Origami: Single-cell oriented 3D shape dynamics of folding epithelia from fluorescence microscopy images

A common feature of morphogenesis is the formation of three-dimensional structures from the folding of two-dimensional epithelial sheets aided by spatio-temporal cell shape changes at the cellular-level. Studying cell shape dynamics and polarised processes that underpin them, requires orienting cells within the epithelial sheet. In epithelia with highly curved surfaces, assigning cell orientation can be difficult to automate in silico. We present ‘Origami’, a MATLAB-based image analysis pipeline to compute oriented cell shape-features. Our automated method accurately computed cell orientation in regions with opposing curvature in synthetic epithelia and fluorescence images of zebrafish embryos. As proof of concept, we identified different cell shape signatures in the developing zebrafish inner ear, where the epithelium deforms in opposite orientations to form different structures. Origami is designed to be user-friendly and is generally applicable to fluorescence images of curved epithelia.


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A common feature of morphogenesis is the formation of three-dimensional structures from the 24 folding of two-dimensional epithelial sheets aided by spatio-temporal cell shape changes at the 25 cellular-level. Studying cell shape dynamics and polarised processes that underpin them, 26 requires orienting cells within the epithelial sheet. In epithelia with highly curved surfaces, 27 assigning cell orientation can be difficult to automate in silico. We present 'Origami', a MATLAB-28 based image analysis pipeline to compute oriented cell shape-features. Our automated method 29 accurately computed cell orientation in regions with opposing curvature in synthetic epithelia and 30 fluorescence images of zebrafish embryos. As proof of concept, we identified different cell shape 31 signatures in the developing zebrafish inner ear, where the epithelium deforms in opposite 32 orientations to form different structures. Origami is designed to be user-friendly and is generally 33 applicable to fluorescence images of curved epithelia.

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Complex morphologies across taxa and tissue types are generated through the deformation of 37 epithelial sheets [1][2][3]. In the embryo, many developing epithelia form highly curved surfaces.

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Epithelial folding processes are driven by polarised mechanical forces and involve three-39 dimensional changes in shape at the cellular level [4,5]. Fluorescence imaging techniques have 40 made it possible to follow such shape changes at cellular resolution, in vivo and in real-time [6-41 8]. These imaging advances have consequently driven the development of tools to quantify 42 epithelial dynamics, especially cell shape changes.

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Orienting cells relative to the known overall polarity of the epithelial sheet is critical, as cell 54 polarised biomechanical processes drive cell shape changes; constriction or expansion can 55 occur along either the apical [24,25] or baso-lateral [26] cell surfaces and can be detected by any 56 skew in mass distribution within a cell along an apico-basal axis of symmetry. Epithelial folding 57 may be initiated or influenced by cell proliferation, cell death, cytoskeletal remodelling, or 58 changes in cell surface properties [27,28]. These mechanisms can lead to changes in cell shape 59 features, including cell height and width, volume, surface area and sphericity.

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Cell orientation or polarity can be defined along the plane of the epithelium (planar cell polarity) 62 or perpendicular to the epithelial plane, along the apico-basal axis of the cell. Existing automated 63 methods for assigning polarity often rely on additional biochemical markers for polarity [29][30][31] We introduce a new automated tool, Origami, for extracting shape features oriented along the 80 apico-basal axis by reconstructing the epithelial surface using a triangular mesh (Fig 1). Origami 81 applies to a wide range of geometries of specimens undergoing morphogenesis and computes 82 the apico-basal axis of the epithelial sheet for known epithelial organisation without requiring 83 additional labels for polarity . We showcase the versatility of our method using data from an 84 assortment of structures at a range of developmental stages within the otic vesicle (developing 85 inner ear) of zebrafish embryos.

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Design and Implementation

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The Origami pipeline is preceded by a membrane-based segmentation step. For this, we 89 employed the open-source ACME segmentation software [14]. The segmented data are 90 subjected to two main operations within Origami; epithelial orientation assignment (Fig 1b) and 91 extraction of shape features (Fig 1c). triangulates the centroids of the segmented cells in 3D space using the Crust algorithm [35,36] 99 (Fig 1b). The Crust method computes a surface mesh from unorganised pointscell centroids in 100 our case, using the Voronoi diagram of the cell centroids.

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Following this, our automated method corrects imperfections in the estimated surface mesh that 103 can cause polarity assignment errors. The mesh is refined by removing duplications (in vertices 104 or triangular faces computed) and any self-intersecting triangular faces. Non-manifold edges, 105 5 that is, those edges shared by more than two triangular faces, are re-meshed as a manifold 106 mesh using the ball-pivoting algorithm [37,38].

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The triangular faces of the refined mesh are ordered in the same direction, and so by applying 109 the right-hand rule when generating normal vectors to the surface mesh, these vectors all point 110 to the same side of the surface (Fig 1b). In the developing zebrafish otic vesicle, the otic In our analysis pipeline, 3D geometric moments were computed from triangular surface meshes 132 generated for each individual segmented cell [43]. In this method, the integral defining the 133 geometric moments of each segmented cell is split into a sum:    (Table 1 and Fig 3).

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The differences in surface area are likely to be attributed to differences in sphericity between the 298 cells in the three structures, but not in dimensions, as the transversal and longitudinal spread 299 showed no significant differences. 300 301 302  The parameters used to segment our datasets in ACME were different for the synthetic dataset 575 and the real light-sheet data in part, due to differences in voxel resolution (0.2 µm x 0.2 µm x 0.2 576 µm for the synthetic dataset and 0.1 µm x 0.1 µm x 0.5 µm for the light-sheet data). These 577 parameters were as follows; 578 579 For synthetic epithelia: