Abstract

For sensory cortices to respond reliably to feature stimuli, the balancing of neuronal excitation and inhibition is crucial. A typical example might be the balancing of phasic excitation within cell assemblies and phasic inhibition between cell assemblies. The former controls the gain of and the latter the tuning of neuronal responses. A change in ambient GABA concentration might affect the dynamic behavior of neurons in a tonic manner. For instance, an increase in ambient GABA concentration enhances the activation of extrasynaptic receptors, augments an inhibitory current, and thus inhibits neurons. When a decrease in ambient GABA concentration occurs, the tonic inhibitory current is reduced, and thus the neurons are relatively excited. We simulated a neural network model in order to examine whether and how such a tonic excitatory-inhibitory mechanism could work for sensory information processing. The network consists of cell assemblies. Each cell assembly, comprising principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia), responds to one particular feature stimulus. GABA transporters, embedded in glial plasma membranes, regulate ambient GABA levels. Hypothetical neuron-glia signaling via inhibitory (Ia-to-glia) and excitatory (P-to-glia) synaptic contacts was assumed. The former let transporters import (remove) GABA from the extracellular space and excited stimulus-relevant P cells. The latter let them export GABA into the extracellular space and inhibited stimulus-irrelevant P cells. The main finding was that the glial membrane transporter gave a combinatorial excitatory-inhibitory effect on P cells in a tonic manner, thereby improving the gain and tuning of neuronal responses. Interestingly, it worked cooperatively with the conventional, phasic excitatory-inhibitory mechanism. We suggest that the GABAergic gliotransmission mechanism may provide balanced intracortical excitation and inhibition so that the best perceptual performance of the cortex can be achieved.

1.  Introduction

Sensory cortices are known to form cell assemblies called feature columns in order to detect specific feature stimuli such as the orientation of a bar in vision, the frequency of a sound in audition, and the sensation of a body surface in somatosensation (for review, see Mountcastle, 1997). For feature columns to respond reliably to sensory stimuli, the balancing of neuronal excitation and inhibition is essential (Moore, Nelson, & Sur, 1999; Zhang, Tan, Schreiner, & Merzenich, 2003; Wehr & Zador, 2003; Tan, Zhang, Merzenich, & Schreiner, 2004; Marino et al., 2005; Okun & Lampl, 2008). A typical example might be the balancing of phasic excitation within cell assemblies and phasic inhibition between cell assemblies. The former controls the gain of and the latter the tuning of neuronal responses.

Gamma-aminobutyric acid (GABA) is the major inhibitory neurotransmitter and mediates inhibition in a phasic manner by activating intrasynaptic GABA receptors, that is, GABA receptors in the synaptic cleft. So-called tonic inhibition occurs when extrasynaptic GABA activates receptors located on membranes outside synapses (Semyanov, Walker, Kullmann, & Silver, 2004; Farrant & Nusser, 2005; Ortinski et al., 2006). GABA molecules in extracellular space and GABA receptors on extrasynaptic membrane regions are referred to as ambient GABA and extrasynaptic GABA receptor, respectively. Extrasynaptic GABAa receptors have been found in the cerebellum (Somogyi, Takagi, Richards, & Mohler, 1989; Nusser, Roberts, Baude, Richards, & Somogyi, 1995; Brickley, Cull-Candy, & Farrant, 1996; Soltesz & Nusser, 2001) and in the cortex (Drasbek & Jensen, 2006; Scimemi et al., 2006).

In the brain, intrasynaptic GABA rises to a millimolar level triggered by a presynaptic action potential (Maconochie, Zempel, & Steinbach, 1994; Jones & Westbrook, 1995). In contrast, ambient GABA changes within the submicromolar-micromolar range (Lerma, Herranz, Herreras, Abraira, & Martin, 1986; Tossman, Jonsson, & Ungerstedt, 1986; Scimemi, Semyanov, Sperk, Kullmann, & Walker, 2005). The lower ambient GABA level is sufficient to activate extrasynaptic but not intrasynaptic GABAa receptors. GABAa receptors containing the δ subunit have been found in extrasynaptic membrane regions (Somogyi et al., 1989; Nusser et al., 1995; Brickley et al., 1996; Soltesz & Nusser, 2001), which are known to have high affinity for GABA (Saxena & Macdonald, 1996; Brown, Kerby, Bonnert, Whiting, & Wafford, 2002) and little desensitization to continuous activation by GABA (Bianchi, Haas, & Macdonald, 2001, 2002). This leads to tonic inhibition of neurons even at lower ambient GABA levels.

As to the maintenance of ambient GABA levels, Richerson and colleagues (Wu, Wang, & Richerson, 2001; Richerson & Wu, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) made an interesting suggestion. A GABA transporter such as GAT-1 is crucial not only for importing (removing) GABA from but also for exporting it into the extracellular space. Transporters, embedded in membranes of glial cells (and interneurons), can regulate ambient GABA levels. They are near equilibrium under normal physiological conditions and will reverse with a small increase or decrease in membrane potential.

A change in ambient GABA concentration might affect the dynamic behavior of neurons in a tonic manner. For instance, an increase in ambient GABA concentration enhances the activation of extrasynaptic receptors, augments an inhibitory current, and thus inhibits neurons. When a decrease in ambient GABA concentration occurs, the tonic inhibitory current is reduced, and thus the neurons are relatively excited. The purpose of this study is to examine whether and how such a tonic excitatory-inhibitory mechanism could work for perceptual information processing. We simulate a neural network model that consists of cell assemblies. Each cell assembly, comprising principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia), responds to one particular feature stimulus.

To regulate ambient GABA levels, we construct a functional model of a glial plasma membrane transporter. Concerning neuron to glia signaling, a variety of types of neuron-glia circuits have been evidenced, including chemical (glutamate, GABA) synapses between presynaptic neurons and postsynaptic glial cells (for review, see Bezzi & Volterra, 2001; Fields & Stevens-Graham, 2002; Overstreet, 2005). We assume neuron-glia signaling via inhibitory Ia-to-glia and excitatory P-to-glia synaptic contacts. The former hyperpolarizes glial cells, thereby letting their transporters import (remove) GABA from the extracellular space and thus exciting P cells. In contrast, the latter depolarizes the glial cells, thereby letting their transporters export GABA into the extracellular space and thus inhibiting the P cells. Namely, the glial membrane transporter gives a combinatorial excitatory-inhibitory effect on P cells in a tonic manner. During exposure to a feature stimulus, neuronal activities (membrane potentials and spikes) are recorded. We examine whether and how the GABAergic gliotransmission mechanism works for balancing neuronal excitation and inhibition and investigate how it contributes to perceptual information processing.

2.  Neural Network Model

As shown in Figure 1, cell assemblies consist of principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia). Each cell assembly () comprises 20 cell units (P, Ia, Ib, glia). Each P cell receives excitatory inputs from other P cells and inhibitory inputs from Ib cells, which receive excitatory inputs from P cells belonging to other cell assemblies. Each Ia cell receives an excitatory input from its accompanying P cell and synaptically connects to a glial cell. P cells synaptically connect to glial cells belonging to other cell assemblies. P cells receive an excitatory current as a sensory input when stimulated. A conductance-based, integrate-and-fire neuron model (Hoshino, 2007a, 2007b, 2008) is employed.

Figure 1:

The neural network model. Multiple cell assemblies constitute the network. Each cell assembly (0 ≤ n ≤ 7) comprises 20 cell units: one principal cell (P), two GABAergic interneurons (Ia, Ib), and one glial cell (glia). The open and filled triangles denote excitatory and inhibitory synapses, respectively. Constant excitatory current is applied to P cells as sensory input (see equations A.1 and A.5 in appendix  A). Inset: A schematic illustration of GABA transport (Hoshino, 2012). P and Ia cells excite and inhibit a glial cell, respectively. Glial plasma membrane transporters import (remove) GABA from or export it into the extracellular space, depending on the membrane potential. Ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

Figure 1:

The neural network model. Multiple cell assemblies constitute the network. Each cell assembly (0 ≤ n ≤ 7) comprises 20 cell units: one principal cell (P), two GABAergic interneurons (Ia, Ib), and one glial cell (glia). The open and filled triangles denote excitatory and inhibitory synapses, respectively. Constant excitatory current is applied to P cells as sensory input (see equations A.1 and A.5 in appendix  A). Inset: A schematic illustration of GABA transport (Hoshino, 2012). P and Ia cells excite and inhibit a glial cell, respectively. Glial plasma membrane transporters import (remove) GABA from or export it into the extracellular space, depending on the membrane potential. Ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

As schematically illustrated in Figure 1 (inset), a gliotransmission-mediated ambient GABA regulatory system is constructed based on our previous study (Hoshino, 2012). P and Ia cells synaptically excite and inhibit a glial cell, respectively. Transporters are distributed in the glial cell membrane, which import (remove) GABA from or export it into the extracellular space, depending on the membrane potential of the glial cell. Ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell. The neural network model is described in appendixes  A to  C, whose parameters and their values are listed in Table 1.

Table 1:
List of Parameters and Their Values.
Description Parameter Value 
Membrane capacitance of type Y (Y = P, Ia, Ib, glia) cell cYm  
Membrane conductance gYm  
Resting potential uYrest  
Maximal conductance for type Z (Z = AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev=0 mV, uGABArev=−80 mV 
Number of cell units within cell assemblies N 20 
Number of cell assemblies M 
Synaptic weight (strength) from j to ith P cell wP,Pij 
Synaptic weight from jth Ib to ith P cell wP,Ibij 1.6 
Synaptic weight from ith P to Ia cell wIa,Pi 30 
Synaptic weight from ith P to Ib cell between different cell assemblies  1.6 
Synaptic weight from ith P to glial cell  
Synaptic weight from ith Ia to glial cell wGl,Iai 
Amount of extrasynaptic GABAa receptors on P cell   
Input current  150 pA 
Broadness of input  2.6 
Channel opening rate for type Z (Z = AMPA, GABA) receptor   
Channel closing rate   
Steepness of sigmoid function for type Y (Y = P, Ia, Ib) cell   
Threshold of sigmoid function   
Decay constant for ambient GABA concentration  0.2 
Basal ambient GABA concentration [GABA]0ext  
Maximal ambient GABA concentration GABAmax  
Minimal ambient GABA concentration GABAmin  
GABA transfer coefficient TGl  
Reversal potential of GABA transporter uGlrev −70 mV 
Description Parameter Value 
Membrane capacitance of type Y (Y = P, Ia, Ib, glia) cell cYm  
Membrane conductance gYm  
Resting potential uYrest  
Maximal conductance for type Z (Z = AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev=0 mV, uGABArev=−80 mV 
Number of cell units within cell assemblies N 20 
Number of cell assemblies M 
Synaptic weight (strength) from j to ith P cell wP,Pij 
Synaptic weight from jth Ib to ith P cell wP,Ibij 1.6 
Synaptic weight from ith P to Ia cell wIa,Pi 30 
Synaptic weight from ith P to Ib cell between different cell assemblies  1.6 
Synaptic weight from ith P to glial cell  
Synaptic weight from ith Ia to glial cell wGl,Iai 
Amount of extrasynaptic GABAa receptors on P cell   
Input current  150 pA 
Broadness of input  2.6 
Channel opening rate for type Z (Z = AMPA, GABA) receptor   
Channel closing rate   
Steepness of sigmoid function for type Y (Y = P, Ia, Ib) cell   
Threshold of sigmoid function   
Decay constant for ambient GABA concentration  0.2 
Basal ambient GABA concentration [GABA]0ext  
Maximal ambient GABA concentration GABAmax  
Minimal ambient GABA concentration GABAmin  
GABA transfer coefficient TGl  
Reversal potential of GABA transporter uGlrev −70 mV 

As will be shown in later sections, the hypothetical P-glia and Ia-glia circuits play key roles in regulating ambient GABA concentration. The former has a role in increasing a level of ambient GABA around stimulus-irrelevant P cells, and the latter has a role in decreasing a level of ambient GABA around stimulus-relevant P cells. These circuits achieve combinatorial regulation of local ambient GABA levels, by which the neuronal gain and tuning to sensory input can be improved. To the best of our knowledge, these specific circuits between different (P, Ia) cells and glia have not been observed. They were assumed based on studies (Bezzi & Volterra, 2001; Fields & Stevens-Graham, 2002; Overstreet, 2005) that indicated a variety of glutamatergic and GABAergic neuron-glia projections.

3.  Results

3.1.  Dynamic Properties of Neuron and Ambient GABA Concentration.

Figure 2 shows fundamental dynamic properties of principal (P) cells (see Figure 2A), ambient GABA concentrations around them (see Figure 2B), and glial cells (see Figure 2C) belonging to respective cell assemblies (). When the network is presented with a feature stimulus (f3), P cells relevant to the stimulus are activated (see n = 3 in Figure 2A). The ambient GABA concentration around P cells relevant to the stimulus is reduced (see the trace marked by n = 3 in Figure 2B). This leads to a decrease in tonic inhibitory current in the stimulus-relevant P cells and thus to their excitation. In contrast, ambient GABA concentrations around P cells irrelevant to the stimulus are increased (see the traces marked by ), which leads to an increase in tonic inhibitory current and thus to their inhibition. These results indicate that the GABAergic gliotransmission mechanism balances intracortical excitation and inhibition in a tonic manner, thereby improving the selective responsiveness of the network to the applied feature stimulus.

Figure 2:

Responses to a feature stimulus. (A) Raster plots of action potentials evoked in principal (P) cells. (B) Ambient GABA concentrations. (C) Glial nembrane potentials. Membrane potentials recorded from stimulus-relevant (n = 3) and stimulus-irrelevant (n = 4) glial cells are shown in an enlarged scale (see the bottom two traces). uGlrev is the reversal potential of the GABA transporter (see equation C.1 in appendix  C).

Figure 2:

Responses to a feature stimulus. (A) Raster plots of action potentials evoked in principal (P) cells. (B) Ambient GABA concentrations. (C) Glial nembrane potentials. Membrane potentials recorded from stimulus-relevant (n = 3) and stimulus-irrelevant (n = 4) glial cells are shown in an enlarged scale (see the bottom two traces). uGlrev is the reversal potential of the GABA transporter (see equation C.1 in appendix  C).

Figure 2C indicates that stimulus-relevant glial cells are hyperpolarized (see the enlarged trace for n = 3), which let their transporters import GABA and thus leads to the decrease in ambient GABA concentration (see the trace marked by n = 3 in Figure 2B), whereas stimulus-irrelevant glial cells are depolarized (e.g., see the enlarged trace for n = 4), which let their transporters export GABA and thus leads to the increase in ambient GABA concentration (see the traces marked by in Figure 2B). Note that uGlrev is the reversal potential of the GABA transporter (see equation C.1 in appendix  C).

3.2.  Improvement of Neuronal Gain Function by GABAergic Gliotransmission.

In this section, we show how the GABAergic gliotransmission mechanism contributes to the improvement of neuronal gain function. Figure 3 presents spikes evoked in P cells (see Figure 3A), ambient GABA concentrations (see Figure 3B), and membrane potentials recorded from glial cells (see Figure 3C) belonging to respective cell assemblies, where the Ia-to-glia projection was cut. Due to the impaired Ia-to-glia projection, stimulus-relevant glial cells are not hyperpolarized, and thus the ambient GABA concentration is not to be reduced (see the solid trace marked by n = 3). This results in a failure to elevate stimulus-related P cell activity (compare Figures 2A and 3A), which is quantitatively shown in Figure 3D. wGl,Iai = 0 corresponds to the impairment of Ia-to-glia projection (see equation A.12 in appendix  A). We found that increasing the Ia-to-glia connection weight elevates the stimulus-evoked neuronal activity. These results indicate that the GABAergic gliotransmission-mediated tonic excitation enhances the neuronal responsiveness.

Figure 3:

Responses to a feature stimulus without GABAergic gliotransmission-mediated tonic excitation via Ia-to-glia signaling. (A) Raster plots of action potentials evoked in principal (P) cells. (B) Ambient GABA concentrations. (C) Membrane potentials recorded from glial cells. (D) Stimulus-evoked activity (firing rate) as a function of Ia-to-glia connection weight.

Figure 3:

Responses to a feature stimulus without GABAergic gliotransmission-mediated tonic excitation via Ia-to-glia signaling. (A) Raster plots of action potentials evoked in principal (P) cells. (B) Ambient GABA concentrations. (C) Membrane potentials recorded from glial cells. (D) Stimulus-evoked activity (firing rate) as a function of Ia-to-glia connection weight.

As shown in Figure 4A (top), phasic excitation by P cells (see wP,Pij in equation A.2) per se (i.e., even without Ia-to-glia signaling) can improve the neuronal gain function. Beyond the maximal connection weight (wP,Pij>6, see the circles), P cells continued firing even after the termination of the stimulus (not shown). We refer to this as “invalid.” Figure 4A (bottom) shows the dependence of the gain function on Ia-to-glia connection weight. Interestingly, the gain function achieved at the maximal connection weight wP,Pij=6 (see the open circles) could be improved by the GABAergic gliotransmission-mediated tonic excitatory mechanism (bottom; see the filled circles), being able to respond to weaker stimuli.

Figure 4:

Improvement of neuronal gain function by GABAergic gliotrans-mission-mediated tonic excitation. (Top) Stimulus-evoked activity (firing rate) as a function of input intensity (excitatory current) without GABAergic gliotransmission-mediated tonic excitation via Ia-to-glia signaling. The weight of recurrent connections between P cells (wP,Pij) was strengthened from 0 (inverted triangles) to 4 (diamonds), 5 (squares), 5.5 (triangles), or 6 (circles). (Bottom) Stimulus-evoked activity as a function of input intensity, where wP,Pij=6. The Ia-to-glia connection weight was strengthened from 0 (open circles) to 1 (triangles), 2 (squares), 3 (diamonds), or 5 (filled circles). Note that the top and bottom open circles are identical. (B) Cooperation of GABAergic gliotransmission-mediated tonic (nonsynaptic) excitation and conventional phasic (synaptic) excitation in order to achieve the best neuronal gain function. (Left) Neuronal responses. wGl,Iai and wP,Pij are Ia-to-glia and P-to-P connection weights, respectively. Beyond the maximal recurrent connection weight (wP,Pi,j>6), P cells continued firing even after the termination of the stimulus (not shown). We refer to this as invalid. (Right) Minimal input currents at which a population response to the stimulus can take place in P cells.

Figure 4:

Improvement of neuronal gain function by GABAergic gliotrans-mission-mediated tonic excitation. (Top) Stimulus-evoked activity (firing rate) as a function of input intensity (excitatory current) without GABAergic gliotransmission-mediated tonic excitation via Ia-to-glia signaling. The weight of recurrent connections between P cells (wP,Pij) was strengthened from 0 (inverted triangles) to 4 (diamonds), 5 (squares), 5.5 (triangles), or 6 (circles). (Bottom) Stimulus-evoked activity as a function of input intensity, where wP,Pij=6. The Ia-to-glia connection weight was strengthened from 0 (open circles) to 1 (triangles), 2 (squares), 3 (diamonds), or 5 (filled circles). Note that the top and bottom open circles are identical. (B) Cooperation of GABAergic gliotransmission-mediated tonic (nonsynaptic) excitation and conventional phasic (synaptic) excitation in order to achieve the best neuronal gain function. (Left) Neuronal responses. wGl,Iai and wP,Pij are Ia-to-glia and P-to-P connection weights, respectively. Beyond the maximal recurrent connection weight (wP,Pi,j>6), P cells continued firing even after the termination of the stimulus (not shown). We refer to this as invalid. (Right) Minimal input currents at which a population response to the stimulus can take place in P cells.

Figure 4B shows how the tonic (nonsynaptic) and phasic (synaptic) excitatory mechanisms cooperatively work. As addressed above, the network operates in the valid but not invalid condition (left). Figure 4B (right) presents minimal input currents at which a population response to the stimulus can take place in P cells. We found that the GABAergic gliotransmission-mediated tonic excitatory mechanism enables the network to respond to weaker sensory stimuli. These results indicate that the neuronal gain function ensured by the conventional phasic excitatory mechanism can be improved by the GABAergic gliotransmission-mediated tonic excitatory mechanism.

3.3.  Improvement of Sensory Tuning by GABAergic Gliotransmission.

In this section, we show how the GABAergic gliotransmission mechanism contributes to the improvement of sensory tuning performance. Figure 5 (top) presents spikes evoked in P cells, where the P-to-glia projection was cut. Stimulus-irrelevant P cells tend to generate trains of spikes (see n = 2 and n = 4), which worsens the sensory tuning. Figure 5 (middle) presents phasic (Ib-to-P) inhibitory current in a stimulus-irrelevant (n = 5) P cell. The frequent, transient reduction in inhibitory current during the stimulation period (see the enlarged trace) would give the stimulus-irrelevant (especially the neighboring n = 2 and n = 4) P cells a chance of activation because they receive a small but significant amount of excitatory current arising from the graded sensory input (see in equation A.5 and Table 1). Figure 5 (bottom) evidences no GABAergic gliotransmission-mediated tonic inhibitory current due to the deletion of P-to-glia projection.

Figure 5:

Relevance of phasic inhibition in neuronal responsiveness. (Top) Raster plots of action potentials evoked in principal (P) cells without GABAergic gliotransmission-mediated tonic inhibition via P-to-glia signaling. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell.

Figure 5:

Relevance of phasic inhibition in neuronal responsiveness. (Top) Raster plots of action potentials evoked in principal (P) cells without GABAergic gliotransmission-mediated tonic inhibition via P-to-glia signaling. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell.

To see how the GABAergic gliotransmission-mediated tonic inhibitory mechanism contributes to the sensory tuning, we cut the Ib-to-P projection. Namely, the neuronal suppression is processed solely by tonic inhibition. As shown in Figure 6 (top), the stimulus-irrelevant P cells (see n = 2, 4, and 5) transiently respond at the onset of sensory input. It takes 1 second or so for the network to tune to the stimulus, when these stimulus-irrelevant P cells cease firing (see the dashed line). Figure 6 (middle) evidences no phasic (Ib-to-P) inhibitory current due to the deletion of Ib-to-P projection. As shown in Figure 6 (bottom), the GABAergic gliotransmission-mediated inhibitory current is gradually increased when stimulated. This slow increase in inhibitory current would give the stimulus-irrelevant P cells a chance to activate at the stimulus onset (top: see n = 2, 4, and 5). The stimulus-irrelevant neuronal activities disappear when the tonic inhibitory current reaches a certain level and the network has finally tuned to the stimulus (top: see the dashed line).

Figure 6:

Relevance of GABAergic gliotransmission-mediated tonic inhibition in neuronal responsiveness. (Top) Raster plots of action potentials evoked in principal (P) cells without phasic (Ib-to-P) inhibition. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell.

Figure 6:

Relevance of GABAergic gliotransmission-mediated tonic inhibition in neuronal responsiveness. (Top) Raster plots of action potentials evoked in principal (P) cells without phasic (Ib-to-P) inhibition. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell.

Figure 7 shows how the tonic (nonsynaptic) and phasic (synaptic) inhibitory mechanisms cooperatively work in order to achieve the best sensory tuning performance (top). The rapid inhibition due to a sudden increase in phasic inhibitory current at the stimulus onset (see the middle) compensates for the insufficient tonic inhibitory current (see the open arrow). The GABAergic gliotransmission-mediated tonic inhibition (see the bottom) compensates for the transient reduction in phasic inhibitory current that frequently takes place during the stimulation period (see the middle) when it reaches a certain level (see the filled arrow). Their cooperation achieves the reliable sensory tuning (see Figure 7, top).

Figure 7:

Relevance of the combinatorial (phasic and tonic) inhibition in sensory tuning. (Top) Raster plots of action potentials evoked in principal (P) cells. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell. The open and filled arrows roughly indicate insufficient and sufficient tonic inhibitory currents, respectively.

Figure 7:

Relevance of the combinatorial (phasic and tonic) inhibition in sensory tuning. (Top) Raster plots of action potentials evoked in principal (P) cells. (Middle) Phasic (Ib-to-P) inhibitory current recorded from a stimulus-irrelevant (n = 5) P cell. (Bottom) GABAergic gliotransmission-mediated tonic inhibitory current recorded from the same P cell. The open and filled arrows roughly indicate insufficient and sufficient tonic inhibitory currents, respectively.

The poor sensory tuning due to the P-to-glia circuitry impairment (see Figure 8A, same as Figure 5) might be overcome if the inhibitory (Ib-to-P) connection weight (wP,Ibij in equation A.3) is strengthened. However, as shown in Figure 8B, this causes a fatal problem: the reaction speed to the stimulus is decelerated (compare the two dashed lines). The poor reaction performance is due largely to hyperpolarization in ongoing-spontaneous membrane potential, as shown in Figure 8C (see the dashed trace). Since membrane hyperpolarization corresponds functionally to an increase in firing threshold, it will lead to a delay in sensory reaction. Our previous studies (Hoshino, 2008, 2009) indicated a close relationship between reaction speed and ongoing-spontaneous membrane potential. We suggested that an ongoing-spontaneous neuronal state, in which neurons oscillated at a subthreshold for firing, might be one of the crucial factors for rapid neuronal responses to sensory input. Figure 8D indicates that the ongoing-spontaneous membrane potential is hyperpolarized as the connection weight increases.

Figure 8:

Sensory tuning achieved solely through conventional phasic inhibition. (A) Raster plots of action potentials evoked in principal (P) cells without GABAergic gliotransmission-mediated tonic inhibition via P-to-glia signaling. (B) Raster plots in which the P-to-glia projection was cut and the Ib-to-P inhibitory connection weight was strengthened from 2 to 5. (C) Membrane potentials recorded from a stimulus-relevant (n = 3) P cell. The solid and dashed traces represent those in panels A and B, respectively. (D) Average ongoing-spontaneous membrane potential as a function of Ib-to-P connection weight.

Figure 8:

Sensory tuning achieved solely through conventional phasic inhibition. (A) Raster plots of action potentials evoked in principal (P) cells without GABAergic gliotransmission-mediated tonic inhibition via P-to-glia signaling. (B) Raster plots in which the P-to-glia projection was cut and the Ib-to-P inhibitory connection weight was strengthened from 2 to 5. (C) Membrane potentials recorded from a stimulus-relevant (n = 3) P cell. The solid and dashed traces represent those in panels A and B, respectively. (D) Average ongoing-spontaneous membrane potential as a function of Ib-to-P connection weight.

Figure 9 presents how the tonic (nonsynaptic) and phasic (synaptic) inhibitory mechanisms cooperatively work in order to achieve the best sensory tuning performance. In Figure 9 (left), the circles represent successful tuning: a population response is evoked only in stimulus-relevant P cells. The crosses represent unsuccessful tuning: a population response is evoked not only in stimulus-relevant P cells but also in stimulus-irrelevant P cells. Figure 9 (right) shows average ongoing-spontaneous membrane potentials. The best sensory tuning performance is achieved, provided that the weights of P-to-glia and Ib-to-P connections are properly chosen (e.g., see the double circle). Namely, the detection of the stimulus is successfully made with ongoing-spontaneous membrane potential less hyperpolarized.

Figure 9:

Cooperation of GABAergic gliotransmission-mediated tonic (nonsynaptic) inhibition and conventional phasic (synaptic) inhibition in order to achieve the best sensory tuning. (Left) Neuronal responses. wGl,Pi and wP,Ibij are P-to-glia and Ib-to-P connection weights, respectively. The circles represent successful sensory tuning: a population response is evoked only in stimulus-relevant P cells. The crosses represent unsuccessful sensory tuning: a population response is evoked not only in stimulus-relevant P cells but also in stimulus-irrelevant P cells. (Right) Average ongoing-spontaneous membrane potentials. The double circle indicates the best sensory tuning performance.

Figure 9:

Cooperation of GABAergic gliotransmission-mediated tonic (nonsynaptic) inhibition and conventional phasic (synaptic) inhibition in order to achieve the best sensory tuning. (Left) Neuronal responses. wGl,Pi and wP,Ibij are P-to-glia and Ib-to-P connection weights, respectively. The circles represent successful sensory tuning: a population response is evoked only in stimulus-relevant P cells. The crosses represent unsuccessful sensory tuning: a population response is evoked not only in stimulus-relevant P cells but also in stimulus-irrelevant P cells. (Right) Average ongoing-spontaneous membrane potentials. The double circle indicates the best sensory tuning performance.

3.4.  Robustness Testing.

In an additional simulation, we carried out a robustness test. Figure 10 shows the dependence of neuronal responsiveness on sensory input broadness (bottom: see in equation A.5). The top and middle panels show stimulus (f3) evoked neuronal (P cell) activities and gain functions, respectively. These results indicate that the neural network model proposed here is robust, ensuring stable and reliable responses to a variety of sensory input stimuli: salient (small values) to unsalient (large values) sensory information available for the network.

Figure 10:

Dependence of neuronal responsiveness on sensory input broadness (see in equation A.5). (Top) Stimulus (f3) evoked neuronal (P cell) activities. (Middle) Gain functions. (Bottom) Narrow () to broad () sensory input profiles.

Figure 10:

Dependence of neuronal responsiveness on sensory input broadness (see in equation A.5). (Top) Stimulus (f3) evoked neuronal (P cell) activities. (Middle) Gain functions. (Bottom) Narrow () to broad () sensory input profiles.

Figure 11A presents changes in neuronal responses if the P-glia circuit was made in an unselective manner. Namely, the P-to-glia projection was made not only between but also within cell assemblies. The unselective P-to-glia projection leads to an increase in tonic inhibitory current in stimulus-relevant P cells and thus to depressing their activities (see the filled rectangle for n = 3). As shown in Figure 11B, this shifts the gain function (see the triangles). The specific network architecture was employed to achieve the optimal network performance (see the open rectangles in Figure 11A and circles in Figure 11B) by which we could clearly show how the GABAergic gliotransmission mechanism contributes to modulating the neuronal gain and tuning to sensory input.

Figure 11:

Dependence of neuronal responsiveness on P-glia circuitry architecture. (A) Stimulus (f3) evoked neuronal (P cell) activities. (B) Gain functions. The P-to-glia projection was made not only between but also within cell assemblies (see the filled rectangles in panel A and triangles in panel B): an unselective circuitry condition. The open rectangles in panel A and circles in panel B represent those obtained under the original (selective) circuitry condition: The P-to-glia projection was made only between different cell assemblies.

Figure 11:

Dependence of neuronal responsiveness on P-glia circuitry architecture. (A) Stimulus (f3) evoked neuronal (P cell) activities. (B) Gain functions. The P-to-glia projection was made not only between but also within cell assemblies (see the filled rectangles in panel A and triangles in panel B): an unselective circuitry condition. The open rectangles in panel A and circles in panel B represent those obtained under the original (selective) circuitry condition: The P-to-glia projection was made only between different cell assemblies.

4.  Discussion

We simulated a neural network model in order to examine whether and how GABAergic gliotransmission balances intracortical excitation and inhibition, and investigated how it contributes to perceptual information processing: detection of feature stimuli. The network comprises principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia). GABA transporters, embedded in glial plasma membranes, regulated ambient GABA levels. Hypothetical neuron-glia signaling via inhibitory (Ia-to-glia) and excitatory (P-to-glia) synaptic contacts was assumed. The former let transporters import (remove) GABA from the extracellular space and excited stimulus-relevant P cells. The latter let them export GABA into the extracellular space and inhibited stimulus-irrelevant P cells. The main finding was that the glial membrane transporter gave a combinatorial excitatory-inhibitory effect on P cells in a tonic manner, thereby improving the gain and tuning of neuronal responses. Interestingly, it worked cooperatively with the conventional, phasic excitatory-inhibitory mechanism. We suggest that the GABAergic gliotransmission mechanism may provide balanced intracortical excitation and inhibition so that the best perceptual performance of the cortex can be achieved.

Figure 12 might help in understanding the important conclusion derived from this study. Normal perceptual performance ensured by the conventional, phasic (synaptic) excitation and inhibition (see “normal perform.”) can be improved by the GABAergic gliotransmission-mediated, tonic (nonsynaptic) excitation and inhibition (see “best perform.”). The GABAergic gliotransmission-mediated tonic excitation improves the neuronal gain function (see the top arrow), and the GABAergic gliotransmission-mediated tonic inhibition improves the sensory tuning (see the left arrow). The GABAergic gliotransmission-mediated, tonic excitatory-inhibitory mechanism leads to the best perceptual performance (see the filled arrow). This study points to a new understanding that the GABAergic gliotransmission-mediated regulation of local ambient GABA levels may modulate the neuronal gain and tuning to sensory input. To the best of our knowledge, the new understanding has not yet been experimentally demonstrated, which we hope will be done in the near future.

Figure 12:

A conceptual scheme for perceptual improvement by the GABAergic gliotransmission-mediated, tonic excitatory-inhibitory mechanism. (Top left) Normal perceptual performance ensured by the conventional, phasic (synaptic) excitatory-inhibitory mechanism. (Top right) Improvement in neuronal gain function by GABAergic gliotransmission-mediated tonic excitation. (Bottom left) Improvement in sensory tuning by GABAergic gliotransmission-mediated tonic inhibition. (Bottom right) The best perceptual performance achieved by the GABAergic gliotransmission-mediated, tonic (nonsynaptic) excitatory-inhibitory mechanism proposed.

Figure 12:

A conceptual scheme for perceptual improvement by the GABAergic gliotransmission-mediated, tonic excitatory-inhibitory mechanism. (Top left) Normal perceptual performance ensured by the conventional, phasic (synaptic) excitatory-inhibitory mechanism. (Top right) Improvement in neuronal gain function by GABAergic gliotransmission-mediated tonic excitation. (Bottom left) Improvement in sensory tuning by GABAergic gliotransmission-mediated tonic inhibition. (Bottom right) The best perceptual performance achieved by the GABAergic gliotransmission-mediated, tonic (nonsynaptic) excitatory-inhibitory mechanism proposed.

Simulation studies (Nadkarni, Jung, & Levine, 2008; De Pitta et al., 2012; Fellin, Ellenbogen, De Pitta, Ben-Jacob, & Halassa, 2012) indicated that glia could modulate synaptic transmission by regulating chemical substances such as glutamate, GABA, D-serine, and ATP, which act on pre- and postsynaptic receptors. It was suggested that glia might regulate extracellular ion concentrations, such as Na+, K+, and Cl, in order to achieve proper functioning of neurons (Volman, Bazhenov, & Sejnowski, 2012; Cressman, Ullah, Ziburkus, Schiff, & Barreto, 2009). The gliotransmission mechanism contributed to modulating neuronal and network functions (i.e., gain and tuning), in which the combinatorial regulation of ambient GABA concentration by glial transporters played a key role. Our previous model (Hoshino, 2013) had transporters on axon terminals, from which GABA molecules were exported into (but not imported from) the extracellular space. The GABA export was enough to show how age-related changes in multistable perception could take place.

Volman, Levine, and Sejnowski (2010) simulated a neural network model and demonstrated that asynchronous release of glutamate from presynaptic terminals could modulate neuronal gain. The novel idea of our study was that the GABAergic gliotransmission mechanism could regulate ambient GABA concentration in a combinatorial manner: an increase around stimulus-irrelevant principal (P) cells and a decrease around stimulus-relevant P cells. The former modulated the tuning and the latter the gain of neuronal responses, thereby improving the network's perceptual performance.

We employed two distinct interneurons: Ia and Ib. A variety of GABAergic interneurons have been found in the cortex, such as horizontal cells and large, medium, and small multipolar cells (for a survey, see Prieto, Peterson, & Winer, 1994). Large multipolar cells with their wide axonal arbors send signals to distant cells, while small multipolar cells with their narrow axonal arbors are limited to proximal cells. Based on their observations, we let the Ib cell (as large multipolar cell) project to all (nearby to distant) P cells within the same cell assembly and the Ia cell (as small multipolar cell) to its proximal glial cell.

The Ia and Ib cells may correspond to fast and late spiking cells (or regular spiking cells), which, respectively, have short and long membrane time constants: 8.82 msec and 20.68 (or 28.512.2) msec (Kawaguchi, 1995; Kawaguchi & Kondo, 2002). Based on these observations, we set the values of membrane capacitance and conductance: cIam=200 pF, cIbm=600 pF and gIam=20 nS, gIbm=15 nS (see Table 1). To make a fast GABAergic gliotransmission-mediated modulatory effect on P cells, we assumed such a short membrane time constant for the Ia cell. If we employ a longer time constant, the reaction time of P cells to sensory input and their firing frequency will be somewhat delayed and decreased, respectively. Nonetheless, we would come to the same conclusion: the GABAergic gliotransmission mechanism can improve the gain and tuning of neuronal responses to sensory input.

Although discussed in detail in our previous study (Hoshino, 2012), we briefly address some important approximations and limitations of our model. A variety of neuron-glia circuits have been evidenced, including chemical (glutamate, GABA) synapses between presynaptic neurons and postsynaptic glial cells (for review, see Bezzi & Volterra, 2001; Fields & Stevens-Graham, 2002; Lin & Bergles, 2004; Overstreet, 2005). Based on their observations, we made the excitatory (P-to-glia) and inhibitory (Ia-to-glia) neuron-to-glia synaptic contacts. Neuron-glia signaling that we neglected here for simplicity might include GABA and glutamate signaling to glia through activation of metabotropic receptors (Verkhratsky, 2010; Velez-Fort, Audinat, & Angulo, 2012).

Glial cells might have a role in regulating extracellular concentrations of transmitters (GABA, glutamate), ions (potassium, hydrogen, calcium), and metabolites (D-serine, ATP) (Fields & Stevens-Graham, 2002; Newman, 2003; Hansson & Rönnbäck, 2003; Verkhratsky, 2010). In this study, we have focused on investigating how ambient GABA-mediated tonic inhibition affects the gain and tuning of neuronal responses. We could model a glial plasma membrane transporter that regulates an ambient GABA level, because the mechanism of GABA transport has been theoretically explained (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003; Richerson, 2004; Wu et al., 2007).

We did not model those that regulate extracellular levels of glutamate and potassium, because their transport mechanisms have not yet been theoretically explained. For instance, several lines of evidence indicate that a calcium-dependent exocytotic process can export glutamate; however, its neuronal mechanism is uncertain (for review, see Newman, 2003). Glial cells are probably the source of GABA responsible for extrasynaptic GABAa receptor-mediated inhibitory current and can export different transmitters (Kozlov, Angulo, Audinat, & Charpak, 2006; Angulo, Le Meur, Kozlov, Charpak, & Audinat, 2008). The question remains: How could each of these different types of gliotransmission be controlled?

If the export of glutamate from glial cells into the extracellular space becomes greater or the import of extracellular potassium into glial cells does not take place, the tonic inhibitory mechanism would not work properly. Due to the limitation of our model (i.e., it was impossible to regulate extracellular levels of glutamate and potassium as addressed above), we cannot declare that glial inhibitory effects are stronger than glial excitatory effects. We propose here a working hypothesis: GABAergic gliotransmission may prevail in intracortical tonic inhibitory processing, for which suitable spatial organization of glial cells would be required.

Appendix A:  The Neural Network Model

Dynamic evolution of membrane potential of the ith P cell that belongs to cell assembly n is defined by
formula
A.1
where IP,Pi(n; t) is an excitatory synaptic current from other P cells, IP,Ibi(n; t) an inhibitory synaptic current from Ib cells, IPi,ext(n; t) an inhibitory nonsynaptic current mediated by ambient GABA via extrasynaptic receptors, and IPinp(n; t) an excitatory input current that is provided when presented with sensory feature finp: . These currents are defined by
formula
A.2
formula
A.3
formula
A.4
formula
A.5
Dynamic evolution of membrane potential of the ith Ia and Ib cells that belong to cell assembly n is defined by
formula
A.6
formula
A.7
where IIa,Pi(n; t) and IIb,Pi(n; t) are excitatory synaptic currents from P cells. These currents are defined by
formula
A.8
formula
A.9
Dynamic evolution of membrane potential of the ith glial cell that belongs to cell assembly n is defined by
formula
A.10
where IGl,Pi(n; t) and IGl,Iai(n; t) are excitatory and inhibitory synaptic currents from P and Ia cells, respectively. These currents are defined by
formula
A.11
formula
A.12

In these equations, rPj(n; t) is the fraction of AMPA receptors in the open state triggered by presynaptic action potentials of the jth P cell. rIbj(n; t) and rIaj(n; t) are the fractions of intrasynaptic GABAa receptors in the open state triggered by presynaptic action potentials of the jth Ib cell and Ia cell, respectively. rPi,ext(n; t) is the fraction of extrasynaptic GABAa receptors, located on the ith P cell, in the open state provoked by ambient GABA. The receptor dynamics and ambient GABA concentration dynamics are defined in Appendixes  B and  C. For model parameters and their values, see Table 1.

Appendix B:  Receptor Dynamics and Action Potential Generation

Receptor dynamics is based on a study (Destexhe, Mainen, & Sejnowski, 1998) and described as
formula
B.1
formula
B.2
formula
B.3
where [Glut]j(n; t) and [GABA]Xj(n; t) are concentrations of glutamate and GABA in synaptic clefts, respectively. [Glut]j(n; t) = 1 mM and [GABA]Xj(n; t) = 1 mM for 1 msec when the presynaptic jth P cell and type X cell fire, respectively. Otherwise, [Glut]j(n; t) = 0 and [GABA]Xj(n; t) = 0. Concentration of ambient GABA, [GABA]Pi,ext(n; t), is defined in Appendix  C.
The probability of neuronal firing is defined by
formula
B.4
When a cell fires, its membrane potential is depolarized to −10 mV, which is kept for 1 msec and then reset to the resting potential. For model parameters and their values, see Table 1.

Appendix C:  Dynamics of Ambient GABA Concentration

Concentration of ambient GABA around the ith P cell that belongs to cell assembly n is defined by
formula
C.1
For the details of model parameters and their values, see Table 1 and our previous studies (Hoshino, 2009, 2010, 2011a, 2011b, 2012, 2013).

Acknowledgments

We express our gratitude to Takeshi Kambara for his helpful discussions and to reviewers for giving us valuable comments and suggestions.

References

Angulo
,
M. C.
,
Le Meur
,
K.
,
Kozlov
,
A. S.
,
Charpak
,
S.
, &
Audinat
,
E.
(
2008
).
GABA, a forgotten gliotransmitter
.
Prog. Neurobiol.
,
86
,
297
303
.
Bezzi
,
P.
, &
Volterra
,
A.
(
2001
).
A neuron-glia signalling network in the active brain
.
Curr. Opin. Neurobiol
,
11
,
387
394
.
Bianchi
,
M. T.
,
Haas
,
K. F.
, &
Macdonald
,
R. L.
(
2001
).
Structural determinants of fast desensitization and desensitization-deactivation coupling in GABAa receptors
.
J. Neurosci.
,
21
,
1127
1136
.
Bianchi
,
M. T.
,
Haas
,
K. F.
, &
Macdonald
,
R. L.
(
2002
).
Alpha1 and alpha6 subunits specify distinct desensitization, deactivation and neurosteroid modulation of GABA(A) receptors containing the delta subunit
.
Neuropharmacology
,
43
,
492
502
.
Brickley
,
S. G.
,
Cull-Candy
,
S. G.
, &
Farrant
,
M.
(
1996
).
Development of a tonic form of synaptic inhibition in rat cerebellar granule cells resulting from persistent activation of GABAa receptors
.
J. Physiol.
,
497
,
753
759
.
Brown
,
N.
,
Kerby
,
J.
,
Bonnert
,
T. P.
,
Whiting
,
P. J.
, &
Wafford
,
K. A.
(
2002
).
Pharmacological characterization of a novel cell line expressing human alpha(4)beta(3)delta GABA(A) receptors
.
Br. J. Pharmacol.
,
136
,
965
974
.
Cressman
,
J. R.
Jr
,
Ullah
,
G.
,
Ziburkus
,
J.
,
Schiff
,
S. J.
, &
Barreto
,
E.
(
2009
).
The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics
.
J. Comput. Neurosci.
,
26
,
159
170
.
De Pitta
,
M.
,
Volman
,
V.
,
Berry
,
H.
,
Parpura
,
V.
,
Volterra
,
A.
, &
Ben-Jacob
,
E.
(
2012
).
Computational quest for understanding the role of astrocyte signaling in synaptic transmission and plasticity
.
Front. Comput. Neurosci.
,
6
,
98
.
Destexhe
,
A.
,
Mainen
,
Z. F.
, &
Sejnowski
,
T. J.
(
1998
).
Kinetic models of synaptic transmission
. In
C. Koch & I. Segev
(Eds.),
Methods in Neuronal Modeling
(pp. 
1
25
).
Cambridge, MA
:
MIT Press
.
Drasbek
,
K. R.
, &
Jensen
,
K.
(
2006
).
THIP, a hypnotic and antinociceptive drug, enhances an extrasynaptic GABAa receptor-mediated conductance in mouse neocortex
.
Cereb. Cortex
,
16
,
1134
1141
.
Farrant
,
M.
, &
Nusser
,
Z.
(
2005
).
Variations on an inhibitory theme: Phasic and tonic activation of GABA(A) receptors
.
Nat. Rev. Neurosci.
,
6
,
215
229
.
Fellin
,
T.
,
Ellenbogen
,
J. M.
,
De Pitta
,
M.
,
Ben-Jacob
,
E.
, &
Halassa
,
M. M.
(
2012
).
Astrocyte regulation of sleep circuits: Experimental and modeling perspectives
.
Front. Comput. Neurosci.
,
6
,
65
.
Fields
,
R. D.
, &
Stevens-Graham
,
B.
(
2002
).
New insights into neuron-glia communication
.
Science
,
298
,
556
562
.
Hansson
,
E.
, &
Rönnbäck
,
L.
(
2003
).
Glial neuronal signaling in the central nervous system
.
FASEB J.
,
17
,
341
348
.
Hoshino
,
O.
(
2007a
).
Spatiotemporal conversion of auditory information for cochleotopic mapping
.
Neural Comput.
,
19
,
351
370
.
Hoshino
,
O.
(
2007b
).
Enhanced sound-perception by widespread onset neuronal responses in auditory cortex
.
Neural Comput.
,
19
,
3310
3334
.
Hoshino
,
O.
(
2008
).
An ongoing subthreshold neuronal state established through dynamic coassembling of cortical cells
.
Neural Comput.
,
20
,
3055
3086
.
Hoshino
,
O.
(
2009
).
GABA transporter preserving ongoing spontaneous neuronal activity at firing subthreshold
.
Neural Comput.
,
21
,
1683
1713
.
Hoshino
,
O.
(
2010
).
Alteration of ambient GABA by phasic and tonic neuronal activation
.
Neural Comput.
,
22
,
1358
1382
.
Hoshino
,
O.
(
2011a
).
Neuronal responses below firing threshold for subthreshold cross-modal enhancement
.
Neural Comput.
,
23
,
958
983
.
Hoshino
,
O.
(
2011b
).
Subthreshold membrane depolarization as memory trace for perceptual learning
.
Neural Comput.
,
23
,
3205
3231
.
Hoshino
,
O.
(
2012
).
Regulation of ambient GABA levels by neuron-glia signaling for reliable perception of multisensory events
.
Neural Comput.
,
24
,
2964
2993
.
Hoshino
,
O.
(
2013
).
Ambient GABA responsible for age-related changes in multistable perception
.
Neural Comput.
,
25
,
1164
1190
.
Jones
,
M. V.
, &
Westbrook
,
G. L.
(
1995
).
Desensitized states prolong GABAa channel responses to brief agonist pulses
.
Neuron
,
15
,
181
191
.
Kawaguchi
,
Y.
(
1995
).
Physiological subgroups of nonpyramidal cells with specific morphological characteristics in layer II/III of rat frontal cortex
.
J. Neurosci.
,
15
,
2638
2655
.
Kawaguchi
,
Y.
, &
Kondo
,
S.
(
2002
).
Parvalbumin, somatostatin and cholecystokinin as chemical markers for specific GABAergic interneuron types in the rat frontal cortex
.
J. Neurocytol.
,
31
,
277
287
.
Kozlov
,
A. S.
,
Angulo
,
M. C.
,
Audinat
,
E.
, &
Charpak
,
S.
(
2006
).
Target cell-specific modulation of neuronal activity by astrocytes
.
Proc. Natl. Acad. Sci. USA
,
103
,
10058
10063
.
Lerma
,
J.
,
Herranz
,
A. S.
,
Herreras
,
O.
,
Abraira
,
V.
, &
Martin
,
D. R.
(
1986
).
In vivo determination of extracellular concentration of amino acids in the rat hippocampus: A method based on brain dialysis and computerized analysis
.
Brain Res.
,
384
,
145
155
.
Lin
,
S. C.
, &
Bergles
,
D. E.
(
2004
).
Synaptic signaling between GABAergic interneurons and oligodendrocyte precursor cells in the hippocampus
.
Nat. Neurosci.
,
7
,
24
32
.
Maconochie
,
D. J.
,
Zempel
,
J. M.
, &
Steinbach
,
J. H.
(
1994
).
How quickly can GABAa receptors open?
Neuron
,
12
,
61
71
.
Marino
,
J.
,
Schummers
,
J.
,
Lyon
,
D. C.
,
Schwabe
,
L.
,
Beck
,
O.
,
Wiesing
,
P.
, …
Sur
,
M.
(
2005
).
Invariant computations in local cortical networks with balanced excitation and inhibition
.
Nat. Neurosci.
,
8
,
194
201
.
Moore
,
C. I.
,
Nelson
,
S. B.
, &
Sur
,
M.
(
1999
).
Dynamics of neuronal processing in rat somatosensory cortex
.
Trends Neurosci.
,
22
,
513
520
.
Mountcastle
,
V. B.
(
1997
).
The columnar organization of the neocortex
.
Brain
,
120
,
701
722
.
Nadkarni
,
S.
,
Jung
,
P.
, &
Levine
,
H.
(
2008
).
Astrocytes optimize the synaptic transmission of information
.
PLoS Comput. Biol.
,
4
,
e1000088
.
Newman
,
E. A.
(
2003
).
New roles for astrocytes: Regulation of synaptic transmission
.
Trends in Neurosci.
,
26
,
536
542
.
Nusser
,
Z.
,
Roberts
,
J. D.
,
Baude
,
A.
,
Richards
,
J. G.
, &
Somogyi
,
P.
(
1995
).
Relative densities of synaptic and extrasynaptic GABAa receptors on cerebellar granule cells as determined by a quantitative immunogold method
.
J. Neurosci.
,
5
,
2948
2960
.
Okun
,
M.
, &
Lampl
,
I.
(
2008
).
Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities
.
Nat. Neurosci.
,
11
,
535
537
.
Ortinski
,
P. I.
,
Turner
,
J. R.
,
Barberis
,
A.
,
Motamedi
,
G.
,
Yasuda
,
R. P.
,
Wolfe
,
B. B.
, …
Vicini
,
S.
(
2006
).
Deletion of the GABA(A) receptor alpha1 subunit increases tonic GABA(A) receptor current: A role for GABA uptake transporters
.
J. Neurosci.
,
26
,
9323
9331
.
Overstreet
,
L. S.
(
2005
).
Quantal transmission: Not just for neurons
.
Trends Neurosci.
,
28
,
59
62
.
Prieto
,
J. J.
,
Peterson
,
B. A.
, &
Winer
,
J. A.
(
1994
).
Morphology and spatial distribution of GABAergic neurons in cat primary auditory cortex (AI)
.
J. Comp. Neurol.
,
344
,
349
382
.
Richerson
,
G. B.
(
2004
).
Looking for GABA in all the wrong places: The relevance of extrasynaptic GABA(A) receptors to epilepsy
.
Epilepsy Curr.
,
4
,
239
242
.
Richerson
,
G. B.
, &
Wu
,
Y.
(
2003
).
Dynamic equilibrium of neurotransmitter transporters: Not just for reuptake anymore
.
J. Neurophysiol.
,
90
,
1363
1374
.
Saxena
,
N. C.
, &
Macdonald
,
R. L.
(
1996
).
Properties of putative cerebellar gamma-aminobutyric acid A receptor isoforms
.
Mol. Pharmacol.
,
49
,
567
579
.
Scimemi
,
A.
,
Andersson
,
A.
,
Heeroma
,
J. H.
,
Strandberg
,
J.
,
Rydenhag
,
B.
,
McEvoy
,
A. W.
, …
Walker
,
M. C.
(
2006
).
Tonic GABA(A) receptor-mediated currents in human brain
.
Eur. J. Neurosci.
,
24
,
1157
1160
.
Scimemi
,
A.
,
Semyanov
,
A.
,
Sperk
,
G.
,
Kullmann
,
D. M.
, &
Walker
,
M. C.
(
2005
).
Multiple and plastic receptors mediate tonic GABAa receptor currents in the hippocampus
.
J. Neurosci.
,
25
,
10016
10024
.
Semyanov
,
A.
,
Walker
,
M. C.
,
Kullmann
,
D. M.
, &
Silver
,
R. A.
(
2004
).
Tonically active GABAa receptors: Modulating gain and maintaining the tone
.
Trends Neurosci.
,
27
,
262
269
.
Soltesz
,
I.
, &
Nusser
,
Z.
(
2001
).
Neurobiology: Background inhibition to the fore
.
Nature
,
409
,
24
25
.
Somogyi
,
P.
,
Takagi
,
H.
,
Richards
,
J. G.
, &
Mohler
,
H.
(
1989
).
Subcellular localization of benzodiazepine/GABAa receptors in the cerebellum of rat, cat, and monkey using monoclonal antibodies
.
J. Neurosci.
,
9
,
2197
2209
.
Tan
,
A. Y.
,
Zhang
,
L. I.
,
Merzenich
,
M. M.
, &
Schreiner
,
C. E.
(
2004
).
Tone-evoked excitatory and inhibitory synaptic conductances of primary auditory cortex neurons
.
J. Neurophysiol.
,
92
,
630
643
.
Tossman
,
U.
,
Jonsson
,
G.
, &
Ungerstedt
,
U.
(
1986
).
Regional distribution and extracellular levels of amino acids in rat central nervous system
.
Acta Physiol. Scand.
,
127
,
533
545
.
Velez-Fort
,
M.
,
Audinat
,
E.
, &
Angulo
,
M. C.
(
2012
).
Central role of GABA in neuron-glia interactions
.
Neuroscientist
,
18
,
237
250
.
doi: 10.1177/1073858411403317
Verkhratsky
,
A.
(
2010
).
Physiology of neuronal-glial networking
.
Neurochem. Int.
,
57
,
332
343
.
Volman
,
V.
,
Bazhenov
,
M.
, &
Sejnowski
,
T. J.
(
2012
).
Computational models of neuron-astrocyte interaction in epilepsy
.
Front. Comput. Neurosci.
,
6
,
58
.
Volman
,
V.
,
Levine
,
H.
, &
Sejnowski
,
T. J.
(
2010
).
Shunting inhibition controls the gain modulation mediated by asynchronous neurotransmitter release in early development
.
PLoS Comput. Biol.
,
6
,
e1000973
.
Wehr
,
M.
, &
Zador
,
A. M.
(
2003
).
Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex
.
Nature
,
426
,
442
446
.
Wu
,
Y.
,
Wang
,
W.
,
Diez-Sampedro
,
A.
, &
Richerson
,
G. B.
(
2007
).
Nonvesicular inhibitory neurotransmission via reversal of the GABA transporter GAT-1
.
Neuron
,
56
,
851
865
.
Wu
,
Y.
,
Wang
,
W.
, &
Richerson
,
G. B.
(
2001
).
GABA transaminase inhibition induces spontaneous and enhances depolarization-evoked GABA efflux via reversal of the GABA transporter
.
J. Neurosci.
,
21
,
2630
2639
.
Wu
,
Y.
,
Wang
,
W.
, &
Richerson
,
G. B.
(
2003
).
Vigabatrin induces tonic inhibition via GABA transporter reversal without increasing vesicular GABA release
.
J. Neurophysiol.
,
89
,
2021
2034
.
Zhang
,
L. I.
,
Tan
,
A. Y.
,
Schreiner
,
C. E.
, &
Merzenich
,
M. M.
(
2003
).
Topography and synaptic shaping of direction selectivity in primary auditory cortex
.
Nature
,
424
,
201
205
.