Information processing in the brain requires that excitation and inhibition are balanced. The main inhibitory neurotransmitter in the brain is gamma-amino-butyric acid (GABA). GABA actions depend on the Cl--gradient, but activation of ionotropic GABA receptors causes Cl--fluxes and thus reduces GABAergic inhibition. Here, we investigated how a coincident membrane depolarization by excitatory glutamatergic synapses influences GABA-induced Cl--fluxes using a biophysical compartmental model of Cl- dynamics, simulating either simple or realistic neuron topologies. We demonstrate that glutamatergic co-stimulation directly affects GABA-induced Cl--fluxes, with the size of glutamatergic effects depending on the conductance, the decay kinetics, and localization of glutamatergic inputs. We also show that the glutamatergic shift in GABAergic Cl--fluxes is surprisingly stable over a substantial range of latencies between glutamatergic and GABAergic inputs. We conclude from these results that glutamatergic co-stimulation alters GABAergic Cl--fluxes and in turn affects the strength of GABAergic inhibition. These coincidence-dependent ionic changes should be considered as a relevant factor of short-term plasticity in the CNS.
Information transfer within networks of single neurons is carried out via synaptic contacts, that use different neurotransmitters acting on pre- and postsynaptic receptors. The two most important neurotransmitters in the mammalian brain are glutamate and γ-amino butyric acid (GABA), which in general exert an excitatory and inhibitory action in the postsynaptic cell, respectively [1]. Beside regulating the excitability of neuronal circuits, GABA is also required for the control of sensory integration, regulation of motor functions, generation of oscillatory activity, and neuronal plasticity [2]. The responses to GABA are mediated by metabotropic GABAB receptors and by ionotropic GABAA receptors, which are ligand-gated anion-channels with a high Cl- permeability and a lower HCO3- permeability [1]. The GABAergic effects therefore depend mainly on the Cl- gradient across the neuronal plasma membrane [1, 3]. The typical inhibitory action of GABA requires a low intracellular Cl- concentration ([Cl-]i), which is typically maintained by the action of a Cl- extruder termed KCC2 [3]. During early development [Cl-]i is maintained at high levels by active Cl- accumulation via the Na+-K+-2Cl- -Symporter NKCC1, rendering GABA responses depolarizing and under certain conditions excitatory [4–6]. Such excitatory GABAergic responses contribute to the generation of spontaneous neuronal activity, which is essential for the correct maturation of nervous systems [7–9].
However, the Cl−-fluxes through GABAA receptors, which underlie GABAergic currents, change [Cl−]i and thus temporarily affect the amplitude of subsequent GABAergic responses, a process termed ionic-plasticity [3, 10, 11]. Such activity-dependent [Cl-]i transients have been observed in various neurons [12–19]. Ionic plasticity plays an important role for physiological functions [20–22] as well as for pathophysiological processes [23, 24]. Theoretical assumptions and computational studies indicate that the amount and duration of [Cl-]i ionic plasticity directly depends on the relation between Cl− influx and the capacity of Cl− extrusion systems [3, 24–28]. In addition, the size and geometrical structure of the postsynaptic compartments critically affect the magnitude, duration and dimensions of [Cl-]i changes upon GABAergic activation [27, 29]. Further analyses also revealed that the membrane resistance, the kinetics of GABAergic responses and the stability of bicarbonate gradients affect the magnitude and duration of [Cl-]i changes [12, 27, 30].
Another factor that directly influences the amount of GABAA receptor-mediated Cl- fluxes is a coincident membrane depolarization [11, 27, 31]. Accordingly, recent in-vitro and in-silico studies demonstrated that coincident glutamatergic depolarization profoundly augments the GABAA receptor mediated Cl- fluxes [32, 33]. However, to our knowledge it has not been analyzed how the interdependency between glutamatergic and GABAergic inputs affects the magnitude and the spatiotemporal properties of activity dependent [Cl-]i changes.
In order to determine the influence of coincident glutamate stimulation on GABAA receptor-induced [Cl-]i transients, we utilized a computational model of [Cl-]i homeostasis in the NEURON environment [25, 30]. Using a simple ball-and-stick geometry, we were able to show that the conductance and decay kinetics of glutamatergic responses directly affect the size of GABAergic [Cl-]i changes, with a complex spatiotemporal dependency between glutamatergic and GABAergic inputs. Furthermore, we employed the model to uncover the contribution of coincident glutamatergic activity on the activity-dependent [Cl-]i transients during simulated giant-depolarizing potentials (GDPs) [17, 30]. GDPs represent correlated spontaneous network events crucial for the development of neuronal circuits [34–36]. These simulations demonstrate for the first time that coincident glutamatergic stimulation with realistic parameters substantially modifies the GABAA receptor-induced [Cl-]i changes.
In order to analyze how co-activation of depolarizing neurotransmitter receptors affects the [Cl-]i transients evoked by GABAA receptor activation, we used a previously established biophysical model of Cl- dynamics in the NEURON environment [17, 25]. The model allows for realistic simulations of activity-dependent transmembrane Cl- fluxes, intracellular Cl- diffusion and corresponding intracellular Cl- accumulation or depletion (see Methods). In a first step we computed the GABA-induced [Cl-]i changes in a ball-and-stick model with a single dendrite (Fig 1A), in order to enable a detailed mechanistic understanding of the interaction between a single or a small group of GABAA receptor-mediated and glutamate receptor-mediated synaptic inputs (Figs 1–6). Subsequently we utilized a model of a reconstructed CA3 pyramidal neuron [17, 30] stimulated by a large number of inputs to compute a more realistic estimation of how the GABAA receptor-mediated [Cl-]i transients in neurons are influenced by correlated co-activation of glutamate receptors (Figs 7–9).
![Effect of AMPA co-activation on GABAA receptor mediated [Cl-]i transients for a single GABAergic and glutamatergic input in the ball-and-stick neuronal model.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g001.jpg)
![Effect of gAMPA on the [Cl-]i transients induced by GABAA and AMPA receptor co-activation.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g002.jpg)
![Effect of τAMPA on the [Cl-]i transients induced by GABAA and AMPA receptor co-stimulation.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g003.jpg)
![Effect of the spatial relation between individual GABA and AMPA synapses on the activity-dependent [Cl-]i transients.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g004.jpg)
![Effect of the temporal relation between single dendritic GABA and AMPA synapses on the activity-dependent [Cl-]i transients.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g005.jpg)
![Effect of the relation between kinetics of individual dendritic GABA and AMPA synapses on the activity-dependent [Cl-]i transients at different temporal relations between both synapses.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g006.jpg)
![Effect of AMPA receptor co-stimulation on GABAA receptor-induced [Cl-]i transients in a morphologically realistic neuronal model stimulated with multiple spatially distributed synaptic inputs replicating GDP-like depolarizations (GDPs are experimentally observed giant depolarizing potentials in immature neurons).](/dataresources/articles/1219/32089/assets/pcbi.1008573.g007.jpg)
![Effect of the decay time of AMPA receptor-mediated currents (τAMPA) on activity-dependent [Cl-]i transients induced by multiple spatially distributed synaptic inputs replicating GDP-like depolarizations.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g008.jpg)
![Effect of spatial and temporal correlation between multiple dendritic GABA and AMPA synapse activation on the activity-dependent [Cl-]i transients.](/dataresources/articles/1219/32089/assets/pcbi.1008573.g009.jpg)
First we analyzed the effect of glutamate receptor co-activation on the GABAA 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 (Em ) 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) (gGABA = 0.789 nS, τGABA = 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 (DFGABA = Em—EGABA) caused a Cl--influx and thus a membrane hyperpolarization. At higher [Cl-]i0 of 25 mM the outwardly directed DFGABA 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 (gAMPA = 0.305 nS, τAMPA = 11 ms), imposed an additional depolarizing drive to the Em 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 gAMPA on the GABAA receptor -mediated [Cl-]i transient. As expected, these simulations showed that GABAA 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 gAMPA 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 gAMPA 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 ECl (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 gAMPA revealed that the GABAA receptor-mediated Cl- fluxes show a logarithmic dependency on gAMPA , 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 gAMPA (Fig 2E and 2F). When [Cl-]i was above 13 mM (corresponding to ECl above -60 mV) addition of gAMPA 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 gAMPA values representing 10–100 spontaneous postsynaptic events, are sufficient to substantially modulate GABAA receptor mediated Cl- fluxes.
Next we analyzed the influence of the kinetics of coincident AMPA receptor activation on the GABAA receptor-induced [Cl-]i transients. For this purpose, we modified the decay time constant of the AMPA synapse (τAMPA) using values between 1 and 100 ms. These simulations were performed under consideration of the experimentally determined values for GABAA receptor-mediated inputs either at gAMPA of 0.305 nS (i.e. the experimentally determined value [17]) or at gAMPA 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 τAMPA (Fig 3A), for τAMPA 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 τAMPA 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 τAMPA 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 (τNMDA = 500 ms) induced at high gNMDA [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 gNMDA, probably reflecting the Mg2+ block [40]. Thus at moderate gNMDA 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 gAMPA of 0.305 nS no AP was induced and thus no additional [Cl-]i influx was induced, at a moderate gAMPA of 3.05 nS only actively back-propagating APs augment the [Cl-]i changes (Fig 3G and 3H). At higher gAMPA 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).
To analyze how the spatial distance between the AMPA and the GABA synapse influences the GABAA 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 (gGABA = 0.789 nS, τGABA = 37 ms, gAMPA = 0.305 nS, τAMPA = 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 Em 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 Em 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 (ΔG[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 ΔG[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 GABAA 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 (gGABA = 0.789 nS, τGABA = 37 ms, gAMPA = 0.305 nS, τAMPA = 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 (ΔG[Cl-]i ) became maximal when GABA and AMPA stimulus were provided simultaneously (Fig 5C). Surprisingly, this AMPA effect on ΔG[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 τGABA (5 ms, 37, ms 50 ms) as well as τAMPA (5 ms, 11 ms, 37, ms 50 ms) and determined ΔG[Cl-]i (Fig 5E). These simulations revealed that, in accordance with the previous results, ΔG[Cl-]i increased at longer τAMPA for all three τGABA tested. While at a short τGABA of 5 ms no plateau phase was observed, such a plateau occurred for τGABA of 37 ms and 50 ms with short τAMPA values of 5 ms or 11 ms (Fig 5E). However, in contrast to our hypothesis that such a plateau phase occurred when τAMPA was shorter than τGABA, for a τGABA ≥ 37 ms and τAMPA ≥ 37 ms ΔG[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 τAMPA of 5 ms and 11 ms the peak ΔG[Cl-]i decreases when τGABA increased from 5 ms to 37 ms (Fig 5E).
To investigate these issues in detail, we next systematically varied τGABA between 5 and 50 ms using fixed τAMPA values of 5, 11, and 37 ms and determined ΔG[Cl-]i at different AMPA/GABA latencies. In these simulations we were able to identify a complex dependency between ΔG[Cl-]i and the relation between τGABA and τAMPA (Fig 6A–6C). For τAMPA of 5 and 11 ms the influence of the AMPA/GABA latency on ΔG[Cl-]i changed from a “peak”-like pattern to a “plateau”-like phase, in which the maximal ΔG[Cl-]i remained rather constant for a progressively longer latency interval between AMPA and GABA stimulation. This “plateau”-like phase occurred under conditions when τGABA is at more than about 3 times larger than τAMPA (Fig 6A and 6B). For τAMPA 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 τGABA of 11 ms, 18 ms and 47 ms for τAMPA of 5 ms, 11 ms and 37 ms, respectively (red plots in Fig 6A), reproducing the observation that prolonging τGABA can reduce ΔG[Cl-]i. From these results it can be concluded, first, that the effect of AMPA co-stimulation on ΔG[Cl-]i depends critically on the timing between both inputs, second, that ΔG[Cl-]i is maximal when τGABA is slightly larger than τAMPA, and, third, that a “plateau”-like interval of stable ΔG[Cl-]i occurred when τGABA is at least 3 times larger than τAMPA.
Next, we investigated how the time course of Em changes contributes to this complex dependency. For this purpose, we used identical stimulation parameters (gGABA = 0.789 nS, τGABA = 37 ms, gAMPA = 0.305 nS, τAMPA = 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 ΔG[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 ΔG[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 ΔG[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 gAMPA and τAMPA (S2 Fig). However, at physiologically relevant values for AMPA receptor-mediated inputs (gAMPA = 0.305 nS and τAMPA = 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).
To investigate in a more physiological setting how the interference between GABAA 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 GABAA 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 Em was determined in the soma.
In a first set of simulations, we investigated the impact of gAMPA 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 gAMPA 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 gAMPA enhanced this impact on activity-dependent [Cl-]i shift (Fig 7F). At gAMPA 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 Em induced by these conditions (Fig 7G). In summary, these results indicate that physiological levels of AMPA co-stimulation can significantly affect the GABAA 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 gAMPA 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 gAMPA 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 τAMPA 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 gAMPA of 0.305 nS and the experimentally determined values for the GABAergic synaptic inputs. Although this slight shift in τAMPA 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 GABAA 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 (ΔG[Cl-]i) was reduced from 1.02 ± 0.06 mM (n = 9 repetitions) at τAMPA = 11 ms to 0.48 ± 0.06 mM at τAMPA = 5 ms (Fig 8B). Similarly, at a [Cl-]i0 of 25 mM, ΔG[Cl-]i was diminished by shortening τAMPA from 11 ms (0.93 ± 0.1 mM) to 5 ms (0.43 ± 0.07 mM) (Fig 8B). In contrast, prolonging τAMPA 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 τAMPA can substantially influence the impact of AMPA co-activation on GABAA 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 (τNMDA = 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 gNMDA 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 gNMDA 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).
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 DFGABA 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 GABAA 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 ΔG[Cl-]i. With all GABA synapses in the proximal dendrites and the AMPA synapses located in the distal dendrites a co-stimulation induced a ΔG[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 ΔG[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 (gAMPA = 0.305 nS/τAMPA = 11 ms) and 100 GABA (gAMPA = 0.789 pS/τAMPA = 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 ΔG[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 ΔG[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), ΔG[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 ΔG[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 ΔG[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 ΔG[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.
Recent studies provide increasing evidence that GABAergic responses show an activity- and compartment-dependent behavior due to ionic plasticity in [Cl-]i [11, 24]. Here we used biophysical modeling to study how coincident glutamatergic inputs enhance the [Cl-]i changes induced by GABAergic activation. The main findings of this computational study can be summarized as follows: 1.) Glutamatergic co-stimulation had a direct effect on the GABAergic [Cl-]i changes, thereby enhancing Cl- influx at low [Cl-]i0 and attenuating or even reversing the Cl- efflux caused at high [Cl-]i0. 2.) Massive glutamatergic co-stimulation promotes Cl- influx at all [Cl-]i0, whereas physiological levels of glutamatergic co-stimulation mediate biphasic [Cl-]i changes at intermediate [Cl-]i levels typical for immature neurons. 3.) Keeping the decay kinetics of glutamatergic inputs below that of GABAergic inputs attenuated the [Cl-]i changes. 4.) The spatial and temporal correlation between glutamatergic and GABAergic inputs has a substantial influence on the [Cl-]i changes, with a surprisingly large temporal interval with correlation-independent [Cl-]i changes. 5.) In a morphologically realistic model with physiologically relevant synaptic activity that replicates GDPs, the conductance and kinetics of correlated glutamatergic activity have a substantial impact on the [Cl-]i changes. 6.) While the spatial correlation between distributed GABA and glutamatergic synapses has only a minor effect on activity-dependent [Cl-]i changes, their temporal correlation has strong effects. 7.) Besides AMPA receptors also NMDA receptors and dendritic action potentials can enhance the GABAergic [Cl-]i changes.
In the present model we emulated the membrane transport processes by two exponentially decaying functions [25, 29]. This model offers the advantage that it is computationally less demanding than other approaches, which model the [Cl-]i dynamics by a set of transmembrane ion transporters that influence [Cl-]i [27, 45]. On the other hand, our model does not consider additional effects that can be mediated by the influence of the glutamatergic Na+ and K+ fluxes on the NKCC1 and KCC2-based [Cl-]i homeostasis [46]. While these oppositely directed Na+ and K+ fluxes will lead to balanced effects in the NKCC1-based [Cl-]i homeostasis typical for immature neurons, it will attenuate the driving force for Cl- extrusion in the mature KCC2-based [Cl-]i homeostasis. Presumably, larger [Cl-]i increases can be expected when more realistic transport processes are considered for the [Cl-]i models. In addition, we used a purely diffusional model without considering electrodiffusion [26, 27], as it has been demonstrated recently that for Cl- ions the diffusional movement is considerably larger than the contribution of electric drift [46].
In this study we investigated the effect of co-activation of glutamatergic AMPA receptors on GABA receptor-dependent [Cl-]i changes over a wide range of [Cl-]i0 , which gave us the opportunity to evaluate the role of ionic plasticity for mature and developing nervous systems [3, 47]. In the mature brain GABAergic activity causes an increase in [Cl-]i [11, 16, 25, 48, 49], thereby decreasing the inhibitory action of the GABAergic system [13, 26, 27, 33]. Note in this respect that inhibition, as defined by a decrease in spike probability, is not necessarily related to a hyperpolarization, but that shunting inhibition considerably contributes to inhibition [1, 42, 50]. The present study demonstrates that glutamatergic co-stimulation enhances the GABAergic Cl--influx and thus enhances the activity-dependent [Cl-]i increase, as has recently been shown in-vitro [32] and in-silico [33]. As a consequence, the inhibitory effect of GABA may be even more impaired upon a co-activation of glutamate receptors [33]. The high basal [Cl-]i in immature neurons leads to GABAergic Cl--efflux and thus to a decrease in [Cl-]i upon GABAergic activation [18, 51]. This [Cl-]i decline can be associated with a loss of excitatory action and/or an enhancement of the shunting inhibitory effect of GABA receptors [21, 50, 52]. The present study demonstrates for the first time that in immature neurons a co-activation of GABA and glutamate receptors attenuates the activity-dependent [Cl-]i decrease, thereby stabilizing the depolarizing actions of GABA.
The absolute values of the additional [Cl-]i changes induced by AMPA co-stimulation in our ball-and-stick simulations are small, however it has to be taken into account that these changes represent the [Cl-]i changes induced at a single synapse with a single synaptic stimulus. Physiological levels of synaptic activity may thus cause significantly larger [Cl-]i changes, as has been shown in-vitro [32]. Even physiological levels of glutamatergic co-stimulation (0.305–3.05 nS, representing 1-10x spontaneous synaptic inputs) mediate in our model a reliable increase in Cl- influx at low [Cl-]i0, implicating that glutamatergic co-stimulation will enhance ionic plasticity in mature neurons. Thereby coincident glutamatergic activity provides an additional challenge for the [Cl-]i homeostasis in mature neurons and can substantially contribute to an activity-dependent decline in the inhibitory action of GABAergic synapses [33, 53, 54]. But even small Cl- changes can cause substantial functional alterations for neuronal computation, as has been recently demonstrated in-silico [45, 55]. Subtle changes in GABAergic membrane responses can directly interfere with the action potential threshold [56], but may also affect the temporal fidelity of inhibitory synaptic inputs, as with a weakening of GABAergic inhibition the temporal window for effective inhibition of excitatory inputs became smaller [52].
In addition, we were also able to demonstrate that several other depolarizing events can augment the GABAergic [Cl-]i changes. Co-activation of NMDA receptors augment the [Cl-]i changes with a steeper dependency on the membrane conductance as compared to AMPA receptors. This behavior is probably reflecting the Mg2+ block of NMDA receptors [40], leading to smaller inward currents as long as Em was below the threshold for the release of the Mg2+ block. Accordingly, at moderate conductances NMDA receptors mediate smaller effects on the [Cl-]i changes than AMPA receptors. But under physiological conditions, with AMPA-NMDA receptor co-activation, we assume that NMDA receptors will provide an additional drive for larger [Cl-]i changes. Accordingly, we observed in the reconstructed neurons that the simulated GDP-like activity generated larger [Cl-]i changes when the AMPA-receptors were replaced with NMDA-receptors, because under this condition the dendritic depolarizations were sufficient to effectively remove the Mg2+ block [40]. In addition, we were able to demonstrate that action potential firing, generated by a Hodgkin-Huxley-like mechanism, mediates an additional increase in the [Cl-]i changes. This suggests that under physiological conditions burst firing can substantially contribute to ionic plasticity. In contrast, the addition of a tonic GABAergic conductance had only a negligible effect of the activity-dependent [Cl-]i changes.
As mentioned before, the high [Cl-]i in immature neurons and the resulting GABAergic Cl--efflux results in a condition in which glutamatergic co-stimulation attenuates GABAergic [Cl-]i loss and thereby stabilizes depolarizing GABAergic actions. In addition, our computational model demonstrates that glutamatergic co-stimulation at physiologically relevant levels (gAMPA of 0.305 to 3.05 nS, corresponding to 1 to 10x of experimentally determined conductance for spontaneous AMPA receptor mediated inputs) causes biphasic [Cl-]i changes at [Cl-]i values between 15 and 35 mM (i.e. in the typical range determined in immature neurons [4, 57, 58]). These biphasic [Cl-]i changes rely on the fact that the activation of glutamatergic receptors transiently pushes the membrane potential above ECl and thus supports a Cl--influx during this interval. The biphasic [Cl-]i changes reduce the maximal [Cl-]i decline at the end of the GABAergic postsynaptic potential. By this process the activity-dependent [Cl-]i decline as well as the burden of glutamatergic co-stimulation on [Cl-]i homeostasis is reduced. It is tempting to speculate that this limitation of activity-dependent Cl--fluxes may be one reason for the inefficient Cl- -transport in the immature CNS [4, 22]. The functional implications of activity dependent [Cl-]i changes in immature neurons are harder to predict, as depolarizing GABAergic responses can mediate inhibitory [59, 60] as well as excitatory actions [61–63]. However, it can be estimated that an attenuation of the GABAergic [Cl-]i depletion will prevent/ameliorate a loss of GABAergic excitation and will prevent/ameliorate an increase in the inhibitory effect of depolarizing GABAergic responses. Thereby coincident glutamatergic activity, which is a typical feature of the correlated network events in developing neuronal systems [36, 37], can stabilize GABAergic functions.
Our simulation demonstrated that τAMPA has, as expected, a substantial influence on ΔG[Cl-]i , with faster AMPA events reducing the amount of ionic plasticity. Thus the shorter AMPA receptor-mediated responses at adult synapses [64, 65] can reduce the impact of AMPA/GABA co-activation on [Cl-]i homeostasis, in addition to making transmission more precise. In this respect, it is also tempting to speculate that conditions which permit the unblocking of NMDA-receptors (a subtype of glutamate receptors that is characterized by a rather long decay and that plays an essential role in learning, [66]), will also lead to more massive burden on [Cl-]i homeostasis. The resulting short-term decline in GABAergic inhibition will make neurons more prone to the induction of long-term potentiation.
In addition to this expected influence of τAMPA on ionic plasticity, our simulations revealed a complex dependency of ΔG[Cl-]i on τGABA and τAMPA. Interestingly the maximal ΔG[Cl-]i values were obtained when τGABA was slightly larger than τAMPA. An additional prolongation of τGABA even reduced ΔG[Cl-]i and thus diminished ionic plasticity. Intriguingly, such a prolongation of τGABA led to the appearance of a “plateau”-like phase, in which ΔG[Cl-]i is insensitive to the latency between GABA and AMPA inputs. The analysis of the Cl--fluxes in the phase diagram revealed that this “plateau”-like phase was due to the fact, that the Cl--fluxes converged over a wide range of AMPA/GABA latencies in the trajectory of [Cl-]i changes obtained by synchronous GABAergic and glutamatergic stimulation. For short τAMPA no “plateau”-like phase could be observed because under these conditions the time course of Em was mainly determined by the membrane time constant. This explanation was supported by our observation that an artificial increase in the membrane time constant by an augmented Cm caused a dissipation in the phase plane plot from two attractors towards more dissociated trajectories. For larger τAMPA of 37 and 50 ms such a “plateau”-line phase was not reached because at this longer time constant the decay of the voltage deflection is determined by both the inactivation of AMPA- and GABAA receptors and thus a gradual decrease in DFGABA occurred during the course of co-activation.
It has been suggested that under mature conditions ionic plasticity of [Cl-]i can act as a coincidence detector for simultaneous GABAergic and glutamatergic synaptic inputs [32]. Via such a coincidence detection GABAergic inhibition will be particularly attenuated by coincident glutamatergic inputs. The resulting [Cl-]i increase and the corresponding reduction in the inhibitory GABAergic capacity will subsequently promote the relay of excitation in neuronal networks. The intriguing finding of the present manuscript, that the effect of glutamatergic co-stimulation on the GABAergic [Cl-]i increase was stable for a considerable latency interval between GABAergic and glutamatergic inputs would allow the system to use a stable mechanism for adjusting the gating of excitatory information. In this respect, the striking asymmetry in ΔG[Cl-]i under physiological conditions of the decay times (τAMPA < τGABA) implies a spike-time dependency of ionic plasticity. While glutamatergic inputs preceding GABAergic inputs have only a small effect on ΔG[Cl-]i, a stable shift in ΔG[Cl-]i was induced when glutamatergic synapses were activated during the decay phase of GABAergic responses. A possible functional implication of this spike-time dependency would be that common feed-forward inhibitory circuits, in which synaptic inhibition always occurs after the glutamatergic inputs, will be only minimally affected by ionic plasticity, guaranteeing an efficient and stable feed-forward inhibition. Only in cases in which glutamatergic excitation was induced during ongoing GABAergic stimulation, a substantial ionic plasticity would operate. By this mechanism the inhibitory capacity of GABA will be reduced particularly in the postsynaptic neurons that receive frequent glutamatergic inputs, thereby facilitating particularly these pathways.
In summary, our results demonstrate that glutamatergic co-activation has a prominent time- and space-dependent effect on the amount of GABA-receptor mediated [Cl-]i changes. This ionic plasticity depends on the properties of glutamatergic inputs and their temporal correlation with the GABAergic inputs. These glutamatergic modulations of GABAergic ionic plasticity could possibly contribute to short-term memory and are likely to influence information processing in the developing and mature nervous system.
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 (Ra) of 34.5 Ωcm and a specific membrane capacitance (Cm) of 1 μFcm-2 were implemented. Cm was varied in two experiments to accelerate/decelerate the membrane time constant. A specific membrane conductance (gpas) 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.
GABAA 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 GABAA conductance (gGABA) into Cl− and HCO3− conductance. ECl and EHCO3 were calculated from the Nernst equation. The GABAA 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 GABAA 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 τNMDA of 500 ms, using similar conductance values for gNMDA 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 GABAA 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−]irest or [HCO3−]irest with a time constant τIon.
Cl− transport was in most experiments (if not otherwise noted) modeled as bimodal process, for [Cl-]i < [Cl-]irest τIon was set to 174 s to emulate an NKCC1-like Cl− transport mechanism. For [Cl-]i > [Cl-]irest τIon 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 Em and [Cl-]i values at the site of the GABAergic synapses. For the reconstructed CA3 neuron we used the somatic Em 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 EGABA 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-]iS) was subtracted from the resting [Cl-]i before the stimulus ([Cl-]iR). For biphasic responses both minimal and maximal [Cl-]iR 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 (ΔG[Cl-]i) was calculated from the Δ[Cl-]i values with/without AMPA co-stimulation as follows:
21 Sep 2020
Dear Dr. Kilb,
Thank you very much for submitting your manuscript "Coincident glutamatergic depolarizations enhance GABAA receptor-dependent Cl- influx in mature and suppress Cl- efflux in immature neurons" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.
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Reviewer #2: Review of manuscript: “Coincident glutamatergic depolarizations enhance GABAA receptor-dependent Cl- influx in mature and suppress Cl- efflux in immature neurons”
The authors perform a systematic exploration of how GABA and Glutamate activations at different time points and locations affect the intracellular Cl- concentration in a hippocampal neuron. This is relevant because the GABA-current depends on the transmembrane concentration gradient of Cl-, and changes in intracellular Cl- leads to a so-called “ionic (synaptic) plasticity” of GABA synapses.
The results section consists of a large number of simulations where different parameters (locations, timing, synaptic conductances, synaptic time constants, the membrane time constant, initial Cl- concentration) are varied, mostly one (or two) at the time. It is not easy to boil all that down to any general take-home message, since the effects will always depend on this or that, but I suppose that a general take-home message might not be expected for an intricate system like this.
The main finding seems solid, though, and is reflected in the manuscript title. When the initial Cl- concentration is low/intermediate (mature neurons), Glutamatergic depolarizations tend to enhance Cl- influx during GABAergic activation. This causes an “ionc plasticity” that decreases the inhibitory action of GABA. Differently, when the initial Cl- concentration is high (immature neurons), GABA activation has a depolarizing effect. Glutamatergic depolarizations then tend to suppress Cl- efflux during GABA-activation, thus preserving the ion reservoir (battery), and stabilizing the deploarizing role of GABA.
The modeling work seems solid, and the paper is well written. I think it is suited for publication in PLoS CB, but I have a some (relatively minor) suggestions to how it might be improved:
1: I get the feeling that the paper could be shortened and written in a way that puts more focus around the key findings. Some of the systematic parameter explorations are nice to include, but do not always lead to all that interesting results. Parts of it might be hidden away as supplementary material and simply summarized in the body text. I do not regard this as a criterion for publication though – just a suggestion that the authors could consider.
2: As Fig. 4 (not surprisingly) shows, the Glutamate-effect on Cl- during AMPA activation is solely due to the membrane depolarization that it evokes. The question is then: Is the EPSP from AMPA-activation generally the main source of membrane depolarization in the dendrites of CA3-neurons? What about back-propagating action potentials, dendritic Ca2+ spikes, or (local) secondary effect of AMPA activation mediated by locally present ion channels? Would these phenomena play an equally important role for ionic plasticity?
I think this issue should be addressed, at least as a passage in the discussion. Perhaps it is
beyond the scope of the current paper to actually explore such effects, but I guess it would be possible to do so, using some existing CA3-neuron model with active dendrites, such as the one by Traub et al. 1991 [Journal of Neurophysiology. 1991; 66(2):635–650], Pinsky & Rinzel 1994 [Journal of computational neuroscience. 1994; 1(1-2):39–60], Migliore et al. 1995 [Journal of neurophysiology, 73(3), 1157-1168.], Hemond et al. 2008 [Hippocampus, 18(4), 411-424], or Sætra et al. 2020 [PLoS Comput Biol 16(4): e1007661], the latter of which also includes ion concentration dynamics.
3. [Ca-]i is used in two different meanings - it denotes both the variable intracellular concentration (e.g., on the y-axis in Fig. 1C) and the (constant) initial condition (e.g. in the legend of Fig. 1b). You should make a distinction, and perhaps add an index “0” when the latter is meant.
4. Line 134 refers to the “passive [Ca-]i “. It sounds odd to call a concentration passive. Perhaps “baseline” is better?
5. Line 157 reads: “These simulations revealed that without co-stimulation GABAA receptor induced Cl- fluxes depended only on the initial [Cl-]i (Fig. 2a).” I don’t think anything is revealed here. The initial [Cl-]i is the only thing being varied, so it could not have depended on anything else?
6. Line 344: When you write “speeding up the kinetics of AMPA and GABA-receptor dependent voltage responses”, you make me think that you change the AMPA and GABA time constants, but here I think you have changed the membrane time constant, which is a more general “speeding up of things”. I think you should rephrase this to avoid confusion.
7. Line 364: You refer to your “full” model as “morphologically and biophysically realistic”, although it is a passive model with no ion channels, so it is unclear what kind of biophysical realism you make claim to. How is it more biophysically realistic than e.g., the ball-and-stick model – they differ solely in terms of morphology?
8. Line 636: “the dendrite was electrically and diffusionally detached from the soma”. This means that the model, in practice, did not have any soma, so you did not use a ball-and-stick model, but a stick model. If you only modelled the dendrite, it should be made clear also in the Results-section. Also, I am a bit surprised by this choice. Why cut off the soma? Wouldn´t you expect more realistic results with it being present?
9. In dilute solutions, the diffusion constants for Cl- and HCO3 are 2.03 μm2/ms and 1.18 μm2/ms, respectively (Table 2.1 in Grodzinsky F. Fields, Forces, and Flows in Biological Systems. Garland Science, Taylor & Francis Group, London & New York.; 2011). They could be smaller than that in the cytoplasm (due to obstacles), but I do not think it is possible that they become any larger. Hence, using a value of 2 μm2/ms for HCO3 (Line 675) is probably incorrect. This is not likely to have any severe impact on the simulation results, I imagine, but if it is not too much work, you might want to fix it.
Reviewer #3: This paper uses computational methods to explore how AMPA mediated glutamatergic input affects GABAAR mediated Cl- dynamics in neurons. The paper is well written, clear and logically developed. Although the results perhaps aren’t “earth shattering” or hugely unexpected over what one would predict conceptually, I found the work to be broadly satisfying and certainly publication worthy in this journal;. I found the modelling of GDPs in morphologically realistic immature CA3 neurons particularly good. I also enjoyed the attention payed to how glutamatergic conductances affect neurons with both low and high initial Cl- concentrations. Compared to some other computational models of Cl- dynamics the authors used a rather simple mechanism to describe Cl- extrusion/ intrusion by KCC2/NKCC1, this is not necessarily a problem and I can see how this would have aided the ease of computation in the more morphologically realistic neurons, but I think the authors do need to be a bit more upfront about some of the limitations of the model.
Major comments:
1) In the author’s model, they use a passive conductance (gpas) that does not include Cl- flux. This is despite the fact that tonic Cl- conductances (including tonic GABAAR) exist in neurons. As a result the authors by definition omit a relevant possible route whereby glutamatergic conductances can change [Cl-]I via affecting the driving force for Cl- flux across GABAARs. For example, in section 2.2 which investigates the influence of τAMPA on GABAA receptor induced [Cl-]i transients AMPA conductances with taus longer than the GABAA taus have no effect on the change in [Cl-]I this makes sense in their model as once the GABAAR conductance is over the AMPA driven change on the GABAAR driving force can no longer affect Cl- flux as there is nor GABAAR conductance. In most neurons though tonic GABAAR exists and hence the longer AMPA conductances should progressively change [Cl-]i (not as much as during the phasic GABAAR conductance, but still a bit!). The authors need to address this issue and either model tonic GABAAR, or justify why they did not. Ie Either they need to explicitly ref the fact that tonic GABAAR is small / minimal in immature CA3 neurons hence why they excluded tonic GABAAR conductances and acknowledge that tonic GABAAR in other cell types could affect their findings / make some predictions – ie what would happen in cells with high tonic GABA? Or they need to do some simulations where tonic Cl- flux is also modelled to explore how this variable affects glut-mediated Cl- changes via GABAARs. Ie what is the difference between cells with low tonic GABAA vs high tonic GABAA - for example some version of the simulations in section 2.2, but where tonic Cl- flux is present (there are various ways this could be modelled.) New simulations are not essential but I think attention to this would certainly strengthen the paper.
2) The second limitation of the model which the authors do not state explicitly is the fact that NMDA receptors are not modelled, just AMPA receptors. The authors need to either state why this was the case, or acknowledge this as a limitation? For example how does NMDA change the ball-and-stick model's results. I realise that τAMPA was changed up to 100 ms. But NMDA does have different kinetics, including reliance on Vm.
3) In addition active voltage-gated conductances also weren’t modelled. In the discussion a sentence should be added about how these are likely to add further complexity / another mechanism which could enhance the ability of glutamatergic input to depolarize the neuron and exacerbate Cl- influx via GABAARs.
Minor comments:
I think an important thing to think about is the colours used in the images, which may be difficult to interpret, especially for those with colour blindness. Here are some colour palettes (from seaborn) and their performance with different vision deficiencies: https://gist.github.com/mwaskom/b35f6ebc2d4b340b4f64a4e28e778486
I thought the final sentence of the discussion was too strong and not justified by the papers findings.
These glutamatergic modulations of GABAergic ionic plasticity can contribute to short-term memory and may profoundly influence information processing in the developing and mature nervous system.
Change to
These glutamatergic modulations of GABAergic ionic plasticity could possibly contribute to short-term memory and are likely to influence information processing in the developing and mature nervous system.
Typos:
Line 358: gAPMA -should be gAMPA
Line 381 (i.e. the experimentally determined number and conductance of GABAergic inputs) - should be AMPA inputs
Line 603: inhibition at will – remove “at”
Reviewer #4: I congratulate the authors for their manuscript.
The authors invetigate how coincident excitatory input shapes inhibition and more precisely how Cl- flux associated with gaba currents and subsequent change in chloride concentration is modulated by concurrent excitation. This phenomenon is explained by the fact that excitatory currents depolarize the membrane, which increases the Cl driving force and shapes Cl flux.
The most impressive part of the manuscript is the systematic manner in which the authors investigate the effect of synaptic events time constant, location and synchronisation on Cl- fluxes. They performed a large number of simulations and made extensive anaysis. In particular to my knowledge, the impact of Ampa time constant on Cl- accumulation has not been investigated before.
The topic is important as the results shed light on the determinants of inhibitions and may help better understand how to restore impaired inhibition in pathologies.
That said, the redaction and presentation could be improved at some places. I give here a list specific comments:
1)In the abstract, the author mention that they model immature CA3 neurons. As chloride homeostasis is strongly influenced by maturity, it would be nice if the authors motivated their choice to model an immature neuron.
2) At page 2, lines 43-44, I don't understand the mean of 'destabilization' in the following: 'enhancing the
destabilization of GABAergic inhibition in the mature nervous systems'
3) At the beginning of introduction, line 63. The expression 'Information processing between neurons' is strange. A single neuron processes information but information is transfered between neurons through synapses. There is a disctinction between processing and transfering information.
4) Introduction line 70
'with a high Cl- permeability and a partial HCO3 permeability'.
It is strange to contrast 'high' with 'partial' instead of 'high' with 'low' or 'full' with 'partial'
5) Line 71, what does 'gaba actions' mean? This is a strange wording. Can actions be replaced by a more specific term
6) Line 75, 'the Na+-dependent K+-2Cl--Symporter NKCC1...' it was my belief that the stochiometry of NKCC1 is rather Na+-K+-2Cl-
7) Page 6, lines 123-124. 'leads' and 'allowed' should have the same verb tense.
8) Line 131, DFGABA should be formally defined.
9) Figure 1 a. Here and elswhere, what is shown in the schematic next to GABA and AMPA? is it the time course of current, of conductance or something less? It would be nice to indicate it on the schematic. Scale bars could be added.
10) Figure 2 a and d. These panels are somewhat difficult to understand quickly because of the broken lines corresponding to biphasic responses. The double blue curves in a could look at first glance like a mistake. Maybe there is another way to display the results? Maybe making two different panels for Cl influx and efflux.
11) Comments 9 and 10 are also valid for figure 3.
12) Page 12, lines 235-237. Where is Em recorded? Is it always somatic Em? This could be specified.
13) Line 240-241, the definition of Delta_G[Cl-]i is difficult to read as an inline equation. Maybe it could be defined in text with a full sentence.
14) Page 13, lines 256-257. Is the decrease really exponential? If so, could you explain why? Did you try to fit an exponential and find the constant of the exponential and goodness of fit?
15) Line 263. Why did you choose the range -49ms-100ms?
16) Figure 5 a and b lower parts. I dont like when several curves are superimposed as it provides little information. Could you provide the difference between the curves so we can see how much they are really alike?
17) Page 16 line 320. What exactly do you mean by complex influence? Could you be more specific?
18) Page 17, line 340. What does voltage 'deflections' mean? Could you use a more specific word.
19)I find figure 7 impressive!!
20) In the legend of figure 7, a line break occurs in the middle of [Cl-]i, this should be corrected.
21) When plus-minus values are given, are they standard deviations? It is not clear what is the random part of the simulation. Is the position of the synapses random? Is the timing of synaptic events random? this could be better explained
22) Page 22, lines 455-456
'Therefore, we next located the GABA and AMPA synapses in different parts of the dendritic compartment.'
What does it exactly means? On the same dendritic branch but at different distances from the soma or on different dendritic branches?
23) Figure 9a, bar graph. Is there any difference between the red and blue bars or are they exactly the same? If they are not exactly the same, the authors should find a way to illustrate the difference. From what I understand, each black bar is repeated twice with pairs of black bars having the exact same value. This should be avoided.
24) Fig 9e. It is extremely hard to decipher this panel.
25) Page 23. Line 485-487. The authors should explain in more details what is random in their simulation and eventually what random distribution is used and why.
26) Page 26 line 523. I don't understand what 'stringent' means in this context. Maybe use a more technical and specific word.
27) Line 533, when the authors mention inhibition, do they mean hyperpolarization or decrease in spike rate? This could be specified.
28) Page 26 line 555. The authors mention coding. The notion of coding in this context is quite complex and subtle. The notion of coding could be exposed and explained a bit.
29) Page 27, line 561. The meaning of 'moderate' is not clear for me.
30) Methods line 646. Why not use GHK flux equations which is more accurate when ionic concentrations fluctuate.
31)Page 31, line 663. What exactly follows a Gaussian distribution? Is it the time separating two consecutive onsets of synaptic events?
32) Page 32. Line 690. The long superscript is hard to read. Maybe the equation could be reformated.
33) Page 33, Lines 697-698. 'abs' should not be in italic.
34) Is the formal definition of DFGABA given somewhere in the manuscript?
35) In the abbreviations, the PHCO3 is the relative permeability. Relative to what? This should be written explicitly
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30 Nov 2020
Dear Dr. Kilb,
We are pleased to inform you that your manuscript 'Coincident glutamatergic depolarizations enhance GABAA receptor-dependent Cl- influx in mature and suppress Cl- efflux in immature neurons' has been provisionally accepted for publication in PLOS Computational Biology.
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Reviewer's Responses to Questions
Comments to the Authors:
Please note here if the review is uploaded as an attachment.
Reviewer #1: Reproducibility report has been uploaded as an attachment.
Reviewer #2: The authors have responded well to my concerns. Congratulations on a nice paper!
Reviewer #3: I am satisfied with the extensive changes and additions performed by the authors in response to my major comments and am therefore in support of publication.
Reviewer #4: A new reading of this manuscript made me appreciate it even more. The technical aspect of the simulations is of great quality. The sheer amount of results and analysis is impressive. The authors have answered satisfactorily toall my comments.
Here are a few minor suggestions
1) Line 82: I think the word 'role' is missing 'Ionic plasticity plays an important for'
2) Line 89: affects should end without an 's'. 'the kinetics of GABAergic responses and the stability
89 of bicarbonate gradients affects the magnitude and'
3) In line 99, affects should also end without an s.
4) Line 208, a space is missing between the seccond 37 and ms. 'sensitive to τAMPA at values < 37 ms, while at values > 37ms'
5) Lines 678-670 not sure of the meaning of 'prevent/ameliorate'.
6) Line 799 maybe the word 'the' is missing between into and and soma 'implemented separately into soma and dendrite'
7) Equations 814, is e[Ion] defined in the text?
8) Line 816-817 the line break should not occur in the middle of [Cl-]i
9) Lines 833, 834, punctuation is missing after equations
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Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.
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Reviewer #2: Yes
Reviewer #3: None
Reviewer #4: Yes
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8 Jan 2021
PCOMPBIOL-D-20-01408R1
Coincident glutamatergic depolarizations enhance GABAA receptor-dependent Cl- influx in mature and suppress Cl- efflux in immature neurons
Dear Dr Kilb,
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