DOI: 10.7302/jgb4-6h13
title: Dataset for analyzing spatial distribution of Y-junctions in flat-mounted retinae

description: This dataset is composed of eight flat-mounted (dissected and fixed) retinae from juvenile and adult zebrafish.

Rows of UV cones have been traced in each retina; additionally, we have identified locations of Y-junctions (row insertions).

Also included is MATLAB code for calculating which Y-junctions belong to grain boundaries.

Please see the readme file for a description of included codes and image files.
description: Zebrafish:
Fish were maintained at approximately 28°C on a 14/10 h light/ dark cycle with standard husbandry procedures. Zebrafish lines, Tg(-5.5sws1: EGFP)kj9, Tg(-3.2sws2: mCherry)mi2007, Tg(trß2: tdTomato), Tg(-3.2sws2: EGFP), Tg(gnat2:H2A-CFP), and pigment mutant ruby carrying albino (slc45a)b4/b4 and roya9/a9 were used. All animal procedures were approved by the Institutional Animal Care and Use Committee at the University of Michigan.
description: Histology:
Retinal dissection, fixation and immunocytochemistry were performed as previously described. Briefly, the isolated retina was fixed in 4% paraformaldehyde with 5% sucrose in 0.1M phosphate buffer, pH 7.4, at 4°C overnight. After antigen retrieval with 10 mM sodium citrate in 0.05% tween 20 (pH 6.0), the retina was incubated in blocking buffer for 2 hours followed by primary antibody incubation, mouse anti-Zonula Occludens (ZO1-1A1, 1:200, ThermoFisher Scientific, Waltham, MA) and rabbit anti-GFP (1:200, ThermoFisher Scientific) at room temperature overnight. Incubation with secondary antibodies (Alexa Fluor 555 and 649, ThermoFisher) was performed at room temperature overnight, and the retina was flat-mounted on a glass slide. For retinal cross sections, affinity-purified rabbit polyclonal opsin antibodies, a gift from Dr. David R. Hyde, were used. Images were acquired with a Zeiss AxioImage ZI Epifluorescent Microscope (Carl Zeiss Microimaging, Thornwood, NY) equipped with an ApoTome attachment for optical sectioning structured illumination, Leica DM6000 Upright Microscope System (Leica Microsystems, Werzlarm Germany) and a Leica TCS SP5 confocal microscope equipped with Leica 40X HCX PL APO CS Oil Immersion lens.
description: Large tile scans of flat-mounted retinae:
Large tile scans of entire flat-mounted retinae from adult Tg(sws1:EGFP) zebrafish immunostained for ZO1 were acquired with a Leica TCS SP8 LSCM (Leica Microsystems) equipped with Leica 20X PL APO Dry lens. The GFP signal was recovered by immunostaining with anti-GFP antibody. The White Light Laser was tuned to 555 nm for Alexa Fluor 555 and 649 nm for Alexa Fluor 649. The Leica HyD hybrid detectors were tuned to 600-641 nm for Alexa Fluor 555 and 701-751 nm for Alexa Fluor 649. Images were acquired at 700 Hz scan speed with a resolution of 2048 x 2048 pixels in the xy dimension with a 2.0 um interval between optical sections in the z-dimension.
description: Row tracing of flat-mounted retinae:
We manually traced rows of UV cones, starting near the region coinciding with the disorder-to-order transition. The row tracing extends over approximately one hundred columns of UV cones from the larval remnant to the periphery, avoiding regions of the retinae that were damaged during flat mounting. Based on the row tracing, we identified where rows are inserted (i.e., Y-Junctions) and where rows are removed (i.e., reverse Y-Junctions).
description: Detection of grain boundaries (in flat-mounted, row-traced retinae):
Because the flat-mounted retinae are of finite size and because grain boundaries can both initiate and terminate within the retinae (forming so-called grain boundary scars), identifying grain boundaries is not as simple as one might intuit based on experience with infinite planar crystals. Even if all Y-junctions form lines that run from the center to the periphery of the retina, if one increases the number of identical grain boundaries, the change in domain orientation associated with each grain boundary drops. Because the degree of “grain boundary”-ness can vary continuously, we would like to find a way to classify a Y-Junction as being in a grain boundary or not being in a grain boundary.
In the flat-mounted retinae, we have the positions of Y-Junctions, which generate row insertions, in the traced regions. In addition, individual rows are traced (meaning that each row has a distinct curve running along it). To define whether a given Y-junction belongs to a grain boundary, we check whether the row orientation of the surrounding domain rotates appreciably in the vicinity of the Y-junction.
This method requires two arbitrary parameters: 
1. the length-scale over which we average the domain rotation (which we will call ∆r)
2. how large the domain rotation must be for a defect to be “in a grain boundary”

We describe positions on the flattened retinae via polar coordinates (where the approximate center of the retina lies at the origin). For each Y-junction, we average the domain orientation in five distinct boxes (which we will use to compute how much the row orientation changes near the Y-Junction):
1. The first box is centered on the Y-junction of interest (at radial coordinate r=r_0 and angular coordinate θ=θ_0). It runs from r=r_0-∆r/2 to r=r_0+∆r/2 and from θ=θ_0-(1/2 ∆r)/r_0  to θ=θ_0+(1/2 ∆r)/r_0 .
2. The second box runs from r=r_0-3 ∆r/2 to r=r_0-∆r/2 and from θ=θ_0-(1/2 ∆r)/r_0  to θ=θ_0+(1/2 ∆r)/r_0 .
3. The third box runs from r=r_0+∆r/2 to r=r_0+3 ∆r/2 and from θ=θ_0-(1/2 ∆r)/r_0  to θ=θ_0+(1/2 ∆r)/r_0 .
4. The fourth box runs from r=r_0-∆r/2 to r=r_0+∆r/2 and from θ=θ_0-3 ( 1/2 ∆r)/r_0  to θ=θ_0-(1/2 ∆r)/r_0 .
5. The fifth box runs from r=r_0-∆r/2 to r=r_0+∆r/2 and from θ=θ_0+(1/2 ∆r)/r_0  to θ=θ_0+3 ( 1/2 ∆r)/r_0 .
To calculate the orientation within each box, we first identify all row lines that run through the box. For each row line (a skeletonized line composed of individual pixels), we calculate its orientation by 
(i)	computing the covariance matrix of the row’s pixels’ positions within the box of interest (cov
description: MATLAB  2016B,  MathWorks,  Natick,  MA)
(ii)	subsequently identifying the direction along which the row’s pixels’ positions vary the most (eig
description: MATLAB  2016B,  MathWorks,  Natick,  MA)
By convention, row lines always run from the center of the retina to its periphery, so we encode each row’s orientation with a unit vector that runs along the row from center to periphery (rather than from periphery to center). Then, within the box of interest, we do a weighted average over the unit vectors (one for each row line within the box), where the weight of each row is simply the number of pixels of that row line that fall within the box. Then, we convert this weighted average of row vectors to a unit vector, which represent the row orientation within the box.
Now that we have the row orientation for each of the five boxes (unit vector (u_1 ) ̂ for box 1, …, unit vector (u_5 ) ̂ for box 5). We calculate how much the row orientation changes about the Y-Junction along the theta direction (∆ϕ_45=acos⁡(dot((u_4 ) ̂,(u_5 ) ̂ ))) as well as along the r direction (∆ϕ_23=acos⁡(dot((u_2 ) ̂,(u_3 ) ̂ ))). If the grain boundaries were purely radial, we could focus on ∆ϕ_45 and ignore ∆ϕ_23. In flat-mounted retina, because of retinal deformations due to cutting and flattening, grain boundaries are frequently not well-aligned with the theta direction. Because of this, we compute: ∆ϕ_rms=√((∆ϕ_45 )^2+(∆ϕ_23 )^2 ). ∆ϕ_rms takes into account the change in row orientation in the vicinity of the Y-Junction about both directions.
To determine whether a Y-Junction is within a grain boundary or not, we compare its ∆ϕ_rms to some cutoff (for example, ten degrees or twelve degrees or fourteen degrees). If ∆ϕ_rms is greater than the chosen cutoff, the Y-Junction is in a grain boundary
description: if not, the Y-Junction is not in a grain boundary. Because by its very nature this cutoff is arbitrary, we vary this parameter (as well as ∆r) to see how the fraction of defects in grain boundaries change with these parameters. We find that the fraction of Y-Junctions depends very weakly on ∆r, but strongly on the cutoff in rotation of row orientation. To see if our simulations and experimental images have similar fractions of Y-Junctions in grain boundaries In addition, we fix the values of these parameters when comparing flat-mounted retinae to simulations.
We note a couple possible pitfall of this method as applied to flat-mounted retinae. 
1. Assume that all regions of the cone mosaic have the same (anisotropic) spacings between UV cones at the time of incorporation
description: we expect that as the retina grows by incorporation of new cones, older regions of the retina are anisotropically deformed as the hemispheric retina dilates. Thus, using a uniform cutoff in ∆ϕ_rms (for “in grain boundary” versus “not in grain boundary”) probably overestimates the fraction of defects in grain boundaries near the center of the retina relative to the fraction of defects in grain boundaries near the periphery of the retina.
2. In regions where the row orientation is slightly warped due to deformation of the retina from the flattening process, Y-junctions may be designated as “in a grain boundary” (even if they are isolated) because of the deformation of row orientations.