Abstract

How is development of cortical maps in V1 coordinated across cortical layers to form cortical columns? Previous neural models propose how maps of orientation (OR), ocular dominance (OD), and related properties develop in V1. These models show how spontaneous activity, before eye opening, combined with correlation learning and competition, can generate maps similar to those found in vivo. These models have not discussed laminar architecture or how cells develop and coordinate their connections across cortical layers. This is an important problem since anatomical evidence shows that clusters of horizontal connections form, between iso-oriented regions, in layer 2/3 before being innervated by layer 4 afferents. How are orientations in different layers aligned before these connections form? Anatomical evidence demonstrates that thalamic afferents wait in the subplate for weeks before innervating layer 4. Other evidence shows that ablation of the cortical subplate interferes with the development of OR and OD columns. The model proposes how the subplate develops OR and OD maps, which then entrain and coordinate the development of maps in other lamina. The model demonstrates how these maps may develop in layer 4 by using a known transient subplate-to-layer 4 circuit as a teacher. The model subplate also guides the early clustering of horizontal connections in layer 2/3, and the formation of the interlaminar circuitry that forms cortical columns. It is shown how layer 6 develops and helps to stabilize the network when the subplate atrophies. Finally the model clarifies how brain-derived neurotrophic factor (BDNF) manipulations may influence cortical development.

Introduction

Topographically organized maps in functional columns have been found in visual (Tootell et al., 1982, 1998; Duffy et al., 1998), auditory (Komiya and Eggermont, 2000; Stanton and Harrison, 2000), somatosensory (Dykes et al., 1980; Grinvald et al., 1986; Wallace and Stein, 1996) and motor (Nieoullon and Rispal-Padel, 1976; Munoz et al., 1991; Chakrabarty and Martin, 2000) thalamic and cortical areas. In cortical area V1, cells tuned to orientation and ocular dominance are found within its map (Blasdel, 1992a,b; Crair et al., 1997a,b; Hubener et al., 1997). Cortical columns show consistent tuning for orientation and ocular dominance along vertical penetrations of this map across multiple cortical layers (Hubel and Wiesel, 1974). An important task in understanding the brain, and in building computational models thereof, is to explain how such maps emerge and are organized within interacting cortical columns.

A rich modeling literature addresses the development of orientation and ocular dominance maps in V1 (von der Malsburg, 1973; Grossberg, 1976; Willshaw and von der Malsburg, 1976; Swindale, 1980, 1992; Kohonen, 1982; Linsker, 1986a,b,c; Miller et al., 1989; Rojer and Schwartz, 1990; Olson and Grossberg, 1998). Most models do not, however, address how maps are distributed or coordinated across the layered circuits of striate cortex to form cortical columns. Furthermore, these models typically do not address the development of key intercolumnar properties, such as the clusters of horizontal connections found in layers 2/3 and 5 (Gilbert and Wiesel, 1983, 1985, 1989; Ts’o et al., 1986; Katz et al., 1989; McGuire et al., 1991; Schmidt et al., 1997a,b, 1999; Sincich and Blasdel, 2001). These connections have been shown to preferentially target other cells of similar ocularity and orientation tuning (Yoshioka et al., 1996; Bosking et al., 1997).

A challenge to modeling is that the orientation maps in layers 4 and 6, and the crude clustering in layers 2/3 and 5, begin to develop before there are interlaminar connections to coordinate the formation of such maps across layers (Callaway and Katz, 1992). These initial preferences are maintained as patterned vision refines them (Callaway and Katz, 1990, 1991). How are these initial preferences coordinated in the absence of interlaminar connections? This article proposes that this problem is solved by the cortical subplate (Kostovic and Molliver, 1974; Rakic, 1976; Luskin and Shatz, 1985; Allendoerfer and Shatz, 1994; Ghosh and Shatz, 1994; Ghosh, 1995; McAllister, 1999). The subplate serves as an early target of thalamocortical connections and in turn makes connections throughout the developing cortical plate (Ghosh and Shatz, 1993; McConnell et al., 1994). Furthermore, ablation of the subplate eliminates the formation of cells tuned to orientation (Kanold et al., 2001) and ocular dominance maps (Ghosh and Shatz, 1992).

A new neural model provides herein a unified account of how development of orientation tuning and ocular dominance columns, clustered horizontal connections, and interlaminar connections occurs to form cortical columns. The model also simulates data about how ablation of the cortical subplate may interfere with the development of OR and OD columns, and the development of vertical interlaminar connections. The model hereby shifts the focus of the modeling literature from the development of cortical maps to the coordinated development of functional columns of cells across cortical layers, of the horizontal and vertical receptive fields of these cells within and between cortical layers, as well as of the maps that organize the spatial arrangement of these cells across the cortex. Some of these results were briefly reported in Seitz and Grossberg (Seitz and Grossberg, 2001, 2002). Modeling simulations emulate the order of biological development. Inputs from the lateral geniculate nucleus (LGN) to the cortical subplate induce a map, which is taught via interlaminar connections from the subplate to the other cortical layers. Connections between the layers of the cortical plate next develop and these connections are shown to be stable after subplate atrophy. Finally, patterned vision segregates ON and OFF receptive fields. The model also clarifies how brain-derived neurotrophic factor (BDNF) manipulations may influence map development (Cabelli et al., 1995, 1997).

Rationale and Methods

This section summarizes key properties that the model clarifies of the laminar organization of cortex, the cortical subplate, orientation tuning, ocular dominance columns, and clustered horizontal connections. The model is then introduced. The Results section compares model simulations of the various developmental stages with physiological and anatomical data.

Laminar Organization of Neocortex

The six characteristic layers of neocortex differ in their configuration of cell types, and the makeup of the layers differs across brain areas (Brodmann, 1909). In V1, layers 4 and 6 receive inputs from the LGN. Layers 2/3 and 5 exhibit long-range horizontal connections between cells in their respective layers.

A fundamental question in cortical development is how do the receptive field properties of the cortical layers develop? The very young cortex looks similar across different brain regions, yet the adult cortex shows remarkable differences. For example, V1 has a prominent layer 4, consisting of multiple sublaminae, whereas motor cortex has almost no layer 4. Competing ‘Protomap’ and ‘Protocortex’ theories have emerged with different explanations of how cortex differentiates (Donoghue and Rakic, 1999). The ‘Protocortex’ theory suggests that different cortical areas have different innate make-ups of patterning molecules, which cause differentiation after cell migration. The ‘Protomap’ theory suggests that the cortex differentiates due to differences found in their thalamic inputs.

During development, cells migrate from the ventricular zone into the cortical plate in an inward out manner: layer 6, then 5, then onwards until layer 2 forms. Cells in different layers come from different generations of cell divisions in the ventricular zone, and have different molecular make-ups (McAllister et al., 1997). Studies in culture demonstrate that cells of each generation innately ‘know’ to what layer to send their axons and dendrites (McConnell and Kaznowski, 1991), although the specification of connections to sublaminae and within layers requires activity-dependent refinement (Callaway, 1998b).

Subplate

The cortical subplate is traditionally thought of as a transient cortical area underlying the cortical plate that is responsible for proper target recognition of developing thalamocortical connections (McConnell et al., 1989). If the V1 subplate is ablated before the LGN growth cones contact cortex, the LGN efferents will grow past V1 and instead innervate other cortical areas (Ghosh and Shatz, 1993). Afferents from the LGN ‘wait’ in the cortical subplate for a period of weeks before growing into the cortical plate (Rakic, 1976; Chun et al., 1987; Kostovic and Rakic, 1990). If the subplate is ablated shortly after the LGN grows into layer 4, ocular dominance columns (Ghosh and Shatz, 1992, 1994) and orientation tuning (Kanold et al., 2001) fail to develop. There exist reciprocal connections between the subplate and layer 4 (Ghosh, 1995). There also exist connections from the subplate to layer 1 (Allendoerfer and Shatz, 1994). Cells in layers 2/3 and 5 have apical dendrites in layer 1 (Callaway, 1998b). Connections also exist from most cortical layers to the subplate (Callaway, 1998b). In addition, afferents from the LGN are pruned in the subplate yielding a retinotopically more precise map (Naegele et al., 1988). Thus, circuits exist by which early activity in each of the layers of the cortical plate may be driven and coordinated by the subplate.

The present model proposes that the subplate contains sufficient circuitry (Kostovic and Rakic, 1980; Chun and Shatz, 1989; Meinecke and Rakic, 1989) to develop its own ocular dominance and orientation maps, including lateral excitation and inhibition, spontaneous inputs from the thalamus, and correlation learning (Grossberg and Olson, 1994). When the LGN efferents grow into layer 4, the subplate also makes connections in layer 4. Teaching signals from the subplate are proposed to guide the growth of the LGN-to-layer 4 connections and result in layer 4 learning the map induced by the subplate inputs. Likewise, the subplate is the main source of drive for layer 2/3, via the apical dendrites of the cells in layer 1. Teaching signals from the subplate are proposed to guide the clustering of horizontal connections in this layer as well. The correlated teaching signals that are provided by the subplate across layers are also proposed to energize the development of vertical interlaminar connections.

Orientation Tuning

Hubel and Wiesel discovered cells in area 17 (V1) of the cat that fire in preference to bars of a particular orientation (Hubel and Wiesel, 1959). The preferred orientation of V1 cells varies smoothly in tangential penetrations and remains mostly constant in vertical penetrations within a cortical column. Hubel and Wiesel (Hubel and Wiesel, 1962) proposed that orientation tuning originates from an oriented pattern of input from the LGN. In this proposal, multiple LGN cells, with spatially offset receptive fields, terminate onto a single V1 simple cell. Other researchers have verified that the input from the LGN to an individual cortical simple cell are oriented along the same axis as the preferred orientation of that cell (Chapman et al., 1991; Reid and Alonso, 1995). The sufficiency of this oriented input to explain data of orientation selectivity is still controversial (Carandini and Ringach, 1997; Anderson et al., 2000; Ferster and Miller, 2000).

The clearest data concerning the development of orientation selectivity comes from two sources: optical imaging and electrophysiology. The data from optical imaging indicates global properties of orientation maps, but since this method necessarily averages the response of many cells within and across layers, it does not give much insight into the tuning curves or receptive fields of individual cells, or of differences across cortical layers. The data from electrophysiology provides tuning curves of single cells, can be used to derive receptive fields, and can look at laminar differences, but does not give clear data on the global organization of the properties of these cells.

Crair et al. (Crair et al., 1998) examined the time course of the development of orientation selectivity in the cat. They found that regular orientation maps were in place by the end of the second postnatal week (W2). At this point, the response from visual input to the contralateral eye was much stronger than that to the ipsilateral eye, but the orientation maps were similar between the two eyes. The orientation map continued to be refined until W4, but the overall pattern of the map remained largely constant.

Albus and Wolf (Albus and Wolf, 1984) conducted a laminar analysis of the development of orientation tuning in the cat. They discovered a number of orientationally tuned cells at the time of eye opening and that, within a few days of patterned vision, both the responsiveness and proportion of orientationally tuned cells increased. They also found that layers 4 and 6 developed light responsiveness and tuning a week or two before the cells in layers 2/3 and 5 become responsive and tuned. During the next few weeks, the proportion of orientationally tuned cells increased dramatically, reaching adult levels by week 6.

Ocular Dominance

Hubel and Wiesel (Hubel and Wiesel, 1962) also found that ocular dominance, or a cell’s preference for one eye’s input over another, varies smoothly in tangential penetrations and remains constant in vertical penetrations. In the input layers of V1, cells are predominantly monocular, and in the output layers, cells are often binocular with a preference for a given eye. Injecting [3H]proline into a single eye revealed alternating stripes of cortex connected to one or the other eye (Shatz et al., 1977). Such ocular dominance columns (ODCs) have been identified in cats, ferrets, new world monkeys and humans.

Older studies using [3H]proline typically first identified ODCs in the third or fourth weeks of life. Since cats open their eyes early in the second week, it was concluded that patterned visual activity was necessary for the formation of ODCs. More recently, optical imaging has been used to identify ODCs that form by the second postnatal week (Crair et al., 2001). It is possible that ODCs exist even earlier than this, as the signal in optical imaging is less reliable in the deeper layers. The data from Albus and Wolf (Albus and Wolf, 1984) indicate that the first visibly responsive cells are monocular and respond to either eye. However, their data do not show the organization of these cells in each layer.

ON and OFF Receptive Fields

Ganglion cells in the retina, the primary retinal output cells, include ON cells that respond to increments of light in the center of their receptive fields, and OFF cells that respond to decrements of light their receptive fields centers. These cell types terminate in different sublaminae of the LGN in ferrets (Weliky and Katz, 1999) and in different subregions of the receptive fields of cortical simple cells (Reid and Alonso, 1995; Alonso et al., 2001). The organization of ON and OFF subregions play a role in the degree of orientation tuning, direction tuning, and construction of complex cells, among other properties.

The receptive field structure of V1 cells changes dramatically over the course of the first few weeks. Young cells have receptive fields that are largely monocular and dominated by contralateral eye inputs (Crair et al., 1998). These cells typically have a single excitatory region dominated by OFF-cell input (Albus and Wolf, 1984). By the fourth week, the typical cell has both ON and OFF regions and is responsive to inputs from each eye. It is likely that the increase of orientation selectivity occurring through the fourth week (Albus and Wolf, 1984; Crair et al., 1998) is due to coordination of OFF and ON activity in response to visual inputs.

Horizontal Connections in Layer 2/3

Layer 2/3 of V1 contains cells that have long-range lateral connections. These intralaminar connections are clustered and primarily connect cells of similar ocular dominance (Löwel and Singer, 1992) and orientation preference (Ts’o et al., 1986) and their long axis is in the same direction as the cells’ preferred orientation (Grossberg and Mingolla, 1985; Schmidt et al., 1997a,b, 1999; Sincich and Blasdel, 2001). These clusters are identified by applying Rhodamine (an anterograde/retrograde tracer) in layers 2/3 or 5 (Gilbert and Wiesel, 1983). These horizontal connections are used to explain perceptual grouping and attentional effects in models of visual processing (Grossberg and Raizada, 2000; Grossberg and Williamson, 2001).

Clustered horizontal connections in layer 2/3 provide important clues about how the early stages of the orientation map develop. Such connections are found by postnatal day 8 (P8), before the age of visual responsiveness in these layers and before the in-growth of connections from layer 4 (Callaway and Katz, 1992). The clusters also form during binocular deprivation (Callaway and Katz, 1991; Ruthazer and Stryker, 1996). The clusters align with the later-forming orientation map in these layers (Callaway and Katz, 1990). They require eye opening in order to refine, and perhaps to grow to their maximum extent, but this refinement typically consists of increased growth of existing clusters, not a reorganization of them (Callaway and Katz, 1990). This fact is important since it has been shown that the later clusters connect iso-oriented areas (Yoshioka et al., 1996; Bosking et al., 1997). These data imply that the maps in layers 4 and 2/3 are coordinated before they connect to each other. Such coordination would seem to require a different input source. The model proposes that this input is the cortical subplate, and supports this hypothesis with a summary of consistent data and simulations showing that such a mechanism works.

How vertical interlaminar connections form is also a key problem for a theory of laminar development. Before eye opening, coarse layer 2/3 clustering makes everything look ‘coarse’. This coarse clustering, however, coexists with precise vertical layer 4-to-2/3 connections. The model proposes how the subplate organizes correlations between layers 4 and 2/3 and thereby guides formation both of coarse horizontal clustering and precise vertical connections between layers.

Models of Map Formation

There is a rich modeling literature on how maps of oriented cells can develop on a cortical sheet. The earliest models showed that an associative learning rule and recurrent lateral inhibition, or competition, produces orientation tuning when presented with oriented inputs (von der Malsburg, 1973; Grossberg, 1976). Linsker (Linsker, 1986a,b,c) subsequently demonstrated self-organization of orientation tuning without oriented inputs. Other modeling work has shown how ocular dominance maps can arise from uncorrelated inputs (Swindale, 1980Kohonen, 1982; Miller et al., 1989; Rojer and Schwartz, 1990), how maps of orientation and ocular dominance may develop simultaneously (Durbin and Mitchison, 1990; Obermayer et al., 1992; Swindale, 1992; Obermayer and Blasdel, 1993, Sirosh and Miikkulainen, 1997), and how the development of orientationally tuned simple cells and their arrangement into cortical maps may progress synchronously (Miller, 1992; Olson and Grossberg, 1998). While the models vary in their details, Rojer and Schwartz (Rojer and Schwartz, 1990) demonstrated that basic filter properties of lateral excitation and inhibition (i.e. a bandpass filter) naturally produce either ocular dominance or orientation maps when they interact with a noise source. Later, Grossberg and Olson (Grossberg and Olson, 1994) analyzed existent models to show that, when three computational principles that are shared by all the models interact together, namely a source of noisy input, a band pass filter, and normalization across all feature dimensions, then maps of orientation and ocular dominance are generated with experimentally observed features like singularities, fractures, and linear zones, as well as the occurrence of nearby pairs of like-oriented simple cells that are sensitive to opposite contrast polarities.

More recent modeling work (Grossberg and Raizada, 2000; Grossberg and Williamson, 2001) proposes how laminar circuits in V1 and V2 help to explain data on development, learning, perceptual grouping, and attention. Callaway (Callaway, 1998a) has examined the same substrate anatomically, and has produced a conceptual model in which a layer with horizontal connections (B) receives both the inputs and outputs of a feedforward layer (A), and thus (B) acts as a control system by feeding back to, and modulating the activity of, layer (A).

Subplate Map Formation and Model Dynamics

The present model builds on and extends the work of previous models. It demonstrates how the orientation and ocular dominance maps form and are coordinated across multiple area V1 layers to form cortical columns and the crude clustering of horizontal connections across columns found in the superficial and deep layers.

The model proposes how the subplate circuits embody a source of noisy input, a band pass filter (see Fig. 1), and normalization, and thus how orientation and ocular dominance maps develop there. In fact, all of the model cortical layers embody variants of a band pass filter and normalization. Both of these properties are simultaneously realized by an on-center off-surround network of interactions between cells that obey membrane, or shunting, equations (Hodgkin and Huxley, 1952; Grossberg, 1973, 1976, 1980). Such networks are ubiquitous in the brain. They realize a balance between cell cooperation and competition that can preserve the sensitivity of cell activations to the relative size of inputs whose total size may vary greatly through time. When the on-center off-surround networks includes recurrent, or feedback, interactions, then they can also contrast-enhance their cell responses to input patterns while also normalizing them. Such contrast-enhancement is important when the initial inputs to the network are very small due to the small size of adaptive weights before learning occurs. The contrast-enhanced activities allow learning to occur in an efficient manner.

Another property of the subplate, and all the networks of the cortical layers, is that they include habituative, or depressing, synaptic transmitters (Grossberg, 1968, 1976, 1980; Abbott et al., 1997). These transmitters gate, or multiply, the signals between cells and habituate in an activity-dependent way. They prevent the earliest cells that win the competition in the network from persistently dominating network dynamics. Such habituative, recurrent on-center off-surround networks define all the information processing within and among the model layers. The associative learning laws that control model development are ones that have been used in many developmental and learning models since they were first used for this purpose in Grossberg (Grossberg, 1976).

After a map is learned in the subplate, it is used as a source of teaching signals to drive map formation in the other layers. This hypothesis provides a theoretical rationale for why, for example, ablation of the subplate results in the lack of formation of orientation selectivity and ocular dominance maps (Ghosh and Shatz, 1992; Kanold et al., 2001). In a similar vein, evolutionary analysis indicates that phylogenic emergence of columns coincides with the emergence of the subplate and, importantly, with the LGN-subplate waiting period (McAllister, 1999).

Another novel feature of the model is that it reflects the temporally ordered process of development. The model starts with a circuit containing the retina, LGN and subplate (Fig. 1A). This first circuit is monocular, based upon several lines of evidence. Physiological recordings in area 17 of kittens show that at eye opening the majority of cells respond only to contralateral eye inputs (Albus and Wolf, 1984). Studies in young ferrets demonstrate that the pattern of activity in the LGN is largely unchanged when the ipsilateral inputs from the retina are cut (Welikey and Katz, 1999). In addition, there is an early bias of oriented OFF cells in the kitten cortex (Albus and Wolf, 1984) and of OFF activity in the retina before eye opening (Wong and Oakley, 1996). Correspondingly this stage of the model contains only OFF ganglion cells.

Spontaneous activity in the retina drives network dynamics and associative learning allows for the development of feedforward and feedback connections between the LGN and subplate. After development, the pattern of feedforward connections to a given subplate cell and the feedback connections from that cell share the same axis of elongation, as has been experimentally reported (Murphy et al., 1999).

The second stage of the model introduces binocular inputs to the subplate in a way that has not been captured by previous models (Fig. 1B). In this simulation, the connections serving the contralateral eye continue developing as activity in the ipsilateral eye is introduced. The contralateral LGN already has developed oriented connections to the subplate at this stage, whereas those from the ipsilateral LGN are introduced as random spatial receptive fields, just like those of the contralateral LGN before refinement. The spontaneous activity in the retina provides intraocular correlations that also drive the formation of ocular dominance columns in the subplate.

An important advantage of having ocular dominance columns develop after the orientation map has been specified is that no special mechanisms are needed to coordinate the orientation map between the two eyes. The orientation map of the contralateral eye is inherited by the ipsilateral eye, just as the receptive fields of the cortical layers inherit properties of the subplate.

Next, the subplate guides map formation in each of the cortical layers as follows: Because the early map development in each of the cortical layers develops independently (i.e. without interlaminar cortical connections), they are described as separate simulations. This is not meant to imply that the there is no interesting time-course in the map development during this stage. In fact, much of the learning in layer 2/3, which contains much younger cells, occurs after layer 4 has developed its orientation map (Callaway and Katz, 1992; Galuske and Singer, 1996).

The development of layer 4 is proposed to occur as follows: afferents from the subplate are introduced in layer 4 and the afferents from the LGN begin to develop into layer 4 (Fig. 1C). Endogenously active inputs in the retina enable signals from the subplate to layer 4 to act as teaching signals that guide the pattern of developing connections from the LGN into layer 4. The layer 4 circuit includes the same types of mechanisms as the subplate, with the exception that layer 4 also receives teaching inputs from the subplate in addition to that from the LGN. The layer 4 weights stabilize once a map similar to that found in the subplate is achieved. As described in greater detail below, maps of ocular dominance and orientation tuning form in layer 6 (Fig. 1E) at a time and manner similar to that in which they develop in layer 4.

The model next describes the development of the horizontal connections in layer 2/3 (Fig. 1D). Here subplate inputs are introduced to the model layer 2/3. The basis of this circuit in vivo are the axonal branches in the marginal zone from the subplate (Ghosh, 1995), where layer 2/3 has dendritic branches (Callaway, 1998b). In this simulation, the connections between layer 2/3 cells develop in response to lateral correlations provided by the subplate inputs. As the connections between layer 2/3 cells develop, the layer 2/3 network amplifies the correlations found in the subplate input and refines the pattern of connections. It is important to realize that the subplate inputs to layer 2/3 are the same as those to layer 4, but in layer 2/3 lateral connections are developed instead of connections from the LGN. While not explicitly modeled, we suggest that the horizontal connections found in layer 5 develop in a similar fashion as those of layer 2/3.

Once maps have developed in each of the cortical layers, interlaminar connections grow (Callaway and Katz, 1992). In the model, layer 4-to-2/3 and layer 6-to-4 connections are developed (Fig. 1E). As the subplate provides the same input to each of the cortical layers, there are strong ‘vertical correlations’ in the activity across layers. These correlations, combined with an appropriate correlational learning law, result in cells that have mostly vertical interlaminar connections. These vertical connections are the basis of stable adult columns and are a vital component of the model. Simulations show that poorer correlations between cortical layers develop in the absence of subplate teaching signals.

Since the subplate is a transient layer, it is important to show that the cortical circuits and maps are stable after the subplate atrophies. With the introduction of layer 6, the model demonstrates how the circuitry and map structure of the layered cortical circuit can be maintained. The model layer 6 receives inputs from the subplate and develops a similar pattern of connections from the LGN as is found from the LGN to layer 4. Layer 6 also develops a set of connections to the LGN, which are similar to those from the subplate to the LGN. As noted above, interlaminar connections from layer 6 to layer 4 are developed. When the layer 6 connections have stabilized, the subplate is removed from the network and simulations demonstrate that this new, adult-like, circuit is stable.

Finally, patterned vision is used to allow for the formation of distinct ON and OFF subregions of simple cell receptive fields. While the earlier orientationally tuned cells found in cortex are monocular and are mostly dominated by OFF inputs, mature cells contain both ON and OFF subregions. The model accomplishes this in a simulation of eye opening. At eye opening, the mean firing rates of the ON and OFF cells in the retina equalizes. More importantly, with the introduction of patterned vision, the ON and OFF cells in the retina become anti-correlated: wherever an ON cell is active, the OFF cell at that location is hyperpolarized and a spatially neighboring OFF cell is active. In vivo, layer 4 cells quickly develop distinct ON and OFF subfields (see Albus and Wolf, 1984). The importance for patterned vision in the segregation of ON and OFF receptive fields is verified in the ferret LGN where dark-raising results in increased convergence of ON and OFF to thalamic relay cells (Akerman et al., 2002).

Ablation of the subplate, shortly after afferents from the LGN contact layer 4, results in a loss of orientation tuning and ocular dominance column development in layer 4. It has been demonstrated that the levels of BDNF increase dramatically at this time (Ghosh and Shatz, 1994). Other data demonstrate that either an increase or decrease of the intrinsic level of BDNF in cortex will result in the loss of ocular dominance columns (Cabelli et al., 1995, 1997). BDNF has been shown to increase the release of both Glutamate and GABA (Berardi and Maffei, 1999).

To model the effects of subplate ablation, the subplate layer is removed from the network and random weights are introduced between the LGN and layer 4. To model the effects of BDNF, a parameter is introduced to the activity equation for layer 4 that equally modulates the effectiveness of the excitatory and inhibitory connections. An increase of BDNF is modeled by increasing this parameter. To model a reduction of BDNF, this term is reduced. A sufficiently large change in either direction interferes with the development of orientation tuning and ocular dominance columns. This result suggests that the balance between excitation and inhibition works best in an intermediate range of cell activation. Such an ‘inverted U’ in cell processing is also known to occur in models of opponent processing where, again, the balance between excitation and inhibition controls cell sensitivity (Grossberg, 2000).

Computational Model

The model equations (see Appendix A, http://cercor.oupjournals.org) are chosen to be consistent with those used in the FACADE model (Grossberg, 1994, 1997; Grossberg and Mcloughlin, 1997; Grossberg et al., 2002) of 3-D vision and figure-ground perception. Earlier modeling of visual development within this framework has illustrated how development of horizontal connections within layer 2/3 can lead to an adult model that can simulate data about adult human psychophysics (Grossberg and Williamson, 2001). The present modeling results are consistent with these demonstrations and extend them to analyze the coordinating role of the subplate in interlaminar development of cortical columns.

The model was implemented in the Matlab simulation environment and run on a dual 1.4 GHz Athlon computer running Linux. In the retina, activity was assumed to react quickly to noise fluctuations and was thus computed at steady state. The other continuous time cell activity equations were solved using an adaptive step size Runge–Kutta 4,5 method. For computational simplicity, the equations for learning by the adaptive weights were solved at a slower time scale using Euler’s method. Each stage of the model was run for 20 000–100 000 input iterations until the weights converged to a stable pattern.

Results

Development of Orientation in the Subplate

The model starts with a circuit containing the retina, LGN and subplate (Fig. 1A). This model is similar to other models of how orientation maps develop and it produces a robust map of oriented cells; see Figure 3A. This figure shows a nine-by-nine region in the center of the network and was constructed by probing the network bars of eight different orientations and measuring the peak response of each cell to each orientation. The orientation of each bar portrays the orientation of the stimulus that elicited the maximum response from that cell. The length of each bar portrays the orientation index of that cell (the difference between the peak and null (stimulus orthogonal to the peak) orientations divided by their sum). Using vector sums to determine the peak and circular variance as an index produce similar maps. Figure 2 also shows the raw receptive fields (Fig. 2B) for four neighboring cells in the middle of the network, their orientation tuning curves (Fig. 2C), and the schematic of their orientation tuning (Fig. 2D).

The receptive fields in this model are spatially defined and thus there is great diversity in the degree of tuning and the shape of the raw receptive fields, shown in Figure 3. Feedback connections from the subplate to LGN are developed simultaneously to the development of the feedforward LGN-to-subplate connections. After development, the feedforward connections to a given subplate cell and the feedback connections from that cell share the same long-axis (Murphy et al., 1999). This figure shows the receptive fields before and after learning. Initial weight profiles from the LGN to subplate are generated as white spatial noise with limited spatial extent (Fig. 3A). After learning, weights from the LGN to subplate are refined and oriented (Fig. 3C). Initial weight profiles from the subplate to LGN are initially uniform and equal to 1 (Fig. 3B). After learning weights from subplate to LGN are also patterned and are oriented in the same manner as their equivalent LGN to subplate weights (Fig. 3D). The coarseness of these receptive fields is due to the extreme computational load of the simulations (requiring many months of computer time), which necessitated a low-resolution grid.

Development of Ocular Dominance in the Subplate

The second stage of the model introduces binocular inputs in the subplate (Fig. 1B). In this simulation, ocular dominance columns emerge, as in Figure 4A. Plotted is the ocularity index (the difference of the ipsilateral and contralateral weights divided by the sum). This index is valued between −1 and 1, where cells with large absolute values are the most monocular. In this simulation, the typical cell has an index of ±0.8 which means that they are highly monocular. At the beginning of the simulation, the cells are all dominated by the contralateral eye. The ipsilateral eye invades territory that was only weakly activated by the contralateral eye. Since the total connection strength to each subplate cell is conserved, competition results in cells that are largely monocular. Since the total input from each eye to the subplate is equal, the number of cells devoted to each eye equalizes (Miller et al., 1989). Finally, the width of the columns approximates the extent of the local excitatory and inhibitory connections (Fitzpatrick et al., 1985; Lund et al., 1995).

Layer 4 Simulations

In this simulation, afferents from the subplate are introduced in layer 4 and the afferents from the LGN begin to grow into layer 4 (Fig. 1C). The layer 4 simulations demonstrate that the orientation and ocular dominance maps, which are learned in the subplate, can be subsequently taught to other cortical layers, as shown in Figure 4. Here it can be seen the orientation and ocular dominance maps are almost identical between the two layers. A comparison of the peak orientations between the subplate and layer 4 shows that 80% of the layer 4 cells have the same orientation peak as is found in the underlying subplate cell. A comparison of the receptive fields between the subplate and layer 4 shows that, in almost every case, pattern weights from the LGN to layer 4 correspond to those from the LGN to the subplate. There is a 96% correlation between these weights in a pixel-by-pixel comparison.

Subplate Ablation and BDNF

Ablation of the subplate results in a loss of orientation tuning and ocular dominance column development in layer 4. It has been demonstrated that the levels of BDNF increase dramatically at this time (Ghosh and Shatz, 1994). Other data demonstrate that either an increase or decrease of the intrinsic level of BDNF in cortex will result in the loss of ocular dominance columns (Cabelli et al., 1995, 1997). BDNF has been shown to increase the release of both Glutamate and GABA (Berardi and Maffei, 1999).

To model the effects of subplate ablation, the subplate inputs were removed from layer 4 and the LGN. A parameter modulating the model’s excitatory (Glutamate) and inhibitory (GABA) transmitter release was introduced to activity equation (12) that describes layer 4. To model the effects of an increase of BDNF, this parameter was increased. As shown in Figure 5, decreasing BDNF levels by 90% caused the initial pattern of weights from the LGN to layer 4, which were initialized to random values, to fail to refine. Thus neither ocular dominance columns nor orientation developed in layer 4. At baseline levels of BDNF, ocular dominance and orientation maps developed in layer 4, but have no relationship to the maps that existed in the subplate before it was ablated. If BDNF levels are reduced by 50%, receptive fields do refine, but are not well oriented and ocular dominance does not develop. In addition, the receptive fields that develop with low values of BDNF are not stable; see Figure 6.

Other simulations have shown that, just as an equal change to both excitation and inhibition will affect map development, so too does a sufficiently large increase of the net level of excitation or inhibition. An increase of excitation reduces the selectivity of cells by enlarging their receptive fields. An increase of inhibition, beyond a certain point, causes a loss of cell response and thus more random receptive fields.

BDNF is involved in many more functions that regulating transmitter release and it is possible that its other activities are important in functional development. For example, an alternate explanation of the role of BDNF is that LGN neurons require BDNF to survive. In cases where BDNF is abundant, the LGN neurons proliferate. Where BDNF is scarce, the LGN inputs atrophy. In this situation, only a certain range of BDNF levels will produce the necessary competition for resources that produce ocular dominance columns.

Development of ON and OFF Receptive Fields

While the early orientationally tuned cells found in cortex are dominated by OFF inputs, mature cells contain both ON and OFF subregions; see Figure 1C. The model simulates how, at eye opening, the mean firing rates of the ON and OFF cells in the retina equalizes, and how patterned vision causes the ON and OFF cells in the retina become anti-correlated, so that, as in vivo, model layer 4 cells quickly develop distinct ON and OFF sub-fields (Albus and Wolf, 1984).

The model uses an input consisting of patterns of randomly configured rectangles, of random luminance and orientation, as described in the Retina section. Filtering such an image separately with ON or OFF filters produces patterns that have spatially offset areas of high activation. In the network, the OFF cell activities are spatially offset from those of the ON cells and, as a result, correlational learning in layer 4 produces cells with distinct ON and OFF subfields; see Figure 7.

Layer 2/3 Simulations

Simulation results of how the subplate instructs the growth of intralaminar connections in layer 2/3 (Fig. 1D) are shown in Figure 8A. Each block represents the lateral connections from a single layer 2/3 cell. Connections of strong weight, in white, are clustered together separated by gaps, in black, of zero or small weight. Here the pattern of horizontal connections is more refined than the scattered horizontal connections found in vivo (Callaway and Katz, 1990). This difference results from the fact that there is no noise in the Difference-of-Gaussian filters used in the simulation. Cluster size is determined by the extent of the local excitatory interactions, whereas cluster spacing is influenced by the extent the local inhibitory connections. If these filters were multiplied with noise, the clustered horizontal connections would be more scattered as found in vivo.

The simulated clusters correspond to underlying subplate cells of all orientations. We predict that the early clusters found before eye opening in vivo are also nonspecific to orientation. This is consistent with the double-label data from Callaway and Katz (Callaway and Katz, 1990), where they applied a retrograde stain in the same area of the same animal at both P15 and P29. These data show that the P29 stain labels areas that were stained with the P15 tracer, but also that the P15 stain labels many areas that are no longer labeled at P29. It seems that during the refinement of the clusters, which occurs when the eyes are opened, connections to ortho-orientations drop off, resulting in horizontal connections to iso-oriented regions of the orientation map (Bosking et al., 1997).

Development of Layer 4-to-2/3 Connections

After clusters form in layer 2/3, connections from layer 4 to layer 2/3 are developed; see Figure 1E. The formation of a map in the subplate and connections of the subplate with other cortical layers provides the ‘vertical correlations’ that are necessary for proper interlaminar connections, which support cortical columns, to form.

The results of this simulation are shown in Figure 8B. In this figure, the white spots in the center of each block demonstrate that cells in layer 4 are connected to the directly overlying layer 2/3 cells. Together, the simulations in Figure 8 show how coarsely clustered intralaminar connections in layer 2/3 can co-exist with precisely organized vertical interlaminar connections.

Death of the Subplate and Rise of Layer 6

Since the subplate is a transient layer, it is important to show that the cortical circuits and maps are stable after the subplate atrophies. With the introduction of layer 6, the model demonstrates how the circuitry and map structure of the layered cortical circuit can be maintained; see Figure 1E.

The results of the layer 6 simulations are almost identical to those shown in Figure 4. Layer 6 has inputs from the subplate and it develops a nearly identical pattern of connections from the LGN as is found from the LGN to layer 4; compare Figure 4A and C with Figure 4B and D. Comparing the receptive fields of layer 6 to those of layer 4 show a 93% correlation in a pixel-by-pixel comparison. Layer 6 develops a set of connections to the LGN, which are similar to those from the subplate to the LGN, with a 96% correlation.

In addition, interlaminar connections from layer 6 to layer 4 are developed; see Figure 9A. These interlaminar connections develop vertically in a similar fashion as the layer 4 to layer 2/3 connections. When all sets of layer 6 connections have stabilized, the subplate is removed from the network as the newly developed layer 6 circuits become active. Simulations have shown that this new circuit is stable.

To demonstrate the importance of the subplate in the vertical development of interlaminar connections, a simulation was run without the influence of the subplate. In this simulation, layers 6 and 4 start off with random connection weights from the LGN. Maps of orientation and ocular dominance develop in both layers, but the maps are not coordinated. In addition, the layer 6-to-4 connections that develop are not vertical; see Figure 9B.

Discussion

The cortical subplate is traditionally thought of as a transient cortical area underlying the cortical plate that is responsible for proper target recognition of developing thalamocortical connections. If the V1 subplate is ablated before the LGN growth cones contact cortex, the LGN efferents will grow past V1 and instead innervate other cortical areas (Ghosh and Shatz, 1993).

We predict that the subplate plays the equally important role of coordinating the development of cortical columns. This hypothesis is consistent with all the data known to us about early cortical development. For example, afferents from the LGN ‘wait’ in the cortical subplate for a period of weeks before growing into the cortical plate (Rakic, 1976; Chun et al., 1987; Kostovic and Rakic, 1990). If the subplate is ablated shortly after the LGN grows into layer 4, ocular dominance columns and orientation tuning (Ghosh and Shatz, 1992, 1994; Kanold et al., 2001) fail to develop. There exist reciprocal connections between the subplate and layer 4 (Ghosh, 1995). There also exist connections from the subplate to layer 1 (Allendoerfer and Shatz, 1994). Cells in layers 2/3 and 5 have apical dendrites in layer 1 (Callaway, 1998b). Connections also exist from most cortical layers to the subplate (Callaway, 1998b). Thus, circuits exist by which early activity in the cortical plate may be driven by the subplate.

The subplate contains sufficient circuitry (Kostovic and Rakic, 1980; Chun and Shatz, 1989; Meinecke and Rakic, 1989) to develop ocular dominance and orientation maps (Allendoerfer and Shatz, 1994); namely, lateral excitation and inhibition, spontaneous inputs from the thalamus, and associative learning (Grossberg and Olson, 1994). It is thus proposed that the subplate learns a map of orientation tuning and ocular dominance. When the LGN efferents grow into layer 4, the subplate also makes connections in layer 4 and correlations from the subplate guide the growth of the LGN-to-layer 4 connections and result in layer 4 developing the same map as found in the subplate. Likewise, the subplate is the main source of drive for layer 2/3, via the apical dendrites of the cells in layer 1, and the correlations from the subplate guide the clustering of horizontal connections in these layers. The fact that the subplate connects to all of the cortical layers results in vertical correlations that instruct the development of interlaminar connections. Once these interlaminar connections are in place, they are self-maintaining and when the subplate atrophies the developed cortical circuit remains stable.

Experiments are needed to verify these predictions. The model predicts that physiological recording of the subplate will reveal cells tuned for orientation. It also predicts that anatomical staining will reveal ocular dominance columns in the subplate. Since the subplate atrophies shortly after eye opening, and is deep in cortex, there exists little physiological recording from this layer, but it is likely that cells are inadvertently recorded from the subplate and mistaken for layer 6 cells, which are orientationally tuned.

The model suggests how map loss after subplate ablation may be due to the resulting increase of BDNF in the cortical plate. It is possible that if the subplate is ablated, or inactivated, and the BDNF levels controlled, that maps of ocular dominance and orientation tuning might still form in cortex, since layers 4 and 6 have the same mechanisms supporting map formation as found in the subplate. We predict that, if this is verified, then vertical electrode penetrations would not initially find iso-oriented cells. Instead, while maps might still form in each cortical layer, they would be less coordinated across the layers. It is important to note that BDNF plays roles other than those discussed in our model which may play a role such an experiment.

We also predict that interlaminar connections that develop after the subplate is ablated would be less ‘vertical’ than found in normal cortex. In the model, the vertical correlations provided by the subplate play an important role in the development of these interlaminar connections. In particular, the lateral correlations found in the horizontal layer 2/3 connections would drive the layer 4-to-2/3 connections in subplate-ablated cortex to be more scattered than in the normal animal.

Molecular and Activity-based Mechanisms in Map Formation

It has been recently suggested that the initial specification of ocular dominance maps in the LGN and V1 is controlled by molecules expressed differently between the two eyes, or between the nasal and temporal regions of each eye. This hypothesis is supported by evidence that ocular dominance columns form in the cat at 2 weeks of age (Crair et al., 2001), and at 3 weeks in the ferret (Crowley and Katz, 1999, 2000), much earlier than first hypothesized and around the time that the LGN first innervates layer 4. Since Crowley and Katz did not eliminate the spontaneous activity between the LGN and subplate, they do not address the mechanisms used in our model. In fact, their data show eye-specific clusters of axons in the subplate before eye opening.

Other evidence against an activity-related mechanism comes from the fact that ocular dominance columns develop prior to visual input (Rakic, 1977). This brings up the important distinction between visually evoked activity and spontaneously evoked activity. Studies have demonstrated spontaneous activity in the retina (Wong et al., 1983), LGN and cortex (Weliky and Katz, 1997) prior to eye opening. Interference with this activity disrupts the segregation of eye-specific layers in the LGN and in V1 (Rakic, 1981).

While some steps of visual map formation might be initially guided by activity-independent signals, such as ephrins (Cheng et al., 1995; Wilkinson, 2001), refined and complex patterning requires activity (Callaway and Katz, 1991; Katz and Shatz, 1996; Weliky and Katz, 1997; Dantzker and Callaway, 1998; Penn et al., 1998; Cook et al., 1999). Activity-based processing is needed if only to offset the lack of precision of the molecular map. On the scale of hundreds of microns, differences in the molecular gradients are too flat for exact target recognition. It may also be the case that maps related to visual features, such as orientation, are too specific for molecular patterning. Spontaneous activity may have evolved as the biological solution to efficient blueprinting. Later, patterned vision may refine these maps by optimizing them to fit environmental statistics, as well as individual differences in eye size and lateral separation. Binocular disparity tuning is a classical example of a process that depends on properties, like changing positions of the eyes in a growing head, that requires visual experience for final tuning (Grunewald and Grossberg, 1998).

Modeling Issues

Simulating development in the model requires running a large number of input iterations until the weights converge to a stable value. Each stage of the model required running 20 000–100 000 iterations, and each iteration takes from 4 s to 1 min to compute, depending on the number of layers and feedback connections. Each simulation thus takes from a day to a month to run on a 1.4 GHz Athlon processor. Thus in order to carry out the full set of simulations, it was necessary to use a relatively small network of 26-by-26 cells for each layer.

While this model produces very good orientation tuning, the orientation map is not very smooth. The reason for this is the granularity of the network. Ocular dominance columns are only a few cells wide, which leaves no room for a full set of orientations. The granularity also introduces aliasing of isotropic filters, which has the result of producing an uneven distribution of orientations. A careful observer will note that there are a greater number of cells that prefer 45° and 135° than other angles. Since the model concerns how the orientation map is co-ordinated across layers, and not the fine-structure properties of such maps, and since fine resolution simulations of orientation maps that obey similar principles have been run elsewhere (Olson and Grossberg, 1998), our hypotheses are not compromised by these effects.

Generality of Model Across Species

The present model attempts to embody key processes during the development of mammals such as cats, ferrets, macaques and humans. While there are important differences between each of these species, they all share a prominent subplate and properties such as orientation and ocular dominance maps, as well as clustered horizontal connections in the infragranular and supra-granualar layers. Although most data used to test the model come from experiments on cats and ferrets, the coordinating role of the subplate may be important in other species as well. Cross-species studies of the subplate indicate that it becomes a more prominent structure in higher species, peaking in size in the macaque and man at twice the thickness of the cortical plate (Kostovic and Rakic, 1990). This increase in size may indicate the increasing role of the subplate in developmental coordination. For in addition to the inputs from the thalamus, discussed in this paper, afferents from the brain stem, basal forebrain, as well as cortico-cortical connections ‘wait’ in the subplate before entering the cortical plate (Kostovic and Rakic, 1990). The subplate may be important in the functional organization of these fibers before they enter the cortical plate (Naegele et al., 1988) and in the coordination of these connections within the cortical plate. Even if accounting for species-specific variations may require model specializations, the general hypothesis of ordered development based upon the waiting period in the subplate is likely to hold across species.

Conclusion

A model is proposed of how the cortical subplate learns a map of orientation and ocular dominance tuning and teaches this map to the other cortical layers via known anatomical connections. The model accounts for the coordination of orientation and ocular dominance maps, the coordination of ON and OFF subregions of simple cells receptive fields, the crude clustering of horizontal connections in layers 2/3, and the development of precise columns of coordinated receptive field properties across the multiple cortical layers. Related modeling work (Grossberg and Raizada, 2000; Grossberg and Williamson, 2001) supplements these results by showing how consistent laminar cortical mechanisms can account for the refinement of the horizontal connections in layer 2/3, develop a correct balance of excitation and inhibition within and between cortical layers, and explain neural recording during psychophysical experiments in adult animals.

Notes

Supported in part by: Air Force Office of Scientific Research (AFOSR F49620-98-1-0108 and F49620-01-1-0397), the Defense Advanced Research Projects Agency and the Office of Naval Research (ONR N00014-95-1-0409), the National Science Foundation (NSF IIS-97-20333), and the Office of Naval Research (ONR N00014-01-1-0624). CAS/CNS Tech Report no. 02-006.

Address correspondence to Dr Stephen Grossberg, Boston University, 677 Beacon Street, Boston, MA 02215, USA. Email: steve@bu.edu.

Supplementary Material

Supplementary material can be found at: http://www.cercor.oupjournals.org.

Figure 1.

Diagram of different model stages. (A) Monocular subplate circuit. Spontaneous activity in retinal OFF cells drives the LGN, which inputs to the subplate. Feedforward weights from the subplate and feedback weights to the LGN develop into a map of oriented receptive fields. (B) Binocular subplate circuit. Here input from a second eye is introduced and a map of ocular dominance develops in the subplate, superimposed on the existing orientation map. (C) Binocular layer 4 circuit. Here the orientation and ocular dominance maps that exist in the subplate are taught to layer 4. In a subsequent simulation, ON retinal ganglion cells are introduced and patterned retinal inputs provide correlations that help to segregate ON and OFF subfields in layer 4. (D) Layer 2/3 circuit. Here clusters of horizontal connections develop in layer 2/3 guided by the correlations provided by the subplate. (E) Circuit of the fully developed model. Here layer 6 is introduced, which develops connections to and from the LGN. Then interlaminar connections are developed from layer 6 to layer 4 and from layer 4 to layer 2/3. Finally the inputs to and from the subplate are removed and the model is shown to be stable. In all figures, black circles denote OFF receptive fields, white circles denote ON receptive fields, ovals denote orientationally tuned cells, lines ending in open circles denote plastic connections. Lines without circles denote feedforward non-additive connections.

Figure 1.

Diagram of different model stages. (A) Monocular subplate circuit. Spontaneous activity in retinal OFF cells drives the LGN, which inputs to the subplate. Feedforward weights from the subplate and feedback weights to the LGN develop into a map of oriented receptive fields. (B) Binocular subplate circuit. Here input from a second eye is introduced and a map of ocular dominance develops in the subplate, superimposed on the existing orientation map. (C) Binocular layer 4 circuit. Here the orientation and ocular dominance maps that exist in the subplate are taught to layer 4. In a subsequent simulation, ON retinal ganglion cells are introduced and patterned retinal inputs provide correlations that help to segregate ON and OFF subfields in layer 4. (D) Layer 2/3 circuit. Here clusters of horizontal connections develop in layer 2/3 guided by the correlations provided by the subplate. (E) Circuit of the fully developed model. Here layer 6 is introduced, which develops connections to and from the LGN. Then interlaminar connections are developed from layer 6 to layer 4 and from layer 4 to layer 2/3. Finally the inputs to and from the subplate are removed and the model is shown to be stable. In all figures, black circles denote OFF receptive fields, white circles denote ON receptive fields, ovals denote orientationally tuned cells, lines ending in open circles denote plastic connections. Lines without circles denote feedforward non-additive connections.

Figure 3.

Pattern of feedforward and feedback connections between the LGN and subplate before and after learning. (A) Initial weight profiles from the LGN to subplate are generated as white spatial noise with limited spatial extent. (B) Initial weight profiles from the subplate to LGN are initially uniform and equal to 1. (C) After learning, weights from the LGN to subplate are refined and oriented. (D) After learning, weights from subplate to LGN are patterned and are oriented in the same manner as the equivalent LGN-to-subplate weights.

Figure 3.

Pattern of feedforward and feedback connections between the LGN and subplate before and after learning. (A) Initial weight profiles from the LGN to subplate are generated as white spatial noise with limited spatial extent. (B) Initial weight profiles from the subplate to LGN are initially uniform and equal to 1. (C) After learning, weights from the LGN to subplate are refined and oriented. (D) After learning, weights from subplate to LGN are patterned and are oriented in the same manner as the equivalent LGN-to-subplate weights.

Figure 5.

Connection weights and ocular dominance columns when BDNF (J(4)) is decreased. (A) and (C) Ocular dominance columns and contralateral eye receptive field profiles for normal BDNF levels (J(4) = 1). In C, the receptive fields profiles that are unpatterned correspond to cells dominated by the ipsilateral eye. (B) and (D) No ocular dominance columns and less oriented receptive field profiles when BDNF levels are reduced (J(4) = 0.1).

Figure 5.

Connection weights and ocular dominance columns when BDNF (J(4)) is decreased. (A) and (C) Ocular dominance columns and contralateral eye receptive field profiles for normal BDNF levels (J(4) = 1). In C, the receptive fields profiles that are unpatterned correspond to cells dominated by the ipsilateral eye. (B) and (D) No ocular dominance columns and less oriented receptive field profiles when BDNF levels are reduced (J(4) = 0.1).

Figure 6.

Stability of weights when BDNF (J(4)) is varied. Plotted is the pixel-by-pixel correlation between the weights at each time point and those of iteration 40 000, for different values of BDNF. For normal BDNF levels (J(4) = 1): these weights are the most stable and, once the weights converge, there is only a slow variation of the weights. For a 50% reduction of BDNF (J(4) = 0.5): weights develop more rapidly, but also are less stable. For a 90% reduction of BDNF (J(4) = 0.1): weights are extremely unstable. For a 50% increase of BDNF (J(4) = 1.5): weights do not develop significantly from initial values. This last case is consistent with experiments about subplate ablation.

Figure 6.

Stability of weights when BDNF (J(4)) is varied. Plotted is the pixel-by-pixel correlation between the weights at each time point and those of iteration 40 000, for different values of BDNF. For normal BDNF levels (J(4) = 1): these weights are the most stable and, once the weights converge, there is only a slow variation of the weights. For a 50% reduction of BDNF (J(4) = 0.5): weights develop more rapidly, but also are less stable. For a 90% reduction of BDNF (J(4) = 0.1): weights are extremely unstable. For a 50% increase of BDNF (J(4) = 1.5): weights do not develop significantly from initial values. This last case is consistent with experiments about subplate ablation.

Figure 9.

Learned connections from layer 6 to layer 4. (A) Normally forming interlaminar connections are vertical. (B) Subplate is ablated before interlaminar connections develop. As a result layer 6-to-4 connections do not develop vertically.

Figure 9.

Learned connections from layer 6 to layer 4. (A) Normally forming interlaminar connections are vertical. (B) Subplate is ablated before interlaminar connections develop. As a result layer 6-to-4 connections do not develop vertically.

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