Establishment of a morphological atlas of the Caenorhabditis elegans embryo using deep-learning-based 4D segmentation

The invariant development and transparent body of the nematode Caenorhabditis elegans enables complete delineation of cell lineages throughout development. Despite extensive studies of cell division, cell migration and cell fate differentiation, cell morphology during development has not yet been systematically characterized in any metazoan, including C. elegans. This knowledge gap substantially hampers many studies in both developmental and cell biology. Here we report an automatic pipeline, CShaper, which combines automated segmentation of fluorescently labeled membranes with automated cell lineage tracing. We apply this pipeline to quantify morphological parameters of densely packed cells in 17 developing C. elegans embryos. Consequently, we generate a time-lapse 3D atlas of cell morphology for the C. elegans embryo from the 4- to 350-cell stages, including cell shape, volume, surface area, migration, nucleus position and cell-cell contact with resolved cell identities. We anticipate that CShaper and the morphological atlas will stimulate and enhance further studies in the fields of developmental biology, cell biology and biomechanics.

(1) 3DUnet During the training stage, an input of size 64 × 64 × 64 was randomly cropped from resampled and annotated images of size 205 × 285 × 134. The batch size was set to 4. Adam optimization was used to train the network with an initial learning rate of 1 × 10 !" . Other settings, including the network structure, were kept consistent with the original repository. Considering the limitation of our computation resources, raw images were resized to 144 × 144 × 144, and corresponding output was resized back to the original size during the inference stage. As the output is a binary membrane mask, the nucleus location was used as a seed for the watershed segmentation in the postprocessing stage.
(2) CellProfiler An advanced pipeline was designed to segment membranes in 3D. Specifically, the membrane channel was processed by RescaleIntensity, GaussianFilter, Threshold and Watershed3DWithEdt sequentially. Here, the Watershed3DWithEdt is a user-defined tool which can apply watershed transformation to the binary membrane mask with the nucleus centroid as the seed. The CellProfiler project file is publicly available at our code depository.

(3) FusionNet
FusionNet was trained and tested on 2D slices obtained from the volumetric data. Slices were resized to 256 × 256 in both the training and testing stages. To obtain the volume result, output slices were stacked together after being resized back to the original dimensions. All other parameters were kept as recommended in the FusionNet paper.
(4) RACE RACE provides a user-friendly GUI tool to segment data. We downloaded the tool and processed C. elegans data according to the user's manual. RACE Seeding was set to nuclei and Intensity Parameters were fixed. We experimentally tuned the Microscope/Specimen Parameters via visual inspection of preliminary results.
Parameters, such as Max 3D Cell Volume and Max 2D Segmentation Area, were adaptively changed for the embryo images at different cell stages. All parameter settings for RACE can be found at our code depository.

(5) SingleCellDetector
Based on the framework used for single cell detection, we retrained the network with sliced raw image and annotation pairs. To get similar results as reported in the original paper, only the data loader parameter was changed, while keeping all other parameters as previously reported. However, we did not divide the normalized image intensity by the middle value, which was zero in our case. Segmentation slices were rendered as a 3D volume to obtain our final predicted distance map. We also designed a 3D version of SingleCellDetector, but the corresponding result was of much lower quality than the result of the original 2D SingleCellDetector. This might be due to a lack of sufficient training data. Thus, these results are not reported.

Supplementary Note 2
In CShaper, there are three discriminative situations whereby the nuclei derived from StarryNite and AceTree 8 cannot be successfully paired to a segmented region: (1) The boundary between two cells (not sisters) is too weak to be extracted by DMapNet. As a result, two cells are segmented as one during the watershed transformation.
(2) Membrane signal is lost at the boundary of the embryo, which leads to the leakage of the background into the embryo.
(3) In CShaper, we determine the accomplishment of a cell division by checking the signal intensity of the line connecting two sister cells' nuclei. However, when the intensity drops at the middle of a cell's lifespan, two cells may be renamed as their mother cell, even though the cell division is completed.
Based on these unsuccessful pairs, we evaluated the segmentation accuracy at the object level in the section Results.

Supplementary Note 3
Given the close-packing structure of equal spheres, the threshold for cell-cell contact area was estimated by solving the problem of how many cells with a radius of 1/3 can occupy the space formed by a neighboring cell with a radius of 1 (Supplementary Figures 17b, c, d, e). To this end, we first generated a hexagonal close-packed structure where a central cell * # is surrounded by 12 neighbors * $~$& . By taking * # as the origin, we established a spherical coordinate system for these 13-unit cells. Thereafter, we replaced one of the neighboring cells, for example, * $ , with + ' identical cells. To search for the maximum radius , ()* that can accommodate + ' cells, we determine + ' cell centers whose inclination and azimuth were sampled from a normal distribution with * $ 's center as the mean and π/3 as the standard deviation. Finally, the radius , ()* of the + ' cells was maximized under the condition such that they were exactly in contact with cell * # but did not overlap each other. Here, + ' was set as 1-5. Sequentially, we derived the , ()* through a trial-and-test method with 10 + trials based on previous samples.
Noticeably, the threshold value for relative contact area obtained here (1/48 ≈ 2.08%) was smaller than the one previously used (6.5%), which was derived from known cell pairs with Notch signaling 9 . However, the contact of the C-ABar cell with Wnt signaling was not previously considered 10 . This contact has a smaller relative contact area such that only 2 of the 17 embryos reach the old threshold value. However, our new assigned value of 1/48 (≈ 2.08%) based on geometrical modeling permits a higher pass rate of 15/17. Considering the outliers of C-ABar and MSappp-ABplpppp contacts, false negatives may be unavoidable, as the actual sensitivity of intercellular signaling is still unknown (see sections Results and Discussion).