Abstract

There are regularly arranged blobs that contain neurons labeled by cytochrome oxidase (CO) in the supragranular layer of the primary visual cortex (V1) of monkeys and cats. This theoretical study demonstrates that CO-blob-like patterns can be reproduced based on the thermodynamic model for the activity-dependent self-organization of afferent inputs from two different groups of neurons to the supragranular layer of the visual cortex. Computer simulation based on the model shows that within a particular parameter range each blob is centered in the ocular dominance (OD) band, as observed in macaque monkeys and galagos. Furthermore, by increasing the strength of correlation in activity between inputs from the two eyes, nearby blobs merge across OD borders, as seen in the cat visual cortex. Finally, for monocular deprivation, blobs in the deprived eyes shrink as observed in monkeys and cats. For binocular deprivation, less intensely labeled blobs were reproduced, while the blob density did not change as observed in monkeys.

Introduction

In the primary visual cortex of monkeys and cats, regions densely stained by cytochrome oxidase (CO) appear like patches arranged over the cortical surface (Livingstone and Hubel, 1984; Murphy et al., 1995), which are called CO blobs. In primate V1, the patch-like pattern of CO blobs has been observed to be dense in layers 2/3, and faint in layers 5/6 (Horton, 1984; Wong-Riley, 1994). In macaques (Horton and Hubel, 1981) and galagos (Condo and Casagrande, 1990), CO blobs have been found along the middle of ocular dominance (OD) bands, which implies that CO blobs and OD columns develop with some mutual interaction. On the other hand, the structural relationship between CO blobs and OD columns in cats (Murphy et al., 1995) and squirrel monkeys (Horton and Hocking, 1996b) is somehow ambiguous. These observations raise a question as to what common mechanism, if any, underlies the formation of CO blobs and OD columns across the species.

It is widely accepted that neuronal activities affect the pattern of synaptic inputs from neurons in the lateral geniculate nucleus (LGN) to neurons in the visual cortex during development. Indeed, the structure of OD maps can be modified by the imbalance of activities between the left and right eyes (Hubel et al., 1977). OD map formation has been demonstrated to occur depending on neuronal activities (Stryker and Harris, 1986) and some theoretical studies have reproduced the OD map formation (Willshaw and von der Malsburg, 1976; Miller et al., 1989; Tanaka, 1991) based on the Hebbian rule (Hebb, 1949): the efficacy of synaptic connections between pre- and postsynaptic cells increases when they tend to be excited simultaneously. Although it is still controversial whether CO blobs form depending on neuronal activities, it can be expected that synaptic inputs from LGN cells to neurons inside or outside CO blobs are elaborated by the Hebbian mechanism.

Barrow et al. (1996) have proposed a model for the formation of CO blobs using the Hebbian learning rule. This model reproduces receptive fields of neurons inside and outside CO blobs. They showed that neurons outside the blobs are selective for orientation, while neurons inside the blobs are selective for color. The theoretical consequences are consistent with the experimental observations in macaque monkeys (Livingstone and Hubel, 1984). In this model, color information is suggested to be an important driving factor. However, CO blobs have also been found in colorblind nocturnal primates (Condo and Casagrande, 1990). Moreover, it has been pointed out that the functional roles of neurons inside CO blobs are not clearly distinguishable from those of neurons outside the blobs (Leventhal et al., 1995). What then is the most essential factor for the formation of CO blobs? This is the issue we attempt to clarify in our theoretical study presented here.

Here, we propose a self-organization model to understand the coordinated development of CO blobs and OD columns in the superficial layer of the visual cortex. In the model, cells projecting synaptic inputs to the superficial layer of the cortex are classified into four distinct groups whose absolute levels of activities and ocularity are different. Computer simulations based on the model reproduce the geometrical relationships between CO blobs and OD columns observed in monkeys and cats. Furthermore, we show that for the simulation condition corresponding to monocular deprivation, blobs receiving the deprived-eye inputs shrink, as observed in monkeys (Wong-Riley, 1994). For the simulation condition corresponding to binocular deprivation, weakly segregated blobs are obtained with the blob density unchanged, which is consistent with the experimental observation of faintly stained CO blobs in binocularly deprived monkeys (Kuljis and Rakic, 1990).

Materials and Methods

Structure of the Model

Four types of inputs are assumed to terminate at layers 2/3 in the visual cortex (Fig. 1). Two of these receive inputs from the left eye and the other two receive inputs from the right eye. The ocularity is represented by subscript µ1: µ1 = L for the left-eye inputs and µ1 = R for the right-eye inputs. These types of inputs are subdivided into groups A and B (see Table 1), which are represented by subscript µ2: µ2 = A for group A and µ2 = B for group B. The superficial layer of the visual cortex receives direct inputs from some neurons in the LGN as well as neurons in layer 4 of the cortex. In primates, for example, koniocellular (K) LGN cells project axons directly into CO blobs in the superficial layer and layer 4 neurons receiving inputs from magnocellular (M) and parvocellular (P) LGN cells project axons into CO blobs or interblobs (Levitt et al., 1996). For simplicity, we assume here that layer 4 neurons relay LGN activity without additional information processing. We do not need to take into account layer 4 neurons explicitly, and deal with the indirect inputs via layer 4 as direct inputs. Consequently, we consider activity-dependent rewiring of connections from the LGN to the superficial layer of the visual cortex. When we assume that group A neurons exhibit higher activities than group B neurons, the simulations show that inputs from group A neurons are clustered together forming a periodic blob pattern in the model cortex, while inputs from group B neurons are terminated outside the blobs forming interblob regions. Clear blob patterns appear under the condition in which average activities of in group A neurons are sufficiently higher than those of group B neurons. In primates, therefore, group A in the model may correspond to a neuronal group composed of K cells and some M and P cells, while group B may correspond to a group composed of some other M and P cells (see Discussion).

Mathematical Description

The positions in the visual field of LGN neurons and the cortical position of afferent input terminals are indicated by k and j, respectively. The synaptic input from an LGN neuron specified by (k, µ 1, µ 2) to the cortical position j is represented by graphic , which takes a value of 1 when connected and 0 when disconnected. Each cortical position receives a single synaptic input due to the winner-takes-all mechanism based on the competition among afferent inputs at the same dendritic spine (Tanaka, 1990). Each cortical position receives either input, satisfying

graphic

The model is described by the following energy function (Tanaka, 1990):

graphic

Here, graphic represents the cortical interaction between afferent inputs at positions j and j′, which is given by the following Gaussian function:

graphic

where λv is the interaction length in the cortex λv = 3.6 and dj;j′ represents the distance between cortical positions j and j′. graphic in the energy function represents the correlation in firings between a pair of neurons specified by (k, µ1, µ2) and (k′, µ1′, µ2′), and is given by

graphic

Here, h represents the strength of correlation in activity between inputs from the left and right eyes in the same-group input pathway and g represents the strength of correlation in activity between inputs from groups A and B in the same-eye input pathway. graphic and graphic are Kronecker’s deltas, which take a value of 1 for µi = µi′ and 0 for µi ≠ µi′. graphic represents the average firing rate conveyed by inputs of µ1 and µ2. Sequences of neuronal spikes can be described approximately by the Poisson process (Rieke et al., 1997), hence the standard deviation of the activity is proportional to the square root of the mean firing rate, graphic . Therefore, the correlation function graphic is scaled by the square root of the mean firing rates of inputs graphic (Nakagama et al., 2000). Rk;l represents the normalized activity of an LGN cell at position k in response to a stimulus at position l in the visual field, which is given by the Gaussian function with correlation length λRF = 6.4:

graphic

The second term of the energy function represents the constraint on the number of synaptic inputs originating from individual projecting neurons so that the total number of synaptic inputs from each projecting neuron graphic tends to be as small as possible. graphic is a positive constant that determines the magnitude of the constraint.

Method of Simulation

An array of 64 × 64 cells is placed on each layer of the model LGN that projects afferent inputs to the model cortex. The recipient layer, which is assumed to be the superficial layer of the cortex, is composed of 256 × 256 grids. The periodic boundary condition is adopted to minimize finite-size effects.

At the beginning of the simulation, we randomize afferent inputs so that each cortical position receives an input from an LGN neuron according to the probability:

graphic

where graphic represents the distance between cortical positions j and Jk retinotopically corresponding to the position k in the LGN. λArb represents the extent of arborization of afferent inputs (λArb = 16.0).

In the simulation, for each trial of rewiring, a new candidate of an afferent input is selected according to the same probability (5) and then the present input is replaced with the new one based on the probability determined by the energy difference between the states before and after the replacement:

graphic

Here, Hbefore and Hafter represent the energy before and after the replacement, respectively. β represents the inverse temperature increasing with the number of trials of afferent input replacement (Nakagama et al., 2000) to obtain a stable pattern of inputs with a lower energy.

Results

Patterns of Afferent Inputs

In the model, four types of inputs are assumed to terminate at layers 2/3 of the visual cortex (Fig. 1). Two of these are inputs from the left eye and the other two are inputs from the right eye. These eye-specific inputs are subdivided into groups A and B, where group A neurons are assumed to exhibit higher activities than group B neurons. At the beginning of the simulation, each cortical position receives a synaptic input randomly from a neuron of the model LGN. In the simulation, synaptic inputs are repetitively rearranged depending on cortical interaction and correlated activities among the LGN neurons. When a synaptic input pattern is stabilized and reaches the equilibrium, the inputs from the left and right eyes are spatially segregated into alternating bands, and the inputs from group A form periodically arranged blobs whereas the inputs from group B are scattered outside the blobs.

Figure 2A shows the patterns of afferent inputs after self-organization. The green and blue pixels indicate left- and right-eye-specific inputs, respectively, while the dark and light pixels represent inputs from groups A and B, respectively. It can be seen that four types of afferent inputs are segregated into different domains. Particularly, the pattern of OD columns is shown in Figure 2B, in which the black and white pixels represent inputs from the left and right eyes, respectively. The band-like segregation of the left- and right-eye inputs reproduces the patterns of OD columns observed in the primary visual cortex of primates (Horton and Hocking, 1996a). Figure 2C shows the pattern of inputs from groups A and B in black and white, respectively. Synaptic inputs from group A, whose activities are higher than those from group B, cluster together forming a periodically arranged blobs. In order for synaptic inputs from groups A and B to form a blob lattice structure, an imbalance in activity between groups A and B is required (γL,A = γR,A = 2.5, γL,B = γR,B = 0.4). This is consistent with the observation that neurons in CO blobs are metabolically more active than neurons outside the blobs (Wong-Riley, 1994). Moreover, it was found that the blobs are located in the middle of the OD bands, as shown in Figure 2A. This geometrical relationship between CO blobs and OD bands has been observed in the primary visual cortex of monkeys (Casagrande and Kaas, 1994).

Pattern of Topographic Net

The receptive field (RF) of neurons graphic at position j in the model visual cortex is calculated from the convolution of RFs of LGN neurons graphic , afferent inputs graphic and the cortical interaction function graphic as follows (Nakagama et al., 2000):

graphic

Likewise, centers of RFs are calculated using the following equation:

graphic

By plotting thus calculated RF centers of cortical neurons in the visual field and connecting the positions of RF centers between cortical neurons for every four pixels with line segments, we obtain the topographic net shown in Figure 3A. We can see that the topographic net expands in some parts, while it is folded in other parts. To examine the distortion of the topography in more detail, we superimpose the topographic net on the patterns of OD columns and CO blobs in Figure 3B and 3C. In Figure 3B, the topographic net is shown to be folded at the borders of OD bands, as reported in a previous theoretical study of OD column formation (Goodhill, 1993). This type of distortion is relevant to the desired property that only neurons located either in the left-eye bands or the right-eye bands can cover the entire visual field. Figure 3C shows that the topographic net tends to expand locally inside the blobs. This indicates that neurons in the blobs sample signals in the visual field sparsely than neurons outside the blobs.

Spacing of CO Blobs and Periodicity of OD Columns

The spacing of CO blobs and the period of OD columns are quantitative features characterizing two-dimensional (2-D) patterns of the CO blobs and OD columns. Therefore, the CO blob spacing and OD column period provide an important basis for the verification of our model. Here, we introduce methods of measuring such typical lengths, which will be used for the comparison of simulated results with experimental data in Discussion. Figure 4A illustrates a pattern of the Delaunay triangulation for the array of CO blobs to determine the nearest pairs of CO blobs. The center of each blob is defined by the position of the local maximum of group A input density smoothed by the Gaussian low-pass filter with a standard deviation of six pixels. The blob spacing is obtained by measuring the distance between thus determined nearest pairs of blobs. The average spacing of blobs shown in Figure 4A is 35.53 ± 7.06 (standard deviation) pixels. Figure 4B shows histograms of the blob spacing. The blue histogram is for the spacings of the nearest pairs of blobs located in the OD bands of the same eye; the red histogram is for the spacings of the nearest blob pairs across the OD borders; and the yellow histogram is for the spacings of the nearest blob pairs irrespective of OD. Although we cannot observe a clear difference in the shape of the three histograms, the average spacing for the case of the same eye is slightly larger (37.39 ± 7.77 pixels) than that for the case of the different eyes (34.32 ± 6.60 pixels).

To obtain the radial power spectrum p(s) from the 2-D power spectrum graphic of the OD, we average the 2-D power spectrum over all directions of the 2-D wave number vector graphic as follows:

graphic

The average width of OD bands can be determined from the peak position of the radial power spectrum of p(s). The wave number at the peak for OD columns shown in Figure 4A is 4.2. By identifying the width of OD bands obtained from the simulation with that of OD bands in macaque monkeys, which is, on average, 825 µm (Blasdel et al., 1995), we can estimate the average spacing of blobs to be 478 ± 95 µm. The spacing of blobs in the same OD bands is 506 ± 105 µm and that across the OD borders is 465 ± 89 µm.

Effects of Positive Correlation Between the Two Eyes

In monkeys, OD columns (Horton and Hocking, 1996a) and CO blobs (Purves and LaMantia, 1993) are observed at birth, indicating that they form before the experience of pattern vision. It is thought that binocular pattern vision enhances the between-eye correlation in activity because the visual images evoke similar activity patterns in the two eyes. It is thus expected that these structures in monkeys can emerge in the absence of correlation between inputs from the two eyes. When the correlation strength between inputs from the two eyes h is set to be 0.0 in the simulation, blobs are placed in the middle of OD bands (Fig. 2A), as observed in monkeys (Casagrande and Kaas, 1994). On the other hand, OD columns (Crair et al., 1998; Rathjen and Löwel, 2000) and CO blobs (Murphy et al., 2001) in cats appear after eye opening. This suggests that OD columns and CO blobs in cats form in the presence of positive between-eye correlation. When h takes a positive value (h = 0.4), nearby blobs tend to merge across the OD borders (Fig. 5A), as observed in the CO staining patterns in cats (Murphy et al., 1995). Figure 5B shows a pattern of synaptic inputs when the activity of inputs from the right eye (γR,A = 0.9γL,A, γR,B = 0.9γL,B) is weaker than that of inputs from the left eye (γL,A = 2.5, γL,B = 0.4). Since a bias of cortical responses toward the contralateral eye is observed in cats particularly during the early postnatal days (Crair et al., 1998), the synaptic input pattern plotted in Figure 5B can be that in the right visual cortex of cats, in which the green area represents the columns of contralateral eye dominance and the blue area represents the columns of ipsilateral eye dominance.

Moreover, the OD bands become narrower as h increases (cf. OD bands in Fig. 5A with those in Fig. 2A). Figure 5C shows the radial power spectra of OD bands, which are defined by equation (9), for the case in which the between-eye correlation h changes from 0.0 to 0.5. When h increases, the peak of the power spectrum shifts to larger wave numbers, indicating that the OD bands become narrower (Goodhill, 1993). Such a dependency of the width of the OD bands on the between-eye correlation should be compared with the finding that OD bands in strabismic cats are broader than those in normal cats (Löwel, 1994). From the consideration that activity correlation between inputs from the two eyes is stronger in normal cats than in strabismic cats, the dependence of OD band width on the between-eye correlation is consistent with the experimental findings of the OD band widths in normal and strabismic cats.

Since columnar patterns in monkeys develop in the presence of independent activities of inputs from the two eyes before birth, correlated activity in the two eyes after eye opening might change the patterns of the columnar structures. Here, we perform simulations to examine whether or not changes in between-eye correlation during development have any effects on the structural relationship between CO blobs and OD columns. First, we investigate a situation in which columnar patterns established without between-eye correlation can be changed by positive correlation introduced afterward. We use afferent inputs obtained above (Fig. 2) as initial connections, which have developed without between-eye correlation (h = 0.0), and obtained synaptic connections depicted in Figure 5D after a simulation with positive between-eye correlation (h = 0.4) and β = ∞. Only a few of adjacent blobs merge together (Fig. 5D, and most of the CO blobs in Figure 5D are left along the middle of OD bands as seen in Figure 2A. Next, we investigate an opposite situation in which columnar patterns established in the presence of positive between-eye correlation can be changed by null correlation introduced afterward. We use afferent inputs depicted in Figure 5A as initial connections, which have developed with h = 0.4 and obtained the afferent input pattern in Figure 5E after a simulation with h = 0.0 and β = ∞. The disappearance of between-eye correlation alters the overall pattern of afferent inputs as shown in Figure 5A and E, and it appears that the pattern develops in the absence of between-eye correlation irrespective of initial connection patterns. Thus, once a connection pattern is formed similar to the pattern in which CO blobs are regularly arranged along the OD bands as observed in monkeys, this pattern is stable and cannot be changed by introducing the positive between-eye correlation afterward. On the other hand, the pattern in which CO blobs straddle the OD borders as observed in cats can be changed to the pattern as in monkeys by decreasing the between-eye correlation.

Finally, to study the effects of the between-eye correlation on blob patterns, we count the average number of blobs in the model cortex and its dependence on the between-eye correlation is shown in Figure 5F. The number of blobs increases when h increases from 0.0 to 0.2. This is because blobs tend to appear in the middle of OD bands whereas the period of OD columns becomes shorter. However, when h increases from 0.2 to 0.5, the number of blobs decreases because adjacent blobs merge. It is suggested that the number of CO blobs does not change so much irrespective of the between-eye correlation.

Effects of Monocular and Binocular Deprivation

The patterns of synaptic inputs self-organized under the condition corresponding to monocular deprivation are shown in Figure 6A for h = 0 and Figure 6B for h = 0.3. Ocular dominance bands of the nondeprived eye inputs (green pixels) expand at the expense of those of the deprived eye inputs (blue pixels), as expected. Nevertheless, qualitative features in the relationship between OD columns and CO blobs are preserved for h = 0 and for h = 0.3: isolated blobs are arranged in the middle of OD bands for h = 0; blobs appear across the OD borders for h = 0.3. Figure 6C shows the normalized number of synaptic inputs from groups A and B for the deprived and nondeprived eyes depending on the imbalance in activity between inputs from the two eyes for h = 0. The number of synaptic inputs originating from the deprived eye decreases as observed in experiments on monocular deprivation (Wong-Riley, 1994). Moreover, when the ratio of activities between inputs from the right and left eyes ( graphic : γL,A = 2.5, γL,B = 0.4) decreases from 1.0 to 0.8, the rate of decrease in the number of synaptic inputs from the deprived eye is more prominent in group A than in group B. This indicates that the shrinkage of deprived-eye bands is observed mainly in the blobs rather than in the interblobs.

The patterns of synaptic inputs simulated under the condition corresponding to binocular deprivation (γ < 1.0: γL,A = γR,A = 2.5γ, γL,B = γR,B = 0.4γ) are shown in Figure 6D and E, which are formed under the conditions of h = 0 and h = 0.3, respectively. Although the overall patterns of OD columns and CO blobs (Fig. 6D,E) are similar to those of the normal cases (Figs 2A and 5B), the blobs become smaller than those of the normal cases. The number of synaptic inputs from group A decreases, suggesting weaker segregation into CO blobs in animals reared under binocular deprivation. Figure 6F shows the average number of blobs self-organized in the model cortex when the between-eye correlation is zero. When the activities of inputs from both eyes γ are between 0.85 and 1.0, the average number of blobs is almost constant, suggesting that the density of the blobs does not change when both eyes are slightly deprived (γ > 0.85). When γ < 0.85, blobs disappear.

Discussion

Synaptic Connections

In the present model, we assumed that LGN neurons, either left-eye specific or right-eye specific, can be classified into groups A and B, and that all intermediate neurons in layer 4 relay the LGN activities without additional information processing. The computer simulations showed that CO blob-like patterns emerge due to the segregation of synaptic inputs based on different absolute levels of activities between group A and group B neurons. However, the actual connection patterns in the visual pathways are more complex than we assume. In primates, while koniocellular (K) LGN cells project axons directly to CO blobs (Lachica and Casagrande, 1992), magnocellular (M) and parvocellular (P) LGN cells project axons to neurons in layer 4 which, in turn, project axons to both CO blobs and interblobs (Levitt et al., 1996). For example, in the macaque visual cortex, Yabuta and Callaway (1998) have found that layer 4Cα, receiving M inputs from the LGN, has three types of neurons. One type is neurons (MY) in the upper layer of 4Cα with dendrites confined to the same layer, projecting axons to layer 4B and CO blobs in layer 2/3, and the recipient neurons in layer 4B, in turn, project the axons into CO blobs in layer 2/3 (Lachica et al., 1993; Yoshioka et al., 1994). Another type is neurons (MX) in the lower layer of 4Cα with narrowly stratified dendrites restricted to lower 4Cα and with dense axons specifically targeting layer 3 interblobs. The other type is neurons (MP) in lower 4Cα with dendrites in lower 4Cα and 4Cβ, presumably receiving P inputs from 4Cβ as well as M inputs from lower 4Cα, and with axons targeting both blobs and interblobs. Yoshioka et al. (1994) have shown, on the other hand, that there are MP-type neurons in the midlayer of 4C (lower 4Cα and upper 4Cβ) with dendrites arborizing to both 4Cα and 4Cβ, which are believed to receive convergent M and P inputs, and project axons only to interblob regions in layer 2/3 as MX-type neurons do. In either case, there seem to exist two distinct pathways in the macaque visual cortex: each projects axons to either blobs or interblobs. Yabuta and Callaway (1998) also have found that neurons in 4Cβ, receiving P inputs from the LGN, have dense axonal arbors in both blobs and interblobs. Therefore, neurons in the P pathway (MP cells in the lower layer of 4Cα and P cells in 4Cβ) may not be involved in the segregation of inputs into the CO blob pattern.

Moreover, Blasdel and Lund (1983) have found that in the magnocellular LGN laminae, there may be two types of afferents: those which arborize in the upper half of 4Cα, with extensive collaterals in layer 6 and those which arborize in the lower two-thirds of 4Cα, with little or no collaterals in layer 6. This suggests that there may be two distinct classes of M cells in the LGN. Kaplan and Shapley (1982) have found that the M laminae in the macaque LGN contain two types of cells, X (MX) and Y (MY) cells, which have similar functional properties to X and Y cells in cats, respectively. It is speculated that MY cells in the LGN project axons to the upper half of 4Cα and MX cells in the LGN project axons to the lower two-thirds of or throughout 4Cα (Yabuta and Callaway, 1998), because a similar structure can be seen in the cat visual pathways, where geniculate Y cells innervate layer 4a, whereas X cells innervate both layers 4a and 4b (Boyd and Matsubara, 1996). Therefore, it may be possible to assume the existence of two distinct subgroups of LGN neurons whose activity correlation may be higher within the same subgroup and lower between different subgroups. Taken together, group A in the present model may consist of K cells in the LGN and MY cells in the LGN that innervate the upper half of 4Cα and group B may consist of MX cells in the LGN that innervate the lower two-thirds of 4Cα.

In other diurnal primate such as squirrel monkeys, the only difference from macaque monkeys is that the interblob regions receive inputs only from the P-dominated layer IVβ (4Cβ) (Lachica and Casagrande, 1992; Lachica et al., 1993). On the other hand, in nocturnal primates such as galagos (Lachica et al., 1993) the interblob regions receive only M inputs via IVα (4Cα). However, it is not clear whether or not there are distinct classes of P neurons in squirrel monkeys and M neurons in galagos that project their axons to either blobs or interblobs. In cats, W and Y cells in the C lamina in the LGN innervate directly to CO blobs (Boyd and Matsubara, 1996) and X cells in the LGN may project axons both inside and outside CO blobs, which are relayed by neurons in layer 4, because X cell terminations apparently include both layers 4a and 4b in the interblobs and at least 4b underneath the blobs (Boyd and Matsubara, 1996).

CO Staining Dependent on Activity Imbalance

Cytochrome oxidase, which is an enzyme in mitochondria, is required for ATP synthesis. Since neurons inside CO blobs contain more CO, they synthesize more ATP than neurons outside CO blobs. ATP synthesized by these neurons provides energy mainly for operating many ion pumps to maintain the ionic concentration against the disturbance due to neuronal activities (Wong-Riley, 1994). That is, the higher the activities of neurons, the more they need to synthesize ATP. This suggests that the average firing rate of neurons inside CO blobs is higher than that of neurons outside CO blobs. In the present model, an imbalance in activity between two groups of afferent inputs is necessary for the formation of blob patterns, and afferent inputs conveying higher neuronal activities cluster together and form the blobs. In cats, for example, Y cells in the LGN, whose outputs terminate inside CO blobs have higher spontaneous activity than X cells (Bullier and Norton, 1979) and are more strongly stained by CO than X cells.

Structure of CO Blob Patterns

When the value of the between-eye correlation is zero in the present model, blobs are localted in the middle of OD bands (Fig. 2A). A similar arrangement of CO blobs and OD columns has been observed in the primary visual cortex of macaque monkeys (Casagrande and Kaas, 1994). Such a geometrical relationship between CO blobs and OD columns characteristic of the macaque visual cortex seems to support our model. In the simulated result, the density of the blobs in the model cortex was estimated to be 5.38/mm2. In the present model, the CO blob density depends on parameters g (the strength of correlation in activity between inputs from groups A and B in the same-eye input pathway) and graphic (the ratio of the mean firing rate of group B neurons to that of group A neurons). For smaller values of g or γB, the blob density becomes lower (data not shown).

In macaque monkeys, the density of CO blobs has been reported by many researchers but the values widely varied, e.g. 3.67/mm2 (Murphy et al., 1998), 4.3/mm2 (Purves and LaMantia, 1993), 5/mm2 (Purves and LaMantia, 1990), 5.6/mm2 (Horton, 1984), 6.08/mm2 (Wong-Riley, 1994) and 6.56/mm2 (Schein and de Monasterio, 1987). It is suspected that the CO blob density depends on individual monkeys and cortical locations in V1. Actually, Horton (1984) has reported that the CO blob density increases in the peripheral binocular cortex and decreases around the optic disks. Compared with the CO blob density obtained in our simulation, our estimated value falls in the range of the experimentally obtained values. This quantitative consistency may lend support to our model for the self-organization of CO blobs and OD columns.

The average spacing between adjacent CO blobs was estimated to be 478 µm for our parameter setting. Moreover, we found that the average spacing between adjacent blobs in the same OD band (506 µm) was slightly larger than the spacing across the OD border (465 µm). The ratio of the two values is ∼1.09 (= 506/465).

In macaque monkeys, the spacing between CO blobs in the same OD band is ∼450 µm (Horton, 1984) and the blob spacing across the OD border is ∼353 µm (Wong-Riley and Carroll, 1984; Wong-Riley, 1994). Murphy et al. (1998) used the Delaunay triangulation for measuring CO blob spacing in the monkey visual cortex as in the present study and estimated the blob spacing to be ∼590 µm. Here we can see the consistency in CO blob spacing between our simulated result and experimental measurements within the range of experimentally measured spacings. For the asymmetry of CO blob spacing along the OD band and across the border, the ratio of spacings was ∼1.27 (= 450/353) in monkeys (Wong-Riley and Carroll, 1984). Regarding spacing asymmetry, we can see again the qualitative agreement between our simulated result and experimental observations.

Murphy et al. (1998) have also found that CO blob spacing was not isotropic, indicating that the blob spacing depends on the spatial orientation along the cortical surface. Even though the anisotropy they found is very small (1.07), this result may account for the asymmetry of blob spacing when we consider that monkey OD columns appear as coherently long sustained stripe patterns.

Effects of Positive Correlation in Activity between Inputs from the Two Eyes

It has been reported that OD bands in strabismic cats are wider than those in normal cats (Löwel, 1994). In normal cats, retinal neurons of the right and left eyes focusing on the same point in the visual field should have a positive correlation in activity because the same visual image evokes similar activities. In strabismic cats, however, it can be considered that the correlation in activity between inputs from the two eyes decreases because different visual images are presented to the left and right eyes. The widened OD bands in the strabismic cats were reproduced in the present model when the between-eye correlation was zero, as shown by the elastic net model (Goodhill, 1993). Moreover, when the between-eye correlation is rather high, nearby blobs tend to merge across the OD borders (Fig. 5B), as found in in the cat visual cortex (Murphy et al., 1995).

It has been reported that strabismus in monkeys does not affect the width of OD bands (Crawford, 1998) or the density of CO blobs (Murphy et al., 1998), while OD bands in strabismic cats appear wider than those in normal cats (Löwel, 1994). Assuming that the critical periods for the formation of OD bands and CO blobs have not yet passed after birth, it is predicted from the present model that monkey OD bands become narrower than before birth because the between-eye correlation increases due to the binocular vision of the same images. However, the width of the OD columns of adult monkeys is almost the same as that of newborn monkeys (Horton and Hocking, 1996a), indicating that the structure of monkey OD maps is robust against changes in between-eye correlation during development.

In order to confirm whether or not strabismus changes the width of OD bands, Sengpiel et al. (1998) performed optical imaging of intrinsic signals to examine the structural changes of OD maps in strabismic cats. The animals were raised under the normal visual condition until postnatal 21 days when the basic structure of OD maps begins to appear, and since then reared under the divergent squint condition during OD sensitivity period. They observed fewer obvious changes in the width of OD bands than those in the previous report (Löwel, 1994). In the case of strabismus, the change in the OD band width indicates the change in the periodicity of OD columns. For monocular deprivation, even though the OD band width of the nondeprived eye expands and the band width of the deprived eye shrinks, the periodicity of OD columns remains unchanged. It is considered that changes in the periodicity of OD columns would require global changes of afferent inputs. Therefore, it is reasonable to assume that once the basic structure of OD maps has been established, it may be difficult to change the global structure such as OD periodicity. This may be a reason why the OD band width did not change when strabismus was introduced at postnatal 21 days. This interpretation is consistent with results of an experiment on monkeys in which it was found that the periodicity of OD maps does not change under the strabismus condition (Crawford, 1998) introduced after the basic structure of OD maps is established.

On the other hand, the structures of OD maps (Crair et al., 1998; Rathjen and Löwel, 2000) and CO blobs (Murphy et al., 2001) in cats begin to appear from the third postnatal week, showing that OD maps and CO blobs form after eye opening at the first postnatal week. Therefore, the correlation in activity between the two eyes during the formation of OD maps should be rather high and strabismus manipulation may decrease the between-eye correlation and reduce the OD band width. The reason why widened OD bands in strabismic cats were observed in Löwel (1994) experiment may be the introduction of strabismus from postnatal second weeks, which is immediately prior to the establishment of the basic structure of OD maps.

Hübener et al. (1997) examined spatial relationships among orientation, OD and spatial frequency (SF) domains in cat area 17 and found a tendency for the low SF domains to avoid the border regions of the OD columns determined by a quantitative analysis, although a visual inspection of the maps did not suggest any apparent relationships. Kim et al. (1999) and Issa et al. (2000) have examined the cortical organization of SF preference in cats by imaging intrinsic optical signals and have found little correlation between SF maps and OD maps. Because it has been shown in the cat visual cortex that CO blobs coincide with domains involved in the processing of low spatial and high temporal frequency content in the visual scene (Shoham et al., 1997), the absence of geometrical relationships between SF maps and OD maps indicates little correlation between CO blobs and OD maps in the cat visual cortex. This is again consistent with our result when the between-eye correlation is high.

Effects of Monocular and Binocular Deprivations

The effects of monocular deprivation on CO blobs have been investigated in monkeys of different ages using different methods of deprivation: e.g. eyelid suture, tetrodotoxin (TTX) injection and monocular enucleation (Wong-Riley, 1994). In eyelid-sutured monkeys, retinal ganglion cells and LGN neurons retain their spontaneous activity, because the eyelids only diminish input light intensity. The loss is mainly in pattern discrimination of high spatial frequencies. However, the size of CO blobs for the deprived eye was significantly reduced at 11 weeks after monocular lid suture. The size reduction effect was greater in juveniles (38%) than in adults (33%) (Trusk et al., 1990). TTX injection inhibits neuronal activity by blocking voltage-dependent sodium channels. The reduction in size of CO blobs following TTX treatment was greater than that following eyelid suture. TTX treatment for 2 or 4 weeks leads to 17 or 57% reduction in the volume of deprived CO blobs (Trusk et al., 1990). The removal of one eye deprives the system of light input, afferent neuronal activity and possible neurotropic factors. The effect of monocular enucleation is the most severe among the three. The volumes of the blobs likewise decreased by 34% 2 weeks after enucleation and by 53% 60 weeks after enucleation (Trusk et al., 1990). When bilateral retinal ablation is performed at the embryonic stage in monkeys, blobs were less intensely labeled by CO than those in normal adult monkeys, while the spacing between CO blobs did not change (Kuljis and Rakic, 1990). In the present model, the shrinkage of blobs receiving inputs from the deprived eye was reproduced under the simulation condition corresponding to monocular deprivation (Fig. 6AC). In addition, for the simulation condition corresponding to binocular deprivation, the segregation of group A inputs into blobs became weak, suggesting that the blobs are less intensely labeled (Fig. 6D,E). In this case, the blob density did not change (Fig. 6F).

Murphy et al. (1995) have investigated the effect of monocular enucleation on the relationship between OD columns and CO blobs. Although they observed severe shrinkage of CO blobs in the regions of the deprived eye, the overall structure, such as that of CO blobs straddling the border of OD bands, was basically the same as that in normal cats. Furthermore, Murphy et al. (2001) have investigated the effects of monocular and binocular deprivations on CO blobs in cats by eyelid suture and found that the pattern of CO blobs did not change for either monocular or binocular deprivation. According to the model, the pattern of CO blobs is expected to change for monocular or binocular deprivation, because the between-eye correlation should become zero. The patterns of OD columns and CO blobs in monocular or binocular deprivation, therefore, should become similar to patterns observed in monkeys. The disagreement between the experiments and our simulation can be explained by the notion that the correlated LGN activities between the two eyes are not only caused by direct retinal inputs, but also by corticogeniculate feedback inputs. The corticogeniculate feedback inputs may work as common inputs to the left-eye- or right-eye-specific LGN cells, and induce correlated firing (Weliky and Katz, 1999).

Activity-independent Formation of Columnar Structure in the Visual Cortex

Crowley and Katz (2000) have proposed a possibility that molecular axon guidance cues are responsible for the initial segregation of LGN eye-specific afferents by showing that ocular dominance columns in the ferret visual cortex are formed immediately after afferent axons innervate the cortex and deprived and nondeprived OD columns have almost the same width even when the contralateral eye is enucleated. Although these findings clearly indicate that neuronal signals conveyed by retinal inputs have no influence on the initial segregation of geniculocortical inputs into OD columns, it does not necessarily rule out the activity-dependent mechanism of OD column formation. If there are LGN neuronal activities either spontaneous or evoked by nonretinal inputs, they may exhibit statistical independence between layers A and A1, and contribute to OD segregation in the visual cortex. To examine whether the initial OD segregation is determined by the activity-dependent mechanism, a molecular interaction mechanism, or a more complex interplay between molecular and activity-dependent mechanisms (Chiu and Weliky, 2002), it will be necessary to examine correlational structure in activity among LGN neurons when the LGN axons arrive at layer 4 of the visual cortex.

Conclusion

The spatial relationships between CO blobs and OD bands imply that there is a common cortical mechanism underlying the formation of these modules. Using the self-organization model based on the assumption that four types of neurons in the LGN project axons to the visual cortex, we found that synaptic inputs segregate into different domains. Inputs from more active neurons form blobs in the middle of OD bands, while inputs from less active neurons terminate outside blobs within a particular parameter range. These results suggest a possibility that the basic structures of CO blobs and OD columns emerge from the activity-dependent Hebbian mechanism. Moreover, the structure of CO blobs and OD columns observed in cats can also be reproduced in another parameter range. The successful reproduction of the CO blob patterns suggests that the chromatic/achromatic dichotomy in the stream of visual information is not essential, but the difference in the absolute level and activity among cells projecting axons to the supragranular layer of the visual cortex is more important for the formation of CO blob patterns.

Address correspondence to Shigeru Tanaka, Laboratory for Visual Neurocomputing, Brain Science Institute, RIKEN, 2–1 Hirosawa, Wako, Saitama 351–0198, Japan. Email: shigeru@postman.riken.go.jp.

Figure 1. Structure of the model.

Figure 1. Structure of the model.

Figure 2. Patterns of synaptic inputs. (A) Patterns of afferent inputs after self-organization. Parameters used here are h = 0.0, g = 0.4, γL,A = γR,A = 2.5, γL,B = γR,B = 0.4, and cA = 0.0006, cB = 0.0005. Dark- and light-green (blue) pixels represent left-eye (right-eye)-specific inputs from groups A and B, respectively.(B) Ocular dominance where black and white pixels represent synaptic inputs from the left and right eyes, respectively. (C) Synaptic inputs of groups A and B where black and white pixels represent synaptic inputs from groups A and B, respectively.

Figure 2. Patterns of synaptic inputs. (A) Patterns of afferent inputs after self-organization. Parameters used here are h = 0.0, g = 0.4, γL,A = γR,A = 2.5, γL,B = γR,B = 0.4, and cA = 0.0006, cB = 0.0005. Dark- and light-green (blue) pixels represent left-eye (right-eye)-specific inputs from groups A and B, respectively.(B) Ocular dominance where black and white pixels represent synaptic inputs from the left and right eyes, respectively. (C) Synaptic inputs of groups A and B where black and white pixels represent synaptic inputs from groups A and B, respectively.

Figure 3. Patterns of topographic net. (A) The center of the gravity of the receptive field of postsynaptic neurons is plotted as a point in retinal space. The centers of the gravity are calculated for every four cortical pixels. (B) Combined map of the topographic net and OD maps. (C) Combined map of the topographic net and the blobs. The data used to plot these figures were the same as those used in Figure 2.

Figure 3. Patterns of topographic net. (A) The center of the gravity of the receptive field of postsynaptic neurons is plotted as a point in retinal space. The centers of the gravity are calculated for every four cortical pixels. (B) Combined map of the topographic net and OD maps. (C) Combined map of the topographic net and the blobs. The data used to plot these figures were the same as those used in Figure 2.

Figure 4. Nearest neighbor analysis of 2-D CO blob pattern. (A) Delaunay triangulation for the array of blob centers. (B) The blue histogram is for the case in which the nearest blobs are in the OD bands of the same eye, the red histogram is for the case in which the nearest blobs are in OD bands of different eyes and the yellow histogram is the total of the two. The horizontal axis represents blob-to-blob spacing and the vertical axis represents the number of edges. The data used to plot these figure are the same as those used in Figure 2.

Figure 4. Nearest neighbor analysis of 2-D CO blob pattern. (A) Delaunay triangulation for the array of blob centers. (B) The blue histogram is for the case in which the nearest blobs are in the OD bands of the same eye, the red histogram is for the case in which the nearest blobs are in OD bands of different eyes and the yellow histogram is the total of the two. The horizontal axis represents blob-to-blob spacing and the vertical axis represents the number of edges. The data used to plot these figure are the same as those used in Figure 2.

Figure 5. Effects of positive between-eye correlation on synaptic input pattern. (A, B) show the patterns of synaptic inputs when the correlation in between-eye correlation h takes a positive value. The parameters used here are h = 0.4 in (A) and h = 0.3, graphic and cA = 0.005 in (B). The other parameters used here are the same as those used in obtaining the results shown in Figure 2. (C) Power spectra of OD maps when h is changed. The horizontal axis represents wave number and the vertical axis represents power. (D, E) Patterns of synaptic inputs when h is changed from 0.0 to 0.4 and from 0.4 to 0.0, respectively. (F) Average number of blobs on the model cortex when the between-eye correlation is changed.

Figure 5. Effects of positive between-eye correlation on synaptic input pattern. (A, B) show the patterns of synaptic inputs when the correlation in between-eye correlation h takes a positive value. The parameters used here are h = 0.4 in (A) and h = 0.3, graphic and cA = 0.005 in (B). The other parameters used here are the same as those used in obtaining the results shown in Figure 2. (C) Power spectra of OD maps when h is changed. The horizontal axis represents wave number and the vertical axis represents power. (D, E) Patterns of synaptic inputs when h is changed from 0.0 to 0.4 and from 0.4 to 0.0, respectively. (F) Average number of blobs on the model cortex when the between-eye correlation is changed.

Figure 6. Effect of monocular and binocular deprivations. (A, B) Patterns of synaptic inputs when the activity of the right eye is weaker than that of the left eye graphic . The parameters used here are h = 0.0, γR = 0.85 and cA = 0.006 in (A) and h = 0.3, γR = 0.8 and cA = 0.005 in (B). The other parameters used here are the same as those used in obtaining the results in Figure 2. (C) Normalized number of synaptic inputs from groups A and B of the deprived and nondeprived eyes. Parameters used here are h = 0.0 and cA = 0.006. The horizontal axis represents γR and the vertical axis represents the normalized number of synaptic inputs. (D, E) Patterns of synaptic inputs when both the left and right eyes are deprived (γ < 1.0: γL,A = γR,A = 2.5, γL,B = γR,B = 0.4). The parameters used here are h = 0.0, γ = 0.85 and cA = 0.006 in (D) and h = 0.3, γL,A = 2.5γL, γR,A = 2.5γR, γL,B = 0.4γL, γR,B = 0.4γR, γL = 0.77, γR = 0.69 and cA = 0.005 in (E). (F) Average number of blobs in the simulated cortex. The parameters used here are h = 0.0 and cA = 0.006. The horizontal axis represents γ and the vertical axis represents the average number of blobs.

Figure 6. Effect of monocular and binocular deprivations. (A, B) Patterns of synaptic inputs when the activity of the right eye is weaker than that of the left eye graphic . The parameters used here are h = 0.0, γR = 0.85 and cA = 0.006 in (A) and h = 0.3, γR = 0.8 and cA = 0.005 in (B). The other parameters used here are the same as those used in obtaining the results in Figure 2. (C) Normalized number of synaptic inputs from groups A and B of the deprived and nondeprived eyes. Parameters used here are h = 0.0 and cA = 0.006. The horizontal axis represents γR and the vertical axis represents the normalized number of synaptic inputs. (D, E) Patterns of synaptic inputs when both the left and right eyes are deprived (γ < 1.0: γL,A = γR,A = 2.5, γL,B = γR,B = 0.4). The parameters used here are h = 0.0, γ = 0.85 and cA = 0.006 in (D) and h = 0.3, γL,A = 2.5γL, γR,A = 2.5γR, γL,B = 0.4γL, γR,B = 0.4γR, γL = 0.77, γR = 0.69 and cA = 0.005 in (E). (F) Average number of blobs in the simulated cortex. The parameters used here are h = 0.0 and cA = 0.006. The horizontal axis represents γ and the vertical axis represents the average number of blobs.

Table 1


 The types of projection neurons classified into groups A and B in the model

 Group A Group B 
Macaque K, MY, (P) cells MX, (P) cells 
Squirrel monkey K, M, P cells P cells 
Galago K, M, P cells M cells 
Cat W, Y, X cells X cells 
 Group A Group B 
Macaque K, MY, (P) cells MX, (P) cells 
Squirrel monkey K, M, P cells P cells 
Galago K, M, P cells M cells 
Cat W, Y, X cells X cells 

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