Effect of GABA and AMPA co-activation for a weak focal synaptic activation

First we analyzed the effect of glutamate receptor co-activation on the GABA_A receptor-induced [Cl^-]_i transients. It is important to emphasize that simulations of single or a low number of synaptic inputs necessarily led to small absolute effects of glutamatergic activation on GABAergic [Cl^-]_i or membrane voltage (E_m) changes (Figs 1–6), but nevertheless allowed for systematic parameter scans important for the detailed understanding of glutamatergic effects (see below). For quantitatively stronger effects during more realistic GABAergic and glutamatergic distributed input activation see Sections 2.4 and 2.5.

Simulation of a single GABA synapse using parameters determined in-vitro for spontaneous GABAergic postsynaptic currents (PSCs) (g_GABA = 0.789 nS, τ_GABA = 37 ms) [17], induced [Cl^-]_i changes (Fig 1B and 1C) that depended on the initial [Cl^-]_i ([Cl^-]_i⁰), as has been shown before [17]. At low [Cl^-]_i⁰ the inwardly directed driving force (DF_GABA = E_m—E_GABA) caused a Cl^--influx and thus a membrane hyperpolarization. At higher [Cl^-]_i⁰ of 25 mM the outwardly directed DF_GABA caused a Cl^--efflux and thus a membrane depolarization, while at an [Cl^-]_i⁰ of 15 mM, which is close to the [Cl^-]_i given by a passive distribution at -60 mV, only a slight [Cl^-]_i efflux was induced (Fig 1B and 1C). The simultaneous co-activation with a simulated single glutamate synapse, using parameters that were determined in-vitro for spontaneous glutamatergic PSCs [17]) and resemble the properties of the AMPA subtype of glutamate receptors (g_AMPA = 0.305 nS, τ_AMPA = 11 ms), imposed an additional depolarizing drive to the E_m responses (Fig 1B, dashed lines). Thereby it caused slight changes in the activity-dependent [Cl^-]_i transients towards higher concentration, thus enhancing the [Cl^-]_i increase at low [Cl^-]_i⁰ and attenuating the [Cl^-]_i decrease at higher [Cl^-]_i⁰ (Fig 1C, dashed lines).

Since physiological and pathophysiological activity is typically characterized by neurotransmitter release from several release sites [37, 38], we next analyzed the effect of varying g_AMPA on the GABA_A receptor -mediated [Cl^-]_i transient. As expected, these simulations showed that GABA_A receptor-induced Cl^- fluxes depended on the [Cl^-]_i⁰ (Fig 2A black trace). However, the Cl^- fluxes were systematically shifted towards Cl^- influx in the presence of AMPA receptor-mediated inputs (Fig 2A and 2B). At a g_AMPA of 305 nS and 30.5 nS (corresponding to 100x and 1000x glutamatergic PSCs) a consistent Cl^- influx was induced even at high [Cl^-]_i (Fig 2A and 2B). At a g_AMPA of 0.305 nS (Fig 2C and 2E) and 3.05 nS (Fig 2D and 2E) bimodal effects, consisting of an initial influx followed by an efflux, were observed within a limited [Cl^-]_i range. These biphasic responses were caused by the fact that the membrane depolarization only temporarily exceeds E_Cl (Fig 2C and 2D). The maximal values of Cl^- in- and efflux are displayed in separate panels in Fig 2E and 2F.

A systematic analysis of the direction of Cl^- fluxes at various g_AMPA revealed that the GABA_A receptor-mediated Cl^- fluxes show a logarithmic dependency on g_AMPA, resulting in sigmoidal curves in a monologarithmic plot (Fig 2F). Only at low [Cl^-]_i concentrations, which permit a Cl^- influx even without AMPA co-stimulation, a monotonous increase in the Cl- fluxes were induced by increasing g_AMPA (Fig 2E and 2F). When [Cl^-]_i was above 13 mM (corresponding to E_Cl above -60 mV) addition of g_AMPA caused biphasic Cl- fluxes (Fig 2E and 2F).

In summary, these results indicate that co-activation of AMPA receptors enhances Cl^- influx at low [Cl^-]_i and attenuates Cl^- efflux at high [Cl^-]_i. with the possibility to even revert the latter to Cl^- influx. Already relatively low, physiologically relevant g_AMPA values representing 10–100 spontaneous postsynaptic events, are sufficient to substantially modulate GABA_A receptor mediated Cl^- fluxes.

Influence of τ_AMPA on GABA_A receptor-induced [Cl^-]_i transients

Next we analyzed the influence of the kinetics of coincident AMPA receptor activation on the GABA_A receptor-induced [Cl^-]_i transients. For this purpose, we modified the decay time constant of the AMPA synapse (τ_AMPA) using values between 1 and 100 ms. These simulations were performed under consideration of the experimentally determined values for GABA_A receptor-mediated inputs either at g_AMPA of 0.305 nS (i.e. the experimentally determined value [17]) or at g_AMPA of 3.05 nS (to estimate the effects of a small number of coincident colocalized glutamatergic inputs). As the depolarizing effect of the AMPA synapse strictly depends on τ_AMPA (Fig 3A), for τ_AMPA values < 37 ms biphasic voltage responses were induced at low [Cl^-]_i (Fig 3A). In contrast, at high [Cl^-]_i (where GABAergic responses are depolarizing) the peak depolarization was enhanced. For τ_AMPA values > 37 ms the depolarization was virtually saturated (Fig 3B). In accordance with this observation the AMPA-mediated shift in the GABAergic [Cl^-]_i transients was sensitive to τ_AMPA at values < 37 ms, while at values > 37ms only minimal additional effects were observed (Fig 3C and 3D). These findings indicate that the kinetics of glutamatergic synaptic inputs have a consistent effect on activity-dependent [Cl^-]_i changes and that shorter glutamatergic postsynaptic potentials (PSPs) will attenuate the effect of AMPA on activity-dependent [Cl^-]_i transients.

Since these results implicate a substantial influence of the time course of depolarizing events on the GABA-induced [Cl^-]_i transients, we also investigated the effect of NMDA-receptors, which possess slow onset and decay kinetics, on the GABA receptor-induced [Cl^-]_i transients. These simulations with an established model for the NMDA receptor [39] revealed that co-activation of NMDA receptors (τ_NMDA = 500 ms) induced at high g_NMDA [Cl^-]_i transients that are similar as the ones induced by AMPA receptor co-activation (Fig 3E). However, the [Cl^-]_i transients showed a steeper dependency on g_NMDA, probably reflecting the Mg²⁺ block [40]. Thus at moderate g_NMDA of ~3 nS the [Cl^-]_i changes were lower for a given NMDA conductance than for a similar AMPA conductance (Fig 3E).

In addition to the long-lasting NMDA receptor mediated responses, short action potentials may also provide a depolarizing drive that enhances the GABA induced [Cl^-]_i transients. To investigate their influence, we implemented an established Hodgkin-Huxley (HH) mechanism [41], either only in the soma or in the soma and the dendrite, to emulate either passively or actively back-propagating actions potentials, respectively. These simulations revealed that action potentials enhanced the effect of AMPA on the GABAergic [Cl^-]_i transients (Fig 3F–3H). While at a low g_AMPA of 0.305 nS no AP was induced and thus no additional [Cl^-]_i influx was induced, at a moderate g_AMPA of 3.05 nS only actively back-propagating APs augment the [Cl^-]_i changes (Fig 3G and 3H). At higher g_AMPA also somatic APs, that spread passively (electrotonically) into the dendritic compartment, were able to augment the [Cl^-]_i transients (Fig 3G). The addition of voltage gated Ca²⁺ channels [41] in the dendrite had no effect on the [Cl^-]_i transients (Fig 3G).

Spatial and temporal constrains of AMPA receptor-mediated shift in GABAergic [Cl^-]_i transients for a weak focal synaptic activation

To analyze how the spatial distance between the AMPA and the GABA synapse influences the GABA_A receptor-induced [Cl^-]_i transients, we systematically moved the AMPA synapse along the dendrite from the somatic (0%) to the distal end (100%) (Fig 4A and 4B) using the experimentally determined parameters for AMPA and GABA inputs (g_GABA = 0.789 nS, τ_GABA = 37 ms, g_AMPA = 0.305 nS, τ_AMPA = 11 ms [17]). These experiments revealed that the membrane potential change depends on the location of the AMPA synapse. The maximal amplitude of the positive shift in E_m induced by the AMPA co-stimulation decreased substantially at distant positions (Fig 4B), due to the leak conductance shunting the synaptic currents (i.e. dendritic filtering). In accordance with these smaller depolarizing E_m shifts, the [Cl^-]_i changes were slightly decreased with increasing distance between AMPA and GABA synapses (Fig 4B). To quantify this effect, we calculated the amount of additional [Cl^-]_i changes induced by AMPA co-stimulation (Δ_G[Cl^-]_i) by subtracting the [Cl^-]_i changes at GABA stimulation from the [Cl^-]_i changes at AMPA/GABA co-stimulation. These simulations revealed that the decrease of Δ_G[Cl^-]_i with increasing distance between both synapses could be perfectly fitted (R² = 0.023) with a monoexponential function, using a decay length constant (λ) of 248 μm (Fig 4C). This is exactly the λ value determined for the attenuation of the peak voltage responses (Fig 4D) and reflects the exponential decay of voltage in a linear cable with homogeneous membrane resistance. These observations indicate that the distance between GABAergic and glutamatergic synapses is a relevant factor determining the effects of co-activation on the activity-dependent [Cl^-]_i transients.

To analyze how the temporal relation between the AMPA- and the GABA-mediated activity influences the GABA_A receptor-induced [Cl^-]_i transients we next systematically varied the delay between the AMPA and the GABAergic stimulus from -49 ms (i.e. AMPA before GABA) to +100 ms (i.e. AMPA after GABA) and determined the impact of this latency shift on the [Cl^-]_i transients (Fig 5A and 5B). The parameters for AMPA and GABA inputs were identical to the parameters used before (g_GABA = 0.789 nS, τ_GABA = 37 ms, g_AMPA = 0.305 nS, τ_AMPA = 11 ms) and both synapses were located at the same position. These simulations revealed that the additional effect of AMPA co-stimulation on the [Cl^-]_i transients (Δ_G[Cl^-]_i) became maximal when GABA and AMPA stimulus were provided simultaneously (Fig 5C). Surprisingly, this AMPA effect on Δ_G[Cl^-]_i remained stable for a latency of ≈20 ms, before it rapidly declined (Fig 5C). To provide a mechanistic explanation for this plateau phase, we next plotted the rate of [Cl^-]_i changes versus the absolute value of the [Cl^-]_i change (Fig 5D). This phase plane plot illustrates that the trajectories of all AMPA stimulations with a latency between 0 and 20 ms converged with the trajectory of the 0 ms latency stimulus (purple line), thus reaching identical minimal [Cl^-]_i values (obtained at the intersection with the y-axis value ∂[Cl^-]_i/∂t = 0 mM/s). Latencies between 22 and 34 ms provided a gradual decline in the minimal [Cl^-]_i. For latencies > 34 ms the additional AMPA-mediated reduction of the Cl^- -efflux was initiated after a minimal [Cl^-]_i was reached, therefore these stimulations did not provide a [Cl^-]_i decrease exceeding the [Cl^-]_i decrease mediated by a pure GABA stimulation (black line).

To investigate how the duration of GABA and AMPA receptor-mediated currents influence this complex time course of [Cl^-]_i transients, we next systematically varied τ_GABA (5 ms, 37, ms 50 ms) as well as τ_AMPA (5 ms, 11 ms, 37, ms 50 ms) and determined Δ_G[Cl^-]_i (Fig 5E). These simulations revealed that, in accordance with the previous results, Δ_G[Cl^-]_i increased at longer τ_AMPA for all three τ_GABA tested. While at a short τ_GABA of 5 ms no plateau phase was observed, such a plateau occurred for τ_GABA of 37 ms and 50 ms with short τ_AMPA values of 5 ms or 11 ms (Fig 5E). However, in contrast to our hypothesis that such a plateau phase occurred when τ_AMPA was shorter than τ_GABA, for a τ_GABA ≥ 37 ms and τ_AMPA ≥ 37 ms Δ_G[Cl^-]_i steadily declined after the maximal value was obtained at simultaneous AMPA/GABA stimulation. Another finding of these simulations that appears counter-intuitive is the fact that for short τ_AMPA of 5 ms and 11 ms the peak Δ_G[Cl^-]_i decreases when τ_GABA increased from 5 ms to 37 ms (Fig 5E).

To investigate these issues in detail, we next systematically varied τ_GABA between 5 and 50 ms using fixed τ_AMPA values of 5, 11, and 37 ms and determined Δ_G[Cl^-]_i at different AMPA/GABA latencies. In these simulations we were able to identify a complex dependency between Δ_G[Cl^-]_i and the relation between τ_GABA and τ_AMPA (Fig 6A–6C). For τ_AMPA of 5 and 11 ms the influence of the AMPA/GABA latency on Δ_G[Cl^-]_i changed from a “peak”-like pattern to a “plateau”-like phase, in which the maximal Δ_G[Cl^-]_i remained rather constant for a progressively longer latency interval between AMPA and GABA stimulation. This “plateau”-like phase occurred under conditions when τ_GABA is at more than about 3 times larger than τ_AMPA (Fig 6A and 6B). For τ_AMPA of 37 ms this “plateau”-like phase was not reached, but a phase with linearly decreasing [Cl^-]_i shifts became visible (Fig 6C). In any way, the maximal AMPA-dependent [Cl^-]_i shift was observed at τ_GABA of 11 ms, 18 ms and 47 ms for τ_AMPA of 5 ms, 11 ms and 37 ms, respectively (red plots in Fig 6A), reproducing the observation that prolonging τ_GABA can reduce Δ_G[Cl^-]_i. From these results it can be concluded, first, that the effect of AMPA co-stimulation on Δ_G[Cl^-]_i depends critically on the timing between both inputs, second, that Δ_G[Cl^-]_i is maximal when τ_GABA is slightly larger than τ_AMPA, and, third, that a “plateau”-like interval of stable Δ_G[Cl^-]_i occurred when τ_GABA is at least 3 times larger than τ_AMPA.

Next, we investigated how the time course of E_m changes contributes to this complex dependency. For this purpose, we used identical stimulation parameters (g_GABA = 0.789 nS, τ_GABA = 37 ms, g_AMPA = 0.305 nS, τ_AMPA = 11 ms, [Cl^-]_i⁰ = 25 mM) and modified the time course of the voltage traces by changing the membrane time constant (S1 Fig). These simulations revealed that reducing the membrane time constant, which enhanced the onset kinetics of AMPA and GABA receptors, as well as the decay of AMPA receptor-mediated voltage responses, had only a minor effect on the observed [Cl^-]_i changes (S1A Fig). The trajectories at different latencies converge virtually in the same manner as at physiological conditions (S1B Fig). On the other hand, a substantial prolongation of the membrane time constant slowed the kinetics of both AMPA and GABA-receptor dependent depolarizations (S1C Fig) and led to significantly different behavior of [Cl^-]_i changes: The delayed GABAergic depolarization increased Δ[Cl^-]_i when GABAergic input was stimulated alone (black trace). In addition, the maximum amount of Δ_G[Cl^-]_i (i.e. the difference between the 0 ms latency trajectory and the GABA only trajectory) was smaller. More importantly, the trajectories for latencies > 4 ms did no longer converge with the trajectory of simultaneous AMPA/GABA stimulation (purple line), which resulted in a steady decline of Δ_G[Cl^-]_i for all conditions in which AMPA was stimulated after the GABA input. In summary, these results indicate a complex interplay between the membrane time constant and the kinetics of AMPA- and GABA-mediated synaptic events. Only in cases in which the kinetics of the receptors dominate the time course of membrane responses, the complex, plateau-like dependency of Δ_G[Cl^-]_i on the latency between GABA and AMPA inputs was observed.

While in these models the background conductance was set by a purely passive conductance, it had been demonstrated that tonic Cl^- currents considerably contribute to the background conductance [42]. Therefore, we additionally implemented a tonic background conductance of 8.75 nS/cm² [43] and reduced the passive conductance to 0.99125 mS/cm², to maintain the input resistance of 188.2 MΩ. These simulations revealed that under this condition a constant increase in the basal [Cl^-]_i occurred. In the presence of this tonic [Cl^-]_i conductance activation of AMPA-mediated synapses led to [Cl^-]_i changes that depended on g_AMPA and τ_AMPA (S2 Fig). However, at physiologically relevant values for AMPA receptor-mediated inputs (g_AMPA = 0.305 nS and τ_AMPA = 11 ms), only a minimal additional [Cl^-]_i increase by 0.1 μM was induced, which slightly increased to 0.85 μM and 3.74 μM at gAMPA of 3.05 nS and 30.05 nS, respectively (Figs 6D and S2). Accordingly, addition of a tonic GABAergic current had no effect on the [Cl^-]_i changes induced by phasic GABAergic inputs, despite a slight shift in the basal [Cl^-]_i (Fig 6E).

Influence of gAMPA and τAMPA on the GABAergic [Cl^-]_i transients in a morphologically realistic neuronal model with multiple distributed synaptic inputs

To investigate in a more physiological setting how the interference between GABA_A and AMPA receptors influence the resulting [Cl^-]_i transients, we implemented GABA and AMPA synapses in a morphologically realistic model of an immature CA3 pyramidal neuron (Fig 7A and 7B), using morphology and membrane parameters determined in in-vitro experiments [17]. In the majority of simulations, we applied experimentally estimated correlated GABAergic and glutamatergic activity recorded during giant depolarizing potentials (GDPs, [17], see Fig 7C). GDPs are highly relevant network events in the immature hippocampus that have been shown to cause substantial [Cl^-]_i changes [8, 17, 35, 44]. Therefore, the use of these neurons and their activity patterns allows to simulate ionic plasticity in a morphologically and physiologically relevant setting. This computational model, which incorporates basic morphological and biophysical properties of hippocampal neurons, generated complex trajectories of [Cl^-]_i within individual dendrites during a simulated GDP (Fig 7D). These [Cl^-]_i changes in the individual neurites are determined by Cl^--fluxes via GABA_A receptors, lateral Cl^- diffusion within the dendritic compartment and transmembrane Cl^--transport [25, 29, 33]. For a better quantification and display, the average [Cl^-]_i over all nodes of all dendrites was calculated at each simulated interval (compare e.g. Fig 7F), while E_m was determined in the soma.

In a first set of simulations, we investigated the impact of g_AMPA on GABAergic [Cl^-]_i changes during a simulated GDP. For the simulation of a GDP, 534 GABAergic synapses were randomly distributed within the dendrites and activated stochastically to emulate the distribution of GABAergic PSCs during a GDP observed in-vitro [17] (see Materials and Methods for detail). In accordance with previous observations [17, 30], the massive GABAergic activity during a GDP led to substantial [Cl^-]_i changes, with a [Cl^-]_i increase by 3.94 ± 0.05 mM (n = 9 repetitions with random distribution/stimulation) at a low [Cl^-]_i⁰ of 5 mM and a [Cl^-]_i decrease by -3.78 ± 0.08 mM (n = 9) at a [Cl^-]_i⁰ of 25 mM (black traces in Fig 7E and 7F). Adding 107 AMPA synapses with a g_AMPA of 0.305 nS (i.e. the experimentally determined number and conductance of AMPA inputs) led to a substantial increase in the activity-dependent [Cl^-]_i transients to 4.95 ± 0.07 mM for a [Cl^-]_i⁰ of 5 mM and significantly attenuated the activity-dependent [Cl^-]_i decrease at 25 mM to -2.88 ± 0.06 mM (Fig 7F red trace). A similar trend was also observed for other [Cl^-]_i⁰ concentrations. Co-stimulation with 107 AMPA inputs increased the [Cl^-]_i transients at low [Cl^-]_i⁰ and attenuated the transients at high [Cl^-]_i⁰ (Fig 7H). Using a larger value for g_AMPA enhanced this impact on activity-dependent [Cl^-]_i shift (Fig 7F). At g_AMPA values of 30.5 and 305 nS at all investigated [Cl^-]_i⁰, an increase in [Cl^-]_i was induced (Fig 7H), in accordance with the depolarized E_m induced by these conditions (Fig 7G). In summary, these results indicate that physiological levels of AMPA co-stimulation can significantly affect the GABA_A receptor induced [Cl^-]_i transients. In line with the results from the ball-and-stick model, implementation of the tonic GABAergic conductance of 8.75 nS/cm² [43] had only a negligible effect (S3 Fig). With this tonic current, the [Cl^-]_i increase at physiological g_AMPA values of 0.305 nS was augmented by only 0.046 mM at a [Cl^-]_i⁰ of 5 mM and the [Cl^-]_i decrease at a [Cl^-]_i⁰ of 25 mM was reduced by only 0.036 mM. Even at higher g_AMPA values the effect of tonic GABAergic conductances remained below 0.1 mM.

In the next series of simulations, we systematically altered the decay time constant τ_AMPA for all 107 AMPA receptor-mediated synaptic inputs during a GDP from the experimentally determined value of 11 ms to 5, 37 and 50 ms, while using g_AMPA of 0.305 nS and the experimentally determined values for the GABAergic synaptic inputs. Although this slight shift in τ_AMPA had only a minor effect on the size of the voltage deflections (Fig 8A and 8C), it significantly modified the effect of AMPA co-stimulation on GABA_A receptor mediated [Cl^-]_i (Fig 8B and 8D). At a [Cl^-]_i⁰ of 5 mM the enhancement of GDP-induced [Cl^-]_i transient by AMPA (Δ_G[Cl^-]_i) was reduced from 1.02 ± 0.06 mM (n = 9 repetitions) at τ_AMPA = 11 ms to 0.48 ± 0.06 mM at τ_AMPA = 5 ms (Fig 8B). Similarly, at a [Cl^-]_i⁰ of 25 mM, Δ_G[Cl^-]_i was diminished by shortening τ_AMPA from 11 ms (0.93 ± 0.1 mM) to 5 ms (0.43 ± 0.07 mM) (Fig 8B). In contrast, prolonging τ_AMPA to 37 or even 50 ms had a substantial impact on the time course and amount of the voltage deflections (Fig 8A). Accordingly, the activity-dependent [Cl^-]_i transients were systematically shifted toward more influx or less efflux, respectively (Fig 8B–8D). In summary, these results indicate that even slight changes in τ_AMPA can substantially influence the impact of AMPA co-activation on GABA_A receptor-mediated [Cl^-]_i transients.

In addition, we also evaluated the effect of NMDA receptors, which possess slow onset and decay kinetics, on the GABA receptor-induced [Cl^-]_i transients. These simulations, using the same temporal and spatial pattern of glutamatergic inputs, but an established model for the NMDA receptor [39], revealed that co-activation of NMDA receptors (τ_NMDA = 500 ms) induced in general larger [Cl^-]_i transients as compared to AMPA receptor co-activation (S4 Fig). While the effects were small at a g_NMDA of 0.305 nS (1.2 ± 0.1 mM vs. 0.9 ± 0.1 mM at [Cl^-]_i⁰ of 5 mM), substantial differences were observed at intermediate g_NMDA values (17.5 ± 0.7 mM vs. 6.1 ± 0.3 mM at 3.05 nS or 29.3 ± 0.8 mM vs. 18.6 ± 0.7 mM at 30.5 nS) (S4 Fig).

Spatial and temporal constrains of AMPA-mediated infuences on GABAergic [Cl^-]_i transients in a morphologically realistic neuronal model

Next we analyzed how the spatial relation between GABA and AMPA synapse activation influences the size of GDP-dependent [Cl^-]_i transients. For this purpose, we first compared whether direct co-localization of each of the 107 AMPA synapses with a GABA synapse (100% spatial correlation) affects the AMPA-mediated shift in the GDP-dependent [Cl^-]_i transients. These simulations revealed that the activity-dependent [Cl^-]_i shifts with this 100% spatially correlated AMPA synapses were not significantly different from models with a random spatial distribution of AMPA synapses (Fig 9A). Also a restriction of AMPA synapses in either the distal 25% or the proximal 25% of the dendrite length had no substantial effect on the magnitude of activity-dependent [Cl^-]_i transients (S5 Fig). We propose that this lack of an effect was caused by the fact that the overall density of GABA and AMPA synapses in each of the 56 dendrites was so high, that independent of the individual synaptic localization comparable effects on DF_GABA were induced. Therefore, we next relocated the GABA and AMPA synapses in distinct parts of the dendritic compartment, with either AMPA synapses located only in the most proximal 12 dendritic branches and the GABA synapses in the most distal 34 dendritic branches, or vice versa (Fig 9B). In these simulations the GABA_A receptor-induced [Cl^-]_i shift without AMPA co-stimulation differ from the previous stimulations, as the Cl^--influx was restricted to a subset of dendrites (Fig 9B). Under this strict regime, the location of the AMPA synapses had a slight effect on Δ_G[Cl^-]_i. With all GABA synapses in the proximal dendrites and the AMPA synapses located in the distal dendrites a co-stimulation induced a Δ_G[Cl^-]_i of 1.25 ± 0.17 mM (n = 9 repetitions) at a [Cl^-]_i⁰ of 5 mM (Fig 9B). In contrast, when all GABA synapses were located in the distal dendrites and all AMPA synapses in the proximal dendrites co-stimulation induced a Δ_G[Cl^-]_i of 0.72 ± 0.07 mM (Fig 9B). A similar tendency was also observed for other [Cl^-]_i⁰ (Fig 9B). In summary, these results indicate that for a massive stimulation, like the modeled GDP, changes in the spatial correlation between AMPA and GABA receptors have only subtle effects on activity-dependent [Cl^-]_i transients.

Finally, we investigated the effect of the temporal correlation between AMPA and GABA synaptic inputs on the activity-dependent [Cl^-]_i changes. Since it was not possible to generate a non-trivial decorrelation of AMPA and GABA synaptic inputs during GDP-like activity, we stimulated 100 AMPA (g_AMPA = 0.305 nS/τ_AMPA = 11 ms) and 100 GABA (g_AMPA = 0.789 pS/τ_AMPA = 37 ms) synaptic inputs at a frequency of 20 Hz, using a random temporal distribution for both types of synapses. While at a [Cl^-]_i⁰ of 5 mM the random stimulation of only GABA synapses induced a [Cl^-]_i increase by 2.06 ± 0.16 mM (n = 9 repetitions), this increase was augmented by 0.04 ± 0.005 mM upon random co-stimulation of AMPA synapses (Fig 9C and 9D. Comparable Δ_G[Cl^-]_i values were also observed for [Cl^-]_i⁰ of 10 mM and 15 mM. For higher [Cl^-]_i⁰ the trend towards larger [Cl^-]_i at AMPA co-stimulation maintained. However, the large variance in the individual maximal [Cl^-]_i responses in each simulation and the resulting high SD values for Δ_G[Cl^-]_i values caused that these changes were not significant. If in this stimulation paradigm the AMPA stimuli occurred exactly at the same time points as the GABAergic inputs (i.e. 100% temporal correlation), Δ_G[Cl^-]_i was significantly increased to 0.065 ± 0.008 mM (at a [Cl^-]_i⁰ of 5 mM), to 0.078 ± 0.009 mM (at 10 mM [Cl^-]_i⁰), and to 0.084 ± 0.034 mM (at 15 mM [Cl^-]_i⁰) (Fig 9D).

To investigate the effect of a decorrelation between GABA and AMPA inputs, we implemented an algorithm that generates refractory periods of 5, 11, and 37 ms around each GABAergic stimulus in which AMPA inputs are omitted (Fig 9E). These experiments revealed that for a [Cl^-]_i⁰ of 5 mM the Δ_G[Cl^-]_i values are significantly decreased from 0.041 ± 0.005 mM (n = 9 repetitions at random correlation) to 0.027 ± 0.004 at a refractory period of 11 ms, and to 0.014 ± 0.003 at a refractory period of 37 ms (Fig 9F). At a refractory period of 5 ms Δ_G[Cl^-]_i decreased only slightly and not significantly to 0.037 ± 0.006. A comparable reduction was also observed for a [Cl^-]_i⁰ of 10 mM (Fig 9F). At 15 mM only for a refractory period of 37 ms a significant reduction in Δ_G[Cl^-]_i was observed (from 0.048 ± 0.026 mM to 0.016 ± 0.011 mM). In summary, these results support the finding that the temporal correlation between GABA and AMPA synapses enhance activity-dependent [Cl^-]_i shifts, in particular if AMPA and GABA inputs are correlated within the time range of their decay time constants.

Compartmental modeling

The biophysics-based compartmental modeling 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 (http://modeldb.yale.edu/266823). For compartmental modelling we used in the first simulations a simple ball-and-stick model (soma with d = 20 μm, linear dendrite with l = 200 μm, diameter 1 μm, and 103 nodes; cell_soma_dendrite.hoc). In the experiment investigating the role of spatial orientation between GABA and AMPA synapses, the length of the dendrite was increased to 1000 μm (cell_soma_dendrite_long.hoc). In further experiments we used a reconstructed CA3 pyramidal cell (Cell1_Cl-HCO3_Pas.hoc; [17]). We used the reconstruction of an immature CA3 pyramidal neuron for this purpose, because coincident GABAergic and glutamatergic activity used for modelling of ionic plasticity was recorded in exactly this neuron population [17]. This reconstructed neuron 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 μFcm^-2 were implemented. C_m was varied in two experiments to accelerate/decelerate the membrane time constant. A specific membrane conductance (g_pas) of 1.0 mS/cm² with a reversal potential of -60 mV was inserted in all neuronal elements. In some experiments we additionally implemented a tonic background conductance of 8.75 μS/cm² [43] and reduced the passive conductance to 0.99125 mS/cm², to maintain the input resistance of 188.2 MΩ.

GABA_A synapses were simulated as a postsynaptic parallel Cl⁻ and HCO₃⁻ conductance with exponential rise and exponential decay: where P is a fractional ionic conductance that was used to split the GABA_A conductance (g_GABA) into Cl⁻ and HCO₃⁻ conductance. E_Cl and E_HCO3 were calculated from the 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). Parameters used in our simulations were as follows: [Cl⁻]_o = 133.5 mM, [HCO3⁻]_i = 14.1 mM, [HCO3⁻]_o = 24 mM, temperature = 31°C, P = 0.18. The conductance values for GABA synapses varied as given in the main text. AMPA synapses were modeled by an Exp2Syn point process using a reversal potential of 0 mV, a tau 1 value of 0.1 ms and a tau2 value of 11 ms, in accordance with the experimentally determined value [17], except where noted. The conductance values for AMPA synapses varied as given in the main text.

For the ball-and-stick model a single GABA_A synapse was placed in the middle of the dendrite, except where noted. The AMPA synapse was placed as indicated in the figure legends. For the simulation of a GDP in the reconstructed CA3 neuron 534 GABAergic synapses and 107 AMPA synapses were randomly distributed within the dendrites of the reconstructed neuron, except where noted. The number of GABA and AMPA synapses replicate the estimated synapse numbers during experimentally recorded GDPs [17]. The properties of these synapses were given in the results part and/or the corresponding figure legends. Nine repetitions of these simulations were generated by altering the seed values for the random functions, which resulted in a redistribution of all synapses within the dendritic compartment and the timing of their activation. The results of these repeated simulations were given and displayed as mean ± SD.

For each synapse, the index of the dendrite as well as the position within this dendrite was randomly determined using a normal distribution. The time points of GABA and AMPA inputs were determined stochastically using a normal distribution (μ = 600 ms, σ = 9000 ms for GABA and μ = 650 ms, σ = 8500 ms for AMPA), which emulates the distribution of GABAergic and glutamatergic PSCs during a GDP observed in immature hippocampal CA3 pyramidal neurons [17]. In a few simulated experiments, the 107 AMPA inputs were stimulated synchronously with a random subgroup of the GABA inputs. Since it was not possible to generate a non-trivial decorrelation of AMPA and GABA synaptic inputs during GDP-like activity, for the decorrelation experiments, we stimulated 100 AMPA and 100 GABA synaptic inputs at a frequency of 20 Hz, using a random temporal distribution for both synapses. For the decorrelation, we used a simple algorithm that generated new random numbers until the time point of an AMPA input was temporally separated by more than the given refractory periods with respect to the time points of all GABA inputs.

For analyzing the effect of NMDA receptors, we included an established model for the NMDA receptor (Exp2NMDA2 from Senselab Model DB ID: 145836 [39]) with an onset time constant of 8.8 ms and a τ_NMDA of 500 ms, using similar conductance values for g_NMDA as for the AMPA receptors. In addition, in a limited set of simulated experiments we inserted an established Hodgkin-Huxley based model of hippocampal action potentials (Model DB ID: 3263 [41]) into soma and dendrite of the ball-and-stick model to emulate somatic and back-propagating dendritic action potentials. This Hodgkin-Huxley-based model also includes a voltage-gated Ca²⁺ conductance, which we also implemented separately in soma and dendrite of the ball-and-stick model to investigate the contribution of Ca²⁺ conductances to [Cl^-]_i transients.

For the modeling of the GABA_A receptor-induced [Cl^-]_i and [HCO₃^-]_i changes, we calculated ion diffusion and uptake by standard compartmental diffusion modeling. In order to keep the computational complexity at reasonable levels, we used a purely diffusional model without considering electrodiffusion [26, 27], as recently it has been demonstrated that for Cl^- ions the diffusional movement is considerably larger than the contribution of electric drift [46]. To simulate intracellular Cl^- and HCO₃^- dynamics, we adapted our previously published model [25, 30]. Longitudinal Cl^- diffusion along dendrites was modeled as the exchange of anions between adjacent compartments. For radial diffusion, the volume was discretized into a series of four concentric shells around a cylindrical core and Cl^- or HCO₃^- was allowed to flow between adjacent shells. The free diffusion coefficient for Cl^- inside neurons was set to 2 μm²/ms [14] and for HCO₃^- to 1.18 μm²/ms [67]. To simulate transmembrane transport of Cl^- and HCO₃^-, we implemented an exponential relaxation process for [Cl^-]_i and [HCO₃^-]_i to resting levels [Cl⁻]_i^rest or [HCO₃⁻]_i^rest with a time constant τ_Ion.

Cl⁻ transport was in most experiments (if not otherwise noted) modeled as bimodal process, for [Cl^-]_i < [Cl^-]_i^rest τ_Ion was set to 174 s to emulate an NKCC1-like Cl⁻ transport mechanism. For [Cl^-]_i > [Cl^-]_i^rest τ_Ion was set to 321 s to emulate passive Cl^- efflux [43].

The impact of GABAergic Cl⁻ currents on [Cl⁻]_i and [HCO₃⁻]_i was calculated as:

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, in accordance with properties of spontaneous GABAergic postsynaptic currents in CA3 pyramidal neurons [17].

For the analysis and display of the data in the ball-and-stick model we used E_m and [Cl^-]_i values at the site of the GABAergic synapses. For the reconstructed CA3 neuron we used the somatic E_m and the mean [Cl^-]_i within the dendritic compartment. The mean [Cl^-]_i of all dendrites was calculated by averaging the [Cl^-]_i at 50% of dendritic length for all 56 dendrites. This procedure mimics the experimental procedure of Lombardi et al. [17], who determined E_GABA by focal application in the dendritic compartment.

For the calculation of Δ[Cl^-]_i, the maximal deviation of [Cl^-]_i upon a GABAergic stimulus ([Cl^-]_i^S) was subtracted from the resting [Cl^-]_i before the stimulus ([Cl^-]_i^R). For biphasic responses both minimal and maximal [Cl^-]_i^R were determined and displayed. In some cases, the manifest Δ[Cl^-]_i for these responses was calculated as:

To quantify the influence of AMPA co-stimulation on the GABAergic [Cl^-]_i transients, the amount of additional [Cl^-]_i changes induced by AMPA co-stimulation (Δ_G[Cl^-]_i) was calculated from the Δ[Cl^-]_i values with/without AMPA co-stimulation as follows: