Interactions between Membrane Resistance, GABA-A Receptor Properties, Bicarbonate Dynamics and Cl−-Transport Shape Activity-Dependent Changes of Intracellular Cl− Concentration

The effects of ionotropic γ-aminobutyric acid receptor (GABA-A, GABAA) activation depends critically on the Cl−-gradient across neuronal membranes. Previous studies demonstrated that the intracellular Cl−-concentration ([Cl−]i) is not stable but shows a considerable amount of activity-dependent plasticity. To characterize how membrane properties and different molecules that are directly or indirectly involved in GABAergic synaptic transmission affect GABA-induced [Cl−]i changes, we performed compartmental modeling in the NEURON environment. These simulations demonstrate that GABA-induced [Cl−]i changes decrease at higher membrane resistance, revealing a sigmoidal dependency between both parameters. Increase in GABAergic conductivity enhances [Cl−]i with a logarithmic dependency, while increasing the decay time of GABAA receptors leads to a nearly linear enhancement of the [Cl−]i changes. Implementing physiological levels of HCO3−-conductivity to GABAA receptors enhances the [Cl−]i changes over a wide range of [Cl−]i, but this effect depends on the stability of the HCO3− gradient and the intracellular pH. Finally, these simulations show that pure diffusional Cl−-elimination from dendrites is slow and that a high activity of Cl−-transport is required to improve the spatiotemporal restriction of GABA-induced [Cl−]i changes. In summary, these simulations revealed a complex interplay between several key factors that influence GABA-induced [Cl]i changes. The results suggest that some of these factors, including high resting [Cl−]i, high input resistance, slow decay time of GABAA receptors and dynamic HCO3− gradient, are specifically adapted in early postnatal neurons to facilitate limited activity-dependent [Cl−]i decreases.


Introduction
GABA (γ-aminobutyric acid) is the main inhibitory neurotransmitter in the mature brain and acts via ionotropic GABA A /GABA C receptors and via metabotropic GABA B receptors [1]. In the adult brain, GABA mediates its inhibitory effect by hyperpolarizing the membrane and by shunting excitatory inputs. GABA A receptors are ligand-gated anion-channels with a high permeability for Cl − 3 experimentally derived parameters of GABAergic synapses and GDP-activity provided by Lombardi et al. [45].

Influence of Membrane Conductance
First, we analyzed the influence of the membrane conductance on the [Cl⁻]i changes induced by a single GABAergic input in an isolated dendrite. In this model, the experimentally determined conductance underlying single spontaneous GABAergic postsynaptic responses (gGABA) was implemented in an isolated dendrite equipped with passive conductances (gpas) varying between 10 ⁻6 S/cm 2   Next we simulated how gpas influences [Cl⁻]i in a reconstructed neuron (Figure 2a,b), which receives complex GABAergic inputs that typically occur during GDP activity [45] (Figure 2c,d). For these experiments we initially equipped the dendrite with 101 GABAergic synapses (g = 0.789 nS, τ = 37 ms; all values from Lombardi et al. [45]), set PHCO3 to 0 and used an initial [Cl⁻]i to 30 mM. Each of these 101 GABAergic synapses was randomly distributed within the dendrites of the reconstructed neuron. The time points for the stimulation of every synapse follows a normal distribution (µ = 600ms, σ = 900 ms). These values were derived from in-vitro experiments and resemble the distribution of GABAergic inputs during a GDP [45] (Figure 2c). In order to reduce the complexity of the analysis and to mimic the procedures of The GABA-induced membrane depolarization also shows a sigmoidal dependency on g pas . (c) Effect of g pas on E m (black lines), E Cl (red lines) and [Cl − ] i (blue lines) in an isolated dendrite using constant GABAergic currents (g GABA = 0.1 µS). Note that at low g pas values (0.1 nS/cm 2 , solid lines) E m approximates E Cl , while at high g pas (18 mS/cm 2 , dashed lines) E m stays below E Cl . Accordingly [Cl − ] i shows only a small transient change at low g pas , while a steady decline in [Cl − ] i occurs at high g pas .
Next we simulated how g pas influences [Cl − ] i in a reconstructed neuron (Figure 2a,b), which receives complex GABAergic inputs that typically occur during GDP activity [45] (Figure 2c,d).
For these experiments we initially equipped the dendrite with 101 GABAergic synapses (g = 0.789 nS, τ = 37 ms; all values from Lombardi et al. [45]), set P HCO 3 to 0 and used an initial [Cl − ] i to 30 mM. Each of these 101 GABAergic synapses was randomly distributed within the dendrites of the reconstructed neuron. The time points for the stimulation of every synapse follows a normal distribution (µ = 600ms, σ = 900 ms). These values were derived from in-vitro experiments and resemble the distribution of GABAergic inputs during a GDP [45] (Figure 2c). In order to reduce the complexity of the analysis and to mimic the procedures of [Cl − ] i estimation used by Lombardi et al. [45] (which estimated [Cl − ] i changes from changes in E Rev determined by focal GABA application within the dendritic compartment) we use for all further analyses the average [Cl − ] i of all dendrites.  The crosses mark values determined experimentally in real CA3 pyramidal neurons. The colored cycles displays the [Cl⁻]i changes computed for the three given RInput values as indicated in (e). Note that for the immature RInput only negligible GPD-induced [Cl⁻]i changes are generated (a, b and c modified and used with permission from [45]).
Using this model, we investigated how different gpas between 10 -6 S/cm 2 and 0.1 S/cm 2 affect the GDPinduced [Cl⁻]i transients. This simulation demonstrated that also in a complex dendritic compartment gpas critically influenced the amount of [Cl⁻]i changes ( Figure 2e). Also, under these conditions the GABAergic depolarization during a GDP approached ECl at low gpas (Figure 2f), which minimized DFCl and the remaining Cl⁻ fluxes. One particular result of this computational study was that the GDP-induced [Cl⁻]i transient amounts to less than 1 mM in a reconstructed CA3 pyramidal neuron equipped with the passive membrane conductance determined experimentally in these neurons (red symbols in Figure 2e-g), which is lower than the experimentally determined [Cl⁻]i changes of 10.3 ± 3.3 mM (n = 4) in a real CA3 pyramidal neuron at comparable conditions [45]. To further specify the influence of gpas on the GDP-induced [Cl⁻]i The colored cycles displays the [Cl − ] i changes computed for the three given R Input values as indicated in (e). Note that for the immature R Input only negligible GPD-induced [Cl − ] i changes are generated (a, b and c modified and used with permission from [45]).
Using this model, we investigated how different g pas between 10 −6 S/cm 2 and 0.1 S/cm 2 affect the GDP-induced [Cl − ] i transients. This simulation demonstrated that also in a complex dendritic compartment g pas critically influenced the amount of [Cl − ] i changes ( Figure 2e). Also, under these conditions the GABAergic depolarization during a GDP approached E Cl at low g pas (Figure 2f), which minimized DF Cl and the remaining Cl − fluxes. One particular result of this computational study was that the GDP-induced [Cl − ] i transient amounts to less than 1 mM in a reconstructed CA3 pyramidal neuron equipped with the passive membrane conductance determined experimentally in these neurons (red symbols in Figure 2e-g), which is lower than the experimentally determined [Cl − ] i changes of 10.3 ± 3.3 mM (n = 4) in a real CA3 pyramidal neuron at comparable conditions [45]. To further specify the influence of g pas on the GDP-induced [Cl − ] i transients, we simulated the peak dendritic [Cl − ] i change for different initial [Cl − ] i at three different g pas . For this purpose we used values of 0.049 mS/cm 2 (corresponding to a R Input of 901 MΩ, typical for immature hippocampal neurons [45]), 0.28 mS/cm 2 (189 MΩ, adult neuron in whole-cell patch-clamp configuration [46]), and 1.8 mS/cm 2 (41 MΩ, adult neuron with sharp electrode [47]). These simulations demonstrated that, if mature properties of g pas were implemented in the simulated neuron, the GDP-induced [Cl − ] i changes were roughly comparable to the values observed in real CA3 pyramidal neurons (Figure 2g), while at g pas typical for immature CA3 pyramidal neurons only marginal GDP-induced [Cl − ] i changes occurred.
In order to adapt the simulation of GDP-induced responses to the physiological properties of CA3 pyramidal neurons we incorporated an inward rectification in the background conductance (Supplementary Figure S1a,b). In addition, we had to increase the number of GABAergic synaptic inputs (n GABA ) to compensate the influence of massive space clamp problems on the experimental determination of this parameter (Supplementary Figure S1c-f). For all further simulations in the reconstructed neurons we used the inward rectifying background conductance and implemented 302, 395, and 523 GABAergic synapses for P HCO 3 values of 0.0, 0.18, and 0.44, respectively. However, even with the inward rectifying conductance and 302 synaptic inputs the GDP-induced [Cl − ] i changes were smaller than observed under in-vitro conditions (Supplementary Figure S1e).

Influence of GABA Receptor Conductivity and Kinetics
Next we analyzed the influence of the GABAergic conductance (g GABA ) on [Cl − ] i transients. Initial experiments in an isolated dendrite showed that initially the [Cl − ] i transient was localized underneath the synapse, and within 3 s a diffusional equilibration throughout the dendrite occurred (Supplementary Figure S2a,b). Therefore, we estimated the total amount of GABA-evoked [Cl − ] i changes by averaging the [Cl − ] i over all nodes of the dendrite 3 s after the GABAergic stimulus. To analyze the relation between total g GABA and the [Cl − ] i changes, we first systematically increase g GABA from 0.789 nS to 78.9 nS (Figure 3a). These simulations demonstrated that the GABA-evoked [Cl − ] i changes rose with increasing g GABA , but did not depend linearly on g GABA (Figure 3b, black line). This nonlinear effect was due to the larger membrane depolarization upon stronger GABAergic stimulation, which reduced DF Cl under this condition (data not shown). In an additional set of simulations, we enhanced the level of GABAergic stimulation by increasing the number of GABAergic synapses (n GABA ) from 1 to 100, with g GABA of 0.789 nS for each synapse. The synapses were for each n GABA evenly distributed across the isolated dendrite. These simulations revealed that this distributed stimulation led to a reduced relative [Cl − ] i decrease at higher n GABA (Figure 3b, red line), as compared to the previous simulation paradigm (Figure 3b, black line). This observation is most probably due to the fact that with distributed synapses E m reaches more depolarized values close to E Cl (−56.9 mV at 1 × 78.9 nS vs. −40.7 mV at 100 × 0.789 nS, data not shown).
To investigate whether a similar dependency between the amount of GABAergic inputs and [Cl − ] i could also be observed during a simulated GDP in a CA3 pyramidal neuron we increased g GABA from 0.789 nS (Figure 3c, blue line) to 7.89 nS (red line) at each of the 302 synapses used to simulate a GDP. This 10× increase in g GABA augmented the maximal GDP-induced [Cl − ] i decrease from 4.3 mM to 6.8 mM (Figure 3d). This surprisingly small effect was due to the fact that the increased g GABA also reduced the average DF Cl from −8.6 mV to −5 mV (Figure 3d). When a similar increase in the amount of GABAergic stimulation was implemented by a 10× increase in n GABA (from 301 to 3010) a slightly larger maximal [Cl − ] i decrease by 7.1 mM was observed (Figure 3c,d, green line/symbols). This result indicates that the GDP-induced [Cl − ] i changes were close to saturation values when realistic values for n GABA , g GABA and R Input were implemented in a simulated CA3 pyramidal neuron.

Contribution of the HCO3⁻ Conductance of GABA Receptors
In all previous experiments, we simulated GABAA mediated responses under the simplified consideration that GABAA receptors are ligand-gated Cl⁻ channels. However, GABAA receptors are anion

Contribution of the HCO3⁻ Conductance of GABA Receptors
In all previous experiments, we simulated GABAA mediated responses under the simplified consideration that GABAA receptors are ligand-gated Cl⁻ channels. However, GABAA receptors are anion

Contribution of the HCO 3 − Conductance of GABA Receptors
In all previous experiments, we simulated GABA A mediated responses under the simplified consideration that GABA A receptors are ligand-gated Cl − channels. However, GABA A receptors are anion channels with a considerable HCO 3 − permeability [1]. The relative HCO 3 − -permeability of GABA A receptors (P HCO 3 ) ranges between 0.18 (determined in spinal cord neurons [48]) and 0.44 (determined in adult hippocampal neurons [49]), although also higher values have been suggested [1]. Therefore, we next simulated how P HCO 3 affects GABAergic E m and [Cl − ] i responses upon stimulation of a single synapse in an isolated dendrite. Addition of a HCO 3 − conductance to GABAergic currents induce a depolarizing shift in the peak depolarizations induced by GABAergic stimulation (Supplementary Figure S3a,b). Since this additional depolarization affected the DF Cl , the GABAergic [Cl − ] i changes were also influenced by P HCO 3 . Under particular conditions, i.e. when E m crossed E Cl during synaptic responses, the GABAergic activation lead to biphasic [Cl − ] i changes ( Figure 5a). For further analysis we plotted for such biphasic responses the maximal and minimal [Cl − ] i upon GABAergic stimulation (e.g. Figure 5b, blue lines). A systematic analysis of the effect of GABAergic inputs on the [Cl − ] i changes revealed that the [Cl − ] i changes were shifted towards more outward fluxes at higher P HCO 3 (Figure 5b), indicating that with increasing P HCO 3 a substantial [Cl − ] i increase is induced by GABAergic stimulation.    However, these initial assumptions neglect the fact that the HCO3⁻ fluxes will also affect [HCO3⁻]i. Rapid regeneration of [HCO3⁻]i levels by carbonic anhydrases, which stabilize [HCO3⁻]i, is absent in immature neurons [50]. Therefore, we first simulated the GABA-induced Em and [Cl⁻]i changes under the assumption that HCO3⁻ will not be replenished (by implementing a HCO3⁻ relaxation time constant (τHCO3⁻) of 10 min) and is only redistributed by diffusion. These simulations revealed that the activation of GABAA receptors induced a rapid decline in

The Stability of HCO3⁻ Gradients Influences Activity-Dependent [Cl⁻]i Transients
The previous results clearly demonstrate that GABAA receptor-mediated [HCO3⁻]i transients massively influence the Em and [Cl⁻]i changes under these conditions. However, the two conditions used in these experiments (stable [HCO3⁻]i or negligible [HCO3⁻]i regeneration at τHCO3 of 10 min) are obviously not physiological in immature neurons, which lack carbonic anhydrases, but in which spontaneous CO2 hydration and/or transmembrane transport of HCO3⁻ can occur [50]. Therefore, we next investigated how τHCO3 influences the stability of [HCO3⁻] gradients and GABA induced [Cl⁻]i transients. For that we systematically changed the decay-time of [HCO3⁻]i relaxation (τHCO3) implemented in the NEURON model  implemented in the NEURON model (Supplementary Figure S4a,b). A systematic simulation in isolated dendrites revealed that [Cl − ] i changes remained rather constant at τ HCO 3 ≥ 90 ms (Figure 7a). The half-maximal [Cl − ] i changes occurred at a τ HCO 3 around 10 ms, which is substantially shorter than the τ HCO 3 of ca. 70 ms for half-maximal [HCO 3 − ] i changes (Supplementary Figure S4b). More than 85% of the maximal [Cl − ] i changes took place at τ HCO 3 below 100 ms (Figure 7a). However, it must also be considered that a decreased temporal stability of the [HCO 3 − ] gradient will also influence the lateral diffusion of HCO 3 − . Indeed, a systematic simulation of the spatial aspects of the activity-dependent   Figure 4a,b). A systematic simulation in isolated dendrites revealed that [Cl⁻]i changes remained rather constant at τHCO3 ≥ 90 ms (Figure 7a). The half-maximal [Cl⁻]i changes occurred at a τHCO3 around 10 ms, which is substantially shorter than the τHCO3 of ca. 70 ms for half-maximal [HCO3⁻]i changes (Supplementary Figure 4b). More than 85% of the maximal [Cl⁻]i changes took place at τHCO3 below 100 ms ( Figure 7a). However, it must also be considered that a decreased temporal stability of the [HCO3⁻] gradient will also influence the lateral diffusion of HCO3⁻. Indeed, a systematic simulation of the spatial aspects of the activity-dependent [HCO3⁻]i transients revealed that the stability of HCO3⁻ massively influenced the [HCO3⁻] gradient along the isolated dendrite (Figure 7b), although the maximal [HCO3⁻]i change at the synaptic site was nearly saturated already at a τHCO3 ≥ 90 ms (Figure 7b). In accordance with the results obtained in isolated dendrites, also in the reconstructed CA3 pyramidal neuron τHCO3 had a large effect on the GDP-induced  GABAergic [51] and glutamatergic [52,53] synaptic transmission is accompanied by substantial pH changes. These pH changes, however, indirectly affect GABAergic transmission, since they alter the [HCO3⁻]i. To estimate, how such pH changes influence activity-dependent [Cl⁻]i transients, we first simulated the effect of such pH shifts by constantly altering the pH value from 7.2 to 7.0 or 7.4 in an isolated dendrite. According to the Henderson-Hasselbalch equation, these pH shifts alter [HCO3⁻]i from 14.1 mM to 9 mM or 22.7 mM, respectively. Because this pH-dependent differences in [HCO3⁻]i affect DFGABA, the membrane depolarization upon GABAA receptor activation was reduced at pH 7.0 and enhanced at a more alkaline pH of 7.4 (Figure 8a). In line with this altered GABAergic membrane depolarization, the DFCl during GABAergic stimulation was also affected, shifting the resulting Cl⁻ fluxes. This can be exemplified at intermediate [Cl⁻]i, where the biphasic Cl⁻ fluxes at a normal pH of 7.2, were transformed to Cl⁻ efflux at a pH of 7.0 and to a Cl⁻ influx at a pH of 7.4 (Figure 8a). A systematic analysis of Cl⁻ fluxes at different initial [Cl⁻]i demonstrated that, in comparison to pH 7.2, the Cl⁻ influx at low initial [Cl⁻]i was decreased at pH 7.0, while it was enhanced at pH 7.4 (Figure 8b). In contrast, the Cl⁻ efflux at high [Cl⁻]i was enhanced GABAergic [51] and glutamatergic [52,53] synaptic transmission is accompanied by substantial pH changes. These pH changes, however, indirectly affect GABAergic transmission, since they alter the     Figure S4i-k). The dominance of diffusional elimination of Cl − was also reflected by the observation that at slow τ Cl ≤ 10s the [Cl − ] i was substantial lower at the proximal than at the distal end of the dendrite (Supplementary Figure S4i-k).

Influence of Transmembrane Cl⁻ Transport
To analyze the influence of τ Cl on the spatial aspects of the [Cl − ] i transients we implemented two simultaneous GABAergic inputs that were located equidistant to the [Cl − ] i recording site at distances of 10 µm, 30 µm, 100 µm and 300 µm and systematically increased τ Cl from 1 ms to 220 s (Figure 9a). These simulations revealed not only that the maximal [Cl − ] i depended on the distance between GABAergic stimulation sites and the node of [Cl − ] i determination, but also that τ Cl critically influenced the [Cl − ] i change at a given distance to the stimulation sites (Figure 9a). This dependency between spatial restrictions of activity-dependent [Cl − ] i changes and τ Cl was quantified by the τ Cl at which half-maximal [Cl − ] i changes occur (τ Cl 50 ). If the distance of the GABAergic synapses was 10 µm τ Cl 50 amounted to 12 ms, and this τ Cl 50 increased to 60.5 ms, 726 ms and 4.6 s at synaptic distances of 30 µm, 100 µm and 300 µm, respectively. To analyze the temporal aspects of [Cl − ] i summation we simulated five consecutive GABA stimulations at frequencies (f GABA ) of 0.3 Hz, 1 Hz, 3 Hz and 10 Hz and determine the [Cl − ] i at the stimulation site, while systematically varying τ Cl (Figure 9b). These simulations revealed a sigmoidal dependency between τ Cl and the temporal summation of [Cl − ] i . A larger amount of [Cl − ] i summation and a lower τ Cl 50 was observed at higher frequencies. The τ Cl 50 amounted to 1.9 s for f GABA of 0.1 Hz, 931 ms for f GABA of 1 Hz, 268 ms for f GABA of 3 Hz, and 53 ms for f GABA of 10 Hz. In summary, these results demonstrated that τ Cl values of less than 1 s are required to prevent substantial activity-dependent [Cl − ] i changes in the spatial and/or temporal domain at f GABA ≥ 1Hz and less than 100 µm distance between synaptic sites. To analyze the influence of τCl on the spatial aspects of the [Cl⁻]i transients we implemented two simultaneous GABAergic inputs that were located equidistant to the [Cl⁻]i recording site at distances of 10 µm, 30 µm, 100 µm and 300 µm and systematically increased τCl from 1 ms to 220 s (Figure 9a). These simulations revealed not only that the maximal [Cl⁻]i depended on the distance between GABAergic stimulation sites and the node of [Cl⁻]i determination, but also that τCl critically influenced the [Cl⁻]i change at a given distance to the stimulation sites (Figure 9a). This dependency between spatial restrictions of activity-dependent [Cl⁻]i changes and τCl was quantified by the τCl at which half-maximal [Cl⁻]i changes occur (τ Cl 50). If the distance of the GABAergic synapses was 10 µm τ Cl 50 amounted to 12 ms, and this τ Cl 50 increased to 60.5 ms, 726 ms and 4.6 s at synaptic distances of 30 µm, 100 µm and 300 µm, respectively. To analyze the temporal aspects of [Cl⁻]i summation we simulated five consecutive GABA stimulations at frequencies (fGABA) of 0.3 Hz, 1 Hz, 3 Hz and 10 Hz and determine the [Cl⁻]i at the stimulation site, while systematically varying τCl (Figure 9b). These simulations revealed a sigmoidal dependency between τCl and the temporal summation of [Cl⁻]i. A larger amount of [Cl⁻]i summation and a lower τ Cl 50 was observed at higher frequencies. The τ Cl 50 amounted to 1.9 s for fGABA of 0.1 Hz, 931 ms for fGABA of 1 Hz, 268 ms for fGABA of 3 Hz, and 53 ms for fGABA of 10 Hz. In summary, these results demonstrated that τCl values of less than 1 s are required to prevent substantial activity-dependent [Cl⁻]i changes in the spatial and/or temporal domain at fGABA ≥ 1Hz and less than 100 µm distance between synaptic sites. In accordance with these results in single dendrites, all previous simulations of GDP-induced [Cl⁻]i transients in the reconstructed CA3 pyramidal cells revealed substantial [Cl⁻]i changes, because in these simulations the experimentally determined τCl of 174 s for NKCC1-mediated active Cl⁻ re-accumulation and of 321 s for passive Cl⁻ reduction were implemented and during a GDP stimulation a high frequency of GABAergic input was applied. In order to get more insights into how the capacity of [Cl⁻]i regulation systems can influence activity-dependent [Cl⁻]i transients within a realistic dendritic compartment, we finally simulated how different τCl influenced the GDP-induced [Cl⁻]i transients in the reconstructed CA3 neuron (Figure 9c,d). This simulation revealed that decreasing τCl from the experimentally determined values >100 s to 10 s or 1 s had only a minimal impact of the GDP-induced [Cl⁻]i transients (Figure 9c). The maximal GDP-induced [Cl⁻]i change amounted to 4.41 mM at a τCl of 10 s and to 4.21 mM at a τCl of 1 s, but were reduced to 2.99 mM at a τCl of 0.1 s and to 0.88 mM at a τCl of 10 ms. These results demonstrate that In accordance with these results in single dendrites, all previous simulations of GDP-induced [Cl − ] i transients in the reconstructed CA3 pyramidal cells revealed substantial [Cl − ] i changes, because in these simulations the experimentally determined τ Cl of 174 s for NKCC1-mediated active Cl − re-accumulation and of 321 s for passive Cl − reduction were implemented and during a GDP stimulation a high frequency of GABAergic input was applied. In order to get more insights into how the capacity of [Cl − ] i regulation systems can influence activity-dependent [Cl − ] i transients within a realistic dendritic compartment, we finally simulated how different τ Cl influenced the GDP-induced [Cl − ] i transients in the reconstructed CA3 neuron (Figure 9c,d). This simulation revealed that decreasing τ Cl from the experimentally determined values >100 s to 10 s or 1 s had only a minimal impact of the GDP-induced [Cl − ] i transients (Figure 9c). The maximal GDP-induced [Cl − ] i change amounted to 4.41 mM at a τ Cl of 10 s and to 4.21 mM at a τ Cl of 1 s, but were reduced to 2.99 mM at a τ Cl of 0.1 s and to 0.88 mM at a τ Cl of 10 ms. These results demonstrate that fast and efficient [Cl − ] i homeostatic processes are required to limit GDP-induced [Cl − ] i transients. Accordingly, the ∆[Cl − ] i vs. DF Cl plot also revealed comparable GDP-induced [Cl − ] i changes at τ Cl of 10 s and 1 s, and smaller [Cl − ] i changes at a τ Cl of 100 ms (Figure 9d). Only a further reduction in τ Cl to 10 ms substantially suppressed GDP-induced [Cl − ] i changes. In summary, these results indicate that τ Cl influences the temporal and spatial properties of activity-dependent [Cl − ] i changes, but that τ Cl values that are substantially smaller than the experimentally determined values are required to suppress activity-dependent [Cl − ] i changes.

Discussion
In the present study we used a detailed biophysical compartmental modeling in the NEURON environment to systematically investigate how several cellular and molecular neuronal parameters influence the GABA A receptor-mediated [Cl − ] i changes. The main observations of this study can be summarized as follows: (i) A high R input reduces activity-dependent [Cl − ] i transients, while at low R input considerable activity-dependent [Cl − ] i transients can be observed. By 1990, it was suggested by Qian and Sejnowski [54] that the Cl − fluxes via activated GABA A receptors will dissipate the Cl − gradient in small compartments and thus mediate potentially instable inhibitory responses. This theoretical assumption was proven by experimental studies, which demonstrated that massive GABAergic activation can shift hyperpolarizing responses toward depolarization [12,21] and induce [Cl − ] i transients [55]. In the past the physiological and pathophysiological consequences of such activity-dependent [Cl − ] i changes have been investigated and discussed [13,17,20,36,56] and the basic principles of activity-dependent [Cl − ] i changes and their implications for neuronal information processing have been modeled [7,15,16,22,57,58]. However, the complex interplay and contribution of passive membrane leak, GABA A conductance, Cl − diffusion/ transport and stability of [HCO 3 − ] gradients to these activity-dependent [Cl − ] i changes have not yet been systematically investigated. Our simulations revealed a strong dependence between R Input and the GABA A receptor induced [Cl − ] i transients. While at high R Input GABA-induced [Cl − ] i changes were minimal, they increased in a nonlinear relation with decreasing R Input (Figure 1c). This relation between R Input and the [Cl − ] i changes is due to the fact that at high R Input even small GABAergic currents bring E m close to E Cl , which minimizes DF Cl and thus the Cl − fluxes (Figure 1c). At low R Input the passive membrane conductance stabilizes E m and thus DF Cl . In consequence, larger Cl − fluxes can be expected. Accordingly, implementation of "adult like" membrane properties [47] in a reconstructed immature neuron massively enhanced activity-dependent [Cl − ] i changes (Figure 1c). In contrast, it seems obvious that immature neurons, with their high R Input [59], are less susceptible to activity-dependent [Cl − ] i changes.
However, in this respect, it is important to consider that in immature neurons [Cl − ] i is high and GABAergic responses are depolarizing [30,60,61], therefore activity-dependent Cl − fluxes are directed outward and are leading to [Cl − ] i decrease [42,44]. In addition, the HCO 3 − -permeability of GABA A receptors also needs to be considered. The high R Input in immature neurons causes E m to approach E GABA , which normally is positive to E Cl due to the HCO 3 − -permeability of GABA A -receptors [1,4].  Figure S3d). But further properties of activity-dependent [Cl − ] i changes observed in our simulations protect immature neurons from excessive [Cl − ] i increases. In particular, we found that the influence of P HCO 3 is relatively small at high [Cl − ] i (Figure 6d), due to the fact that under this condition the contribution of E HCO 3 to E GABA is small (as described by the shifts ( [18], but see [62]). We conclude from these observations that the lack of carbonic anhydrase VII in immature neurons [50,65] Figure S4b). This fast relaxation time requires fast molecular processes that allow effective elimination of HCO 3 − . Indeed, carbonic anhydrases, the enzymes that mediate the degradation or regeneration of HCO 3 − into/from H 2 O and CO 2 , are among the fastest enzymes known. The k cat of murine carbonic anhydrase VII for the hydration oh CO 2 is 4.5 × 10 5 s −1 at physiological pH [66]. as the reaction mediated by carbonic anhydrases includes H + ions, the kinetics and thermodynamics of this process depends on the intracellular pH [67]. Thus dendritic H + -buffering and handling indirectly also affects activity-dependent [Cl − ] i changes [15]. The acidification associated with neuronal activity [52,53] will slow down the kinetics of carbonic anhydrases [66]. However, this effect is negligible in comparison to the effect of the intracellular pH on [HCO 3 − ] i . The intracellular pH is an essential parameter that determines [HCO 3 − ] i [67]. Thus the intracellular acidification observed upon activation of GABAergic and glutamatergic synapses [51][52][53] will alter [HCO 3 − ] i and subsequently influence GABAergic transmission. Our simulation revealed that an intracellular acidification will reduce the activity-dependent [Cl − ] i changes at low [Cl − ] i . This result, which is in accordance with a previous simulation [15], indicate that in adult neurons a parallel acidification will limit Cl − influx and thus stabilize inhibitory transmission In contrast, at a high [Cl − ] i typical for immature neuron the intracellular acidification enhanced the activity-dependent Cl − efflux and may contribute to the loss of depolarizing drive and putative excitatory effects after strong GABAergic stimulation.
Another factor that has a stringent effect on activity-dependent [Cl − ] i changes in our simulations is τ GABA. This confirmed and extended previous computational analyses (c.f. Figure 4d in [7]). It has been found that in general the decay kinetics of GABAergic transmission get faster during development [68]. Therefore the slow decay kinetics of GABAergic transmission in immature neurons [68,69] may be a factor that enables activity-dependent [Cl − ] i transients, while the faster GABAergic postsynaptic currents in mature neurons not only improve the temporal precision of GABAergic transmission [68], but also the stability of inhibition. While a stable inhibition is a prerequisite for the proper function of mature neuronal networks, dynamic changes in [Cl − ] i can be mandatory for physiological relevant functional features of the immature central nervous system. It has been suggested that activity-dependent changes in [Cl − ] i , and the resulting switch from GABAergic inhibition to excitation, can underlie oscillatory activity [13]. In addition, in the immature nervous system the resting [Cl − ] i is decreased by GABAergic activity, which will result in a diminished excitatory drive and/or a dominance of shunting inhibition and may thus serve to limit a possible excitatory effect of GABA [40]. Therefore, for immature neurons an unstable [Cl − ] i homeostasis may be functionally relevant, as it allows activity-dependent scaling of [Cl − ] i -dependent synaptic transmission [42,43].
In consequence, the molecular configuration of immature neurons (high [Cl − ] i , long τ GABA and missing CA-VII) will generate conditions that allow limited activity-dependent [Cl − ] i decreases. This, in addition to the aforementioned effect of the high input resistance, may be an explanation why the [Cl − ] i homeostasis of immature neurons is maintained by a relatively ineffective transmembrane Cl − transport [29]. In contrast, in mature neurons the situation is different. In the adult brain, the low [Cl − ] i is needed to maintain hyperpolarizing inhibition [1] and an activity-dependent [Cl − ] i increase will attenuate membrane hyperpolarization. While it is obvious that massive changes in [Cl − ] i will impair GABAergic inhibition and can lead to hyperexcitability [18], recent modeling experiments demonstrate that even minimal changes in the capacity of Cl − -extrusion can have strong effects on information processing and storage in neurons [22]. Although the low R Input and the fast τ GABA counteracts activity-dependent [Cl − ] i increase in adult neurons, their low [Cl − ] i and their effective carbonic anhydrases can lead to substantial [Cl − ] i changes in their dendrite. The adverse effect of such local activity-dependent [Cl − ] i increases is enhanced by the more elaborated dendritic compartment in mature neurons, which limits diffusional elimination of Cl − -ions [13].
Our simulations reveal that the connection of an isolated dendrite to the soma drastically reduces the equilibrium [Cl − ] i after synaptic stimulation (Supplementary Figure S4f-k), demonstrating the important role of diffusional Cl − elimination under this condition. The large volume to surface ratio (and thus volume to conductance ratio) of the soma enables this compartment to serve as Cl − sink in these in-silico experiments. Also in-vitro it has been demonstrated that activation of dendritic GABA A receptors induced massive shifts in E GABA , whereas only minimal changes were observed upon perisomatic stimulation [10,12,26]. The dominance of perisomatic GABAergic terminals [70] may be related to the requirement of stable [Cl − ] gradients to maintain stable inhibition over a wide range of activity levels. However, the diffusion of [Cl − ] i through dendrite is a relatively slow and inefficient process, due to the small diameter in distal dendrites [7,55]. Addition of spines to dendrites drastically slow down diffusion along dendrites [16], suggesting that the complexity of the dendritic compartment (i.e. the number of arborizations that enhance tortuosity in the dendritic compartment) hinders Cl − -elimination by diffusion to the soma. Therefore, active elimination of Cl − from the cytoplasm is required to prevent or minimize activity-dependent [Cl − ] i changes in the elaborated dendritic compartment of adult neurons.
The elementary role of transmembrane Cl − transporters for neuronal [Cl − ] i homeostasis has been shown by a variety of studies [2,29,32,58,71]. Modeling studies revealed that slightly altered rates of transmembrane Cl − -transport, which does only marginally affect resting [Cl − ] i levels, have a strong effect on the spatiotemporal distribution of activity-dependent [Cl − ] i -transients in dendrites [15]. Therefore it is not surprising that the simulation of an enhanced capacity of transmembrane Cl − transport by increasing τ Cl attenuates activity-dependent [Cl − ] i transients. However, to minimize these [Cl − ] i transients a rather low τ Cl of < 100 ms is required. These low τ Cl values are several orders of magnitude below the experimentally determined kinetics of the NKCC1-mediated Cl − -accumulation (τ Cl = 158 s) in immature neurons [29]. Because of this slow kinetic of transmembrane transport of Cl − in immature neurons, we also consider that a Cl − /HCO 3 − exchange mediated by the anion exchanger in immature neurons [72] [15]. While it is generally assumed that the neuron-specific Cl − -extruder KCC2 mediates more efficient Cl − transport than NKCC1, only few experimental studies addressed the kinetics of KCC2-dependent Cl − -extrusion. Experiments in brain stem neurons demonstrated that KCC2 mediated Cl − -extrusion after [Cl − ] i increase by ca. 10 mM requires several minutes [73]. In contrast, in-vivo experiments revealed that the activity-dependent [Cl − ] i increase after an epileptic seizure recovered within less than 30 s [9] and in hippocampal slices GABA-induced [Cl − ] i transients recovered back to low steady-stale levels with a time constant of 3.3 s [12]. However, it is not clear how diffusional processes and/or the kinetics of the used Cl − sensor contribute to these kinetic properties. Simulations suggest that with realistic KCC2 levels τ Cl in the distal dendrites (≥ 200 µm from the soma) is between 100 ms and 200 ms [15], and thus probably lower than estimated from experimental data. Even this time constant is higher than the τ Cl required in our simulations to prevent local activity-dependent [Cl − ] i changes, suggesting that considerable [Cl − ] i changes can occur at GABAergic synaptic sites. While our and other simulations [15] suggest these transients may be restricted to local dendritic domains, it must be emphasized that subtle changes in the efficacy of KCC2 mediated Cl − -transport can already enhance the excitability in single neurons because activity-dependent [Cl − ] i transients may superimpose these effects [22]. In consequence, impairments of KCC2 mediated Cl − transport can led to a breakdown of sufficient inhibition in neuronal networks and contribute to hyperexcitability [15,17,20,56,74]. In this respect it is also relevant to consider that the activity of both NKCC1 and KCC2 are regulated by a variety of processes [75][76][77][78]. This indicates that the spatiotemporal [Cl − ] i dynamics in the dendritic compartment may be adapted to the functional states.
The limitation of our model to fully describe GDP-induced [Cl − ] i transients in CA3 pyramidal neurons is obvious from the fact, that we massively underestimate the [Cl − ] i decrease observed in real CA3 pyramidal neurons at high [Cl − ] i (e.g. Figure 6e). Therefore, additional factors must be proposed, which enhance the GABA A -receptor-mediated Cl − efflux. Possible mechanisms that improve Cl − efflux are e.g. an inhomogeneous distribution of voltage-activated K + channels in the dendritic compartment, an underestimation of n GABA in our in-vitro experiments due to voltage-clamp errors in the elaborated dendrite [79], or the effect of glutamatergic transmission during a GDP [20,80]. In addition, we also found that τ GABA has a major impact on the GDP-induced [Cl − ] i transients, and it might well be that the decay kinetics of spontaneous GABAergic PSCs of 37 ms [45] reflect the kinetic properties of a subpopulation of GABAergic inputs, that is less involved in the generation of GDPs. Finally, in our simulations the dendrite was implemented as a hollow tube with a diameter determined from the histological reconstruction. Under realistic assumptions the neuron is, however, filled with cytoplasm that contains large proteins, particles of different sizes and vesicles and tubes of intracellular organelles. Thus the free, "unexcluded" volume in the cytoplasm is restricted to an estimated fraction of ca. 60%, a principle termed cytoplasmic crowding [81]. This restricted free cytoplasmic water volume will increase the size of [Cl − ] i transients upon identical Cl − fluxes.

Compartmental Modeling
The biophysically realistic compartmental modelling was performed using the NEURON environment (neuron.yale.edu). The source code of models and stimulation files used in the present paper can be found in ModelDB [82] at http://modeldb.yale.edu/253369 (access date 14 March 2019) and was included in the supplementary material of this publication. For compartmental modelling we used either a simple ball and stick model (soma with d = 20 µm, linear dendrite with l = 200 µm and 103 nodes) or a reconstructed CA3 pyramidal cell (from Lombardi et al. [45]). Except where noted the dendrite was detached from the soma to analyse dendritic [Cl − ] i transients. The reconstructed neuron resembled the somatodendritic morphology of a typical immature CA3 pyramidal neuron (see Figure 2a,b). For this purpose images of a biocytin-filled neuron [83,84] were taken with 60× oil-immersion objectives and the somatodendritic morphology was reconstructed using Fiji (www.fiji.sc). It contained a soma (d = 15 µm), a dendritic trunk (d = 2 µm, l = 32 µm, 9 segments) and 56 dendrites (d = 0.36 µm, 9 segments each). In all of these compartments a specific axial resistance (R a ) of 34.5 Ωcm and a specific membrane capacitance (C m ) of 1 µF cm −2 ; were implemented. The specific membrane conductance (g pas ) varied (see Figures 1a  and 2e) and in the majority of the experiments was modeled by a voltage dependent process given by a Boltzmann-like equation: with g max = 0.002800 S/cm 2 (experimentally determined g Input at depolarized potentials, see Supplementary Figure S1a), gmin = 0.000660 S/cm 2 (experimentally determined minimal g Input at hyperpolarized potentials, see Figure 3a), e50 = −31 mV (half-maximal voltage), s = −6 (slope of the voltage-dependency). The reversal potential of this voltage-depended g pas was set to −60 mV. GABA A synapses were simulated as a postsynaptic parallel Cl − and HCO 3 − conductance with exponential rise and exponential decay [7]: where P is a fractional ionic conductance that was used to split the GABA A conductance (g GABA ) into Cl − and HCO 3 − conductance. E Cl and E HCO 3 were calculated from Nernst equation. The GABA A conductance was modeled using a two-term exponential function, using separate values of rise time (0.5 ms) and decay time (variable, mostly 37 ms) [45].  [49]. For the ball and stick model a single GABA A synapse was placed in the middle of the dendrite, except where noted. For the simulation of a GDP in the reconstructed CA3 neuron 101-3020 GABAergic synapses were randomly distributed within the dendrites of the reconstructed neuron. GABA inputs were activated stochastically using a normal distribution (µ = 600ms, σ = 900 ms) that emulates the distribution of GABAergic PSCs during a GDP observed in immature hippocampal CA3 pyramidal neurons [45]. The properties of these synapses were always given in the results part and/or the corresponding figure legends. From the quotient between the charge transfer of a GDP and of spontaneous GABAergic postsynaptic currents at a holding potential (V Hold ) of 0 mV it was estimated that 101 GABAergic inputs underlie a GDP [45]. To compensate for the space-clamp problems during a GDP, that were not considered by Lombardi et al. [45], we simulated the charge transfer during a GDP under their experimental conditions ([Cl − ] i = 10 mM, V Hold = 0 mV) and determined that 302, 395, and 523 (for P HCO 3 values of 0.0, 0.18, and 0.44, respectively) GABAergic synapses are required to generate the observed GDP-induced charge transfer (Supplementary Figure S1c-f). For these experiments we implement the single-electrode voltage clamp procedure provided by NEURON, using an access resistance of 5 MΩ. The charge transfer was calculated from the integral of the holding currents (I Hold ) during the GDP.
For the modeling of the GABA A receptor-induced [Cl − ] i and [HCO 3 − ] i changes, we calculated ion diffusion and uptake by standard compartmental diffusion modeling [16,[85][86][87]. To simulate intracellular Cl − and HCO 3 − dynamics, we adapted our previously published model [7]. Longitudinal Cl − and HCO 3 − diffusion along dendrites was modeled as the exchange of anions between adjacent compartments. For radial diffusion, the volume was discretized into a series of 4 concentric shells around a cylindrical core [85] and Cl − or HCO 3 − was allowed to flow between adjacent shells [88].
The free diffusion coefficient of Cl − inside neurons was set to 2 µm 2 /ms [55,89]. Since the cytoplasmatic diffusion constant for HCO 3 − is, to our knowledge, unknown, we also used a value of 2 µm 2 /ms. To simulate the GABAergic activity during a GDP, a unitary peak conductance of 0.789 nS and a decay of 37 ms were applied to each GABAergic synapse. These values resulted in a unitary currents of pA, which was in accordance with the mean amplitude of spontaneous GABAergic postsynaptic currents in CA3 paramidal neurons [45].
The driving-force of Cl − (DF Cl ) was calculated from the difference between the average E m during a GDP and E Cl (DF Cl = E m -E Cl ). To calculate the ratio between transmembrane [Cl − ] i transport and diffusional [Cl − ] i depletion into the soma, we normalized the diffusional exchange between the last somatic node and the soma (as calculated from Fick's law) to conditions were transmembrane [Cl − ] i loss was absent (τ Cl = 10 9 ms) and diffusional dendrite to soma transport was allowed to equilibrate for 2 min.
All electrophysiological data were taken from our previous publication [45]. However, for a comparison of these results with the simulations, we had to take different P HCO 3 into account. Therefore the GDP-induced [Cl − ] i changes were recalculated using P HCO 3 values of 0.0, 0.18 (determined in spinal cord neurons [48]) and 0.44 (determined in adult hippocampal neurons [49]