Abstract

We examined how the depression of intracortical inhibition due to a reduction in ambient GABA concentration impairs perceptual information processing in schizophrenia. A neural network model with a gliotransmission-mediated ambient GABA regulatory mechanism was simulated. In the network, interneuron-to-glial-cell and principal-cell-to-glial-cell synaptic contacts were made. The former hyperpolarized glial cells and let their transporters import (remove) GABA from the extracellular space, thereby lowering ambient GABA concentration, reducing extrasynaptic GABAa receptor-mediated tonic inhibitory current, and thus exciting principal cells. In contrast, the latter depolarized the glial cells and let the transporters export GABA into the extracellular space, thereby elevating the ambient GABA concentration and thus inhibiting the principal cells. A reduction in ambient GABA concentration was assumed for a schizophrenia network. Multiple dynamic cell assemblies were organized as sensory feature columns. Each cell assembly responded to one specific feature stimulus. The tuning performance of the network to an applied feature stimulus was evaluated in relation to the level of ambient GABA. Transporter-deficient glial cells caused a deficit in GABAergic gliotransmission and reduced ambient GABA concentration, which markedly deteriorated the tuning performance of the network, broadening the sensory tuning. Interestingly, the GABAergic gliotransmission mechanism could regulate local ambient GABA levels: it augmented ambient GABA around stimulus-irrelevant principal cells, while reducing ambient GABA around stimulus-relevant principal cells, thereby ensuring their selective responsiveness to the applied stimulus. We suggest that a deficit in GABAergic gliotransmission may cause a reduction in ambient GABA concentration, leading to a broadening of sensory tuning in schizophrenia. The GABAergic gliotransmission mechanism proposed here may have an important role in the regulation of local ambient GABA levels, thereby improving the sensory tuning performance of the cortex.

1.  Introduction

Deficits in basic perceptual function have been evidenced in schizophrenia. For instance, Rojas and colleagues (2002) reported magnetoencephalographic (MEG) data, suggesting that tonotopic mapping in auditory cortex might be disturbed in patients with schizophrenia. Their follow-up study (Rojas, Slason, Teale, & Reite, 2007) examined auditory tuning (at 1 KHz) in patients with schizophrenia. They found a significant broadening of tuning in the schizophrenic group and suggested that the depression of intracortical inhibition between cortical frequency columns might disturb tonotopic mapping and therefore broaden the auditory tuning.

Gamma-aminobutyric acid (GABA) is the major inhibitory neurotransmitter and has been the focus on the research for neuronal mechanisms of cognitive deficits in schizophrenia. Experimental studies (Yoon et al., 2010; Rokem et al., 2011) estimated GABA levels in the visual cortex. The researchers used magnetic resonance spectroscopy (MRS) to measure global GABA levels in subjects with schizophrenia and in healthy controls. Their studies indicated a reduction in GABA concentration in the schizophrenic group. They examined a relationship between GABA concentration and orientation-specific surround suppression (Yoon et al., 2010) and a relationship between GABA concentration and orientation tuning (Rokem et al., 2011). They found a highly significant positive correlation between these variables, indicating that the reduction of ambient GABA levels might lead to the depression of intracortical inhibition and impair perceptual information processing in schizophrenia. One important question remained: What is the underlying neuronal mechanism?

As to the maintenance of ambient GABA levels, Richerson and colleagues (Richerson & Wu, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) made an interesting suggestion that 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 plasma membranes of glial cells (and GABAergic interneurons), can clamp ambient GABA at a certain level. They are near equilibrium under normal physiological conditions and will reverse with a relatively small increase in plasma membrane potential. Using cultured hippocampal cells, the researchers demonstrated that an increase in tonic inhibitory current was prevented not by blocking vesicular GABA release but by GABA transporter antagonists. Glial cells are thought to be one of the possible sources of GABA responsible for extrasynaptic GABAa receptor-mediated tonic inhibitory current (Kozlov, Angulo, Audinat, & Charpak, 2006; Angulo, Le Meur, Kozlov, Charpak, & Audinat, 2008). Experimental studies (Lewis, 2000; Volk, Austin, Pierri, Sampson, & Lewis, 2001) suggested that GAT1-deficient cortical interneurons, observed in schizophrenic patients, might lead to disturbing GABAergic neurotransmission.

The purpose of this study is to elucidate how the depression of intracortical inhibition due to a reduction in ambient GABA concentration impairs perceptual information processing in schizophrenia. To regulate ambient GABA concentration in a neural network, we proposed in a previous study (Hoshino, 2012) a functional model of a glial plasma membrane transporter. A level of ambient GABA is increased or decreased depending on the activity of glial cells. We assume here two types of neuron-glia signaling via inhibitory interneuron to glial cell and via excitatory principal cell to glial cell synaptic contacts. The former hyperpolarizes glial cells and lets their transporters import (remove) GABA from the extracellular space, thereby lowering ambient GABA concentration, reducing extrasynaptic GABAa receptor-mediated tonic inhibitory current and thus exciting principal cells. In contrast, the latter depolarizes the glial cells and lets the transporters export GABA into the extracellular space, thereby elevating the ambient GABA concentration and thus inhibiting the principal cells.

A reduction in ambient GABA concentration is assumed for a schizophrenia network. Multiple dynamic cell assemblies are organized as sensory feature columns, each with specific responsiveness to one feature stimulus. To adjust a level of ambient GABA, we systematically change the value of GABA transfer coefficient in the glial plasma membrane transporter model, whose decrease corresponds to transporter-deficient glial cells. At various ambient GABA levels, we record neuronal responses (spikes and membrane potentials) to a feature stimulus. The tuning performance of the network to the applied feature stimulus is quantitatively evaluated in relation to the level of ambient GABA.

2.  Neural Network Model

As shown in Figure 1A, 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 that 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. In general, a single glial cell oversees large groups of neuronal processes and synapses (Bushong, Martone, Jones, & Ellisman, 2002). In this study, we let a single glial cell act on one principal cell for simplicity. A conductance-based, integrate-and-fire neuron model (Hoshino, 2007a, 2007b, 2008) is employed.

Figure 1:

The neural network model. (A) Neuronal circuitry. Each cell assembly (), as a sensory feature column, consists of cell units: one principal cell (P), two GABAergic interneurons (Ia, Ib), and one glial cell (glia). The open and filled triangles represent excitatory and inhibitory synapses, respectively. (B) Graded sensory input. When presented with feature fn, P cells belonging to cell assembly n receive the most intense input current, its neighbors (n−1, n+1) the second most, and so on, which is schematically indicated by the size of arrows. (C) A conceptual scheme of GABA transport by glial plasma membrane transporters (Hoshino, 2012). P and Ia cells synaptically connect to a glial cell. Transporters on the glial cell import (remove) GABA molecules from or export them into the extracellular space, depending on plasma membrane potential. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

Figure 1:

The neural network model. (A) Neuronal circuitry. Each cell assembly (), as a sensory feature column, consists of cell units: one principal cell (P), two GABAergic interneurons (Ia, Ib), and one glial cell (glia). The open and filled triangles represent excitatory and inhibitory synapses, respectively. (B) Graded sensory input. When presented with feature fn, P cells belonging to cell assembly n receive the most intense input current, its neighbors (n−1, n+1) the second most, and so on, which is schematically indicated by the size of arrows. (C) A conceptual scheme of GABA transport by glial plasma membrane transporters (Hoshino, 2012). P and Ia cells synaptically connect to a glial cell. Transporters on the glial cell import (remove) GABA molecules from or export them into the extracellular space, depending on plasma membrane potential. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

We use graded sensory input (see in equation A.5). This is a simple representation observed in early sensory cortices. Tuning (orientation) properties of visual cortical cells reflect responses of lateral geniculate nucleus (LGN) (Series, Latham, & Pouget, 2004). The LGN afferences provide broad tuning curves that are subsequently sharpened in the visual cortex. Namely, the broadly tuned input from the LGN provides a poor representation of orientation for the visual cortex. Similarly, tuning (frequency) properties of auditory cortical cells reflect responses of medial geniculate nucleus (MGB) (Oswald, Schiff, & Reyes, 2006). The MGB afferences provide broad tuning curves that are subsequently sharpened in the auditory cortex.

When the network is presented with a feature stimulus fn, P cells receive a graded (broadly tuned) sensory input. Namely, P cells belonging to cell assembly n receive the most intense input current, its neighbors (n−1, n+1) the second most, and so on, which is schematically indicated by the size of arrows in Figure 1B. The broadness of input to the network is determined by (see equation A.5). Throughout the simulations, we use , because this parameter value enables us to clearly show how the tuning performance of the network is improved when the GABAergic gliotransmission mechanism works.

As schematically illustrated in Figure 1C, 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 that are distributed in the glial cell membrane import (remove) GABA from or export it into the extracellular space, which depends on the membrane potential of the glial cell. Ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell. For simplicity, extrasynaptic GABAa receptors are located on P cells but not on Ia and Ib cells. 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.
DescriptionParameterValue
Membrane capacitance of type K (K = P, Ia, Ib, glia) cell cKm cPm=500 pF, cIam=200 pF, cIbm=600 pF, cGlm=45 pF 
Membrane conductance gKm gPm=25 nS, gIam=20 nS, gIbm=15 nS, gGlm=9 nS 
Resting potential uKrest uPrest=−65 mV, uIarest=uIbrest=uGlrest=−70 mV 
Maximal conductance for type Z (Z = AMPA, GABA) receptor   nS, nS 
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 jth to ith P cell wP,Pij 
Synaptic weight from jth Ib to ith P cell wP,Ibij 
Synaptic weight from ith P to Ia cell wIa,Pi 30 
Synaptic weight from ith P to Ib cell between different cell assemblies  
Synaptic weight from ith P to glial cell  
Synaptic weight from ith Ia to glial cell wGl,Iai 10 
Amount of extrasynaptic GABAa receptors on P cell   
Input current  300 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   mV, mV 
Decay constant for ambient GABA concentration  
Basal ambient GABA concentration [GABA]0ext  
Maximal ambient GABA concentration GABAmax  
Minimal ambient GABA concentration GABAmin  
GABA transfer coefficient TGl  
Reversal potential of transporter uGlrev −70 mV 
DescriptionParameterValue
Membrane capacitance of type K (K = P, Ia, Ib, glia) cell cKm cPm=500 pF, cIam=200 pF, cIbm=600 pF, cGlm=45 pF 
Membrane conductance gKm gPm=25 nS, gIam=20 nS, gIbm=15 nS, gGlm=9 nS 
Resting potential uKrest uPrest=−65 mV, uIarest=uIbrest=uGlrest=−70 mV 
Maximal conductance for type Z (Z = AMPA, GABA) receptor   nS, nS 
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 jth to ith P cell wP,Pij 
Synaptic weight from jth Ib to ith P cell wP,Ibij 
Synaptic weight from ith P to Ia cell wIa,Pi 30 
Synaptic weight from ith P to Ib cell between different cell assemblies  
Synaptic weight from ith P to glial cell  
Synaptic weight from ith Ia to glial cell wGl,Iai 10 
Amount of extrasynaptic GABAa receptors on P cell   
Input current  300 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   mV, mV 
Decay constant for ambient GABA concentration  
Basal ambient GABA concentration [GABA]0ext  
Maximal ambient GABA concentration GABAmax  
Minimal ambient GABA concentration GABAmin  
GABA transfer coefficient TGl  
Reversal potential of transporter uGlrev −70 mV 

Concerning Ib-to-P and Ia-to-glia circuits, a variety of GABAergic interneurons have been found in the cortex, such as large, medium, and small size 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. As will be shown in later sections, the Ib-to-P projection contributes to suppressing stimulus-irrelevant P cell activity and the Ia-to-glia projection enhancing stimulus-relevant P cell activity. The specific network architecture enables us to clearly show how a reduction in ambient GABA concentration leads to deterioration of sensory tuning performance in schizophrenia.

Concerning the neuron-glia signaling, a variety of neuron-glia circuits have been evidenced, including chemical (glutamate, GABA) synapses between presynaptic neurons and glial cells (for review, see Bezzi & Volterra, 2001; Fields & Stevens-Graham, 2002; Lin & Bergles, 2004; Overstreet, 2005). Based on their observations, we assume excitatory (P-to-glia) and inhibitory (Ia-to-glia) neuron-to-glia synaptic contacts. Neuron-glia signaling that we neglect here for simplicity might include GABA and glutamate signaling to glia through activation of metabotropic receptors (Verkhratsky, 2010; Velez-Fort, Audinat, & Angulo, 2012).

3.  Results

3.1.  Influence of GABAergic Gliotransmission on Neuronal Behavior.

In this section, we show how GABAergic gliotransmission affects neuronal behavior and examine whether and how a reduction in ambient GABA concentration due to a deficit in GABAergic gliotransmission deteriorates the perceptual performance of a schizophrenia network. Figure 2A shows membrane potentials of (see the top traces) and ambient GABA concentrations around (see the bottom traces) P cells belonging to respective cell assemblies () when presented with sensory feature f3. Due to the graded sensory input (: see equation A.5 and Table 1), stimulus-irrelevant P cells tend to respond at the onset of the stimulus (e.g., see n = 2, 4). Nonetheless, the network can finally tune to the input (see n = 3).

Figure 2:

Dynamics of membrane potential and ambient GABA concentration. (A) Control condition (CR). Top: Membrane potentials recorded from P cells belonging to respective cell assemblies (). Bottom: Ambient GABA concentrations around P cells. (B) Schizophrenic condition (SZ). All conventions are identical to those in panel A. (C) Stimulus-evoked neuronal (population-averaged P cell firing) activities recorded in respective cell assemblies () of the control network (open bars) or the schizophrenia network (filled bars).

Figure 2:

Dynamics of membrane potential and ambient GABA concentration. (A) Control condition (CR). Top: Membrane potentials recorded from P cells belonging to respective cell assemblies (). Bottom: Ambient GABA concentrations around P cells. (B) Schizophrenic condition (SZ). All conventions are identical to those in panel A. (C) Stimulus-evoked neuronal (population-averaged P cell firing) activities recorded in respective cell assemblies () of the control network (open bars) or the schizophrenia network (filled bars).

As shown in Figure 2A (bottom), the cessation of firing in the stimulus-irrelevant P cells arises largely from the enhanced ambient GABA-mediated tonic inhibition (see the traces marked by ). Interestingly, the ambient GABA concentration around the stimulus-relevant P cells is reduced (see the trace marked by n = 3), ensuring their responsiveness to the stimulus. As will be shown in Figure 3, the elevation of ambient GABA concentration arises from GABA export through glial membrane depolarization triggered by P-to-glia excitation, while the reduction of ambient GABA concentration arises from GABA import (removal) through glial membrane hyperpolarization triggered by Ia-to-glia inhibition.

Figure 3:

Gliotransmission-mediated regulation of local ambient GABA levels for efficient sensory tuning. (A) Responses of a stimulus-irrelevant P cell (n = 7: top) and a stimulus-relevant P cell (n = 3: middle). Ambient GABA concentrations around them are shown (bottom). (B) Responses of a stimulus-irrelevant glial cell (n = 7: top) and a stimulus-relevant glial cell (n = 3: bottom). uGlrev is the reversal potential of GABA transporter.

Figure 3:

Gliotransmission-mediated regulation of local ambient GABA levels for efficient sensory tuning. (A) Responses of a stimulus-irrelevant P cell (n = 7: top) and a stimulus-relevant P cell (n = 3: middle). Ambient GABA concentrations around them are shown (bottom). (B) Responses of a stimulus-irrelevant glial cell (n = 7: top) and a stimulus-relevant glial cell (n = 3: bottom). uGlrev is the reversal potential of GABA transporter.

Figure 2B shows membrane potentials (top) and ambient GABA concentrations (bottom) in a schizophrenia network. The value of GABA transfer coefficient (see TGl in equation C.1 and Table 1) was decreased from to , which may correspond to transporter-deficient glial cells. This causes a deficit in GABAergic gliotransmission, impairing ambient GABA augmentation (see the bottom traces). Due to the insufficient increase in ambient GABA levels, the stimulus-irrelevant P cells continue firing throughout the stimulation period (see the traces for n = 2, 4 at the top). Figure 2C shows stimulus-evoked neuronal (population-averaged P cell firing) activities recorded in respective cell assemblies () of the control network (open rectangles) or the schizophrenia network (filled rectangles). These results indicate that the tuning performance of the schizophrenia network is deteriorated compared to the control network.

We explain how the selective responsiveness (sensory tuning performance) of the control network could be ensured in the control network. Figure 3A shows the responses of a stimulus-irrelevant P cell (n = 7: top) and a stimulus-relevant P cell (n = 3: middle). Ambient GABA concentrations around them are shown (bottom), indicating that the concentration around the stimulus-irrelevant P cell is augmented and the concentration around the stimulus-relevant P cell is reduced. These concentration changes are made through GABA export and import by transporters on glial cells (see Figure 1C).

When presented with sensory feature stimulus f3, P cells corresponding to the stimulus receive input current (see the arrow in the inset of Figure 3B). These stimulus-relevant P cells send action potentials to glial cells belonging to other cell assemblies (: e.g., see n = 7 in the inset) and activate them (see the small dashed oval in the inset). As shown in Figure 3B (see the top trace for n = 7), these glial cells are depolarized (see the large dashed oval) and cross the reversal potential of transporter (uGlrev). This triggers GABA export and augments ambient GABA around the stimulus-irrelevant P cells (see the bottom trace marked by n = 7 in Figure 3A).

The stimulus-relevant P cells send their axons to interneurons (Ia cell: see n = 3 in the inset) and activate them, which then inhibit glial cells (see the small dashed rectangle in the inset). As shown in Figure 3B (see the bottom trace for n = 3), these glial cells are hyperpolarized (see the large dashed rectangle) and cross the reversal potential of transporter (uGlrev). This triggers GABA import and reduces ambient GABA around the stimulus-relevant P cells (see the bottom trace marked by n = 3 in Figure 3A). These results indicate that the gliotransmission-mediated regulation of local ambient GABA levels ensures the selective responsiveness of the network to the applied feature stimulus: suppressing the firing of stimulus-irrelevant P cells (see the top trace in Figure 3A) while enhancing the firing of stimulus-relevant P cells (see the second trace in Figure 3A). Note that ambient GABA molecules act on extrasynaptic GABAa receptors, thereby providing tonic inhibitory current for P cells (see Figure 1C).

Figures 4A and 4B show how the two types of neuron-to-glia (P-to-glia, Ia-to-glia) signaling contribute to the neuronal responsiveness (top) and the modulation of local ambient GABA levels (bottom). If the P-to-glia circuit is cut off, ambient GABA cannot be augmented (see Figure 4A, bottom). This deteriorates the tuning performance of the network (see Figure 4A, top). If the Ia-to-glia circuit is cut off, ambient GABA around the stimulus-relevant P cells cannot be reduced (see Figure 4B, bottom), which is fatal to their responsiveness to the stimulus (see n = 3 at the top of Figure 4B). These results indicate that the P-to-glia and Ia-to-glia signaling contribute to the regulation of global and local levels of ambient GABA, respectively. Their combination is essential for improving the tuning performance of the network.

Figure 4:

Influences of neuron-glia signaling on membrane potential and ambient GABA concentration. (A) P-to-glia circuit was cut off. Top: Membrane potentials recorded from P cells belonging to respective cell assemblies (). Bottom: Ambient GABA concentrations around P cells. (B) Ia-to-glia circuit was cut off. All conventions are identical to those in panel A.

Figure 4:

Influences of neuron-glia signaling on membrane potential and ambient GABA concentration. (A) P-to-glia circuit was cut off. Top: Membrane potentials recorded from P cells belonging to respective cell assemblies (). Bottom: Ambient GABA concentrations around P cells. (B) Ia-to-glia circuit was cut off. All conventions are identical to those in panel A.

3.2.  Enhancement of Sensory Tuning by GABAergic Gliotransmission.

In this section, we show how impairment in augmenting ambient GABA concentration due to a deficit in GABAergic gliotransmission causes a broadening of sensory tuning in a schizophrenia network. Figure 5A shows the dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity (top) and ambient GABA concentration (bottom) on GABA transfer coefficient (TGl: see equation C.1 and Table 1), recorded in each cell assembly (). These results indicate that the larger the transfer coefficient value, the greater the suppression of stimulus-irrelevant P cell activities, for which the augmentation of ambient GABA is responsible (bottom; see ). Interestingly, the level of ambient GABA around stimulus-relevant P cells can be kept low (bottom; see n = 3), which ensures their responsiveness (top; see n = 3).

Figure 5:

Tuning performance of the network improved by GABAergic gliotransmission. (A) Top: Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on GABA transfer coefficient (TGl: see equation C.1 and Table 1), recorded in each cell assembly (). Bottom: Dependence of ambient GABA concentration on TGl. (B) Dependence of stimulus-evoked neuronal activity and ambient GABA concentration on TGl in which the P-to-glia circuit was cut off (see Figure 1). (C) Dependence of stimulus-evoked neuronal activity and ambient GABA concentration on TGl in which the Ia-to-glia circuit was cut off. (D) Relationship between feature bias (FB: see equation 3.1) and maximal ambient GABA concentration ([GABA]maxext: see equation 3.2). The open and filled circles represent those shown in panels A and C, respectively, and the diamonds those in panel B. CR and SZ denote the control and schizophrenia networks, respectively.

Figure 5:

Tuning performance of the network improved by GABAergic gliotransmission. (A) Top: Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on GABA transfer coefficient (TGl: see equation C.1 and Table 1), recorded in each cell assembly (). Bottom: Dependence of ambient GABA concentration on TGl. (B) Dependence of stimulus-evoked neuronal activity and ambient GABA concentration on TGl in which the P-to-glia circuit was cut off (see Figure 1). (C) Dependence of stimulus-evoked neuronal activity and ambient GABA concentration on TGl in which the Ia-to-glia circuit was cut off. (D) Relationship between feature bias (FB: see equation 3.1) and maximal ambient GABA concentration ([GABA]maxext: see equation 3.2). The open and filled circles represent those shown in panels A and C, respectively, and the diamonds those in panel B. CR and SZ denote the control and schizophrenia networks, respectively.

As shown in Figure 5B, if the P-to-glia circuit is cut off, the neuronal responses show no significant change (top), which is due largely to the lower modulation of ambient GABA levels (bottom). If the Ia-to-glia circuit is cut off, the lower level of ambient GABA around the stimulus-relevant P cells cannot be ensured (see the open circle for n = 3 at the bottom of Figure 5C), and thus their responses to the stimulus are depressed (see the open circle for n = 3 at the top of Figure 5C). These results indicate that the GABAergic gliotransmission mechanism works for improving sensory tuning performance.

To quantitatively evaluate the tuning performance of the network, we measured feature bias, defined by
formula
3.1
R(k) is the firing rate of a P cell when presented with feature stimulus fk (). FB is a measure similar to orientation bias (OB) that is used for visual systems such as lateral geniculate nucleus (Xu, Ichida, Shostak, Bonds, & Casagrande, 2002) and primary visual cortex (Leventhal, Thompson, Liu, Zhou, & Ault, 1995). We briefly explain it. Responses of a cell to different orientations (angles) of a bar stimulus are stored as a series of vectors. The vectors are added and divided by the sum of the absolute values of the vectors. The angle and the length of the resultant vector provide, respectively, the preferred direction and the degree of orientation preference of that cell. The degree of orientation preference is termed orientation bias (OB). Since the periodicity of orientation is , these angles are multiplied by a factor of two. As a consequence, OB ranges from 0 to 1.0, with 0 being completely insensitive to any orientation and 1.0 responding to only one orientation.
Figure 5D shows a relationship between feature bias (FB) and maximal ambient GABA concentration, defined as
formula
3.2
where [GABA]avgext(n) is average ambient GABA concentration in cell assembly n. CR and SZ denote the control () and schizophrenia () networks, respectively (see the open circles). The reduction of ambient GABA concentration in the schizophrenia network results in deteriorating the sensory tuning performance (see the open circle marked by SZ). Note that without P-to-glia signaling, ambient GABA is not augmented and thus the sensory tuning performance cannot be improved (see the diamonds). Without Ia-to-glia signaling, we found no significant improvement in sensory tuning even with ambient GABA augmented (see the filled circles).

3.3.  Significance of GABAergic Gliotransmission in Sensory Tuning.

In this section, we show how the depression of intracortical inhibition due to deficits in other possible GABAergic inhibitory mechanisms affects the sensory tuning performance. Figure 6A shows the dependence of stimulus-evoked P cell activity (top) and ambient GABA concentration (bottom) on basal ambient GABA concentration ([GABA]0ext: see equation C.1 and Table 1). GABA transporters were completely removed by setting TGl=0. The increase in basal ambient GABA concentration leads to overall neuronal depression, where we found a small improvement in sensory tuning at [GABA]maxext = 1 M, as shown in Figure 6B (see the triangles). It is far below that achieved by the GABAergic gliotransmission mechanism (see the circles).

Figure 6:

Tuning performance of the network without GABA transport. (A) Top: Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on basal ambient GABA concentration ([GABA]0ext: see equation C.1 and Table 1). TGl=0 was set. Bottom: Dependence of ambient GABA concentration on [GABA]0ext. (B) Relationship between feature bias (FB) and maximal ambient GABA concentration ([GABA]maxext: see the triangles). The circles are identical to those in Figure 5D.

Figure 6:

Tuning performance of the network without GABA transport. (A) Top: Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on basal ambient GABA concentration ([GABA]0ext: see equation C.1 and Table 1). TGl=0 was set. Bottom: Dependence of ambient GABA concentration on [GABA]0ext. (B) Relationship between feature bias (FB) and maximal ambient GABA concentration ([GABA]maxext: see the triangles). The circles are identical to those in Figure 5D.

In the primary sensory cortex, a phasic inhibitory mechanism between neuronal columns plays a major role in tuning to a feature stimulus. Hence, we tried to see how the lateral inhibitory (Ib-to-P; see Figure 1A) circuit affects the tuning performance of the network. Figure 7A shows the dependence of stimulus-evoked P cell activity on the weight of Ib-to-P connection (see wP.Ibij in equation A.3 and Table 1). GABA transporters and GABA molecules in the extracellular space were completely removed by setting TGl=0 and [GABA]0ext=0. As shown in Figure 7B (see the squares), we found a significant improvement in sensory tuning as the connection weight increases. Yet it is still below that achieved by the GABAergic gliotransmission mechanism (see the circles).

Figure 7:

Tuning performance of the network achieved solely through phasic inhibition. (A) Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on Ib-to-P connection weight (see wP,Ibij in equation A.3 and Table 1). TGl=0 and [GABA]0ext=0 were set. (B) Relationship between feature bias (FB) and Ib-to-P connection weight (wP,Ibij: see the squares). The circles are identical to those in Figure 5D.

Figure 7:

Tuning performance of the network achieved solely through phasic inhibition. (A) Dependence of stimulus-evoked neuronal (population-averaged P cell firing) activity on Ib-to-P connection weight (see wP,Ibij in equation A.3 and Table 1). TGl=0 and [GABA]0ext=0 were set. (B) Relationship between feature bias (FB) and Ib-to-P connection weight (wP,Ibij: see the squares). The circles are identical to those in Figure 5D.

Figure 8 shows in more detail how these different GABAergic inhibitory mechanisms (see Figures 5, 6, and 7) affect stimulus-evoked neuronal activity. The GABAergic gliotransmission mechanism can suppress stimulus-irrelevant P cell activities (see ), while maintaining (or even enhancing) the stimulus-relevant P cell activity (see the arrow for n = 3). As shown in Figure 8B (top), without P-to-glia signaling, the network shows no significant change in neuronal responses. As shown in Figure 8B (bottom), without Ia-to-glia signaling, the network shows overall neuronal depression. As shown in Figures 8C and 8D, the other possible intracortical inhibitory mechanisms (see Figures 6 and 7) suppress the stimulus-irrelevant P cell activities but cannot maintain the stimulus-relevant P cell activity (see n = 3 in Figures 8C and 8D).

Figure 8:

Changes in stimulus-evoked neuronal activity under different intracortical inhibitory conditions. (A) Control and schizophrenia conditions: see Figure 5A. The GABA transfer coefficient (see TGl in equation C.1) was varied between and . (B) Impaired GABAergic gliotransmission conditions. The P-to-glia (top) or Ia-to-glia (bottom) circuit was cut off: see Figures 5B and 5C. (C) Constant tonic inhibitory condition. GABA transporters were removed: see Figure 6. The basal ambient GABA concentration ([GABA]0ext) was varied between 0 and 3 M. (D) Phasic inhibitory condition: see Figure 7. Ambient GABA was not considered. The Ib-to-P connection weight (wP,Ibij) was varied between 0 and 6.

Figure 8:

Changes in stimulus-evoked neuronal activity under different intracortical inhibitory conditions. (A) Control and schizophrenia conditions: see Figure 5A. The GABA transfer coefficient (see TGl in equation C.1) was varied between and . (B) Impaired GABAergic gliotransmission conditions. The P-to-glia (top) or Ia-to-glia (bottom) circuit was cut off: see Figures 5B and 5C. (C) Constant tonic inhibitory condition. GABA transporters were removed: see Figure 6. The basal ambient GABA concentration ([GABA]0ext) was varied between 0 and 3 M. (D) Phasic inhibitory condition: see Figure 7. Ambient GABA was not considered. The Ib-to-P connection weight (wP,Ibij) was varied between 0 and 6.

Figure 9A shows how the broadness of sensory input (see in equation A.5) affects the tuning performance: FB. As expected, the broader the sensory input, the smaller the FB values. Interestingly, this can be improved by GABAergic gliotransmission: TGl>0. Figure 9B presents changes in FB when the GABAergic gliotransmission mechanism works. Enhancement in FB becomes greater as the sensory input broadens (see the larger values). These results indicate that the GABAergic gliotransmission mechanism contributes to improving the tuning performance of the network.

Figure 9:

Improvement of tuning to broader sensory input by GABAergic gliotransmission. (A) Dependence of feature bias (FB) on the broadness of sensory input (: see equation A.5) and on the GABA transfer coefficient (TGl: see equation C.1). (B) FB improvement by GABAergic gliotransmission: TGl>0.

Figure 9:

Improvement of tuning to broader sensory input by GABAergic gliotransmission. (A) Dependence of feature bias (FB) on the broadness of sensory input (: see equation A.5) and on the GABA transfer coefficient (TGl: see equation C.1). (B) FB improvement by GABAergic gliotransmission: TGl>0.

3.4.  Spectral Analyses.

Figure 10A shows how the spectral distribution of membrane potential oscillation changes, depending on the value of GABA transfer coefficient TGl. For calculating the spectra, we recorded the local field potential, which is the sum of membrane potentials of all (20) P cells belonging to the stimulus-relevant cell assembly (n = 3). Figure 10B (left) shows a relationship between TGl and ambient GABA concentration ([GABA]maxext: see equation 3.2). Figure 10B (right) shows a relationship between ambient GABA concentration and the population-averaged firing rate recorded from stimulus-relevant P cells, indicating that the stimulus-evoked spiking activity is elevated as the level of ambient GABA increases.

Figure 10:

Dependence of field potential spectral distribution on ambient GABA concentration. (A) Power spectra. The value of the GABA transfer coefficient (see TGl in equation C.1) was varied between and . (B) Left: Relationship between TGl and ambient GABA concentration ([GABA]maxext: see equation 3.2). Right: Relationship between ambient GABA concentration and population-averaged firing rate of stimulus-relevant P cells.

Figure 10:

Dependence of field potential spectral distribution on ambient GABA concentration. (A) Power spectra. The value of the GABA transfer coefficient (see TGl in equation C.1) was varied between and . (B) Left: Relationship between TGl and ambient GABA concentration ([GABA]maxext: see equation 3.2). Right: Relationship between ambient GABA concentration and population-averaged firing rate of stimulus-relevant P cells.

Figure 11 shows how the level of ambient GABA affects the dominant gamma-band oscillatory frequency (left) and its power (right), derived from the spectra shown in Figure 10. We found that a decrease in ambient GABA concentration leads to a decrease in dominant gamma-band oscillatory frequency (left) and a reduction in its power (right). Interestingly, the change in dominant frequency is large (15 Hz), compared to that in firing rate (5 Hz: see Figure 10B). This result indicates that ambient GABA affects gamma-band oscillatory neuronal behavior.

Figure 11:

Dependence of dominant gamma-band oscillatory frequency (left) and its power (right) on ambient GABA concentration ([GABA]maxext). They were derived from those in Figure 10.

Figure 11:

Dependence of dominant gamma-band oscillatory frequency (left) and its power (right) on ambient GABA concentration ([GABA]maxext). They were derived from those in Figure 10.

The GABAergic system is known to be impaired in schizophrenia (Lewis, Hashimoto, & Volk, 2005). A simulation study by Volman, Behrens, and Sejnowski (2011) showed that parvalbumin-deficient cortical GABAergic interneurons in schizophrenia had increased asynchronous GABA release, which led to a reduction in gamma-band oscillatory power and a decrease in dominant oscillation frequency. This letter may provide another possible neuronal mechanism for the reduction in gamma-band neuronal oscillation observed in schizophrenia (Gallinat, Winterer, Herrmann, & Senkowski, 2004; Light et al., 2006; Ferrarelli et al., 2008; Spencer, Niznikiewicz, Shenton, & McCarley, 2008).

3.5.  Influence of Neuronal Circuitry Architecture.

Figure 12A shows changes in neuronal responses if the P-glia projection was made in an unselective manner (see the triangles). Namely, the P-to-glia projection was made not only between but also within cell assemblies (). The circles express those obtained under the original (selective) circuitry condition: the P-to-glia projection was made only between different cell assemblies. The unselective P-to-glia circuitry condition leads to an increase in tonic inhibitory current in stimulus-relevant P cells and thus to depressing the stimulus-evoked activity (see the open triangle for n = 3), compared to the selective circuitry condition (see the open circle for n = 3).

Figure 12:

Influences of neuronal circuitry architecture. (A) Dependence of neuronal (population-averaged P cell) responses (firing rates) on P-glia circuitry architecture. The P-to-glia projection was made not only between but also within cell assemblies (see the triangles): an unselective circuitry condition. The circles denote those obtained under the original (selective) circuitry condition. Namely, the P-to-glia projection was made only between different cell assemblies. The open and filled symbols denote the control (CR) and schizophrenia (SZ) networks, respectively. (B) Dependence of feature bias (FB) on the synaptic weight between P cell's axon and its own dendrite (see the dashed square in the inset). The open and filled circles denote the control (CR) and schizophrenia (SZ) networks, respectively.

Figure 12:

Influences of neuronal circuitry architecture. (A) Dependence of neuronal (population-averaged P cell) responses (firing rates) on P-glia circuitry architecture. The P-to-glia projection was made not only between but also within cell assemblies (see the triangles): an unselective circuitry condition. The circles denote those obtained under the original (selective) circuitry condition. Namely, the P-to-glia projection was made only between different cell assemblies. The open and filled symbols denote the control (CR) and schizophrenia (SZ) networks, respectively. (B) Dependence of feature bias (FB) on the synaptic weight between P cell's axon and its own dendrite (see the dashed square in the inset). The open and filled circles denote the control (CR) and schizophrenia (SZ) networks, respectively.

The value of the GABA transfer coefficient (see TGl in equation C.1 and Table 1) was changed from (control network: CR, see the open triangles), to (schizophrenia network: SZ, see the filled triangles), and the tuning performance was evaluated. We came to the same conclusion: a reduction in ambient GABA concentration due to a deficit in GABAergic gliotransmission deteriorates the tuning performance of the schizophrenia network (see the filled triangles) compared to the control network (see the open triangles).

Another specific circuitry that we hypothesized was the selective P-to-Ib projection between different cell assemblies. This circuitry was employed in order to enhance intracortical lateral inhibition in a phasic manner, suppressing stimulus-irrelevant P cell activities, especially at the stimulus onset (Hoshino, 2012). To examine how this specific circuitry condition affects the sensory tuning performance, we carried out an additional simulation in which the P-to-Ib projection was made not only between but also within cell assemblies (). We observed the deterioration of sensory tuning performance (not shown). The specific circuitry architecture enabled the network to achieve optimal performance, by which we could clearly show how the GABAergic gliotransmission mechanism contributes to tuning to sensory input.

In another simulation, we investigated whether and how autapses on principal (P) cells affect the tuning performance of the network. Figure 12B shows how the synaptic weight between a P cell's axon and its own dendrite (see the dashed square in the inset) affects the tuning performance evaluated by feature bias (FB): see equation 3.1. Strengthening the weight significantly enhances the tuning performance of the schizophrenia (see the filled circles) but not the control (see the open circles) network. This result indicates that the deterioration of tuning performance of the schizophrenia network can be overcome to some degree by strengthening autaptic synapses.

Note that in the schizophrenia network, the ambient GABA concentration around stimulus-relevant P cells is not reduced due to the deficient GABAergic gliotransmission via Ia-to-glia circuitry (see the inset). Hence, ambient GABA-mediated tonic inhibitory current in these P cells is not to be reduced. This results in a lower FB value for the schizophrenia network (see the filled arrow). Interestingly, the autapses on P cells could compensate for this high tonic inhibitory current by increasing the phasic excitatory current (see the dashed square in the inset), thereby improving FB (see the open arrow).

4.  Discussion

As a possible cause of depression of intracortical inhibition in schizophrenia, we speculated transporter-deficient glial cells. This led to a deficit in GABAergic gliotransmission and thus to a reduction in ambient GABA concentration. Other possible causes might include reductions of glutamate decarboxylase (GAD: an enzyme to catalyze the synthesis of GABA) and GABAergic interneurons, whose influences on sensory tuning were partly shown (see Figures 6 and 7). This letter showed that a reduction in ambient GABA concentration due to a deficit in GABAergic gliotransmission markedly deteriorated the tuning performance of the network (see the open circles in Figure 5D).

We showed that the GABAergic gliotransmission mechanism could regulate local ambient GABA levels. Namely, it augmented ambient GABA around stimulus-irrelevant principal cells while reducing ambient GABA around stimulus-relevant principal cells (see Figure 5A, bottom), thereby ensuring their selective responsiveness to the applied feature stimulus. The GABAergic gliotransmission mechanism proposed here may have an important role in the regulation of local ambient GABA levels, thereby improving the sensory tuning performance of the cortex.

The P-glia coupling had a role in increasing a level of ambient GABA around stimulus-irrelevant P cells. The Ia-glia coupling had a role in decreasing a level of ambient GABA around stimulus-relevant P cells. These couplings achieved combinatorial regulation of local ambient GABA levels, by which we could investigate whether and how the poor control of ambient GABA concentration due to deficient GABAergic gliotransmission leads to the deterioration of sensory tuning performance as observed in schizophrenic patients (Rojas et al., 2007; Yoon et al., 2010; Rokem et al., 2011). To the best of our knowledge, these specific couplings 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.

As is well known, GABAa receptors mediate both phasic and tonic inhibition in the cortex. It has been suggested that in addition to the alteration of intrasynaptic GABA-mediated phasic inhibition, the alteration of extrasynaptic (ambient) GABA-mediated tonic inhibition has significant relevance to schizophrenia (for a review, see Hines, Davies, Moss, & Maguire, 2012). A decrease in tonic inhibition is expected when ambient GABA levels are decreased in the visual cortex with schizophrenia (Yoon et al., 2010; Rokem et al., 2011). A decrease in tonic inhibition is also expected when the expression of extrasynaptic GABAa receptor subunits such as the subunit is decreased in cortices including the primary visual cortex with schizophrenia (Hashimoto et al., 2008). In this letter, we showed that a reduction in tonic GABA strength due to deficient gliotransmission resulted in the reduced ability of the network to tune to an applied sensory stimulus (see Figure 5). We suggest that in addition to the phasic GABA mechanism, the gliotransmission-mediated, tonic GABA mechanism, proposed here, may be another critical component in etiology of schizophrenia.

Although discussed in detail in our previous study (Hoshino, 2012), we briefly address some important approximations and limitations of the the neural network model presented here. Glial cells might have a role in regulating extracellular concentrations of transmitters (GABA, glutamate), ions (potassium, hydrogen, calcium) and metabolites (ATP) (Fields & Stevens-Graham, 2002; Newman, 2003; Hansson & Rönnbäck, 2003; Verkhratsky, 2010). In this letter, we focused on investigating how ambient GABA-mediated intracortical inhibition affects sensory tuning performance. We could model a glial plasma membrane transporter that regulates an ambient GABA level (Hoshino, 2012), because the mechanism of GABA transport has been theoretically explained (Richerson & Wu, 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 et al., 2006; Angulo et al., 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 tuning 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 sensory tuning, 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 the 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 the presynaptic action potentials of the jth Ib cell and Ia cell, respectively. rPi,ext(n; t) is the fraction of extrasynaptic GABAa receptors in the open state provoked by ambient GABA. Receptor dynamics and ambient GABA concentration dynamics are defined in appendixes  B and  C, respectively. For these parameters, see Table 1.

Appendix B:  Dynamics of Receptor 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 ms 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 these parameters, see our previous studies (Hoshino, 2009, 2010, 2011a, 2011b, 2013) and 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 these parameters, see our previous study (Hoshino, 2012) and Table 1.

Acknowledgments

I express my gratitude to Takeshi Kambara, Masayoshi Naito, and Naoki Tanaka for their helpful discussions and to reviewers for giving me valuable comments and suggestions.

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