Genetic influence on quantitative features of neocortical architecture

Abstract

The layout of functional cortical maps exhibits a high degree of interindividual variability that may account for individual differences in sensory and cognitive abilities. By quantitatively assessing the interindividual variability of orientation preference columns in the primary visual cortex, we demonstrate that column sizes and shapes as well as a measure of the homogeneity of column sizes across the visual cortex are significantly clustered in genetically related animals and in the two hemispheres of individual brains. Taking the developmental timetable of column formation into account, our data indicate a substantial genetic influence on the developmental specification of visual cortical architecture and suggest ways in which genetic information may influence an individual's visual abilities.

Fig. 1.

Preprocessing leaves the essential spatial properties of the 2-DG patterns unaffected. a, Typical 2-DG pattern. b, Preprocessed 2-DG pattern. c, The zero contours of the preprocessed 2-DG pattern (yellow lines) are superimposed on the original autoradiograph ina. Note that the zero contours closely follow theoutlines of the labeled domains.

Fig. 2.

Analyzing the shape of orientation columns.a, Examples of wavelets ψ_θ,x with different orientation θ superimposed on a stripe-like region of 2-DG-labeled orientation columns. The real parts of the complex-valued wavelets are shown. Positive regions are delineated by white lines; negative regions are delineated by dark lines. The wavelet of optimal orientation (solid lines) and one example of nonoptimal orientation (dotted lines) are shown.b, The normalized squared modulus of the wavelet coefficients: $\Vert {\tilde{I}}^{\prime }(\theta ,\mathbf{x}){\Vert }^2=\Vert \widehat{I}(\theta ,\mathbf{x}){\Vert }^2/\underset{0}{\overset{180}{\int }}\Vert \widehat{I}(\theta ,\mathbf{x}){\Vert }^2\frac{d\theta }{180},$as a function of orientation θ. For a vertically oriented wavelet, θ = 0°, 180°. c, Wavelets ψ_θ,x superimposed on a patchy region of 2-DG-labeled orientation columns and the respective coefficients (d) (description as in a and b). Note that for the stripe-like region, ‖Ĩ‖²is strongly modulated and exhibits a pronounced peak at the wavelet orientation θ matching the stripe orientation. This is not the case for the patchy region.

Fig. 3.

Layout properties of 2-DG-labeled OR domains in the primary visual cortex (area 17) of cats and their quantification.a, Representative examples from the analyzed data pool: 2-DG-labeled OR domains appear as dark gray to black patches or stripes on a lighter gray background. The 2-DG patterns were visualized on cortical flatmount sections and thus contain OR domains within the entire area 17. Anterior is at the top of each figure, and posterior is at the bottom. lat, Lateral; med, medial. b, Variability of pattern properties. OR domains vary in both the spacing of adjacent domains (left column, small; right column, large) and in the degree of anisotropy of domain shape (top row, band-like;bottom row, patchy). c, d, Quantitative analysis of the spacing (c) and shape (d) of OR columns.c, 2D map of local column spacing Λ(x) (left) of a representative 2-DG pattern (left pattern ina) obtained by wavelet analysis, coded ingrayscale: light gray regions exhibit larger-than-average spacing; dark gray regions exhibit smaller-than-average spacing. In the histogram of local column spacings (right), the mean column spacing Λ and the SD ς_Λ of local column spacings (spacing inhomogeneity) are marked by red and blue arrows, respectively.d, Local anisotropy parameter s(x) (yellow bars) superimposed on the analyzed 2-DG pattern (left): The lengths of the yellow bars are proportional to the measure of local bandedness ‖s(x)‖, withlong bars indicating bandlike regions and short bars indicating patchy regions of the pattern. The barsare oriented perpendicular to the calculated local band orientation. The histogram of ‖s(x)‖ (right) exhibits a broad peak with low and high values of ‖s‖ corresponding to patchy and bandlike regions in the 2-DG pattern. The mean bandedness α and the SD ς_α of local bandedness (shape inhomogeneity) are marked by red and blue arrows, respectively. Scale bars: a, c, d, 10 mm;b, 5 mm.

Fig. 4.

Interindividual variability (a, b, d, e) and relative independence (c, f) of the spacing and shape parameters mean spacing (Λ; a), spacing inhomogeneity (ς_Λ; b), bandedness (α;d), and shape inhomogeneity (ς_α;e) in 48 hemispheres from 31 animals. Values from individual hemispheres are indicated by ×s arranged along the x-axis in a, b, d, and e. Error bars show the SEM of the estimated parameter values. Scatter plots of the spacing and shape parameters are displayed in c and f. Note that the values of all four parameters display significant interindividual variability: Mean column spacings vary between 1.0 and 1.4 mm (a) and spacing inhomogeneities (ς_Λ) vary between 0.1 and 0.27 mm (b) in different animals. The shape parameters α and ς_α exhibit an even larger interindividual variability: Mean bandedness α varies by more than a factor of two between 0.14 for very patchy patterns and 0.3 for patterns largely composed of bands (d). Shape inhomogeneity varies between 0.06 and 0.14 (e). Thedashed–dotted lines in a, b,d, and e mark the total range of interindividual variability.

Fig. 5.

Examples of the similarity of patterns of 2-DG-labeled orientation columns in the two hemispheres of individual animals. The patterns of both the left (a, c) and right (b, d) hemispheres of cats C16 (a, b) and C1 (c, d) are displayed in a way so that the 17/18 border appears left in all panels (to this end, the right hemisphere patterns were mirror-inversed) to aid comparison. Note that the general appearance of the orientation column patterns (patchiness or bandedness of the pattern, spacing of adjacent domains, etc.) looks rather similar in the left and right hemispheres of both animals. Note furthermore that the quantified parameters (column spacing Λ and bandedness α) quantitatively reflect this similarity: Column spacing in the left and right area 17 of cat C16 was 1.05 and 1.09 mm, bandedness was 0.30 and 0.28, respectively. In cat C1, column spacings in the left and right area 17 were 1.10 and 1.06 mm; bandedness was 0.23 in both hemispheres. In the illustrated cases, column spacing Λ differed by only 40 μm in the left and right hemisphere of individual brains, whereas column spacing may differ by up to 400 μm among hemispheres from unrelated animals. Similarly, bandedness α differed by 0.02 at most in the illustrated hemisphere pairs, whereas this parameter may differ by up to 0.15 among hemispheres from unrelated animals.

Fig. 6.

2D maps of local column spacing (a, b, e, f) and local bandedness (c, d, g, h) for the patterns obtained from left–right pairs of hemispheres displayed in Figure 5. The maps are arranged as in Figure 5: the maps ina and c were derived from the pattern in Figure5a, the maps in b and d were derived from the pattern in Figure 5b, the maps in e andg were derived from the pattern in Figure 5c, and the maps in f and h were derived from the pattern in Figure 5d.

Fig. 7.

Examples of the similarity of patterns of 2-DG-labeled orientation columns in littermates. The orientation column patterns of the related cats C4 and C5 (a, b) and C6 and C7 (c, d) are displayed such that the 17/18 border appearsleft in all panels. Note that the general appearance of the orientation column patterns (patchiness or bandedness of the pattern, spacing of adjacent domains, etc.) is rather similar in the littermates. Note furthermore that the quantified parameters (column spacing Λ and bandedness α) quantitatively reflect this similarity: Column spacing in the right area 17 of cats C4 and C5 was 1.10 and 1.12 mm, and bandedness was 0.26 and 0.24, respectively. In the littermate cats C6 and C7, column spacings in the right area 17 were 1.23 mm for both animals, and bandedness was 0.24 and 0.23, respectively. As for pairs of left and right hemispheres from individual animals (Fig. 5), the differences in parameter values in littermates are very small compared with the overall interindividual variability (compare Fig. 4).

Fig. 8.

2D maps of local column spacing (a, b, e, f) and local bandedness (e, d, g, h) for the patterns in littermates displayed in Figure 7. The maps are arranged as in Figure 7: the maps in a and c were derived from the pattern in figure 7a, the maps in b andd were derived from the pattern in Figure 7b, the maps in e and g were derived from the pattern in Figure 7c, and the maps in f and hwere derived from the pattern in Figure 7d.

Fig. 9.

Examples of the dissimilarity of orientation column patterns in unrelated cats (cats C24 and C7). Arrangement of the patterns is as in Figures 5 and 7. Column spacing in the two cats was 1.09 and 1.23 mm, respectively; anisotropy was 0.30 and 0.23, respectively, indicating very dissimilar patterns (compare with Figs. 5and 7).

Fig. 10.

Clustering of parameter values in left and right hemispheres and among littermates. a, e, i, Mean column spacing Λ. b, f, j, Spacing inhomogeneity ς_Λ. c, g, k, Bandedness α. d, h, l, Shape inhomogeneity ς_α. a–d, Comparison of the parameter values in the left and right visual cortices of 17 animals. Left and right hemisphere values are marked by ×s and ⋄s, respectively. For comparison, the distributions of parameter values from all hemispheres are plotted on the right side of the figures (horizontal lines). Note that values in the left and right hemispheres are often rather similar and that significant correlations were found for mean column spacing, spacing inhomogeneity, and bandedness, but not for shape inhomogeneity (r = 0.17; p = 0.26). In addition, there were no systematic differences in the architecture of left and right area 17 (i.e., no signs of lateralization for the measured parameter set) (p > 0.15; permutation test for the average sign of left–right differences).e–h, Littermate clustering: Comparison of the parameter values in six litters. Data points from littermates are marked by identical symbols (∗, ⋄, ▵, ■, ×, and + fromleft to right). For comparison, the distributions of parameter values from all hemispheres of animals raised in the same environment are plotted on the right side of the figures (horizontal lines). Note that values from littermates cluster, whereby the degree of clustering varies between litters and for different parameters. i–l, Permutation tests for genetic influences on quantified parameters of visual cortical OR maps. Analysis of 6 × 10⁶ randomly generated pseudolitters demonstrates statistically significant littermate clustering for mean column spacing (i), spacing inhomogeneity (j), and bandedness (k): It is highly unlikely to observe the ADLMs ΔΛ (i), Δς_Λ (j) and Δα (k) of real litters (arrows) by chance if no genetic component is present. Littermate clustering observed for shape inhomogeneity ς_α (l) is, however, not statistically significant in our data set (l:P_I = 0.092; P_II= 0.083). The ADLM values calculated for the real litters are compared with two distributions obtained by either (I) assigning animals raised in the same environment to random pseudolitters (left histograms; see i or (II) first forming pseudobrains of randomly chosen hemispheres, which were then assigned to pseudolitters (right histograms; see i). If correlations of left and right hemisphere parameter values are of entirely epigenetic origin, randomization scheme I applies and extinguishes all genetic influences. However, if these correlations are of genetic origin, randomization scheme II extinguishes all genetic influences by generating pseudobrains with uncorrelated parameter values in the left and right hemispheres. For all four parameters, the real ADLMs are smaller than the large majority of ADLMs calculated from randomized data.

Fig. 11.

The total number of orientation hypercolumns (HCs) in cat area 17 is determined by the column spacing Λ and the area size A. a, Scatter plot of HC size Λ² versus area size A. Note that there is only a weak correlation of HC size and area size (r = 0.34; p = 0.035), indicating that larger areas 17 do not necessarily contain larger HCs. b, c, Scatter plots of the total number of HCs in area 17 (A/Λ²) versus HC size (b) (r = −0.51; p = 0.001) and versus area size (c) (r = 0.63; p = 0.0001). Dash-dotted lines are regression lines. Note that both HC size and area size explain substantial fractions of the interindividual variability in HC number (Λ², 26%;A, 39%), indicating that, on average, large areas 17 and areas 17 with small HCs contain more modules.