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

Abstract

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

Keywords: CA3; Cl−-homeostasis; Na+-K+-Cl−-Cotransporter, Isoform 1 (NKCC1); computational neuroscience; development; giant depolarizing potentials; hippocampus; ionic plasticity; mouse.

Figure 1

Passive membrane conductance (g_pas) influences GABA-induced [Cl⁻]_i transients. At low g_pas values, GABAergic currents induce strong depolarization, attenuating the driving force for Cl⁻ ions and thereby decreasing Cl⁻ fluxes. (a) The [Cl⁻]_i transients induced by a single GABAergic stimulation (g = 0.789 nS, τ = 37 ms, P_HCO3 = 0, [Cl⁻]_i = 30 mM) show a strong dependency on g_pas. Three typical traces are displayed as inset. (b) The GABA-induced membrane depolarization also shows a sigmoidal dependency on g_pas. (c) Effect of g_pas on E_m (black lines), E_Cl (red lines) and [Cl⁻]_i (blue lines) in an isolated dendrite using constant GABAergic currents (g_GABA = 0.1 µS). Note that at low g_pas values (0.1 nS/cm², solid lines) E_m approximates E_Cl, while at high g_pas (18 mS/cm², dashed lines) E_m stays below E_Cl. Accordingly [Cl⁻]_i shows only a small transient change at low g_pas, while a steady decline in [Cl⁻]_i occurs at high g_pas.

Figure 2

Passive membrane conductance (g_pas) influences GABA-induced [Cl⁻]_i transients in a reconstructed CA3 pyramidal neuron. Similar to the simulations in the isolated dendrite (Figure 1), GABAergic depolarization during a GDP approaches ECl at low g_pas values, thereby minimizing the driving force for Cl⁻ fluxes. (a) Immunofluorescence image of a biocytin labeled CA3 pyramidal neuron. (b) Reconstruction of this CA3 neuron as instrumented for NEURON simulation, with the colors representing the [Cl⁻]_i during an exemplary GDP. (c) Typical E_m trace of a GDP recorded in a real CA3 pyramidal neuron (black trace) and a simulated E_m trace of the reconstructed neuron upon stimulation with GDP-derived parameters (red trace). (d) Representative [Cl⁻]_i transients during a GDP displayed for 4 arbitrary dendrites. Note the asynchronous onset of individual [Cl⁻]_i transients and that [Cl⁻]_i transients are composed of synaptic Cl⁻ influx and diffusion from adjacent elements. (e) The average dendritic [Cl⁻]_i depends on the total conductance (g_tot) of the simulated cell. Please note that a cell that resembles the passive conductance of an immature hippocampal neurons (red symbol: R_Input = 901 MΩ) shows only a marginal [Cl⁻]_i decrease, while in cells equipped with a mature g_pas (cyan symbol: R_Input = 189 MΩ, green symbol: R_Input = 41 MΩ) larger GPD-induced [Cl⁻]_i transients occur. (f) Effect of g_tot on the peak depolarization during a GDP. Symbols are marked as indicated in (e). (g) Relationship between GABAergic driving force (DF_Cl) and GDP-induced [Cl⁻]_i transients. The crosses mark values determined experimentally in real CA3 pyramidal neurons. The colored cycles displays the [Cl⁻]_i changes computed for the three given R_Input values as indicated in (e). Note that for the immature R_Input only negligible GPD-induced [Cl⁻]_i changes are generated (a, b and c modified and used with permission from [45]).

Figure 3

Influence of the GABAergic conductance (g_GABA) on GABA-induced [Cl⁻]_i transients. (a) Time course of average [Cl⁻]_i in an isolated dendrite upon single synaptic stimulation using g_GABA between 3.945 nS and 39.45 nS. (b) Average [Cl⁻]_i in an isolated dendrite stimulated at a single synapse with g_GABA between 0.789 nS (red trace) and 78.9 nS (black trace). Note the non-linear dependency between [Cl⁻]_i changes and g_GABA. In an additional set of simulations, the total GABAergic current was varied by increasing the number (n_GABA) of evenly distributed single synapses (with g_GABA = 0.789 nS) from 1 to 100 (red trace). Note that under these conditions, smaller [Cl⁻]_i changes occur. (c) GDP-induced average [Cl⁻]_i and E_m changes in a reconstructed CA3 pyramidal neuron under control conditions (τ = 37 ms, P_HCO3 = 0, g_GABA = 0.789 nS, n_GABA = 302, blue trace) and upon enhanced stimulation by either increasing the conductance (g_GABA = 7.89 nS, n_GABA = 302, red trace) or the number of synapses (g_GABA = 0.789 nS, n_GABA = 3020, green trace). (d) Dependency between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained with different stimulation conditions.

Figure 4

Influence of the decay time constant of GABA receptors (τ_GABA) on GABA-induced [Cl⁻]_i transients. (a) Relationship between average [Cl⁻]_i and τ_GABA at g_GABA of 0.789 nS (black trace) or 15.78 nS (red trace) upon a single synaptic stimulation (P_HCO3 = 0, [Cl⁻]_i = 30 mM) in an isolated dendrite. (b) GDP-induced average [Cl⁻]_i and E_m changes (n_GABA = 302, g_GABA = 0.789 nS, P_HCO3 = 0) using τ_GABA of 37 ms (red trace) and 370 ms (blue trace) in a reconstructed CA3 pyramidal neuron. (c) Relationship between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained with different τ_GABA of 3.7 ms (green), 37 ms (blue) and 370 ms (red).

Figure 5

Influence of the relative HCO₃⁻ conductivity (P_HCO3) on GABA-induced membrane depolarization and [Cl⁻]_i transients in an isolated dendrite. Activity-dependent decline in [HCO₃⁻]_i reduces GABAergic depolarization and affects [Cl⁻]_i changes. (a) Time course of E_m and [Cl⁻]_i changes (Δ[Cl⁻]_i) upon a single synaptic stimulation (g_GABA = 7.89 nS, τ = 37 ms, P_HCO3 = 0.18, [HCO₃⁻]_i = 14.1 mM) at initial [Cl⁻]_i of 30 mM (dark blue), 40 mM (middle) and 50 mM (light blue). Note that at intermediate [Cl⁻]_i, a synaptic stimulus can induce biphasic [Cl⁻]_i responses. (b) Dependency between Δ[Cl⁻]_i and [Cl⁻]_i upon a single synaptic stimulation (g_GABA = 7.89 nS, τ = 37 ms, [HCO₃⁻]_i = 14.1 mM) for different P_HCO3. Note the biphasic responses for P_HCO3 of 0.18 (represented by the two blue lines) and that at higher P_HCO3 the [Cl⁻]_i fluxes are shifted towards influx even for high initial [Cl⁻]_i. (c) Dependency between [HCO₃⁻]_i and [Cl⁻]_i upon a single synaptic stimulation using a model with dynamic [HCO₃⁻]_i (g_GABA = 7.89 nS, τ = 37 ms, initial [Cl⁻]_i = 30 mM, initial [HCO₃⁻]_i = 14.1 mM). (d) Dependency between peak depolarization and [Cl⁻]_i upon a single synaptic stimulation (conditions as in c) at different P_HCO3. Note that the implementation of dynamic [HCO₃⁻]_i (plain lines) massively reduces peak depolarization as compared to conditions with static [HCO₃⁻]_i (shaded lines). (e) Dependency between [Cl⁻]_i changes and [Cl⁻]_i upon a single synaptic stimulation (conditions as in c). Dual lines with identical colors represent biphasic responses. Note the reduced [Cl⁻]_i changes with dynamic [HCO₃⁻]_i as compared to static [HCO₃⁻]_i conditions (shown in b) and that the [Cl⁻]_i at which Cl⁻ influx changes to Cl⁻ efflux was shifted to lower [Cl⁻]_i.

Figure 6

Influence of P_HCO3 on GABA-induced [Cl⁻]_i transients in a reconstructed CA3 pyramidal neuron. (a) Time course of E_m and average [Cl⁻]_i during a simulated GDP at different P_HCO3 (g_GABA = 0.789 nS, initial [Cl⁻]_i = 30 mM, [HCO₃⁻]_i = 14.1) using a model with a constant [HCO₃⁻]_i. (b) E_m, average [Cl⁻]_i and [HCO₃⁻]_i during a simulated GDP at different P_HCO3 (g_GABA = 0.789 nS, initial [Cl⁻]_i = 30 mM,) using a model that implements dynamic [HCO₃⁻]_i. Note that membrane depolarization and [Cl⁻]_i transients are diminished upon implementation of dynamic [HCO₃⁻]_i. (c) Maximal E_m during a GDP at different initial [Cl⁻]_i and P_HCO3 using static (shaded lines) or dynamic [HCO₃⁻]_i (plain lines). (d) GDP-induced [Cl⁻]_i changes at different initial [Cl⁻]_i and P_HCO3 using static (shaded lines) or dynamic [HCO₃⁻]_i (plain lines). (e) Dependency between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained with different P_HCO3 under dynamic [HCO₃⁻]_i conditions at P_HCO3 of 0 (red), 0.18 ms (blue) and 0.44 (green).

Figure 7

Influence of the stability of HCO₃⁻ gradients (via variations in τ_HCO3) on GABA-induced membrane depolarization and [Cl⁻]_i transients. (a) Dependency between [Cl⁻]_i changes (determined 1 s after stimulus) and τ_GABA at P_HCO3 of 0.18 and 0.44 upon a single synaptic stimulation (g_GABA = 7.89 nS, τ = 37 ms, P_HCO3 = 0.18, initial [Cl⁻]_i = 30 mM) in an isolated dendrite. Note that at τ_HCO3 of ca. 1 s the maximal [Cl⁻]_i changes are reached. (b) Spatial profile of maximal [HCO₃⁻]_i changes upon the single synaptic stimulation (parameters as in a) at different τ_HCO3. Note that τ_HCO3 influences the spatial profile of [HCO₃⁻]_i, although the peak [HCO₃⁻]_i values are mainly comparable. (c) Dependency between maximal GDP-induced [Cl⁻]_i changes (g_GABA = 0.789 nS, τ = 37 ms, P_HCO3 = 0.18, n_GABA = 395, initial [Cl⁻]_i = 30 mM) and initial [Cl⁻]_i for different τ_HCO3 in the reconstructed CA3 pyramidal neuron. Note that the influence of τ_HCO3 on [HCO₃⁻]_i changes is largest at low [Cl⁻]_i, but that overall τ_HCO3 has only a minimal impact on the [Cl⁻]_i changes. (d) Dependency between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained with different τ_HCO3 (shadings as in c).

Figure 8

Influence of pH on GABA-induced membrane depolarization and [Cl⁻]_i transients. (a) Time course of E_m and [Cl⁻]_i upon a single synaptic stimulation (g_GABA = 7.89 nS, τ = 37 ms, P_HCO3 = 0.18, initial [Cl⁻]_i = 30 mM) in an isolated dendrite at different pH. Note the effect of pH on the depolarizations and that the biphasic [Cl⁻]_i at pH 7.2 was transformed into Cl⁻ efflux at pH 7.0 and to Cl⁻ influx at pH 7.4. (b) Dependency between GDP-induced [Cl⁻]_i changes and initial [Cl⁻]_i for different pH. For each pH the two lines represent maximal and minimal [Cl⁻]_i changes. Note that pH 7.0 shifts [Cl⁻]_i changes towards Cl⁻ efflux, whereas pH 7.4 shifts [Cl⁻]_i changes towards Cl⁻ influx. (c) Time course of GDP-induced depolarization and [Cl⁻]_i changes in the reconstructed CA3 pyramidal neuron (g_GABA = 0.789 nS, τ = 37 ms, P_HCO3 = 0.18, n_GABA = 395, initial [Cl⁻]_i = 30 mM) at different pH (color code as in a). Note that the GDP-induced [Cl⁻]_i changes are diminished at pH 7.0 and enhanced at pH 7.4. (d) Dependency between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained at different pH. Note that at pH 7.0 the GDP-induced [Cl⁻]_i increase was diminished, while the [Cl⁻]_i decrease was slightly enhanced.

Figure 9

Influence of Cl⁻ diffusion and the kinetics of transmembrane Cl⁻ transport on GABA-induced [Cl⁻]_i transients. (a) Dependency between τ_Cl and [Cl⁻]_i determined in the middle between 2 simultaneously stimulated synapses (parameters as in a) located 10 µM, 30 µM, 100 µM and 100 µm from the node of [Cl⁻]_i recording. The inset represents a schematic illustration of the spatial arrangement. (b) Analysis of temporal summation of activity-dependent [Cl⁻]_i transients upon 5 consecutive GABA stimuli (parameters as in a) provided at frequencies of 0.3 Hz, 1 Hz, 3 Hz and 10 Hz in the dendrite + soma arrangement. The inset illustrates typical [Cl⁻]_i traces obtained at 3 Hz with τ_Cl of 41 ms and 4.1 s. The ratio in the [Cl⁻]_i between the first and fifth stimulus (rel. [Cl⁻]_i^5/1) shows a sigmoidal dependency on τ_Cl. Note that with higher stimulus frequencies faster τ_Cl are required to prevent summation of [Cl⁻]_i transients. (c) Dependency between maximal GDP-induced [Cl⁻]_i changes (g_GABA = 0.789 nS, τ_GABA = 37 ms, P_HCO3 = 0.18, τ_HCO3 = 1 s, n_GABA = 395) and initial [Cl⁻]_i for different τ_Cl in the reconstructed CA3 neuron (d) Dependency between DF_Cl and the GDP-induced [Cl⁻]_i transients obtained with different τ_Cl.