DOI: 10.5061/dryad.c2fqz61d4
title: Active cell divisions generate fourfold orientationally ordered phase in living tissue

description: Morphogenesis, the process through which genes generate form, establishes
 tissue scale order as a template for constructing the complex shapes of
 the body plan. The extensive growth required to build these ordered
 substrates is fuelled by cell proliferation, which, naively, should
 destroy order. Understanding how active morphogenetic mechanisms couple
 cellular and mechanical processes to generate order — rather than
 annihilate it — remains an outstanding question in animal development. We
 show that cell divisions are the primary drivers of tissue flow leading to
 a fourfold orientationally ordered phase. Waves of anisotropic cell
 proliferation propagate across the embryo with precise patterning. Defects
 introduced into the nascent lattice by cell divisions are moved out of the
 tissue bulk towards the boundary by subsequent divisions. Specific cell
 proliferation rates and orientations enable cell divisions to organize
 rather than fluidize the tissue. We observe this using live imaging and
 tissue cartography to analyse the dynamics of fourfold tissue ordering in
 the trunk segmental ectoderm of the crustacean Parhyale hawaiensis
 beginning 72 hours after egg laying. The result is a robust, active
 mechanism for generating global orientational order in a non-equilibrium
 system that sets the stage for the subsequent development of shape and
 form.
description: <strong>Light Sheet Microscopy</strong>
 For live imaging of transgenic parhyale embryos, we utilized a
 custom-built MuVi SPIM [1]. This microscope has two excitation and two
 detection branches. Both used water dipping objectives (App LWD 5x, NA
 1.1, Nikon Instruments Inc. for detection, and CFI Plan Fluor 10x, NA 0.3
 for excitation). Furthermore, each detection branch consisted of a filter
 wheel (HS-1032, Finger Lakes Instrumentation LLC), with emission filters
 (BLP02-561R25, Semrock Inc.), tube lens (200 mm, Nikon Instruments Inc.)
 and a camera (sCMOS - Hamamtsu Flash 4.0 V2), with effective pixel size of
 0.262 mm. The illumination branches featured a tube lens (200 mm, Nikon
 Instruments Inc.), scan lens (S4LFT0061/065, Sill optics GmbH and Co. KG),
 galvanometric mirror (6215 hr, Cambridge Technology Inc.), and discrete
 laser line (561LS OBIS 561nm). Optical section employed a translation
 stage from Physik Instrumente GmbH and Co. KG (P-629.1CD with E-753
 controller), a rotation stage (U-628.03 with C-867 controller), and a
 linear actuator (M-231.17 with C-863 controller).  
 Data Post Processing and Microscope Automation
 To operate the microscope, we used Micro Manager [2], installed
 on a Super Micro 7047GR-TF Server, with 12 Core Intel Xeon 2.5 GHz, 64 GB
 PC3 RAM, and hardware Raid 0 with 7 2.0 TB SATA hard drives. For each
 sample, we recorded 4 views, separated by 90° rotated views, with optical
 sectioning of 2 μm, and temporal resolution of 5 min. We embedded the
 embryos in agarose-containing beads as a diagnostic specimen. This was
 used to register individual views into a common frame by utilizing the
 Fiji multi-view deconvolution plugin [3], resulting in a final image with
 isotropic resolution of 0.2619 μm. Data Set Curation
 for Quantitative Analysis A total of four embryos were
 used to generate the analysis in this work. Due to the challenges
 associated with live imaging of <em>Parhyale</em>, it was not
 possible to image all of the embryos for the complete duration of germband
 extension. Two data sets featuring transgenic embryos with a fluorescent
 nuclear marker were produced. One embryo was imaged from 55.8–91.9 h AEL,
 but only the period from 72.5–91.9 h AEL was included in the analysis
 since the first part of the movie preceded germband extension. A second
 extended movie of a transgenic embryo with a fluorescent nuclear marker,
 filmed between 79.4–93.0 h AEL, was also analyzed and tracked. This second
 dataset had been previously analyzed in [4], without the use of tissue
 cartography (see below). Two movies featuring a lipid membrane dye FM-464
 marker, rather than a nuclear marker, were also filmed between 75.8–79.4 h
 AEL and 80.0–83.1 h AEL, respectively.  Extraction of
 Dynamical Surfaces of Interest The output of the
 lightsheet microscope is a time series of 3D grids whose voxel values
 correspond to intensity of the nuclear label or lipid dye. Extraction of
 the dynamical surface of interest from these data sets was performed in
 two stages: (1) 3D surface extraction and (2) 2D pullback map
 construction. In the surface extraction stage, the volumetric data of a
 representative time point was classified over the nuclear label/dye using
 the machine learning software Ilastik [5]. The resultant probability map
 was then fed into MATLAB and a static surface of interest was extracted
 using the morphological active contours method [6], a type of
 level-set-based segmentation algorithm well suited to segmented
 complicated, closed surfaces. The output of this segmentation is a 3D
 binary level-set, with identical dimensions to the data, where `1'
 values corresponded to the interior of the closed surface (all embryonic
 tissue and yolk) and `0' values corresponded to regions external to
 the <em>Parhyale</em> egg.  The boundary of this binary
 level-set is point cloud, a subset of which included voxels corresponding
 to the embryonic tissue. This point cloud was subsequently triangulated
 using Poisson surface reconstruction [7]. The result was a topologically
 spherical mesh triangulation. In the next processing
 step, this static surface was used as a seed to extract the dynamically
 changing surface at each time point. At this developmental stage, the
 embryonic tissue is a topological disk sitting on top of the spherical
 yolk. The embryonic tissue was therefore contained in a disk-like
 subregion of the sphere-like surface triangulation. In order to extract
 this region of interest, the entire sphere-like mesh was mapped into the
 plane using the orbifold Tutte embedding method [8]. This method generates
 a topologically consistent parameterization of the sphere in the plane
 allowing us to view the entire surface at once with minimal geometric
 distortion. Next, a static submesh of the region of interest on the static
 surface was selected by hand using the orbifold pullbacks. Although
 static, this region of interest was large enough that it contained all
 relevant sections of the embryo as it grew and deformed over time.  A set
 of `onion layers' was then created by displacing the submesh along
 its positive and negative normal directions. A stack of pullback images
 was then created for each time point with one image in the stacks for each
 displaced onion layer. The number of layers and the inter-layer spacing
 were chosen so that all of the geometric features of the dynamic surfaces
 were captured for the various time points somewhere within the image
 stack. These stacks were then fed back into Ilastik and batch processed
 again over the nuclear label/dye. The result was a time-dependent field of
 normal displacements over the static seed surface that transformed the
 static surface into the corresponding dynamic surface for each time point.
 These dynamic triangulations of the evolving region of interest were then
 separately mapped into the unit disk conformally via Ricci flow [9]. Such
 a conformal mapping is only unique up to a Möbius automorphism of the unit
 disk. In other words, unless care is taken to register the pullbacks, the
 resultant images may be wildly misaligned in pullback space from time
 point to time point. With this in mind, the time series of conformal
 pullbacks was iteratively registered to fix the conformal degrees of
 freedom within the pullbacks. Essentially, corresponding mesh vertices at
 subsequent times were approximately matched in 2D by finding an optimal
 Möbius automorphism of the unit disk that registered as many points as
 possible without sacrificing the conformality of the parameterization
 [10]. The final result was a sequence of maximally aligned conformal
 pullbacks of the growing embryo to the plane. 
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description: Code needed to process/view the simulated data can be found at
 https://github.com/DillonCislo/DefectDrivenMorphogenesisPublic.git