to a resting membrane potential of -78 mV (Figures 3A,B). Over time, the V M reaches a stationary level of -73 mV. This is in sharp contrast to the anticipated depolarization to 0 mV as predicted by the GHK equation for K + -free electrode solution ( Figure 3A). The initial V M recording (V M,I ) reflects the true resting V M of an astrocyte Kiyoshi et al., 2018). In hippocampal astrocyte syncytium, the steady-state V M (V M,SS ) in [Na + ] P recordings is ∼5 mV more depolarized than V M,I .

The Ionic Mechanisms Engaged in the Establishment of V M,SS
To biophysically explain how the quasi-physiological V M,SS is established, different size of syncytia, i.e., syncytia containing varying number of astrocytes, were used for V M,SS recordings, and computational modeling was used to simulate the underlying ionic mechanisms . The rupture of an astrocyte with [Na + ] p initiates dialysis of Na + to the recorded astrocyte and associated syncytium (Figure 3B 1 ). In the recorded cell, the Na + dialysis dissipates the endogenous K + content hence abolishes the physiological V M established by the across membrane K + gradient. To the coupled syncytium, the Na + dialysis generates a Na + gradient and current flow across gap junctions that depolarizes neighboring astrocytes and hyperpolarizes the recorded cell. The latter is the major contributor to the quasi-physiological V M,SS . Additionally, the dissipation of K + content in the recorded cell attracts an influx of K + from neighboring astrocytes. The accumulated K + has the potential to establish a hyperpolarizing potential in the recorded cell therefore additionally contributes to the totality of the quasiphysiological V M,SS . As shown in Figure 3B 2 , these two ionic flows take approximately 5 min to reach a steadystate after rupture of whole-cell recording (Figure 3B 2 ).
How does the strength of syncytial isopotentiality influence the intensity of the Na + and K + current flows? As noted above, in the [Na + ] p recorded astrocyte, there are two ionic current flows in opposite directions and collectively contribute to the measured V M,SS ; the outward-going Na + current from recorded cell to the coupled cells, and inward-going K + current flow from the coupled astrocytes to the recorded cell. To simplify the analysis, we take the outward-going Na + (I Na,out ) to one of the coupled astrocytes as an example, the proximity of the potentials in these two cells can be expressed as the difference of the voltages between the Na + -loaded astrocyte (V Na ) and a coupled neighbor (V N ) where (V N -V Na ) = 0 mV is a theoretically ideal isopotentiality achieved between the two cells. Assuming I Na,out is a constant determined by its chemical gradient down the neighboring cell, then a higher strength of isopotentiality, i.e., lower (V N -V Na ), is correlated to a lower junctional resistance (R gap ). Secondly, as (V N -V Na ) approaches the ideal isopotentiality of 0 mV, the I Na,out also diminishes to ∼ 0 pA. By extension, closer proximity of potentials between the recorded cell and its associated astrocytes, the less outward-going Na + current flow from [Na + ] p recorded astrocyte toward its associated syncytium.
Likewise, the intensity of the inward-going K + current (I K,in ) and syncytial coupling strength follows with the same relationship: where the inward-going K + current is impeded by increasing proximity of the V Na to V N. It should be noted that K + cannot be substantially buildup due to efflux of K + through membrane K + channels in the [Na + ] p recorded astrocyte; consequently, less hyperpolarizing potential can be built up to make a significant contribution to the recorded V M, SS .
In summary, we described a method that uses [Na + ] p to disrupt the continuity of a syncytial isopotentiality, and that in turn informs of the existence and the strength of the isopotentiality in an astrocyte syncytium. Biophysically, gap junctional ionic movement occurs during the equalization of the potential differences in a syncytium, therefore a strong syncytial isopotentiality means a less ionic movement inside a syncytium. Additionally, a larger syncytium has a greater capacity to minimize the ionic movement, which has been simulated in a computational model . Functionally, in the event of local extracellular environment changes, e.g., neuronal firing induced high K + , syncytial isopotentiality provides a sustained driving force to individual astrocytes for high efficient K + uptake, spatial transfer and release of K + to regions where neuronal activity is low (Terman and Zhou, 2019).

V M,SS as a Functional Readout of Coupling Strength (S) of Syncytial Coupling
Based on the discussion above, the V M,SS is established and regulated by the R gap and the number of astrocytes in a coupled syncytium, therefore can lean to a more hyperpolarizing V M in the neighboring astrocytes, or a more depolarizing V M established by intracellular Na + . Thus, the V M,SS serves as a dynamic readout of the strength of syncytial coupling. To be able to quantitatively correlate the changes of V M,SS with S, a computational model has been established (Figures 3C,D) where a stronger syncytial coupling leads to a stronger compensation of the V M,ss towards the physiological V M of neighboring astrocytes established by 140 mV [K + ] i , whereas a weaker coupling shifts the V M,ss toward GHK predicted E K for the Na + electrode solution. More details about the biophysical principles and assumptions used to build up this computational model are available in this publication . In addition, this model can be used for analysis of the dynamic change of coupling strength, for instance, during neuronal activation .
This method comprises several advantages. First, differing from paired recordings, V M,SS is measured from single electrode recordings. Second, this method allows for dynamic monitoring of the coupling strength of a syncytium over time. Third, this method can be incorporated with astrocyte syncytial anatomy studies. For example, ALDH1L1-eGFP reporter mice were use for a priori astrocyte identification and examination of syncytial isopotentiality across brain regions. Additionally, the recorded brain slices were then further processed with the tissue-clearing method (Susaki et al., 2014(Susaki et al., , 2015, i.e., depletion of the brain lipid content, for high-resolution confocal imaging study of the cellular morphology and spatial organization patterns of astrocytes . This study showed that in different layers of the visual cortex, the anatomy, in terms of cell density, interastrocytic distance and the number of the nearest neighbors vary in morphometric analysis. However, S does not differ between layers. Additionally, S of the visual cortex was found to be stronger than in the hippocampal CA1 region . Fourthly, this method can be incorporated with tracer coupling to map the directionality and spatial coupling of a syncytium (see also "Tracer Coupling"). For example, in the cerebellum, Bergmann glia and velate astrocytes are derived from the same progenitor pool but are strikingly different in their morphology (Kita et al., 2013). Bergmann glia are characterized by having their cell bodies arranged in rows alongside with the soma of Purkinje neurons and extension of their processes along the Purkinje cell layer toward the pia of the cerebellum. Velate astrocytes are cerebellar protoplasmic astrocytes that exhibit characteristic velate sheath processes and are more dispersed in arrangement (Chan-Palay and Palay, 1972). S is significantly weaker in Bergmann glia networks than those established by velate astrocytes at the granular layer. In the tracer coupling analysis, the injection of tracer revealed the coupling of Bergmann glia and velate astrocytes. Thus, despite a striking difference in syncytial anatomy, the syncytial isopotentiality occurs to syncytial networks established by both subtypes of astrocytes .
A limitation in this method is the inference of a syncytial isopotentiality based on biophysical principles and electrophysiological measurements. Significant progress has been made in the technique of genetically encoded voltage indicator (Kang et al., 2019). However, this state-of-the-art technique is still below the threshold to detect the subtle variation of voltages in an astrocyte syncytium, and therefore, future optimization of this technique is crucial to recruit advanced imaging techniques to study the physiology and pathology of astrocyte syncytial networks.

Tracer Coupling
Aside this direct measurement of cell-to-cell coupling, tracer coupling can be utilized to mimic diffusion within in the network. Tracers are usually loaded for several minutes into a single cell via the backfill of the patch pipette. Simultaneously, tracers diffuse within the gap junction network. The tracer concentration is highest in the patched cell and declines within the network with increasing distance as it diffuses. There are various tracers available comprising different advantages and disadvantages ( Table 1; see also Abbaci et al., 2008). An often used tracer is LY (Kawata et al., 1983). It is a fluorescent dye that allows direct observation of diffusion within the network. Subsequently, LY labeling can be combined with immunohistochemistry to determine the identity of coupled cells (Binmoller and Muller, 1992;Konietzko and Muller, 1994). However, it comprises low permeability at gap junctions consisting of Cx30 (Rackauskas et al., 2007). As Cx30 expression increases during early postnatal development (Nagy et al., 1999;Griemsmann et al., 2015;Augustin et al., 2016;Wadle et al., 2018), LY will only highlight a fraction of coupling in more mature tissue. In addition, LY has a low solubility and tends to clog electrodes. As LY interferes with endogenous electrophysiological properties, it is rather not suitable to be combined with electrophysiological analyses (Tasker et al., 1991). Further fluorophores, e.g., Alexa Fluor (AF) dyes, can be used for tracing coupled cells as well (Han et al., 2013). Like LY, spreading of AF dyes can be assessed directly. However, they do not pass through Cx30 containing gap junctions and just insufficiently through other gap junctions requiring administration at high concentration (Weber et al., 2004). At lower concentrations, there is almost no diffusion to neighboring cells so that AF dyes can be used to label the patchclamped cell (Augustin et al., 2016;Wadle et al., 2018;Eitelmann et al., 2019). Two other tracers, namely neurobiotin (Nb) and biocytin (Horikawa and Armstrong, 1988;Huang et al., 1992), are colorless and require fixation and further processing of the tissue. Thus, their diffusion cannot be assessed directly. The two tracers are recognized by streptavidin and avidin (Livnah et al., 1993). The latter ones can be linked to either fluorophores or enzymes. Using a fluorophore allows the combination with further immunohistochemical processing of the tissue (Schools  Augustin et al., 2016;Eitelmann et al., 2019Eitelmann et al., , 2020. Using peroxidases produces a light-stable product that is not sensitive to photo-bleaching (Konietzko and Muller, 1994;D'Ambrosio et al., 1998). Alternatively, fluorescent glucose analogues can be used (Speizer et al., 1985;Yamada et al., 2000). They allow to visualize activity-dependent, directed glucose redistribution in otherwise spherical networks (Rouach et al., 2008). However, it has to be kept in mind that, for example, 2-NBDG enters the glycolytic pathway and is degraded to a non-fluorescent derivative (Yoshioka et al., 1996). Gap junctional coupling is not uniform, e.g., it was shown to increase developmentally (Binmoller and Muller, 1992;Schools et al., 2006;Houades et al., 2008;Langer et al., 2012;Griemsmann et al., 2015). Furthermore, there are many examples of spherical networks upon radial tracer diffusion in certain brain regions (Binmoller and Muller, 1992;Houades et al., 2006;Muller et al., 2009). However, in others-in particular in sensory systemstracer spreading is unequal in different directions (Houades et al., 2008;Augustin et al., 2016;Claus et al., 2018;Condamine et al., 2018a;Wadle et al., 2018). There, network anisotropy strongly correlates with anatomical and functional organization of the underlying neuronal circuitry. The anisotropy of tracer spreading originates from astrocyte topography (Anders et al., 2014;Augustin et al., 2016;Ghezali et al., 2018;Wadle et al., 2018). Interestingly, in the lateral superior olive-a conspicuous nucleus in the auditory brainstem-absence of spontaneous cochlea-driven neuronal activity leading to disturbed neuronal circuitry (Hirtz et al., 2012;Muller et al., 2019) causes altered astrocyte topography followed by altered orientation of tracercoupled networks (Eitelmann et al., 2020). In recent years, several different approaches were developed to analyze the anisotropy of tracer-coupled networks (Figure 4). Most approaches are able to reliably detect network anisotropy; however, some are working only in certain brain regions (Eitelmann et al., 2019). The different approaches rely on (1) distance of the farthest cells that are labeled, (2) labeling intensity, (3) position of all coupled cells, or (4) a combination of the aforementioned parameters. Most approaches use the ratio of the diffusion range and/or brightness (B) Approaches to study the topography of tracer-coupled networks. Anisotropy is often determined by the ratio of tracer spread (distance and/or intensity) in two directions that are orthogonal to each other (B 1−4,6 ). Alternatively, a purely vector-based approach can be used (B 5 ). (C) In case of ratio-based analyses, rotation of the coordinate system allows the precise determination of maximal anisotropy and orientation (C 1 ; exemplarily shown for vector means, B 6 ). Afterward, results can be gathered in a radar diagram to denote the degree of anisotropy and orientation of networks (C 2 ). Frontiers in Cellular Neuroscience | www.frontiersin.org of the tracer in two directions. The most convenient approach is to measure the extent of tracer spreading in two directions orthogonal to each other ("YX ratio"). Here, anisotropy is determined by the four outermost cells showing tracer signal (Figure 4B 1,2 ; Houades et al., 2006Houades et al., , 2008Augustin et al., 2016;Ghezali et al., 2018;Wadle et al., 2018). However, since the tracer signal is declining with distance to the loaded cell, it can be difficult to determine the correct extension of the network. Alternatively, the product of network extension multiplied with the somatic tracer intensity for two directions orthogonal to each other can be calculated ("Intensity + coordinates"; Figure 4B 3 ; Anders et al., 2014). However, elevated somatic signal intensities FIGURE 5 | Na + diffusion in glial networks. (A) Cells in the center of the inferior colliculus can be loaded with the fluorescent Na + indicator SBFI-AM (left). Astrocytes and bona fide oligodendrocytes can be distinguished by sulforhodamine (SR) 101-labeling. (B) Electrical stimulation results in Na + load of a single astrocyte (a 1 ). Subsequently, neighboring astrocytes (a 3 -a 5 ,a 7 ; SR + ) and bona fide oligodendrocytes (a 2 ,a 6 ; SR -), show elevated Na + transients as well. (C,D) Na + diffusion can be elicited by stimulation of both astrocytes (C) and bona fide oligodendrocytes (D). The amplitude of Na + transients depends on the distance from the stimulated cell. Figure modified from Wadle et al. (2018). due to expression of endogenous biotin (Bixel and Hamprecht, 2000;Yagi et al., 2002) might result in a distorted ratio. In another approach, the labeling intensity of somata and processes is analyzed to determine network anisotropy ("Intensity profiles"; Figure 4B 4 ; Claus et al., 2018). Here, intensity plot profiles of two rectangles orthogonal to each other and the ratio of respective full-width at half-maximum (FWHM) are calculated. However, cell number or individual positions are neglected and must be analyzed separately, if required. Finally, there are two vector-based approaches. The first calculates the "Vector sum" (Figure 4B 5 ; Condamine et al., 2018a,b). However, it only works in brain regions with defined borders, i.e., diffusion barriers resulting from reduced gap junction coupling. Examples of such brain regions are the trigeminal main sensory nucleus and the columns of the barrel cortex. In both, gap junction coupling is stronger within the nucleus and columns compared to areas outside. However, anisotropic tracer diffusion will be visualized only if the tracer is injected into an astrocyte that is not located in the center (Houades et al., 2008;Condamine et al., 2018a) as the "Vector sum" approach is not capable to detect the anisotropy of tracer-coupled networks if they are symmetric with respect to a point (Eitelmann et al., 2019). The second vector-based approach calculates the "Vector means" in four 90 • sectors and the ratio of tracer extension is calculated ( Figure 4B 6 ; Eitelmann et al., 2019Eitelmann et al., , 2020. However, analyzing the anisotropy of tracer spreading using only two fixed axes might result in falsified results. For example, if an anisotropic network is turned by 45 • from one of the two axes, all ratiobased approaches will postulate spherical network. Therefore, a subsequent analysis using a rotating coordinate system will not only determine the maximal anisotropy of a network, but will also define the preferred orientation ( Figure 4C; Eitelmann et al., 2019). Taken together, heterogeneity of gap junctional coupling can be visualized excellently by tracer coupling studies. However, they often provide only a snap-shot of coupling using a non-physiological tracer.
Wide Field (Na + ) Imaging Imaging of intracellular ion concentration can be a good tool to supplement tracer coupling studies. For the interpretation of ion diffusion within the gap junction network, it is beneficial to analyze the spread of ions that is less effected by signaling cascades. Thus, Ca 2+ is a less suitable candidate as signaling to neighboring cells is generated by intra-and extracellular pathways (Giaume and Venance, 1998;Bernardinelli et al., 2004;Scemes and Giaume, 2006). However, intercellular Na + spread depends on gap junctional coupling as deletion of Cx43 and Cx30 prevents ion exchange between neighboring astrocytes (Wallraff et al., 2006;Langer et al., 2012). However, it has to be kept in mind that intracellular Na + is not completely independent from signaling cascades as it is linked to Ca 2+ via the Na + /Ca 2+ exchanger (Felix et al., 2020a). For Na + imaging, cells are dyeloaded, e.g., with the membrane-permeable form of SBFI (SBFIacetoxymethyl ester). After cleavage by endogenous esterases SBFI allows ratiometric imaging of [Na + ] i (Figure 5; Minta and Tsien, 1989;Meier et al., 2006). Na + load into a single cell can be achieved via direct electrical stimulation. This will result in Na + rise in the stimulated and in neighboring cells (Figure 5B; Langer et al., 2012;Augustin et al., 2016;Moshrefi-Ravasdjani et al., 2017;Wadle et al., 2018). Measuring the maximal [Na + ] i increase allows for the calculation of the length constant λ using a mono-exponential function (Figures 5C,D; Augustin et al., 2016;Moshrefi-Ravasdjani et al., 2017;Wadle et al., 2018), which demonstrates, how efficient Na + is redistributed and how strong gap junctional coupling is. It was shown that spatial spread of Na + between astrocytes was halfway far in the corpus callosum compared to other brain regions, i.e., hippocampus, lateral superior olive, and inferior colliculus (Langer et al., 2012;Augustin et al., 2016;Moshrefi-Ravasdjani et al., 2017;Wadle et al., 2018). Furthermore, Na + diffusion is stronger within homocellular networks. In contrast, in heterocellular (panglial) networks Na + redistribution is reduced (Figure 5D; Moshrefi-Ravasdjani et al., 2017;Wadle et al., 2018), which likely results from a lower permeability of connexons, which are incorporated into the heterotypic gap junction channels (Bedner et al., 2006). Taken together, imaging of ion sensitive dyes is a good supplement to tracer coupling studies to further characterize gap junctional communication.

CONCLUSION
Gap junctional communication between glial cells is important for ion and neurotransmitter homeostasis and ensures stabilization of their membrane potential. Though astrocytes throughout the brain share similar properties, they exhibit a considerable amount of region-dependent heterogeneity. To unravel these particular differences suitable approaches are necessary. In this review, we summarized and described well-established and recently developed methods that will allow electrophysiology and imaging laboratories to analyze gap junctional coupling in acute tissue slices.

AUTHOR CONTRIBUTIONS
JS and MZ designed the study. JS, MZ, and SE wrote the manuscript. SE designed and arranged the figures. All authors contributed to the article and approved the submitted version.