LongAxis: a MATLAB-based program for 3D quantitative analysis of epithelial cell shape and orientation

Abstract

Epithelial morphogenesis, a fundamental aspect of development, generates 3-dimensional tissue structures crucial for organ function. Underlying morphogenetic mechanisms are, in many cases, poorly understood, but mutations that perturb organ development can affect epithelial cell shape and orientation – difficult features to quantify in three dimensions. The basic structure of the eye is established via epithelial morphogenesis: in the embryonic optic cup, the retinal progenitor epithelium enwraps the lens. We previously found that loss of the extracellular matrix protein laminin-alpha1 (lama1) led to mislocalization of apical polarity markers and apparent misorientation of retinal progenitors. We sought to visualize and quantify this phenotype, and determine whether loss of the apical polarity determinant pard3 might rescue the phenotype. To this end, we developed LongAxis, a MATLAB-based program optimized for the retinal progenitor neuroepithelium. LongAxis facilitates 3-dimensional cell segmentation, visualization, and quantification of cell orientation and morphology. Using LongAxis, we find that retinal progenitors in the lama1^−/− optic cup are misoriented and slightly less elongated. In the lama1;MZpard3 double mutant, cells are still misoriented, but larger. Therefore, loss of pard3 does not rescue loss of lama1, and in fact uncovers a novel cell size phenotype. LongAxis enables population-level visualization and quantification of retinal progenitor cell orientation and morphology. These results underscore the importance of visualizing and quantifying cell orientation and shape in three dimensions within the retina.

Introduction

Organogenesis requires assembly of cells into precise 3-dimensional structures which are crucial for function. Disruptions to this morphogenetic process can lead to organ dysfunction, and are a common cause of birth defects. Cellular and molecular mechanisms governing organ morphogenesis are generally not well understood: many signals and pathways have been identified, often on the basis of genetic studies and mutant phenotypes. Despite this, analyzing genetic interactions and dissecting how different factors impact morphogenesis has been a challenge, since, in many cases, it has not been trivial to visualize and quantify phenotypes in three dimensions.

The vertebrate eye forms via a complex morphogenetic process, during which the optic vesicle, an outpocketing of the forebrain, undergoes cell and tissue movements to become the optic cup, in which the hemispherical retina enwraps the lens. At the end of optic cup morphogenesis, the retinal epithelium is comprised of progenitor cells which are elongated and oriented toward the lens. In fish, mouse, and chick, genetic screens, candidate approaches, and conditional genetic studies have identified factors involved in optic cup tissue organization [1–6]. The optic cup acquires apicobasal polarity throughout optic cup morphogenesis and loss of either apical or basal polarity cues can have severe effects on future development of the retina and RPE [7–14]. One key factor governing optic cup tissue organization and morphogenesis is the extracellular matrix, a complex proteinaceous layer that surrounds epithelial tissues and provides polarity, survival, and signaling cues [15–19]. It has long been known that a complex extracellular matrix layer surrounds the nascent developing eye of all vertebrate species examined to date [20–28], and functional roles for specific extracellular matrix molecules in early eye development are starting to be resolved using molecular genetic approaches [29–33]. We previously found that loss of laminin-alpha1 (lama1) results in disruption of tissue polarity and cellular disorganization within the retinal epithelium of the zebrafish optic cup [29]. At the single-cell level, retinal progenitors appeared misoriented, although this seemed variable between individual mutant embryos and was largely inferred by scanning through volume data (z-stacks acquired by confocal microscopy). In addition to the tissue disorganization defect, the lama1 mutant displayed ectopic localization of the apical marker pard3 at inappropriate locations, including what would normally be the basal surface of the optic cup. We wondered whether the establishment of ectopic apical surfaces might cause the disorganization phenotype, and whether removal of the apical determinant pard3 could rescue it.

Although we had questions, we lacked the methodology to adequately and quantitatively analyze such phenotypes. We were not previously able to visualize or quantify cell orientation in 3-dimensions, phenotypic variability between embryos, nor how changes in cell shape or volume might contribute to mutant phenotypes. With these goals in mind, we have developed LongAxis, a MATLAB-based program which allows us to qualitatively and quantitatively assay multiple aspects of cell morphology and organization, optimized for the developing retina. Using a combination of automated segmentation and refinement (or filtering) via user selections to remove outliers and incompletely segmented cells, we can visualize and analyze cell orientation and shape in 3-dimensions throughout the tissue. Cell orientation, length, length/width ratio, and cell volume can be calculated for thousands of cells simultaneously; these features can be displayed in the intuitively simple “urchin plot”, which conveys the cell’s extent of elongation (length/width ratio) and orientation.

Using LongAxis, we finally resolved questions regarding the lama1 mutant optic cup phenotype, including how cell orientation and morphology are quantitatively affected, and whether genetic removal of the apical polarity determinant pard3 is able to rescue it. We find that in the lama1 mutant optic cup, retinal progenitors are indeed misoriented, and that misoriented cells cluster together in domains. Cells are shorter and less elongated, but not smaller than wild type cells. In the lama1;MZpard3 double mutant, retinal progenitors are still misoriented, and we uncover a cellular-level phenotype: cells are larger than either wild type or lama1 single mutants. Therefore, loss of pard3 does not rescue the lama1 mutant tissue organization phenotype. Importantly, rather than 2-dimensional measurements in a small number of sparsely labeled cells, LongAxis allows us to discover population-level alterations in cell morphology and organization, and underscores the importance of quantitative analysis of cellular level phenotypes.

Results

Pipeline for 3-dimensional cell segmentation

Our goal is to understand the molecular basis of cell and tissue organization within the embryonic optic cup. Although many factors have been identified as playing a role in this process, our analysis has largely been limited to 2-dimensional analysis of a small sampling of cells. Dissecting genetic interactions and mechanisms would ideally be carried out by quantitatively evaluating cell orientation and morphology throughout the retinal progenitor cell population. To this end, we developed LongAxis, a program to facilitate visualization and quantification of cell morphology within the zebrafish optic cup.

The goal of this software is accurate single cell segmentation and automated quantitative analysis of cell shape and orientation within the context of the tissue, therefore, a crucial initial optimization step is obtaining image data of adequate quality. To avoid distortion and changes in volume that accompany tissue fixation, we imaged live embryos at optic cup stage (24 hours post fertilization (hpf) in zebrafish), in which all membranes were labeled using EGFP-CAAX. Images were acquired at 1024×1024 resolution, and we aimed for adequate axial sampling without photobleaching, deciding upon a voxel size of 0.21×0.21×0.42 μm (x:y:z ratio of 1:1:2; Movie 1).

In LongAxis, cell segmentation begins with eight steps of 2D processing applied to every slice, with the goal of enhancing boundaries (Figure 1B; see also Methods, LongAxis MATLAB code). The processing steps outlined here are optimized for our specific data sets, the goal being to visualize and analyze retinal epithelial cells. In our experience, the key step was to correct for variations in signal (i.e. some regions of membrane around any particular cell might be brighter or dimmer than others) in order to ensure that the cells were segmented along membrane boundaries accurately. Once 2D processing has been carried out, the user selects the 3D subvolume of interest within the image data for 3D segmentation and rendering. This allows the user to analyze a particular region of interest, or to crop the data volume of blank space. Once the subvolume of interest has been selected, 3D processing functions are applied to enhance and connect boundaries across slices (Figure 1C). This initially yields 3D cell segmentation throughout the volume data (Figure 1D, E). In our case, this includes the neural retina as well as non-retinal cells, such as prospective brain, lens, and overlying ectoderm. The user-selected subvolume is then refined to restrict the 3D cell segmentation only to cells within the particular region of interest (Figure 1F–H). This allows us to focus our analysis specifically on the retinal epithelium. Segmentation can be examined in small volume regions for visual validation at this stage (Figure 1I–J; Movies 2, 3).

Figure 1. LongAxis workflow, image processing, and segmentation.

(A) LongAxis workflow

(B) 2D image processing steps (starting with 8-bit datasets): the goal is to enhance cell boundaries and correct for variations in signal while removing noise. Raw image pixels are saturated to 1% at both ends (a). Median filter (11×11) (b), smoothing filter (3×3) (c), and Tophat filter (d) are applied. The image is saturated to 10% at both ends (e), and a coherence filter (anisotropic diffusion) is applied (f) to enhance connected structures, followed by a slight erosion (g). The image is then binarized by thresholding at 30/255 (h).

(C) 3D image processing steps: images are representative 2D slices of 3D volumes. The negative of the 2D distance transform is calculated (i). Filters (ordfilt and 3×3×3 median) are applied to reduce noise (j). 3D extended minima regions are set to -infinity to prevent oversegmentation (k). The 3D watershed function is applied to yield a binarized image (l).

(D-J) Views of segmented cells and image data. (D) Single confocal image slice and cells associated with the slice. (E) 3D volume of selected region of data set with all segmented cells and single confocal section shown. (F) Same region as (E), but with only retinal regions selected for quantitative analysis. (G) Same view as (F) but with xz cutaway shown. (H) View of entire optic cup cell segmentation with xy and yz sections shown. (I) Selected region of optic cup and segmented cells with raw image data for “fly-through” visual validation. (J) Different selected region of optic cup and segmented cells, including xz/yz cutaways, with raw image data for “fly-through” visual validation.

Following this, the set of segmented cells is further refined: cell segmentation needs to be validated, and unwanted cells, particularly those in which segmentation failed, are removed from the data set. To this end, a process of “informed filtering” is carried out (Figure 1A). The basic idea is to validate cell shapes in a manner unbiased with respect to the orientation of the cell; assaying changes in cell orientation is a major goal of this software. To carry out filtering, an expert user (i.e. someone experienced with looking at these data) views 3-dimensional segmented cell shapes (away from the image data), and manually validates cells which appear to have a retinal epithelial morphology. If need be, the user can cross-check the position of the cell to ensure that cells within the retinal epithelium are being selected, or the user can also check the cell rendering against the original image data. The ability to cross-check may be useful in cases (e.g. mutants) where cell morphologies could be dramatically altered, but again, the basic idea is to carry out these selections in an unbiased manner with respect to position and orientation of the cell within the tissue.

Once the user has selected cells, the user-selected data set is analyzed: minimum and maximum values for cell volume, length, and length/width ratio are derived. These minimum/maximum (min/max) values for these three criteria are applied to refine and filter the entire data set (all segmented cells in the region of interest); this process thereby excludes “outlier” cells with respect to these three specific criteria. This “filtered” cell set is used for quantitative analysis of cell morphology and orientation and 3-dimensional visualization.

LongAxis analysis and outputs

Once cells are segmented, a variety of outputs can be acquired, including 3-dimensional visualization of cell shape, and quantitative outputs including cell length, cell width, length/width ratio (a metric of how elongated the cell is), and cell orientation (Figure 2A–D; Movie 4). Cell orientation is quantified within the 3-dimensional tissue by deriving the cell convergence point: the average of all midpoints of closest approach for all cell orientation vector pairs (Figure 2E, average (asterisk) of midpoints of closest approach (red dots); Movie 5). This was empirically derived for each embryo independently: we found that existing landmarks (e.g. the lens center of mass) incurred too much variability between embryos, as lens shape, size, and even position can vary slightly with respect to the retinal epithelium. Once the vector convergence point is obtained (Figure 2F, marked by black dot), the long axis, which is derived from the ellipsoid fit, is used to calculate an angle of deviation (or deflection) from that convergence point for each cell (Figure 2F, marked by red asterisk). In addition to the quantitative output, angles of deviation and length/width ratio can all be represented in an “urchin plot”, a 3-dimensional visual representation of cell orientation and shape within the tissue (Figure 2G). In the urchin plot, the angle of deviation is represented by a heat map, in which close adherence to the expected angle is coded in bluer colors, and significant deviation is encoded by warmer colors. The length of the vector is proportional to the length/width ratio of the cell, to represent one aspect of cell shape.

Figure 2. LongAxis data analysis and outputs.

(A) Cell shape and cell volume. 3D plot of segmented cell shape.

(B) Cell length. Segmented cell in minimum bounding sphere (lavender), where diameter equals cell length.

(C) Cell orientation. Segmented cell with ellipsoid fit (red), where long axis of the ellipse is the long axis (orientation vector) of the cell (blue).

(D) Cell width. The plane (hexagon) perpendicular to the cell’s long axis and passing through the cell’s centroid is calculated. Next, the minimum bounding circle (black) of the plane-cell intersection (cyan) is calculated, defined as the cell width.

(E) Calculation of convergence point: three example rays are shown to represent the long axes of three different cells. Red dots show the pairwise midpoints of closest approach and the asterisk is the derived convergence point (average of all midpoints).

(F) Calculation of angle of deviation: the degrees deflected from the convergence point derived for that embryo.

(G) Urchin plot with heat map. Vectors are in the direction of the cell-ellipsoid fit long axis and the vector lengths are proportional to the cell length/width ratios. Heat map represents angle of deviation.

Validating segmentation and filtering

To determine how well the workflow performs, segmentation and filtering validation steps were carried out on three independent subregions of the image volume data (one example in Figure 3A). First, because segmented cell shapes were initially viewed in an isolated manner, away from the image data, we visually examined all segmented cells in each subregion against the original image data. We used xy, xz, and yz cutaways to evaluate how well the segmentation matched the membrane signal, including whether the process correctly segmented single cells. Segmentation accuracy for all cells was scored manually (by a user) on a scale of 1–5, with 1–4 corresponding to how well the segmentation matched the membrane boundaries in the image data (1 = 90–100% matching boundaries; 2 = 70–90%; 3 = 50–70%; 4 = <50%), and a score of 5 representing unsuccessful segmentation resulting in fused cells. Despite presence of some variability in rendering quality, cell orientation was largely unaffected for cells in categories 1–3. The proportions of cells in each category is shown in Figure 3B.

Figure 3. Filtering analysis and validation.

(A) Example region for segmentation validation: a subvolume is selected, usually containing 50–70 cells. Rendered cells are examined individually against xy/xz/yz cross-sections of the original image data to determine how well segmentation matches the image information (1 = 90–100% match of the cell segmentation to the image data; 2 = 70–90%; 3 = 50–70%; 4 = <50%; 5 = fused cells).

(B) Effect of filtering on cells in the data set: class 4 and 5 cells are preferentially removed by filtering.

(C) Filtering analysis: plot of number of cells excluded by filtering against number of cells selected by the user, with an exponential decay curve fit to the data.

(D-G) Comparison of segmented cells: all cells vs. filtered cells vs. user selections to determine how filtering might change the quantitative aspects of the data set. (D) Angle of deviation (density plot) for one wild type embryo. (E) Cell length. (F) Cell length/width ratio. (G) Cell volume. Letters in E-G represent different statistical groups as analyzed by ANOVA followed by Tukey’s test. In E and F, the user selections were significantly different from the all cells and filtered cells data sets (P<0.01). In G, the all cells set was significantly different from the filtered cells and the user selections (P<0.01).

We then asked how filtering (using parameters derived from user selections for cell volume, cell length, and length/width ratio) affected the number of cells in each group. We examined the subset of cells that passed the filtering criteria, and we found that indeed, although filtering is not perfect, poorly segmented (class 4) and fused cells (class 5) are preferentially removed from the filtered data set (Figure 3B; number of cells removed from each class 1–5, in order: 3, 5, 2, 12, 13). These analyses suggest that the segmentation identifies cells in 3-dimensions and filtering helps to remove unsuccessfully segmented cells, leaving us with a data set appropriate for population-level quantitative analysis.

Determining filter parameters and the size of the user-selected data set

Accurate filtering relies on having a set of cells selected by an expert user; filtering parameters are derived from this user-selected cell set. How many cells does the user need to choose to generate reliable filtering parameters? We tested this in 4 different wild type embryos by examining the relationship between number of cells selected and number of cells filtered out, the rationale being that as the number of selected cells increases, more reliable filter parameters will be generated. This, however, only works up to a point at which selecting more cells has no more benefit; the user set will have already captured the full range of appropriately segmented cells. We find that the relationship between number of cells selected and number of cells filtered out obeys exponential decay (Figure 3C; Figure S1A); deriving the equation to describe this graph allows us to easily calculate the number of cells which need to be selected to carry out filtering (using the mean lifetime equation τ = λ⁻¹, where λ is the decay rate and τ represents the mean lifetime, or here, the average number of selections it takes to remove a cell). For the 4 wild type embryos examined, although substantial numbers of cells were manually selected by the user (1269, 1788, 2420, and 1582, respectively), significantly fewer cells (using the mean lifetime equation to solve for τ: 253, 119, 120, and 61, respectively) needed to be selected in order to exclude the inappropriately segmented cells without inappropriately removing correctly segmented cells (Figure 3C; Figure S1A). While the number of user-selected cells necessary for adequate filtering needs only to be a small proportion of the total number of cells, filtering quality clearly increases with more user-selected and validated cells. In addition, the derived equation reveals that there is a minimum of cells that will be excluded in each wild type embryo (using the exponential decay equation (see Methods) and solving for y_f: 192, 132, 200, and 515, respectively); based on our manual validation, these are likely to represent poorly segmented and fused cells. We think the variability in this number between embryos is due to variation in image quality, which will affect the success of the segmentation process.

This post hoc analysis reveals that there is not one single baseline number of cells for a user to select, however, the software is simple to use, and selecting a few hundred cells will likely yield high quality filtering information necessary to remove unwanted cells.

Filtering poorly segmented cells does not change the data set

Given that filtering does change the number of cells being used for quantitative analysis (Table 1), we asked how it might alter, at the population level, the quantitative measurements of interest: angle of deviation, cell length, length/width ratio, and volume (Figure 3D–G; Figure S1B–E). We find that in the cases of angle of deviation, cell length, and length/width ratio, the distributions of filtered cells are not altered from the original (full) set of segmented cells (Figure 3D–F; Figure S1B–D, letters in graphs (A, B) represent different statistical groups). In contrast, cell volume is changed such that the filtered set is not statistically different from the user selections (Figure 3G; Figure S1E), consistent with the idea that inappropriately segmented, and especially fused cells (which are larger) are removed from the filtered data set. Importantly, distributions of orientation angles do not change (Figure 3D; in 3 out of 4 wild type embryos, two-sample Kolmogorov-Smirnov tests show no significant difference between the set of all segmented cells and the filtered set), so filtering would not influence large-scale analysis of cell orientation and tissue organization. We conclude from these analyses that filtering works to preferentially remove outlier cells, without changing the population distribution of the data with respect to cell length, length/width ratio, and angle of deviation.

Wild type embryos exhibit slight morphological variability between cell populations

With our new tool in hand, we first set out to examine multiple wild type embryos to determine the amount of variability we might detect between samples of the same genotype. Development in zebrafish is not deterministic, and we expect there to be some variability between individuals with respect to eye size and cell number. To examine this, four different wild type embryos were imaged and analyzed using the LongAxis pipeline, with filtering parameters and cell convergence points derived independently for each individual embryo (Figure 4A–A’”, Movie 6). In Movie 6, isosurfaces show highest density regions of midpoints of closest approach for all pairwise vector combinations, and black dot shows the derived convergence point (the average of all calculated midpoints) which was used for angle of deviation measurements. Urchin plots were generated to visualize cell orientation in a qualitative manner (Figure 4B–C’”, Movie 7), and at this level of resolution, the optic cups exhibit some variation in size and shape (including lens shape). Despite this, the cells (represented as vectors in the urchin plot) largely appear to be aligned toward the calculated convergence point (labeled as colors in the blue range in the heat map), with the reproducible exception of the optic fissure opening at the ventronasal side of the eye (Figure 4B–C’”, asterisks). These data are represented quantitatively as a density plot of angles of deviation (Figure 4D); the distributions of angles of deviation appear similar between the four embryos, with a peak ~20°. Quantitative analysis and comparison of these 4 wild type embryos reveals other notable features. First, the numbers of retinal epithelial cells vary between the optic cups (1824, 2413, 3752, and 2019, respectively; Table 1), but these numbers are in the same range as previously calculated using a completely independent method which relied on counting nuclei (Kwan et al., 2012). This serves as a convenient independent validation of our approaches. Next, the distributions of cell length and volume appear different, but fall only into two statistical groups (Figure 3E, G; mean length (μm): 16.26, 15.9, 16.29, 16.59; mean volume (μm³): 346.28, 305.28, 337.3, 341.05). There is no significant difference in cell length/width ratio between the four embryos (Figure 3F; mean length/width ratio: 2.06, 2.08, 2.09, 2.1). Taken together, these data indicate that the quantitative analysis can distinguish between individual embryos of the same genotype, due to normal phenotypic variability; therefore, multiple embryos must be used to compare different experimental conditions and genotypes.

Figure 4. Quantitative comparison of variability in wild type optic cups.

(A-A’”) Single confocal sections of wild type #1 (A), wild type #2 (A’), wild type #3 (A”), and wild type #4 (A’”).

(B-B’”) Urchin plots (lateral views) of wild type #1 (B), wild type #2 (B’), wild type #3 (B”), and wild type #4 (B’”). Asterisks, optic fissure opening.

(C-C’”) Urchin plots (anterior views) of wild type #1 (C), wild type #2 (C’), wild type #3 (C”), and wild type #4 (C’”).

(D) Angle of deviation (density or cumulative distribution plot) for all four wild type embryos.

(E) Cell length for all four wild type embryos.

(F) Cell length/width ratio for all four wild type embryos.

(G) Cell volume for all four wild type embryos.

Letters in E-G represent different statistical groups as analyzed by ANOVA followed by Tukey’s test. n.s., not significant. In E, wild type #2 was significantly different from wild type #3 (P<0.05) and wild type #4 (P<0.01). In G, wild type #2 was significantly different from wild type #1, 3, and 4 (P<0.01).

Putting the software to the test: genetics of apicobasal polarity and tissue organization in the optic cup

Having determined that we could segment cells and carry out quantitative analysis on cell morphology and orientation, we turned our attention to the original biological question at hand. We previously demonstrated that loss of lama1 leads to disruptions to epithelial polarity and apparent disorganization of the retinal progenitor epithelium [29]. Although we hypothesized that the cause of this phenotype was cell misorientation as opposed to gross changes in cell size or shape, we had no way at the time to visualize or quantitatively test this. In addition to the retinal disorganization, we found that tissue polarity is disrupted in lama1 mutants: apical markers such as pard3 are mislocalized and even ectopically localized to subcellular locations that would, in a wild type embryo, be the basal surface. We wondered whether ectopic localization of apical determinants was the cause of the structural disorganization in the lama1 mutant optic cup, and therefore, whether the lama1 mutant phenotype might be rescued by genetic removal of pard3.

With LongAxis in hand, we set out to answer these questions. We generated double mutants for lama1 and pard3, in which pard3 was both maternally and zygotically lost (lama1;MZpard3), as pard3 is maternally loaded [34]. We compared wild type optic cups to the lama1 single mutants and the lama1;MZpard3 double mutants. When initially viewing single optical sections of all three genotypes (Figure 5A–A”), the lama1 single mutant exhibits the expected disorganized retinal epithelium with cells that appear cuboidal in cross section (Figure 5A’, Movie 8). The lama1;MZpard3 optic cup initially appeared as though the disorganized retinal progenitor cell phenotype might be partially rescued (Figure 5A”, Movie 9); in this optical section, some cells are elongated and oriented toward the lens.

Figure 5. Quantification of tissue organization in extracellular matrix and polarity mutants.

(A-A”) Single confocal sections of (A) wild type, (A’) lama1 single mutant, and (A”) lama1;MZpard3 double mutant.

(B-B”) Urchin plots, lateral views for (B) wild type, (B’) lama1 single mutant, and (B”) lama1;MZpard3 double mutant.

(C-C”) Urchin plots, anterior views for (C) wild type, (C’) lama1 single mutant, and (C”) lama1;MZpard3 double mutant.

(D-D”) Angle of deviation for (D) wild type, (D’) lama1 single mutant, and (D”) lama1;MZpard3 double mutant.

(E-E”) Cell length for (E) wild type, (E’) lama1 single mutant, and (E”) lama1;MZpard3 double mutant. The lama1 single mutant is significantly different from either wild type or lama1;MZpard3 double mutant (P<0.01).

(F-F”) Cell length/width ratio for (F) wild type, (F’) lama1 single mutant, and (F”) lama1;MZpard3 double mutant. All three genotypes are significantly different from each other (P<0.01).

(G-G”) Cell volume for (G) wild type, (G’) lama1 single mutant, and (G”) lama1;MZpard3 double mutant. The lama1;MZpard3 double mutant is significantly different from either wild type or lama1 single mutant (P<0.01).

This, however, underscores the importance of our approach, as 3-dimensional visualization and quantification are necessary to actually resolve whether the phenotype is rescued or not. Three independent embryos of each genotype (lama1^−/− and lama1^−/−;MZpard3^−/−) were imaged, processed through our LongAxis pipeline, and compared to the wild type optic cups. First, cell convergence points were derived (Movie 10) and urchin plots were generated to qualitatively visualize and compare cell orientation (Figure 5B–C”; Movies 11, 12). Because of the heat map coding of the vectors, it is intuitively clear that significant regions of the optic cup in both lama1 and lama1;MZpard3 double mutant eyes are comprised of misoriented cells. Substantial patches of the urchin plots are populated by vectors in the red-orange-yellow range, indicating an angle of deviation >60°. Interestingly, misoriented cells were found clustered, as opposed to individually randomly scattered throughout the eye.

This is also represented quantitatively in the angle of deviation density plots (Figure 5D–D”): the four wild type embryos all have a peak ~20°, indicating a small deviation from the convergence point, and a small trailing tail out beyond 60° (Figure 5D; Movie 7). In contrast, the lama1 single mutants show a very different distribution in angles of deviation: in one embryo, there is a visible peak ~20°, similar to wild type embryos, but in the other two embryos, there is no clear peak, rather, angles of deviation are distributed more evenly from 20–90° (Figure 5D’; Movie 11). Similarly, all three lama1;MZpard3 double mutants show an even distribution of angles of deviation from 20–90°, without a clear peak (Figure 5D”; Movie 12). This indicates that at the population level, cells are significantly misoriented in both the lama1 single mutant and lama1;MZpard3 double mutant optic cups.

In our previous work, we quantified morphology of a small number of cells to determine whether tissue disorganization might actually be caused by changes in cell length or length/width ratio. Assaying limited numbers of cells primarily in 2 dimensions, we found that retinal progenitor cell length was diminished, but length/width ratio was unaffected [29]. Although we had obtained a preliminary answer to our question, we wanted to determine if these trends held true with more thorough quantification of cell morphology across the population of retinal progenitors.

Using our LongAxis pipeline, we compared retinal progenitor cell length, length/width ratio, and volume at the population level, with >1000 cells per eye. First, in terms of cell length (Figure 5E–E”), we find that lama1 mutant retinal progenitor cells are shorter than wild type; this is consistent with our previous data [29]. In contrast, however, lama1;MZpard3 double mutant retinal progenitor cell length is indistinguishable from wild type (wild type 16.25±4.77 μm; lama1^−/− 15.92±5.04 μm; lama1^−/−;MZpard3^−/− 16.19±4.97 μm). Next, we examined length/width ratio: although our previous 2-dimensional analysis indicated that length/width ratio was unaffected by loss of lama1 in our small sampling of cells, our 3-dimensional analysis demonstrates that loss of lama1 or loss of both lama1 and pard3 leads to diminished length/width ratio (Figure 5F–F”; wild type 2.08±0.50; lama1^−/− 2.03±0.55; lama1^−/−;MZpard3^−/− 1.97±0.39). The difference between wild type and lama1 mutants appears subtle but is significant, likely due to the large numbers of cells measured. Finally, we assayed retinal progenitor cell volume: loss of lama1 does not affect retinal progenitor cell volume, however, lama1;MZpard3 double mutant cells are larger than either wild type or lama1 single mutant (Figure 5G–G”; wild type 331.97±183.42 μm³; lama1^−/− 333.86±201.88 μm³; lama1^−/−;MZpard3^−/− 369.94±229.80 μm³).

Taken together, these measurements are a rich source of quantitative information from which to draw a number of conclusions. First, there is variability in the lama1 mutant misorientation phenotype. We had previously observed this, but did not have a way to quantify it. Mutant embryos can display varying degrees of tissue disorganization, potentially due to the degree to which the cells might self-organize (possibly influenced by aberrant localization of apical polarity complexes) in the absence of extrinsic polarity cues from laminin. Second, although cell size and shape are slightly different in the lama1 single mutant compared to wild type, change in cell morphology is unlikely to be the cause of the misorientation phenotype. In contrast, the lama1;MZpard3 double mutant has larger, less elongated cells (greater volume, diminished length/width ratio). Finally, and importantly, at the population level, retinal progenitor cells in lama1 single mutants and lama1;MZpard3 double mutants are dramatically misoriented compared to wild type. Despite the appearance of partial rescue in a single optical section (Figure 5A–A”), these data clearly demonstrate that loss of pard3 does not rescue the tissue disorganization phenotype in the lama1 mutant. These 3-dimensional visualization and quantitative analyses underscore the utility of our approach.

Discussion

A key part of epithelial organogenesis is the establishment of tissue-specific structures which are crucial for eventual organ function. Within these epithelial tissues, cells take on a stereotypical 3-dimensional organization. Much work has gone into identifying molecular signals and pathways that influence this organization. The vertebrate eye is a somewhat unique structure, in which the hemispherical retinal epithelium enwraps the lens. We originally set out to determine how changes in one such class of molecules, the extracellular matrix, affect tissue organization: previously, we found that loss of lama1 leads to disruptions to tissue polarity and apparent disorganization of the retinal epithelium. 2-dimensional analysis of a limited sampling of cells suggested that cell length was shorter, but length-width ratio seemed unaffected. In addition, loss of lama1 resulted in ectopic localization of the apical determinant pard3 and other apical markers, and we wondered whether loss of pard3 could rescue these phenotypes. Due to limitations in our ability to visualize and quantitatively analyze 3-dimensional cell shape and orientation, we were not able to test this until now.

LongAxis allows us to take volume data (e.g. confocal z-stacks that are simple to acquire for zebrafish embryos), and run it through a 3-dimensional cell segmentation and analysis pipeline, which includes manual cell selections and filtering based on parameters derived from the manually selected cells. After filtering, LongAxis provides intuitive visualization (in the form of the “urchin plot”) and quantitative analysis of cell orientation and a number of cell morphology descriptors, including length, width, length-width ratio, and volume. The power of LongAxis is in the ability to analyze cell shape and organization at the population level – thousands of cells per eye – rather than manually measuring 2-dimensional features on a limited sampling of cells. This allows us to examine distributions within the cell population as well as variability between individual embryos.

Using LongAxis, we validated our pipeline via manual validation of segmentation and filtering, finding that filtering preferentially removes poorly and incompletely segmented cells. Next, given that vertebrate embryonic development is not deterministic and that variability exists between embryos of the same genotype, we compared results between wild type embryos, finding that LongAxis indeed allows us to detect differences between embryos of the same genotype. Therefore, analysis of multiple embryos of the same genotype is necessary to provide a complete quantitative picture of the phenotype range encompassed.

Finally, we returned to the biological question we initially sought to answer. lama1 mutant optic cups are comprised of misoriented retinal progenitors which are shorter and slightly less elongated than their wild type counterparts. We had not previously detected the elongation defect, likely due to combination of 2-dimensional analysis and small sample size. Misoriented retinal progenitors appear to cluster together in domains of the optic cup, rather than being scattered throughout the tissue randomly. We speculate that this is due to the ability of cells to self-organize in the absence of extrinsic polarity cues. We did indeed detect and were able to quantify variability between individual lama1 mutant embryos, with one embryo exhibiting less disruption to cell orientation than the other two. Did removal of the apical determinant pard3 rescue these phenotypes? Although certain single optical sections looked as though cells were well-oriented toward the lens, 3-dimensional urchin plots demonstrate that cell orientation in lama1;MZpard3 double mutant optic cups is clearly not rescued; again, misoriented cells cluster together in domains of the optic cup. Further, we detected a change in cell size and shape in the double mutants: cells are larger and less elongated than their wild type or lama1 single mutant counterparts. The underlying cause of this change in cell size is unknown, but pard3 has been linked to regulation of proliferation in some systems, for example, mouse cortical cells in vitro [35]. In vivo, however, pard3 has been linked to neuronal fates and not proliferative fates [36]; how these mechanisms impact cell size in the eye will be interesting to explore moving forward.

LongAxis allows us to assay thousands of cells within a single retina for population level analysis of cell size and orientation. This ability to quantitatively visualize and analyze 3-dimensional orientation represents a significant step forward: this type of analysis has historically been challenging in the developing eye, a curved epithelial tissue, where cell shape throughout the population cannot be easily inferred from a single optical section. Our program will facilitate quantitative dissection of the genetic networks governing tissue organization in the eye.

Despite these strides forward, this current version of LongAxis has some limitations, upon which we will be looking to improve as we move forward. First, because of the axial resolution currently necessary to yield reliable 3D cell segmentation, acquiring datasets suitable for analysis with LongAxis is a relatively slow process, depending on the microscope (in our case, 40–45 minutes on a Zeiss LSM710 or 15–20 minutes on a Zeiss LSM880). This currently impedes our ability to carry out this analysis on, for example, timelapse datasets that we commonly acquire for other studies (time-step between z-stacks ~2 minutes, with less axial resolution than LongAxis datasets). Lightsheet microscopy, with its rapid acquisition speed, could potentially provide a useful alternative; one would need to determine if the signal-to-noise ratio in a densely labeled tissue is adequate to support automated cell segmentation. In addition, because of the time involved in manual cell selection for each dataset (3–5 hours per dataset, depending on the rendering speed and graphics capability of the computer), analysis using LongAxis is relatively low-throughput (though we feel that this limitation is outweighed by the amount of quantitative information acquired). In the future, we aim to optimize segmentation algorithms to deal with more challenging imaging parameters, for example, with lower axial resolution. This may enable us, in the future, to accurately capture the dynamics involved in the tissue organization process.

LongAxis is currently optimized for the zebrafish optic cup, but could be modified for other epithelial organs. Tissue organization is a crucial aspect of the development of numerous other organs, including brain, ear, and gut. LongAxis is already potentially capable of cell size and morphology quantification in these other systems; by modifying the code provided, cell orientation analysis could be adapted for a different specific 3-dimensional structure of interest: for example, the convergence point in the eye could be modified to be the midline plane in the developing brain. Some knowledge of MATLAB coding would be necessary, and the code we provide is annotated for ease of identifying key portions for editing. LongAxis also has an interactive feature to allow a user to roughly define a reference feature of interest, for example, a plane or specific object, which involves moving a marker around the rendering environment and recording XYZ locations. An equation fit of that feature would have to be executed outside of LongAxis by someone with minor programming or mathematical expertise.

Even if MATLAB coding expertise were not readily available, LongAxis allows a user to export cell data, including position and volume, so that calculations can be carried out using other software (for example, Excel). Importantly, one can export ellipsoid orientation data from LongAxis, in the form of xyz vector components; using these data and a manually defined reference position, one can calculate cell orientation without editing the LongAxis code.

As imaging technologies and approaches continue to improve our ability to visualize the cellular basis of tissue assembly and morphogenesis, it is important that our analysis methods also evolve to take advantage of this rich source of 3-dimensional quantitative information. Tools such as LongAxis will help us connect molecular genetics to cell biology to uncover the mechanisms underlying morphogenesis and development of the visual system and other organs of interest.

Experimental Procedures

Zebrafish husbandry and mutant/transgenic lines

All zebrafish husbandry (Danio rerio) was performed under standard care conditions in accordance with University of Utah Institutional Animal Care and Use Committee (IACUC) Protocol approval (Protocol #18–02006). Embryos were raised at 28.5–30°C and staged according to time post fertilization and morphology [37]. Mutant lines were previously described: lama1^UW1 [29, 33]; pard3^fh305 [34]. In all cases, maternal-zygotic pard3 mutants (MZpard3) were used. lama1 mutant embryos were derived from heterozygous incrosses, and lama1;MZpard3 mutant embryos were derived from adults heterozygous for the lama1 mutation and homozygous for the pard3 mutation. Embryos were genotyped after imaging.

lama1^UW1 genotyping protocol.

A dCAPS strategy [38] was used with the following primers: 5’ GCAGATGCAGCAACCACAGCCAGTCATGTGACCTGCACACCGGCCAACACCT; 3’ GGCTTTCCCCCTCTGATGACACGTAC. PCR annealing temperature, 58°. PCR products were digested with DraIII, which cuts WT (231+47 bp), not mutant (278 bp). Digest products were run on 3.2% Metaphor or 1% Metaphor/1% agarose gel.

pard3^fh305 genotyping protocol.

A CAPS strategy was used with the following primers: 5’ ATTGGCTTCAGCAGTTTTAAGAAA; 3’ ATGATTGGCACTGAGTGAAGAAC. PCR annealing temperature, 61°. PCR products were digested with HpyCH4IV, which cuts mutant (87+68 bp), not WT (155 bp). Digest products were run on 3.2% Metaphor or 1% Metaphor/1% agarose gel.

RNA synthesis and injections

Capped RNA was synthesized using a pCS2 template (pCS2-EGFP-CAAX) and the mMessage mMachine SP6 kit (Ambion). RNA was purified (Qiagen RNeasy Mini Kit) and ethanol precipitated. 150 pg RNA was injected into the cell of 1-cell embryos.

Imaging

Embryos were dechorionated at 24 hpf and embedded in 1.6% low melting point agarose (in E2+gentamycin) in Delta T dishes (Bioptechs (#0420041500C)). Images were acquired using a Zeiss LSM710 or LSM880 laser scanning confocal microscope. E2+gentamycin was overlaid, and the dish covered to prevent evaporation. All imaging was performed with a 40× water-immersion objective (1.1 NA). Datasets were acquired with the following parameters: 1024×1024; 0.21 × 0.21 × 0.42 μm voxel size. The entire depth of the optic cup was imaged, resulting in z-stacks of 340–480 slices. All imaging was of live embryos, to avoid distortions that accompany tissue fixation.

LongAxis MATLAB code

The full LongAxis MATLAB code is available here with annotations:

www.kwan-lab.org/longaxis

LongAxis Segmentation Validation

Segmentation accuracy for all cells was scored manually, by selecting a subvolume, usually containing 50–70 cells. Each cell in the subvolume was examined individually against xy/xz/yz cutaways of the original image data to determine how well the segmentation matched the image data. Accuracy was scored on a scale of 1–5, with 1–4 corresponding to how well the segmentation matched the image data (1 = 90–100%; 2 = 70–90%; 3 = 50–70%; 4 = <50%), and a score of 5 representing unsuccessful segmentation resulting in fused cells.

Plots

Density, violin (with box and whisker), and stacked bar plots were generated using the ggplot2 package in R. Exponential decay equations were derived and plotted in R using the self-starting asymptotic regression function (SSasymp). Exponential decay equations followed the formula: y(t) = y_f + (y₀-y_f)e^-λt, where y is the number of excluded cells; y starts at y₀ and decays towards y_f at rate λ.

Statistics

For comparisons of length, length-width ratio, and volume between wild type embryos, and against lama1 single mutant and lama1;MZpard3 double mutant, data were compared using ANOVA, followed by Tukey’s test. This allowed for multiple comparisons between the groups (ANOVA) to evaluate for differences between the means of the populations; if differences were found, the Tukey multiple comparison test was used to derive P-values for pairwise comparisons. For comparisons of distributions of angles of deviation, a two-sample Kolmogorov-Smirnov test was carried out in R; we chose the Kolmogorov-Smirnov test because the data are continuous, and no assumptions about the underlying distribution need to be made.

Supplementary Material

1

Figure S1, associated with Figure 3. Wild type embryo (#2, #3, #4) decay curves, comparative plots of angle, length, length/width ratio, and volume.

3

Movie 1. Movie through a wild type optic cup z-stack. Dorsal view. EGFP-CAAX (membranes, gray).

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Movie 2. Cell segmentation “fly-through”: rotation of representative section of segmentation with raw image data (z-stack) passing through.

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Movie 3. Cell segmentation “fly-through”: different representative section of cell segmentation with raw image data (z-stack) passing through, including xz/yz cutaways.

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Movie 4. Extrapolation of qualitative and quantitative data from segmentation. Segmented cell is placed in minimum bounding sphere (lavender) to derive cell length; an ellipse (red) is fit to derive the long axis of the cell (blue); perpendicular to the long axis of the cell (hexagon), a minimum bounding sphere (black) is placed at the cell centroid (red dot) to derive cell width (cell outline at that plane is shown in cyan).

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Movie 5. Visualization of convergence point derivation. Three rays (representing long axes of three different cells) are shown; red dots show pairwise points of closest approach, and the convergence point (asterisk) is the mean of all pairwise convergences.

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Movie 6. Vector convergence point rotation for wild type. Mesh surface of the lens is shown for reference; red dot is lens center of mass. 3D isosurfaces display the highest density regions (10%, 30%, 50%, and 70%) of the pairwise convergence points for all cells; black dot shows calculated convergence point used for angle of deviation measurements. This demonstrates that the derived convergence point is an average of pairwise convergence points, and is different from the lens center of mass.

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Movie 7. Urchin plot with heat map for a wild type optic cup. Vectors are aligned along the long axis of the cell, length represents relative length/width ratio of the cell, and heat map represents angle of deviation from the derived convergence point. Most cells are in the blue range of colors, indicating a small angle of deviation.

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Movie 8. Movie through a lama1^UW1 single mutant optic cup z-stack. Dorsal view. EGFP-CAAX (membranes, gray).

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Movie 9. Movie through a lama1^UW1;MZpard3^fh305 double mutant optic cup z-stack. Dorsal view. EGFP-CAAX (membranes, gray).

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Movie 10. Vector convergence point rotation for single and double mutant. Mesh surface of the lens is shown for reference; red dot is lens center of mass. 3D isosurfaces display the highest density regions (10%, 30%, 50%, and 70%) of the pairwise convergence points for all cells; black dot shows calculated convergence point used for angle of deviation measurements. These volumes are much more spread out than that of the wild type (compare to Movie 6); this shows the greater variability in position of the pairwise convergence points.

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Movie 11. Urchin plot with heat map for a lama1^UW1 single mutant optic cup. Vectors are aligned along the long axis of the cell, length represents relative length/width ratio of the cell, and heat map represents angle of deviation from the derived convergence point. Note the patches of vectors in the red-orange-yellow range of colors, indicating >60° angle of deviation.

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Movie 12. Urchin plot with heat map for a lama1^UW1;MZpard3^fh305 double mutant optic cup. Vectors are aligned along the long axis of the cell, length represents relative length/width ratio of the cell, and heat map represents angle of deviation from the derived convergence point. Note the patches of vectors in the red-orange-yellow range of colors, indicating >60° angle of deviation.

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Table 1. Numbers of segmented cells analyzed for each condition and embryo genotype.

2

Figure S2, associated with Figure 5. lama1 single mutant and lama1;MZpard3 double mutant decay curves.

Highlights.

• Previously arduous to quantify/visualize 3D cell shape in zebrafish neural retina

• LongAxis enables quantitative analysis of retinal cell morphology and orientation

• Retinal cell shape and orientation are now quantitative readouts of gene function

• Can assay changes in cell shape at the population level throughout the retina