Steerable-filter based quantification of axonal populations at the developing optic chiasm reveal significant defects in Slit2 ^−/− as well as Slit1 ^−/− Slit2 ^−/− embryos

Quantitative analysis of labelled axons at the wild-type chiasm

We first examined DiI-labelled axons at the optic chiasm of wild-type mice (Figure 1). Figure 1A shows an example of the optic chiasm in a horizontal section at embryonic day 13.5 (E13.5). E13.5 was selected because retinal axons have recently crossed the midline at this age, having first penetrated the diencephalon at E12.5 Erskine et al., [8]. It is, therefore, the earliest age offering the opportunity to observe potential defects of guidance at the chiasm in mutants.

Figure 1B is a high magnification view of the same chiasm as in Figure 1A, showing detail of the DiI labelled axons. Axons such as these were analyzed using Gaussian steerable filters, examples of which are illustrated as oriented spatial functions in Figure 1C. The filters were convolved with the images of DiI-labelled chiasms. Only data derived from points along axons were retained; points that were not on axons were excluded using non- maximum suppression, which removed data from areas that did not lie on ridges of high intensity with respect to the surrounding landscape of the image. Figure 1D illustrates the outcome: the orientations of filter that gave the best response at each position along the axon are shown as arrows pointing away from the DiI-injected eye (referred to as directions). An example of applying the algorithm to all the axons at the chiasm is illustrated in Figure 1E, which shows only a small subset of directions (or oriented vectors) for purposes of clarity. The subset is <0.01 of the size of the full set, allowing the arrows to be shown enlarged compared to those in Figure 1D. The algorithm provides a method to quantify automatically a vector field representing the orientations of axons in a given image and also the curls of the vector fields, which measure the degree of curvature of axons at each point. Notice that the arrows representing direction (red arrows in Figure 1D,E) have a constant magnitude whereas those representing curvature (green arrows in Figure 1E,F) have both direction and length, with the length proportional to the amount of turning.

Axon locations in Slit1^−/−, Slit2^−/− and Slit1^−/−; Slit2^−/−embryos

Figure 2 illustrates the results of applying the steerable filter algorithm to sets of E13.5 embryos that were wild-type (Figure 2A,E,I; n = 9 embryos), Slit1^−/− (Figure 2B,F,J; n = 11 embryos), Slit2^−/− (Figure 2C,G,K; n = 5 embryos) or Slit1^−/−Slit2^−/− (Figure 2D,H,L; n = 4 embryos). Figure 2A-D shows individual examples of chiasms analyzed as outlined in Figure 1. As can be seen, there is considerable variation in the appearance of these examples, particularly between those that are Slit2^−/− or Slit1^−/−Slit2^−/− and those that are wild-type or Slit1 ^−/− . To assess whether this variation can be accounted for by differences in genotype, we combined results from applying the algorithm to all embryos of each genotype. Figure 2E-H shows examples of vectors (i.e. subsets, as described above) representing axonal directions from all embryos of each genotype. Data from different embryos are shown in different colours, providing a sample of the routes taken by axons in all embryos of each genotype. Data from embryos within each genotype group were aligned using the grid system shown in Figure 1A. The mean distance between the centre of the two eyes did not vary significantly with genotype, varying by < 8% between groups. The plots in Figure 2E-H suggest an anterior shift in the position of the optic chiasm in Slit2^−/− and Slit1^−/−Slit2^−/− embryos compared to wild-type and Slit1 ^−/− embryos.

To test this statistically, the area of each chiasm was split into a 32 × 32 grid. Figure 2I-L shows the spatial distributions of the mean numbers of oriented vector fields (i.e. the total numbers of arrows, as exemplified in red in Figure 1D) across the chiasms of all embryos of each genotypes (higher numbers are towards the red end of the spectrum). All vectors were included (i.e. not the samples explained above and used for illustrative purposes in Figures 1 and 2). These values were proportional to the mean densities of axon within each square for each genotype, since in all cases analysis with steerable filters was done at constant intervals and filtering using non-maximum suppression prevented the inclusion of data from areas that contained no axons. Note that while these values are proportional to the densities of axon within each square, and can therefore be used to examine distributions of axon, they can not be used to derive values for the absolute numbers of individual axons across the chiasm. Our approach does not attempt to trace individual axons and can not, therefore, give their absolute numbers.

The graphs in Figure 2I-L suggest an anteriorization of the population of chiasmatic axons in Slit2^−/− and Slit1^−/−Slit2^−/− embryos. For each area of the chiasm we tested for significant differences (taking account of multiple testing, see Methods) between the values from wild-type and Slit1^−/−, Slit2^−/− or Slit1^−/−Slit2^−/− embryos: results are plotted in Figure 3A,E, I. There were no significant differences between wild-type and Slit1^−/− embryos (Figure 3A), but significantly larger densities of axon were located in abnormally anterior positions in both Slit2^−/− and Slit1^−/−Slit2^−/− embryos (Figure 3E,I). There were no significant differences between Slit2^−/− and Slit1^−/−Slit2^−/− embryos (not shown).

Axon orientations and curvatures in Slit1^−/−, Slit2^−/− and Slit1^−/−; Slit2^−/−embryos

The same procedure was then applied to values of orientation, curvature angle and curvature magnitude from each area across the chiasm. These values were the averages of the vectors within each square of the 32 × 32 grid and, therefore, took no account of the trajectories of individual axons, e.g. whether they crossed each other or not. Comparison of wild-type and Slit1^−/− embryos showed only a few areas returning statistically significant differences in either axon orientation or angle of curvature (Figure 3B,C). Comparison of wild-type and either Slit2^−/− or Slit1^−/−Slit2^−/− embryos showed many more areas returning statistically significant differences in axon orientation, many of which were located lateral to the midline (Figure 3F,J; the midline runs vertically through the centre of each panel). In Slit1^−/−Slit2^−/− double-mutant embryos there were also significant abnormalities of axonal orientations in a posterior area contralateral to the injected eye (areas in the bottom right of Figure 3J) that were not present in Slit2^−/− mutants. Regarding the angle of axon curvature, most differences between genotypes were found around the midline (Figure 3G,K). No comparison returned any significant differences in magnitudes of curvature (Figure 3D,H,L). Overall, these data indicate that, in Slit2^−/− and Slit1^−/−Slit2^−/− embryos, many axons are oriented abnormally in their route across the chiasm, an observation that agrees with our finding described above that many axons are mislocated. In Slit1^−/− embryos there were few axon orientation defects, in line with there being no detectable axonal mislocation.

Comparison of axonal defects with patterns of Slit expression

In agreement with previous studies, in situ hybridizations at E13.5 revealed strong Slit1 mRNA expression both anterior and posterior to the junction of the optic nerve and the brain (Figure 4A) [8] whereas expression of Slit2 was strongest anterior to the point of entry of retinal axons (Figure 4B) [7, 8]. The analysis above revealed that many retinal axons of Slit2^−/− and Slit1^−/−Slit2^−/− mutants crossed at abnormally anterior locations and here we examined the spatial relationship between the orientations of these axons and the normal Slit2 expression pattern.

Using the same strategy described above for analysis of axons, we combined data from three separate comparably-developed in situ hybridizations to give a map of the average staining intensity for Slit2 across the ventral midline in 150 μm horizontal sections at the level of retinal axonal entry. The system illustrated in Figure 1A was used to align data on gene expression in wild-types with data on retinal axons from wild-type or mutant embryos. Results are shown in Figure 5. The following vector-fields were obtained. For axons, mean orientations (red/magenta in Figure 5B-D) and mean directions and magnitudes of curvature (green in Figure 5B-D) were obtained within each square in the 32 × 32 grid (described above), using data from all embryos of each genotype. Also within each square, the mean vector representing the gradient of Slit2 expression was calculated (yellow in Figure 5B-D; the lengths of the lines represent the magnitudes of the gradient with arrowheads pointing from high to low intensity of label). The location of these vector fields in the brain is shown in Figure 5A.

Axons were labelled from the left eye. In wild-types (Figure 5B) labelled axons about 200μm to the left of the midline were oriented roughly 45–75° relative to the midline. They turned to run roughly orthogonal to the midline as they as they approached it (note the green vectors representing curvature concentrated near to the midline in Figure 5B). In taking this course, the axons were oriented roughly (± about 30°) orthogonal to the vectors representing the Slit2 gradient and, therefore, avoided the anterior region of high Slit2 expression (Figure 5B). In contrast, axons on the left of the midline in Slit2 ^−/− mutants were oriented roughly orthogonal to the midline throughout their approach, thereby entering the anterior areas where Slit2 would normally be expressed. Many turned at the midline to exit through the contralateral area of high Slit2 expression (Figure 5C). A similar pattern was observed in Slit1^−/−Slit2^−/− mutants (Figure 5D).

All these analyses together provide a consistent picture in which loss of either Slit2 alone or Slit1 and Slit2 together result in many retinal axons being misoriented on approach and exit from the ventral midline and many being located abnormally anteriorly, where Slit2 would normally be expressed. It appears that Slit2 is required to prevent retinal axons from taking this anterior route.

Mice and mutant alleles

The licence authorising this work was approved by the University of Edinburgh Ethical Review Committee of 22^nd September 2008 (application number PL35-08) and by the Home Office on 6^th November 2008 (licence number 60/3913). Animal husbandry was in accordance with the UK Animals (Scientific Procedures) Act 1986 regulations. Slit1 and Slit2 mutant alleles were described by Plump et al. [10]. The Slit1 ^- allele was identified by multiplex PCR using primers 5-ACCCTTAGCTTCTACCAACC-3, 5- TCTCCTTTGATCTGAGACCG-3 and 5-AGGTTTCTCGAGCGTCATAG-3: the wild-type allele gives a 544bp product, the mutant allele gives a 393bp product. The Slit2 ^- allele was identified by multiplex PCR using primers 5-AAGACCTGTCGCTTCTGTCAG- 3, 5-AAACAGGTTTCTACCGCACG-3, and 5-AAGTCTAGTAGAGTCGAGCG-3: the wild-type allele gives a 600bp product, the mutant allele gives a 350bp product. All mice were C57BL6.

DiI tract tracing

E13.5 embryonic heads were fixed at 4°C in 4% paraformaldehyde in phosphate buffered saline (PBS) overnight, and 1,1-dioctadecyl-3,3,3,3-tetramethyl-indocarbocyanine perchlorate (DiI) crystals (Invitrogen, San Diego, CA) were placed into the optic cup of one eye, after removal of the lens, to label axons leaving the retina. Heads were returned to 4%paraformaldehyde in the dark at room temperature for 4 weeks to allow tracers to diffuse along axons. Heads were then sectioned (150 μm) with a vibratome, cleared in 9:1 glycerol: PBS and mounted in Vectashield (Vector Laboratories, Burlingame, CA). Images were acquired at ×40 using a Zeiss Axiovert confocal LSM 510 microscope in tile-scan mode to collect serial optical sections, which were then combined to create a projection. The section thickness was sufficient to include the entire chiasm but where, due to the position of the cuts, part of it was in a second section, both sections were imaged and a composite was generated so that the entire depth of the chiasm was analyzed in all cases.

Image analysis

Images were imported into MATLAB (MathWorks, Natick, MA) and convolved with a bank of three 2D 2nd-derivative Gaussian filters of width 1.8 μm. The maximum filter response was calculated. The method is described in full in Freeman and Adelson [11]. Imaging was done with consistent confocal settings chosen to avoid saturation at high magnification. Rather than adjust settings, where small areas of saturation did occur and the filters did not activate, vector orientations in the saturated area were interpolated based on the orientations the vectors were taking on the edges of that area. In practice, this approach only applied in very small areas in some images. Non-maximum suppression was then performed by considering the two orthogonal pixels at any given point in the direction vector field and keeping it if both these flanking pixels gave a lower filter response. A global threshold was then applied that removed all pixels for which the intensity was less than twice the median intensity across all pixels or whose filter response was less than twice the median. The orientation vector field was then smoothed with a Gaussian of 30 μm to remove noise (which is of a higher frequency) and the curl of this vector field was calculated to give the curvature of the axon trajectories at any given point. Non-maximum suppression was applied a second time.

Statistical comparison of genotypes

To compare different genotypes with respect to axon number, axon direction and axon curvature across the image, the vector fields were rotated and scaled to a universal grid with the left eye of the embryo defining the origin and the right eye defining the position (0, 1), as shown in Figure 1A. The area of the chiasm was split into a 32 × 32 grid covering the region (0.4 : 0.6, 0.05 : 0.25), highlighted in Figure 1A. The axon number, mean axon orientation, mean curvature direction and mean curvature magnitude were put into each of these bins for every sample. A Student’s t-test was applied for axon number and the Watson-Williams test was used to compare axon orientations and angle of curvature between samples, as provided by the CircStat MATLAB toolbox (circular statistics is appropriate for analysis of curvatures and orientations) [13]. To control for false positives, FDR (False Discovery Rate) [14] was used, given the large number of hypotheses present. For all tests we took α = 0.05. These methods are commonly used for dealing with multiple comparisons in other areas of spatial statistics.

In situ hybridization

Embryonic heads were fixed overnight in 4% paraformaldehyde in phosphate buffered saline (pH 9.5 at 4°C). In situ hybridizations for Slit1 or Slit2 used 100 μm vibratome sections and digoxigenin-labeled antisense riboprobes synthesed from rat cDNAs encoding Slit1 and Slit2 as templates, as previously described Erskine et al., [8].