Changes in Astroglial K+ upon Brief Periods of Energy Deprivation in the Mouse Neocortex

Malfunction of astrocytic K+ regulation contributes to the breakdown of extracellular K+ homeostasis during ischemia and spreading depolarization events. Studying astroglial K+ changes is, however, hampered by a lack of suitable techniques. Here, we combined results from fluorescence imaging, ion-selective microelectrodes, and patch-clamp recordings in murine neocortical slices with the calculation of astrocytic [K+]. Brief chemical ischemia caused a reversible ATP reduction and a transient depolarization of astrocytes. Moreover, astrocytic [Na+] increased by 24 mM and extracellular [Na+] decreased. Extracellular [K+] increased, followed by an undershoot during recovery. Feeding these data into the Goldman–Hodgkin–Katz equation revealed a baseline astroglial [K+] of 146 mM, an initial K+ loss by 43 mM upon chemical ischemia, and a transient K+ overshoot of 16 mM during recovery. It also disclosed a biphasic mismatch in astrocytic Na+/K+ balance, which was initially ameliorated, but later aggravated by accompanying changes in pH and bicarbonate, respectively. Altogether, our study predicts a loss of K+ from astrocytes upon chemical ischemia followed by a net gain. The overshooting K+ uptake will promote low extracellular K+ during recovery, likely exerting a neuroprotective effect. The resulting late cation/anion imbalance requires additional efflux of cations and/or influx of anions, the latter eventually driving delayed astrocyte swelling.


Introduction
A classical function of astrocytes is the regulation and maintenance of a low potassium concentration in the extracellular space ([K + ] o ) [1]. By taking up K + released from active neurons, astrocytes keep [K + ] o below the so-called ceiling level of about 10 mM [2][3][4]. This prevents detrimental accumulation of K + in the extracellular space, protecting neurons from excessive K + -induced depolarization [5,6]. The mechanisms of astrocytic K + uptake involve plasma membrane transporters as well as K + channels [7,8]. Astrocytic Na + /K + -ATPase (NKA) apparently plays a predominant role, but the sodium-potassium-chloride cotransporter 1 (NKCC1) is likely to aid K + clearance upon more severe rises in [K + ] o [9,10].
Maintenance of [K + ] o by astrocytes is thus largely dependent on their NKA activity and on intact energy metabolism. In the core region of an ischemic stroke, failure of energy metabolism results in a breakdown of astrocyte K + regulation and [K + ] o homeostasis [5,6,11,12]. A failure of astrocytic K + uptake will not only hamper clearance of extracellular K + , but will also cause a loss of K + from astrocytes, contributing to the rise in [K + ] o and promoting neuronal depolarization during energy failure [13,14]. As opposed to the ischemic core region, available energy resources in the neighboring penumbra may allow full recovery upon timely reperfusion [15]. The penumbra, however, is exposed to
For preparation of acute tissue slices of the neocortex, brains of mice at P14-21 were prepared and cut in a modified preparation ACSF, containing 0.5 mM CaCl 2 and 6 mM MgCl 2 to dampen glutamate-induced cellular excitation. To label astrocytes, slices were then incubated for 20 min at 34 • C in preparation ACSF containing 0.5-1 µM sulforhodamine (SR) 101, followed by another 10 min at 34 • C in SR101-free standard ACSF [35]. Afterward, slices were kept in standard ACSF at room temperature (20)(21)(22) • C) until used for experiments.
Experiments were performed in layers II/III of the somatosensory cortex and were carried out at room temperature. Slices were perfused with ACSF at a rate of 2.5 mL/min. Transient chemical ischemia was induced by perfusing slices with glucose-free standard ACSF containing the cytochrome C oxidase inhibitor sodium azide (NaN 3 ; 5 mM) and the non-metabolizable glucose analog 2-deoxyglucose (2-DG; 2 mM) [19,36].
All chemicals were purchased from Merck/Sigma-Aldrich (St. Louis, MO, USA) or AppliChem (Darmstadt, Germany) if not stated otherwise.

Imaging of ATP
Imaging of intracellular ATP was performed in organotypic slice cultures using the FRET-sensor ATeam1.03 YEMK ("ATeam") [37]. In brief, 0.5 µL of a vector (AAV5/2) carrying the code for ATeam under the control of astrocyte-specific promotor GFAP was applied to the top of a slice after 1-3 days in culture as described before [34]. Slices were maintained in the incubator for a total of at least 10 days before performing experiments.
Fluorescence was collected from ROIs representing cell bodies of SR101-positive astrocytes and analyzed offline employing "OriginPro 2019/2021". SBFI-emission from individual ROIs was background corrected [38] and corrected for bleaching. For BCECF, the fluorescence ratio (F 458 /F 488 ) was calculated after background correction. Changes in SBFI emission and BCECF ratio were converted into mM [Na + ] and pH units, respectively, using established in situ calibration procedures [19,38,39].
Baseline [Na + ] i of layer II/III neocortical astrocytes was determined recently in our laboratory employing an approach introduced by Mondragao et al. [40,41]. This approach was adapted to determine baseline pH i . In brief, slices were loaded with BCECF-AM, and the baseline ratio of a selected cell was recorded. Subsequently, this cell was subjected to whole-cell patch-clamp using a pipette solution with a pH of 7.3, which contained 0.5 mM BCECF. The initial baseline pH i of the undisturbed cell was calculated from the change in BCECF ratio upon membrane rupture and the known pH in pipette solution (and calibration parameters determined before).
For cell-attached recordings [42], pipettes were filled with either ACSF or standard pipette solution. The latter contained (in mM): 116 K-methansulfonate, 32 KCl, 10 HEPES, 8 NaCl, 4 Mg-ATP, and 0.4 Na 2 -GTP; pH 7.3. The offset potential was corrected to account for the potential resulting from concentration differences between pipette solution and ACSF [42]. To record E M in the cell-attached mode, seal resistance must be at least 100-fold higher than the membrane resistance (R M ) of the recorded cell [42]. R M in cortical astrocytes was around 10 MΩ in 2-3 weeks old animals, and recordings were only accepted if the seal resistance was larger than 1 GΩ, which was continuously monitored using test pulses (−50 pA) every 30 s.
Whole-cell current-clamp recordings were performed to determine the relative Na + versus K + permeability of the plasma membrane (α = P Na /P K ) [43]. To this end, pipettes were filled with standard pipette solution. Voltage traces were sampled at 100 Hz. Measurements were rejected if the seal resistance exceeded 15 MΩ to ensure sufficient electrical and diffusional access to the patched cell. The liquid junction potential was not corrected. Data were analyzed using "IGOR Pro" (WaveMetrics, Lake Oswego, OR, USA), "MS Excel", and "OriginPro 2021".

Data Presentation and Statistics
Each set of experiments was performed on tissue slices taken from at least 3 different animals. Results given in the text represent mean ± standard deviation (SD). Data were illustrated in box plots showing individual data points (grey diamonds), mean (square), median (horizontal line), SD (box), and min/max (whiskers). Data were statistically analyzed using "WinSTAT" (R. Fitch Software, Bad Krozingen, Germany) and "OriginPro 2019/2021". Data were first tested for outliers. Thereafter, normal distribution was assessed using a Kolmogorov-Smirnov test. In case of normal distribution, results were assessed by two-tailed, paired, or unpaired Student's t-tests. Otherwise, results were assessed by the Wilcoxon test and U-test (Mann-Whitney) for paired and unpaired data, respectively. ρ represents the error probability, * ρ < 0.05, ** ρ < 0.01, *** ρ < 0.001. n represents the number of cells or experiments per slice per animal. In case of two comparisons, data were statistically analyzed by the tests described above under post hoc Šidák correction (SC) of critical values [44]: * p < 0.0253, ** p < 0.005, *** p < 0.0005.

Effect of Transient Energy Depletion on Intracellular ATP
The goal of the present study was to gain insight into changes in astrocytic [K + ] i upon transient energy depletion, simulating the situation in the ischemic penumbra. Energy failure was induced by transient inhibition of glycolysis and oxidative phosphorylation ("chemical ischemia") as described earlier [19,36]. To evaluate the effect of brief chemical ischemia on cellular ATP levels, we expressed the nanosensor ATeam1.03 YEMK ("ATeam") in organotypic tissue slices of the neocortex ( Figure 1A) [34,37]. Perfusion of slices with the metabolic inhibitors for 2 min caused a well-detectable, reversible decrease in the ATeam ratio by 17.3 ± 5.3% of the baseline level determined in standard ACSF (n = 27 cells, 4 tissue slices, 3 animals) (Figure 1B,C; Table 1). Based on our recent calibrations using this sensor [45], these data imply a decline in the intracellular ATP concentration by about 1 mM in response to this manipulation. The ATeam ratio recovered slowly towards baseline, and 15 min after reperfusion with standard saline, ATeam levels were still about 3% lower than the initial baseline value. Data were analyzed using "IGOR Pro" (WaveMetrics, Lake Oswego, OR, USA), "MS Excel", and "OriginPro 2021".

Data Presentation and Statistics
Each set of experiments was performed on tissue slices taken from at least 3 different animals. Results given in the text represent mean ± standard deviation (SD). Data were illustrated in box plots showing individual data points (grey diamonds), mean (square), median (horizontal line), SD (box), and min/max (whiskers). Data were statistically analyzed using "WinSTAT" (R. Fitch Software, Bad Krozingen, Germany) and "OriginPro 2019/2021". Data were first tested for outliers. Thereafter, normal distribution was assessed using a Kolmogorov-Smirnov test. In case of normal distribution, results were assessed by two-tailed, paired, or unpaired Student's t-tests. Otherwise, results were assessed by the Wilcoxon test and U-test (Mann-Whitney) for paired and unpaired data, respectively. ρ represents the error probability, * ρ < 0.05, ** ρ < 0.01, *** ρ < 0.001. n represents the number of cells or experiments per slice per animal. In case of two comparisons, data were statistically analyzed by the tests described above under post hoc Šidák correction (SC) of critical values [44]: * p < 0.0253, ** p < 0.005, *** p < 0.0005.

Effect of Transient Energy Depletion on Intracellular ATP
The goal of the present study was to gain insight into changes in astrocytic [K + ]i upon transient energy depletion, simulating the situation in the ischemic penumbra. Energy failure was induced by transient inhibition of glycolysis and oxidative phosphorylation ("chemical ischemia") as described earlier [19,36]. To evaluate the effect of brief chemical ischemia on cellular ATP levels, we expressed the nanosensor ATeam1.03 YEMK ("ATeam") in organotypic tissue slices of the neocortex ( Figure 1A) [34,37]. Perfusion of slices with the metabolic inhibitors for 2 min caused a well-detectable, reversible decrease in the ATeam ratio by 17.3 ± 5.3% of the baseline level determined in standard ACSF (n = 27 cells, 4 tissue slices, 3 animals) (Figure 1B,C; Table 1). Based on our recent calibrations using this sensor [45], these data imply a decline in the intracellular ATP concentration by about 1 mM in response to this manipulation. The ATeam ratio recovered slowly towards baseline, and 15 min after reperfusion with standard saline, ATeam levels were still about 3% lower than the initial baseline value. These results demonstrate that chemical ischemia induction for 2 min causes a transient decrease in cellular ATP levels in astrocytes. In all following experiments, preparations were perfused with the metabolic inhibitors for 2 min to result in moderate transient metabolic stress. These results demonstrate that chemical ischemia induction for 2 min causes a transient decrease in cellular ATP levels in astrocytes. In all following experiments, preparations were perfused with the metabolic inhibitors for 2 min to result in moderate transient metabolic stress.

Changes of Ion Homeostasis and Astrocytic Membrane Potential during Chemical Ischemia
Owing to the lack of suitable techniques for quantitative experimental determination of [K + ] i in astrocytes in situ, we employed a combined empirical-theoretical approach. The latter exploits the dominating K + permeability of the plasma membrane of astrocytes, which, together with a minor permeability for Na + , allows an approximation of their membrane potential (E M ) by a simplified GHK equation [27,43]: where R is the universal gas constant, T is the absolute temperature, F is the Faraday constant, [X z ] o/i are respective ion concentrations outside and inside of the cell, and α is the relative membrane permeability for Na + versus K + (P Na /P K ). Rearranging Equation (1) then enables the calculation of [K + ] i : For a realistic approximation of [K + ] i using Equation (2), we determined all other parameters ([Na + ] i , [Na + ] o , [K + ] o , E M , and α) experimentally in astrocytes in acutely isolated tissue slices, thereby going beyond former studies using this approach (e.g., [14]).
Wide field imaging with the Na + -sensitive fluorescent dye SBFI was employed to measure [Na + ] i [38]. Recent work from our laboratory showed that neocortical astrocytes exhibited an average baseline [Na + ] i of 12.1 mM [41]. Perfusion with metabolic inhibitors for 2 min caused a rapid increase in astrocytic [Na + ] i by 24.4 ± 7.2 mM (p = 2 × 10 −29 , *** after SC) (Figure 2A). Peak [Na + ] i was reached within 137 ± 21 s and [Na + ] i declined towards the initial baseline within 10-11 min after reperfusion (p = 6 × 10 −28 , *** after SC, n = 34/4/4) (Figure 2A 1 ,A 2 ). In the extracellular space, a baseline [Na + ] o of 157.4 ± 1.5 mM was determined using ion-sensitive microelectrodes [22]. In response to induction of chemical ischemia, [Na + ] o decreased by 1.9 ± 1.0 mM (p = 0.003, ** after SC) within 158 ± 24 s and then fully recovered within about 3 min upon washout of the drugs (p = 0.002, ** after SC; n = 22/22/11) ( Figure 2B; data summarized in Table 1). For the determination of α (P Na /P K ), the E M of astrocytes was recorded in the wholecell patch-clamp mode. In this configuration, astrocytic [Na + ] i and [K + ] i were determined by their respective concentrations in the pipette saline (see methods). α was calculated, rewriting Equation (1) revealing an α of 0.0100 ± 0.0031 in neocortical astrocytes. As mentioned, whole-cell patch-clamp results in a rapid dialysis of the recorded soma with the pipette saline. This, however, will also result in a partial clamping of intracellular ion concentrations during chemical ischemia, mitigating eventual changes in cellular membrane potentials [14]. To circumvent these effects, measurement of E M induced by metabolic inhibition was performed in the cell-attached mode. After the formation of a GΩ seal, the recorded potential slowly shifted towards more negative values, attaining a stable value of −90.7 ± 5.1 mV within about 10-20 min (n = 6/6/4; not shown). Upon perfusion with metabolic inhibitors for 2 min, astrocytes transiently depolarized by 15.5 ± 3.8 mV (p = 0.003, ** after SC) ( Figure 3B 1 -B 3 ). The peak depolarization was reached after 201 ± 65 s ( Figure 3B 4 ), where after E M showed an undershoot by 4.8 ± 3.2 mV. Subsequently, E M fully recovered to baseline within about 11 min after reperfusion with standard saline (p = 4 × 10 −4 , *** after SC) (Figure 3B 1 -B 3 ; data summarized in Table 1). soma with the pipette saline. This, however, will also result in a partial clamping of intracellular ion concentrations during chemical ischemia, mitigating eventual changes in cellular membrane potentials [14]. To circumvent these effects, measurement of EM induced by metabolic inhibition was performed in the cell-attached mode. After the formation of a GΩ seal, the recorded potential slowly shifted towards more negative values, attaining a stable value of −90.7 ± 5.1 mV within about 10-20 min (n = 6/6/4; not shown). Upon perfusion with metabolic inhibitors for 2 min, astrocytes transiently depolarized by 15.5 ± 3.8 mV (p = 0.003, ** after SC) ( Figure 3B1-B3). The peak depolarization was reached after 201 ± 65 s ( Figure  3B4), where after EM showed an undershoot by 4.8 ± 3.2 mV. Subsequently, EM fully recovered to baseline within about 11 min after reperfusion with standard saline (p = 4 × 10 −4 , *** after SC) ( Figure 3B1-B3; data summarized in Table 1).   Table 1). tion (2). This revealed an average baseline of astrocytic [K + ]i of 146.1 mM ( Figure 4B). Upon metabolic inhibition, [K + ]i decreased by 42.8 mM within 229 s to a minimum level of 103.4 mM. After this decline, [K + ]i slowly increased again, showing a transient overshoot of 16 mM that peaked roughly 6 min after washout. Finally, [K + ]i slowly recovered to a level close to the initial baseline, which was reached within about 18 min after reperfusion with standard ACSF (Figure 4B; data summarized in Table 1).   (2). The grey envelope again depicts the 95% confidence interval, which was calculated from the individual confidence intervals given in (A).

Cation-Anion Balance during Transient Chemical Ischemia
Our results presented thus far indicate a mismatch between the calculated maximum loss of K + (43 mM) and the experimentally determined maximum Na + load of astrocytes (24 mM). This apparent cation imbalance requires additional transport of charged molecules across the membrane to maintain electroneutrality. One possibility is the passage of Cl − , but recent work indicated that [Cl − ] i of neocortical astrocytes does not undergo significant changes in response to brief chemical ischemia [36]. An alternative candidate is HCO 3 − , for which astrocytes possess efficient transport mechanisms across the plasma membrane [46,47]. The [HCO 3 − ] is intimately linked to pH via the activity of carbonic anhydrases [48], and we thus studied extra-and intracellular pH to address this possibility.
The Henderson-Hasselbalch equation, which describes the relation between pH and [HCO3 − ] was solved for [HCO3 − ]o to enable calculation of changes in [HCO3 − ]o in response to chemical ischemia as shown in Figure 5C: Finally, we used Equation (5) to calculate [HCO3 − ]i ( Figure 5D) as reported before [49]: To reveal the presumed contribution of a movement of HCO3 − to the cation-anion balance during transient chemical ischemia, we first subtracted the averaged traces of astrocytic [Na + ]i and [K + ]i. This uncovered a biphasic anion gap, predicting an additional loss of anions during the initial decline in [K + ]i, which turned into an anion gain during the overshoot in [K + ]i ( Figure 6A). In a second step, we subtracted the calculated reduction in [HCO3 − ]i from the first curve, which reduced the initial anion gap by about 50% as shown To reveal the presumed contribution of a movement of HCO 3 − to the cation-anion balance during transient chemical ischemia, we first subtracted the averaged traces of astrocytic [Na + ] i and [K + ] i . This uncovered a biphasic anion gap, predicting an additional loss of anions during the initial decline in [K + ] i , which turned into an anion gain during the overshoot in [K + ] i ( Figure 6A). In a second step, we subtracted the calculated reduction in [HCO 3 − ] i from the first curve, which reduced the initial anion gap by about 50% as shown in Figure 6B. The ongoing acidification (and ongoing decrease in [HCO 3 − ] i ), however, even aggravated the remaining anion gap in the second phase of recovery ( Figure 6B). To reveal the presumed contribution of a movement of HCO3 − to the cation-anion balance during transient chemical ischemia, we first subtracted the averaged traces of astrocytic [Na + ]i and [K + ]i. This uncovered a biphasic anion gap, predicting an additional loss of anions during the initial decline in [K + ]i, which turned into an anion gain during the overshoot in [K + ]i ( Figure 6A). In a second step, we subtracted the calculated reduction in [HCO3 − ]i from the first curve, which reduced the initial anion gap by about 50% as shown in Figure 6B. The ongoing acidification (and ongoing decrease in [HCO3 − ]i), however, even aggravated the remaining anion gap in the second phase of recovery ( Figure 6B).  Table 1 summarize the data presented in this work. Our results demonstrate that brief chemical ischemia, induced by inhibition of cellular metabolism for 2 min, Taken together, these results indicate that changes in [HCO 3 − ] i significantly contribute to the changes in the cation-anion balance of astrocytes induced by chemical ischemia. Flux of [HCO 3 − ] i can, however, not compensate the observed intracellular cation/anion imbalance, suggesting additional movement of other charged molecules across the plasma membrane. Table 1 summarize the data presented in this work. Our results demonstrate that brief chemical ischemia, induced by inhibition of cellular metabolism for 2 min, results in a transient decrease in the astrocytic ATP concentration. This is accompanied by a depolarization, an increase in [Na + ] i , and an acidification of astrocytes. At the same time, [Na + ] o transiently decreases and [K + ] o increases followed by an undershoot in [K + ] o , while pH o undergoes a biphasic alkaline-acid shift. Calculation of astrocytic [K + ] i based on these experimentally determined parameters predicts an initial loss of astrocytic [K + ] i , followed by a net, overshooting gain in [K + ] i during late recovery. Finally, our results show a mismatch of the intracellular cation-anion balance of astrocytes during and after chemical ischemia. This indicates a requirement for additional ion flux across the astrocytic membrane, which is most pronounced in the late recovery phase during which our data predict a net overshoot in [K + ] i . pHo undergoes a biphasic alkaline-acid shift. Calculation of astrocytic [K + ]i based on these experimentally determined parameters predicts an initial loss of astrocytic [K + ]i, followed by a net, overshooting gain in [K + ]i during late recovery. Finally, our results show a mismatch of the intracellular cation-anion balance of astrocytes during and after chemical ischemia. This indicates a requirement for additional ion flux across the astrocytic membrane, which is most pronounced in the late recovery phase during which our data predict a net overshoot in [K + ]i.  n.a. Data show peak changes after a 2 minutes' chemical ischemia. Note that [K + ]o moreover undergoes an undershoot and that [K + ]i overshoots in the recovery phase as described in the results. Data are given as mean ± SD. n: number of cells or experiments per slice per animal; p: error probability; asterisks depict significance levels after Šidák correction: * p < 0.0253, ** p < 0.005, *** p < 0.0005; n.a.: not applicable; § : from [41].

Baseline [K + ] i of Astrocytes
While it is widely accepted that glial cells maintain a high [K + ] i [7,50], direct measurements of astrocytic [K + ] i are rare due to the lack of suitable techniques. Earlier estimates and measurements in several types of glial cells and based on different indirect methods predicted a baseline [K + ] i of 100-170 mM [6,27,28,51]. Values determined with ionselective microelectrodes in rodent glial cells were generally lower [52][53][54][55], which may have been caused by a loss of K + due to impalement with the large-tip electrodes. Employing non-invasive imaging with the fluorescent K + indicator Asante Potassium Green-1, Rimmele et al. determined a [K + ] i of 133 mM in cultured rat astrocytes [23]. This dye, however, has not been employed for studying [K + ] i in glial cells in more intact preparations, probably because it does not load well in astrocytes in brain tissue slices (unpublished observations, Rose laboratory). More recently, genetically encoded K + nanosensors were developed, which owing to their low apparent affinities for K + , are more suitable for the determination of extracellular [K + ] [24,25]. A sensor published by Shen et al. enabled the measurement of relative changes in [K + ] i in HEK cells [26], but its suitability for quantitative imaging of [K + ] i in brain tissue has not been established yet.
To gain information on [K + ] i and changes thereof in response to energy deprivation in astrocytes in situ, we, therefore, followed earlier approaches combining experimental determination of different cellular parameters with calculation of [K + ] i using the GHK equation. This strategy is based on the observation that mature astrocytes express a battery of different K + channels, including inwardly rectifying Kir4.1, the two-pore domain channels (TWIK-1 and TREK-2) as well as large-conductance calcium-activated K + channels (BK Ca ) [56]. Owing to their high K + permeability at rest [27,57], the membrane potential of astrocytes can be fairly well approximated by a modified GHK equation assuming an additional small Na + permeability [27,43]. Recent work has also demonstrated that shortterm ischemic conditions neither alter the intrinsic properties of astrocytic K + channels nor affect the overall membrane conductance, suggesting that their depolarization largely arises from the accompanying changes in [K + ] o and [K + ] i [14,58].
The GHK equation evidently also allows for calculation of [K + ] i , provided that all other parameters are known. Here, going beyond earlier reports, we not only measured [K + ] o , [Na + ] o and E M , but also [Na + ] i as well as the relative Na + permeability in our preparation experimentally, enabling a realistic approximation of [K + ] i . We determined a relative membrane permeability for Na + versus K + (P Na /P K ) of 0.01 in neocortical astrocytes, which is lower than that of astrocytes in the mouse hippocampal CA1 area (0.015; [43]). Under the given conditions and ion concentrations (e.g., a baseline [K + ] o of 2.7 mM), we obtained a baseline [K + ] i of 146 mM for neocortical astrocytes. This value is somewhat higher than that reported for astrocytes cultured from the mouse cortex (133 mM) [23]. As in the latter study, astrocytes were bathed in 5.4 mM [K + ] o , they were most likely more depolarized, probably yielding a lower [K + ] i as compared to our study.

Changes in Astroglial [K + ] i during Energy Deprivation
A central function of astrocytes is the uptake of K + released by active neurons, thereby controlling and maintaining homeostasis of [K + ] o in the brain [7,9]. Consequently, several studies reported a rise in astrocytic [K + ] i in response to neuronal stimulation and/or a rise in [K + ] o [23,51,52,59]. Glial K + uptake is mainly mediated by the NKA, but other transporters such as the NKCC1 and/or channel-mediated influx may come into play depending on the amplitude and spatio-temporal properties of the [K + ] o elevation [9,10,[60][61][62].
Breakdown of [K + ] o homeostasis is one of the first consequences of anoxic/ischemic conditions and a restriction in cellular energy supply [13,50,63]; whereas the ischemic core undergoes a complete breakdown of ion homeostasis and massive cell death, recovery is possible in the neighboring ischemic penumbra, which experiences a reduction in cerebral blood flow to 20-40% of normoxic conditions [64]. Repeated waves of spreading depolarizations, however, will impose additional transient ion loads and metabolic stress onto the already stressed cells of the penumbra [15][16][17][18]. Here, we mimicked ischemia-like conditions in the penumbra undergoing waves of spreading depolarizations by brief perfusion of tissue slices with metabolic inhibitors [19,36]. Noteworthy, this chemical ischemia does not represent a complete model of spreading depolarizations developing in the ischemic penumbra. Our experiments, however, confirm a rapid reduction of ATP in neocortical astrocytes after transient inhibition of metabolism, followed by a slow recovery [34]. In a recent study, we performed an in situ calibration of ATeam fluorescence [45]. This was achieved by exposure of organotypic tissue slices to the saponin ß-escin, resulting in a permeabilization of cellular plasma membranes for ATP. Defined changes in the [ATP] then resulted in defined changes in the ATeam FRET-ratio that followed Michaelis-Menten kinetics, revealing an apparent K D of 2.7 mM for ATeam1.03 YEMK in both neurons and astrocytes. A linear plot between 1 and 3 mM ATP showed that a 10% change in fluorescence ratio corresponded to a change in [ATP] i by 0.56 mM. Based on this calibration [45], astrocytic ATP exhibited an estimated decrease by about 1 mM in response to chemical ischemia for 2 min in the present study. Such transient, moderate reduction in cellular ATP is one of the hallmarks accompanying the generation of spreading depolarizations [65].
In addition, inhibition of cellular metabolism resulted in a transient decrease in [Na + ] o , an increase in [K + ] o , an increase in astrocytic [Na + ] i , and a depolarization of astrocytes, confirming earlier observations [5,6,13,19,58,66,67]. All changes induced by a chemical ischemia for 2 min recovered towards baseline after washout of the inhibitors, with [K + ] o and glial E M showing an additional undershoot below baseline and hyperpolarization, respectively [58,67]. As discussed above, ion changes were accompanied by a decrease and subsequent recovery of astrocytic ATP, suggesting a direct correlation between ATP levels and NKA activity, a phenomenon already reported from CA1 pyramidal neurons [68].
Earlier work suggested that the depolarization of astrocytes when exposed to brief periods of ischemic conditions is mainly due to a loss of K + from cells [14,58]. Our simulation based on the GHK equation supports this notion, indicating a decrease in astrocytic [K + ] i by about 43 mM upon brief inhibition of cellular energy production, most likely as a direct consequence of the decline in cellular ATP and the resulting decrease of NKA activity. Besides channel-mediated loss of K + , activation of astrocytic glutamate transporters might, at least partly, contribute to the decline in astrocytic [K + ] i [19,23].
While initial K + efflux from astrocytes under ischemic conditions will aggravate the accumulation of extracellular K + induced by its release from neurons, our simulation also predicts a delayed gain of astrocytic K + during the late recovery phase. This phenomenon arises from the mismatch in the experimentally determined time courses of the undershoot in [K + ] o and the astrocytic hyper-and repolarization, respectively. It again suggests ongoing increased activation of the NKA following metabolic inhibition, probably because of the still-elevated [Na + ] i and/or in response to an increase in [Ca 2+ ] i [19,58,60,69]. In addition, astrocytic K + uptake might at least partly be mediated by increased activity of inward NKCC1 [11,36,70].
Notably, the overcompensating uptake of K + by astrocytes reduces [K + ] o below its initial baseline. The latter will exert a hyperpolarizing effect on neurons and reduce neuronal excitability [8,50], while at the same time increasing the driving force for astroglial glutamate uptake [71]. Astrocytes will thereby exert a neuroprotective role following transient energy depletion through a [K + ] o -mediated dampening of network activity and reduction of neuronal ATP consumption, supporting the recovery of neurons from metabolic stress.

Astroglial Cation-Anion Balance during Energy Deprivation
The K + movements across the astrocytic membrane predicted by our simulation require the additional flux of ions to preserve electroneutrality [6]. While Na + influx compensates for about 50% of the predicted initial loss of K + from astrocytes, it does not fully counteract the simultaneous cation efflux, an observation also reported by earlier studies [6,67]. What is more, owing to its slow recovery, still elevated [Na + ] i even adds to the delayed predicted gain of K + in the second phase of recovery. This mismatch in the cellular cation-anion balance must be balanced by an additional net gain of cations, followed by additional cation loss in the second recovery phase and/or an initial net loss of anions, followed by a gain of anions. Besides loading with Na + , astrocytes are subject to a transient increase in [Ca 2+ ] i [19] and [H + ] i (this study) during brief chemical ischemia. While this might reduce the anion gap in the first phase, the slow recovery from both Ca 2+ signals and acidification result in its aggravation in the second phase.
A mobile anion which will contribute to the cation-anion balance is HCO 3 − [6]. Our experiments demonstrate a decrease in astrocytic pH i and [HCO 3 − ] i , respectively, in response to chemical ischemia, significantly reducing the predicted imbalance in the first phase. The slow recovery from the intracellular acidification and ongoing decrease in [HCO 3 − ] i , however, will again worsen the anion gap in the second recovery phase. While the initial charge imbalance may thus be compensated for through influx of additional cations (Ca 2+ , H + ) and a reduction in [HCO 3 − ] i , these processes will later even increase the predicted anion gap.
Cl − is another candidate for compensation of the predicted delayed charge imbalance. Earlier work has demonstrated rapid channel-and transporter-mediated movement of Cl − across astrocytic membranes [72][73][74]. Accumulation of Cl − moreover contributes to astrocyte swelling in ischemic conditions [11,[75][76][77][78]. Conversely, a recent study employing fluorescence lifetime imaging in layer II/III astrocytes only reported negligible changes in their [Cl − ] i in response to a chemical ischemia for 2-5 min [36]. This was probably due to the simultaneous activation of different anion transporters mediating Cl − accumulation (NKCC1) and Cl − efflux (KCC's and glutamate transporters) [36]. An increase in astrocytic [Cl − ] i was, however, observed upon a 10 min' exposure to the metabolic inhibitors, showing that a net gain in Cl − is indeed observed upon more severe conditions (i.e., a larger decline in cellular ATP and/or longer period of energy deprivation). On the other hand, earlier reports demonstrating an apparent mismatch between K + and Cl − movement in astrocytes speculated that in addition to Cl − , the net flux of lactate or other anionic osmolytes such as taurine, glutamate or aspartate might help maintaining the cellular cation-anion balance [11,51,79].
While these assumptions are thus supported by earlier work [11,51,79], it should be kept in mind that the proposed anion mismatch was not directly measured but inferred from the calculated [K + ] i . Several factors could have biased our simulation. Among them is the influence of space clamp errors in patch-clamp measurements, a factor especially critical for astrocytes, which not only exhibit a very low input resistance but are also extensively coupled via gap junctions [1,35,56]. Moreover, experimentally determined changes in extracellular ion concentrations might represent underestimates of ion transients occurring in the intact tissue owing to the relatively large tip size of the ion-selective microelectrodes (around 1 µm) [22]. Finally, our intracellular ion measurements represent bulk measurements from cell bodies only, and changes in fine, diffusion-restricted astrocytic processes might be larger in amplitude as well [38,41].
With these considerations in mind, we conclude from our data that the predicted net gain of K + (and positive charge) by astrocytes in the late recovery phase from chemical ischemia will be accompanied by an additional efflux of cations and/or influx of anions. The overshooting uptake of K + by astrocytes will promote and aid the recovery of [K + ] o , thereby exerting a dampening effect on neuronal excitability. Conversely, any net gain of osmolytes by astrocytes will eventually be accompanied by uptake of water, which will promote harmful cell swelling upon prolonged metabolic inhibition [11,75,80]. Identifying the nature of the additional ionic species or charged molecules transported across the plasma membrane is thus highly desirable to shed more light on the mechanisms of astrocytic swelling following brain ischemia [62,76].

Institutional Review Board Statement:
All procedures reported in this study were carried out in accordance with the institutional guidelines of the Heinrich Heine University Düsseldorf, as well as the European Community Council Directive (2010/63/EU) and were communicated to and approved by the animal welfare office of the animal care and use facility of the Heinrich Heine University Düsseldorf (institutional act number: O52/05). To prepare brain slices, mice older than P10 were anaesthetized with CO 2 . All animals were quickly decapitated, and their brains rapidly removed. In accordance with the German Welfare Act (TSchG; Section 4, paragraph 3), no additional approval for postmortem removal of brain tissue was necessary.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.