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.

Light Sheet Microscopy

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 Parhyale, 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 Parhyale 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.

[1] U. Krzic, S. Gunther, T. E. Saunders, S. J. Streichan. & L. Hufnagel, Nature Methods 9, 730–733 (2012).

[2] A. D. Edelstein, M. A. Tsuchida, N. Amodaj, H. Pinkard, R. D. Vale & N. Stuurman, Journal of Biological Methods 1, e10 (2014).

[3] S. Preibisch, F. Amat, E. Stamataki, M. Sarov, R. H. Singer, E. Myers & P. Tomancak, Nature Methods 11, 645–648 (2014).

[4] C. Wolff, J.-Y. Tinevez, T. Pietzsch, E. Stamataki, B. Harich, L. Guignard, S. Preibisch, S. Shorte, P.J. Keller, P. Tomancak & A. Pavlopoulos, eLife 7, e34410 (2018).

[5] S. Berg, D. Kutra, T. Kroeger, C. N. Straehle, B. X. Kausler, C. Haubold, M. Schiegg, J. Ales, T. Beier, M. Rudy, K. Eren, J. I. Cervantes, B. Xu, F. Beuttenmueller, A. Wolny, C. Zhang, U. Koethe, F. A. Hamprecht & A. Kreshuk,  Nature Methods 16, 1226–1232 (2019).

[6] P. Marquez-Neila, L. Baumela & L. Alvarez, IEEE Transactions on Pattern Analysis and Machine Intelligence 36, 2–17 (2014).

[7] M. Kazhdan & H. Hoppe, ACM Transactions on Graphics 32, 1–13 (2013).

[8] N. Aigerman & Y. Lipman, ACM Transactions on Graphics 34, 1–12 (2015).

[9] W. Zeng & X. D. Gu, X. D. Ricci Flow for Shape Analysis and Surface Registration, Springer New York, New York, NY, (2013).

[10] H. Le, T.-J. Chin & D. Suter,  2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2016-Decem (IEEE, 2016), 2507–2516.

Code needed to process/view the simulated data can be found at https://github.com/DillonCislo/DefectDrivenMorphogenesisPublic.git