Computable early Caenorhabditis elegans embryo with a phase field model

Geometric factors for cell arrangement: How do cells determine their position in vivo?

The spatial arrangement of cells plays a crucial role in ensuring robust development of organisms, directing cells to their specific fates in the right place and at the right time. In early embryogenesis, the cell arrangement is determined by several factors such as the cell division axis, cell-cell interactions, and surrounding geometric constraints. While many species utilize similar principles to determine the cell arrangement, the precise dynamics of cell arrangement differ among species, even at early stages. In particular, geometric constraints significantly impact cell arrangement. Nematode species exhibit diverse cell arrangement dynamics due to their rigid eggshells, which intensively confine the internal cells. In this paper, we review the mechanisms of cell arrangement with a focus on geometric constraints, drawing from interdisciplinary perspectives. We also review mathematical models developed to enhance our understanding of these mechanisms and discuss future directions for theoretical approaches in exploring geometric effects on cell arrangement in various tissues of various species.

Cell lineage-resolved embryonic morphological map reveals signaling associated with cell fate and size asymmetry

How cells change shape is crucial for the development of tissues, organs and embryos. However, studying these shape changes in detail is challenging. Here we present a comprehensive real-time cellular map that covers over 95% of the cells formed during Caenorhabditis elegans embryogenesis, featuring nearly 400,000 3D cell regions. This map includes information on each cell's identity, lineage, fate, shape, volume, surface area, contact area, and gene expression profiles, all accessible through our user-friendly software and website. Our map allows for detailed analysis of key developmental processes, including dorsal intercalation, intestinal formation, and muscle assembly. We show how Notch and Wnt signaling pathways, along with mechanical forces from cell interactions, regulate cell fate decisions and size asymmetries. Our findings suggest that repeated Notch signaling drives size disparities in the large excretory cell, which functions like a kidney. This work sets the stage for in-depth studies of the mechanisms controlling cell fate differentiation and morphogenesis.

Image-based force inference by biomechanical simulation

During morphogenesis, cells precisely generate forces that drive cell shape changes and cellular motion. These forces predominantly arise from contractility of the actomyosin cortex, allowing for cortical tension, protrusion formation, and cell division. Image-based force inference can derive such forces from microscopy images, without complicated and time-consuming experimental set-ups. However, current methods do not account for common effects, such as physical confinement and local force generation. Here we propose a force-inference method based on a biophysical model of cell shape, and assess relative cellular surface tension, adhesive tension between cells, as well as cytokinesis and protrusion formation. We applied our method on fluorescent microscopy images of the early C. elegans embryo. Predictions for cell surface tension at the 7-cell stage were validated by measurements using cortical laser ablation. Our non-invasive method facilitates the accurate tracking of force generation, and offers many new perspectives for studying morphogenesis.

Temporal variability and cell mechanics control robustness in mammalian embryogenesis

How living systems achieve precision in form and function despite their intrinsic stochasticity is a fundamental yet ongoing question in biology. We generated morphomaps of preimplantation embryogenesis in mouse, rabbit, and monkey embryos, and these morphomaps revealed that although blastomere divisions desynchronized passively, 8-cell embryos converged toward robust three-dimensional shapes. Using topological analysis and genetic perturbations, we found that embryos progressively changed their cellular connectivity to a preferred topology, which could be predicted by a physical model in which actomyosin contractility and noise facilitate topological transitions, lowering surface energy. This mechanism favored regular embryo packing and promoted a higher number of inner cells in the 16-cell embryo. Synchronized division reduced embryo packing and generated substantially more misallocated cells and fewer inner-cell-mass cells. These findings suggest that stochasticity in division timing contributes to robust patterning.

Characterizing Cellular Physiological States with Three-Dimensional Shape Descriptors for Cell Membranes

The shape of a cell as defined by its membrane can be closely associated with its physiological state. For example, the irregular shapes of cancerous cells and elongated shapes of neuron cells often reflect specific functions, such as cell motility and cell communication. However, it remains unclear whether and which cell shape descriptors can characterize different cellular physiological states. In this study, 12 geometric shape descriptors for a three-dimensional (3D) object were collected from the previous literature and tested with a public dataset of ~400,000 independent 3D cell regions segmented based on fluorescent labeling of the cell membranes in Caenorhabditis elegans embryos. It is revealed that those shape descriptors can faithfully characterize cellular physiological states, including (1) cell division (cytokinesis), along with an abrupt increase in the elongation ratio; (2) a negative correlation of cell migration speed with cell sphericity; (3) cell lineage specification with symmetrically patterned cell shape changes; and (4) cell fate specification with differential gene expression and differential cell shapes. The descriptors established may be used to identify and predict the diverse physiological states in numerous cells, which could be used for not only studying developmental morphogenesis but also diagnosing human disease (e.g., the rapid detection of abnormal cells).

A mathematical framework for understanding the spontaneous emergence of complexity applicable to growing multicellular systems

In embryonic development and organogenesis, cells sharing identical genetic codes acquire diverse gene expression states in a highly reproducible spatial distribution, crucial for multicellular formation and quantifiable through positional information. To understand the spontaneous growth of complexity, we constructed a one-dimensional division-decision model, simulating the growth of cells with identical genetic networks from a single cell. Our findings highlight the pivotal role of cell division in providing positional cues, escorting the system toward states rich in information. Moreover, we pinpointed lateral inhibition as a critical mechanism translating spatial contacts into gene expression. Our model demonstrates that the spatial arrangement resulting from cell division, combined with cell lineages, imparts positional information, specifying multiple cell states with increased complexity-illustrated through examples in C.elegans. This study constitutes a foundational step in comprehending developmental intricacies, paving the way for future quantitative formulations to construct synthetic multicellular patterns.

Modulating cell proliferation by asymmetric division: A conserved pattern in the early embryogenesis of nematode species

In the early stage of the nematode Caenorhabditis elegans embryogenesis, the zygote divides asymmetrically into a symmetric fast lineage and an asymmetric slow lineage, producing 16 and 8 cells respectively almost at the same time, followed by the onset of gastrulation. It was recently reported that this cell division pattern is optimal for rapid cell proliferation. In this work, we compare the cell lineages of 9 nematode species, revealing that this pattern is conserved for >60 million years. It further suggests that such lineage design has an important functional role and it might speed up embryonic development in the nematode kingdom, not limited to C. elegans , and independent of the maternal-zygotic transition dynamics.

MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies

The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.

Interacting active surfaces: A model for three-dimensional cell aggregates

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

Computational approaches for simulating luminogenesis

Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.

Delineating the mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised-based on accurate determinations of developmental processes afforded by analyses of imaging data-to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.