Generic Theoretical Models to Predict Division Patterns of Cleaving Embryos

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.

Manipulation of Embryonic Cleavage Geometry Using Magnetic Tweezers

The geometry of reductive divisions that mark the development of early embryos instructs cell fates, sizes, and positions, by mechanisms that remain unclear. In that context, new methods to mechanically manipulate these divisions are starting to emerge in different model systems. These are key to develop future innovative approaches and understand developmental mechanisms controlled by cleavage geometry. In particular, how cell cycle pace is regulated in rapidly reducing blastomeres and how fate diversity can arise from blastomere size and position within embryos are fundamental questions that remain at the heart of ongoing research. In this chapter, we provide a detailed protocol to assemble and use magnetic tweezers in the sea urchin model and generate spatially controlled asymmetric and oriented divisions during early embryonic development.

Length limitation of astral microtubules orients cell divisions in murine intestinal crypts

Planar spindle orientation is critical for epithelial tissue organization and is generally instructed by the long cell-shape axis or cortical polarity domains. We introduced mouse intestinal organoids in order to study spindle orientation in a monolayered mammalian epithelium. Although spindles were planar, mitotic cells remained elongated along the apico-basal (A-B) axis, and polarity complexes were segregated to basal poles, so that spindles oriented in an unconventional manner, orthogonal to both polarity and geometric cues. Using high-resolution 3D imaging, simulations, and cell-shape and cytoskeleton manipulations, we show that planar divisions resulted from a length limitation in astral microtubules (MTs) which precludes them from interacting with basal polarity, and orient spindles from the local geometry of apical domains. Accordingly, lengthening MTs affected spindle planarity, cell positioning, and crypt arrangement. We conclude that MT length regulation may serve as a key mechanism for spindles to sense local cell shapes and tissue forces to preserve mammalian epithelial architecture.

Quantitative models for building and growing fated small cell networks

Small cell clusters exhibit numerous phenomena typically associated with complex systems, such as division of labour and programmed cell death. A conserved class of such clusters occurs during oogenesis in the form of germline cysts that give rise to oocytes. Germline cysts form through cell divisions with incomplete cytokinesis, leaving cells intimately connected through intercellular bridges that facilitate cyst generation, cell fate determination and collective growth dynamics. Using the well-characterized Drosophila melanogaster female germline cyst as a foundation, we present mathematical models rooted in the dynamics of cell cycle proteins and their interactions to explain the generation of germline cell lineage trees (CLTs) and highlight the diversity of observed CLT sizes and topologies across species. We analyse competing models of symmetry breaking in CLTs to rationalize the observed dynamics and robustness of oocyte fate specification, and highlight remaining gaps in knowledge. We also explore how CLT topology affects cell cycle dynamics and synchronization and highlight mechanisms of intercellular coupling that underlie the observed collective growth patterns during oogenesis. Throughout, we point to similarities across organisms that warrant further investigation and comment on the extent to which experimental and theoretical findings made in model systems extend to other species.

The extra-embryonic space and the local contour are crucial geometric constraints regulating cell arrangement

In multicellular systems, cells communicate with adjacent cells to determine their positions and fates, an arrangement important for cellular development. Orientation of cell division, cell-cell interactions (i.e. attraction and repulsion) and geometric constraints are three major factors that define cell arrangement. In particular, geometric constraints are difficult to reveal in experiments, and the contribution of the local contour of the boundary has remained elusive. In this study, we developed a multicellular morphology model based on the phase-field method so that precise geometric constraints can be incorporated. Our application of the model to nematode embryos predicted that the amount of extra-embryonic space, the empty space within the eggshell that is not occupied by embryonic cells, affects cell arrangement in a manner dependent on the local contour and other factors. The prediction was validated experimentally by increasing the extra-embryonic space in the Caenorhabditis elegans embryo. Overall, our analyses characterized the roles of geometrical contributors, specifically the amount of extra-embryonic space and the local contour, on cell arrangements. These factors should be considered for multicellular systems.

Summary: The local contour and the extra-embryonic space, the empty space within the eggshell not occupied by embryonic cells, are important geometric constraints in cell arrangement of nematode embryos.

Aster repulsion drives short-ranged ordering in the Drosophila syncytial blastoderm

Biological systems are highly complex, yet notably ordered structures can emerge. During syncytial stage development of the Drosophila melanogaster embryo, nuclei synchronously divide for nine cycles within a single cell, after which most of the nuclei reach the cell cortex. The arrival of nuclei at the cortex occurs with remarkable positional order, which is important for subsequent cellularisation and morphological transformations. Yet, the mechanical principles underlying this lattice-like positional order of nuclei remain untested. Here, using quantification of nuclei position and division orientation together with embryo explants, we show that short-ranged repulsive interactions between microtubule asters ensure the regular distribution and maintenance of nuclear positions in the embryo. Such ordered nuclear positioning still occurs with the loss of actin caps and even the loss of the nuclei themselves; the asters can self-organise with similar distribution to nuclei in the wild-type embryo. The explant assay enabled us to deduce the nature of the mechanical interaction between pairs of nuclei. We used this to predict how the nuclear division axis orientation changes upon nucleus removal from the embryo cortex, which we confirmed in vivo with laser ablation. Overall, we show that short-ranged microtubule-mediated repulsive interactions between asters are important for ordering in the early Drosophila embryo and minimising positional irregularity.

Symmetry-breaking of animal cytokinesis

Cytokinesis is a mechanism that separates dividing cells via constriction of a supramolecular structure, the contractile ring. In animal cells, three modes of symmetry-breaking of cytokinesis result in unilateral cytokinesis, asymmetric cell division, and oriented cell division. Each mode of cytokinesis plays a significant role in tissue patterning and morphogenesis by the mechanisms that control the orientation and position of the contractile ring relative to the body axis. Despite its significance, the mechanisms involved in the symmetry-breaking of cytokinesis remain unclear in many cell types. Classical embryologists have identified that the geometric relationship between the mitotic spindle and cell cortex induces cytokinesis asymmetry; however, emerging evidence suggests that a concerted flow of compressional cell-cortex materials (cortical flow) is a spindle-independent driving force in spatial cytokinesis control. This review provides an overview of both classical and emerging mechanisms of cytokinesis asymmetry and their roles in animal development.

Combined effect of cell geometry and polarity domains determines the orientation of unequal division

Cell division orientation is thought to result from a competition between cell geometry and polarity domains controlling the position of the mitotic spindle during mitosis. Depending on the level of cell shape anisotropy or the strength of the polarity domain, one dominates the other and determines the orientation of the spindle. Whether and how such competition is also at work to determine unequal cell division (UCD), producing daughter cells of different size, remains unclear. Here, we show that cell geometry and polarity domains cooperate, rather than compete, in positioning the cleavage plane during UCDs in early ascidian embryos. We found that the UCDs and their orientation at the ascidian third cleavage rely on the spindle tilting in an anisotropic cell shape, and cortical polarity domains exerting different effects on spindle astral microtubules. By systematically varying mitotic cell shape, we could modulate the effect of attractive and repulsive polarity domains and consequently generate predicted daughter cell size asymmetries and position. We therefore propose that the spindle position during UCD is set by the combined activities of cell geometry and polarity domains, where cell geometry modulates the effect of cortical polarity domain(s).

Blastocoel morphogenesis: A biophysics perspective

The blastocoel is a fluid-filled cavity characteristic of animal embryos at the blastula stage. Its emergence is commonly described as the result of cleavage patterning, but this historical view conceals a large diversity of mechanisms and overlooks many unsolved questions from a biophysics perspective. In this review, we describe generic mechanisms for blastocoel morphogenesis, rooted in biological literature and simple physical principles. We propose novel directions of study and emphasize the importance to study blastocoel morphogenesis as an evolutionary and physical continuum.

A theoretical understanding of mammalian preimplantation development

The blastocyst has long been a hallmark system of study in developmental biology due to its importance in mammalian development and clinical relevance for assisted reproductive technologies. In recent years, the blastocyst is emerging as a system of study for mathematical modelling. In this review, we compile, to our knowledge, all models describing preimplantation development. Coupled with experiments, these models have provided insight regarding the morphogenesis and cell-fate specification throughout preimplantation development. In the case of cell-fate specification, theoretical models have provided mechanisms explaining how proportion of cell types are established and maintained when confronted to perturbations. For cell-shape based models, they have described quantitatively how mechanical forces sculpt the blastocyst and even predicted how morphogenesis could be manipulated. As theoretical biology develops, we believe the next critical stage in modelling involves an integration of cell fate and mechanics to provide integrative models of development at distinct spatiotemporal scales. We discuss how, building on a balanced base of mechanical and chemical models, the preimplantation embryo will play a key role in integrating these two faces of the same coin.

Cell division geometries as central organizers of early embryo development

Early cellular patterning is a critical step of embryonic development that determines the proper progression of morphogenesis in all metazoans. It relies on a series of rapid reductive divisions occurring simultaneously with the specification of the fate of different subsets of cells. Multiple species developmental strategies emerged in the form of a unique cleavage pattern with stereotyped division geometries. Cleavage geometries have long been associated to the emergence of canonical developmental features such as cell cycle asynchrony, zygotic genome activation and fate specification. Yet, the direct causal role of division positioning on blastomere cell behavior remain partially understood. Oriented and/or asymmetric divisions define blastomere cell sizes, contacts and positions, with potential immediate impact on cellular decisions, lineage specification and morphogenesis. Division positions also instruct daughter cells polarity, mechanics and geometries, thereby influencing subsequent division events, in an emergent interplay that may pattern early embryos independently of firm deterministic genetic programs. We here review the recent literature which helped to delineate mechanisms and functions of division positioning in early embryos.

Mechanical and genetic control of ascidian endoderm invagination during gastrulation

Gastrulation is a near universal developmental process of animal embryogenesis, during which dramatic morphogenetic events take place: the mesodermal and endodermal tissues are internalized, the ectoderm spreads to cover the embryo surface, and the animal body plan and germ layers are established. Morphogenesis during gastrulation has long been considered the result of spatio-temporally localised forces driven by the transcriptional programme of the embryo. Recent work has shown that tissue rheological properties, which define the mechanical response of tissues to internally-generated or external forces, are also important dynamic regulators of gastrulation. Here, we first introduce how embryonic mechanics can be represented, before outlining current knowledge of the mechanical and genetic control of gastrulation in ascidians, invertebrate marine chordates which develop with invariant cell lineages and a solid-like rheological behaviour until the neurula stages. We discuss the potential of these organisms for the experimental and computational whole-embryo characterisation of the mechanisms shaping gastrulation, and how they may inform the more complex tissue internalization strategies used by other model organisms.

Roadmap for the multiscale coupling of biochemical and mechanical signals during development

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

Physical constraints on early blastomere packings

At very early embryonic stages, when embryos are composed of just a few cells, establishing the correct packing arrangements (contacts) between cells is essential for the proper development of the organism. As early as the 4-cell stage, the observed cellular packings in different species are distinct and, in many cases, differ from the equilibrium packings expected for simple adherent and deformable particles. It is unclear what are the specific roles that different physical parameters, such as the forces between blastomeres, their division times, orientation of cell division and embryonic confinement, play in the control of these packing configurations. Here we simulate the non-equilibrium dynamics of cells in early embryos and systematically study how these different parameters affect embryonic packings at the 4-cell stage. In the absence of embryo confinement, we find that cellular packings are not robust, with multiple packing configurations simultaneously possible and very sensitive to parameter changes. Our results indicate that the geometry of the embryo confinement determines the packing configurations at the 4-cell stage, removing degeneracy in the possible packing configurations and overriding division rules in most cases. Overall, these results indicate that physical confinement of the embryo is essential to robustly specify proper cellular arrangements at very early developmental stages.

At the initial stages of embryogenesis, the precise arrangement of cells in the embryo is critical to ensure that each cell gets the right chemical and physical signals to guide the formation of the organism. Even when the embryo is made of only four cells, different species feature varying cellular arrangements: cells in mouse embryos arrange as a tetrahedron, in the nematode worm C. elegans cells make a diamond and in sea urchins cells arrange in a square configuration. How do cells in embryos of different species control their arrangements? Using computer simulations, we studied how cell divisions, physical contacts between cells and the confinement of the embryo by an eggshell affect the arrangements of cells when the embryos have only 4 cells. We find that the shape of the confining eggshell plays a key role in controlling the cell arrangements, removing unwanted arrangements and robustly specifying the proper contacts between cells. Our results highlight the important roles of embryonic confinement in establishing the proper cell-cell contacts as the embryo starts to develop.

Apical Relaxation during Mitotic Rounding Promotes Tension-Oriented Cell Division

Global tissue tension anisotropy has been shown to trigger stereotypical cell division orientation by elongating mitotic cells along the main tension axis. Yet, how tissue tension elongates mitotic cells despite those cells undergoing mitotic rounding (MR) by globally upregulating cortical actomyosin tension remains unclear. We addressed this question by taking advantage of ascidian embryos, consisting of a small number of interphasic and mitotic blastomeres and displaying an invariant division pattern. We found that blastomeres undergo MR by locally relaxing cortical tension at their apex, thereby allowing extrinsic pulling forces from neighboring interphasic blastomeres to polarize their shape and thus division orientation. Consistently, interfering with extrinsic forces by reducing the contractility of interphasic blastomeres or disrupting the establishment of asynchronous mitotic domains leads to aberrant mitotic cell division orientations. Thus, apical relaxation during MR constitutes a key mechanism by which tissue tension anisotropy controls stereotypical cell division orientation.

In Vitro Reconstitution of Dynein Force Exertion in a Bulk Viscous Medium

The forces generated by microtubules (MTs) and their associated motors orchestrate essential cellular processes ranging from vesicular trafficking to centrosome positioning [1, 2]. To date, most studies have focused on MT force exertion by motors anchored to a static surface, such as the cell cortex in vivo or glass surfaces in vitro [2-4]. However, motors also transport large cargos and endomembrane networks, whose hydrodynamic interactions with the viscous cytoplasm should generate sizable forces in bulk. Such forces may contribute to MT aster centration, organization, and orientation [5-14] but have yet to be evidenced and studied in a minimal reconstituted system. By developing a bulk motility assay, based on stabilized MTs and dynein-coated beads freely floating in a viscous medium away from any surface, we demonstrate that the motion of a cargo exerts a pulling force on the MT and propels it in opposite direction. Quantification of resulting MT movements for different motors, motor velocities, over a range of cargo sizes and medium viscosities shows that the efficiency of this mechanism is primarily determined by cargo size and MT length. Forces exerted by cargos are additive, allowing us to recapitulate tug-of-war situations or bi-dimensional motions of minimal asters. These data also reveal unappreciated effects of the nature of viscous crowders and hydrodynamic interactions between cargos and MTs, likely relevant to understand this mode of force exertion in living cells. This study reinforces the notion that endomembrane transport can exert significant forces on MTs.

Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution

The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.

The Perinuclear ER Scales Nuclear Size Independently of Cell Size in Early Embryos

Nuclear size plays pivotal roles in gene expression, embryo development, and disease. A central hypothesis in organisms ranging from yeast to vertebrates is that nuclear size scales to cell size. This implies that nuclei may reach steady-state sizes set by limiting cytoplasmic pools of size-regulating components. By monitoring nuclear dynamics in early sea urchin embryos, we found that nuclei undergo substantial growth in each interphase, reaching a maximal size prior to mitosis that declined steadily over the course of development. Manipulations of cytoplasmic volume through multiple chemical and physical means ruled out cell size as a major determinant of nuclear size and growth. Rather, our data suggest that the perinuclear endoplasmic reticulum, accumulated through dynein activity, serves as a limiting membrane pool that sets nuclear surface growth rate. Partitioning of this local pool at each cell division modulates nuclear growth kinetics and dictates size scaling throughout early development.

Contact area-dependent cell communication and the morphological invariance of ascidian embryogenesis

Marine invertebrate ascidians display embryonic reproducibility: Their early embryonic cell lineages are considered invariant and are conserved between distantly related species, despite rapid genomic divergence. Here, we address the drivers of this reproducibility. We used light-sheet imaging and automated cell segmentation and tracking procedures to systematically quantify the behavior of individual cells every 2 minutes during Phallusia mammillata embryogenesis. Interindividual reproducibility was observed down to the area of individual cell contacts. We found tight links between the reproducibility of embryonic geometries and asymmetric cell divisions, controlled by differential sister cell inductions. We combined modeling and experimental manipulations to show that the area of contact between signaling and responding cells is a key determinant of cell communication. Our work establishes the geometric control of embryonic inductions as an alternative to classical morphogen gradients and suggests that the range of cell signaling sets the scale at which embryonic reproducibility is observed.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Simulations of sea urchin early development delineate the role of oriented cell division in the morula-to-blastula transition

The sea urchin morula to blastula transition has long been thought to require oriented cell divisions and blastomere adherence to the enveloping hyaline layer. In a computer simulation model, cell divisions constrained by a surface plane division rule are adequate to effect morphological transition. The hyaline membrane acts as an enhancer but is not essential. The model is consistent with the orientation of micromere divisions and the open blastulae of direct developing species. The surface plane division rule precedes overt epithelization of surface cells and acts to organize the developing epithelium. It is a universal feature of early metazoan development and simulations of non-echinoid cleavage patterns support its role throughout Metazoa. The surface plane division rule requires only local cues and cells need not reference global positional information or embryonic axes.

Why and how the nematode's early embryogenesis can be precise and robust: a mechanical perspective

The early embryogenesis in the nematode Caenorhabditis elegans is well-known for its stereotypic precision of cell arrangements and their lineage relationship. Much research has been focused on how biochemical processes achieve the highly reproducible cell lineage tree. However, the origin of the robustness in the cell arrangements is poorly understood. Here, we set out to provide a mechanistic explanation of how combining mechanical forces with the order and orientation of cell division ensures a robust arrangement of cells. We used a simplified mechanical model to simulate the arrangement of cells in the face of different disturbances. As a result, we revealed three fail-safe principles for cell self-organization in early nematode embryogenesis: ordering, simultaneity, and the division orientation of cell division events. Our work provides insight into the developmental strategy and contributes to the understanding of how robust or variable the cell arrangement can be in developing embryos.

Cytoskeleton Force Exertion in Bulk Cytoplasm

The microtubule and actin cytoskeletons generate forces essential to position centrosomes, nuclei, and spindles for division plane specification. While the largest body of work has documented force exertion at, or close to the cell surface, mounting evidence suggests that cytoskeletal polymers can also produce significant forces directly from within the cytoplasm. Molecular motors such as kinesin or dynein may for instance displace cargos and endomembranes in the viscous cytoplasm yielding friction forces that pull or push microtubules. Similarly, the dynamics of bulk actin assembly/disassembly or myosin-dependent contractions produce cytoplasmic forces which influence the spatial organization of cells in a variety of processes. We here review the molecular and physical mechanisms supporting bulk cytoplasmic force generation by the cytoskeleton, their limits and relevance to organelle positioning, with a particular focus on cell division.

Organelle size scaling over embryonic development

Cell division without growth results in progressive cell size reductions during early embryonic development. How do the sizes of intracellular structures and organelles scale with cell size and what are the functional implications of such scaling relationships? Model organisms, in particular Caenorhabditis elegans worms, Drosophila melanogaster flies, Xenopus laevis frogs, and Mus musculus mice, have provided insights into developmental size scaling of the nucleus, mitotic spindle, and chromosomes. Nuclear size is regulated by nucleocytoplasmic transport, nuclear envelope proteins, and the cytoskeleton. Regulators of microtubule dynamics and chromatin compaction modulate spindle and mitotic chromosome size scaling, respectively. Developmental scaling relationships for membrane-bound organelles, like the endoplasmic reticulum, Golgi, mitochondria, and lysosomes, have been less studied, although new imaging approaches promise to rectify this deficiency. While models that invoke limiting components and dynamic regulation of assembly and disassembly can account for some size scaling relationships in early embryos, it will be exciting to investigate the contribution of newer concepts in cell biology such as phase separation and interorganellar contacts. With a growing understanding of the underlying mechanisms of organelle size scaling, future studies promise to uncover the significance of proper scaling for cell function and embryonic development, as well as how aberrant scaling contributes to disease. This article is categorized under: Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Early Embryonic Development > Fertilization to Gastrulation Comparative Development and Evolution > Model Systems.

A Tug-of-War between Cell Shape and Polarity Controls Division Orientation to Ensure Robust Patterning in the Mouse Blastocyst

Oriented cell division patterns tissues by modulating cell position and fate. While cell geometry, junctions, cortical tension, and polarity are known to control division orientation, relatively little is known about how these are coordinated to ensure robust patterning. Here, we systematically characterize cell division, volume, and shape changes during mouse pre-implantation development by in toto live imaging. The analysis leads us to a model in which the apical domain competes with cell shape to determine division orientation. Two key predictions of the model are verified experimentally: when outside cells of the 16-cell embryo are released from cell shape asymmetry, the axis of division is guided by the apical domain. Conversely, orientation cues from the apical domain can be overcome by applied shape asymmetry in the 8-cell embryo. We propose that such interplay between cell shape and polarity in controlling division orientation ensures robust patterning of the blastocyst and possibly other tissues.

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Cell division, volume, and shape changes are characterized by in toto embryo imaging

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Cell shape and the apical domain compete to determine division orientation

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Two key predictions of the model are verified experimentally

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The tug-of-war mechanism ensures robust cell allocation and patterning

Emergence of Embryo Shape During Cleavage Divisions

Cells are arranged into species-specific patterns during early embryogenesis. Such cell division patterns are important since they often reflect the distribution of localized cortical factors from eggs/fertilized eggs to specific cells as well as the emergence of organismal form. However, it has proven difficult to reveal the mechanisms that underlie the emergence of cell positioning patterns that underlie embryonic shape, likely because a systems-level approach is required that integrates cell biological, genetic, developmental, and mechanical parameters. The choice of organism to address such questions is also important. Because ascidians display the most extreme form of invariant cleavage pattern among the metazoans, we have been analyzing the cell biological mechanisms that underpin three aspects of cell division (unequal cell division (UCD), oriented cell division (OCD), and asynchronous cell cycles) which affect the overall shape of the blastula-stage ascidian embryo composed of 64 cells. In ascidians, UCD creates two small cells at the 16-cell stage that in turn undergo two further successive rounds of UCD. Starting at the 16-cell stage, the cell cycle becomes asynchronous, whereby the vegetal half divides before the animal half, thus creating 24-, 32-, 44-, and then 64-cell stages. Perturbing either UCD or the alternate cell division rhythm perturbs cell position. We propose that dynamic cell shape changes propagate throughout the embryo via cell-cell contacts to create the ascidian-specific invariant cleavage pattern.

Evolutionary modification of AGS protein contributes to formation of micromeres in sea urchins

Evolution is proposed to result, in part, from acquisition of new developmental programs. One such example is the appearance of the micromeres in a sea urchin that form by an asymmetric cell division at the 4th embryonic cleavage and function as a major signaling center in the embryo. Micromeres are not present in other echinoderms and thus are  considered as a derived feature, yet its acquisition mechanism is unknown. Here, we report that the polarity factor AGS and its associated proteins are responsible for micromere formation. Evolutionary modifications of AGS protein seem to have provided the cortical recruitment and binding of AGS to the vegetal cortex, contributing to formation of micromeres in the sea urchins. Indeed, introduction of sea urchin AGS into the sea star embryo induces asymmetric cell divisions, suggesting that the molecular evolution of AGS protein is key in the transition of echinoderms to micromere formation and the current developmental style of sea urchins not seen in other echinoderms.

Cell shape and intercellular adhesion regulate mitotic spindle orientation

Cell division orientation plays an essential role in tissue morphogenesis and cell fate decision. Recent studies showed that either cell shape or adhesion geometry can regulate the orientation of mitotic spindles and thereby the cell division orientation. However, how they together regulate the spindle orientation remains largely unclear. In this work, we use a general computational model to investigate the competitive mechanism of determining the spindle orientation between cell shape and intercellular adhesion in epithelial cells. We find the spindle orientation is dominated by the intercellular adhesion when the cell shape anisotropy is small, but dominated by the cell shape when the shape anisotropy is large. A strong adhesion and moderate adhesive size can ensure the planar division of epithelial cells with large apico-basal elongation. We also find the spindle orientation could be perpendicular to the adhesive region when only one side of the cell is adhered to an E-cadherin-coated matrix. But after the cell is compressed, the spindle orientation is governed by the cell shape and the spindle will be parallel to the adhesive region when the cell shape anisotropy is large. Finally, we demonstrate the competition between cell shape and tricellular junctions can also effectively regulate the spindle orientation.

Self-Similar Dynamics of Nuclear Packing in the Early Drosophila Embryo

Embryonic development starts with cleavages, a rapid sequence of reductive divisions that result in an exponential increase of cell number without changing the overall size of the embryo. In Drosophila, the final four rounds of cleavages occur at the surface of the embryo and give rise to ∼6000 nuclei under a common plasma membrane. We use live imaging to study the dynamics of this process and to characterize the emergent nuclear packing in this system. We show that the characteristic length scale of the internuclear interaction scales with the density, which allows the densifying embryo to sustain the level of structural order at progressively smaller length scales. This is different from nonliving materials, which typically undergo disorder-order transition upon compression. To explain this dynamics, we use a particle-based model that accounts for density-dependent nuclear interactions and synchronous divisions. We reproduce the pair statistics of the disordered packings observed in embryos and recover the scaling relation between the characteristic length scale and the density both in real and reciprocal space. This result reveals how the embryo can robustly preserve the nuclear-packing structure while being densified. In addition to providing quantitative description of self-similar dynamics of nuclear packings, this model generates dynamic meshes for the computational analysis of pattern formation and tissue morphogenesis.

Asymmetric division through a reduction of microtubule centering forces

Asymmetric divisions are essential for the generation of cell fate and size diversity. They implicate cortical domains where minus end-directed motors, such as dynein, are activated to pull on microtubules to decenter asters attached to centrosomes, nuclei, or spindles. In asymmetrically dividing cells, aster decentration typically follows a centering phase, suggesting a time-dependent regulation in the competition between microtubule centering and decentering forces. Using symmetrically dividing sea urchin zygotes, we generated cortical domains of magnetic particles that spontaneously cluster endogenous dynein activity. These domains efficiently attract asters and nuclei, yielding marked asymmetric divisions. Remarkably, aster decentration only occurred after asters had first reached the cell center. Using intracellular force measurement and models, we demonstrate that this time-regulated imbalance results from a global reduction of centering forces rather than a local maturation of dynein activity at the domain. Those findings define a novel paradigm for the regulation of division asymmetry.

Modeling Embryonic Cleavage Patterns

The division patterns of early invertebrate and vertebrate embryos are key to the specification of cell fates and embryo body axes. We here describe a generic computational modeling method to quantitatively test mechanisms which specify successive division position and orientation of eggs and early blastomeres in 3D. This approach should serve to motivate and guide future experimental work on the mechanisms controlling early embryo morphogenesis.

Predicting Division Planes of Three-Dimensional Cells by Soap-Film Minimization

One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal plant body organization. To determine the importance of cell geometry in division plane orientation, we designed a three-dimensional probabilistic mathematical model to directly test the century-old hypothesis that cell divisions mimic soap-film minima. According to this hypothesis, daughter cells have equal volume and the division plane occurs where the surface area is at a minimum. We compared predicted division planes to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was directly adjacent to the predicted division site to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant cells (maize [Zea mays] epidermal cells and developing ligule cells and Arabidopsis thaliana guard cells) and animal cells (Caenorhabditis elegans embryonic cells) to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

Predicting Division Planes of Three-Dimensional Cells by Soap-Film Minimization

One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal plant body organization. To determine the importance of cell geometry in division plane orientation, we designed a three-dimensional probabilistic mathematical model to directly test the century-old hypothesis that cell divisions mimic soap-film minima. According to this hypothesis, daughter cells have equal volume and the division plane occurs where the surface area is at a minimum. We compared predicted division planes to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was directly adjacent to the predicted division site to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant cells (maize [Zea mays] epidermal cells and developing ligule cells and Arabidopsis thaliana guard cells) and animal cells (Caenorhabditis elegans embryonic cells) to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters

In early embryos, microtubules form star-shaped aster structures that can measure up to hundreds of micrometres, and move at high speeds to find the geometrical centre of the cell. This process, known as aster centration, is essential for the fidelity of cell division and development, but how cells succeed in moving these large structures through their crowded and fluctuating cytoplasm remains unclear. Here, we demonstrate that the positional fluctuations of migrating sea urchin sperm asters are small, anisotropic, and associated with the stochasticity of dynein-dependent forces moving the aster. Using in vivo magnetic tweezers to directly measure aster forces inside cells, we derive a linear aster force-velocity relationship and provide evidence for a spring-like active mechanism stabilizing the transverse position of the asters. The large frictional coefficient and spring constant quantitatively account for the amplitude and growth characteristics of athermal positional fluctuations, demonstrating that aster mechanics ensure noise suppression to promote persistent and precise centration. These findings define generic biophysical regimes of active cytoskeletal mechanics underlying the accuracy of cell division and early embryonic development.

Combinatorial Contact Cues Specify Cell Division Orientation by Directing Cortical Myosin Flows

Cell division axes during development are specified in different orientations to establish multicellular assemblies, but the mechanisms that generate division axis diversity remain unclear. We show here that patterns of cell contact provide cues that diversify cell division orientation by modulating cortical non-muscle myosin flow. We reconstituted in vivo contact patterns using beads or isolated cells to show two findings. First, we identified three contact-dependent cues that pattern cell division orientation and myosin flow: physical contact, contact asymmetry, and a Wnt signal. Second, we experimentally demonstrated that myosin flow generates forces that trigger plasma membrane movements and propose that their anisotropy drives cell division orientation. Our data suggest that contact-dependent control of myosin specifies the division axes of Caenorhabditis elegans AB, ABa, EMS cells, and the mouse AB cell. The contact pattern-dependent generation of myosin flows, in concert with known microtubule/dynein pathways, may greatly expand division axis diversity during development.

Dynamic interplay of cell fate, polarity and force generation in ascidian embryos

A fundamental challenge in developmental biology is to understand how forces produced by individual cells are patterned in space and time and then integrated to produce stereotyped changes in tissue-level or embryo-level morphology. Ascidians offer a unique opportunity to address this challenge by studying how small groups of cells collectively execute complex, but highly stereotyped morphogenetic movements. Here we highlight recent progress and open questions in the study of ascidian morphogenesis, emphasizing the dynamic interplay of cell fate determination, cellular force generation and tissue-level mechanics.

How cells sense their own shape - mechanisms to probe cell geometry and their implications in cellular organization and function

Cells come in a variety of shapes that most often underlie their functions. Regulation of cell morphogenesis implies that there are mechanisms for shape sensing that still remain poorly appreciated. Global and local cell geometry features, such as aspect ratio, size or membrane curvature, may be probed by intracellular modules, such as the cytoskeleton, reaction-diffusion systems or molecular complexes. In multicellular tissues, cell shape emerges as an important means to transduce tissue-inherent chemical and mechanical cues into intracellular organization. One emergent paradigm is that cell-shape sensing is most often based upon mechanisms of self-organization, rather than determinism. Here, we review relevant work that has elucidated some of the core principles of how cellular geometry may be conveyed into spatial information to guide processes, such as polarity, signaling, morphogenesis and division-plane positioning.

Regulating positioning and orientation of mitotic spindles via cell size and shape

Proper location of the mitotic spindle is critical for chromosome segregation and the selection of the cell division plane. However, how mitotic spindles sense cell size and shape to regulate their own position and orientation is still largely unclear. To investigate this question systematically, we used a general model by considering chromosomes, microtubule dynamics, and forces of various molecular motors. Our results show that in cells of various sizes and shapes, spindles can always be centered and oriented along the long axis robustly in the absence of other specified mechanisms. We found that the characteristic time of positioning and orientation processes increases with cell size. Spindles sense the cell size mainly by the cortical force in small cells and by the cytoplasmic force in large cells. In addition to the cell size, the cell shape mainly influences the orientation process. We found that more slender cells have a faster orientation process, and the final orientation is not necessarily along the longest axis but is determined by the radial profile and the symmetry of the cell shape. Finally, our model also reproduces the separation and repositioning of the spindle poles during the anaphase. Therefore, our work provides a general tool for studying the mitotic spindle across the whole mitotic phase.

An asymmetric attraction model for the diversity and robustness of cell arrangement in nematodes

During early embryogenesis in animals, cells are arranged into a species-specific pattern in a robust manner. Diverse cell arrangement patterns are observed, even among close relatives. In the present study, we evaluated the mechanisms by which the diversity and robustness of cell arrangements are achieved in developing embryos. We successfully reproduced various patterns of cell arrangements observed in various nematode species in Caenorhabditis elegans embryos by altering the eggshell shapes. The findings suggest that the observed diversity of cell arrangements can be explained by differences in the eggshell shape. Additionally, we found that the cell arrangement was robust against eggshell deformation. Computational modeling revealed that, in addition to repulsive forces, attractive forces are sufficient to achieve such robustness. The present model is also capable of simulating the effect of changing cell division orientation. Genetic perturbation experiments demonstrated that attractive forces derived from cell adhesion are necessary for the robustness. The proposed model accounts for both diversity and robustness of cell arrangements, and contributes to our understanding of how the diversity and robustness of cell arrangements are achieved in developing embryos.

Summary: The cell arrangement pattern at the four-cell stage in nematode embryos is both diverse and robust. A numerical model that incorporates attractive, as well as repulsive, forces was constructed to explain this diversity and robustness.

Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data

Modern fluorescence microscopy enables fast 3D imaging of biological and inert systems alike. In many studies, it is important to detect the surface of objects and quantitatively characterize its local geometry, including its mean curvature. We present a fully automated algorithm to determine the location and curvatures of an object from 3D fluorescence images, such as those obtained using confocal or light-sheet microscopy. The algorithm aims at reconstructing surface labelled objects with spherical topology and mild deformations from the spherical geometry with high accuracy, rather than reconstructing arbitrarily deformed objects with lower fidelity. Using both synthetic data with known geometrical characteristics and experimental data of spherical objects, we characterize the algorithm's accuracy over the range of conditions and parameters typically encountered in 3D fluorescence imaging. We show that the algorithm can detect the location of the surface and obtain a map of local mean curvatures with relative errors typically below 2% and 20%, respectively, even in the presence of substantial levels of noise. Finally, we apply this algorithm to analyse the shape and curvature map of fluorescently labelled oil droplets embedded within multicellular aggregates and deformed by cellular forces.

The invariant cleavage pattern displayed by ascidian embryos depends on spindle positioning along the cell's longest axis in the apical plane and relies on asynchronous cell divisions

The ascidian embryo is an ideal system to investigate how cell position is determined during embryogenesis. Using 3D timelapse imaging and computational methods we analyzed the planar cell divisions in ascidian early embryos and found that spindles in every cell tend to align at metaphase in the long length of the apical surface except in cells undergoing unequal cleavage. Furthermore, the invariant and conserved cleavage pattern of ascidian embryos was found to consist in alternate planar cell divisions between ectoderm and endomesoderm. In order to test the importance of alternate cell divisions we manipulated zygotic transcription induced by β-catenin or downregulated wee1 activity, both of which abolish this cell cycle asynchrony. Crucially, abolishing cell cycle asynchrony consistently disrupted the spindle orienting mechanism underpinning the invariant cleavage pattern. Our results demonstrate how an evolutionary conserved cell cycle asynchrony maintains the invariant cleavage pattern driving morphogenesis of the ascidian blastula.

DOI:http://dx.doi.org/10.7554/eLife.19290.001

The position of cells within an embryo early in development determines what type of cells they will become in the fully formed embryo. The embryos of ascidians, commonly known as sea squirts, are ideal for studying what influences cell positioning. These embryos consist of a small number of cells that divide according to an “invariant cleavage pattern”, which means that the positioning and timing of the cell divisions is identical between different individuals of the same species. The pattern of cell division is also largely the same across different ascidian species, which raises questions about how it is controlled.

When a cell divides, a structure called the spindle forms inside it to distribute copies of the cell’s genetic material between the new cells. The orientation of the spindle determines the direction in which the cell will divide. Now, by combining 3D imaging of living ascidian embryos with computational modeling, Dumollard et al. show that the spindles in every equally dividing cell tend to all align in the long length of the cell’s “apical” surface. Such alignment allows the cells to be on the outside of the embryo and implements the ascidian invariant cleavage pattern.

The cells in the embryo do not all divide at the same time. Indeed, the shape of the cells (and especially their apical surface) depends on two layers of cells in the embryo not dividing at the same time; instead, periods of cell division alternate between the layers. A network of genes in the embryo regulates the timing of these cell divisions and makes it possible for the cells to divide according to an invariant cleavage pattern.

However, this network of genes is not the only control mechanism that shapes the early embryo. A structure found in egg cells (and hence produced by the embryo’s mother) causes cells at the rear of the embryo to divide unequally, and this influences the shape of all the cells in the embryo. Thus it appears that maternal mechanisms work alongside the embryo’s gene network to shape the early embryo.

The next step will be to determine how physical forces – for example, from the cells pressing against each other – influence the position of the embryo’s cells. How do gene networks relay the biomechanical properties of the embryo to help it take shape?

DOI:http://dx.doi.org/10.7554/eLife.19290.002