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Previous Article | Next Article
Volume 17, Number 23, Issue of December 1, 1997
Spatial Relationships among Three Columnar Systems in Cat Area 17
Mark Hübener1, Doron Shoham2, Amiram Grinvald2, and Tobias Bonhoeffer1 1 Max-Planck-Institut für Psychiatrie, 82152 Martinsried, Germany, and 2 The Weizmann Institute of Science, Rehovot 76100, Israel
ABSTRACT
In the primary visual cortex, neurons with similar response properties are arranged in columns. As more and more columnar systems are discovered it becomes increasingly important to establish the rules that govern the geometric relationships between different columns. As a first step to examine this issue we investigated the spatial relationships between the orientation, ocular dominance, and spatial frequency domains in cat area 17. Using optical imaging of intrinsic signals we obtained high resolution maps for each of these stimulus features from the same cortical regions. We found clear relationships between orientation and ocular dominance columns: many iso-orientation lines intersected the borders between ocular dominance borders at right angles, and orientation singularities were concentrated in the center regions of the ocular dominance columns. Similar, albeit weaker geometric relationships were observed between the orientation and spatial frequency domains. The ocular dominance and spatial frequency maps were also found to be spatially related: there was a tendency for the low spatial frequency domains to avoid the border regions of the ocular dominance columns. This specific arrangement of the different columnar systems might ensure that all possible combinations of stimulus features are represented at least once in any given region of the visual cortex, thus avoiding the occurrence of functional blind spots for a particular stimulus attribute in the visual field.
Key words: cat; area 17; visual cortex; functional architecture; map; columns; orientation preference; ocular dominance; spatial frequency; optical imaging
INTRODUCTION
A characteristic feature of the cortex is that neurons with similar response properties are clustered together in columns extending radially through the whole thickness of the cortex. In the visual cortex it has been recognized early on that neurons are grouped according to their key response properties, orientation preference, and ocular dominance (Hubel and Wiesel, 1962
, 1963
In recent years increasing evidence has accumulated that in addition to orientation, ocular dominance, and color selectivity neurons in the visual cortex are organized in columns with respect to other stimulus parameters, such as direction of movement (Payne et al., 1981
In the visual cortex of macaques, geometric relationships between ocular dominance and orientation columns have been demonstrated (Bartfeld and Grinvald, 1992
Here we use optical imaging of intrinsic signals (Grinvald et al., 1986
Preliminary results have been published previously in abstract form (Hübener et al., 1995
MATERIALS AND METHODS
Optical imaging of intrinsic signals was used to visualize functional maps in the primary visual cortex (area 17) of 13 cats ranging in age from 2 to 5 months. Most experiments were performed on 2- or 3-month-old cats. The rationale for using young animals was that the signal-to-noise ratio of the optical signals was often larger than in adult animals. This was particularly true when ocular dominance and spatial frequency maps were imaged. A comprehensive description of the techniques used in this study can be found in Bonhoeffer and Grinvald (1996)
Optical imaging. Animals were initially anesthetized with ketamine (15-30 mg/kg, i.m.) and xylazine (1.5-2 mg/kg, i.m.) supplemented by atropine (0.15 mg/kg, i.m.). A tracheotomy was performed, and the cats were artificially respirated (40-50% N2O, 50-60% O2, 0.8-1.5% halothane). Electrocardiogram, electroencephalogram, arterial oxygen saturation (SpO2), and rectal temperature were monitored throughout the experiment. The end-tidal CO2 was measured and kept at ~3.5% by adjusting the rate and volume of the respirator. Relaxation was accomplished by intravenous infusion of gallamine triethiodide (30 mg · kg 1 · hr
The cortex was illuminated with red light (peak transmission: 707 nm) by means of two flexible light guides. A Peltier cooled, slow-scan CCD camera (Princeton Instruments, Trenton, NJ, or Theta System-ORA 2001, Optical Imaging, Germantown, NY) equipped with a tandem lens arrangement (Ratzlaff and Grinvald, 1991
Visual stimulation. Large field stimuli (80° wide, 60° high) were generated with the program "Stim" (Kaare Christian, The Rockefeller University) and projected onto a frosted glass screen with a video projector. Stimuli consisted of high-contrast (90%) square-wave gratings presented at four orientations and two spatial frequencies (usually 0.2 cycles/degree and 0.6 cycles/degree) in a pseudo-random sequence. During each presentation the grating was moved back and forth at different speeds (10°/sec and 3.3°/sec) that were chosen to keep the temporal frequency constant for all stimuli (at 2 Hz). Computer-controlled shutters in front of the eyes allowed for randomly alternating monocular stimulation. Each individual stimulus cycle consisted of 3 sec of moving stimulus, during which data were acquired, followed by a period of 7 sec to allow the signal to return to baseline. During this 7 sec period the grating that was to be drifted during the next stimulus cycle was placed on the screen and held stationary. This standing-moving sequence was chosen to avoid unwanted stimulus-on responses during the data acquisition period. Depending on the noise level of the functional maps, each stimulus was repeated between 32 and 160 times. The responses to 16 identical stimuli were accumulated on line, with the resulting reflectance image serving as the basic data set for the computation of functional maps.
Computation of functional maps. In most cases we discarded the first frame captured during each stimulus presentation, because it usually contained almost no stimulus-related signal. As the next step in data analysis, "single-condition maps" were calculated in the "cocktail blank" mode (Bonhoeffer and Grinvald, 1993
Quantitative analysis of geometric relationships. The geometric relationships between the different columnar systems were assessed with a detailed quantitative analysis. The intersection angles of iso-orientation lines with ocular dominance borders were determined by computing, for both maps, the gradient fields. The angular difference between the two gradient fields corresponded to the intersection angles at the different locations of the map. This calculation was applied only to pixels located on borders between ocular dominance columns. In a similar way we computed the intersection angles between iso-orientation lines and borders between spatial frequency domains.
To determine the positions of the pinwheel-centers with respect to the ocular dominance and spatial frequency domains, we first had to locate the pinwheel-centers. To this end, for each point in the vectorial orientation preference map we calculated the sum of the absolute values of divergence and curl. Next we searched for local maxima in the resulting array and sorted these maxima in descending order of value. Then we applied a threshold to discard, under visual control, all maxima below a certain value that were not located on pinwheel-centers. With this standardized procedure we were able to find the exact positions of all pinwheel-centers in the orientation preference maps. The center and border regions of ocular dominance columns were defined by way of the pixel values in the differential maps. Each map was divided into 10 regions of equal area, with those parts encompassing the pixels with the lowest or highest values corresponding to the centers of the contralateral or ipsilateral eye columns. Thus, the combined center regions made up 20% of the area of an ocular dominance map. Accordingly, the border regions were defined as 20% of the area of a map with intermediate pixel values. The center and border regions of the spatial frequency domains were defined in the same manner. It should be noted that this definition of the "centers" of domains is a functional rather than a geometrical one.
To analyze the relationships between low spatial frequency domains [and thus the cytochrome oxidase blobs (Shoham et al., 1997
All statistical testing was done under the assumption of two-tailed distributions; the average values are given as mean ± SEM.
RESULTS
Ocular dominance columns
To visualize ocular dominance columns with optical imaging, we presented grating stimuli of four different orientations to each eye separately in a randomly interleaved manner. All orientations were presented at two spatial frequencies. Figure 1A-H shows the resulting eight iso-orientation maps from one such experiment. In each map the dark patches are those regions of the cortex that were activated by the respective stimulus. Iso-orientation domains obtained with monocular stimulation appear as round or elongated and sometimes irregularly shaped patches with a width of ~0.5 mm and a center-to-center spacing of ~1 mm. A comparison of the contra- and ipsilateral orientation maps at a given orientation reveals that the two corresponding maps have a different layout, reflecting the well known segregation into ocular dominance columns. A more detailed inspection of these pairs of maps reveals that most of the orientation domains in one of the maps are located in close proximity to domains in the map of the other eye. To facilitate comparison of the contra- and ipsilateral orientation maps at one orientation we have outlined the patches in the 135° map of the contralateral eye (Fig. 1D) and overlaid these outlines on the ipsilateral orientation map (Fig. 1H). As can be seen, the maps are clearly different, but in some instances patches in the contralateral orientation map are partially overlapping with patches in the ipsilateral orientation map. Such regions of overlap are thus more or less equally well activated by stimulation via the left or the right eye.
Fig. 1. Monocular stimulation of the contra- and ipsilateral eye produces different activity patterns in cat area 17. A-H, Iso-orientation maps obtained after monocular stimulation with gratings of four different orientations. The dark patches denote regions that were activated by the respective stimulus. Active regions in the contralateral 135° map shown in D were outlined and transferred to the corresponding ipsilateral map in H to facilitate comparison. Both maps are clearly different, thus suggesting also a segregation according to ocular dominance. I, Cortical blood vessel pattern of the imaged region. A, Anterior; P, posterior; M, medial; L, lateral. Scale bar, 1 mm.
[View Larger Version of this Image (105K GIF file)]
From the eight maps shown in Figure 1 we then calculated two functional maps: the orientation-preference "angle map" (Fig. 2A) and the ocular dominance map (Fig. 2B). For the orientation-preference map we first added the contra- and ipsilateral orientation maps for each of the four orientations and then used vector addition to produce the angle map in which the preferred orientation is color-coded according to the oriented bars shown in Figure 2A (right). The patchy character of the orientation columns becomes obvious again. As described previously (Bonhoeffer and Grinvald, 1991 
Fig. 2. Orientation preference "angle map" and ocular dominance map from the same patch of cortex. A, Orientation preference map calculated from the iso-orientation maps shown in Figure 1. The angle of the preferred orientation is color-coded according to the key shown on the right. As described previously, orientation domains are organized in a pinwheel-like manner. B, Ocular dominance map. Black codes for contralateral and white for ipsilateral eye preference. The layout of the ocular dominance map is clearly different from that of the iso-orientation maps shown in Figure 1. Scale bar, 1 mm.
[View Larger Version of this Image (113K GIF file)]
The ocular dominance map (Fig. 2B) was calculated by adding up all four iso-orientation maps of the contralateral eye and dividing the result by the sum of the four maps of the ipsilateral eye. Thus, in this map black codes for contralateral eye preference, and white codes for ipsilateral eye preference. One can see immediately that the layout of the ocular dominance map differs strongly from that of the iso-orientation maps shown in Figure 1. The ocular dominance columns have the shape of curved bands running across the cortex over a distance of a few millimeters. The width of individual bands in this map is fairly constant, in most instances between 0.4 and 0.5 mm. We observed, however, a considerable amount of variability between maps from different cats, as can be seen in Figure 3, which shows ocular dominance maps from two other animals. In these maps the spacing of the ocular dominance columns is wider on average; in some cases the bands have a width of up to 1 mm. Compared with the ocular dominance map presented in Figure 2 the general layout of the maps shown in Figure 3 seems to be more irregular, with strong fluctuations in the width of individual bands giving them a beaded appearance. 
Fig. 3. Variability in the width and shape of ocular dominance bands between animals. A, B, Ocular dominance maps from two additional cats. Black regions were activated stronger by the contralateral eye. Compared with the map shown in Figure 2, the spacing of the columns is wider, and the overall layout seems to be more irregular. C, D, The same maps as shown in A and B, respectively, but now with a reversed gray scale: black regions were activated stronger by the ipsilateral eye. The coding was reversed to facilitate comparison between regions activated by the contra- and ipsilateral eye. There do not seem to be strong differences between the size of the cortical representations of the two eyes. Scale bar, 1 mm.
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In previous studies that have used anterograde transport or 2-deoxyglucose mapping to visualize ocular dominance columns in cat area 17, it has been observed that the columns are often arranged in parallel and perpendicularly to the border between areas 17 and 18 (Shatz et al., 1977 Relationship between ocular dominance and orientation maps
Having obtained the orientation-preference and ocular dominance maps from the same region of cortex, it became possible to examine the question of whether there are spatial relationships between these maps. In Figure 4A both maps derived from the experiment shown in Figure 2 are superimposed. The colored lines in this illustration are iso-orientation lines that were obtained from the orientation-preference map shown in Figure 2A. All cortical points along a line of a given color respond best to the same orientation. The pinwheel-centers are clearly discernible as those points where lines of all colors converge. The thick black lines denote the borders between ocular dominance columns, with those of the contralateral eye marked with gray and those of the ipsilateral eye marked with white. Because both maps do not have a very rigid structure it is difficult to find specific geometric relationships between the two systems at first glance. However, a closer inspection reveals that relationships do exist. First, it turns out that the majority of the iso-orientation lines that connect neighboring pinwheel-centers cross the border between adjacent ocular dominance columns. This simply means that most orientation domains are split into two halves, one with contralateral and one with ipsilateral eye-preference. Second, and related to this, the iso-orientation lines have a clear tendency to intersect the borders between ocular dominance columns at right angles. This can be clearly seen in Figure 4B, which shows an enlarged detail from the map in Figure 4A. Although the portions of the ocular dominance columns visible here make rather sharp turns, the nearly orthogonal relationship between iso-orientation lines and ocular dominance borders is maintained. Thus, when moving along an ocular dominance column border the preferred orientation changes rapidly, while it stays relatively constant when moving perpendicular to it. Because the pinwheel-centers are such a prominent feature of the orientation preference maps, it seems natural to ask where they are located with respect to the ocular dominance columns. As can be seen in Figure 4A, in many cases the pinwheel-centers lie in the middle of ocular dominance columns.
Fig. 4. Relationship between ocular dominance and orientation maps. A, The colored iso-orientation lines were derived from the orientation preference map shown in Figure 2. All points on lines with a given color prefer the same orientation. The contours of the ocular dominance columns were obtained from the ocular dominance map of the same cortical region, using an objective automated procedure; gray denotes contralateral eye dominance. On closer inspection it becomes clear that both systems are spatially related: many iso-orientation lines cross the borders between ocular dominance columns close to right angles, and the pinwheel-centers are preferentially located in the middle of the ocular dominance columns. B, Enlarged detail from A (see small rectangle on the left side of the map), showing that the tendency for perpendicular intersections is maintained even in regions where the ocular dominance bands make sharp turns.
[View Larger Version of this Image (86K GIF file)]
Ocular dominance and spatial frequency domains In cat visual cortex the low spatial frequency domains coincide with the cytochrome oxidase blobs (Shoham et al., 1997
To quantify the geometric relationships between the orientation and ocular dominance maps we measured the angles between iso-orientation lines and ocular dominance column borders as described in Materials and Methods. It should be noted that the algorithm we used does not determine these angles only for the iso-orientation lines shown in Figure 4. To avoid a sampling bias attributable to the fact that only discrete iso-orientation lines are shown in this figure, we calculated the intersection angle for every point on the borders between ocular dominance columns. The distributions of these angles for maps imaged in three cats are shown in Figure 5. In all cases there is a clear shift toward right angles. One might argue that because of simple geometric reasons a higher proportion of right angles is always to be expected when the relationship between a circular pattern (the radially arranged orientation domains) and a linear pattern (the ocular dominance columns) is analyzed. One straightforward way to test this is to analyze the relationship between maps originating from different animals, that is, to overlay an orientation map from one cat with an ocular dominance map from another cat (Fig. 5, gray histograms). As can be seen, in these control cases the distribution of the intersection angles is essentially flat. The mean of the average angle for all cats from which we obtained ocular dominance columns was 51.7 ± 0.8° (n = 6), whereas in the control cases it was 45.8 ± 1.2° (n = 6) (p < 0.05; Wilcoxon signed-rank test), a value that comes very close to the expected average angle of 45°. 
Fig. 5. Quantitative analysis of intersection angles between iso-orientation lines and ocular dominance borders. Nine histograms are shown in the form of a 3 × 3 matrix. The black histograms along the diagonal show the distribution of intersection angles from three cats. In all cases there is a clear predominance of large intersection angles. Each of the gray histograms off the diagonal was computed by overlaying an orientation map from one cat with an ocular dominance map from a different cat. In these control cases the distributions are nearly flat.
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To verify our observation that the pinwheel-centers are preferentially located in the middle of ocular dominance columns we first applied a search algorithm to find the pinwheel-centers. Next we determined the center regions of the ocular dominance columns: those 10% of the pixels in an ocular dominance map with the highest values were defined as corresponding to the centers of the columns of one eye, whereas the 10% with the lowest pixel values defined the centers of the columns of the other eye. Thus, the combined center regions made up 20% of the area of an ocular dominance map. Accordingly, the border regions were defined as 20% of the area of a map with intermediate pixel values. Analysis of our maps (n = 6) in this way revealed a steady decline in pinwheel-center density when moving from the central regions of the ocular dominance columns toward their borders (Fig. 6). The total number of pinwheel-centers found in the central 20% of the ocular dominance maps is significantly higher than the value one would expect if the pinwheel-centers were distributed randomly (p < 0.01; 2 test).
Fig. 6. Relative frequency of pinwheel-centers in different subregions of ocular dominance maps. The maps (n = 6) were divided into five regions of equal area, with the 0-20 percentile denoting the center and the 80-100 percentile denoting the border regions of the ocular dominance columns (error bars are SEM). The dotted line indicates the expected value (20%) if the pinwheel-centers were distributed randomly. There is a high incidence of pinwheel-centers in the center regions of the ocular dominance columns.
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In summary, we find that specific spatial relationships are present between the orientation and ocular dominance maps in cat area 17. The pinwheel-centers tend to lie in the middle of ocular dominance columns, and the iso-orientation lines that connect neighboring pinwheel-centers in adjacent ocular dominance columns often cross the borders between these columns at right angles. Relationship between spatial frequency and orientation maps
Figure 7 shows two sets of iso-orientation maps obtained after binocular stimulation with different spatial frequencies. At each orientation the two maps of a pair have a rather similar layout overall, but they clearly differ in the exact size, shape, and position of the patches. This becomes evident if one compares, for instance, the outlines of the patches from the 90° low spatial frequency map (Fig. 7C) with the activated regions in the 90° high spatial frequency map (Fig. 7G). The orientation preference and the spatial frequency map calculated from these iso-orientation maps are depicted in Figure 8. As can be seen in the spatial frequency map in Figure 8B, there is an imbalance between the cortical regions preferring stimuli of low and high spatial frequencies that we noted in many experiments: the low spatial frequency domains (dark patches) seem to be embedded in a matrix of high spatial frequency preference. Figure 9 shows the combined orientation and spatial frequency maps. Again, at first sight it seems rather difficult to find any obvious relationships between both maps. Although in many instances individual orientation columns consist of two regions, one preferring high and the other low spatial frequencies, there are also orientation columns that clearly stay confined to either a low or a high spatial frequency domain. To test whether both maps are spatially related, we therefore used the same quantitative analysis that was used for the ocular dominance and orientation maps. The distribution of the crossing angles between iso-orientation lines and the borders of spatial frequency domains are illustrated in Figure 10. A predominance of right angles becomes evident again, although the shift toward right angles is not as strong as for the ocular dominance columns. The average crossing angle was 49.7 ± 0.8° (n = 13) for orientation and spatial frequency maps from the same cat and 46.1 ± 0.8° (n = 13) in the control cases (p < 0.05; Wilcoxon signed-rank test).
Fig. 7. Stimulation with different spatial frequencies causes different activity patterns. A-H, Iso-orientation maps obtained after stimulation with oriented gratings at a low (0.2 cycles/degree) and a high (0.6 cycles/degree) spatial frequency. At a given orientation the low and high spatial frequency maps are similar, but not identical (see outlines from the map in C, copied to the map in G). I, Cortical blood vessel pattern. Scale bar, 1 mm.
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Fig. 8. Stimulus preference maps derived from the iso-orientation maps shown in Figure 7. A, Orientation preference map. B, Spatial frequency map. Dark patches were activated by low spatial frequencies, and lighter regions preferred high spatial frequencies. Note that the low spatial frequency patches tend to form islands in a matrix of high spatial frequency preference. Scale bar, 1 mm.
[View Larger Version of this Image (121K GIF file)]
Fig. 9. Relationship between spatial frequency and orientation maps. The iso-orientation lines and contours of the spatial frequency domains were obtained from the maps shown in Figure 8; gray regions preferred low spatial frequencies. Scrutiny of this image reveals that the iso-orientation lines tend to cross the borders between spatial frequency domains at right angles, and that the pinwheel-centers are often located in the centers of either low or high spatial frequency domains.
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Fig. 10. Intersection angles of iso-orientation lines with borders between spatial frequency domains. Nine histograms are shown in the form of a 3 × 3 matrix. The black histograms along the diagonal show the distribution of intersection angles from three kittens. Large angles (black histograms) are clearly over-represented, whereas this is not the case in the controls (gray histograms).
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We also analyzed whether the locations of the pinwheel-centers are in any way correlated with the spatial frequency domains. Here too it turned out that the density of pinwheel-centers in the central regions of the spatial frequency domains is slightly but significantly higher than expected according to chance (Fig. 11) (p < 0.05; 
Fig. 11. Relative frequency of pinwheel-centers in different regions of spatial frequency maps (n = 13). Same conventions as in Figure 6. Pinwheel-centers are found more often in the center regions than near the borders of spatial frequency domains.
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Relationship between ocular dominance and spatial frequency maps
Finally, we also analyzed whether a geometric relationship exists between the ocular dominance and the spatial frequency domains. This issue is of particular interest because we have found recently that the low spatial frequency domains in cat visual cortex correspond to the cytochrome oxidase blobs (Shoham et al., 1997
Fig. 12. Relationship between ocular dominance and spatial frequency domains. In this overlay contralateral eye dominance is coded by light gray with red outlines, and low spatial frequency is coded by dark gray with black outlines. No obvious spatial relationships are discernible at a first glance. Quantitative analysis, however, reveals that the centers of low spatial frequency domains tend to avoid the borders of the ocular dominance columns (see Fig. 13).
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Fig. 13. Frequency of centers of low spatial frequency domains in different regions of ocular dominance maps (n = 6). Same conventions as in Figure 6. Only very few low spatial frequency domains (and thus blobs) are centered on the border regions of ocular dominance columns.
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DISCUSSION
We performed most of our experiments on 8- to 12-week-old cats. Although cats of this age are still within the critical period (Hubel and Wiesel, 1970Spatial relationships between columnar systems in the visual cortex
Orientation and ocular dominance Hubel and Wiesel (1972Orientation and spatial frequency Only a few studies have examined the geometric relationship between orientation and spatial frequency maps. This is most likely caused by the fact that the concept of a columnar organization for spatial frequency, although demonstrated by Tootell and colleagues (1981), has never gained strong influence on ideas about the functional architecture of cat visual cortex. Maffei and co-workers (Maffei and Fiorentini, 1977
With the development of the optical imaging technique it became possible to visualize the complete orientation preference map (Blasdel and Salama, 1986
Interestingly, a recent study on squirrel monkey visual cortex reported that the blobs in this species are not aligned with ocular dominance columns (Horton and Hocking, 1996a Functional significance of geometric relationships between columnar systems
A number of studies that examined relationships between columnar systems in other systems basically came to conclusions similar to ours (Bartfeld and Grinvald, 1992
The presence of columns in the visual cortex creates a sampling problem: each point in the visual world has to be analyzed with respect to all possible stimulus features. For the cortex to achieve a complete "coverage" (a term originally coined for the retina) (e.g., Wässle and Boycott, 1991
One problem concerning the demand for complete coverage arises from the fact that the cat's visual cortex contains more than just the three columnar systems analyzed here. Among others, direction maps (Swindale et al., 1987
It is important to note, however, that although a complete coverage is accomplished in the retina, the situation in the cortex is likely to be different: visual information is processed in parallel channels, which are at least partially segregated. This principle has been clearly demonstrated in primates (Livingstone and Hubel, 1988
In summary then, we find that specific rules govern the geometric relationships between orientation, ocular dominance, and spatial frequency domains in cat primary visual cortex. These rules most likely ensure optimal coverage. However, they are not rigidly followed, and therefore the visual cortex cannot be considered a "crystalline" structure built from identical modules, but rather it is composed of "mosaics" of functional domains for the different properties that are arranged in a nonrandom manner.
FOOTNOTES
Received Aug. 14, 1997; revised Sept. 22, 1997; accepted Sept. 23, 1997.
This work was supported by the Max-Planck Gesellschaft (T.B.) and by grants from the Minerva Foundation, the Mijan Foundation (A.G.), the Human Frontier Science Program (T.B.), the European Commission Biotech Program (M.H., T.B.), and Ms. Enoch (A.G.). We thank Gerhard Brändle for the development of the programs for the geometric analysis of cortical maps and Frank Brinkmann for technical assistance and help with the preparation of the figures. We also thank Frank Sengpiel for comments on this manuscript. We are indebted to Silke Schulze for allowing us to use some of her experimental data in this study.
Correspondence should be addressed to Dr. Mark Hübener, Max-Planck-Institut für Psychiatrie, Am Klopferspitz 18A, D-82152 Martinsried, Germany.
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