Abstract

In visual information processing, feedforward projection from primary to secondary visual cortex (V1-to-V2) is essential for integrating combinations of oriented bars in order to extract angular information embedded within contours that represent the shape of objects. For feedback (V2-to-V1) projection, two distinct types of pathways have been observed: clustered projection and diffused projection. The former innervates V1 domains with a preferred orientation similar to that of V2 cells of origin. In contrast, the latter innervates without such orientation specificity. V2 cells send their axons to V1 domains with both similar and dissimilar orientation preferences. It is speculated that the clustered feedback projection has a role in contour integration. The role of the diffused feedback projection, however, remains to be seen. We simulated a minimal, functional V1-V2 neural network model. The diffused feedback projection contributed to achieving ongoing-spontaneous subthreshold membrane oscillations in V1 cells, thereby reducing the reaction time of V1 cells to a pair of bars that represents specific angular information. Interestingly, the feedback influence took place even before V2 responses, which might stem largely from ongoing-spontaneous signaling from V2. We suggest that the diffusive feedback influence from V2 could act early in V1 responses and accelerate their reaction speed to sensory stimulation in order to rapidly extract angular information.

1.  Introduction

As an early visual system, the primary visual cortex (V1) receives information from the lateral geniculate nucleus (LGN) and sends it to the secondary visual cortex (V2). V1 cells have specific responsiveness to elemental visual attributes such as the orientation of bars (Ts'o & Roe, 1995). V2 cells respond to their combinations, extracting the angular information embedded within contours that represent the shape of objects (Ito & Komatsu, 2004). Convergent feedforward projections from V1 to V2 might have a crucial role in integrating the combination of oriented bars.

Concerning the feedback (V2-to-V1) projection, two distinct types of pathways have been observed: clustered feedback projection and diffused feedback projection (Sincich & Horton, 2005). The former innervates V1 domains with preferred orientation similar to that of V2 cells of origin. In contrast, the latter innervates without such orientation specificity. Namely, V2 cells send their axons to V1 domains with both similar and dissimilar orientation preferences. An experimental study (Stettler, Das, Bennett, & Gilbert, 2002) demonstrated that the feedback projection from V2 to V1 is more diffusive than intrinsic horizontal connections within V1, but it nevertheless is clustered to some extent (Shmuel et al., 2005). It was speculated that the clustered feedback projection might have a role in contour integration (Shmuel et al., 2005; Angelucci et al., 2002). The role of the diffused feedback projection in neuronal information processing, however, remains to be seen.

The purpose of this study is to elucidate the possible roles of diffused feedback projection and its significance in hierarchical sensory information processing. We simulate a simple, functional neural network model of V1 and V2, between which convergent feedforward (V1-to-V2) and divergent (diffused) feedback (V2-to-V1) axonal projections are made. The feedforward projection makes the V2 network sum responses from pairs of V1 orientation columns (Boynton & Hegde, 2004), by which the V2 network can integrate specific combinations of oriented bars (Boynton & Hegde, 2004; Anzai, Peng, & Van Essen, 2007). The V2 network sends axonal output back to the V1 network in a diffusive manner, namely, to all the V1 cells regardless of their orientation specificity.

In V1, horizontal synaptic connection is a prominent characteristic of intrinsic circuitry, originating primarily from pyramidal cells. Lateral synaptic connections in V1 are formed by pyramidal cell axons that extend up to several millimeters, where two distinct zones of connectivity have been observed (Malach, Amir, Harel, & Grinvald, 1993; Bosking, Zhang, Schofield, & Fitzpatrick, 1997; Eysel, 1999). Beyond hundreds of microns, axons tend to project selectively to cells that have similar orientation preferences. In contrast, within hundreds of microns, axons of pyramidal cells branch to form distributed connections to cells with both similar and dissimilar orientation preferences. We employ a V1 model for the latter case: a neural network with short-range, uniform connections. This V1 circuitry correlates combinations of oriented bars (Totoki, Matsuo, Zheng, & Hoshino, 2010), by which the V2 network can extract their angular information efficiently.

The V1 network is presented with a pair of bars, and the activities (membrane potentials and spikes) of V1 and V2 cells are recorded. Statistically analyzing them, we investigate how the diffused feedback projection affects the responsiveness of V1 and V2 networks. Comparing with those obtained by the clustered feedback projection scheme, we try to elucidate the significance of the diffused feedback projection scheme in hierarchical sensory information processing.

2.  The Neural Network Model

Figure 1A shows the neural network model in which a primary (V1) and a secondary (V2) visual cortical area are reciprocally connected. The V1 and V2 networks have responsiveness to the specific orientation of bars and their combinations, respectively. Angular information expressed by combinations of bars ranges from π/8 (see A07) to 7π/8 (see A34). Between V1 and V2 networks, we assume convergent feedforward (the solid lines) and divergent (diffused) feedback (the dashed lines) projections. When a pair of bar stimuli (e.g., θ2 and θ5) is presented, the V1 columns corresponding to that pair receive input signals from the lateral geniculate nucleus (LGN) and generate action potentials. This let the single V2 column (see A25) generate action potentials responding to that pair, which then excites all the V1 columns in a feedback manner regardless of their orientation specificity.

Figure 1:

Neural network model. (A) An overview of a minimal, functional V1-V2 neural network model. A primary (V1) and a secondary visual (V2) area are reciprocally connected. The V1 receives combinatorial inputs from the lateral geniculate nucleus (LGN) when presented with a pair of bar stimuli. The V2 sends feedback axonal projections to the V1. For clarity, only the pathways between the columns (θ2, θ5, A25) relevant to the paired stimuli (θ2, θ5) are shown. (B) V1 orientation columns and V2 angular columns comprising cell units (e.g., see the gray circle): one principal cell (P), interneurons (F) and (L). ffw and fdb denote the feedforward (V1-to-V2) and feedback (V2-to-V1) axonal projections, respectively.

Figure 1:

Neural network model. (A) An overview of a minimal, functional V1-V2 neural network model. A primary (V1) and a secondary visual (V2) area are reciprocally connected. The V1 receives combinatorial inputs from the lateral geniculate nucleus (LGN) when presented with a pair of bar stimuli. The V2 sends feedback axonal projections to the V1. For clarity, only the pathways between the columns (θ2, θ5, A25) relevant to the paired stimuli (θ2, θ5) are shown. (B) V1 orientation columns and V2 angular columns comprising cell units (e.g., see the gray circle): one principal cell (P), interneurons (F) and (L). ffw and fdb denote the feedforward (V1-to-V2) and feedback (V2-to-V1) axonal projections, respectively.

As shown in Figure 1B, V1 columns consist of cell units (see the gray circle) that contain one principal cell (P) and two inhibitory cells (F, L). There are 20 units in each V1 (and V2) column. Each P cell receives excitatory inputs from P cells that belong to the same column, an inhibitory input from its accompanying F cell, and inhibitory inputs from L cells that receive excitatory inputs from P cells belonging to other columns. Each F cell receives an excitatory input from its accompanying P cell.

The V1 network receives a tuned (from narrow to broad) input from LGN determined by τP (see equation A.8 in appendix  A). For simplicity, we do not model the LGN and directly provide each V1 P cell with a graded excitatory current as a tuned input when presented with a particular bar stimulus (see ILGNn; θinp) of equations A.1 and A.8). τP is changed for all V1 columns equally. Cells in a V1 column have receptive fields with the same orientation and the same spatial position. Cells in different V1 columns have receptive fields with different orientations and the same spatial position. This might be the simplest way of integrating combinations of (short) bars that are presented in the same spatial position.

The F cell has a role in inhibiting pyramidal (P) cells in a feedback manner if they are activated excessively through recurrent excitation. The L cell has a role in inhibiting P cells in a lateral manner so that stimulus-irrelevant P cells are deactivated, while stimulus-relevant P cells are being active. The F and L cells respectively send narrow and wide axonal arbors to P cells, which may correspond to GABAergic interneurons such as small and large basket cells observed in the visual cortex, respectively (Fairen, DeFelipe, & Regidor, 1984). The details of network dynamics regulated by these inhibitory interneurons have been reported in our previous study (Hoshino, 2006).

The V1 cell has a minimal receptive field size and is not influenced by the RF surround. The untuned inhibition of P cells within the receptive field, achieved by short-range uniform (P-to-L) connections, ensure the integration of combinations of bars in the simplest way. Although it is evident that the RF surround affects visual information processing, we focused here on how the diffused and clustered feedback projections affect V1 responses in a simple perceptual task: detection of combinations of bars.

The V2 network has the same neuronal circuit structure as the V1 network. The V1 and V2 networks are connected by feedforward (see ffw) and feedback (see fdb) projections. We assume the excitatory feedback based on experiments that demonstrated that pathways from V2 to V1 send mainly excitatory input (Shao & Burkhalter, 1996; Hupe, James, Girard, & Bullier, 2001) preferentially to pyramidal cells (Johnson & Burkhalter, 1996). A conductance-based, integrate-and-fire neuron model is employed (Hoshino, 2006, 2008, 2009); it is mathematically defined in appendixes  A and  B, and its parameters are listed in Table 1.

Table 1:
Parameters and Their Values.
DescriptionParameterValue
Membrane capacitance of type Y (Y = P, F, L) cell cYm cPm = 0.5 nF, cFm = 0.2 nF, cLm = 0.6 nF 
Membrane conductance gYm gPm = 25 nS, gFm = 20 nS, gLm = 15 nS 
Resting potential uYrest 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 cell assemblies N 20 
Synaptic strength from jth to ith P cell within orientation   
 θn or angular Akl column   
Synaptic strength from ith F to P cell  wP,Fin) = 30, wP,Fi(Akl) = 20 
Synaptic strength from jth L to ith P cell  wP,Lijn) = wP,Lij(Akl) = 15 
Lateral synaptic strength from jth to ith P cell between   
 different (n′ ≠ n)columns   
Feedback (top-down) synaptic strength from ith V2 to V1 P cell wP,Pi,fdbn, AklwFDB = 11, τfdb = 100 (see equations A.6 and A.7
Feedforward (bottom-up) synaptic strength from ith V1 to V2 P cell wP,Pi,ffw(Akl, θnwFFW = 11 (see equations A.17 and A.18
Input current into the V1 network ILGNn; θinpαP = 1.2 × 10−10, τP = 0.5 (see equation A.8
Synaptic strength from ith P to F cell  wF,Pin) = wF,Pi(Akl) = 30 
Synaptic strength from ith P to L cell between   
 different (n′ ≠ n, kl′ ≠ kl) columns   
Channel closure rate for type Z (Z = AMPA, GABA) receptor βZ βAMPA = 190, βGABA = 180 
Concentration of glutamate in synaptic cleft released from P cell GlutPmax 1 mM 
Concentration of GABA in synaptic cleft released from type GABAYmax GABAFmax = GABALmax = 1 mM 
 Y (Y = F, L) cell   
Steepness of sigmoid function for type Y (Y = P, F, L) cell ηY ηP = 220, ηF = ηL = 180 
Threshold of sigmoid function for type Y (Y = P, F, L)   
 cell belonging to column X (θn, AklζXY ζXP = −36 mV, ζXF = ζXL = −38 mV 
DescriptionParameterValue
Membrane capacitance of type Y (Y = P, F, L) cell cYm cPm = 0.5 nF, cFm = 0.2 nF, cLm = 0.6 nF 
Membrane conductance gYm gPm = 25 nS, gFm = 20 nS, gLm = 15 nS 
Resting potential uYrest 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 cell assemblies N 20 
Synaptic strength from jth to ith P cell within orientation   
 θn or angular Akl column   
Synaptic strength from ith F to P cell  wP,Fin) = 30, wP,Fi(Akl) = 20 
Synaptic strength from jth L to ith P cell  wP,Lijn) = wP,Lij(Akl) = 15 
Lateral synaptic strength from jth to ith P cell between   
 different (n′ ≠ n)columns   
Feedback (top-down) synaptic strength from ith V2 to V1 P cell wP,Pi,fdbn, AklwFDB = 11, τfdb = 100 (see equations A.6 and A.7
Feedforward (bottom-up) synaptic strength from ith V1 to V2 P cell wP,Pi,ffw(Akl, θnwFFW = 11 (see equations A.17 and A.18
Input current into the V1 network ILGNn; θinpαP = 1.2 × 10−10, τP = 0.5 (see equation A.8
Synaptic strength from ith P to F cell  wF,Pin) = wF,Pi(Akl) = 30 
Synaptic strength from ith P to L cell between   
 different (n′ ≠ n, kl′ ≠ kl) columns   
Channel closure rate for type Z (Z = AMPA, GABA) receptor βZ βAMPA = 190, βGABA = 180 
Concentration of glutamate in synaptic cleft released from P cell GlutPmax 1 mM 
Concentration of GABA in synaptic cleft released from type GABAYmax GABAFmax = GABALmax = 1 mM 
 Y (Y = F, L) cell   
Steepness of sigmoid function for type Y (Y = P, F, L) cell ηY ηP = 220, ηF = ηL = 180 
Threshold of sigmoid function for type Y (Y = P, F, L)   
 cell belonging to column X (θn, AklζXY ζXP = −36 mV, ζXF = ζXL = −38 mV 

3.  Results

3.1.  Feedback Influences on V1 Responses.

In this section, we show how the diffused feedback (V2-to-V1) projection affects V1 P cell responses. A pair of bar stimuli (θ2 and θ5) was presented to the V1 network. The raster plots are shown in Figure 2, where the feedback mechanism worked (A) or not (B). To disable the feedback mechanism, we elevated the threshold value for V2 P cells from −36 mV to −30 mV (: see equation B.3 in appendix  B and Table 1).

Figure 2:

Responses to visual stimulation. (A) Raster plots of action potentials evoked in V1 (θ0−7) and V2 (A34−07) P cells, in which a pair of bar stimuli (θ2 and θ5) as a visual corner (A25) was presented to the V1 network. (B) Raster plots in which V2 P cells were deactivated by elevating their firing threshold () from −36 mV to −30 mV.

Figure 2:

Responses to visual stimulation. (A) Raster plots of action potentials evoked in V1 (θ0−7) and V2 (A34−07) P cells, in which a pair of bar stimuli (θ2 and θ5) as a visual corner (A25) was presented to the V1 network. (B) Raster plots in which V2 P cells were deactivated by elevating their firing threshold () from −36 mV to −30 mV.

Figure 3A presents spike counts (bin = 1msec) for Figure 2, and their cumulative representations are shown in Figure 3B. Bair, Cavanaugh, Smith, and Movshon (2002) reported that the onset and offset latencies were approximately 50 msec and 30 msec, respectively. We confirmed roughly similar onset (see downward arrows at the top) and offset (see the downward arrow at the bottom) latencies. Interestingly, the onset latency can be shortened (i.e., the reaction speed can be accelerated) by the feedback mechanism (compare the downward and upward arrows at the top). In comparison, the feedback influence on the offset latency appears to be slight (compare the downward and upward arrows at the bottom).

Figure 3:

Onset and offset response latencies. (A) Spike counts from each column (20 P cells) with (top) or without (bottom) feedback influence, where the threshold value for V2 cells was kept at −36 mV (top) or elevated to −30 mV (bottom). Time bin was 1 msec. (B) Cumulative representations of the spike counts. The onset latency can be shortened by the feedback mechanism (the downward arrows at the top). Offset latencies are indicated by the arrows (bottom).

Figure 3:

Onset and offset response latencies. (A) Spike counts from each column (20 P cells) with (top) or without (bottom) feedback influence, where the threshold value for V2 cells was kept at −36 mV (top) or elevated to −30 mV (bottom). Time bin was 1 msec. (B) Cumulative representations of the spike counts. The onset latency can be shortened by the feedback mechanism (the downward arrows at the top). Offset latencies are indicated by the arrows (bottom).

Figure 4A shows spike counts (bin = 1msec) at around the onset of the stimuli. Figure 4B (top) presents the differences in cumulative spike counts between the two conditions (with or without feedback influence); see in Figure 3B the traces marked by = −36 mV (with feedback influence) and those marked by = −30 mV (without feedback influence). The filled arrow in Figure 4B indicates the initiation of feedback influence. Interestingly, it takes place even before the V2 response (see the open arrow). This earlier influence on V1, preceding the V2 response, might stem largely from ongoing-spontaneous feedback signaling from the V2. Stimulus-evoked feedback signaling from the V2 might have an influence on V1 after the V2 response, presumably enhancing the V1 response (see Figure 3B, bottom). An experiment (Girard, Hupe, & Bullier, 2001) estimated that the V2-to-V1 feedback influence takes place within 10 msec after the V2 response.

Figure 4:

Feedback influence on the V1 response. (A) Spike counts at around the onset of the stimuli (θ2, θ5), where the feedback mechanism worked ( = −36 mV). Time bin was 1 msec. (B) Top: Differences in cumulative spike counts (V1) between the two conditions (with or without feedback influence, see the traces marked by = −36 mV and −30 mV in Figure 3B). Bottom: Cumulative spike counts (V2) with feedback influence ( = −36 mV). The filled arrow indicates the initiation of feedback influence, which takes place even before the V2 response (see the open arrow).

Figure 4:

Feedback influence on the V1 response. (A) Spike counts at around the onset of the stimuli (θ2, θ5), where the feedback mechanism worked ( = −36 mV). Time bin was 1 msec. (B) Top: Differences in cumulative spike counts (V1) between the two conditions (with or without feedback influence, see the traces marked by = −36 mV and −30 mV in Figure 3B). Bottom: Cumulative spike counts (V2) with feedback influence ( = −36 mV). The filled arrow indicates the initiation of feedback influence, which takes place even before the V2 response (see the open arrow).

Figure 5 presents the ongoing-spontaneous membrane potential of a P cell sensitive to θ2 (A), θ5 (B) or their combination (A25: C), where the feedback mechanism worked (top) or not (bottom). Figure 6A presents their two-dimensional expressions. The x-axis represents the ongoing-spontaneous membrane potential of a P cell relevant to θ2 (top left), θ5 (top right) or A25 (bottom), where the threshold value for V2 P cells was kept at −36 mV (see the top of Figures 5A–5C). The y-axis represents the ongoing-spontaneous membrane potential of the same P cell, where the threshold value was elevated to −30 mV (see the bottom of Figures 5A–5C). At identical times, these two membrane voltages (e.g., see the traces marked by x and y in Figure 5A) were plotted on the two-dimensional plane (x, y) at 1 millisecond intervals (see Figure 6A; top left). To focus on the subthreshold membrane behavior, we omitted the action potentials in the two-dimensional expressions.

Figure 5:

Ongoing-spontaneous membrane oscillation. (A) Ongoing-spontaneous membrane potential of a θ2-sensitive P cell with (top) or without (bottom) feedback influence. To disable the feedback mechanism, we deactivated V2 P cells by elevating their threshold value () from −36 mV to −30 mV. (B, C) Ongoing-spontaneous membrane potentials of a θ5-sensitive and an A25-sensitive P cell, respectively.

Figure 5:

Ongoing-spontaneous membrane oscillation. (A) Ongoing-spontaneous membrane potential of a θ2-sensitive P cell with (top) or without (bottom) feedback influence. To disable the feedback mechanism, we deactivated V2 P cells by elevating their threshold value () from −36 mV to −30 mV. (B, C) Ongoing-spontaneous membrane potentials of a θ5-sensitive and an A25-sensitive P cell, respectively.

Figure 6:

Ongoing-spontaneous subthreshold membrane depolarization. (A) Two-dimensional expressions of membrane potentials of a θ2-sensitive (top left), a θ5-sensitive (top right) V1 P cell and an A25-sensitive V2 P cell (bottom) for an ongoing-spontaneous time period (10 sec) shown in Figure 5. The ordinate and abscissa are the membrane potentials recorded for the elevated ( = −30 mV) and original ( = −36 mV) V2 threshold values, respectively. (B–D) Dependence of ongoing-spontaneous subthreshold membrane oscillation on the threshold value that was changed between −33 and −37 mV. (B) Histograms (left) and their cumulative representations (right) of ongoing-spontaneous membrane potentials of a θ2-sensitive V1 P cell. (C) Those for a θ5-sensitive V1 P cell or (D) for a A25-sensitive V2 P cell.

Figure 6:

Ongoing-spontaneous subthreshold membrane depolarization. (A) Two-dimensional expressions of membrane potentials of a θ2-sensitive (top left), a θ5-sensitive (top right) V1 P cell and an A25-sensitive V2 P cell (bottom) for an ongoing-spontaneous time period (10 sec) shown in Figure 5. The ordinate and abscissa are the membrane potentials recorded for the elevated ( = −30 mV) and original ( = −36 mV) V2 threshold values, respectively. (B–D) Dependence of ongoing-spontaneous subthreshold membrane oscillation on the threshold value that was changed between −33 and −37 mV. (B) Histograms (left) and their cumulative representations (right) of ongoing-spontaneous membrane potentials of a θ2-sensitive V1 P cell. (C) Those for a θ5-sensitive V1 P cell or (D) for a A25-sensitive V2 P cell.

The result shown in Figure 6A (top) indicates that the feedback projection contributes to slightly depolarizing V1 P cells. Interestingly, the feedback signaling slightly depolarizes V2 P cells themselves (bottom). Note that these membrane depolarizations are below firing threshold. Our previous studies (Hoshino, 2006, 2008, 2009) found a close relationship between reaction speed and ongoing-spontaneous membrane potential and suggested that such an ongoing-spontaneous subthreshold neuronal state is one of the crucial factors for the acceleration of the reaction speed of neurons to sensory stimulation.

Figures 6B to 6D (left) present ongoing-spontaneous membrane potential histograms for V1 (see Figures 6B and 6C) and V2 (see Figure 6D) P cells. Their cumulative representations (normalized) are shown (right), depending on the V2 threshold value (). P cells tend to be slightly depolarized as the threshold lowers: −33 → −37 mV. As quantitatively shown in Figure 7A, threshold values that are too low (e.g., mV) increase ongoing-spontaneous spiking activity (see the open circles), resulting in the depression of stimulus-evoked activity in V1 (see the open squares in Figure 7B). We found an optimal range for the threshold value, mV, at which stimulus-evoked activity in V1 is the highest (see the arrow). Note that the stimulus-evoked activity was calculated by subtracting the ongoing-spontaneous spike count from the spike count when stimulated (stimulus-related spike count: see the open circles and triangles).

Figure 7:

Dependence of ongoing-spontaneous and stimulus-evoked neuronal activities on V2 threshold value. (A) Ongoing-spontaneous and (B) stimulus-evoked activities of a V1 and a V2 P cell as a function of the V2 threshold value (). The stimulus-evoked activity (see the squares) was calculated by subtracting the ongoing-spontaneous spike count from the stimulus-related spike count (the spike count when stimulated: see the circles and triangles).

Figure 7:

Dependence of ongoing-spontaneous and stimulus-evoked neuronal activities on V2 threshold value. (A) Ongoing-spontaneous and (B) stimulus-evoked activities of a V1 and a V2 P cell as a function of the V2 threshold value (). The stimulus-evoked activity (see the squares) was calculated by subtracting the ongoing-spontaneous spike count from the stimulus-related spike count (the spike count when stimulated: see the circles and triangles).

3.2.  Comparison with Clustered Feedback Projection Scheme.

In this section, we devised a simulation in which the clustered (instead of diffused) feedback projection was employed. Comparing it with the diffused feedback projection scheme, we tried to elucidate its significance in hierarchical sensory information processing.

Figure 8A presents two-dimensional expressions of membrane potentials of V1 (top) and V2 (bottom) P cells for an ongoing-spontaneous time period (10 sec). The clustered feedback projection was made by decreasing the value of τfdb (see equation A.7) from 100 to 0.01. The abscissa and ordinate are the membrane potentials recorded for the diffused and clustered feedback projection schemes, respectively. We found that the diffused feedback projection contributes to depolarizing V1 P cells below firing threshold.

Figure 8:

Influences of the diffusiveness of feedback projection (τfdb; see equation A.7 in appendix  A) on ongoing-spontaneous and stimulus-evoked neuronal activities. (A) Two-dimensional expressions of membrane potentials of a θ2-sensitive (top-left), a θ5-sensitive (top-right) V1 P cell, and an A25-sensitive V2 P cell (bottom) for an ongoing-spontaneous time period (10 sec). The ordinate and abscissa are the membrane potentials recorded for the clustered and diffused feedback projection schemes, respectively. (B) Average firing rate of stimulus-relevant (see the circles) or stimulus-irrelevant (see the triangles) V1 P cells, where the squares denote their differences. (C) Cumulative hyperpolarization that measures a degree of membrane hyperpolarization (see equation 3.1). (D) Dependence of the membrane hyperpolarization (see the diamonds on the “hyperpol. index” axis) and the selective responsiveness (see the squares on the “difference” axis) on the diffusiveness of feedback projection.

Figure 8:

Influences of the diffusiveness of feedback projection (τfdb; see equation A.7 in appendix  A) on ongoing-spontaneous and stimulus-evoked neuronal activities. (A) Two-dimensional expressions of membrane potentials of a θ2-sensitive (top-left), a θ5-sensitive (top-right) V1 P cell, and an A25-sensitive V2 P cell (bottom) for an ongoing-spontaneous time period (10 sec). The ordinate and abscissa are the membrane potentials recorded for the clustered and diffused feedback projection schemes, respectively. (B) Average firing rate of stimulus-relevant (see the circles) or stimulus-irrelevant (see the triangles) V1 P cells, where the squares denote their differences. (C) Cumulative hyperpolarization that measures a degree of membrane hyperpolarization (see equation 3.1). (D) Dependence of the membrane hyperpolarization (see the diamonds on the “hyperpol. index” axis) and the selective responsiveness (see the squares on the “difference” axis) on the diffusiveness of feedback projection.

To investigate how the diffusiveness of feedback projection affects the responsiveness of V1 P cells, we varied τfdb between 0.01 and 10,000. Note that τfdb = 0.01 and 10,000 achieve almost complete clustered and diffused feedback projections, respectively. Figure 8B presents the average firing rates of stimulus-relevant (see the circles) and stimulus-irrelevant (see the triangles) V1 P cells, where the squares denote their differences. A small difference signifies an unselective response. As expected, the selective responsiveness is degraded as τfdb increases (see the squares).

To quantitatively assess the influence of diffusiveness of feedback projection on ongoing-spontaneous subthreshold membrane oscillation, we calculated cumulative hyperpolarization, which measures a degree of membrane hyperpolarization and is defined by
formula
3.1
Figure 8C indicates that the enhancement of diffusive nature by increasing τfdb can alleviate hyperpolarization and thus contributes to achieving the ongoing-spontaneous subthreshold neuronal state.

Figure 8D indicates that the clustered feedback projection scheme (see the smaller τfdb values) is advantageous for the selective responsiveness (see the squares at the difference axis), whereas the diffused feedback projection scheme (see the larger τfdb values) is advantageous for the ongoing-spontaneous subthreshold membrane oscillation (see the diamonds at the ”hyperpol. index” axis). We found that the clustered feedback projection that still has a diffusive nature (see τfdb = ∼3) provides the best network performance: it allows V1 P cells to respond selectively to the stimuli, while still keeping the ongoing-spontaneous subthreshold neuronal activity.

As addressed in section 1, we assumed the distributed lateral excitatory connections between orientation columns in V1. Figures 9A and 9B present how the lateral excitation affects ongoing-spontaneous subthreshold membrane oscillations, in which the connection weight (; see equation A.5) was changed from the original value 0.2 (abscissa) to 0 (see Figure 9A, ordinate) or 0.4 (see Figure 9B, ordinate). We found that the increase in the weight leads to ongoing-spontaneous subthreshold membrane oscillations. Note that it should be restricted: . Otherwise the ongoing-spontaneous spiking activity of V1 P cells became too great and resulted in depressing stimulus-evoked neuronal activity (not shown).

Figure 9:

Dependence of ongoing-spontaneous subthreshold membrane oscillation on the weight of lateral excitatory connections between V1 columns: ) (see equation A.5). Two-dimensional expressions of membrane potentials of a θ2-sensitive V1 P cell (left) and an A25-sensitive V2 P cell (right). The ordinate is the membrane potential recorded for the (A) weakened or (B) strengthened connection weight.

Figure 9:

Dependence of ongoing-spontaneous subthreshold membrane oscillation on the weight of lateral excitatory connections between V1 columns: ) (see equation A.5). Two-dimensional expressions of membrane potentials of a θ2-sensitive V1 P cell (left) and an A25-sensitive V2 P cell (right). The ordinate is the membrane potential recorded for the (A) weakened or (B) strengthened connection weight.

3.3.  Responses to Broadly Tuned Input.

In this section, we show whether and how the diffused feedback projection affects the responsiveness of V1 and V2 networks to broadly tuned input. Raster plots of action potentials evoked in V1 (θ0−7) and V2 (A34−07) P cells are shown in Figure 10A, where a broadly tuned input was applied to the V1 network (see the horizontal bar). For that input, we changed τP (see equation A.8) from the original value of 0.5 to 2.6 (see Table 1). At the beginning of the input, stimulus-irrelevant V1 P cells happen to wrongly respond (see θ1) which is eventually taken over by stimulus-relevant P cells (see θ5 and θ2). In contrast, as shown in Figure 10B the stimulus-irrelevant V1 P cells continue firing (see θ1) if the clustered (instead of diffused) feedback projection scheme works. These results indicate that the diffused feedback projection contributes to reliably extracting the angular information. Note that V1 columns are laterally inhibited via L cells. This circuitry allows only one V1 column to respond to a single bar stimulus: a winner-take-all operation takes place. Only two V1 columns are allowed to respond in order to accomplish such a simple perceptual task: detection of combinations of bars.

Figure 10:

Responses to broadly tuned input. (A) Raster plots of action potentials evoked in V1 (θ0−7) and V2 (A34−07) P cells. A broadly tuned input, which was made by increasing τP from 0.5 to 2.6 (see equation A.8), was applied to the V1 network. The mild spike generation in A16-sensitive P cells (see the circled 1) is induced by the transient activation of stimulus-irrelevant V1 P cells (see θ1). (B) Raster plots in which the clustered (instead of diffused) feedback projection scheme worked.

Figure 10:

Responses to broadly tuned input. (A) Raster plots of action potentials evoked in V1 (θ0−7) and V2 (A34−07) P cells. A broadly tuned input, which was made by increasing τP from 0.5 to 2.6 (see equation A.8), was applied to the V1 network. The mild spike generation in A16-sensitive P cells (see the circled 1) is induced by the transient activation of stimulus-irrelevant V1 P cells (see θ1). (B) Raster plots in which the clustered (instead of diffused) feedback projection scheme worked.

To understand how the diffused feedback projection scheme allows the networks to respond correctly to the broadly tuned input, we recorded field potentials from stimulus-relevant V1 (θ2 and θ5) and V2 (A25) cell assemblies and from stimulus-irrelevant (A16) cell assembly. The field potential was calculated simply as the sum of membrane potentials of P cells belonging to the same cell assembly. As shown in Figure 11, at the beginning of input, stimulus-irrelevant V2 (A16) P cells are activated (see the circled 1). Note that the moderately elevated field potential reflects the mild spike generation (indicated by the circled 1 in Figure 10A), which is supposed to be induced by the bursts of spikes that are transiently generated in stimulus-irrelevant V1 P cells (see θ1 in Figure 10A). This then excites stimulus-relevant P cells (see the solid trace marked by the circled 2 in Figure 11A), followed by their continual spike generation (see the solid trace marked by the circled 3). This then excites stimulus-relevant V2 P cells (see the solid trace marked by the circled 4), followed by their continual spike generation (see the solid trace marked by the circled 5). This then excites stimulus-relevant V1 cells (see the solid trace marked by the circled 6), followed by their continual spike generation (see the solid trace marked by the circled 7). This sequence of excitation finally leads to the persistent spiking in these stimulus-relevant V1 (see the solid traces for θ2 and θ5) and V2 (see the solid trace for A25) P cells.

Figure 11:

Temporal sequence of neuronal activation by broadly tuned input. (A) Field potentials recorded from stimulus-relevant V1 (θ2, θ5), V2 (A25) and stimulus-irrelevant V2 (A16) cell assemblies. The horizontal bar indicates the stimulation period. The dashed traces are those obtained by the clustered feedback projection scheme. The circled numbers indicate a sequence of neuronal excitation. (B) Differences between field potentials obtained by the diffused and clustered feedback projection schemes (i.e., the differences between the solid and dashed traces in panel A). These differences demonstrate the recovering process of stimulus-relevant columns (θ2, θ5, A25) from their missed responses, that is, the stimulus-irrelevant columns (θ1, θ6, A16) wrongly respond.

Figure 11:

Temporal sequence of neuronal activation by broadly tuned input. (A) Field potentials recorded from stimulus-relevant V1 (θ2, θ5), V2 (A25) and stimulus-irrelevant V2 (A16) cell assemblies. The horizontal bar indicates the stimulation period. The dashed traces are those obtained by the clustered feedback projection scheme. The circled numbers indicate a sequence of neuronal excitation. (B) Differences between field potentials obtained by the diffused and clustered feedback projection schemes (i.e., the differences between the solid and dashed traces in panel A). These differences demonstrate the recovering process of stimulus-relevant columns (θ2, θ5, A25) from their missed responses, that is, the stimulus-irrelevant columns (θ1, θ6, A16) wrongly respond.

The major cause of the incorrect response observed for the clustered feedback projection scheme (see Figure 10B) might be a lack of excitation of stimulus-relevant V1 P cells (see the dashed traces marked by the circled 2 and 2’) by stimulus-irrelevant (A16) V2 P cells (see the circled 1→2 and 1→2’). Note that the diffused (but not clustered) feedback projection scheme allows the stimulus-relevant (θ2- and θ5-sensitive) V1 P cells to receive feedback signals from the stimulus-irrelevant (A16-sensitive) V2 P cells. Figure 11B presents the differences between these field potentials (see the solid and dashed traces in Figure 11A). The temporal sequences of excitation show how the wrong response can be taken over by the correct response when the diffused feedback projection scheme works.

The transient activation of the stimulus-irrelevant (θ1) P cells (see Figure 10A) stems largely from a stochastic process. Figure 12 shows the probability that the θn-sensitive (0 ≤ n ≤ 7) column responds first when V1 P cells receive a finely (τP = 0.5, top left) to broadly (τP = 2.0, bottom right) tuned input. The finely tuned input almost perfectly activates P cells relevant to the stimuli (θ2, θ5; see the top left), whereas the broadly tuned input allows P cells that are irrelevant to the stimuli to be transiently activated with a low but significant probability (see the bottom right). Note that the response probabilities of θ3- and θ4-sensitive P cells are higher than those of the other stimulus-irrelevant (θ0, θ1, θ6, θ7) P cells. Since these stimulus-irrelevant (θ3, θ4) columns are between the stimulus-relevant (θ2, θ5) columns, they receive larger graded, summed excitatory currents (see equation A.8 in appendix  A), thereby increasing their firing probabilities (see equation B.3).

Figure 12:

Probability that the θn-sensitive (0 ≤ n ≤ 7) column responds first to stimuli (θ2, θ5). V1 P cells received a finely (τP = 0.5) to broadly (τP = 2.0) tuned input. The same stimuli (θ2, θ5) were presented repeatedly (20 times) at different (random) onset times.

Figure 12:

Probability that the θn-sensitive (0 ≤ n ≤ 7) column responds first to stimuli (θ2, θ5). V1 P cells received a finely (τP = 0.5) to broadly (τP = 2.0) tuned input. The same stimuli (θ2, θ5) were presented repeatedly (20 times) at different (random) onset times.

As shown in Figure 13A, the time period required for the takeover of the wrong response by the correct response (see the arrows) is prolonged as the broadness of input (τP) increases. We presented the same stimuli (θ2, θ5) repeatedly (20 times) at random onset times for different τP values (0.5 ≤ τP ≤ 2) and measured takeover times, which are quantitatively shown in Figure 13B. We found that the takeover time is shorter (by several tens of milliseconds) for narrower inputs: τP < 1. The longer takeover times (τP>1) might stem largely from the competition among V1 columns as dynamic cell assemblies, which we hope will become experimentally evident in the future.

Figure 13:

Time periods required for the takeover of stimulus-irrelevant by stimulus-relevant V1 P cells. (A) Raster plots when presented repeatedly (20 times) with the same stimuli (θ2, θ5) at random onset times for different τP values (0.5 ≤ τP ≤ 2). The wrong responses are eventually taken over by the correct responses (see the arrows). (B) Quantitative representations of the takeover times for θ2-sensitive (circles), θ5-sensitive (triangles), and A25-sensitive (squares) P cells.

Figure 13:

Time periods required for the takeover of stimulus-irrelevant by stimulus-relevant V1 P cells. (A) Raster plots when presented repeatedly (20 times) with the same stimuli (θ2, θ5) at random onset times for different τP values (0.5 ≤ τP ≤ 2). The wrong responses are eventually taken over by the correct responses (see the arrows). (B) Quantitative representations of the takeover times for θ2-sensitive (circles), θ5-sensitive (triangles), and A25-sensitive (squares) P cells.

4.  Discussion

To understand the significance of a diffused feedback projection scheme in hierarchical information processing, we simulated a minimal, functional V1-V2 neural network model. It contributed to achieving ongoing-spontaneous subthreshold membrane oscillations in V1 cells, thereby reducing their reaction time to sensory stimuli. Diffused feedback projection that still had to some extent a clustered nature gave the best network performance (see Figure 8D): it allowed V1 cells to oscillate near firing threshold during the ongoing-spontaneous time period, while still keeping their selective responsiveness to the stimuli. This result may help understand the significance of the fact that the feedback projection from V2 to V1 is more diffusive than intrinsic horizontal connections within V1, but it nevertheless is to some extent clustered (Shmuel et al., 2005).

In general, a lower network receives peripheral input signals and transmits them to a higher network. The higher network then exerts a feedback influence on the lower network. This sequential signal transmission process implies that the feedback influence might act later in lower network responses to peripheral stimulation, namely, after the higher network is driven by the feedforward signals from the lower network. However, we found evidence of a fast-feedback influence on V1 responses (see Figure 4B). We suggest that the diffusive feedback influence from V2 can act even early in V1 responses and may have a role in accelerating their reaction speed to sensory stimuli. The earlier feedback influence on V1 responses that precedes V2 responses might stem largely from ongoing-spontaneous signaling from the V2.

One interesting finding might be that the diffused feedback projection scheme allowed the networks to respond correctly to a broadly tuned input, whereas the clustered projection scheme resulted in wrongly responding (see Figure 10). We suggest that the diffused feedback projection may have another important role: reliable extraction of angular information, especially when salient sensory information is unavailable.

In general, V2 cells receive inputs from V1 cells across a region of space larger than individual V1 receptive fields (Shushruth, Ichida, Levitt, & Angelucci, 2009). The larger receptive field size might be necessary for the V2 cells to extract complex shape information from natural visual scenes (Hegde & Van Essen, 2000, 2007). In this study, to simply integrate combinations of bars, it was sufficient for the V2 cells to receive inputs from the individual (corresponding) V1 cells. However, the larger V2 receptive field might affect V1 responses and have an important role in extracting complex visual information in the real world.

To integrate a pair of bars in the simplest way, we employed a linear sum integration method. However, an experiment by Ito and Komatsu (2004) suggested that combinations of bars might be integrated in a nonlinear manner. An experiment by Anzai and colleagues (2007) suggested that nonlinear inhibitory interaction might have a crucial role in integrating combinations of bars, for which a number of hypothetical neuronal circuitries was proposed. The nonlinear integration might have an important role in extracting complex shape information from natural visual scenes.

Appendix A:  The Neural Network Model

Dynamic evolution of the membrane potential of the ith P cell that belongs to column θn (0 ≤ n ≤ 7) in V1 is defined by
formula
A.1
where IP,Pin; t) is an excitatory current from other P cells within the same column, IP,Fin; t) an inhibitory current from an F cell, IP,Lin; t) an inhibitory current from L cells, and IP,Pi,latn; t) a lateral excitatory current from P cells belonging to other columns. IP,Pi,fdbn; t) is a feedback excitatory current from P cells of V2. ILGNn; θinp) is an excitatory input current triggered by an oriented bar stimulus (θinp), where θinp ∈ {θ0, θ1, θ2, θ3, θ4, θ5, θ6, θ7}. 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
where (k, l) = (3, 4), (2, 5), (1, 6), (0, 7) (see Figure 1A). Dynamic evolution of membrane potential of the ith F cell that belongs to column θn is defined by
formula
A.9
where IF,Pin; t) is an excitatory current from its accompanying P cell and defined by
formula
A.10
Dynamic evolution of the membrane potential of the ith L cell that belongs to column θn is defined by
formula
A.11
where IL,Pin; t) is an excitatory current from P cells and defined by
formula
A.12
The V2 network is similarly defined by
formula
A.13
formula
A.14
formula
A.15
formula
A.16
formula
A.17
formula
A.18
formula
A.19
formula
A.20
formula
A.21
formula
A.22
where IP,Pi,ffw(Akl; t) is a feedforward excitatory current from V1 P cells. For model parameters and their values, see Table 1.

Appendix B:  Receptor Dynamics and Action Potential Generation

We employ the receptor dynamics proposed by Destexhe, Mainen, and Sejnowski (1998). rPj(X; t) (X = θn, Akl) is the fraction of AMPA receptors in the open state induced by presynaptic action potentials of the jth P cell belonging to column X at time t. rFj(X; t) and rLj(X; t) are the fractions of GABAa receptors in the open state induced by presynaptic action potentials of the jth F and L cells, respectively. The receptor dynamics is defined by
formula
B.1
formula
B.2
where [Glut]Pj(X; t) and [GABA]Yj(X; t) are the concentrations of glutamate and GABA in the synaptic cleft, respectively. [Glut]Pj(X; t) = GlutPmax and [GABA]Yj(X; t) = GABAYmax for 1 msec when the presynaptic jth P and Y cells fire, respectively. Otherwise, [Glut]Pj(X; t) = 0 and [GABA]Yj(X; t) = 0.
The probability of firing the jth Y-type cell belonging to X-type column is defined by
formula
B.3

When a cell fires, its membrane potential is depolarized toward −10 mV, which is kept for 1 msec and then reset to the resting potential. For model parameters and their values, see Table 1.

Acknowledgments

We express our gratitude to the reviewers for giving us valuable comments and suggestions on an earlier draft of this letter.

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