Abstract

Multisensory integration (such as somatosensation-vision, gustation-olfaction) could occur even between subthreshold stimuli that in isolation do not reach perceptual awareness. For example, when a somatosensory (subthreshold) stimulus is delivered within a close spatiotemporal congruency, a visual (subthreshold) stimulus evokes a visual percept. Cross-modal enhancement of visual perception is maximal when the somatosensory stimulation precedes the visual one by tens of milliseconds. This rapid modulatory response would not be consistent with a top-down mechanism acting through higher-order multimodal cortical areas, but rather a direct interaction between lower-order unimodal areas. To elucidate the neuronal mechanisms of subthreshold cross-modal enhancement, we simulated a neural network model. In the model, lower unimodal (X, Y) and higher multimodal (M) networks are reciprocally connected by bottom-up and top-down axonal projections. The lower networks are laterally connected with each other. A pair of stimuli was presented to the lower networks, whose respective intensities were too weak to induce salient neuronal activity (population response) when presented alone. Neurons of the Y network were slightly depolarized below firing threshold when a cross-modal stimulus was presented alone to the X network. This allowed the Y network to make a rapid (within tens of milliseconds) population response when presented with a subsequent congruent stimulus. The reaction speed of the Y network was accelerated, provided that the top-down projections were strengthened. We suggest that a subthreshold (nonpopulation) response to a cross-modal stimulus, acting through interaction between lower (primary unisensory) areas, may be essential for a rapid suprathreshold (population) response to a congruent stimulus that follows. Top-down influences on cross-modal enhancement may be faster than expected, accelerating reaction speed to input, in which ongoing-spontaneous subthreshold excitation of lower-order unimodal cells by higher-order multimodal cells may play an active role.

1.  Introduction

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 meaningful objects or 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; 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). In a recent view, multisensory integration is already present in lower-order areas. It has been suggested that direct connections between lower-order areas would make them multimodal (Schroeder & Foxe, 2005).

Interestingly, multisensory integration could occur even between subthreshold stimuli, for example, gustatory and olfactory (Dalton, Doolittle, Nagata, & Breslin, 2000) and visual and somatosensory (Ramos-Estebanez et al., 2007) stimuli that in isolation do not reach perceptual awareness. We briefly explain the latter study. The researchers applied to human subjects visual stimulation (transcranial magnetic stimulation, TMS), together with somatosensory stimulation (peripheral electrical stimulation, PES), which were individually below their respective detection thresholds. The occipital cortex was stimulated directly with TMS to induce phosphenes as visual percepts, and PES was applied to either the right or left (congruent or incongruent) index finger (pulse duration, 200 μs). When a somatosensory stimulus was delivered within a close spatiotemporal congruency, a visual stimulus evoked a visual percept. Cross-modal enhancement of visual perception was maximal when the somatosensory stimulation preceded the visual one by approximately 60 msec.

The researchers suggested that this rapid modulatory response 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. For the former possibility, direct projections between primary sensory cortical areas have in fact been evidenced (Falchier, Clavagnier, Barone, & Kennedy, 2002; Rockland & Ojima, 2003; Cappe & Barone 2005; Schroeder & Foxe, 2005). The details of subthreshold cross-modal enhancement, however, still remain largely unknown.

The purpose of this study is to understand how subthreshold cross-modal enhancement takes place and to elucidate its essential neuronal mechanisms. We propose a neural network model in which lower-order unimodal areas and a higher-order multimodal area are reciprocally connected through feedforward (bottom-up) and feedback (top-down) axonal projections. Direct bilateral axonal projections between lower networks are assumed. The lower networks are presented with a pair of stimuli, whose respective intensities are too weak to induce salient neuronal activity (population response) when presented alone.

We investigate how a cross-modal (subthreshold) stimulus assists the perception of a congruent (subthreshold) stimulus that follows and how an interstimulus delay (interstimulus time difference) influences subthreshold cross-modal enhancement. Devising simulations by selectively impairing bilateral or top-down projections, we try to elucidate its essential neuronal mechanisms. Membrane oscillations below firing threshold are carefully analyzed, because we believe that a subthreshold (nonpopulation) response to the preceding cross-modal stimulus might have a crucial role in a rapid suprathreshold (population) response to the following congruent stimulus.

2.  Neural Network Model

A neural network model is schematically illustrated in Figure 1A (left), where X and Y denote unimodal networks and M a multimodal network. As shown in Figure 1A (right), populations of neurons (cell assemblies; see the ovals) are connected via selective bottom-up (feedforward; X, Y to M) and top-down (feedback; M to X, Y) projections. The M network responds to specific combinations of multisensory features Xn and Yn, denoted as Mn (n = 0–3). Note that as addressed in section 1, we assume direct bilateral projections between relevant unimodal cell assemblies, namely, between Xn and Yn (e.g., see the dashed line for n = 2). A pair of features is presented to the lower networks (see “multisens. inp.” in Figure 1B).

Figure 1:

Neuronal architecture. (A) Left: A schematic illustration of a neural network model. Two lower unimodal (X, Y) networks are bilaterally connected. One higher multimodal (M) network is connected with lower networks by bottom-up (feedforward) and top-down (feedback) projections. Right: Projections between cell assemblies (see the ovals). Only the projections for the cell assemblies relevant to n = 2 are shown for clarity. A pair of multisensory features is presented to the lower networks (e.g., see X2 and Y2). (B) Neuronal circuitry. Each cell assembly consists of cell units (e.g., see the gray circle)—one principal cell (P), and two GABAergic interneurons (F, L). The open and filled triangles denote excitatory and inhibitory synapses, respectively.

Figure 1:

Neuronal architecture. (A) Left: A schematic illustration of a neural network model. Two lower unimodal (X, Y) networks are bilaterally connected. One higher multimodal (M) network is connected with lower networks by bottom-up (feedforward) and top-down (feedback) projections. Right: Projections between cell assemblies (see the ovals). Only the projections for the cell assemblies relevant to n = 2 are shown for clarity. A pair of multisensory features is presented to the lower networks (e.g., see X2 and Y2). (B) Neuronal circuitry. Each cell assembly consists of cell units (e.g., see the gray circle)—one principal cell (P), and two GABAergic interneurons (F, L). The open and filled triangles denote excitatory and inhibitory synapses, respectively.

As shown in Figure 1B, cell assemblies consist of cell units (see the gray circle), each of which contains one principal (P) cell and two GABAergic (F, L) cells. Each P cell receives excitatory inputs from P cells that belong to the same cell assembly, an inhibitory input from its accompanying F cell, and inhibitory inputs from L cells that receive excitatory inputs from P cells belonging to other cell assemblies. Each F cell receives an excitatory input from its accompanying P cell. One cell assembly (Xn, Yn, Mn; n = 0–3) comprises 20 cell units. Within cell assemblies, P cells are mutually and fully connected with each other. We provide each of the stimulus-relevant P cells with a constant excitatory current as an input. Unimodal P cells receive synaptic inputs from P cells belonging to the other modality and from multimodal P cells.

A conductance-based, integrate-and-fire neuron model (Hoshino, 2006, 2008) with an ambient (extrasynaptic) GABA regulatory system (Hoshino, 2009) is employed. GABA transporters are located on the axon terminals of L and F cells. GABA transporters on L cells regulate an overall level of ambient GABA across cell assemblies, and those on F cells do so within individual cell assemblies. Ambient GABA is accepted by extrasynaptic GABAa-receptors and tonically inhibits neurons. Through this transport mechanism, ambient GABA concentration is kept within a submicromolar range, which contributes to achieving ongoing-spontaneous subthreshold membrane oscillations in principal cells. As will be shown later, such an ongoing-spontaneous subthreshold neuronal state plays an important role in making a population response to subthreshold multimodal stimuli. Fundamental properties of the GABA regulatory system have been reported (Hoshino, 2009). The neural network model is described in appendix A, whose parameters and their values are listed in Table 1.

Table 1:
Parameters and Their Values.
DescriptionParameterValue
Membrane capacitance of type cKm cPm = 0.5 nF, cFm = 0.2 nF, 
   K (K = P, F, L) cell  cLm = 0.6 nF 
Membrane conductance gKm gPm = 25 nS, gFm = 20 nS, 
  gLm = 15 nS 
Resting potential uKrest uPrest = −65 mV, uFrest = uLrest 
  =−70 mV 
Maximal conductance for type   
   Z (Z = AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev = 0 mV, uGABArev 
  =−80 mV 
Number of cell-units within N 20 
   cell assemblies   
Synaptic strength from j to ith P cell wP,Pij(XnwP,Pij(Xn) = wP,Pij(Yn) = 5.5, 
   within unimodal (Xn, Yn) and wP,Pij(YnwP,Pij(Mn) = 6.2 
   multimodal (Mn) cell assemblies wP,Pij(Mn 
Synaptic strength from ith F to P cell wP,Fi(XnwP,Fi(Xn) = wP,Fi(Yn
 wP,Fi(Yn=wP,Fi(Mn) = 20 
 wP,Fi(Mn 
Synaptic strength from jth L to ith P cell wP,Lij(XnwP,Lij(Xn) = wP,Lij(Yn
 wP,Lij(Yn=wP,Lij(Mn) = 15 
 wP,Lij(Mn 
Lateral synaptic strength from wP,Pij(Xn, YnwP,Pij(Xn, Yn) = wP,Pij(Yn, Xn
   unimodal (Yn) jth to unimodal (Xn) ith wP,Pij(Yn, Xn=1 
P cell, and vice versa   
Feedback (top-down) synaptic strength wP,Pij(Xn, MnwP,Pij(Xn, Mn) = wP,Pij(Yn, Mn
   from multimodal (Mn) jth to unimodal wP,Pij(Yn, Mn=0.5 
(Xn, Yn) ith P cell   
Feedforward (bottom-up) synaptic wP,Pij(Mn, XnwP,Pij(Mn, Xn) = wP,Pij(Mn, Yn
   strength from unimodal (Xn, Yn) jth to wP,Pij(Mn, Yn=1.8 
   multimodal (Mn) ith P cell   
Synaptic strength from ith P to F cell wF,Pi(XnwF,Pi(Xn) = wF,Pi(Yn
 wF,Pi(Yn=wF,Pi(Mn) = 30 
 wF,Pi(Mn 
Synaptic strength from ith P to L cell   
   between different (n′ ≠ n) cell   
   assemblies   
Amount of extrasynaptic GABAa δK δP = 8 × 103, δF = δL 
   receptors on type K (K = P, F, L) cell  =1 × 104 
Input current to P cell εP 180 pA 
Channel opening rate for type αZ  
   Z (Z = AMPA, GABA) receptor  =5 × 106 
Channel closure rate for type βZ  
   Z (Z = AMPA, GABA) receptor   
Steepness of sigmoid function for type ηK ηP = 220, ηF = ηL = 180 
   K (K = P, F, L) cell   
Threshold of sigmoid function for type ζK ζP = −35 mV, ζF = ζL 
   K (K = P, F, L) cell  =−38 mV 
Decay constant for ambient γ 0.5 
   GABA concentration   
Basal concentration  0.2 μM 
Transfer coefficient of GABA for type TK TF = 0.01, TL = 0.03 
   K (K = F, L) cell   
Reversal potential of transporter for type uKrev  
   K (K = F, L) cell  =−69 mV 
DescriptionParameterValue
Membrane capacitance of type cKm cPm = 0.5 nF, cFm = 0.2 nF, 
   K (K = P, F, L) cell  cLm = 0.6 nF 
Membrane conductance gKm gPm = 25 nS, gFm = 20 nS, 
  gLm = 15 nS 
Resting potential uKrest uPrest = −65 mV, uFrest = uLrest 
  =−70 mV 
Maximal conductance for type   
   Z (Z = AMPA, GABA) receptor   
Reversal potential uZrev uAMPArev = 0 mV, uGABArev 
  =−80 mV 
Number of cell-units within N 20 
   cell assemblies   
Synaptic strength from j to ith P cell wP,Pij(XnwP,Pij(Xn) = wP,Pij(Yn) = 5.5, 
   within unimodal (Xn, Yn) and wP,Pij(YnwP,Pij(Mn) = 6.2 
   multimodal (Mn) cell assemblies wP,Pij(Mn 
Synaptic strength from ith F to P cell wP,Fi(XnwP,Fi(Xn) = wP,Fi(Yn
 wP,Fi(Yn=wP,Fi(Mn) = 20 
 wP,Fi(Mn 
Synaptic strength from jth L to ith P cell wP,Lij(XnwP,Lij(Xn) = wP,Lij(Yn
 wP,Lij(Yn=wP,Lij(Mn) = 15 
 wP,Lij(Mn 
Lateral synaptic strength from wP,Pij(Xn, YnwP,Pij(Xn, Yn) = wP,Pij(Yn, Xn
   unimodal (Yn) jth to unimodal (Xn) ith wP,Pij(Yn, Xn=1 
P cell, and vice versa   
Feedback (top-down) synaptic strength wP,Pij(Xn, MnwP,Pij(Xn, Mn) = wP,Pij(Yn, Mn
   from multimodal (Mn) jth to unimodal wP,Pij(Yn, Mn=0.5 
(Xn, Yn) ith P cell   
Feedforward (bottom-up) synaptic wP,Pij(Mn, XnwP,Pij(Mn, Xn) = wP,Pij(Mn, Yn
   strength from unimodal (Xn, Yn) jth to wP,Pij(Mn, Yn=1.8 
   multimodal (Mn) ith P cell   
Synaptic strength from ith P to F cell wF,Pi(XnwF,Pi(Xn) = wF,Pi(Yn
 wF,Pi(Yn=wF,Pi(Mn) = 30 
 wF,Pi(Mn 
Synaptic strength from ith P to L cell   
   between different (n′ ≠ n) cell   
   assemblies   
Amount of extrasynaptic GABAa δK δP = 8 × 103, δF = δL 
   receptors on type K (K = P, F, L) cell  =1 × 104 
Input current to P cell εP 180 pA 
Channel opening rate for type αZ  
   Z (Z = AMPA, GABA) receptor  =5 × 106 
Channel closure rate for type βZ  
   Z (Z = AMPA, GABA) receptor   
Steepness of sigmoid function for type ηK ηP = 220, ηF = ηL = 180 
   K (K = P, F, L) cell   
Threshold of sigmoid function for type ζK ζP = −35 mV, ζF = ζL 
   K (K = P, F, L) cell  =−38 mV 
Decay constant for ambient γ 0.5 
   GABA concentration   
Basal concentration  0.2 μM 
Transfer coefficient of GABA for type TK TF = 0.01, TL = 0.03 
   K (K = F, L) cell   
Reversal potential of transporter for type uKrev  
   K (K = F, L) cell  =−69 mV 

3.  Results

3.1.  Subthreshold Cross-Modal Enhancement.

Raster plots of action potentials of P cells of X (X0−3), Y (Y0−3), and M (M0−3) networks are shown in Figure 2A. A pair of feature stimuli (X2 and Y2), as a multisensory input (see “multisens. inp.”), was presented to the lower (X and Y) networks. Population responses are induced in unimodal (X2, Y2) and multimodal (M2) P cells. As shown in Figure 2B, they evoke no population response when presented alone. Namely, they are subthreshold stimuli.

Figure 2:

Responses to subthreshold stimuli. (A) Raster plots of action potentials of P cells of X, Y, and M networks. A pair of subthreshold stimuli (X2 and Y2) was applied to respective X and Y networks with a spatiotemporal congruency. (B) No population response induced by Y2-stimulation alone. (C) Dependence of activity of a Y2-relevant P cell on input current (“input (Y2)”), influenced by the preceding cross-modal X2-stimulation (“input (X2)”). (D) Minimal input current to Y2 cells for population response as a function of input current to X2 cells.

Figure 2:

Responses to subthreshold stimuli. (A) Raster plots of action potentials of P cells of X, Y, and M networks. A pair of subthreshold stimuli (X2 and Y2) was applied to respective X and Y networks with a spatiotemporal congruency. (B) No population response induced by Y2-stimulation alone. (C) Dependence of activity of a Y2-relevant P cell on input current (“input (Y2)”), influenced by the preceding cross-modal X2-stimulation (“input (X2)”). (D) Minimal input current to Y2 cells for population response as a function of input current to X2 cells.

Figure 2C shows the dependence of activity of a Y2-relevant P cell on input current (”input (Y2)”), influenced by the preceding cross-modal input current (input (X2)). This reveals two distinct dynamical regimes: nonpopulation response (firing less than several Hz) and population response (firing more than 30 Hz). Figure 2D shows minimal currents in Y2 cells, beyond which population responses take place, indicating that the preceding stimulation (input (X2)) reduces a minimal current (Y2) for a population response. Note that the input currents in X2 and Y2 cells shown in Figures 2A and 2B were 0.18 nA, which were below their respective detection (as reflected in population response) thresholds: 0.28 nA (X2) and 0.33 nA (Y2).

To assess the influences of the preceding X2 stimulation on Y2 (P) cells, we recorded their membrane potentials (see Figure 3A), where its congruent stimulus (Y2) was not present. We observed small depolarization that does not reach firing threshold (e.g., see the dashed circle and its enlargement indicated by the filled arrow). Namely, it slightly depolarizes (see the solid trace) from that with no input (the dashed trace), when the P cell does not fire. We randomly chose 1 among 20 P cells for each cell assembly (X2, Y2, M2). Ten of them are shown in Figure 3B for the Y2-relevant cell assembly, where the input was provided (top) or not (bottom). The open arrow indicates the chosen cell. We call the spiking activity induced by the cross-modal input alone the subthreshold (nonpopulation) response.

Figure 3:

Subthreshold (nonpopulation) response to a cross-modal stimulus. (A) Membrane potentials of P cells when the stimulus X2 was presented alone (see the solid traces). The dashed traces denote those recorded for an ongoing-spontaneous time period (i.e., no input). The cross-modal stimulation slightly depolarizes P cells (e.g., see the dashed circle and its enlargement indicated by the filled arrow). (B) Membrane potentials of 10 among 20 Y2-relevant P cells with (top) or without (bottom) input. The open arrow indicates the chosen cell in A.

Figure 3:

Subthreshold (nonpopulation) response to a cross-modal stimulus. (A) Membrane potentials of P cells when the stimulus X2 was presented alone (see the solid traces). The dashed traces denote those recorded for an ongoing-spontaneous time period (i.e., no input). The cross-modal stimulation slightly depolarizes P cells (e.g., see the dashed circle and its enlargement indicated by the filled arrow). (B) Membrane potentials of 10 among 20 Y2-relevant P cells with (top) or without (bottom) input. The open arrow indicates the chosen cell in A.

Figure 4A shows membrane potentials during X2 stimulation (ordinate) and ongoing-spontaneous (i.e., no input) (abscissa) time periods. The X2 stimulation slightly depolarizes P cells. It is greater in the X2 cells (top) than the Y2 (middle) and M2 (bottom) cells, because the X2 cells receive the input directly, while the Y2 and M2 cells receive the input indirectly. Figures 4B and 4C show the dependence of the average membrane potential and evoked neuronal activity (spikes) on input current to X2 cells, respectively. A small increase in the firing rate in the X2 cells only slightly depolarizes the Y2 cells.

Figure 4:

Subthreshold membrane depolarization. (A) Membrane potentials induced by cross-modal X2 stimulation alone (ordinate) and those recorded for the ongoing-spontaneous (i.e., no input) time period (abscissa). (B) Dependence of average membrane potential on input current to X2 cells. (C) Dependence of evoked neuronal activity (spikes) on input current to X2 cells.

Figure 4:

Subthreshold membrane depolarization. (A) Membrane potentials induced by cross-modal X2 stimulation alone (ordinate) and those recorded for the ongoing-spontaneous (i.e., no input) time period (abscissa). (B) Dependence of average membrane potential on input current to X2 cells. (C) Dependence of evoked neuronal activity (spikes) on input current to X2 cells.

To see when the cross-modal interaction among few spiking neurons induces a population response, we measured a threshold for it. Figure 5A (top) shows the membrane potential of a Y2-relevant P cell when presented with paired stimuli X2 and Y2 (see the horizontal bars). The same current 40 pA was provided to the X network, while that to the Y network was varied. We found a minimal current 130 pA (see the open arrow) beyond which population responses occur. Figure 5A (bottom) shows the average membrane potential for the stimulation period as a function of input current to the Y network. We determined the threshold membrane potential (see the filled arrow) above which population responses can take place. Figure 5B shows the threshold as a function of the input current to the X network. Interestingly, an increase in cross-modal (X2) influence lowers the threshold of the Y network for its population response.

Figure 5:

Threshold for population response. (A) Top: Membrane potentials of a Y2-relevant P cell when stimulated with features X2 and Y2 (see the horizontal bars). The same current 40 pA was provided to the X network, while that to the Y network was varied. The open arrow indicates a minimal current beyond which a population response can take place. Bottom Average membrane potential for the stimulation period as a function of input current to the Y network. The filled arrow indicates the threshold membrane potential for population response. (B) Threshold membrane potential for population response as a function of input current to the X network.

Figure 5:

Threshold for population response. (A) Top: Membrane potentials of a Y2-relevant P cell when stimulated with features X2 and Y2 (see the horizontal bars). The same current 40 pA was provided to the X network, while that to the Y network was varied. The open arrow indicates a minimal current beyond which a population response can take place. Bottom Average membrane potential for the stimulation period as a function of input current to the Y network. The filled arrow indicates the threshold membrane potential for population response. (B) Threshold membrane potential for population response as a function of input current to the X network.

Note that these stimuli were provided for a longer time period (2 seconds), while we employed brief stimuli (100 milliseconds) for simulating subthreshold cross-modal enhancement (e.g., see Figure 2). For reliably determining the threshold values, a stable and longer, but not a brief, time series of membrane potential was necessary. Nonetheless, these results may give some insight into the understanding of subthreshold cross-modal enhancement. Namely, a population response takes place when crossing the threshold, which can be lowered through cross-modal interaction among few spiking neurons.

To investigate the influence of interstimulus time difference on subthreshold cross-modal enhancement, we provided X2 stimulation at different onset times with respect to Y2 stimulation. As shown in Figures 6A and 6B, we observed salient firing in Y2 cells within a time range between −60 and 20 milliseconds. Note that less than 0 msec implies that stimulus X2 precedes Y2. As shown in Figure 6C, the optimal timing, at which the speed of membrane depolarization becomes the fastest, is about −40 msec.

Figure 6:

Influences of interstimulus time difference on subthreshold cross-modal enhancement. (A) Action potentials of a Y2-relevant P cell, where cross-modal stimulus X2 was presented at different onset times with respect to congruent stimulus Y2. Times less than 0 msec imply that the stimulus X2 precedes Y2. (B) Dependence of Y2 activity on interstimulus time difference. (C) Membrane potentials of the Y2 cell around the stimulus onset.

Figure 6:

Influences of interstimulus time difference on subthreshold cross-modal enhancement. (A) Action potentials of a Y2-relevant P cell, where cross-modal stimulus X2 was presented at different onset times with respect to congruent stimulus Y2. Times less than 0 msec imply that the stimulus X2 precedes Y2. (B) Dependence of Y2 activity on interstimulus time difference. (C) Membrane potentials of the Y2 cell around the stimulus onset.

The unimodal (X) to unimodal (Y) projection plays a key role in subthreshold cross-modal enhancement. Figure 7A shows the impact of its strength weight(XY) (see wP,Pij(Yn, Xn) in Table 1) on the evoked activity of Y2-relevant P cells, where X2 stimulation precedes (<0 msec) or follows (>0 msec) Y2 stimulation. We confirmed that the network behavior becomes stable provided that the strength is in a certain range (1.0–1.4), which may reflect, to some extent, its robustness. Note that beyond 1.4, the evoked activity tended to continue even after the stimulation was terminated (not shown), which is due largely to excessive lateral excitation between X and Y networks. The preceding X2 stimulation does not enhance the subsequent Y2 response (see the triangles and squares) if it is below 1.0. Hence, we set the projection strength to 1.0 and other parameters to values at which the network can perform the task (feature detection) in a stable manner. The population responses of stimulus-relevant (X2, Y2, M2) P cells are shown in Figure 7B.

Figure 7:

Influences of unimodal (X) to unimodal (Y) projection on subthreshold cross-modal enhancement. (A) Evoked activity of a Y2-relevant P cell. Times less than 0 msec imply that stimulus X2 precedes Y2. The projection strength weight(XY) was varied between 0.6 and 1.4. (B) Raster plots of stimulus-relevant (X2, Y2, M2) P cells. Cross-modal stimulus X2 was presented at different onset times (between −80 msec and +40 msec).

Figure 7:

Influences of unimodal (X) to unimodal (Y) projection on subthreshold cross-modal enhancement. (A) Evoked activity of a Y2-relevant P cell. Times less than 0 msec imply that stimulus X2 precedes Y2. The projection strength weight(XY) was varied between 0.6 and 1.4. (B) Raster plots of stimulus-relevant (X2, Y2, M2) P cells. Cross-modal stimulus X2 was presented at different onset times (between −80 msec and +40 msec).

3.2.  Top-Down and Bilateral Influences on Subthreshold Cross-Modal Enhancement.

In this section, we show top-down and bilateral influences on subthreshold cross-modal enhancement. Figure 8A presents the membrane potentials of P cells relevant to the paired stimuli (see the solid traces). If the top-down (Figure 8B) or bilateral (Figure 8C) projections were impaired, the P cells did not show a population response. Figure 9A presents the evoked activity of a Y2-relevant P cell as a function of input current. The intact (original) circuitry ensures that population responses, greater than approximately 30 spikes (see the circles), provided that the input current exceeds approximately 0.16 nA. Without top-down (the triangles) or bilateral (the squares) projection, population responses do not take place. As shown in Figure 9B, the impairment of top-down (left) or bilateral (right) projection leads to ongoing-spontaneous hyperpolarization, which would hamper a population response (see the triangles and squares in Figure 9A).

Figure 8:

Top-down and bilateral influences on subthreshold cross-modal enhancement. (A) Membrane potentials of P cells corresponding to the paired stimuli (X2Y2) under the intact (original) condition (see the solid traces). The top-down (B) or bilateral (C) projection was cut off. The dashed traces denote those recorded for the ongoing-spontaneous time period (i.e., no input).

Figure 8:

Top-down and bilateral influences on subthreshold cross-modal enhancement. (A) Membrane potentials of P cells corresponding to the paired stimuli (X2Y2) under the intact (original) condition (see the solid traces). The top-down (B) or bilateral (C) projection was cut off. The dashed traces denote those recorded for the ongoing-spontaneous time period (i.e., no input).

Figure 9:

Top-down and bilateral influences on stimulus-evoked and ongoing-spontaneous neuronal activity. (A) Stimulus-evoked Y2 activity as a function of input current. Population responses are ensured for the intact condition (see the circles; input(Y2)>0.16 nA). If the top-down (triangles) or bilateral (squares) projection was impaired, no population response took place. (B) Ongoing-spontaneous membrane potentials recorded under the intact (abscissa) or impaired (ordinate) condition, where the top-down (left) or bilateral (right) projection was cut off.

Figure 9:

Top-down and bilateral influences on stimulus-evoked and ongoing-spontaneous neuronal activity. (A) Stimulus-evoked Y2 activity as a function of input current. Population responses are ensured for the intact condition (see the circles; input(Y2)>0.16 nA). If the top-down (triangles) or bilateral (squares) projection was impaired, no population response took place. (B) Ongoing-spontaneous membrane potentials recorded under the intact (abscissa) or impaired (ordinate) condition, where the top-down (left) or bilateral (right) projection was cut off.

Figure 10A shows the evoked activity of a Y2-relevant P cell as functions of top-down weight(X, YM) (see wP,Pij(Xn, Mn) = wP,Pij(Yn, Mn) in Table 1) and bilateral weight(XY) (see wP,Pij(Xn, Yn) = wP,Pij(Yn, Xn) in Table 1) projection strengths. If the bilateral circuitry was impaired (weight(XY) = 0), Y2 cells could not detect the subthreshold stimulus. It is interesting that a population response is possible even without top-down circuitry, that is, at weight(X, YM) = 0, provided that the bilateral projection strength is enhanced (weight(XY)⩾ 1.6).

Figure 10:

Dependence of stimulus-evoked neuronal activity on top-down and bilateral projection strengths. (A) Stimulus-evoked Y2-activity as functions of top-down weight(X, YM) and bilateral weight(XY) projection strengths. (B) Stimulus-evoked Y2 activity, where the projection from Y to X network was cut off. (C) Stimulus-evoked Y2 activity as a function of input current (see the open circles) under the condition in B (see the asterisk). The filled circles denote stimulus-evoked activity without cross-modal X2-stimulation.

Figure 10:

Dependence of stimulus-evoked neuronal activity on top-down and bilateral projection strengths. (A) Stimulus-evoked Y2-activity as functions of top-down weight(X, YM) and bilateral weight(XY) projection strengths. (B) Stimulus-evoked Y2 activity, where the projection from Y to X network was cut off. (C) Stimulus-evoked Y2 activity as a function of input current (see the open circles) under the condition in B (see the asterisk). The filled circles denote stimulus-evoked activity without cross-modal X2-stimulation.

We assumed bilateral projections between lower X and Y networks (see Figure 1). However, the brain may instead create a unilateral projection. To examine how the unilateral (X-to-Y) circuitry affects cross-modal enhancement, we devised a simulation in which the pathway from Y to X network was cut off (see Figure 10B). We found that cross-modal enhancement is impossible without top-down signals (weight(X, YM) = 0)), where the strengthening of a lateral (X-to-Y) projection is not effective as it was in Figure 10A. Nonetheless, the unilateral (X-to-Y) circuitry is still beneficial, provided that the top-down projection is strengthened (weight(X, YM)⩾ 0.7)). Figure 10C indicates that a combinatorial (top-down and unilateral) circuit (e.g., see the asterisk in Figure 10B) can reduce the minimal current in Y2 cells for their population response (see the open circles and the arrow: 0.32 → 0.16 nA). Note that the filled circles represent those without cross-modal (X2) stimulation.

The symmetrical, bilateral projections between unimodal X and Y networks allowed the Y network to make a population response, even when Y2 stimulation preceded X2 (e.g., see 0 < timing < 20 msec in Figure 7A). If we assume asymmetrical projections, by weakening Y-to-X projection strength (see the arrows in Figure 11), evoked activity could be ensured only if X2 stimulation precedes Y2 (see timing < 0 msec). This asymmetrical response is consistent with responses observed in a recent experiment (Ramos-Estebanez et al., 2007) that demonstrated that a somatosensory stimulus preceding a visual one resulted in visual perception, while there was no perception when a visual stimulus preceded a somatosensory one. Projections between somatosensory and visual areas may be somewhat asymmetric.

Figure 11:

Influences of unimodal (Y) to unimodal (X) projection on subthreshold cross-modal enhancement. Times less than 0 msec imply that stimulus X2 precedes Y2. The projection strength weight(YX) was varied between 0.6 and 1.0.

Figure 11:

Influences of unimodal (Y) to unimodal (X) projection on subthreshold cross-modal enhancement. Times less than 0 msec imply that stimulus X2 precedes Y2. The projection strength weight(YX) was varied between 0.6 and 1.0.

3.3.  Top-Down Influences on Subthreshold Cross-Modal Enhancement.

In general, to be multimodal, a higher-order area is likely to receive clustered, selective projections from lower-order unimodal areas as we assumed (see Figure 1). However, it is not always true that a multimodal area innervates unimodal domains with a preferred feature similar to that of their neurons of origin. To investigate how the distribution of top-down projections affects subthreshold cross-modal enhancement, we devised a simulation in which diffused, unselective feedback projections were made. Namely, the M network sends axons broadly and uniformly (for simplicity) to X and Y domains (cell assemblies) with both similar and dissimilar sensory preferences. As shown in Figure 12A, we found that the diffused top-down projection leads unimodal cells to slightly depolarize during an ongoing-spontaneous time period, when they do not fire.

Figure 12:

Top-down influences on subthreshold cross-modal enhancement. (A) Ongoing-spontaneous membrane potentials recorded for the circuitry with clustered (abscissa) or diffused (ordinate) top-down projection. (B) Stimulus-evoked Y2 activity as a function of input current, recorded for the clustered (see the open circles) or the diffused (see the asterisks) circuitry. The filled circles denote those for the clustered circuitry without cross-modal X2 stimulation. (C) Dependence of minimal current in Y2 cells, beyond which a population response occurs, on top-down (feedback) projection strength. The circles and triangles denote the clustered and diffused top-down circuits, respectively, and the asterisks their changes; deceases in minimal current by diffusing top-down projection. (D) Action potentials of a Y2-relevant P cell. Stimulus Y2 was presented at time = 0, which was preceded by cross-modal X2-stimulation. We varied the top-down projection strength between 0.1 (see the bottom trace) and 0.9 (see the top trace).

Figure 12:

Top-down influences on subthreshold cross-modal enhancement. (A) Ongoing-spontaneous membrane potentials recorded for the circuitry with clustered (abscissa) or diffused (ordinate) top-down projection. (B) Stimulus-evoked Y2 activity as a function of input current, recorded for the clustered (see the open circles) or the diffused (see the asterisks) circuitry. The filled circles denote those for the clustered circuitry without cross-modal X2 stimulation. (C) Dependence of minimal current in Y2 cells, beyond which a population response occurs, on top-down (feedback) projection strength. The circles and triangles denote the clustered and diffused top-down circuits, respectively, and the asterisks their changes; deceases in minimal current by diffusing top-down projection. (D) Action potentials of a Y2-relevant P cell. Stimulus Y2 was presented at time = 0, which was preceded by cross-modal X2-stimulation. We varied the top-down projection strength between 0.1 (see the bottom trace) and 0.9 (see the top trace).

Such subthreshold membrane depolarization reduces a minimal current in P cells for their population response (see IIIII in Figure 12B). Figure 12C shows the minimal current as a function of projection strength from M to X and Y networks; weight(X, YM) (see wP,Pij(Xn, Mn) = wP,Pij(Yn, Mn) in Table 1). The circles and triangles denote the clustered and diffused top-down projections, respectively, and the asterisks their changes—deceases in minimal current by diffusing top-down projection. The diffusive top-down circuitry contributes to reducing the minimal current. Note that top-down projection strength (weight(X, YM)>1) that was too strong and diffusive led to unselective neuronal responses, evoking spikes not only in stimulus-relevant (Y2) but also in stimulus-irrelevant (Yn; n ≠ 2) cells (not shown).

Lateral interaction between lower networks was essential for the rapid (within tens of milliseconds) modulatory response (see Figure 6). In contrast, it is expected that the top-down influence would be slower. However, we found that its impact was fast. Figure 12D shows evoked action potentials in a P cell where stimulus Y2 was presented at time = 0. Its reaction time is reduced as top-down projection strength increases (0.1 → 0.9). This result implies that the top-down influence on population response is fast; the ongoing-spontaneous excitation of unimodal cells by multimodal cells (see Figure 9B) may play an active role. In section 4, we discuss this issue in relation to a visual system (V1 ↔ V2).

4.  Discussion

In this study, we proposed a neural network model in which lower-order unimodal networks are connected by bilateral axonal projections. A higher-order multimodal network is connected with lower-order unimodal networks through bottom-up (feedforward) and top-down (feedback) axonal projections. The higher network sums the neuronal responses from lower networks and responds to specific combinations of multisensory features. The lower networks were presented with a pair of stimuli whose respective intensities were not enough to induce salient neuronal activity (population response) when presented alone. Namely, they were subthreshold stimuli.

A preceding cross-modal stimulus induced small depolarization that does not reach the firing threshold, which we called a subthreshold (nonpopulation) response (see Figure 3) and was essential for a rapid suprathreshold (population) response to a congruent stimulus that followed (see Figure 2A). The subthreshold membrane depolarization was maximal at an interstimulus delay of several tens of milliseconds (see Figure 6), leading to the best cross-modal enhancement. The top-down (multimodal to unimodal) influence was faster than expected, accelerating the speed of population response (see Figure 12D).

Ramos-Estebanez and colleagues (2007) found optimal subthreshold cross-modal enhancement at an interstimulus delay of 60 msec: somatosensory stimulation precedes the visual one. The researchers suggested that such a rapid modulatory response would not be consistent with a top-down mechanism acting through higher-order cortical areas such as parietal areas. Response latencies in these areas are typically longer. Thus, the rapid (60 msec) neuromodulatory effect would be more consistent with a direct interaction between primary visual and somatosensory cortical areas or a bottom-up mechanism from subcortical areas such as the putamen or superior colliculus. Our study supports the former possibility. One notable finding here might be that the ongoing-spontaneous excitation of unimodal cells by multimodal cells in a top-down manner (see Figure 9B; left) could enhance the modulatory (population) response, accelerating its speed (see Figure 12D).

Theoretical models based on Bayes’ rule can explain to some extent the multisensory enhancement observed in psychological experiments (Anastasio, Patton, & Belkacem-Boussaid, 2000; Deneve, & Pouget, 2004). Neural network models can provide some neuronal explanations for it (Ursino, Cuppini, Magosso, Serino, & di Pellegrino, 2009; Cuppini, Ursino, Magosso, Rowland, & Stein, 2010). Our neuronal modeling study may provide new insight into the understanding of multisensory integration for subthreshold stimuli. One notable finding might be that the intercortical interaction among a few active neurons can induce a population response that results in subthreshold cross-modal enhancement. Note that the cross-modal stimulus was so weak that it alone could not induce a population response. A prediction, which we hope will be confirmed experimentally, is that small depolarization that does not reach firing threshold, achieved through intercortical interaction among few active neurons, may be crucial for subthreshold cross-modal enhancement.

Concerning the manner of top-down projections, Shmuel and colleagues (2005) conducted an optical imaging study in visual systems. The researchers found that top-down projections from V2 to V1 are clustered and suggested that this circuitry might contribute to mediating contour integration. In contrast, Stettler, Das, Bennett, and Gilbert (2002) evidenced completely diffused V2-to-V1 projections. We showed here that the diffusive top-down circuitry could reduce the minimal current for population response (see IIIII in Figure 12B). The existence of diffusive top-down circuitry in other sensory cortices is, to the best of our knowledge, uncertain. Nonetheless, our finding gives an important notion that the manner of top-down projections (selective, diffusive, or their combination) may have an active role in subthreshold cross-modal enhancement.

Multisensory integration is evident for a variety of sensory modalities, such as visual-auditory, visual-somatosensory, auditory-somatosensory, and even visual-auditory-somatosensory (Meredith, 2004). The lower unimodal (X and Y) networks may correspond to the primary auditory (A1), visual (V1), and somatosensory (S1) cortices, and the higher multimodal (Y) network to the association cortex (Ghazanfar & Schroeder, 2006). Simulating a functional neural network model, we tried to elucidate their common, basic neuronal mechanisms, focusing especially on subthreshold cross-modal enhancement. Note that there is a difference between a neuron's being multisensory (i.e., responding to more than one sensory modality) and engaging in multisensory integration (responding differently to a cross-modal stimulus). The neurons in our model engage in multisensory integration to achieve cross-modal enhancement for a subthreshold stimulus.

Ambient GABA, which provides neurons with tonic inhibitory currents, was employed to achieve ongoing-spontaneous subthreshold membrane oscillations in P cells. To induce a population response by subthreshold stimulation, P cells should be near firing threshold. Note that because the stimulation was so weak that, presented alone, it could not induce a population response, it might be advantageous for P cells to be near threshold for their action potential generation. Our previous paper (Hoshino, 2009) investigated how ambient GABA contributes to maintaining ongoing-spontaneous subthreshold neuronal activity. We briefly explain it. GABA transporters on GABAergic interneurons (F and L) were modeled in a cortical neural network. At membrane potentials below the reversal potential of a transporter, there is a net influx of GABA, whereas at membrane potentials above the reversal potential, there is a net efflux of GABA. Through this transport mechanism, ambient GABA concentration can be kept within a submicromolar range during ongoing-spontaneous time periods. The study showed that the transporter-mediated ambient-GABA regulation contributes to achieving ongoing-spontaneous subthreshold membrane oscillations in principal cells, by which the network can respond rapidly and effectively to subsequent sensory input.

As shown in Figure 13, the transporter has another important role: it terminates the persistent neuronal activity soon after stimulus offset (left), which might be advantageous for the brain to prepare for the next sensory input. Without the ambient-GABA regulation (i.e., when it is fixed), the principal cells continue firing even after the input is switched off (right).

Figure 13:

A ready neuronal state achieved through transporter-mediated regulation of ambient (extrasynaptic) GABA. Responses to the paired stimuli, where the GABA transport mechanism worked (left) or not (right). Ambient GABA concentrations in each cell assembly are shown (see the bottom traces).

Figure 13:

A ready neuronal state achieved through transporter-mediated regulation of ambient (extrasynaptic) GABA. Responses to the paired stimuli, where the GABA transport mechanism worked (left) or not (right). Ambient GABA concentrations in each cell assembly are shown (see the bottom traces).

We employed two distinct interneurons, F and L, that contributed to inhibiting P cells in a different manner. The F cell has a role in limiting the excessive activity of stimulus-relevant P cells caused by their mutual excitation. The L cell has a role in suppressing stimulus-irrelevant P cells, when stimulus-relevant P cells are active, thereby improving the tuning property of the network. Namely, they are conventional feedback (F) and lateral (L) inhibitory cells.

A variety of GABAergic interneurons have been found in the cortex, such as horizontal cells and large, medium, and small multipolar cells (for a survey, see Prieto, Peterson, & Winer, 1994). Large multipolar cells with their wide axonal arbors can send signals to distant principal cells, while small multipolar cells with their narrow axonal arbors limit signals to proximal principal cells. Based on these observations, we let the L cell (as a large multipolar cell) project simply to all (nearby to distant) P cells within cell assemblies and the F cell (as a small multipolar cell) only to its proximal P cell.

Appendix A:  The Network Model

The 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 within the same cell assembly. IP,Fi(Xn; t) is an inhibitory synaptic current from its accompanying F cell, IP,Li(Xn; t) an inhibitory synaptic current from L cells, IP,Pi,lat(Xn; t) an lateral excitatory synaptic current from P cells belonging to the other unimodal cell assembly (Yn), IP,Pi,fdb(Xn; t) an 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
formula
A.7
formula
A.8
The dynamic evolution of the membrane potential of the ith F and L cells that belong to cell assembly Xn is defined by
formula
A.9
formula
A.10
where IF,Pi(Xn; t) and IL,Pi(Xn; t) are excitatory synaptic currents. IFi,ext(Xn; t) and ILi,ext(Xn; t) are inhibitory nonsynaptic currents. These currents are defined by
formula
A.11
formula
A.12
formula
A.13
formula
A.14
rPj(Xn; t) is the fraction of AMPA receptors in the open state triggered by the presynaptic action potentials of the jth P cell. rFj(Xn; t) and rLj(Xn; t) are the fractions of intrasynaptic GABAa receptors in the open state triggered by the presynaptic action potentials of the jth F cell and L cell, respectively. rGABAext(Xn; t) is the fraction of extrasynaptic GABAa receptors in the open state provoked by ambient GABA. The receptor dynamics and ambient GABA concentration are defined in appendixes B and C.

The Y and M networks were similarly defined. The Yn cell assembly receives a lateral projection from Xn and a feedback projection from Mn. Mn receives feedforward projections from Xn and Yn (see Figure 1). For model parameters and their values, see Table 1.

Appendix B:  Receptor Dynamics and Action Potential Generation

Receptor dynamics is based on a study by 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 in cell assembly Xn, [GABA]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 to 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

We briefly explain how ambient (extrasynaptic) GABA could be regulated by the transporter. As suggested by Richerson and colleagues (Richerson & Wu, 2003; Wu, Wang, & Richerson, 2003; Richerson, 2004; Wu, Wang, Diez-Sampedro, & Richerson, 2007), a transporter is not simply a vacuum 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 the 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 calculated when the electrochemical potential = 0, namely, at equilibrium. Under normal conditions, it is close to the resting potential of neurons. At membrane potentials below the reversal potential, the net influx of GABA, called forward transport or GABA uptake, takes place. In contrast, at membrane potentials above the reversal potential, net efflux of GABA, called reverse transport or GABA release, takes place. Through this transport mechanism, ambient GABA can be clamped at a certain level, within a submicromolar range at rest. The transporter is near equilibrium under normal physiological conditions and will reverse with a relatively small increase in membrane potential. The ambient GABA, even though its concentration is low, acts on extrasynaptic GABAa receptors and mediates to provide neurons with tonic inhibitory currents.

Depending on the level of ambient GABA (GABA concentration), inhibitory currents flow in P, F, and L cells (Hoshino, 2009). The concentration of ambient GABA in cell assembly Xn is defined by
formula
C.1
where JGABA(Xn; t) is the amount of forward or reverse transport of GABA, which depends on the activities of F and L cells and is functionally described as
formula
C.2
Those for Yn and Mn cell assemblies were similarly defined. For model parameters and their values, see Table 1.

Acknowledgments

I express my gratitude to Hiromi Ohta for her encouragement throughout this study and to the reviewers for giving me valuable comments and suggestions on the earlier drafts.

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