Animals
Mice were purchased from Jackson Laboratories at 4–6 weeks of age, housed on a 12:12 light:dark cycle in same sex groups in standard laboratory animal cages (5 animals per cage). All experimental procedures were performed in accordance with the Guidelines for the Care and Use of Laboratory Animals published by the National Institutes of Health (publication 86–23) and the Vanderbilt University Animal Care and Use Committee. Mice were provided a standardized diet and clean water ad libitum. Mice at this age are not compromised by known visual and or auditory sensorineural deficits common to older animals of these strains. None of the mice used had visible body or facial wounds.
Tissue
At 6–8 weeks of age (14 day age span), young adult mice were brought to complete anesthesia with a sodium pentobarbital overdose (100 mg/kg) injected intraperitoneally (IP), and then transcardially perfused with 0.1 M phosphate buffered 0.9% saline wash followed by 3% buffered paraformaldehyde fixative. Intact brains were removed from the skull, and the cortex was dissected free of the underlying white matter. Dissected cortices were flattened between glass slides and transferred to 30% sucrose for 12–18 hours. Cortices were sectioned parallel to the cortical surface at a thickness of 70–80 μm on a freezing, sliding microtome, stained for cytochrome oxidase according to the method of Wong-Riley [30], mounted on glass slides, air dried, and coverslipped. Thicker sections encourage all cortical areas to be within a single section, and are less prone to deformation or tearing.
Landmarks
A scale bar and the outlines of cortical regions of interest (ROIs) were drawn under a light microscope with a camera lucida attachment. Regions of interest included neocortex (C), visual cortex (V1), auditory cortex (A1), somatosensory cortex (S1), and select barrels of the posterior medial barrel subfield (PMBSF). Barrels drawn in rows A, B, C, D, and E were standardized to 5, 4, 6, 7, and 8 barrels, respectively (alpha, beta, gamma, and delta barrels were also included). Digital scans of the drawings were imported into a computer and landmark coordinates acquired with NIH ImageJ software after scale bar calibration [31]. All data were acquired blind to animal and strain identity, and the order of acquisition was independent of animal or strain.
Two landmark configurations were generated for this study, the first to assess local shape differences in the PMBSF, the second to assess global shape differences across the cortical sheet (see Figure 2). Landmarks are points that can be located precisely (repeatedly) on the anatomical structure under study and display a one-to-one correspondence among the specimens included in the study. The first landmark configuration consisted of 34 barrel centroids. Centroids are the average coordinates of a set of coordinates. In ImageJ a centroid is the average X and Y from all pixel coordinates within a region of interest. Due to missing data in some animals for barrels alpha, beta, gamma, delta, A4–A5, B4, and D7, the final data set consisted of 26 landmarks for barrels A1–A3, B1–B3, C1–C6, D1–D6, and E1–E8, in 13 C57BL/6J mice (4 males, 9 females) and 12 DBA/2J mice (8 males, 4 females). The methods of shape analysis used in this paper required that all landmarks be present in all cortices measured. The second landmark configuration consisted of 7 landmarks, 3 that reduced V1 to a triangle, 3 that reduced S1 to a triangle, and 1 that was the centroid of A1. For this configuration, 16 C57BL/6J mice (6 males, 10 females) were compare to 15 DBA/2J mice (9 males, 6 females). In this paper sex effects in the cortical area maps were not a focus, and sex was determined not to be a significant factor by Goodall's F tests performed separately on each strain for each landmark configuration (each P > 0.05). Li et al., [14], also recently looked at the barrels of C57BL/6J, DBA/2J, and a small sample of derivative BXD lines, and found no sex differences in PMBSF area, although shape was not examined. Li et al., also found no differences in PMBSF area over a 21 day age spanning the same ages sampled in this study. In our data, over a 14 day age span, we found no significant difference that we could attribute to age, in either strain for either landmark configuration (Goodall's F tests, each P > 0.05). No substantive differences in equipment or procedures confounded the significant strain differences we report in this paper.
Reliability of landmark configurations was assessed by acquiring (drawing) each landmark configuration in triplicate for each animal. The first set of drawings was discarded to avoid training effects. The second and third sets were tested for between set differences, using shape analysis. None were found for either landmark configuration (Goodall's F tests, P > 0.05). The final data set used for shape analysis was formed by averaging over the second and third drawing sets, as well as hemisphere within animal, if two hemispheres were drawn. If two hemispheres were drawn, they were appropriately flipped to the same orientation. In this paper we do not consider average differences in left and right hemispheric cortical maps. Studies in rats [15] and mice [14] found no left and right hemispheric differences in PMBSF area, although shape was not examined. Before shape analysis, final data sets were preanalyzed by the program tpsSmall [32] to confirm variation was appropriate (small enough) for shape analysis.
Shape
The collection of complex multivariate statistical methods used to analyze shape are organized around Kendall's definition of shape [33]. Shape is defined as all the geometric information that remains when location, scale and rotational effects are filtered out from an object or landmark configuration. Shape analysis in this study made use of generalized Procrustes analysis (GPA) to superimpose landmark configurations and remove nonshape variation in the landmark coordinates [34, 20, 35]. The algorithm of this method involves three transformations [7, 9]. First, the centroid of each configuration is translated to the origin by subtracting centroid coordinates from each landmark. Second, the configuration is then scaled by dividing each landmark coordinate by the centroid size of that configuration. The centroid size is the square root of the summed squared distances of each landmark from the centroid of the landmark configuration. Third, with respect to a given configuration, another configuration is rotated to minimize the summed squared distances between labeled landmarks. In tpsRegr, this is done iteratively: one reference configuration is chosen and every other configuration is fitted to it, but from the second round on, the average of the coordinates in the previous fit is used as a reference. Final superimposition is not influenced by which landmark configuration is chosen to begin the procedure.
In the analysis of shape, there are both uniform and non-uniform components to shape variance. When considering an elastic sheet of graph paper, uniform changes are those that leave parallel lines parallel. Non-uniform changes bend lines. Figure 8 shows two kinds of uniform changes, compression and shearing (E-F), that alter shape. Translation, scaling, and rotation (A-D) are not components of shape change, because shape is by definition invariant to these transformations. Uniform components of shape variation can be computed separately [20] and represented separately. It is not clear if separating the uniform shape component is helpful or more interpretable for a given biological question. Considering that the cortical area map is thought to be specified by overlapping early gradients or local enrichment of secreted ligands or gradually expressed transcription factors [3], a combination of uniform and non-uniform shape changes might be predicted. Hamasaki et al., [5] increased the slope of a rostrocaudal gradient of the transcription factor Emx2 in the cortex of transgenic mice relative to wild-type mice. Phenotypically, transgenic caudal cortical areas were increased in size and shifted anteriorly, at the expense of rostral cortical areas, but the total cortical sheet was unchanged in size. An over-simplified analogy might be a ladder of fixed length, where the rung distance decreases from the bottom of the ladder to the top, and landmarks are where the rungs are bolted to the rails. Although geometric morphometrics provides methods to describe and disentangle both uniform and non-uniform components of cortical area map shape, in both ne-Emx2 mice and the C57BL/6J and DBA/2J inbred strains, shape seems best characterized by the total shape variation.
A statistical test adapted to the coordinates produced by Procrustes fit is Goodall's F test [36], which compares the difference in mean shape between two samples relative to the shape variation found within the samples. To determine statistical significance we employed a permutation test based on Goodall's F statistic. In this test, the data are permuted (randomized) and Goodall's F statistic is calculated. This is done 10,000 times. The proportion of Goodall's F statistics from permuted data sets as great or greater than the Goodall's statistic on the original data set is given as the significance probability. Use of permutation relaxes some of the restrictive assumptions of Goodall's F test. Goodall's F test only considers the total amount of shape variation, and does not consider the directionality of the variation. With small samples (relative to the number of landmark coordinates), as in this study, this is a useful property. Indeed, the sample size in this study is too small to use alternative MANOVA multivariate statistics to test for shape differences in the PMBSF, given the number of barrel landmarks and the number of mice measured.
In addition to scatter plots of Procrustes transformed landmark data, broken down by symbol to represent strain (e.g., Figure 3 above), thin-plate spline deformation grid plots are used (e.g., Figure 4 above). A thin-plate spline deformation grid represents a smooth interpolation, mapping the coordinates of one landmark configuration into another. These plots are analogous to an elastic sheet of graph paper that is stretched to map one morph to another, and are in the spirit of the historically famous efforts of D'Arcy W. Thompson [37]. Deformation grids are useful for visualizing changes between landmarks over an entire configuration. Aside from deformation grids, vector plots are also provided. These represent the change in landmark positions by a vector with size proportional to the observed differences.
Although the statistical methods used in this paper are complex, reliable software for geometric morphometrics is readily and freely available and makes these methods accessible to neuroscientists. The primary software used in this study was tpsRegr by statistician F. James Rohlf [32]. The strain differences reported above were confirmed using two additional software titles that implement Procrustes fit and Goodall's F test: TwoGroup by H. D. Sheets [9], and shapes, an R package by Ian Dryden [7].