Abstract

Activities of sensory-specific cortices are known to be suppressed when presented with a different sensory modality stimulus. This is referred to as cross-modal inhibition, for which the conventional synaptic mechanism is unlikely to work. Interestingly, the cross-modal inhibition could be eliminated when presented with multisensory stimuli arising from the same event. To elucidate the underlying neuronal mechanism of cross-modal inhibition and understand its significance for multisensory information processing, we simulated a neural network model. Principal cell to and GABAergic interneuron to glial cell projections were assumed between and within lower-order unimodal networks (X and Y), respectively. Cross-modality stimulation of Y network activated its principal cells, which then depolarized glial cells of X network. This let transporters on the glial cells export GABA molecules into the extracellular space and increased a level of ambient (extrasynaptic) GABA. The ambient GABA molecules were accepted by extrasynaptic GABAa receptors and tonically inhibited principal cells of the X network. Cross-modal inhibition took place in a nonsynaptic manner. Identical modality stimulation of X network activated its principal cells, which then activated interneurons and hyperpolarized glial cells of the X network. This let their transporters import (remove) GABA molecules from the extracellular space and reduced tonic inhibitory current in principal cells, thereby improving their gain function. Top-down signals from a higher-order multimodal network (M) contributed to elimination of the cross-modal inhibition when presented with multisensory stimuli that arose from the same event. Tuning into the multisensory event deteriorated if the cross-modal inhibitory mechanism did not work. We suggest that neuron-glia signaling may regulate local ambient GABA levels in order to coordinate cross-modal inhibition and improve neuronal gain function, thereby achieving reliable perception of multisensory events.

1.  Introduction

There has been much evidence that neurons of sensory cortices can be activated by stimuli from different sensory modalities. A human brain imaging study (Calvert et al., 1997) showed that linguistic visual cues were sufficient to activate auditory cortex in the absence of auditory speech sounds. Neuromagnetic responses were recorded over the left hemisphere, in which auditory stimuli (syllables) were presented together with videotaped face articulation (Sams et al., 1991). The researchers found that visual information from articulatory movements has an entry into the auditory cortex. These studies suggest that sensory-specific cortices could be activated by stimuli from other senses. This is known as cross-modal excitation and presumably contributes to the perceptual amplification of multisensory events.

In contrast, cross-modal inhibition operates to suppress activities of sensory-specific cortices when presented with a different sensory modality stimulus in order to reduce distracting neuronal activity, thereby presumably increasing the salience of a specific unisensory event. Laurienti and colleagues’ (2002) functional magnetic resonance imaging (fMRI) study demonstrated that ongoing-spontaneous neuronal activity in visual cortex was suppressed by auditory stimulation (a white noise burst of 250 msec). They confirmed that neuronal activity in auditory cortex could be suppressed by visual stimulation (a black and white checkerboard for 250 msec) as well. Interestingly, cross-modal inhibition was eliminated when multisensory (visual, auditory) stimuli arising from the same event were presented to subjects.

The researchers suggested that the conventional synaptic mechanism is unlikely to work for the cross-modal inhibition because the operation of a local inhibitory circuit would induce a metabolically synaptic activity that is similar to an excitatory synaptic activity, as reflected in an increase in the fMRI signal. The result of the fMRI study could be understood as a reduction in the resting level of synaptic activity. Several important questions remain unanswered: What is the neuronal mechanism of cross-modal inhibition if the brain achieves it without using a local synaptic circuit? How could cross-modal inhibition be eliminated when presented with multisensory stimuli that arise from the same event? And what is the significance of cross-modal inhibition for multisensory information processing, in which is going to disappear?

Gamma-aminobutyric acid (GABA) is the major inhibitory neurotransmitter and mediates synaptic inhibition in a phasic manner by activating intrasynaptic GABA receptors, that is, GABA receptors in the synaptic cleft. It has been suggested that tonic inhibition takes place when extrasynaptic GABA molecules activate receptors on membranes outside synapses and that such nonsynaptic inhibition affects neuronal information processing (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). Extrasynaptic GABA receptors might include perisynaptic GABA receptors.

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 is maintained within a range of submicromolar to several micromolar levels (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 found in extrasynaptic membrane regions (Somogyi et al., 1989; Nusser et al., 1995; Brickley et al., 1996; Soltesz & Nusser, 2001) 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 (Bianchim, Haas, & Macdonald, 2001, 2002). This leads to tonic inhibition of neurons even at lower ambient GABA levels.

Glial plasma membrane transporters such as GAT-1, GAT-2, and GAT-3 are known to play an important role in regulating neuronal activity by modulating ambient GABA levels (Barakat & Bordey, 2002; Koch & Magnusson, 2009; Eulenburg & Gomeza, 2010). Experimental and theoretical studies by Richerson and colleagues (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007) suggest that the GABA transporter is not simply an importer removing GABA from the extracellular space. Instead, it operates in an ion-coupled manner, pursuing an equilibrium point that is determined by the stoichiometry of transporter, the concentration gradients of substrates, and the membrane potential. Under normal physiological conditions, a thermodynamic reaction cycle involves coupled translocation of two Na+ ions, one Cl ion, and one uncharged GABA molecule. The co-transported molecules (2Na+, Cl, GABA) cross the membrane together. The driving force for the coupled transport is the electrochemical potential, which is the sum of the electropotential and the chemical potential.

The reversal potential of transporter is the equilibrium membrane voltage of glial cells at which the value of electrochemical potential is equal to 0. Under normal conditions, the reversal potential was estimated to be 67.1 ± 6.47 mV for cultured hippocampal neurons (Wu et al., 2007), which we assume for modeling the transporter on glial cells. At membrane potentials below the reversal potential, net influx of GABA, called forward transport, takes place. If membrane potential is above the reversal potential, net efflux of GABA, called reverse transport, takes place. Through this transport mechanism, ambient GABA can be clamped at a certain level: within a submicromolar range at rest.

We propose here a neural network model with a glia-mediated ambient GABA regulatory system. The network consists of lower-order unimodal networks (X, Y) and a higher-order multimodal network (M), which are reciprocally connected by feedforward (bottom-up) and feedback (top-down) axonal projections. Principal cell to and GABAergic interneuron to glial cell projections are made between and within lower-order unimodal networks (X and Y), respectively. Cross-modality stimulation of Y network activates its principal cells, which then depolarizes glial cells of X network. This let GABA transporters on the glial cells export GABA molecules into the extracellular space and increase the level of ambient GABA. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit principal cells of the X network. Namely, cross-modal inhibition takes place in a nonsynaptic manner. Identical modality stimulation of X network activates its principal cells, which then activates interneurons and hyperpolarizes glial cells of the X network. This lets their transporters import (remove) GABA molecules from the extracellular space and reduce tonic inhibitory current in principal cells, thereby improving their gain function. Top-down signals from the M network affect the dynamic behavior of the X and Y networks.

In this study, we seek to elucidate how cross-modal inhibition takes place and how it could be eliminated when presented with multisensory stimuli arising from the same event. We also try to understand the significance of cross-modal inhibition for multisensory information processing.

2.  Neural Network Model

The neural network model is schematically shown in Figure 1A, where X and Y denote lower-order unimodal networks and M a higher-order multimodal network. We record responses from X neurons (see the gray region) while presenting an identical modality stimulus to the X network (see Xinp), presenting a cross-modality stimulus to the Y network (see Yinp) in order to see how cross-modal inhibition takes place, or presenting a pair of stimuli (Xinp, Yinp) to the respective X and Y networks in order to see how the perception of a multisensory event is processed. As shown in Figure 1B, populations of neurons (cell assemblies—see the ovals) are connected by selective bottom-up (feedforward: X, Y to M) and top-down (feedback: M to X, Y) projections. A set of cell assemblies responds (see the gray ovals) when presented with a pair of stimuli that arise from a multisensory event (X2-Y2).

Figure 1:

The neural network model. (A) Model structure. Two lower unimodal (X, Y) networks are bilaterally connected. One higher multimodal (M) network is connected with the two lower networks by bottom-up (feedforward) and top-down (feedback) projections. An identical modality stimulus (Xinp) and/or a cross-modality stimulus (Yinp) is presented, and the activities of the networks are recorded. (B) Projections between cell assemblies (the ovals). Only the projections for the cell assemblies relevant to an event n = 2 are shown for clarity. Multisensory stimuli that arise from the same event are presented to the lower networks (see X2 and Y2)

Figure 1:

The neural network model. (A) Model structure. Two lower unimodal (X, Y) networks are bilaterally connected. One higher multimodal (M) network is connected with the two lower networks by bottom-up (feedforward) and top-down (feedback) projections. An identical modality stimulus (Xinp) and/or a cross-modality stimulus (Yinp) is presented, and the activities of the networks are recorded. (B) Projections between cell assemblies (the ovals). Only the projections for the cell assemblies relevant to an event n = 2 are shown for clarity. Multisensory stimuli that arise from the same event are presented to the lower networks (see X2 and Y2)

As shown in Figure 2A, cell assemblies consist of principal cells (P), GABAergic interneurons (Ia, Ib), and glial cells (glia). Each cell assembly (Xn, Yn, Mn; 0 ⩽ n ⩽ 3) 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 the other modality (see the dashed lines). P cells receive an excitatory current as a sensory input (see the arrows).

Figure 2:

Neuronal circuitry. (A) Each cell assembly 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) A conceptual scheme of GABA import-export by glial transporters. P and Ia cells synaptically connect to a glial cell. Transporters that are distributed in the membrane of the glial cell import GABA molecules from or export them into the extracellular space. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

Figure 2:

Neuronal circuitry. (A) Each cell assembly 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) A conceptual scheme of GABA import-export by glial transporters. P and Ia cells synaptically connect to a glial cell. Transporters that are distributed in the membrane of the glial cell import GABA molecules from or export them into the extracellular space. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

We explain in more detail the target outputs of the feedforward and feedback circuits. For the feedforward circuit, P cells relevant to congruent unimodal events Xn and Yn send their outputs to the P cells relevant to the multimodal event Mn (Xn-Yn) but not to those irrelevant to it: (n' ≠ n). For the feedback circuit, P cells relevant to a multimodal event Mn (Xn-Yn) send their outputs to the P cells relevant to the congruent unimodal events (Xn and Yn) but not to those irrelevant to them: and (n’ ≠ n). For example, X2 and Y2 send their outputs to M2 but not to Mn (n ≠ 2), which provides an additive feedforward effect on M2 and no effect on Mn (n ≠ 2). M2 sends their output to X2 and Y2 but not to Xn and Yn (n ≠ 2), which provides a selective feedback effect on X2 and Y2 and no effect on Xn and Yn (n ≠ 2).

A conductance-based integrate-and-fire neuron model (Hoshino, 2006, 2008, 2009, 2010, 2011) is employed. A glia-mediated ambient GABA regulatory system is constructed. As shown in Figure 2B, transporters are distributed in the membrane of a glial cell and regulate the level of ambient GABA around a P cell. The extrasynaptic GABAa receptors accept ambient GABA molecules and tonically inhibit the 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:
Parameters and Their Values.
DescriptionParameterValue
Membrane capacitance of type K (K = P, Ia, Ib, glia) cell cKm  
Membrane conductance gKm  
Resting potential uKrest  
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 
Synaptic strength from jth to ith P cell within unimodal (Xn, Yn) and multimodal (Mn) cell assemblies   
Synaptic strength from jth Ib to ith P cell   
Feedback (top-down) synaptic strength from multimodal (Mn) jth to unimodal (Xn, Yn) ith P cell   
Feedforward (bottom-up) synaptic strength from unimodal (Xn, Yn) jth to multimodal (Mn) ith P cell   
Synaptic strength from ith P to Ia cell  wIa,Pi(Xn) = wIa,Pi(Yn) = 30 
Synaptic strength from ith P to Ib cell between different (n′ ≠ n) cell assemblies   
Synaptic strength from ith P to glial cell between X and Y networks   
Synaptic strength from ith Ia to glial cell  wGl,Iai(Xn) = wGl,Iai(Yn) = 8 
Amount of extrasynaptic GABAa receptors on type K (K = P, Ia, Ib) cell δK δP = 8 × 103, δIa = δIb = 1 × 104 
Sensory input current coefficient αP 880 pA 
Broadness of sensory input τP 
Channel opening rate for type Z (Z = AMPA, GABA) receptor αZ  
Channel closure rate βZ βAMPA = 190, βGABA = 180 
Steepness of sigmoid function for type K (K = P, Ia, Ib) cell ηK ηP = 220, ηIa = ηIb = 180 
Threshold of sigmoid function ζK ζP = −35 mV, ζIa = ζIb = −38 mV 
Decay constant for ambient GABA concentration γtrn 
Basal concentration [GABA]0ext 0.5 μM 
Maximal GABA concentration GABAmax 5 μM 
Minimal GABA concentration GABAmin 0 μM 
GABA transfer coefficient TGl 8 × 1011 
Reversal potential of transporter uGlrev −70 mV 
DescriptionParameterValue
Membrane capacitance of type K (K = P, Ia, Ib, glia) cell cKm  
Membrane conductance gKm  
Resting potential uKrest  
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 
Synaptic strength from jth to ith P cell within unimodal (Xn, Yn) and multimodal (Mn) cell assemblies   
Synaptic strength from jth Ib to ith P cell   
Feedback (top-down) synaptic strength from multimodal (Mn) jth to unimodal (Xn, Yn) ith P cell   
Feedforward (bottom-up) synaptic strength from unimodal (Xn, Yn) jth to multimodal (Mn) ith P cell   
Synaptic strength from ith P to Ia cell  wIa,Pi(Xn) = wIa,Pi(Yn) = 30 
Synaptic strength from ith P to Ib cell between different (n′ ≠ n) cell assemblies   
Synaptic strength from ith P to glial cell between X and Y networks   
Synaptic strength from ith Ia to glial cell  wGl,Iai(Xn) = wGl,Iai(Yn) = 8 
Amount of extrasynaptic GABAa receptors on type K (K = P, Ia, Ib) cell δK δP = 8 × 103, δIa = δIb = 1 × 104 
Sensory input current coefficient αP 880 pA 
Broadness of sensory input τP 
Channel opening rate for type Z (Z = AMPA, GABA) receptor αZ  
Channel closure rate βZ βAMPA = 190, βGABA = 180 
Steepness of sigmoid function for type K (K = P, Ia, Ib) cell ηK ηP = 220, ηIa = ηIb = 180 
Threshold of sigmoid function ζK ζP = −35 mV, ζIa = ζIb = −38 mV 
Decay constant for ambient GABA concentration γtrn 
Basal concentration [GABA]0ext 0.5 μM 
Maximal GABA concentration GABAmax 5 μM 
Minimal GABA concentration GABAmin 0 μM 
GABA transfer coefficient TGl 8 × 1011 
Reversal potential of transporter uGlrev −70 mV 

3.  Results

3.1.  Role of Cross-Modal Inhibition in Multisensory Information Processing.

Figure 3 shows raster plots of action potentials evoked in P cells of X, Y, and M networks. When an identical modality stimulus (X2) is presented to the X network, population responses are evoked (see X2 and M2). As shown in Figure 3B, multisensory stimuli that arise from the same event (X2-Y2) evoke population responses that are relevant to these stimuli. Figure 3C shows their activities (firing rates) when presented with the identical modality stimulus X2 (the white rectangles) or with the multisensory stimuli X2-Y2 (the gray rectangles). The activity of X2-relevant P cells is increased when presented together with the stimulus Y2 (the gray rectangle for X2). Namely, multisensory enhancement takes place. Top-down signals contribute to that enhancement, because it is abolished if the M-to-X projection is cut off (the black rectangle for X2).

Figure 3:

Neuronal responses. (A) Raster plots of action potentials evoked in P cells, when presented with an identical modality stimulus (X2). (B) Raster plots for multisensory stimulation (X2-Y2). (C) Evoked neuronal (P) activities, when presented with stimulus X2 (white rectangles), with multisensory stimuli X2-Y2 (the gray rectangles), or with the same multisensory stimuli in which the M-to-X projection was cut off (the black rectangles). (D) Evidence of cross-modal inhibition. Ongoing-spontaneous activity of X network (the shaded rectangles for Xn; 0 ⩽ n ⩽ 3) is suppressed by cross-modality stimulus Y2 (the black rectangles for Xn; 0 ⩽ n ⩽ 3).

Figure 3:

Neuronal responses. (A) Raster plots of action potentials evoked in P cells, when presented with an identical modality stimulus (X2). (B) Raster plots for multisensory stimulation (X2-Y2). (C) Evoked neuronal (P) activities, when presented with stimulus X2 (white rectangles), with multisensory stimuli X2-Y2 (the gray rectangles), or with the same multisensory stimuli in which the M-to-X projection was cut off (the black rectangles). (D) Evidence of cross-modal inhibition. Ongoing-spontaneous activity of X network (the shaded rectangles for Xn; 0 ⩽ n ⩽ 3) is suppressed by cross-modality stimulus Y2 (the black rectangles for Xn; 0 ⩽ n ⩽ 3).

Without these top-down signals, the Y2 cell assembly wins against X2 (compare the black rectangles for X2 and Y2). This might happen when the two dynamic cell assemblies compete through cross-modal inhibition. As shown in Figure 3D, the resting levels of synaptic activities, as reflected in ongoing-spontaneous firing rates (see the shaded rectangles for Xn; 0 ⩽ n ⩽ 3), are decreased by the cross-modality stimulus Y2 (the black rectangles for Xn; 0 ⩽ n ⩽ 3). This result evidences cross-modal inhibition.

To see whether and how the cross-modal inhibition contributes to the perception of the multisensory (X2-Y2) event, we cut off the P-to-gila projection. As shown in Figure 4A, the selective responsiveness of X and Y networks is blurred by the activation of stimulus-irrelevant P cells, which is quantitatively shown in Figure 4B (the black rectangles for Xn-Yn: n ≠ 2). This result indicates that the cross-modal inhibition contributes to tuning into the multisensory event. Note that these multisensory stimuli (X2Y2) can activate P cells that are irrelevant to these stimuli (XnYn: n ≠ 2) as well, because they receive a weak but significant (graded amount of) input current (see τP of equation A.6 in appendix  A and Table 1).

Figure 4:

Multisensory perceptual processing without cross-modal inhibition. (A) Raster plots of action potentials evoked in P cells, where the P-to-glia projection was cut off. Multisensory stimuli (X2-Y2) were presented to the respective (X and Y) networks. (B) Stimulus-evoked activity obtained for the intact (white rectangles) or impaired (black rectangles) P-to-glia circuitry.

Figure 4:

Multisensory perceptual processing without cross-modal inhibition. (A) Raster plots of action potentials evoked in P cells, where the P-to-glia projection was cut off. Multisensory stimuli (X2-Y2) were presented to the respective (X and Y) networks. (B) Stimulus-evoked activity obtained for the intact (white rectangles) or impaired (black rectangles) P-to-glia circuitry.

To elucidate how the sensory tuning could be improved, we measured ambient GABA concentration around a P cell for each cell assembly. As shown in Figure 5A (top), the augmentation of ambient GABA concentrations for stimulus-irrelevant cell assemblies (Xn, Yn: n ≠ 2) is greater than that for stimulus-relevant cell assemblies (X2, Y2). Since an increase in ambient GABA concentration leads to an increase in tonic inhibitory current, the greater increases in local ambient GABA concentrations for stimulus-irrelevant cell assemblies (see Figure 5A, top) are advantageous for the sensory tuning. As shown in Figure 5A (bottom), the activation of glial cells is responsible for the augmentation of ambient GABA concentrations. The Ia-to-glia signaling constrains the GABA augmentation for stimulus-relevant cell assemblies (see X2 and Y2 in Figure 5A, top) and improves the gain function of P cells, which will be quantitatively shown in Figure 5D (the circles).

Figure 5:

Regulation of local ambient GABA levels by glial transporter. (A) Top: Ambient GABA concentration around a P cell for each cell assembly. Ambient GABA concentrations are increased when stimulated. The traces for X2 and Y2 indicate that the augmentation of ambient GABA for stimulus-relevant cell assemblies is constrained. Bottom: Membrane potentials of glial cells. (B) Ambient GABA concentrations and membrane potentials of glial cells, where the P-to-glia projection was cut off. (C) Mean membrane potentials of glial cells during the stimulation period obtained for the intact (white rectangles) or impaired (black rectangles) P-to-glia circuitry. (D) Evoked neuronal (P) activity as a function of input current for the intact (the circles) or impaired (the squares) Ia-to-glia circuitry.

Figure 5:

Regulation of local ambient GABA levels by glial transporter. (A) Top: Ambient GABA concentration around a P cell for each cell assembly. Ambient GABA concentrations are increased when stimulated. The traces for X2 and Y2 indicate that the augmentation of ambient GABA for stimulus-relevant cell assemblies is constrained. Bottom: Membrane potentials of glial cells. (B) Ambient GABA concentrations and membrane potentials of glial cells, where the P-to-glia projection was cut off. (C) Mean membrane potentials of glial cells during the stimulation period obtained for the intact (white rectangles) or impaired (black rectangles) P-to-glia circuitry. (D) Evoked neuronal (P) activity as a function of input current for the intact (the circles) or impaired (the squares) Ia-to-glia circuitry.

As shown in Figure 5B, if the P-to-glia projection is cut off, the glial cells do not depolarize (bottom), and thus ambient GABA concentrations are unlikely to be augmented (top). This results in the poor sensory tuning (see Figure 4). In Figure 5C, the P-to-glia signaling depolarizes the glial cells (the white rectangles), thereby exporting GABA into the extracellular space (see Figure 5A, top). Note that the glial cells begins to export GABA when its membrane potential crosses the reversal potential: uGlrev = −70 mV (see equation C.1 in appendix  C).

To see whether and how the Ia-to-glia signaling works, we measured the gain (input-output relationship) of P cells of X network. A unisensory stimulus X2 was presented to the X network, and action potentials were recorded. Figure 5D presents evoked neuronal activity as a function of input current with (the circles) or without (the squares) Ia-to-glia signaling, indicating that the Ia-to-glia signaling can improve the gain function. Note that the activation of Ia cells by stimulus-relevant P cells hyperpolarizes glial cells, thereby importing GABA from the extracellular space. This leads to enhancing the activity of stimulus-relevant P cells and therefore improving the gain function.

Strengthening the P-to-Ib connection weight (i.e., enhancing the lateral inhibition) might compensate the poor sensory tuning due to the impairment of P-to-glia projection (see Figure 4 and Figure 6A, top). As expected, the sensory tuning is improved, when stimulus-irrelevant P cells become silent (see the bottom raster plots in Figure 6A). However, this treatment causes a fatal problem: deceleration of reaction speed to the sensory stimulation (compare the two dashed lines). As shown in Figure 6B (bottom), the ongoing-spontaneous membrane hyperpolarization caused by the enhancement of lateral inhibition (the dashed trace) might be responsible for that deceleration. Since membrane hyperpolarization corresponds functionally to an increase in firing threshold, it will lead to a delay to reach the firing threshold and therefore to the deceleration of reaction speed.

Figure 6:

Sensory tuning achieved solely by lateral inhibition. (A) Raster plots of action potentials evoked in P cells when presented with an identical modality stimulus (X2). Top: The P-to-glia projection was cut off. Bottom: The P-to-glia projection was cut off, and the weight of lateral inhibitory connection P(X)-to-Ib(X) was strengthened. (B) Membrane potentials recorded from a P cell. The P-to-glia projection was intact (top) or impaired (middle) in which the P(X)-to-Ib(X) connection weight was strengthened. The bottom is their overlaid traces.

Figure 6:

Sensory tuning achieved solely by lateral inhibition. (A) Raster plots of action potentials evoked in P cells when presented with an identical modality stimulus (X2). Top: The P-to-glia projection was cut off. Bottom: The P-to-glia projection was cut off, and the weight of lateral inhibitory connection P(X)-to-Ib(X) was strengthened. (B) Membrane potentials recorded from a P cell. The P-to-glia projection was intact (top) or impaired (middle) in which the P(X)-to-Ib(X) connection weight was strengthened. The bottom is their overlaid traces.

3.2.  Coordination of Cross-Modal Inhibition by Neuron-Glia Signaling.

As we noted in section 1, the conventional synaptic mechanism is unlikely to work for cross-modal inhibition. That is why we propose the glia-mediated nonsynaptic inhibitory mechanism. Nonetheless, we can see how the synaptic inhibitory mechanism operates, which might lead us to understand the significance of the hypothetical neuron-glia signaling for multisensory information processing.

To achieve cross-modal inhibition in a synaptic manner, we made projections from P cells of Y network to Ib cells of X network and vice versa (the dashed lines in Figure 7A) instead of the P-to-glia projection (the dashed lines in Figure 2A). Figure 7B shows raster plots of action potentials evoked in P cells when presented with multisensory stimuli X2-Y2. Figure 7C shows their firing rates when presented with an identical modality stimulus X2 (the white rectangles), with multisensory stimuli X2-Y2 (the gray rectangles) or with the same multisensory stimuli in which the M-to-X top-down projection was cut off (black rectangles). Responses of X2-relevant P cells are suppressed when presented together with the stimulus Y2 (see the gray rectangle for X2). Namely, cross-modal inhibition is not eliminated but still prevails, worsening the multisensory perceptual performance. Figure 7D shows that the ongoing-spontaneous activity of X network is suppressed by the cross-modality stimulus Y2 (the black rectangles for Xn; 0 ⩽ n ⩽ 3), whose level is almost identical to that of the glia-mediated (nonsynaptic) cross-modal inhibition (see Figure 3D).

Figure 7:

Multisensory perceptual processing achieved by synaptic cross-modal inhibition. (A) A neuronal circuit for synaptic cross-modal inhibition. Projections from P cells of the Y network to Ib cells of the X network and vice versa were made (the dashed lines) instead of the P-to-glia projection (see the dashed lines in Figure 2A). (B) Raster plots of action potentials evoked in P cells, when presented with multisensory stimuli X2-Y2. (C) Evoked neuronal (P) activities, when presented with an identical modality stimulus X2 (white rectangles), with multisensory stimuli X2-Y2 (gray rectangles) or with the same multisensory stimuli in which the M-to-X projection was cut off (black rectangles). (D) Evidence of cross-modal inhibition. Ongoing-spontaneous activity of X network (shaded rectangles for Xn; 0 ⩽ n ⩽ 3) is suppressed by a cross-modality stimulus Y2 (black rectangles for Xn; 0 ⩽ n ⩽ 3).

Figure 7:

Multisensory perceptual processing achieved by synaptic cross-modal inhibition. (A) A neuronal circuit for synaptic cross-modal inhibition. Projections from P cells of the Y network to Ib cells of the X network and vice versa were made (the dashed lines) instead of the P-to-glia projection (see the dashed lines in Figure 2A). (B) Raster plots of action potentials evoked in P cells, when presented with multisensory stimuli X2-Y2. (C) Evoked neuronal (P) activities, when presented with an identical modality stimulus X2 (white rectangles), with multisensory stimuli X2-Y2 (gray rectangles) or with the same multisensory stimuli in which the M-to-X projection was cut off (black rectangles). (D) Evidence of cross-modal inhibition. Ongoing-spontaneous activity of X network (shaded rectangles for Xn; 0 ⩽ n ⩽ 3) is suppressed by a cross-modality stimulus Y2 (black rectangles for Xn; 0 ⩽ n ⩽ 3).

Then the question is why the conventional synaptic mechanism cannot eliminate the cross-modal inhibition even when presented with the multisensory stimuli. To answer it, we investigated how these two (nonsynaptic and synaptic) mechanisms exert cross-modal inhibition. Figure 8A presents membrane potentials of a stimulus-relevant (the solid traces) and a stimulus-irrelevant (the dashed traces) P cell of X network recorded for the nonsynaptic (left) or synaptic (right) cross-modal inhibitory condition when presented with cross-modality stimulus Y2. The hyperpolarization of the stimulus-irrelevant (the dashed traces) P cell reflects the cross-modal inhibition. The stimulus-relevant P cell is transiently hyperpolarized, which is followed by depolarization below the firing threshold (the solid traces). Note that this subthreshold membrane depolarization, induced by top-down (excitatory) signals from multimodal cell assembly M2, might be essential for the multisensory enhancement (see Figures 3B and 3C).

Figure 8:

Influence of cross-modal inhibition on ongoing-spontaneous neuronal behavior. (A) Membrane potentials of a stimulus-relevant (solid traces) and a stimulus-irrelevant (dashed traces) P cell of X network recorded for the nonsynaptic (left) or synaptic (right) cross-modal inhibitory condition, when presented with a cross-modality stimulus Y2. The stimulus-irrelevant P cell is hyperpolarized (dashed traces). The stimulus-relevant P cell is depolarized below firing threshold after its transient hyperpolarization (solid traces). (B) Left: Distributions of ongoing-spontaneous membrane potentials of the P cells during the cross-modal stimulation period recorded for the nonsynaptic (solid traces) or synaptic (dashed traces) cross-modal inhibitory condition. Right: Their cumulative representations.

Figure 8:

Influence of cross-modal inhibition on ongoing-spontaneous neuronal behavior. (A) Membrane potentials of a stimulus-relevant (solid traces) and a stimulus-irrelevant (dashed traces) P cell of X network recorded for the nonsynaptic (left) or synaptic (right) cross-modal inhibitory condition, when presented with a cross-modality stimulus Y2. The stimulus-irrelevant P cell is hyperpolarized (dashed traces). The stimulus-relevant P cell is depolarized below firing threshold after its transient hyperpolarization (solid traces). (B) Left: Distributions of ongoing-spontaneous membrane potentials of the P cells during the cross-modal stimulation period recorded for the nonsynaptic (solid traces) or synaptic (dashed traces) cross-modal inhibitory condition. Right: Their cumulative representations.

Figure 8B presents distributions of ongoing-spontaneous membrane potentials of the P cells (left) during the cross-modal stimulation period (the horizontal bars of Figure 8A) obtained for the nonsynaptic (the solid traces) or synaptic (the dashed traces) cross-modal inhibitory condition. Their cumulative representations are shown in the right panel. We found that the conventional (synaptically mediated) inhibition causes frequent, transient, deep membrane hyperpolarization, which would break the persistent neuronal firing and thus lead to a decrease in stimulus-relevant P cell activity (the gray rectangle for X2 in Figure 7C). These results indicate that the P-to-glia signaling coordinates cross-modal inhibition in order to achieve reliable perception of multisensory events.

3.3.  Spatiotemporal Property of Glial-Neuronal Interaction.

To explore the issue of the spatiotemporal property of glial-neuronal interaction, we made additional simulations. Figure 9 shows overlaid membrane potentials of P cells of the X network when presented with a cross-modality stimulus Y2, recorded from 10 P cells (among 20 P cells) for each cell assembly (n= 0, 1, 2, 3) under the P-to-glia (original: nonsynaptic) (see Figure 9A) or P-to-Ib (alternative: synaptic) (see Figure 9B) cross-modal inhibitory condition (see Figures 2A and 7A, dashed lines). The cross-modality stimulus induces a synchronous reduction in cell assembly activity.

Figure 9:

Cross-modal inhibitory effect on populations of neurons. A cross-modality stimulus Y2 was presented and membrane potentials were recorded from 10 P cells (among 20 P cells) in the X network, whose overlaid representation is shown for each cell assembly (n = 0, 1, 2, 3). (A) Nonsynaptic cross-modal inhibition via P-to-glia (original) circuitry (see Figure 2A). (B) Synaptic cross-modal inhibition via P-to-Ib (alternative) circuitry (see Figure 7A).

Figure 9:

Cross-modal inhibitory effect on populations of neurons. A cross-modality stimulus Y2 was presented and membrane potentials were recorded from 10 P cells (among 20 P cells) in the X network, whose overlaid representation is shown for each cell assembly (n = 0, 1, 2, 3). (A) Nonsynaptic cross-modal inhibition via P-to-glia (original) circuitry (see Figure 2A). (B) Synaptic cross-modal inhibition via P-to-Ib (alternative) circuitry (see Figure 7A).

Figure 10A shows the temporal aspect of the membrane potential oscillatory behavior. Differences between membrane potentials with and without cross-modality stimulation are shown, where the P-to-glia (original: nonsynaptic) (top) or P-to-Ib (alternative: synaptic) (bottom) circuit was employed for exerting the cross-modal inhibitory effect. As shown in Figure 10B, their cumulative representations indicate that the cross-modal inhibition is slower in P-to-glia (the solid traces) than in P-to-Ib circuitry condition (the dashed traces).

Figure 10:

Temporal property of cross-modal inhibition. (A) Differences between membrane potentials with and without cross-modality stimulation. Top: Nonsynaptic cross-modal inhibition via P-to-glia (original) circuitry (see Figure 2A). Bottom: Synaptic cross-modal inhibition via P-to-Ib (alternative) circuitry (see Figure 7A). (B) Cumulative representations for A. The solid and dashed traces denote the nonsynaptic and synaptic cross-modal inhibitory conditions, respectively.

Figure 10:

Temporal property of cross-modal inhibition. (A) Differences between membrane potentials with and without cross-modality stimulation. Top: Nonsynaptic cross-modal inhibition via P-to-glia (original) circuitry (see Figure 2A). Bottom: Synaptic cross-modal inhibition via P-to-Ib (alternative) circuitry (see Figure 7A). (B) Cumulative representations for A. The solid and dashed traces denote the nonsynaptic and synaptic cross-modal inhibitory conditions, respectively.

4.  Discussion

To elucidate the underlying neuronal mechanism of cross-modal inhibition and understand its significance for multisensory information processing, we simulated a neural network model. Principal cell to and GABAergic interneuron to glial cell projections were assumed between and within lower-order unimodal networks (X and Y), respectively. Cross-modality stimulation of Y network activated its principal cells, which then depolarized the glial cells of the X network. This let transporters on the glial cells export GABA molecules into the extracellular space and increased a level of ambient GABA. The ambient GABA molecules were accepted by extrasynaptic GABAa receptors and tonically inhibited principal cells of the X network. Namely, cross-modal inhibition took place in a nonsynaptic manner.

Identical modality stimulation of X network activated its principal cells (P), which then activated GABAergic interneurons (Ia) and hyperpolarized glial cells of the X network. This let their transporters import (remove) GABA molecules from the extracellular space and reduced tonic inhibitory current in P cells, thereby improving their gain function. Top-down signals from a higher-order multimodal network (M) contributed to the elimination of the cross-modal inhibition when presented with multisensory stimuli that arose from the same event. Tuning into the multisensory event was deteriorated if the cross-modal inhibitory mechanism did not work. Cross-modal inhibition that was based on the conventional synaptic mechanism could not be eliminated even when provided with these top-down signals, worsening the perception of the multisensory event. We suggest that the neuron-glia signaling may regulate local ambient GABA levels in order to coordinate cross-modal inhibition and improve neuronal gain function, thereby achieving reliable perception of multisensory events.

To create a unified percept, it is necessary for the brain to integrate information from multiple senses. This ability, referred to as multisensory integration, is known to enhance the salience of perceptual events (Ghazanfar, Maier, Hoffman, & Logothetis, 2005; Ghazanfar & Schroeder, 2006; Stein & Stanford, 2008). Concerning its neuronal mechanisms, two (traditional and recent) views have been advocated (see Schroeder & Foxe, 2004, and Ghazanfar & Schroeder, 2006, for a review). In the traditional view, multisensory integration takes place within higher-order areas only after unisensory processing within lower-order areas. Classical higher-order multimodal areas include the superior temporal sulcus, intraparietal sulcus, and frontal cortex (Ghazanfar & Schroeder, 2006). Based on these studies, we assumed the projections between the lower (X, Y) and higher (M) networks.

For the recent view, Ramos-Estebanez and colleagues (2007) found optimal cross-modal interaction at an interstimulus delay of 60 msec: somatosensory stimulation precedes the visual one. The researchers suggested that this rapid modulatory effect would not be consistent with a top-down mechanism acting through higher-order multimodal (intraparietal) cortical areas, but rather a direct interaction between lower-order unimodal (visual and somatosensory) cortical areas or a bottom-up mechanism (e.g., from subcortical areas such as putamen and superior colliculus) might be responsible. In fact, direct projections between primary sensory cortical areas have been evidenced (Falchier, Clavagnier, Barone, & Kennedy, 2002; Rockland & Ojima, 2003; Cappe & Barone, 2005; Schroeder & Foxe, 2005). Based on their observations, we assumed the direct projections between the lower (X, Y) networks.

Our simulation result showed a similar rapid modulatory effect (see Figure 10). However, we do not have anatomical data that support the connectivity pattern between the X and Y networks. Namely, it is a hypothetical neuronal circuit that can explain how cross-modal interaction takes place in a nonsynaptic manner, which we hope will be experimentally evidenced in the future.

The number of neuron units (P, Ia, Ib, glia) was small (there were 20) but sufficient to deal with processing such a simple perceptual task: detection of a bimodal sensory event. We investigated here how cross-modal inhibition can take place without using a conventional local synaptic inhibitory circuit, especially focusing on elucidating its underlying neuronal mechanism and understanding its significance for multisensory information processing. This study may contribute to the construction of neural networks by which biophysical studies that focus on some specific aspect of multisensory interaction will be made.

We employed two distinct GABAergic interneurons Ia and Ib. The Ia cell has a role in hyperpolarizing glial cells, thereby importing GABA molecules from the extracellular space and improving the gain function of P cells. The Ib cell has a role in inhibiting stimulus-irrelevant P cells while stimulus-relevant P cells are being active, thereby improving the sensory tuning. A variety of GABAergic interneurons has been found in the cortex, such as large, medium, and small-sized multipolar cells. (For a survey, see Prieto, Peterson, & Winer, 1994.) Large multipolar cells with their wide axonal arbors can send signals to distant cells, while small multipolar cells with their narrow axonal arbors 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 cell assemblies and the Ia cell (as small multipolar cell) to its proximal glial cell.

An additional population of interneurons may achieve similar functionality (cross-modal inhibition) as the glial cells. However, many more interneurons with extremely weak synaptic weights would be required for eliminating the deep hyperpolarization components (see Figure 8) that arise from the phasic (synaptic) inhibition. This may lead to inefficient multisensory information processing, because the brain has to consume more metabolic energy to execute the synaptic inhibition due to the increased number of interneurons. Note that such deep membrane hyperpolarization is disadvantageous for a stable response to a sensory stimulus because it breaks stimulus-evoked persistent neuronal firing (see the gray rectangles marked by X2 in Figure 7C).

Concerning the neuron-glia signaling, a variety of neuron-glia circuits has 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 assumed the excitatory (P-to-glia) and inhibitory (Ia-to-glia) neuron-to-glia synaptic contacts. Note that the 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).

To see how the network responds if the glial cells are activated not only by interneurons but also by principal cells, we made an additional simulation. As shown in Figure 11A (the thick dashed lines), principal-to-glial-cell (P-to-glia) connections were made between different cell assemblies within unimodal (X, Y) networks. Multisensory stimuli (X2, Y2) were presented during which firing rate and ambient GABA concentration were recorded. As shown in Figure 11B (left), activation of stimulus-irrelevant glial cells by stimulus-relevant principal cells leads to exporting GABA into the extracellular space around stimulus-irrelevant principal cells (see the filled rectangles for Xn and Yn: n ≠ 2). As shown in Figure 11B (right), this results in suppression of stimulus-irrelevant principal cells (the filled rectangles for Xn and Yn: n ≠ 2). The open rectangles represent those without the P-to-glia connections. These results indicate that the glial activation by principal cells reinforces the synaptic lateral inhibition via P-to-Ib circuitry (see Figure 11A) and thus enhances the tuning effect.

Figure 11:

Enhanced lateral inhibition by P-to-glia signaling. (A) A neural network model in which P-to-glia projection was assumed within unimodal networks (thick dashed lines). (B) Responses to multisensory stimuli (X2, Y2). Left: Ambient GABA concentrations around P cells. Right: Firing rates of P cells. The filled and open rectangles denote that the P-to-glia projection was added or not, respectively.

Figure 11:

Enhanced lateral inhibition by P-to-glia signaling. (A) A neural network model in which P-to-glia projection was assumed within unimodal networks (thick dashed lines). (B) Responses to multisensory stimuli (X2, Y2). Left: Ambient GABA concentrations around P cells. Right: Firing rates of P cells. The filled and open rectangles denote that the P-to-glia projection was added or not, respectively.

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 study, we focused on investigating how ambient GABA contributes to cross-modal inhibition. We could model a glial cell transporter that regulates an ambient GABA level because the mechanism of GABA transport has been theoretically explained (Richerson & Wu, 2003; Wu et al., 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 a Newman 2003). Glial cells are probably the source of GABA responsible for extrasynaptic GABAa receptor-mediated 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 cross-modal 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: the glial inhibitory effect may overwhelm the glial excitatory effect in cross-modal inhibition, for which suitable spatial organization of glial cells would be required. We hope these issues will be addressed by experiments in the future.

de Jong and colleagues (de Jong, Hodiamont, van den Stockde, & Gelder, 2009; de Jong, Hodiamont, & de Gelder, 2010) investigated the audiovisual integration of emotional faces and voices in three groups: schizophrenic patients, nonschizophrenic psychosis patients, and mentally healthy controls. Facial emotion was either congruent or incongruent with vocal emotion. Subjects were instructed to ignore facial affect while categorizing voices. Categorization of emotional (e.g., happy and fear) voices was more accurate when subjects were presented with emotion-congruent faces compared to those with emotion-incongruent faces. The effect of cross-modal influence of the face on the voice was larger in the nonschizophrenic psychosis patients and mentally healthy controls than in the schizophrenic patients. Our simulation results indicated that a cross-modal inhibitory effect contributed to achieving reliable perception of multisensory events. We suggest that the diminished cross-modal influence of emotional faces on emotional voice categorization in schizophrenic patients may be due in part to deterioration of cross-modal inhibitory function.

In postmortem studies of schizophrenic patients, cortical interneurons show reduced parvalbumin (PV) and glutamic acid decarboxylase 67 (GAD67), an enzyme that synthesizes GABA (for a review, see Powell, Sejnowski, & Behrens, 2012). Volman, Behrens, and Sejnowski's (2011) simulation study demonstrated that reductions in PV and GABA resulted in a diminished gamma-band oscillatory activity in response to stimuli, similar to that observed in schizophrenic patients. They found that an alteration of GABA release (an increase in asynchronous GABA release) from interneurons was responsible for the decreased level of excitation and thus reduced gamma-band activity. Our simulation results indicated that a reduction in ambient GABA concentration depressed cross-modal inhibition, leading to unreliable perception of multisensory events. We suggest that an alteration of GABA export (a decrease in GABA export) into the extracellular space from glial cells may cause cortical dysfunction in schizophrenia: deterioration of cross-modal inhibitory function.

As has been shown in Figure 9A, in cross-modal inhibitory processing, the timescale of activation and response in principal (P) cells is slow (∼100 msec or so) because it is subject to the dynamics of ambient GABA concentration. The timescale for glial cells is restricted by the activation and response profile of P cells (and Ia cells), even though the glial cells have a faster membrane time constant: shorter than several milliseconds (Amzica & Neckelmann, 1999; Barakat & Bordey, 2002; Lin & Bergles, 2002; Pivonkova, Benesova, Butenko, Chvatal, & Anderova, 2010). Ambient GABA may coordinate glial activation and response and multisensory interaction.

Appendix A:  The Neural Network Model

Dynamic evolution of the membrane potential of the ith P cell belonging to cell assembly Xn is defined by
formula
A.1
where IP,Pi(Xn; t) is an excitatory synaptic current from other P cells, IP,Ibi(Xn; t) an inhibitory synaptic current from Ib cells, IP,Pi,fdb(Xn; t) a feedback excitatory synaptic current from P cells belonging to multimodal cell assembly Mn, IPi,ext(Xn; t) an inhibitory nonsynaptic current mediated by ambient GABA via extrasynaptic receptors, and IPinp(Xn; t) an excitatory input current. These currents are defined by
formula
A.2
formula
A.3
formula
A.4
formula
A.5
formula
A.6
Dynamic evolution of membrane potential of the ith Ia and Ib cells that belong to cell assembly Xn is defined by
formula
A.7
formula
A.8
where IIa,Pi(Xn; t) and IIb,Pi(Xn; t) are excitatory synaptic currents. IIai,ext(Xn; t) and IIbi,ext(Xn; t) are inhibitory nonsynaptic currents. These currents are defined by
formula
A.9
formula
A.10
formula
A.11
formula
A.12
Dynamic evolution of membrane potential of the ith glial cell that belongs to cell assembly Xn is defined by
formula
A.13
where IGl,Pi(Xn; t) and IGl,Iai(Xn; t) are an excitatory and an inhibitory synaptic current, respectively. These currents are defined by
formula
A.14
formula
A.15
where rPj(Xn; t) is the fraction of AMPA receptors in the open state triggered by the presynaptic action potentials of the jth P cell. rIbj(Xn; t) and rIaj(Xn; 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. rKi,ext(Xn; t) is the fraction of extrasynaptic GABAa receptors in the open state provoked by ambient GABA for type K (K = P, Ia, Ib) cell. The receptor dynamics and ambient GABA concentration are defined in appendixes  B and  C.

Y and M networks were similarly defined. Yn cell assembly receives projections from Xn and Mn. Mn receives projections from Xn and Yn (see Figures 1 and 2). The M network does not have Ia and glial cells for simplicity. For model parameters and their values, see Table 1. For the glial cell, see Amzica and Neckelmann (1999), Barakat and Bordey (2002), Lin and Bergles (2002), and Pivonkova et al. (2010).

Appendix B:  Receptor Dynamics and Action Potential Generation

Receptor dynamics is based on Destexhe, Mainen, and Sejnowski (1998) and described as
formula
B.1
formula
B.2
formula
B.3
where [Glut]j(Xn; t) and [GABA]Kj(Xn; t) are concentrations of glutamate and GABA in synaptic clefts, respectively. [Glut]j(Xn; t) = 1 mM and [GABA]Kj(Xn; t) = 1 mM for 1 ms when the presynaptic jth P cell and type K cell fire, respectively. Otherwise, [Glut]j(Xn; t) = 0 and [GABA]Kj(Xn; t) = 0. The concentration of ambient GABA around type cell for cell assembly Xn, 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. The same definition was employed for Yn and Mn cell assemblies. For model parameters and their values, see Table 1.

Appendix C:  Dynamics of Ambient GABA

Concentration of ambient GABA around the ith P cell belonging to cell assembly Xn is defined by
formula
C.1
For simplicity, concentrations of ambient GABA around Ia, Ib cells were set to the basal concentration: [GABA]Iai,ext(Xn; t) = [GABA]Ibi,ext(Xn; t) = [GABA]0ext. The same definition was employed for cell assembly Yn. Ambient GABA was not considered in the M network. For model parameters and their values, see Table 1.

Acknowledgments

I express my gratitude to Takeshi Kambara for his encouragement throughout this study and to reviewers for giving me valuable comments and suggestions on earlier drafts of this letter.

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