Abstract

We examined whether and how the balancing of crossmodal excitation and inhibition affects intersensory facilitation. A neural network model, comprising lower-order unimodal networks (X, Y) and a higher-order multimodal network (M), was simulated. Crossmodal excitation was made by direct activation of principal cells of the X network by the Y network. Crossmodal inhibition was made in an indirect manner: the Y network activated glial cells of the X network. This let glial plasma membrane transporters export GABA molecules into the extracellular space and increased the level of ambient GABA. The ambient GABA molecules were accepted by extrasynaptic GABAa receptors and tonically inhibited principal cells of the X network. Namely, crossmodal inhibition was made through GABAergic gliotransmission. Intersensory facilitation was assessed in terms of multisensory gain: the difference between the numbers of spikes evoked by multisensory (XY) stimulation and unisensory (X-alone) stimulation. The maximal multisensory gain (XY-X) could be achieved at an intermediate noise level by balancing crossmodal excitation and inhibition. This result supports an experimentally derived conclusion: intersensory facilitation under noisy environmental conditions is not necessarily in accord with the principle of inverse effectiveness; rather, multisensory gain is maximal at intermediate signal-to-noise ratio (SNR) levels. The maximal multisensory gain was available at the weakest signal if noise was not present, indicating that the principle of inverse effectiveness is a special case of the intersensory facilitation model proposed here. We suggest that the balancing of crossmodal excitation and inhibition may be crucial for intersensory facilitation. The GABAergic glio-transmission-mediated crossmodal inhibitory mechanism effectively works for intersensory facilitation and on determining the maximal multisensory gain in the entire SNR range between the two extremes: low and high SNRs.

1.  Introduction

A subject's ability of sensing a certain modality stimulus can be improved when exposed simultaneously to another modality stimulus, especially in noisy environments. For instance, viewing a speaker's articulatory movements substantially improved a listener's ability under noisy environmental conditions (Ross et al., 2007). The researchers demonstrated in an auditory word identification task that multisensory gain, which measures the impact of intersensory facilitation, was maximally tuned at an intermediate auditory signal-to-noise ratio (SNR) level: −12 dB between −24 dB and 0 dB. Chandrasekaran, Lemus, Trubanova, Gondan, and Ghazanfar (2011) demonstrated that multisensory gain for the perception of vocalization in monkeys was maximal at an intermediate auditory SNR level: 5 dB between −10 dB and 22 dB.

Concerning intersensory facilitation, pioneering studies (for review, see Stein & Stanford, 2008) proposed a principle known as inverse effectiveness. According to this principle, multisensory gain is maximal at the weakest signal. The experimental results (Ross et al., 2007; Chandrasekaran et al., 2011) we have addressed pose important questions: How are these maximal multisensory gains, observed at intermediate SNR levels, determined? What is its underlying neuronal mechanism?

Crossmodal excitation and inhibition have great impacts on multisensory neuronal information processing. For instance, a human brain imaging study (Calvert el 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 indicated that sensory-specific cortices could be activated by stimuli from other senses, which is known as crossmodal excitation and presumably contributes to the perceptual amplification of multisensory events.

In contrast, crossmodal 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) made a functional magnetic resonance imaging (fMRI) study that demonstrated that ongoing-spontaneous neuronal activity in visual cortex was suppressed by auditory stimulation (a white noise burst: 250 msec). Neuronal activity in auditory cortex could be suppressed by visual stimulation (a black and white checkerboard: 250 msec) as well.

These studies led us to speculate that the balancing of crossmodal excitation and inhibition might be crucial for intersensory facilitation. The purpose of this study is to examine our speculation and elucidate its essential neuronal mehchanisms. Simulations are carried out for a cortical neural network model with a gliotransmission-mediated ambient GABA regulatory system (Hoshino, 2012). The model 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) projections. Principal-cell-to-principal-cell projection and principal-cell-to-glial-cell projection are made between X and Y networks. The former projection exerts crossmodal excitation and the latter crossmodal inhibition. This assumption accords with a hypothetical principle: co-occurrence of multisensory cooperation (facilitation) and competition (Sinnett, Soto-Faraco, & Spence, 2008).

In our neural network model, crossmodal excitation is made by direct activation of principal cells of the X network by principal cells of the Y network. Crossmodal inhibition is made in an indirect manner: crossmodality stimulation of Y network activates its principal cells, which then activates and depolarizes glial cells of X network. This lets transporters, embedded in membranes of 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, crossmodal inhibition is made through GABAergic gliotransmission.

Identical modality stimulation of X network activates its principal cells, which then activates interneurons and hyperpolarizes glial cells of the X network. This lets glial plasma membrane transporters import (remove) GABA molecules from the extracellular space and reduce tonic inhibitory current in principal cells, thereby enhancing their responsiveness. Top-down signals from the M network affect the dynamic behavior of the X and Y networks (Hoshino, 2011a).

We record responses of the X network to a feature stimulus (as signal input) with simultaneous presentation of its congruent feature stimulus to the Y network. Distractor stimuli (as noise input) are presented to signal-irrelevant P cells of the X network. To elucidate how the maximal multisensory gain is determined, we evaluate the difference between the number of spikes evoked by multisensory stimulation and by unisensory stimulation.

2.  Neural Network Model

We construct a neural network model based on our previous studies (Hoshino, 2011a, 2012). The neural network model is schematically illustrated in Figure 1A. 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) or presenting a pair of stimuli (Xinp, Yinp) to the respective X and Y networks in order to see how intersensory facilitation takes place. 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. The X and Y networks are connected by crossmodal excitatory (solid lines) and inhibitory (dashed lines) projections in a distributed manner, whose details will be shown in Figure 2A. A set of cell assemblies responds (see the gray ovals) when presented with a pair of feature stimuli that originate from a multisensory event (e.g., M2: 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 (Hoshino, 2011a). An identical modality stimulus (Xinp) and a crossmodality stimulus (Yinp) are presented, during which the activity of X network is recorded. (B) Projections between cell assemblies (see the ovals). The X and Y networks have distributed crossmodal projections. The X and Y networks and the M network have selective feedforward and feedback projections. The open and filled triangles schematically illustrate excitatory and inhibitory projections, respectively. Only the projections for the cell assemblies relevant to a multisensory event, M2, are shown for clarity. Multisensory stimuli that originate from that 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 (Hoshino, 2011a). An identical modality stimulus (Xinp) and a crossmodality stimulus (Yinp) are presented, during which the activity of X network is recorded. (B) Projections between cell assemblies (see the ovals). The X and Y networks have distributed crossmodal projections. The X and Y networks and the M network have selective feedforward and feedback projections. The open and filled triangles schematically illustrate excitatory and inhibitory projections, respectively. Only the projections for the cell assemblies relevant to a multisensory event, M2, are shown for clarity. Multisensory stimuli that originate from that event are presented to the lower networks (see X2 and Y2).

Figure 2:

Neuronal circuitry. (A) Cell assemblies consisting of cell units, with each cell unit comprising 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. The projections marked by “for crossmodal excitation” and “for crossmodal inhibition” exert crossmodal excitation and inhibition, respectively. Sensory input (signal or noise) is provided to P cells (see the filled arrows). (B) A conceptual scheme of GABA transport by glial plasma membrane transporter (Hoshino, 2012). P and Ia cells synaptically connect to a glial cell. Transporters, which are embedded in the membrane of the glial cell, import GABA molecules from or export them into the extracellular space depending on glial plasma membrane potential. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

Figure 2:

Neuronal circuitry. (A) Cell assemblies consisting of cell units, with each cell unit comprising 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. The projections marked by “for crossmodal excitation” and “for crossmodal inhibition” exert crossmodal excitation and inhibition, respectively. Sensory input (signal or noise) is provided to P cells (see the filled arrows). (B) A conceptual scheme of GABA transport by glial plasma membrane transporter (Hoshino, 2012). P and Ia cells synaptically connect to a glial cell. Transporters, which are embedded in the membrane of the glial cell, import GABA molecules from or export them into the extracellular space depending on glial plasma membrane potential. The ambient GABA molecules are accepted by extrasynaptic GABAa receptors and tonically inhibit a P cell.

As shown in Figure 2A, the cell assemblies consist of principal cells (P), GABAergic interneurons (Ia, Ib) and glial cells (glia). Each cell assembly (Xn, Yn, Mn; ) contains 20 cell units, and each cell unit comprises 1 P cell, 1 Ia cell, 1 Ib cell, and 1 glial cell. 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 in a distributed manner, which exerts crossmodal inhibition through GABAergic gliotransmission. P cells connect to P cells belonging to the other modality in a distributed manner, which exerts crossmodal excitation. P cells receive an excitatory current as a sensory (signal or noise) input (see the filled arrows).

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

A conductance-based, integrate-and-fire neuron model (Hoshino, 2011a) is employed. Based on our previous study (Hoshino, 2012), a gliotransmission-mediated ambient GABA regulatory system is constructed. As shown in Figure 2B, transporters are embedded in the membrane of a glial cell and regulate a level of ambient GABA around a P cell. Extrasynaptic GABAa receptors accept ambient GABA molecules and tonically inhibit the P cell. For simplicity, the 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  
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 weight (strength) from jth to ith P cell within unimodal (Xn, Yn) and multimodal (Mn) cell assemblies wP,Pij(MnwP,Pij(Xn)=wP,Pij(Yn)=wP,Pij(Mn)=1 
Synaptic weight from jth to ith P cell between X and Y networks   
Synaptic weight from jth Ib to ith P cell wP,Ibij(MnwP,Ibij(Xn)=wP,Ibij(Yn)=wP,Ibij(Mn)=25 
Feedback (top-down) synaptic weight from multimodal (Mn) jth to unimodal (Xn, Yn) ith P cell  wP,Pij(Xn, Mn)=wP,Pij(Yn, Mn)=1.6 
Feedforward (bottom-up) synaptic weight from unimodal (Xn, Yn) jth to multimodal (Mn) ith P cell  wP,Pij(Mn, Xn)=wP,Pij(Mn, Yn)=2.2 
Synaptic weight from ith P to Ia cell  wIa,Pi(Xn)=wIa,Pi(Yn)=30 
Synaptic weight from ith P to Ib cell between different cell assemblies   
Synaptic weight from ith P to glial cell between X and Y networks   
Synaptic weight from ith Ia to glial cell  wGl,Iai(Xn)=wGl,Iai(Yn)=10 
Amount of extrasynaptic GABAa receptors on P cell   
Signal input current to X or Y network   
Noise input current to X network  400 pA 
Channel opening rate for type Z (Z = AMPA, GABA) receptor   
Channel closing rate   
Steepness of sigmoid function for type K (K = P, Ia, Ib) cell   
Threshold of sigmoid function   
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 GABA transporter uGlrev −71 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 weight (strength) from jth to ith P cell within unimodal (Xn, Yn) and multimodal (Mn) cell assemblies wP,Pij(MnwP,Pij(Xn)=wP,Pij(Yn)=wP,Pij(Mn)=1 
Synaptic weight from jth to ith P cell between X and Y networks   
Synaptic weight from jth Ib to ith P cell wP,Ibij(MnwP,Ibij(Xn)=wP,Ibij(Yn)=wP,Ibij(Mn)=25 
Feedback (top-down) synaptic weight from multimodal (Mn) jth to unimodal (Xn, Yn) ith P cell  wP,Pij(Xn, Mn)=wP,Pij(Yn, Mn)=1.6 
Feedforward (bottom-up) synaptic weight from unimodal (Xn, Yn) jth to multimodal (Mn) ith P cell  wP,Pij(Mn, Xn)=wP,Pij(Mn, Yn)=2.2 
Synaptic weight from ith P to Ia cell  wIa,Pi(Xn)=wIa,Pi(Yn)=30 
Synaptic weight from ith P to Ib cell between different cell assemblies   
Synaptic weight from ith P to glial cell between X and Y networks   
Synaptic weight from ith Ia to glial cell  wGl,Iai(Xn)=wGl,Iai(Yn)=10 
Amount of extrasynaptic GABAa receptors on P cell   
Signal input current to X or Y network   
Noise input current to X network  400 pA 
Channel opening rate for type Z (Z = AMPA, GABA) receptor   
Channel closing rate   
Steepness of sigmoid function for type K (K = P, Ia, Ib) cell   
Threshold of sigmoid function   
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 GABA transporter uGlrev −71 mV 

3.  Results

3.1.  Multisensory Gain Under Noisy Environmental Conditions.

Figure 3 shows membrane potentials recorded from P cells of X, Y, and M networks. When a feature stimulus (as signal input) is presented to the X network simultaneously with its congruent feature stimulus to the Y network, responses are evoked in P cells relevant to these stimuli (see X2, Y2, and M2). Distractor stimuli (as noise input) are presented to P cells that are irrelevant to the signal input (see X0, X1, and X3). Ambient GABA concentrations around P cells belonging to respective cell assemblies (Xn, Yn where ) are shown (bottom).

Ambient GABA concentrations around noise-relevant P cells are elevated (see the traces marked by X0, X1, and X3) while keeping the GABA concentration around signal-relevant P cells low (see the trace marked by X2). As has been addressed in section 2, GABA molecules in the extracellular space act on extrasynaptic GABAa receptors and tonically inhibit P cells. Hence, the increase in ambient GABA concentrations around noise-relevant P cells suppresses their activities (see X0, X1, and X3 in Figure 3A). In contrast, the decrease in ambient GABA concentration around the signal-relevant P cells enhances their activities (see X2 in Figure 3A). This enables the X network to tune to the signal under the noisy environmental condition.

Figure 3:

Neuronal responses. (A) Membrane potentials recorded from P cells of X, Y, and M networks. A feature stimulus (as signal input) was presented to the X network (see X2) simultaneously with its congruent feature stimulus to the Y network (see Y2). Distractor stimuli (as noise input) were presented to signal-irrelevant P cells (see X0, X1, and X3). (B) Ambient GABA concentrations around P cells belonging to respective cell assemblies (Xn, Yn where ).

Figure 3:

Neuronal responses. (A) Membrane potentials recorded from P cells of X, Y, and M networks. A feature stimulus (as signal input) was presented to the X network (see X2) simultaneously with its congruent feature stimulus to the Y network (see Y2). Distractor stimuli (as noise input) were presented to signal-irrelevant P cells (see X0, X1, and X3). (B) Ambient GABA concentrations around P cells belonging to respective cell assemblies (Xn, Yn where ).

Figure 4A (top) shows how the signal-relevant P cells respond to the unisensory (X2-alone) stimulus (see the dashed trace) or to the multisensory (X2-Y2) stimuli (see the solid trace) as a function of the level of noise: noise input current. We evaluated multisensory gain: the difference between the numbers of spikes evoked by the multisensory (XY) stimuli and by the unisensory (X) stimulus. During the simulations, we kept the signal level constant: 600 pA. Figure 4A (bottom) indicates that the multisensory gain (XY-X) is maximal at an intermediate signal-to-noise ratio level: SNR = 600pA/400pA. This result supports an experimentally derived conclusion: intersensory facilitation under noisy environmental conditions is not necessarily in accord with the principle of inverse effectiveness; rather, multisensory gain is maximal at intermediate signal-to-noise ratio (SNR) levels (Ross et al., 2007; Chandrasekaran et al., 2011). As shown in Figure 4B, we observed a similar neuronal behavior for multimodal P cells (M2) that are relevant to the (congruent) multisensory stimuli: X2-Y2.

Figure 4:

Influence of noise on intersensory facilitation. (A) Multisensory gain of the X network. Top: Firing rate of a P cell when presented with the unisensory (X2-alone) stimulus (see the dashed trace) or with the multisensory (X2-Y2) stimuli (see the solid trace) as a function of the level of noise: noise input current. Bottom: Dependence of multisensory gain on noise level. Multisensory gain (XY-X) is defined as the difference between the numbers of spikes evoked by the multisensory (XY) stimuli and the unisensory (X) stimulus. The signal level was kept constant: 600 pA. (B) Multisensory gain of the M network. All conventions are identical to those in panel A.

Figure 4:

Influence of noise on intersensory facilitation. (A) Multisensory gain of the X network. Top: Firing rate of a P cell when presented with the unisensory (X2-alone) stimulus (see the dashed trace) or with the multisensory (X2-Y2) stimuli (see the solid trace) as a function of the level of noise: noise input current. Bottom: Dependence of multisensory gain on noise level. Multisensory gain (XY-X) is defined as the difference between the numbers of spikes evoked by the multisensory (XY) stimuli and the unisensory (X) stimulus. The signal level was kept constant: 600 pA. (B) Multisensory gain of the M network. All conventions are identical to those in panel A.

3.2.  Combinatorial Influence of Crossmodal Excitation and Inhibition on Multisensory Gain.

As addressed in section 1, we speculated that the balancing of crossmodal excitation and inhibition might be crucial for intersensory facilitation. In this section, we examine this speculation.

We changed the P-to-P and P-to-glia connection weights between X and Y networks and measured multisensory gains. Note that the former connection mediates crossmodal excitation and the latter crossmodal inhibition (see Figure 2A). Interestingly, as shown in Figure 5, we found that the maximal multisensory gain (XY-X) could vary between the two extremes: low (see the bottom arrow) and high (see the top arrow) noise levels involving an intermediate noise level (see the middle arrow). These results indicate that the balancing of crossmodal excitation and inhibition is crucial for determining the maximal multisensory gain between the two extremes: low and high SNRs.

Figure 5:

Combinatorial influence of crossmodal excitation and inhibition on intersensory facilitation. Dependence of multisensory gain (XY-X) on noise level was assessed. The crossmodal (P(Y)-to-P(X), P(Y)-to-glia(X)) connection weights (see ) and ) in equations A.2 and A.12 in appendix  A) were changed. The arrows indicate the maximal multisensory gains.

Figure 5:

Combinatorial influence of crossmodal excitation and inhibition on intersensory facilitation. Dependence of multisensory gain (XY-X) on noise level was assessed. The crossmodal (P(Y)-to-P(X), P(Y)-to-glia(X)) connection weights (see ) and ) in equations A.2 and A.12 in appendix  A) were changed. The arrows indicate the maximal multisensory gains.

Figure 6A indicates that the GABAergic gliotransmission exerted by the Ia-to-glia circuitry is necessary for the intersensory facilitation. We observed weaker facilitation if this circuitry was cut (see the circles) compared to the intact circuitry condition (see the squares). As shown in Figure 6B, without the top-down (M to X, Y) circuitry, we observed weaker facilitation (see the circles) compared to the intact circuitry condition (see the squares).

Figure 6:

Roles of GABAergic gliotransmission and top-down signaling in intersensory facilitation. (A) Multisensory gain of the X network. Top: Firing rate of a P cell when presented with the unisensory (X2-alone) stimulus (see the dashed trace) or with the multisensory (X2-Y2) stimuli (see the solid trace) as a function of the level of noise: noise input current. Cutting the Ia-to-glia projection eliminated GABAergic gliotransmission (see the circles). The squares are those obtained under the intact circuitry condition. Bottom: Dependence of multisensory gain on noise level. The signal level was kept constant: 600 pA. (B) Multisensory gain of the X network. The top-down M-to-X and M-to-Y projections were cut (see the circles). All conventions are identical to those in panel A.

Figure 6:

Roles of GABAergic gliotransmission and top-down signaling in intersensory facilitation. (A) Multisensory gain of the X network. Top: Firing rate of a P cell when presented with the unisensory (X2-alone) stimulus (see the dashed trace) or with the multisensory (X2-Y2) stimuli (see the solid trace) as a function of the level of noise: noise input current. Cutting the Ia-to-glia projection eliminated GABAergic gliotransmission (see the circles). The squares are those obtained under the intact circuitry condition. Bottom: Dependence of multisensory gain on noise level. The signal level was kept constant: 600 pA. (B) Multisensory gain of the X network. The top-down M-to-X and M-to-Y projections were cut (see the circles). All conventions are identical to those in panel A.

3.3.  Roles of GABAergic Gliotransmission in Crossmodal Inhibitory Processing.

To exert crossmodal inhibition, we assumed the crossmodal P(Y)-to-glia(X) circuitry (see Figure 2A). However, structurally, the alternative crossmodal P(Y)-to-Ib(X) circuitry could exert crossmodal inhibition as well, where the GABAergic neurotransmission (instead of GABAergic gliotransmission) mechanism works. To indicate the significant role of GABAergic gliotransmission in intersensory facilitation, we carried out a simulation in which P-to-Ib (instead of P-to-glia) projections were made between the X and Y networks. Multisensory gains were measured. As shown in Figure 7A, the alternative crossmodal P(Y)-to-Ib(X) circuitry does not significantly enhance the intersensory facilitation (bottom: see the triangles and squares) compared to the original crossmodal P(Y)-to-glia(X) circuitry (see Figure 4A).

Figure 7:

Roles of GABAergic gliotransmission-mediated crossmodal inhibition in intersensory facilitation. (A) Top: Firing rate of a P cell as a function of the level of noise, where P-to-Ib (instead of P-to-glia) projections were made between X and Y networks. Namely, the GABAergic neurotransmission (instead of GABAergic gliotransmission) mechanism worked for the crossmodal inhibitory processing. The unisensory (X2-alone) stimulus (see the dashed traces) or the multisensory (X2-Y2) stimuli (see the solid traces) were presented. The crossmodal P(Y)-to-Ib(X) connection weight was changed between 0 and 0.4. Bottom: Dependence of the multisensory gain on noise level. The signal level was kept constant: 600 pA. (B) Dependence of firing rate and ambient GABA concentration on the alternative crossmodal P(Y)-to-Ib(X) circuitry connection weight (see the open symbols) or on the original crossmodal P(Y)-to-glia(X) circuitry connection weight (see the filled symbols). Top: Firing rate. Bottom: Ambient GABA concentration.

Figure 7:

Roles of GABAergic gliotransmission-mediated crossmodal inhibition in intersensory facilitation. (A) Top: Firing rate of a P cell as a function of the level of noise, where P-to-Ib (instead of P-to-glia) projections were made between X and Y networks. Namely, the GABAergic neurotransmission (instead of GABAergic gliotransmission) mechanism worked for the crossmodal inhibitory processing. The unisensory (X2-alone) stimulus (see the dashed traces) or the multisensory (X2-Y2) stimuli (see the solid traces) were presented. The crossmodal P(Y)-to-Ib(X) connection weight was changed between 0 and 0.4. Bottom: Dependence of the multisensory gain on noise level. The signal level was kept constant: 600 pA. (B) Dependence of firing rate and ambient GABA concentration on the alternative crossmodal P(Y)-to-Ib(X) circuitry connection weight (see the open symbols) or on the original crossmodal P(Y)-to-glia(X) circuitry connection weight (see the filled symbols). Top: Firing rate. Bottom: Ambient GABA concentration.

To understand why the GABAergic neurotransmission-mediated crossmodal inhibition, exerted by the alternative crossmodal P(Y)-to-Ib(X) circuitry, shows weaker intersensory facilitation, we assessed the dependence of stimulus-evoked neuronal activity and ambient GABA concentration on the P(Y)-to-Ib(X) connection weight. As shown in Figure 7B (top: see the open symbols), we observed a decrease not only in noise-related P cell activity (see the open squares for X0, X1, and X3) but also in signal-related P cell activity (see the open square for X2) as the weight increases. Interestingly, the GABAergic gliotransmission-mediated crossmodal inhibition, exerted by the original crossmodal P(Y)-to-glia(X) circuitry, prevents such a signal reduction (top: see the filled square for X2) by decreasing the ambient GABA concentration around the signal-relevant P cells (bottom: see the filled square for X2). The noise-related P cell activities (top: see the filled squares for X0, X1 and X3) are suppressed by increasing the ambient GABA concentrations around the noise-relevant P cells (bottom: see the filled squares for X0, X1 and X3).

We do not test here whether a disinhibitory mechanism similar to the glial-mediated disinhibitory mechanism (see the filled squares for X2) is possible via neural-mediated inhibition. Namely, adding another inhibitory interneuron I, which receives a projection from a P cell, might secure the activity of the P cell by suppressing its accompanying Ib cell via I-to-Ib inhibition. The neuronal-mediated (phasic) inhibition is fast and responsible for sensory information processing. In contrast, the glial-mediated (tonic) inhibition is slow; however, it is enough to modulate sensory information processing (Hoshino, 2013b; Zheng, Matsuo, Miyamoto, & Hoshino, in press). It allows principal cells that have a limited dynamic rage originating from intrinsic synaptic circuitry to operate over a wide dynamic range. This neuronal modulation could improve signal processing: gain and tuning. Understanding the relationship between phasic neuronal inhibition and tonic glial inhibition may be a fruitful avenue for future work.

3.4.  Relevance to the Principle of Inverse Effectiveness.

As addressed in section 1, the principle of inverse effectiveness declares that multisensory gain is maximal at the weakest signal. In this section, we show whether and how our model obeys this principle. The feature stimulus (as signal input) was presented to the X network without the distractor stimuli (as noise input). As shown in Figure 8A, the X network responds more selectively to the signal compared to that under the noisy environmental condition (see Figure 3).

Figure 8:

Neuronal responses under an unnoisy environmental condition. (A) Membrane potentials recorded from P cells of X, Y, and M networks. A feature stimulus (as signal input) was presented to the X network simultaneously with its congruent feature stimulus to the Y network. Distractor stimuli (as noise input) were not present. (B) Ambient GABA concentrations around P cells belonging to respective cell assemblies (Xn, Yn where ).

Figure 8:

Neuronal responses under an unnoisy environmental condition. (A) Membrane potentials recorded from P cells of X, Y, and M networks. A feature stimulus (as signal input) was presented to the X network simultaneously with its congruent feature stimulus to the Y network. Distractor stimuli (as noise input) were not present. (B) Ambient GABA concentrations around P cells belonging to respective cell assemblies (Xn, Yn where ).

To see how the balancing of crossmodal excitation and inhibition affects intersensory facilitation, we changed the crossmodal (P(Y)-to-P(X), P(Y)-to-glia(X)) connection weights and measured multisensory gains. As shown in Figure 9, we found that the maximal multisensory gain is achieved at the weakest signal (see the arrow). The multisensory gain function obtained at () = (3, 2) accords with the principle of inverse effectiveness. Note that the selective responsiveness of the X network could not be ensured if the weights were beyond these values: or (not shown).

Figure 9:

Combinatorial influence of crossmodal excitation and inhibition on intersensory facilitation, where distractor stimuli (as noise input) were not present. Dependence of multisensory gain on signal level was assessed. The crossmodal (P(Y)-to-P(X), P(Y)-to-glia(X)) connection weights (see ) and ) in equations A.2 and A.12 in appendix  A) were changed. The arrow indicates the maximal multisensory gain.

Figure 9:

Combinatorial influence of crossmodal excitation and inhibition on intersensory facilitation, where distractor stimuli (as noise input) were not present. Dependence of multisensory gain on signal level was assessed. The crossmodal (P(Y)-to-P(X), P(Y)-to-glia(X)) connection weights (see ) and ) in equations A.2 and A.12 in appendix  A) were changed. The arrow indicates the maximal multisensory gain.

As has been addressed in section 1, under the noisy condition, the multisensory gain is maximal at intermediate signal-to-noise ratio (SNR) levels. This contradicts the principle of inverse effectiveness. We showed that the balanced crossmodal excitation and inhibition resulted in the highest multisensory gain at the intermediate SNR level (see Figures 4 and 5). The principle of inverse effectiveness is a special case of the intersensory facilitation model proposed here (see Figure 9). These results indicate that the intersensory facilitation model based on the balanced crossmodal excitation and inhibition scheme combines the two contradictory theories into one.

4.  Discussion

We examined whether and how the balancing of crossmodal excitation and inhibition affects intersensory facilitation. A neural network model, comprising lower-order unimodal networks (X, Y) and a higher-order multimodal network (M), was simulated. Crossmodal excitation was made by direct activation of principal cells of the X network by the Y network. Crossmodal inhibition was made in an indirect manner: the Y network activated glial cells of the X network. This let glial plasma membrane transporters export GABA molecules into the extracellular space and increased the level of ambient GABA. The ambient GABA molecules were accepted by extrasynaptic GABAa receptors and tonically inhibited principal cells of the X network. Namely, crossmodal inhibition was made through GABAergic gliotransmission. Intersensory facilitation was assessed in terms of multisensory gain: the difference between the number of spikes evoked by multisensory (XY) stimulation and by unisensory (X-alone) stimulation.

We showed that the maximal multisensory gain (XY-X) could be achieved at an intermediate noise level by balancing crossmodal excitation and inhibition. This result supports an experimentally derived conclusion: intersensory facilitation under noisy environmental conditions is not necessarily in accord with the principle of inverse effectiveness; rather multisensory gain is maximal at intermediate signal-to-noise ratio (SNR) levels. The maximal multisensory gain was available at the weakest signal if noise was not present, indicating that the principle of inverse effectiveness is a special case of the intersensory facilitation model proposed here. We suggest that the balancing of crossmodal excitation and inhibition may be crucial for intersensory facilitation. The GABAergic gliotransmission-mediated crossmodal inhibitory mechanism effectively works for intersensory facilitation and on determining the maximal multisensory gain in the entire SNR range between the two extremes: low and high SNRs.

In general, cortical neurons receive input spikes, by which they are depolarized and generate output spikes. The behavior of a neural network is influenced by both the timing and the number of input spikes. In this study, principal (P) cells received excitatory input current, by which they were depolarized and generated output spikes. The reason for the employment of excitatory input current (but not spikes) was that we could precisely manipulate it, which enabled us to clearly show how the multisensory gain depends on the amount of signal or noise input. The temporal content of signal and noise inputs (i.e., the timing of input spikes) presumably affects the network behavior and thus multisensory gain. This is another issue to be investigated.

Although discussed in detail in our previous studies (Hoshino, 2011a, 2012), we briefly address some important approximations and limitations of the neural network model presented here. To create a unified percept, it is necessary for the brain to integrate information from multiple senses. This ability is referred to as multisensory integration and 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 (for reviews, see Schroeder & Foxe, 2004; Ghazanfar & Schroeder, 2006). 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 made the projections between the lower (X, Y) and higher (M) networks.

For the recent view, Ramos-Estebanez and colleagues (2007) indicated optimal crossmodal facilitation at an interstimulus delay of 60 msec: somatosensory stimulation precedes visual one stimulation. 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. 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 these studies, we made direct projections between the lower (X, Y) networks. Due to a lack of anatomical evidence that supports crossmodal projections between relevant cell assemblies in one-to-one correspondence (: ), we made distributed projections between the X and Y networks.

Concerning neuron-glia signaling, a variety of neuron-glia circuits have been evidenced, including chemical (glutamate, GABA) synapses between presynaptic neurons and postsynaptic glial cells (for a review, see Bezzi & Volterra, 2001; Fields & Stevens-Graham, 2002; Lin & Bergles, 2004; Overstreet, 2005). Based on these studies, we made the excitatory (P-to-glia) and inhibitory (Ia-to-glia) neuron-to-glia synaptic contacts. Neuron-glia signaling that we neglected here for simplicity might include GABA and glutamate signaling to glia through activation of metabotropic receptors (Verkhratsky, 2010; Velez-Fort, Audinat, & Angulo, 2011).

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 GABAergic gliotransmission-mediated crossmodal inhibition affects intersensory facilitation. We could model a glial plasma membrane transporter that regulates an ambient GABA level because the mechanism of GABA transport has been theoretically explained (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007).

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

If the export of glutamate from glial cells into the extracellular space becomes greater or the import of extracellular potassium into glial cells does not take place, the crossmodal inhibitory mechanism would not work properly. Due to the limitation of our model (i.e., it does not regulate extracellular levels of glutamate and potassium as addressed above), we do not declare that glial inhibitory effects are stronger than glial excitatory effects. We proposed in a previous study (Hoshino, 2012) a working hypothesis: GABAergic gliotransmission prevails in crossmodal inhibitory processing, for which suitable spatial organization of glial cells is required.

Appendix A:  The Neural Network Model

Dynamic evolution of membrane potential of the ith P cell that belongs 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 (as signal or noise) current. These currents are defined by
formula
A.2
formula
A.3
formula
A.4
formula
A.5
formula
A.6
Dynamic evolution of the 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 from P cells. These currents are defined by
formula
A.9
formula
A.10
Dynamic evolution of membrane potential of the ith glial cell that belongs to cell assembly Xn is defined by
formula
A.11
where IGl,Pi(Xn; t) and IGl,Iai(Xn; t) are excitatory and inhibitory synaptic currents from P and Ia cells, respectively. These currents are defined by
formula
A.12
formula
A.13

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

Appendix B:  Receptor Dynamics and Action Potential Generation

Receptor dynamics is based on a study (Destexhe, Mainen, & Sejnowski, 1998) and described as
formula
B.1
formula
B.2
formula
B.3
where [Glut]j(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. Concentration of ambient GABA, [GABA]Pi,ext(Xn; 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. The same definition was employed for cell assemblies Yn and Mn. For model parameters and their values, see Table 1 and Hoshino (2007a, 2007b, 2008, 2011a).

Appendix C:  Dynamics of Ambient GABA Concentration

Concentration of ambient GABA around the ith P cell that belongs to cell assembly Xn is defined by
formula
C.1
The same definition was employed for cell assembly Yn. For simplicity, ambient GABA was not considered in the M network. For model parameters and their values, see Table 1 and Hoshino (2009, 2010, 2011b, 2012, 2013a, 2013b).

Acknowledgments

I express my gratitude to Takeshi Kambara for helpful discussion and to reviewers for giving me valuable comments and suggestions.

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