Size scaling in collective cell growth

Uncovering the patterns and the mechanisms underlying the growth of organisms has been a longstanding goal in biology. Propelled by D'Arcy Thompson's and Julian Huxley's seminal work over one century ago, scientists have since devised increasingly sophisticated methods to capture and analyze growth in its many forms and at scales that span a large dynamic range (Thompson, 1917; Huxley, 1932; Sharpe, 2017). In particular, numerous studies have focused on uncovering growth dynamics of cells and their substructures; cells are the primary building blocks of more-complex structures, and the proper physical dimensions of a cell and relative sizes of its organelles are important for proper structure and function (Chan and Marshall, 2010, 2012; Jorgensen et al., 2007; Neumann and Nurse, 2007; Levy and Heald, 2012; Marshall et al., 2012; Ginzberg et al., 2015). Previous work, primarily focusing on X. laevis and C. elegans, has provided many of the established quantitative methods for characterizing size regulation and scaling in single cells, thus elucidating how these features regulate key biological processes, such as the cell cycle (Arata et al., 2015; Arata and Takagi, 2019; Jevti′c and Levy, 2015; Levy and Heald, 2010; Masui and Wang, 1998; Wang et al., 2000).

In contrast to studies of growth of individual cells, studies of coordinated growth in multicellular clusters have been slow to emerge (Macklin, 2019). A particularly important class of multicellular growth problems arises during the development of gametes. Across species, oocytes and sperm develop within clusters of connected cells, called germline cysts (Pepling et al., 1999; Matova and Cooley, 2001; Woznica et al., 2016; Yamashita, 2018). These structures have a relatively few number of cells (several to tens) and are conserved, thus providing a highly tractable and relevant system for studying the growth dynamics of cells in a multicellular context. With the ever-increasing power of modern technologies and emergence of machine learning, it has now become possible to systematically analyze large datasets, to extract three-dimensional measurements of cells and their substructures, and to identify the relationships characterizing the coordinated growth of these multicellular structures and their underlying mechanisms (Sommer et al., 2011; Machado et al., 2019; Zhang et al., 2019; Tokuoka et al., 2020).

Here, we study collective growth during invertebrate oogenesis, during which a small number of connected support cells grow rapidly and significantly, while synthesizing the molecules and molecular machines required for supporting the growth and early embryonic life of the oocyte (Matova and Cooley, 2001; Haglund et al., 2011; Lei and Spradling, 2016). To determine whether there are laws that govern the growth of clusters of connected cells, we focused on the Drosophila egg chamber, a powerful and relevant experimental system, the invariant structure of which allows identification and unique labeling of each cell in the cyst. An egg chamber comprises 16 germline cells enveloped by an epithelium (Fig. 1A) (Koch and King, 1969; King, 1970). The germline cyst arises from a differentiated stem cell that undergoes four rounds of cell division with incomplete cytokinesis, leaving cells connected through stabilized intercellular bridges or ring canals (King, 1970; Mahajan-Miklos and Cooley, 1994). At ∼1-10 m, ring canals allow for intercellular communication and transport – processes that are essential for oocyte development and growth (Cooley and Theurkauf, 1994). One of the two cells with four ring canals becomes the oocyte, while the remaining 15 cells become supporting nurse cells (King, 1970; Diegmiller et al., 2021).

Over the course of 3 days, the egg chamber grows by four orders of magnitude; however, that volume increase is not partitioned equally among its 16 cells (King, 1970). While the oocyte becomes transcriptionally quiescent, the nurse cells undergo ∼8-10 endoreplication cycles that significantly increase their ploidy, thus enabling them to synthesize the materials necessary for future developmental events (Edgar and Orr-Weaver, 2001; Fox and Duronio, 2013; Navarro-Costa et al., 2016; Doherty et al., 2021). Furthermore, studies have shown that, within the nurse cell cluster itself, a hierarchy of cell sizes emerges (Brown and King, 1964; Dapples and King, 1970; Imran Alsous et al., 2017, 2018). Nurse cell nuclear volumes increase with increasing ploidy, but the nurse cells also grow in concert with the oocyte; it is therefore unclear how the nuclei and cells scale during egg chamber development. Nucleolar size has been shown to correlate with ribosomal density, which is linked to cell growth rates (Rudra and Warner, 2004; Uppaluri et al., 2016); however, given the syncytial nature of these cell clusters, and the ability of RNA and protein products to be exchanged within nurse cells and between nurse cells and the oocyte through ring canals, it is not clear whether each nurse cell nucleolus scales with the size of its own nucleus.

We therefore sought to investigate the coordinated growth of germline cells and their substructures during Drosophila oogenesis, using a high-throughput, data-driven approach. This paper was largely inspired by the previous work of Dr Charles Dapples and Dr Robert King, who over 50 years ago analyzed the shapes and volumes of nuclei and nucleoli in developing egg chambers (Dapples and King, 1970). Motivated to overcome the limitations of 2D studies, researchers of the King lab at Northwestern University set out to generate 3D visualizations of these organelles (Charles C. Dapples, personal communication). Armed with cutting-edge electron microscopy equipment at the time, the researchers began by serially sectioning entire egg chambers, manually tracing each acquired electron micrograph onto graph paper, and mapping the locations of nucleolar regions. For each of the ∼50-100 micrographs obtained for each cell, this information was transferred to punch cards and fed into a computer, creating a 3D array of the nucleolar region. This laborious process took months to complete; furthermore, the resolving power of the micrographs limited the statistical power and scope of this study. Nonetheless, these efforts yielded the first insights into the unique 3D structure of this organelle (Fig. 1B).

Technology has come far since, yet to obtain measurements of cell volumes, numerous studies still assume that cells are spherical objects or rely on interpolation of circular areas across slices (Arata et al., 2015; Arata and Takagi, 2019; Masui and Wang, 1998; Wang et al., 2000). The approach presented in this paper allowed us to determine the morphological features and to measure the volumes of cells and their organelles for each cell in egg chambers across several orders of magnitude, while circumventing these limitations. Our results shed light on several properties relating to the groupwise developmental dynamics of these multicellular clusters. More generally, this work establishes an automated pipeline for high-throughput data processing and systematic analysis that is unencumbered by large datasets and can be readily applied to characterize collective growth in a several multicellular systems, including early mammalian embryos and germline cysts.

As live imaging is limited to a few hours, we set out to establish scaling relationships in Drosophila egg chambers for each of the 16 cells in the germline cyst using fixed samples with fluorescently labeled cell membranes, ring canals, nuclei and nucleoli (see Materials and Methods). Although formaldehyde fixation may disturb the integrity of living materials, the cells of the egg chamber and substructures appeared largely unaffected (Fig. 2). Each cell in the cyst was uniquely identified using a supervised learning approach. For each of the 15 nurse cells, the volumes of the cells, as well as their nuclei and nucleoli were measured, and their sizes reconstructed over ∼60 h of oogenesis, i.e. from stages 3 to 10A (King, 1957; Spradling, 1993). This supervised learning program yielded probabilistic pixel information based on minimal training (Sommer et al., 2011; Berg et al., 2019). Once these probability maps were exported to MATLAB to isolate each feature within each egg chamber, we were able to uniquely identify each cell in the cyst, reconstruct its morphology, measure its volume and also extract those features for its nucleus. The unique identification of nurse cells was made possible through implementation of an assignment algorithm relating the identified cell-cell connections based on the positions of ring canals within the system. After identifying the oocyte, each cell in the egg chamber is identifiable by its number of ring canals and the cells to which it is connected. The automated reassignment algorithm allowed each nurse cell to be distinctly labeled in a given egg chamber and compared with the same cell in other egg chambers across developmental stages (Kuhn, 1955; Umeyama, 1988). This automated pipeline for image processing and reconstruction (Fig. 2) facilitates extraction of quantitative information regarding the temporal evolution and development of the connected network of cells.

Discovery of the emergent pattern of cell sizes within the nurse cell cluster was first enabled through measurements from 2D sections, and subsequently confirmed through painstaking manual measurements and 3D reconstructions (Brown and King, 1964; Imran Alsous et al., 2017, 2018). These studies formed the basis for interrogating features and dynamics of cell and organelle growth through the more advanced, higher throughput and automated computational and image processing tools featured here.

Previous work has demonstrated that nuclear volumes correlate with distance from the oocyte – i.e. that the number of ring canals between a nurse cell and the oocyte correlate with the nuclear volume of a cell (Brown and King, 1964; Imran Alsous et al., 2017). We first sought to verify this finding using the automated reconstructions and to expand its scope to total nurse cell volumes. We recovered a strong correlation between nurse cell volume rank and nuclear volume rank (Fig. S1A), thus validating the accuracy of the aforementioned approach and establishing an important link between previous manual reconstructions and the automated versions presented here.

Previous work has also demonstrated that nurse cells exhibit differential growth, and that four groups of nurse cell sizes emerge, correlating with the distance of the cells from the oocyte. This pattern of cell sizes is already present in egg chambers that have exited the germarium, the stem cell niche (Brown and King, 1964; Imran Alsous et al., 2017, 2018); furthermore, once the pattern emerges from uniform initial conditions, it persists throughout oogenesis until the onset of nurse cell dumping, when the volumes of nurse cells start to decrease markedly through rapid transport of their cytoplasmic contents to the oocyte (Theurkauf and Hazelrigg, 1998; Imran Alsous et al., 2021).

In addition to confirming these findings, we found that the volume fraction of each nurse cell in a given egg chamber between stages 3 and 10A does not depend on developmental stage (Fig. S1B) (Jia et al., 2016; King, 1957). That is, the size of the egg chamber does not have predictive power for the relative nurse cell sizes. Instead, volume fractions appear to be conserved across developmental stages and are roughly uniform based on distance from the oocyte. In particular, there is a clear deviation for the four cells directly connected to the oocyte, while the other cells in the cyst appear to be more uniformly distributed. Given the size hierarchy of nurse cells, conservation of relative nurse cell volume fractions across all measured samples implies that the observed size divergence of nurse cells based on distance from the oocyte must have occurred at a time point before the earliest egg chamber measured in this study (∼stage 3) (Jia et al., 2016; Imran Alsous et al., 2017; Doherty et al., 2021).

We next explored the total growth rates of nucleolar and nuclear regions within developing egg chambers. Starting from early ∼stage 3 egg chambers, we found that nurse cell nuclear and nucleolar volumes scale at the same rates with respect to each other through developmental time (Fig. 3A,B) (Jia et al., 2016). This observation is consistent with that made half a century ago by Dapples and King (Dapples and King, 1970). Across various stages of oogenesis, the relationship between nuclear and nucleolar size within each nurse cell remains consistent, scales isometrically with cell size and is independent of distance from the oocyte or location in the cell lineage tree. Taken together, these data suggest that nurse cell nuclear volumes change at constant rates across developmental stages.

Although relative nurse cell growth remains constant throughout development, oocyte volume does not follow this trend. During the early stages of oogenesis (∼stages 3 through 7-8), the oocyte grows roughly isometrically with the rest of the cells in the cyst; however, when the total egg chamber reaches a volume of roughly 10⁵ μm³, oocyte growth begins to diverge, becoming much larger than the other cells in the developing cyst (Fig. 4).

We found that although nurse cells as a whole appear to have one rate of growth throughout oogenesis relative to the entire egg chamber (Fig. S1C), two distinct growth rates exist for the oocyte. This sharp increase in growth rate relative to the growth of the egg chamber occurs around stage 9, when developmental processes such as yolk uptake take place (Spradling, 1993; Jia et al., 2016). This developmental checkpoint appears to split oocyte growth into two distinct phases: early isometric growth relative to the nurse cells; and later divergent growth, where the oocyte grows at around twice the rate as the nurse cells.

The work presented here highlights the utility and feasibility of automated reconstruction algorithms in quantifying developmental processes. The key strength of this approach is its flexibility: given either stacks of fixed images or movies of developing multicellular structures, a minimal amount of training on images is required before one is able to uniquely identify each cell within a given system, make quantitative measurements at varying scales and glean insights into developmental trajectories. We demonstrate this approach here by quantifying the relative growth rates of oocyte, nurse cells and their subparts in the Drosophila egg chamber, thus uncovering properties of their growth dynamics.

A key aspect of this analysis was comparing the growth rates of nucleoli and nuclei across development and within the nurse cell cluster. During oogenesis, ribosomal RNA is rapidly synthesized in nurse cell nucleoli (Jorgensen et al., 2007; Uppaluri et al., 2016). As ribosomes are required for protein translation, an increase in the number of ribosomes promotes an increase in cell growth, as occurs in the nurse cells (Rudra and Warner, 2004). As nurse cell nucleoli and nuclei grow at roughly the same rates, ribosomal density is most likely constant throughout Drosophila oogenesis. This observation implies that nurse cell growth rates are constant across developmental stages, consistent with our other findings. Nuclear and nucleolar sizes also scale with cell size (Fig. 3A). This relationship has been observed in a range of organisms and cell types, and implies that nuclear size is most likely regulated by cytoplasmic volume and contents (Gregory, 2005; Levy and Heald, 2012).

A key feature of nucleoli in nurse cells is their ‘lava lamp’ morphology, with the nucleolus loosely wrapped by the surrounding DNA (Fig. 3A, inset) (Dapples and King, 1970). This unusual structure is a departure from the more familiar dense, olive pit-like region observed in other cell types (Jorgensen et al., 2007; Neumann and Nurse, 2007; Windner et al., 2019). Given the ploidy and high biosynthetic capacity of nurse cells, such morphology may allow a relatively higher surface area to volume ratio than the more compactly packed configuration – a hypothesis that can be tested by applying the pipeline developed here to flies with mutations in rRNA structural gene locus, such as bobbed (bb), which is known to cause delayed development, with oogenesis progressing at significantly reduced rates (Kay and Jacobs-Lorena, 1987).

A striking feature of Drosophila oogenesis is the rapid growth of the egg chamber around stage 9, which correlates with the uptake of yolk by the oocyte (Fig. 4) and cannot be accounted for by the isometric growth rates of the nurse cells (King, 1970; Bownes, 1982; Spradling, 1993; Jia et al., 2016). Indeed, although the oocyte and the nurse cells reside within a shared cytoplasm, they exhibit strikingly different nuclear behaviors and sizes (Fig. 1A). Future work is required to investigate the factors that control the scaling of nuclei in the egg chamber, both temporally throughout oogenesis, and spatially within the network. Notably, the functionally and morphologically different nuclei of the egg chamber are reminiscent of the macro- and micronuclei that reside within the same cell in the protozoan Tetrahymena thermophila, where differences in nuclear size and behavior have been attributed to differences in nuclear pore complexes (Levy and Heald, 2012).

Last, the presented approach can be adapted to developmental systems where the structure of intercellular connections is known and invariant, such as the tardigrade Dactylobiotus parthenogeneticus and the Argentine ant Linepithema humile (Poprawa et al., 2015; Eastin et al., 2020). The key adjustment would only be in the application of the assignment algorithm that uniquely identifies each cell (Umeyama, 1988). As in Drosophila, the known matrix of connections between uniquely identifiable cells would need to be compared with that of each reconstructed sample, allowing the proper identification and analysis of multicellular growth in a variety of developmental contexts.

Fibrillarin-RFP flies were used in all studies as a marker for nucleolar regions within each nurse cell (Falahati and Wieschaus, 2017). The flies were maintained with standard cornmeal, molasses and yeast media.

Ovaries were fixed in 4% paraformaldehyde in 0.1% Tween-20 in PBS for 20 min at room temperature on a nutator. After washing in 0.1% Tween in PBS, the ovaries were then blocked for 2 h in blocking solution (1% BSA in PBS) before adding the primary antibody rabbit anti-Phosphotyrosine (1:500) and rocked overnight at 4°C overnight. The following secondary antibodies and additional stains were then used: donkey anti-rabbit Alexa-Fluor 647 nm (1:400) (Invitrogen), Alexa Fluor 488 phalloidin (1:1000) (Invitrogen) and DAPI (250 ng/ml).

Dissected ovaries were mounted in a 1:1 mixture of RapiClear 1.47 (SUNJin Lab) and Aqua-Poly/Mount (Polysciences). Imaging was performed on a Leica SP5 confocal microscope using a 63×/1.3 NA oil objective. Three dimensional stacks were acquired using 405, 488, 546 and 647 nm in series with 3× line averaging. Stacks acquired were usually between 70 and 120 z-slices of 16-bit, 1024×1024 images. Each image was isometric in the x and y directions, tuned to best match the necessarily larger z length. Most acquired images were 246 nm in x and y, and 250 nm in z. Calibration of volume measurements was performed using 1.8 μm diameter spherical beads to confirm accuracy of measurements in all three directions.

Raw image stacks were pre-processed using FIJI to isolate individual egg chambers within each stack. The channels for each egg chamber were then split and recombined to create three stacks: a stack containing nuclear and nucleolar data, a stack containing ring canal data, and a stack containing cell membrane data. Multiple representative stacks for each type of data were uploaded into the Pixel Classification module for training within ilastik, a freely accessible semi-supervised machine learning program (Sommer et al., 2011; Berg et al., 2019). For each type of data, training was performed by manually identifying pixels that belong to each class of interest. Based on a minimal number of these examples, the program then developed probabilities for each pixel of a stack to belong to each of these classes. Owing to the morphological and volumetric differences between early- and late-stage egg chambers, two sets of training data were used to more accurately identify the relevant features for each class of samples. Each classifier was trained to identify the relevant features for all three stacks, yielding an output matrix of probabilities across all three dimensions.

The processed stacks, containing information about the probability of each pixel in the image to belong to either the cell membrane, ring canal, nucleus, nucleolus or image background, were imported into MATLAB for final object identification, post-processing and data quantification. Cell membrane probability maps were used to identify the areas of lowest probability lying inside the egg chamber, which were used as seeds for the watershed transformation. After applying this transformation and applying a Gaussian smoothing kernel based on the size of the image being analyzed, this process yielded the 16 objects most likely to be the cells within the developing cyst and assign each object a unique identifier. Applying a simple probability threshold (usually taken to be 0.5 or 50% certainty for a given pixel to have come from a certain class) allowed the ring canals, nuclear and nucleolar regions to all be identified within the cluster. As each ring canal connected two cells in the cluster, each necessarily touched the boundary of the connected cells. Exploiting this fact allowed an adjacency matrix to be built that contained information about which cells are connected. This was achieved by creating an n-by-n matrix A, where n is the number of cells, where for each pair of connected nurse cells i and j, A_ij and A_ji were set to 1. Connections between the oocyte and nurse cells were instead weighted by a factor of 2.

Identifying the oocyte required the segmentation of the nucleus and nucleolus of each cell in the cluster. As the nuclei and nucleoli of each cell were classified in a previous step, this was performed by identifying the location of each nucleolar region and identifying which cell each region was within. Because the oocyte is transcriptionally quiescent throughout these stages of oogenesis (Edgar and Orr-Weaver, 2001; Fox and Duronio, 2013), nuclear staining in this cell appears less intense, allowing it to be identified as the oocyte. Once the oocyte was properly identified, all nurse cells and their respective organelles could be uniquely identified due to the bilateral symmetry of connections within the cell cluster. This was achieved by applying a graph matching algorithm in which the cell-cell connections identified through ring canals were compared with the known adjacency matrix of the uniquely labeled cyst and re-allocated (Kuhn, 1955; Umeyama, 1988). This matrix reallocation process is based on the Hungarian algorithm, an optimization algorithm applied in this context to find the best configuration for assigning label j from the known adjacency matrix to object i from the sample adjacency matrix for all labels and objects. For each sample, this automatic segmentation and identification algorithm produced a set of objects from which quantitative data was obtained for further statistical analyses. Once each nurse cell was uniquely defined, volumes were measured by calculating the number of voxels within each object of interest and scaling by the voxel size in all three dimensions, thus approximating each volume as the sum of many small rectangular prisms. A subset of these samples was compared with egg chambers reconstructed manually in Imaris to confirm the absence of systematic biases in volume measurements or segmentation.

Simple linear regression was performed using standard functions in MATLAB, assuming that the relationship between two properties, x and y, could be best represented as ln(y)=mln(x)+ln(b). Rearranging these relationships yields the relationship y=bx^m, which shows that the slope of the regression, m, is the scaling factor between the two properties.

The authors thank Gary Laevsky for help and expertise throughout this work, and acknowledge the Molecular Biology Confocal Imaging Facility, which is a Nikon Center of Excellence. The authors additionally acknowledge Li Cao and Maysam Shahedi for open-source MATLAB codes implementing the Hungarian algorithm (Cao, munkres) and helpful visualization (Shahedi, imagesc3D). In addition, the authors also thank Eric Wieschaus, Trudi Schüpbach and Charles Dapples for helpful discussions.