Cellular organization can be defined as the sum total of how all of a cell’s components are arranged within it, generating an overall characteristic size, shape and appearance for a cell of a given type. The models and laws for understanding and predicting cellular organization and its pivotal role as a determinant of cellular phenotype remain to be determined. A first step towards this goal is to identify interpretable and testable principles, or ‘rules’, that govern cell organization. One approach is through a systematic analysis of the locations and quantitative relationships among many different cellular structures within large populations of cells and how these relationships vary with the morphology and behaviour of the cell itself. To define cell organization precisely and quantitatively, however, requires measuring multiple distinct aspects of organization; for example, the size (or number) and shape of each structure, its locations in the cell, its direct and indirect interactions with all the other structures and the temporal changes. A population of putatively identical cells might exhibit substantial cell-to-cell variability as they respond sensitively to their ever-changing internal and external contexts, such as the cell cycle, differentiation or changes in their environment. Furthermore, an abnormal cell quantitative phenotype might exhibit not only a shift in the mean but also a shift in the variability5. Thus, a meaningful description of cell organization requires a formal definition and categorization that includes robust, objective and quantitative measurements of both the mean and the variability in the descriptors of organization.

Creating such a nuanced, formal quantitative view of cell organization will enable the statistical comparisons that identify generalizations and elucidate how cell organization differs within and across different cell populations and during transitions among normal or abnormal cell behaviours. It will also permit deeper investigations that integrate cell organization with cell behaviour and cell identity, including the integration of distinct data types (for example, images and various ‘omics), leading to more meaningful and useful definitions of cell types and states6,7,8,9,10,11,12.

We have initiated our study of cellular organization by focusing on the integrated organization of 25 cellular structures that represent major intracellular machines and organelles, generating an extensive, high-replicate baseline dataset of 3D live-cell images of normal human induced pluripotent stem cells (hiPS cells): the WTC-11 hiPSC Single-Cell Image Dataset v1. This dataset was used to develop a generalizable and extensible quantitative analysis framework based on two conceptually distinct coordinate systems to analyse the cells. The first coordinate system defines the cell and nuclear shape of each individual cell with respect to the total variation in the observed population. The second coordinate system specifies the spatial location of every cellular structure within an individual cell. When combined, the two coordinate systems permitted the development of a suite of statistical measurements to quantify distinct aspects of cell organization, formally distinguishing among three kinds of change while controlling for the effects of natural cell-shape variation: (1) changes in the average location of individual structures; (2) changes in the variability of these locations; and (3) changes in the pairwise interactions among structures. We applied our framework to three subsets of cells in the dataset—the large baseline population of cells in interphase, the cells at the outer edges of the epithelial-like hiPS cell colonies, and cells undergoing reorganization during early mitosis—and developed data-visualization approaches to summarize these results in a way conducive to data exploration.

WTC-11 hiPSC Single-Cell Image Dataset v1

hiPS cells represent an early embryonic cell state and are a useful model system for human cells. hiPS cells are naturally immortal, karyotypically normal and can be induced to differentiate into other cell types13. We previously developed methods and quality-control workflows to create the ten inaugural hiPS cell lines in the Allen Cell Collection14 (described at, each expressing a single endogenously tagged protein representing a particular organelle or cellular structure. For this study, we created 15 new Allen Cell Collection lines that provide a holistic view of cells at the level of 25 of their major organelles, cellular structures and compartments (Fig. 1a). We built an automated and standardized microscopy imaging pipeline to generate the living colonies, imaged the cells in 3D using spinning-disk confocal microscopes and then processed the images to create the WTC-11 hiPSC Single-Cell Image Dataset v1 (Fig. 1 and Extended Data Fig. 1). We included fluorescent cell-membrane and DNA dyes to reference the locations of fluorescent protein (FP)-tagged cellular structures relative to the cell boundary and the nucleus or mitotic chromosomes. For each of the 25 cellular structures, we used 3D segmentations of the tagged protein to identify the location and morphology of the structure itself, rather than the location of the FP-tagged protein signal (Extended Data Fig. 2). The tightly packed, epithelial-like nature of hiPS cells, as well as the need for highly accurate 3D cell boundaries to minimize the misassignment of cellular structures to neighbouring cells required deep-learning-based segmentation approaches to create a robust, scalable and highly accurate 3D cell and nuclear segmentation algorithm15 (Methods), which was applied to all 18,100 fields of view (FOVs) to extract the 215,081 cells presented in this dataset (Extended Data Fig. 1). Both the FOV images and the single-cell dataset are available as downloadable files (see Data availability) and through interactive online visual-analysis tools that require no software installation or expertise ( For the analyses described below, we used subsets of the dataset including the baseline interphase dataset (202,847 cells), cells at the edge of colonies (5,169 cells) and cells in early mitosis (3,182 cells) (Extended Data Fig. 1d).

Fig. 1: The WTC-11 hiPSC Single-Cell Image Dataset v1 includes 25 cell lines that represent key cellular structures located throughout all of the major compartments of the cell.
figure 1

a, Maximum intensity projections of one representative cell example per cellular structure, based on segmentations of the structure (white), the cell membrane (magenta) and the DNA (cyan). The fluorescently tagged protein representing the structure and the cellular compartment (Fig. 3d) are indicated. DFC, dense fibrillar component; ER, endoplasmic reticulum; GC, granular component. b, Top and side views (single slice) of hiPS cells with FP-tagged microtubules (via α-tubulin), grown in tightly packed, epithelial-like colonies and labelled with cell-membrane (magenta) and DNA (cyan) dyes to permit imaging and segmenting of cells and nuclei. Cells were most frequently imaged halfway towards the centres of large, well-packed colonies (blue) where they behave most consistently, but were also imaged at other locations within the colony, such as at the edges of colonies (red). zlab denotes the lab frame of reference. c, Three-dimensional visualization of cell and DNA segmentations within a colony of hiPS cells. Total numbers of acquisition days, FOVs and cells per cellular structure are in Supplementary Data 1 and Extended Data Fig. 1d. Scale bars, 10 µm.

A PCA-based cell and nuclear shape space

To embrace the great diversity of the 202,847 3D images of cells in interphase spanning 25 cellular structures, and to directly compare cellular organization across this large population, we built a cell and nuclear shape-based coordinate system (Fig. 2), adapting a standard principal component analysis (PCA)-based dimensional reduction approach16. We aligned all cells along their longest axis in the xy plane, preserving their biologically relevant, epithelial-like apical–basal axis. We then used a spherical harmonic expansion (SHE)17,18 to accurately parameterize each 3D cell and nuclear shape with a set of orthogonal periodic basis set functions, defined on the surface of a sphere (Fig. 2a and Extended Data Fig. 3). The joint vectors for all cells (578 SHE coefficients) were then subjected to PCA. We found that the first eight principal components represented about 70% of the total variance in cell and nuclear shape (Fig. 2b). Thus, with this dimensionality reduction, the cell and nuclear shapes for each individual cell can be approximately reconstructed from a small vector with only eight components. This dimensionality reduction also organizes the cells into a simple, intuitive eight-dimensional (8D) generative ‘shape space’. For example, the origin (0,0,0,0,0,0,0,0) of the shape space can be reconstructed through the values of the SHE coefficients representing this location in the 8D coordinate system, and can then be visualized as an idealized cell shape that statistically represents the average, or mean, shape (‘mean cell shape’) of all of the cells in the dataset (Fig. 2c). Similarly, idealized shapes can be reconstructed by traversing across each of the eight orthogonal axes in the shape space (Extended Data Fig. 3b).

Fig. 2: A PCA-based cell and nuclear shape space reveals interpretable modes of hiPS cell-shape variation.
figure 2

a, Segmented 3D images of a cell and its nucleus are rotated in the xy plane by θcell degrees around the cell centroid such that the longest axis of the cell is parallel to the x axis. These aligned images are the input for SHE of degree Lmax = 16, resulting in a total of 578 SHE coefficients (289 for each the cell and the nucleus), which are used to reconstruct the cell and nuclear shape and nuclear location with high accuracy. xlab, ylab and zlab denote the lab frame of reference and xcell and ycell the rotated cell frame of reference. Scale bar, 10 μm. b, Frequency of cells per map point bin (left) and explained variance (right) for the first eight principal components (PCs) of the PCA applied to the SHE coefficients for interphase cells (n = 202,847). Blue denotes one map point bin. c, Eight shape modes comprise the cell and nuclear shape space. Each is a normalized PC (standard deviation (s.d.), σ, units) sampled at nine map points (−2σ to 2σ in steps of 0.5σ). Three-dimensional shape reconstructions can be created at each of these map points—here yellow dots at the origin (0,0,0,0,0,0,0,0)—using an inverse PCA transform and its resultant SHE coefficients. Three 2D views of the 3D shape are shown. d, Most relevant 2D view of 3D shapes reconstructed at each of the nine map points for each of the eight shape modes (given names that can be interpreted by humans). Supplementary Video 1 shows all three 2D views. The centre bin in all modes is the identical mean cell shape. e, Overlay of 2D views of the cell (magenta) and nucleus (cyan) for the two most extreme map points (at −2σ, lighter, and 2σ, darker) of each shape mode.

Source data

To build a human-interpretable understanding of the modes of shape variation in our population, we reconstructed cell and nuclear shapes at regular intervals along every axis of this shape space (Fig. 2d and Supplementary Video 1). These idealized cells represent ‘map points’ within the shape space that can be used to identify and cluster individual real cells that are similar in shape to each idealized map point and to each other. Intuitively, these mathematically orthogonal modes of shape variation appear to describe expected variable cell-shape features that are independent of one another. Shape mode 1 appeared to largely reflect the height of the cell (Extended Data Fig. 3c), which was mainly determined by the surface area of the hiPS cell colony and the position of the cell in the colony (Supplementary Methods). Shape mode 2 appeared to largely reflect the overall volume of the cell, representative of cell-cycle progression. The correlation between cell height and cell volume was relatively modest (R = 0.34; Extended Data Fig. 3c), meaning that cells with a given height may have a wide range of volumes and vice versa. Shape mode 1 and shape mode 2 thus disentangle cell volume and cell height from each other. The remaining shape modes 3 to 8 represented other systematic ways in which the shapes of these epithelial-like cells might vary, such as tilting along the major or minor xy axes (shape modes 3 and 4). In shape modes 1, 2 and 5, nuclear shape changed concomitant with cell shape, whereas for the other shape modes it was the position and orientation of the nucleus within the cell that adjusted concomitant with cell shape (Fig. 2d,e and Supplementary Video 1).

Integrated average morphed cells

This standardized cell and nuclear shape space permits the clustering of similarly shaped cells and thus facilitates an investigation of the location of cellular structures within the confines of cells with similar 3D outer cell boundaries and nuclear spatial constraints. For example, to determine the average locations of cellular structures within the mean cell and nuclear shape, we first identified all of the cells within an ‘8-dimensional sphere’ with its origin at the very centre of the shape space encompassing the 35,636 cells that lie in this region closest to this origin (Fig. 3a and Methods). To directly and quantitatively compare the locations of each of the 25 cellular structures in these relatively similarly shaped individual cells, we developed an intracellular location coordinate system that took advantage of the SHE describing the outer cell boundary, the outer nuclear boundary and the centre of the nucleus and then interpolated between the relevant SHE coefficients. This permitted us to map the presence or absence of a structure within an individual cell at all of the possible points along these concentric 3D shells and store this information in a parameterized intracellular location representation (PILR). We could then ‘morph’ the locations of this structure, through the PILR, into the equivalent locations in an identically bounded reconstructed cell shape that represents that cell’s actual shape (Fig. 3b, Extended Data Fig. 4 and Methods). For each structure, we averaged the PILRs across all of the similarly shaped cells in the 8-dimensional sphere and then morphed the average PILR into the equivalent locations within the mean cell shape, creating the ‘average morphed cell’ for that structure (Fig. 3b and Extended Data Fig. 5). These average morphed cells represent the relative likelihood of a structure being at a location in the cell, conceptually similar to previous approaches that have been used to analyse images of cells grown on micropatterns19. We then combined these 25 average morphed cells to create an integrated visualization of the average locations of all 25 structures (Fig. 3c and Supplementary Video 2).

Fig. 3: Creating an average pairwise spatial interaction map of cellular structures.
figure 3

a, Diagram illustrating the clustering of the 35,633 cells closest to the origin of an 8-dimensional sphere centred at the origin of the shape space. b, Creating average morphed cells. Top left, 3D visualization of the segmentations of a cell (magenta), nucleus (cyan), and cellular structure (here Golgi in white). Bottom left, the equivalent for the mean cell and nuclear shape. ‘Cellular mapping’ shows the results of interpolating the SHE coefficients to generate 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 mapping, respectively. The presence or absence of the structure is recorded at each mesh point location, resulting in a PILR, shown in matrix format for the Golgi of this cell. The PILR of an individual cell or the ‘average PILR’ of the 1,058 Golgi-tagged cells within the 8-dimensional sphere can be mapped into the mean cell and nuclear shape, generating ‘morphed’ and ‘average morphed’ cells, respectively. Scale bars, 5 μm. c, Integrated 3D visualization of 17 of the 25 structures to illustrate their average relative spatial relationships (Supplementary Video 2). d, Average pairwise spatial interaction map of cellular structures. Heat map of the average location similarities (Pearson correlations between average PILRs; Extended Data Fig. 4g) for every pair of 25 cellular structures for cells in the 8-dimensional sphere. A clustering algorithm generates the dendrogram (left) with coloured branches of the six top-level clusters lengths representing the distance between clusters. e, Average spatial interactions are robust to systematic variations in cell and nuclear shape. Heat maps for the −2σ (bottom triangle) and 2σ (top triangle) shape space map points for each of the eight shape modes (numbers of cells and heat map data in Supplementary Data 1). f, Side view 1 of average morphed cells for three structures and three bins (0, −1 and −2σ) along shape mode 3 (major tilt). Scale bars, 5 μm.

Source data

Average pairwise spatial interaction map

To measure the relationships of the average locations of each of the 25 cellular structures relative to all the others after computational integration, we calculated the 2D pixel-wise Pearson correlation between the averaged PILRs for all pairs of structures within the 8-dimensional sphere, representing a measure of the ‘average location similarity’ between two structures (Extended Data Fig. 4g). In principle, the overall average location similarity among structures could span a range. At one extreme, all structures could be coupled, for example, every structure depending on every other structure, whereas at the other extreme, every structure could be independent from every other structure. We performed a hierarchical clustering analysis of these correlation values to create a purely data-driven ‘average pairwise spatial interaction map’ of cellular structures. Notably, we found that the cellular structures clustered naturally into an ordered radial compartmentalization of the cell, from the centre of the nucleus outward (Fig. 3d), and also separated between the apical and basal domains of the cell. The six top-level clusters included structures localized to the nucleus, nuclear periphery, cytoplasm, apical domain (in a dispersed way), cell periphery and basal domain, respectively. The spatial interaction map hierarchy confirmed the expected strong location similarities within several sets of cellular structures (for example, two nucleolar structures (DFC and GC), two ER structures (SEC61β and SERCA) and three actin-related structures (actin filaments, actin bundles and actomyosin bundles)), validating this analysis approach. We found a very high location similarity between lysosomes and Golgi, consistent with their enrichment in location in the apical cytoplasm and the known role of the Golgi in regulating lysosome localization20,21. Mitochondria shared greater location similarity with the ER (SEC61β and SERCA) than any other structures, consistent with the functional interactions between these cellular structures22,23.

Average spatial interactions are robust

The ability to analyse the location of cellular structures throughout a human-interpretable standardized cell and nuclear shape space allows us to ask how robust the relative average locations of cellular structures are when they are subjected to the systematic variation in cell and nuclear shape that is present in this dataset. For example, we can compare differences in average structure locations between flat and tall cells, small and large cells or cells with shapes that are less or more polarized. We clustered all cells in the dataset into 9 bins along each of the 8 shape modes in regular intervals (as in Fig. 2) to create a total of 65 cell-shape map points (the centre bin is the same in all modes), into which we morphed each of the 25 structures (Supplementary Video 3). Of note, we found very little change in the overall average location interaction map of these 25 structures throughout the shape space (Fig. 3e and Extended Data Fig. 4h). Instead, structures filled whatever cytoplasmic space was available to them in the particular shape while maintaining their appropriate apical–basal localization and their relative average locations (three examples for shape mode 3 in Fig. 3f; all 25 structures through the shape space in Supplementary Video 3).

Variations in structure locations

The combination of the two coordinate systems—the shape space and the PILR—creates an analysis framework to investigate not only the average locations and pairwise interactions, but also their variability. We calculated the 2D pixel-wise Pearson correlation between the PILRs for all pairs of the 35,636 individual cells, including all 25 cellular structures, within the 8-dimensional sphere centred at the mean cell and nuclear shape, regardless of whether any 2 cells have the same or different tagged structures. This creates a matrix of pairwise structure PILR correlation values for all pairs of individual cells (Extended Data Fig. 6a). Correlation values from this matrix can then be averaged within all pairs of structures to create an average correlation matrix to obtain two distinct measurements of structure location and its variability: the ‘location stereotypy’ and the ‘location concordance’ (Extended Data Fig. 6b). The diagonal of this matrix is the location stereotypy; that is, the average of all the pairwise PILR correlation values for a given structure. Structures with a high stereotypy value have little cell-to-cell variability in their overall absolute positions, whereas structures with a low stereotypy value may be more often found in distinct locations amongst different cells. Comparing the stereotypy for each structure permitted us to rank structures that are most to least stereotyped in their locations within the mean cell and nuclear shape (Extended Data Figs. 6b and 7a).

The off-diagonal values in the average correlation matrix are the location concordances between pairs of structures—a measure analogous to the stereotypy, but representing aspects both of how similar the absolute locations of two structures are and how variable those relative locations may be among different cells (Extended Data Fig. 6b). For example, in the average spatial interaction map (Fig. 3d), the average location of peroxisomes was more similar to that of other cytoplasmic organelles (endosomes and mitochondria) than structures in the nucleus or at the cell periphery, and this relationship is maintained in the concordance between these structures. However, from cell to cell, the absolute locations of peroxisomes are very variable (amongst the lowest stereotypy owing to their sparse, punctate nature) and thus their concordance with other cytoplasmic structures (that is, the correlation between their absolute locations) is very low. We investigated how much the stereotypy and concordance changed in response to changes in cell shape and found that in addition to the average pairwise structure locations (Fig. 3e), the variability in individual and pairwise structure locations was also extremely robust to overall cell-shape variation in this dataset (Extended Data Figs. 6c,d and 7, Supplementary Data 1 and Methods).

Systematic analysis of structure size

Cellular structures also exhibit cell-to-cell variability in their structure size (or number). It has previously been shown that the volume of several cellular structures in the cell correlates with the overall cell volume, including the nucleus and mitochondria24. We therefore used our large dataset to perform a systematic and comparative analysis of the relationship between cellular structure volume and five relevant size metrics (cell volume, cell surface area, nuclear volume, nuclear surface area and cytoplasmic volume) for 15 of the cellular structures in this dataset (Extended Data Fig. 8). Although nuclear structures seemed to be most tightly coupled to nuclear size metrics, cytoplasmic structures ranged more widely in how well the variance in their volumes was uniquely attributable to cell versus nuclear size metrics. Unexpectedly, the variance in nuclear speckle (SON) volumes was most uniquely attributable to the nuclear surface area and not the nuclear volume, although speckles localize throughout the nucleoplasm. This is notable in light of the possible connection between transcript splicing (which occurs at nuclear speckles) and increased rates of nuclear export25. We found that contributions from other shape modes were negligible (Extended Data Fig. 8), suggesting that cell and nuclear size, and not other aspects of shape, affect the variability in the size of cellular structures. Overall, these results show that the degree to which cell and nuclear size metrics account for the variation in cytoplasmic structure volumes is structure dependent, consistent with the wide range of cell functions that these structures regulate.

Polarized reorganization in edge cells

Most cells within the tightly packed, epithelial-like hiPS cell colonies form cell–cell contacts with their neighbouring cells in a continuous circumferential band. Cells located at the edges of colonies (edge cells), however, have a distinct morphology because they lack cell–cell junctions along their outermost edge and have been shown to differ in their transcriptional profiles and metabolic activity26,27. To determine whether, and precisely how, the cellular organization of edge cells differs from that of cells not at the edge, we extended the two-coordinate-system analysis framework to permit the comparative analysis of integrated cellular organization in a second, distinct cell population within the dataset. We aligned edge cells such that their positive x axis was oriented towards the outer edge of the colony (Fig. 4a), and then mapped them into the baseline cell and nuclear shape space. On average, consistent with expectations, edge cells were much more tilted than the baseline interphase population (Fig. 4b,c). To directly compare cellular organization in similarly shaped cells, we took advantage of the very large size of the baseline dataset to identify a set of non-edge cells that were the most similarly shaped to each edge cell (Extended Data Fig. 9a). The resultant ‘shape-matched’ dataset comprises two distinct populations—edge and non-edge cells—with almost identical cell-shape distributions (Fig. 4b,c).

Fig. 4: Cellular structure locations are polarized but cellular structure location wiring is unaltered in cells at the edge of hiPS cell colonies.
figure 4

a, Alignment. Cells at the edge of the colony are rotated in xy so that the axis between the cell centroid and the external contour midpoint is parallel to the x axis and the outer contour edge of the cell is oriented to the right. b, Mean cell (magenta or purple) and nuclear (cyan or green) shape for all interphase cells (left), edge cells (centre) and the shape-matched non-edge cells and edge cells combined. Three 2D views of the 3D shape are shown. Scale bar, 5 μm. c, Frequency of cells for the eight shape modes (SM) for all interphase (grey), non-edge (black) and edge (red) cells. d, Average morphed cells for mitochondria in non-edge and edge cells. e, ALP via LDA. PILR-LDA-based reconstructions of mitochondria in average morphed cells at five positions (in σ units) along the LDA axis. Dotted lines correspond to the locations of the mean non-edge (black) and edge (red) cells in d. f, Frequency of cells along the LDA axis within non-edge and edge cell populations. Dotted vertical lines indicate the means. g, Top view and side view 1 of three examples of non-edge and edge cells along the LDA axis. Top row shows the original and bottom row the morphed visualizations for each of these cells. Images are average projections of the segmented structure. h, The ALP for 25 cellular structures in edge cells. i,j, Heat maps of the average location similarity (i), stereotypy (j, left) and concordance (j, right) in non-edge cells (top triangle or left column in stereotypy) and edge cells (bottom triangle or right column in stereotypy). Numbers of cells and heat map data are in Supplementary Data 1. Scale bars, 5 μm.

Source data

We compared the average locations (through the average morphed cells) of the 25 structures in edge cells and shape-matched non-edge cells (Fig. 4d, Extended Data Fig. 9b,d and Supplementary Video 4). We found a noticeable polarization of cytoplasmic structures and organelles (for example, mitochondria, microtubules, lysosomes and Golgi apparatus), as well as structures representing the actin cytoskeleton (for example, actin filaments, actin and actomyosin bundles) towards the outer periphery of edge cells. Adherens junctions were polarized away from the colony periphery, supporting the lack of cell–cell junctions at the edge. To quantify the changes in the locations of cellular structures between the two distinct shape-matched populations, we took advantage of the PILR as a high-dimensional representation of the intracellular location space. We reduced the PILR dimensionality down to the primary axis of greatest difference in intracellular location for each cellular structure, first through a PCA and then by a linear discriminant analysis (LDA) to identify the linear combination of PCs that best separates non-edge and edge cells (Extended Data Fig. 9c and Methods). We then reconstructed PILRs and generated morphed cells at positions along the one-dimensional LDA axis representing the full range of the location phenotype for each structure. For example, the more versus less polarized location phenotypes of mitochondria and actin bundles seen in the average morphed cells could be reconstructed at their appropriate positions along the LDA axis and the polarized nature of this location phenotype extrapolated by comparing the reconstructions further away from the means (Fig. 4d,e, Extended Data Fig. 9d,e and Supplementary Video 4). Individual cells could now also be sorted along this LDA axis and further analysed, for example through histograms that represent the entire edge and non-edge cell populations (Fig. 4f,g and Extended Data Fig. 9f–h). The PILR-LDA approach, together with visual assessment of average and individual morphed cells (Methods), permitted the determination of the biological average location phenotype (ALP) for each of the 25 cellular structures in edge cells (Fig. 4h). This analysis confirmed a polarized relocation of cytoplasmic organelles and actin cytoskeletal structures towards the edges of colonies in edge cells when compared with shape-matched non-edge cells. Thus, cell shape alone does not drive integrated intracellular organization.

We compared the average location similarities, stereotypy and concordance between edge and non-edge cells and found little—if any—differences in these (Fig. 4i,j and Extended Data Fig. 9i), despite the ALPs found in edge cells for many of these structures. We also compared the average structure volumes (15 structures validated for volume analysis) and found very few changes between edge and non-edge cells (Methods and Supplementary Data 1). One notable result, however, was that the median volume ratio of mitochondria relative to cell size was greater in edge cells (0.099; n = 322) than in non-edge cells (0.087, n = 299; 14% effect size increase, rank-sum test P = 9.2 × 10−11). These results may reflect previous observations of differences in mitochondrial protein composition and function in colony edge cells26 and of mitochondrial abundance in cells grown at different densities9. Overall, these results suggest that although the average location of many cellular structures is changed in edge cells, the relative wiring of these structures to each other and the extent to which their locations vary is maintained. This suite of measurements thus facilitates a more nuanced identification of which distinct aspects of integrated intracellular organization are changed between different populations of cells, instead of a more generic change in cellular organization.

Integrated early mitotic reorganization

We took advantage of the marked intracellular reorganization that occurs as cells enter mitosis28 to further examine the relationship between our suite of measurements of the average and relative locations and the variability of cellular structures. We focused on the two earliest stages of mitosis—prophase (m1) and early prometaphase (m2), when the condensing chromosomes still largely form an aggregated, nuclear-like structure that could be biologically interpreted in the context of our interphase (i) cell and nuclear shape-based coordinate system (Extended Data Fig. 10a). We mapped the shapes of m1 and m2 cells into the cell and nuclear shape space. Although cells in m1 were generally larger than average interphase cells, as expected, they were also mostly of similar overall shape to cells in interphase. By m2, however, cells exhibited mitosis-related changes in shape, including increased height and a more uniform rounder cell shape. Analogously to our analysis of edge cells, we created the appropriate shape-matched datasets for m1 and m2, matched to interphase cell subsets i1 and i2, respectively (Extended Data Fig. 10b,c). We extended the analysis framework to incorporate a time component through four timing of change (TOC) categories (Fig. 5b–d and Methods) permitting the analysis of intracellular reorganization over three sequential cell-cycle stages. We also developed a standardized process to systematically identify and flag all entries in the average correlation matrix (stereotypy and concordance values) that changed in a significant way between two conditions (Extended Data Fig. 10d–f and Methods). This approach permitted us to determine whether and when structures underwent a change in their individual or pairwise relative locations or in the variability in these locations.

Fig. 5: Integrated intracellular reorganization in early mitosis.
figure 5

a, Individual cell examples (top) and average morphed cells (bottom) for four cellular structures in prophase (m1) and early prometaphase (m2), shape matched to interphase cell subsets i1 and i2, respectively (Extended Data Fig. 10b). Cyan DNA outlines were left out for the histones and nuclear envelope to better see their locations at the nuclear periphery. Scale bars, 5 μm. b, The ALP and its timing of change (TOC) for 25 cellular structures in early mitosis. Asterisk indicates centriole ALP determined by visual inspection (Supplementary Methods). c, Left, heat maps of stereotypy (blue to red) and stereotypy differences (green to purple) in early mitosis. Black dots indicate values below the measurable cut-offs (Methods). Right, flagged significant stereotypy differences for each structure between interphase and both early mitotic stages (filled black boxes) as well as the resultant stereotypy TOC. The stereotypy of the plasma membrane was so high that, although the absolute difference in stereotypy values passed the flag criteria, the relative values were extremely small (denoted with ‘x’). d, Timing and types of change in concordance, through the PILR average correlation matrix. Bottom triangle: the concordance TOC assignments for all pairs of structures. Heat maps of intermediate steps are in Extended Data Fig. 10d–g and Supplementary Data 1. Top triangle: types of changes in concordance relative to changes in stereotypy as described in the results (Methods). Numbers range from n = 6 to 256 cells depending on the structure and stage (Supplementary Data 1). Coloured bars at the left of heat or colour maps in bd indicate the cellular structure. Owing to the low number of cells in mitosis for some structures, we could not quantitatively analyse differences in the average location similarities, although their qualitative results matched those based on the concordance values (Extended Data Fig. 10g). e, Summary of examples of changes in distinct aspects of organization observed throughout this study. Specific examples are indicated with numbers: (1) structures that maintained locations in edge cells and early mitosis; (2) structures that polarized in edge cells; (3) for example, histones and microtubules at m1; (4) for example, histones and microtubules at m2; (5) most structures during early mitosis.

Source data

We found that the ALPs of the 25 structures fell into three classes (also at (1) the locations of structures at the cell periphery for example, the plasma membrane, actin-related structures, cell–cell adhesions) were largely maintained; (2) most structures within or surrounding the nucleus (for example, nucleoli, nuclear envelope and ER) disassembled and the FP-tagged proteins were recompartmentalized; and (3) most structures within the bulk of the cytoplasm (for example, mitochondria and lysosomes) reorganized and redistributed throughout the cytoplasm as the microtubules themselves reorganized and redistributed towards the condensing chromosomes and the centre of the cell (Fig. 5a,b and Supplemenrary Video 5). Almost all structures that changed locations in early mitosis did so both in m1 and in m2 (stepwise TOC category). Exceptions included nuclear speckles and cohesins, which did not change location until m2, when they began to disassemble. This was at a later stage of mitosis than all of the other nuclear and nuclear periphery structures. Peroxisomes and endosomes also did not noticeably redistribute towards the centre of the cell until m2.

For most nuclear and nuclear periphery-related structures (for example, nuclear envelope, speckles and ER), a change in their location coincided with a change in how variable that location was (for example, a matched TOC for ALP and stereotypy in Fig. 5b,c). However, for other structures, including most of the cytoplasmic structures, there was a discrepancy between the timing of change in average location and its variability (for example, mitochondria, Golgi, lysosomes in m1 as well as histones and microtubules in m2). Some structures that did not show any changes in stereotypy were discrete, punctate structures with very low stereotypy, for which changes in stereotypy could not be determined with statistical confidence (for example, cohesins, endosomes and desmosomes). All of the structures that maintained their location at the cell periphery, and that had stereotypies higher than the statistical detection threshold, also did not change how variable their locations were (for example, plasma membrane and actin-related structures). All changes in stereotypy in early mitosis were due to a decrease in stereotypy, except for histones, which increased in stereotypy. Together, these observations show that although a concomitant change (or lack of change) in both average location and location variability dominated for most structures during early mitotic reorganization, these two distinct aspects of an individual structure’s reorganization were separable for some cellular structures.

We next analysed changes in the relative pairwise locations and their variability in early mitosis through the concordance (Fig. 5d and Extended Data Fig. 10d–f). We found that structures that maintained their locations and their stereotypies also maintained their concordance when paired with each other. Another 64 of the possible 300 pairs of structures changed concordance during early mitosis and these changes were highly linked to changes in stereotypy (Fig. 5d): 61/64 pairs of structures changed in concordance at the same time that at least one of the two structures also changed in stereotypy. For example, the three cytoplasmic organelles, the mitochondria, lysosomes and Golgi, all changed in stereotypy at m2 and all changed concordance with each other at m2. In 36 of these cases a concordance change occurred at the time of the first stereotypy change of at least one of the two structures (Fig. 5d). For example, the time of the first stereotypy change for mitochondria and microtubules was at m1 because that was when the microtubules changed stereotypy, whereas the mitochondria did not change stereotypy until m2. However, the concordance between this pair of structures already changed at m1, along with the microtubules (and then further at m2, making the concordance stepwise). These results suggest a strong—but not exclusive—relationship between changes in average location, stereotypy, and concordance for many cellular structures during early mitotic reorganization. For 4 out of 64 cases, concordance and stereotypy changed independently for at least one time point (Fig. 5d). Most notable were the histones and microtubules, both of which are central to early mitotic reorganization. For both of these structures, their stepwise ALP was accompanied by a change in stereotypy from interphase to m1 and then a change in concordance from m1 to m2, demonstrating that stereotypy and concordance measurements are separable even for the same pair of structures at two different stages of mitosis.

We performed a meta-analysis to examine all of the possible combinations of the distinct measurements of cell organizational changes used in this analysis framework (Fig. 5e). In this study, all observed examples of changes in any aspect of intracellular organization included a change in the average location of individual cellular structures. Furthermore, in most cases, a change in the relative locations and variability of pairs of structures (concordance) was associated with a change in the variability of at least one of the structures (stereotypy). However, this association between stereotypy and concordance was not absolute, as exemplified by the behaviour of DNA and microtubules in early mitosis.


In summary (Extended Data Fig. 11), in this study we introduced the WTC-11 hiPSC Single-Cell Image Dataset v1 and used this resource dataset to develop an analysis framework for integrated intracellular organization. We applied this analysis framework to a large baseline population of cells in interphase, as well as to two subpopulations of cells in the dataset, cells at the edges of colonies and cells in early mitosis. The results of the meta-analysis investigating the association between distinct aspects of cell organization observed throughout this study suggest a possible hierarchy of dependencies as cells reorganize: (1) the average location of an individual structure changes; (2) the variability in that structure location changes but only when the structure location changes; and (3) the interactions with other structures change, but only when location and/or location variability change. However, our observations also show that this simple proposed hierarchy among these distinct aspects of organization is not absolute—the stereotypy and concordance changed independently in several examples, including for two of the primary structures responsible for early mitotic reorganization, the DNA and the microtubules. It is possible that these potential dependencies, or ‘rules’ of cell organization, are general and apply to a range of genetic perturbations, differentiation, signalling factors, environmental signals and so on. It is also possible that there is a larger set of cell-type or state-dependent organizational rules.

Together, the raw image data of cells in the dataset, the visualizations and reconstructions of the average locations of cellular structures among the three subsets of cells in this study and the data visualizations constitute a rich resource for further discovery and hypothesis generation. The conceptual aspect of this analysis framework is generalizable and extensible; the establishment of the two conceptual coordinate systems and their application to perform robust statistical analyses on cell shape and intracellular spatial locations and their variability could be useful across different cell types and different types of cell population comparisons. The experimental and algorithmic implementations of this analysis framework are modular, and the choice of which to use is dependent on the specific application. We have demonstrated one specific application to one particular cell type, the hiPS cell, a karyotypically normal cell-culture model system that grows in epithelial-like colonies with a mostly consistent appearance, including an assessment of the required number of cells for these analyses (Supplementary Methods). The specific biological question, cell type or application will dictate the specific inputs required, such as how many cells or cellular structures are needed, what kind of precision is possible or what kinds of segmentation and data-analysis algorithms should be used.

Other systematic image-based approaches have catalogued the location of human proteins in several cell types and used the locations of proteins and structures within cells to identify differences in intracellular spatial patterns among cells in distinct states6,7,8,9,10,11,12,19,29. Our work complements these approaches with its focus on analyses of 3D cell organization at the intermediate level of cellular structures (rather than individual proteins), and on the generation of quantitative measurements of distinct aspects of organization, which enables statistical comparisons and provides a more nuanced, systematic definition of cellular organization and reorganization. Together, these studies bring a crucial missing dimension—that is, the spatiotemporal component—to the single-cell revolution30. The full image dataset and analysis algorithms introduced here, as well as all the reagents, methods, and tools needed to generate them, are shared in an easily accessible way ( These data are available to all for further biological analyses and as a benchmark for the development of tools and approaches moving towards a holistic understanding of cell behaviour.


Cell lines, cell culturing and quality control

Each gene-edited cell line was created using the parental WTC-11 hiPS cell line31 and contains a fluorescent protein endogenously tagged to a protein representing a distinct cellular structure (Fig. 1a). Cell lines were generated using CRISPR–Cas9-mediated genome editing14 . The tagging strategy for AAVS1 safe harbour targeting was altered for expression of CAAX-mTagRFP-T32,33. Fifteen additional Allen Cell Collection lines were generated using the same methods. The complete list of cell lines and reagents can be found in Supplementary Data 2. The cell lines are described at and are available through Coriell at For all non-profit institutions, detailed MTAs for each cell line are listed on the Coriell website. Please contact Coriell regarding for-profit use of the cell lines as some commercial restrictions may apply. All cell lines were cultured on an automated cell-culture platform developed on a Hamilton Microlab STAR Liquid Handling System (Hamilton Company). Cells were cultured in a Cytomat 24 (Thermo Fisher Scientific) at 37 °C and 5% CO2 in mTeSR1 medium with and without phenol red (STEMCELL Technologies), supplemented with 1% penicillin–streptomycin (Thermo Fisher Scientific). Cells were passaged every four days as single cells for up to ten passages post-thaw. For imaging, cells were plated on Matrigel-coated glass-bottom, black-skirt, 96-well plates with 1.5 optical grade cover glass (Cellvis). Cells were regularly assessed for morphology, cell stemness marker expression and outsourced cytogenetic analyses throughout the three years of data acquisition of the WTC-11 hiPSC Single-Cell Image Dataset v1 (ref. 34). Standard protocols are available at Further details are provided in the Supplementary Methods.


Imaging was performed on three identical ZEISS spinning-disk confocal microscopes with 10×/0.45 NA Plan-Apochromat or 100×/1.25 W C-Apochromat Korr UV Vis IR objectives (Zeiss) and ZEN 2.3 software (blue edition; ZEISS) unless otherwise specified. The spinning-disk confocal microscopes were equipped with a 1.2× tube lens adapter for a final magnification of 12× or 120×, respectively, a CSU-X1 spinning-disk scan head (Yokogawa) and two Orca Flash 4.0 cameras (Hamamatsu). Standard laser lines were used at the following laser powers measured with 10× objectives; 405 nm at 0.28 mW, 488 nm at 2.3 mW, 561 nm at 2.4 mW and 640 nm at 2.4 mW unless otherwise specified. An Acousto-Optic Tunable Filter (AOTF) was used to simultaneously modulate the intensity of the four laser lines. The following Band Pass (BP) filter sets (Chroma) were used to collect emission from the specified fluorophore: 450/50 nm for detection of DNA dye, 525/50 nm for detection of mEGFP tag, 600/50 nm for detection of mTagRFP-T tag and 706/95 nm for detection of cell-membrane dye. Images were acquired with an exposure time of 200 ms unless otherwise specified. Cells were imaged in phenol red-free mTeSR1 medium on the stage of microscopes outfitted with a humidified environmental chamber to maintain cells at 37 °C with 5% O2 during imaging. Transmitted light (bright-field) images were acquired using a white LED light source with broad emission spectrum (pipeline 4.0–4.2) or a red LED light source with peak emission of 740 nm with narrow range and a BP filter 706/95 nm for bright-field light collection (Pipeline 4.4 only). A Prior NanoScan Z 100 mm piezo z stage (ZEISS) was used for fast acquisition in z (Pipeline 4.4 only). Optical control images were acquired daily at the start of each data acquisition to monitor microscope performance. Laser power was measured monthly and the corresponding percentage adjusted accordingly for each wavelength.

Image acquisition

The image acquisition workflow and experimental set-up evolved over the three years of dataset collection and was versioned into four pipelines. Adjustments included single versus dual camera, filter and light sources, as well as addition of a photoprotective cocktail (Supplementary Methods and Extended Data Fig. 1d). Low magnification (12×), 2D bright-field overview images of cells in wells were collected for cell morphology assessment and for selection of imaging positions for high-magnification (120×), 3D, multichannel imaging. Cells were imaged in three modes to acquire a variation of locations within hiPS cell colonies. Selection of FOV position was performed manually using the stage function in ZEN software or using an automated method, depending on the mode and the cell line. After the selection of FOV position from the well overview acquisition, the DNA of cells was first stained for 20 min with NucBlue Live (Thermo Fisher Scientific). Then the cell membrane was stained with CellMask Deep Red (CMDR, Thermo Fisher Scientific) in the continued presence of NucBlue Live for an additional 10 min, and cells were washed once before imaging for a maximum of 2.5 h. Three-dimensional FOVs at 120× were acquired at the pre-selected positions. Four channels were acquired at each z-step (interwoven channels) in the following order: bright field, mEGFP or mTagRFP-T, CMDR and NucBlue Live. Further details are provided in the Supplementary Methods.

3D FOV image quality control

FOV images acquired with two cameras underwent a channel alignment procedure. All 3D FOV images underwent an image quality-control procedure, including three automated FOV quality-control steps. Typical FOV exclusion criteria were related to microscope acquisition system failures (laser, exposure time, z-slice positioning in relation to cell height, empty or out of order channels), analysis steps to identify outliers or any other issues that would cause downstream processing, such as cell, nuclear and cellular structure segmentation, to fail in a systematic batch manner. Total days of acquisition and FOV number per cellular structure are provided in Supplementary Data 1. Further details are provided in the Supplementary Methods.

3D cell and nuclear segmentation

To segment each individual cell and its corresponding DNA from the membrane dye and DNA dye channels of each 3D z-stack, we used the deep-learning-based cell and nuclear instance segmentation algorithm developed as part of Allen Cell & Structure Segmenter, an open-source, Python-based 3D segmentation software package15. We combined the Segmenter’s Iterative Deep Learning workflow and the Training Assay approach to ensure accurate and robust segmentation at scale (18,100 FOVs) for downstream quantitative analysis. We manually validated a subset of the cell and nuclear segmentation results and found that over 98% of individual cells were well-segmented and over 80% of images generated successful cell and nuclear segmentations for all cells in the entire FOV. On the basis of these validation results, we decided that the cell and nuclear instance segmentation algorithm was sufficiently reliable to be applied to all of the FOVs in the dataset. In addition, all cells in the final dataset were manually reviewed for basic quality criteria. Further details are provided in the Supplementary Methods.

3D cellular structure segmentation

We applied a collection of modular segmentation workflows from the Classic Segmentation component of the Segmenter, each optimized for the particular morphological features of the target cellular structures15. Representative examples for each of the 25 FP-tagged cellular structures are shown in Extended Data Fig. 2. For each structure, the results of the segmentation workflow were evaluated on sets of images representing the variation observed across imaged cells (for example, different regions of colonies) to ensure consistent segmentation quality across all images for each structure. We performed an additional validation step to determine whether a given target structure segmentation was sufficient for interpretation in the cellular structure volume analysis (Extended Data Fig. 8). We identified ten structures for which there were obvious caveats to the ability to use their target structure segmentation for biological interpretations of how much of the target structure was present in each cell and thus these ten structures were excluded from the structure volume analysis (Extended Data Fig. 2b–d). Further details are provided in the Supplementary Methods.

Single-cell datasets, feature extraction and quality control

To build the WTC-11 hiPSC Single-Cell Image Dataset v1, we extracted all complete individual cells in each FOV automatically from the cell segmentation results (around 12 complete cells per FOV, on average). All images were rescaled to isotropic voxel size (0.108333 µm in x,y and z). A cropping region of interest (ROI) was created for each cell and applied to each of the original intensity z-stacks and cell, nuclear and structure segmentations. Features that were calculated for each cell included FOV-based features (for example, the lowest and highest z position of all cells in the FOV), colony-based features (for example, size of the colony), single-cell-based features (for example, cell, nuclear, and cellular structure volume), and single-cell deep-learning-based annotations of cell-cycle stage (for example, interphase or mitotic). The baseline interphase dataset was created by removing all of the 11,190 mitotic cells, as well as approximately 0.5% of outlier cells. We performed an extensive analysis to identify and account for any potential experimental contributions to cell-shape variation (Extended Data Fig. 12). All of the results together confirmed that although cell line identity can contribute to variation in cell height because each cell line was imaged under a particular set of imaging conditions, which varied throughout the imaging pipeline timeline, cell line identity itself does not greatly contribute to the variation in cell height observed in the baseline interphase dataset. Total numbers of cells per cellular structure and per dataset can be found in Extended Data Fig. 1d and Supplementary Data 1. Further details are provided in the Supplementary Methods.

SHE of cell and nuclear shapes

We used SHE coefficients as shape descriptors for cell and nuclear shape18,35. We created a publicly available Python package, aics-shparam (see Code availability) to extract SHE coefficients from segmented images of cells and nuclei. Cells and nuclei were first rotated in the xy plane such that the longest cell axis falls along the x axis. The z axis in the lab frame of reference was preserved as it represents the apical–basal axis of these epithelial-like cells. We expanded, up to degree Lmax = 16, resulting in 289 coefficients for each input. Therefore, the shape of each cell in our dataset can be represented by a total of 578 coefficients (Fig. 2a). We could also do the reverse and recreate the 3D mesh representation of a particular set of SHE coefficients with aics-shparam. Further details are provided in the Supplementary Methods.

Building the cell and nuclear shape space

We used PCA to reduce the dimensionality of our joint vectors for all cells (578 SHE coefficients) down to eight principal components. We used the PCA implementation from the Python library scikit-learn36 with default parameters (Fig. 2b). Because the sign of a given PC is arbitrary, we adjusted the signs where needed to match the naming of the shape modes (for example, larger cells have a more positive PC). We also translated the location of the nuclear mesh back to its correct location relative to the centre of the cell. To prevent cells with extreme shapes from affecting the interpretation of the PCs, we excluded all cells that fell into the range 0th to 1st or 99th to 100th percentiles of each PC from subsequent analysis (remaining n = 175,147 cells) We z-scored all PCs independently by dividing the PC values by the standard deviation (σ) of that PC. The combination of the first eight ‘shape modes’ (z-scored PCs) created the 8D shape space. We used the inverse of the PCA transform generated above to map coordinates from the shape space back into SHE coefficients, which, in turn, were used to reconstruct the corresponding 3D shape. For example, the eight-component vector (0,0,0,0,0,0,0,0) represents the origin of the shape space and its corresponding 3D shape is called the ‘mean cell and nuclear shape’ (Fig. 2c). In addition to the joint cell and nuclear shape space, we also generated independent cell-only and nucleus-only shape spaces for the baseline interphase dataset (Extended Data Fig. 3e–f), a joint cell and nuclear shape space for cells located at the edges of hiPS cell colonies, and one each joint cell and nuclear shape space for cells in prophase and in early prometaphase. Finally, we created three joint cell and nuclear shape spaces for the three shape-matched datasets described below. Further details are provided in the Supplementary Methods.


The nuclear centroid of each cell was defined as the SHE coefficients representing a one-pixel radius (0.108 µm) 3D spherical mesh. Then, pre-computed SHE coefficients were interpolated to create a series of successive 3D concentric mesh shells from the centroid of the nucleus to the nuclear boundary and from the nuclear boundary to the cell boundary. The xyz coordinates of points in the 3D meshes map to corresponding xyz locations in the aligned segmented images that were used to generate the SHE coefficients in the first place. Thus, the presence or absence of a segmentation result at each mesh xyz coordinate could be organized as a matrix as shown in Fig. 3b. This matrix encodes a PILR of the cell. This process could also be performed using the intensity value at a given xyz location in the original FP image (Extended Data Fig. 4). A PILR could then be used to map the cellular structure locations from one cell and nuclear shape into the equivalent locations in any other cell and nuclear shape, thus generating a ‘morphed cell’ and its reconstructed image. Further details are provided in the Supplementary Methods.

Integrating average morphed cells in the mean cell and nuclear shape

We identified and grouped a set of cells by their absolute proximity in 8D space to the origin of the shape space, map point (0,0,0,0,0,0,0,0). We determined the radius of a sphere centred at this origin such that the number of cells per structure within this sphere was as similar as possible to the average number of cells found in the centre bins of all of the shape modes. A total of 35,633 cells across all 25 structures were found to be within this radius of 2.1σ (see Supplementary Data 1 for numbers of cells per structure). We computed the average of all the PILRs for each structure for all cells within the 8-dimensional sphere. We then morphed these average PILRs into the mean cell and nuclear shape, creating an integrated average morphed cell. Any cellular structures could be rendered simultaneously to illustrate the spatial relationships of different structures on the basis of their average location in cells of a particular shape.

Pairwise average interaction map of cellular structures

We calculated the 2D pixel-wise Pearson correlation between the averaged PILRs for all pairs of cellular structures within the 8-dimensional sphere, representing a measure of the average location similarity between two structures (Extended Data Fig. 4g). All correlation values used throughout this paper were calculated using the function corrcoef from the Python package NumPy37. The average location similarities were organized in a 25 × 25 matrix that represents an average pairwise spatial interaction map of cellular structures (Fig. 3d). This correlation matrix was used as input for a hierarchical clustering algorithm to cluster all 25 cellular structures according to their average location similarities. We used the function cluster.hierarchy.linkage of type ‘average’ from the Python package scipy38 to produce the clustering represented by the dendrogram in Fig. 3d. We also computed the average location similarity for every map point along each shape mode. For a given map point, the correlations were computed between the averaged PILRs over all cells that fall into the corresponding map point bin. The heat maps of the resulting matrices for all shape modes and bins between −2σ and 2σ are shown in Fig. 3e and Extended Data Fig. 4h and the data can be found in Supplementary Data 1.

Location stereotypy and location concordance

We calculated the 2D pixel-wise Pearson correlation between the PILRs for all pairs of individual cells within the 8-dimensional sphere centred at the origin of our shape space. This computation results in a 35,633 × 35,633 correlation matrix (Extended Data Fig. 6a). Correlation values from this matrix were averaged within each pair of structures to create an average correlation matrix. Two distinct measurements of structure location and its variation were derived from this average correlation matrix. The diagonal values are the location stereotypy of a given structure and the off-diagonal values are the location concordance between two structures (Extended Data Fig. 6b). We also computed the average correlation matrices for every map point along each shape mode. For a given map point, the correlations were computed between PILRs over all cells that fall into the corresponding map point bin and then averaged. Heat maps and values of location stereotypy and location concordance for all shape modes and map points can be found in Extended Data Figs. 6c,d and 7c,d and Supplementary Data 1.

Shape-matched datasets

To compare a second, distinct population of cells, such as cells at the edges of colonies or cells in early mitosis, with the baseline interphase cell dataset we created shape-matched datasets. We first mapped cell and nuclear shapes from the second population into the shape space of the baseline dataset by transforming the SHE coefficients from the second population using the same PCs obtained for the baseline dataset. Here we did not exclude cells that fell into the range 0th to 1st or 99th to 100th percentiles of each PC in the baseline dataset because these cells could have shapes more similar to the second population. We then calculated the distance in 8D shape space between every possible pair of cells in both datasets (Extended Data Fig. 9a). Finally, for every cell in the second dataset, we flagged its nearest neighbour within the baseline dataset. The same cell in the baseline dataset could be flagged more than once for multiple different cells within the second dataset. This occurred roughly 12% of the time. The resultant shape-matched dataset is the set of unique flagged cells in the baseline dataset combined with cells in the second dataset. The mean cell shape of this shape-matched dataset is the cell and nuclear shape corresponding to the origin of the corresponding shape-matched shape space. Further details are provided in the Supplementary Methods.


We performed a PCA dimensionality reduction on all of the PILRs for a given cellular structure in a given shape-matched dataset. This reduced the initial dimensionality of 532,610 pixels in each PILR down to 32 dimensions (or the total number of cells available if fewer than 32). The dimensionally reduced data were then used as input for a LDA to identify the linear combination of reduced dimensions that best separated the two populations of cells within the shape-matched dataset. LDA generates a discriminant axis along which we could reconstruct corresponding PILRs using the inverse of the PCA transform (Extended Data Fig. 9c and Supplementary Methods). These PILR reconstructions were morphed into the mean cell and nuclear shape for that shape-matched dataset (for example, Supplementary Videos 4 and 5). These reconstructions represent the full range of the ALP for that structure. Each cell was also assigned a location along the discriminant axis (for example, histograms in Extended Data Fig. 9h and Supplementary Videos 4 and 5).

Workflow to flag significant changes in location stereotypy and concordance in early mitosis

To flag whether a difference in location stereotypy or concordance was significant, we first set a threshold cut-off value of Pearson correlation ρ = 0.03, below which a stereotypy or concordance value was too low to be used for the subsequent detection of a difference between the baseline dataset and its shape-matched comparison dataset. Next, we set a cut-off threshold for the Pearson correlation value of the difference (ρdiff) in stereotypy or concordance of ρdiff = 0.02 (Supplementary Methods). We next applied this workflow to flag all entries in the three early mitotic average correlation difference matrices that showed a significant change between interphase, prophase and early prometaphase (i1–m1, i2–m2 and m1–m2). The first cut-off, ρ = 0.03, was applied to the interphase cells when comparing to each early mitotic (i1 for i1–m1; i2 for i2–m2) and to prophase when comparing between the two early mitotic stages (m1 for m1–m2) as in Fig. 5c and Extended Data Fig. 10f. This flagging procedure resulted in three binarized versions of the matrix, in which each flagged entry is marked in black. The combined pattern of flags in these three matrices permits us to identify the TOC for each of the flagged entries (Fig. 5c,d). The four TOC categories included: (1) m1-only: changes that occurred from interphase to m1 but not any further in m2; (2) stepwise: changes that occurred both from interphase to m1 and from m1 to m2; (3) m2-change: changes that occurred from m1 to m2 only; and (4) no change or cases for which changes could not be determined for technical reasons (Fig. 5b and Supplementary Methods). We used all possible combinations of the TOC for the two stereotypies and single concordance for each pair of structures to assess the overall relationship between stereotypy and concordance in early mitosis, which we consolidated and summarized into three categories (top triangle; Fig. 5d and Supplementary Methods).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.