Extended Data Fig. 4: Creating and comparing integrated average cells throughout the shape space via SHE coefficient-based parameterization and 3D morphing.

a. “3-channel original z-stack” (bottom left image), shows a 3D visualization of the original FP intensities of tagged mitochondria (grayscale) in a single cell and nucleus, visualized via cell-membrane dye (magenta) and DNA dye (cyan). Moving rightward along the bottom row are the steps to create the PILR of the mitochondria via the FP signal in this cell. “3D reconstruction” (second image) shows the SHE-based 3D reconstruction meshes of the segmentations of this cell and nucleus. Next, “cellular map**” shows the result of interpolating the SHE coefficients to create a series of successive 3D concentric mesh shells (different colours) from the centroid of the nucleus (black dot) to the nuclear (inner) and then to the cell (outer) boundary to create the nuclear and cytoplasmic map**, respectively. The intensity values in the FP channel are recorded at each mesh vertex location, resulting in the “PILR” that is shown in matrix format in the fourth image. “Voxelization” shows the result when this PILR is converted back into a 3D image, voxel by voxel, into the same reconstructed cell and nuclear shape. Because this internal map** is discrete, the resultant reconstructed image will have gaps. At the top, “original FP image (left) is the original image and “nearest neighbour interpolation” (right) is the voxelized PILR, now with the gaps filled using nearest neighbour interpolation. Voxel-wise Pearson correlation in 3D is used to compare these original and reconstructed FP images. b. Example PILRs (in matrix format as in a) for one cell for each of five cellular structures. Top view and side view 1 are shown on the far left. Top and bottom PILR matrices for each structure are based on the original FP image (grayscale on black background) or the structure segmentations (binary on white background), respectively. c. The FP-image-based PILR takes all intensities in the image into account, including any FP-tagged protein not localized to the target structure that the protein represents. For example, FP-tagged paxillin localized to matrix adhesions at the bottom of the cell but also throughout the cytoplasm. Two images of multiple cells (cell membrane indicated by magenta lines) in an FOV with labelled matrix adhesions (via paxillin) at two z positions in the z-stack. Top left triangles in each image show the original FP image. Matrix adhesions are visible near the bottom of the cells (left) but considerable FP-tagged paxillin signal is visible both at the bottom and centre (right) of cells. However, the segmentation target defined for this cell line included only the high intensity regions representing the matrix adhesions near the bottom of the cells. Bottom right triangles in each image show the result of the matrix adhesion specific segmentation. Total numbers of acquisition days, FOVs, and cells for FP-tagged paxillin are in Supplementary Data 1 and Extended Data Fig. 1d. d. Using the structure segmentation-based PILR permits the creation of average morphed cells containing the locations of the cellular structures that each tagged protein represents. Average morphed cells representing matrix adhesions (top row) and mitochondria (bottom row) generated using either the original FP images (left column) or the target structure segmentations (right column) of cells within the 8-dimensional sphere morphed into the mean cell shape. The analyses in this paper focus on the structure segmentation-based PILRs; but conceptually the same approach could also be applied to the raw intensity images. e. Bar graphs of voxel-wise Pearson correlation between original intensity images of FP-tagged proteins (left) or of structure segmentations (right) and the images reconstructed from the PILR. Error bars represent ± one standard deviation around the mean (n = 32 cells per structure). Cells were selected from centre bin of Shape Mode 1. The correlation for cohesins (via segmentations) is indicated with a striped fill pattern. This structure has a significantly changing target structure segmentation depending on how much tagged cohesin has re-entered the nucleus after mitosis, causing the much lower correlation value (Extended Data Fig. 2d). f. Example cell from the top of (a) to show the original and PILR-based reconstructed image but here based on the structure segmentations. Numbered insets are zoomed in regions. Cell and nuclear boundaries in a–f are shown in magenta and cyan lines, respectively. g. Overview of the process to calculate the average location similarity between all pairwise-combinations of the 25 cellular structures within the 8-dimensional shape space sphere. The 2D pixel-wise Pearson correlation was calculated between pairs of averaged PILRs for each structure. This created a correlation matrix including each of the 25 cellular structures with elements of this matrix representing the average location similarity between two cellular structures. h. Heat maps for the −2σ and 2σ shape space map points for each of the eight shape modes as in Fig. 3e, but here heat map values correspond to the difference in average structure similarity between the mean cell shape and either, the −2σ and 2σ shape space map points (bottom and top triangles, respectively), for each of the eight shape modes (numbers of cells in Supplementary Data 1). Due to technical considerations related to the PILR construction (Methods) or due to especially low number of cells in some bins (Supplementary Data 1), some structures displayed changes in the magnitude of the average location similarity with other structures in the shape mode bins furthest from the mean (−2σ and 2σ, mainly for Shape Mode 1) and so these decreases may not be biologically meaningful. Additional difference heat maps for intermediate shape mode bins are available in Supplementary Data  1.

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