Scutoids are a geometrical solution to three-dimensional packing of epithelia

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes, adopting a shape named 'scutoid' that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here, we use live imaging of the sea star embryo coupled with deep learning-based segmentation to dissect the relative contributions of cell density, tissue compaction and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing immediately after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

Morphoelastic models discriminate between different mechanisms of left-right asymmetric stomach morphogenesis

The mechanisms by which the vertebrate stomach undergoes its evolutionarily conserved leftward bending remain incompletely understood. Although the left and right sides of the organ are known to possess different gene expression patterns and undergo distinct morphogenetic events, the physical mechanisms by which these differences generate morphological asymmetry remain unclear. Here, we develop a continuum model of asymmetric stomach morphogenesis. Using a morphoelastic framework, we investigate the morphogenetic implications of a variety of hypothetical, tissue-level growth differences between the left and right sides of a simplified tubular organ. Simulations reveal that, of the various differential growth mechanisms tested, only one category is consistent with the leftward stomach curvature observed in wild-type embryos: equal left and right volumetric growth rates, coupled with transversely isotropic tissue thinning on the left side. Simulating this mechanism in a defined region of the model over a longer period of growth leads to mature stomach-like curvatures.

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes adopting a shape named "scutoid" that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here we use live-imaging of the sea star embryo coupled with deep learning-based segmentation, to dissect the relative contributions of cell density, tissue compaction, and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing just after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Morphology of the cornea and iris in the Australian lungfish Neoceratodus forsteri (Krefft 1870) (Dipnoi): Functional and evolutionary perspectives of transitioning from an aquatic to a terrestrial environment

The Australian lungfish, Neoceratodus forsteri (Krefft 1870), is the sole extant member of the Ceratodontidae within the Dipnoi, a small order of sarcopterygian (lobe-finned) fishes, that is thought to be the earliest branching species of extant lungfishes, having changed little over the last 100 million years. To extend studies on anatomical adaptations associated with the fish-tetrapod transition, the ultrastructure of the cornea and iris is investigated using light and electron (transmission and scanning) microscopy to investigate structure-function relationships and compare these to other vertebrate corneas (other fishes and tetrapods). In contrast to previous studies, the cornea is found to have only three main components, comprising an epithelium with its basement membrane, a stroma with a Bowman's layer and an endothelium, and is not split into a dermal (secondary) spectacle and a scleral cornea. The epithelial cells are large, relatively low in density and similar to many species of non-aquatic tetrapods and uniquely possess numerous surface canals that contain and release mucous granules onto the corneal surface to avoid desiccation. A Bowman's layer is present and, in association with extensive branching and anastomosing of the collagen fibrils, may be an adaptation for the inhibition of swelling and/or splitting of the stroma during its amphibious lifestyle. The dorsal region of the stroma possesses aggregations of pigment granules that act as a yellow, short wavelength-absorbing filter during bright light conditions. Desçemet's membrane is absent and replaced by an incomplete basement membrane overlying a monocellular endothelium. The iris is pigmented, well-developed, vascularised and contractile containing reflective crystals anteriorly. Based upon its ultrastructure and functional adaptations, the cornea of N. forsteri is more similar to amphibians than to other bony fishes and is well-adapted for an amphibious lifestyle.

Dispersive Modeling of Normal and Cancerous Cervical Cell Responses to Nanosecond Electric Fields in Reversible Electroporation Using a Drift-Step Rectifier Diode Generator

This paper creates an approximate three-dimensional model for normal and cancerous cervical cells using image processing and computer-aided design (CAD) tools. The model is then exposed to low-frequency electric pulses to verify the work with experimental data. The transmembrane potential, pore density, and pore radius evolution are analyzed. This work adds a study of the electrodeformation of cells under an electric field to investigate cytoskeleton integrity. The Maxwell stress tensor is calculated for the dispersive bi-lipid layer plasma membrane. The solid displacement is calculated under electric stress to observe cytoskeleton integrity. After verifying the results with previous experiments, the cells are exposed to a nanosecond pulsed electric field. The nanosecond pulse is applied using a drift-step rectifier diode (DSRD)-based generator circuit. The cells' transmembrane voltage (TMV), pore density, pore radius evolution, displacement of the membrane under electric stress, and strain energy are calculated. A thermal analysis of the cells under a nanosecond pulse is also carried out to prove that it constitutes a non-thermal process. The results showed differences in normal and cancerous cell responses to electric pulses due to changes in morphology and differences in the cells' electrical and mechanical properties. This work is a model-driven microdosimetry method that could be used for diagnostic and therapeutic purposes.

Geometric Angles and Gene Expression in Cells for Structural Bone Regeneration

Geometry and angles play crucial roles in cellular processes; however, its mechanisms of regulation remain unclear. In this study, a series of three dimensional (3D)-printed microfibers with different geometries is constructed using a near-field electrostatic printing technique to investigate the regulatory mechanisms of geometry on stem cell function and bone regeneration. The scaffolds precisely mimicked cell dimensions with high porosity and interoperability. Compared with other spatial topography angles, microfibers with a 90° topology can significantly promote the expression of osteogenic gene proteins in bone marrow-derived mesenchymal stem cells (BMSCs). The effects of different spatial structures on the expression profiles of BMSCs differentiation genes are correlated and validated using microRNA sequencing. Enrichment analysis shows that the 90° microfibers promoted osteogenesis in BMSCs by significantly upregulating miR-222-5p/cbfb/Runx2 expression. The ability of the geometric architecture to promote bone regeneration, as assessed using the cranial defect model, demonstrates that the 90° fiber scaffolds significantly promote new bone regeneration and neovascular neural network formation. This study is the first to elucidate the relationship between angular geometry and cellular gene expression, contributing significantly to the understanding of how geometric architecture can promote stem cell differentiation, proliferation, and function for structural bone regeneration.

CartoCell, a high-content pipeline for 3D image analysis, unveils cell morphology patterns in epithelia

Decades of research have not yet fully explained the mechanisms of epithelial self-organization and 3D packing. Single-cell analysis of large 3D epithelial libraries is crucial for understanding the assembly and function of whole tissues. Combining 3D epithelial imaging with advanced deep-learning segmentation methods is essential for enabling this high-content analysis. We introduce CartoCell, a deep-learning-based pipeline that uses small datasets to generate accurate labels for hundreds of whole 3D epithelial cysts. Our method detects the realistic morphology of epithelial cells and their contacts in the 3D structure of the tissue. CartoCell enables the quantification of geometric and packing features at the cellular level. Our single-cell cartography approach then maps the distribution of these features on 2D plots and 3D surface maps, revealing cell morphology patterns in epithelial cysts. Additionally, we show that CartoCell can be adapted to other types of epithelial tissues.

General, open-source vertex modeling in biological applications using Tissue Forge

Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering open-source, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in the C, C++ and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.

Tissues as networks of cells: towards generative rules of complex organ development

Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

The functional anatomy of the cornea of the Shorthead lamprey, Mordacia mordax (Mordaciidae, Agnatha): A comparison between downstream and upstream migrants

The Shorthead lamprey Mordacia mordax (Mordaciidae, Agnatha) represents one of the earliest stages of vertebrate evolution. This study investigates the ultrastructural anatomy of the cornea, iris and anterior chamber in the eyes of this species in both the downstream and upstream migrant phases of its protracted lifecycle to assess the morphological and quantitative changes associated with growth, corneal function and vision. Using light and both scanning and transmission electron microscopy, the cornea is found to be divided into dermal and scleral components separated by a mucoid layer. A range of distinguishing corneal features are compared in the two adult phases of the lifecycle, including epithelial microprojections, mucus-secreting epithelial cells, the number, thickness, formation and level of branching and anastomosing of collagen lamellae, the type and distribution of vertical sutures, the structure of the mucoid layer and annular ligament and the number and distribution of a large number of basement membranes throughout the cornea. Significant differences are found between the two phases, which are thought to reflect adaptations to the variable environmental conditions encountered throughout this species' lifecycle. The study provides insights into the evolutionary pressures on extant representatives of the earliest stages in the evolution of the vertebrate eye.

Time-Lapse Imaging and Morphometric Analysis of Tracheal Development in Drosophila

Detailed and quantitative analyses of the cellular events underlying the formation of specific organs or tissues is essential to understand the general mechanisms of morphogenesis and pattern formation. Observation of live tissues or whole-mount fixed specimens has emerged as the method of choice for identifying and quantifying specific cellular and tissular structures within the organism. In both cases, cell and subcellular structure identification and good quality image acquisition for these analyses are essential. Many markers for live imaging and fixed tissue are now available for detecting cell membranes, subcellular structures, and extracellular structures like the extracellular matrix (ECM). Combination of live imaging and analysis of fixed tissue is ideal to obtain a general and detailed picture of the events underlying embryonic development. By applying morphometric methods to both approaches, we can, in addition, obtain a quantitative evaluation of the specific parameters under investigation in morphogenetic and cell biological studies. In this chapter, we focus on the development of the tracheal system of Drosophila melanogaster, which provides an ideal paradigm to understand the formation of branched tubular organs. We describe the most used methods of imaging and morphometric analysis in tubulogenesis using mainly (but not exclusively) examples from embryonic development. We cover embryo preparation for fixed and live analysis of tubulogenesis, together with methods to visualize larval tracheal terminal cell branching and lumen formation. Finally, we describe morphometric analysis and quantification methods using fluorescent images of tracheal cells.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Cellular shape reinforces niche to stem cell signaling in the small intestine

Niche-derived factors regulate tissue stem cells, but apart from the mechanosensory pathways, the effect of niche geometry is not well understood. We used organoids and bioengineered tissue culture platforms to demonstrate that the conical shape of Lgr5⁺ small intestinal stem cells (ISCs) facilitate their self-renewal and function. Inhibition of non-muscle myosin II (NM II)-driven apical constriction altered ISC shape and reduced niche curvature and stem cell capacity. Niche curvature is decreased in aged mice, suggesting that suboptimal interactions between old ISCs and their niche develop with age. We show that activation of NM IIC or physical restriction to young topology improves in vitro regeneration by old epithelium. We propose that the increase in lateral surface area of ISCs induced by apical constriction promotes interactions between neighboring cells, and the curved topology of the intestinal niche has evolved to maximize signaling between ISCs and neighboring cells.

Entropy as a Geometrical Source of Information in Biological Organizations

Considering both biological and non-biological polygonal shape organizations, in this paper we introduce a quantitative method which is able to determine informational entropy as spatial differences between heterogeneity of internal areas from simulation and experimental samples. According to these data (i.e., heterogeneity), we are able to establish levels of informational entropy using statistical insights of spatial orders using discrete and continuous values. Given a particular state of entropy, we establish levels of information as a novel approach which can unveil general principles of biological organization. Thirty-five geometric aggregates are tested (biological, non-biological, and polygonal simulations) in order to obtain the theoretical and experimental results of their spatial heterogeneity. Geometrical aggregates (meshes) include a spectrum of organizations ranging from cell meshes to ecological patterns. Experimental results for discrete entropy using a bin width of 0.5 show that a particular range of informational entropy (0.08 to 0.27 bits) is intrinsically associated with low rates of heterogeneity, which indicates a high degree of uncertainty in finding non-homogeneous configurations. In contrast, differential entropy (continuous) results reflect negative entropy within a particular range (−0.4 to −0.9) for all bin widths. We conclude that the differential entropy of geometrical organizations is an important source of neglected information in biological systems.

A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia

Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.

Single-cell atlases: shared and tissue-specific cell types across human organs

The development of single-cell and spatial transcriptomics methods was instrumental in the conception of the Human Cell Atlas initiative, which aims to generate an integrated map of all cells across the human body. These technology advances are bringing increasing depth and resolution to maps of human organs and tissues, as well as our understanding of individual human cell types. Commonalities as well as tissue-specific features of primary and supportive cell types across human organs are beginning to emerge from these human tissue maps. In this Review, we highlight key biological insights obtained from cross-tissue studies into epithelial, fibroblast, vascular and immune cells based on single-cell gene expression data in humans and contrast it with mechanisms reported in mice.

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.

Patterns can form in biological systems as a net effect of dynamical interactions that are excitatory over short distances and inhibitory over larger distances. Patterns that form in this way are known to reflect the shape of the boundary conditions that contain them. But observing that a particular pattern is contained by a boundary is not enough to determine whether or not that boundary was a constraint on pattern formation. Here we develop a novel test for the influence of boundary shape on pattern formation, based on comparing patterns contained by boundaries whose shapes tessellate and thus are geometrically related. Applying this test to patterns of cell density measured in the developing neocortex confirms that cortical column boundaries constrain pattern formation during the first postnatal weeks. In more general terms, our analysis reveals that strong relationships between patterns that form in adjacent biological domains are to be expected based purely on geometrical effects, even if no information is exchanged between those domains during the process of pattern formation. Our analysis provides a means for testing current theories about the fundamental role that constraints play in organising biological systems.

Coordinated activities of Myosin Vb isoforms and mTOR signaling regulate epithelial cell morphology during development

The maintenance of epithelial architecture necessitates tight regulation of cell size and shape. However, mechanisms underlying epithelial cell size regulation remain poorly understood. We show that the interaction of Myosin Vb with Rab11 prevents the accumulation of apically derived endosomes to maintain cell-size, whereas that with Rab10 regulates vesicular transport from the trans-Golgi. These interactions are required for the fine-tuning of the epithelial cell morphology during zebrafish development. Furthermore, the compensatory cell growth upon cell-proliferation inhibition involves a preferential expansion of the apical domain, leading to flatter epithelial cells, an efficient strategy to cover the surface with fewer cells. This apical domain growth requires post-trans-Golgi transport mediated by the Rab10-interacting Myosin Vb isoform, downstream of the mTOR-Fatty Acid Synthase (FASN) axis. Changes in trans-Golgi morphology indicate that the Golgi synchronizes mTOR-FASN-regulated biosynthetic input and Myosin Vb-Rab10 dependent output. Our study unravels the mechanism of polarized growth in epithelial cells and delineates functions of Myosin Vb isoforms in cell size regulation during development.

Common principles of surface deformation in biology

Living organisms, whether they are cells or multicellular organisms, are separated from their environment by an interface. For example, cells are delimited by lipid bilayers while embryos or individuals are delimited by epithelia, ectoderms or epiderms. These biological interfaces, while being different in nature and composition, and at very different scales, share common properties: they are surfaces, their thickness being very small compared to their size. They are materials of chemical composition or cell type that is unique and different from the core of the material they envelop. They are visco-elastic sheets, meaning that components can flow in the plane of the surface. The shape of cells and of embryos is inherently dictated by the shape of their envelope, and because these interfaces have common properties, we explore in this commentary article the different mechanisms that remodel these different biological surfaces, and their common principles.

The Functional Anatomy of the Cornea and Anterior Chamber in Lampreys: Insights From the Pouched Lamprey, Geotria australis (Geotriidae, Agnatha)

Extant lampreys (Petromyzontiformes) are one of two lineages of surviving jawless fishes or agnathans, and are therefore of critical importance to our understanding of vertebrate evolution. Anadromous lampreys undergo a protracted lifecycle, which includes metamorphosis from a larval ammocoete stage to an adult that moves between freshwater and saltwater with exposure to a range of lighting conditions. Previous studies have revealed that photoreception differs radically across the three extant families with the Pouched lamprey Geotria australis possessing a complex retina with the potential for pentachromacy. This study investigates the functional morphology of the cornea and anterior chamber of G. australis, which is specialised compared to its northern hemisphere counterparts. Using light microscopy, scanning and transmission electron microscopy and microcomputed tomography, the cornea is found to be split into a primary spectacle (dermal cornea) and a scleral cornea (continuous with the scleral eyecup), separated by a mucoid layer bounded on each side by a basement membrane. A number of other specialisations are described including mucin-secreting epithelial cells and microholes, four types of stromal sutures for the inhibition of stromal swelling, abundant anastomosing and branching of collagen lamellae, and a scleral endothelium bounded by basement membranes. The structure and function of the cornea including an annular and possibly a pectinate ligament and iris are discussed in the context of the evolution of the eye in vertebrates.

3D cell neighbour dynamics in growing pseudostratified epithelia

During morphogenesis, epithelial sheets remodel into complex geometries. How cells dynamically organise their contact with neighbouring cells in these tightly packed tissues is poorly understood. We have used light-sheet microscopy of growing mouse embryonic lung explants, three-dimensional cell segmentation, and physical theory to unravel the principles behind 3D cell organisation in growing pseudostratified epithelia. We find that cells have highly irregular 3D shapes and exhibit numerous neighbour intercalations along the apical-basal axis as well as over time. Despite the fluidic nature, the cell packing configurations follow fundamental relationships previously described for apical epithelial layers, that is, Euler's polyhedron formula, Lewis' law, and Aboav-Weaire's law, at all times and across the entire tissue thickness. This arrangement minimises the lateral cell-cell surface energy for a given cross-sectional area variability, generated primarily by the distribution and movement of nuclei. We conclude that the complex 3D cell organisation in growing epithelia emerges from simple physical principles.

Dynamic changes in epithelial cell packing during tissue morphogenesis

Cell packing - the spatial arrangement of cells - determines the shapes of organs. Recently, investigations of organ development in a variety of model organisms have uncovered cellular mechanisms that are used by epithelial tissues to change cell packing, and thereby their shapes, to generate functional architectures. Here, we review these cellular mechanisms across a wide variety of developmental processes in vertebrates and invertebrates and identify a set of common motifs in the morphogenesis toolbox that, in combination, appear to allow any change in tissue shape. We focus on tissue elongation, folding and invagination, and branching. We also highlight how these morphogenetic processes are achieved by cell-shape changes, cell rearrangements, and oriented cell division. Finally, we describe approaches that have the potential to engineer three-dimensional tissues for both basic science and translational purposes. This review provides a framework for future analyses of how tissues are shaped by the dynamics of epithelial cell packing.

Mechanics and self-organization in tissue development

Self-organization is an all-important feature of living systems that provides the means to achieve specialization and functionality at distinct spatio-temporal scales. Herein, we review this concept by addressing the packing organization of cells, the sorting/compartmentalization phenomenon of cell populations, and the propagation of organizing cues at the tissue level through traveling waves. We elaborate on how different theoretical models and tools from Topology, Physics, and Dynamical Systems have improved the understanding of self-organization by shedding light on the role played by mechanics as a driver of morphogenesis. Altogether, by providing a historical perspective, we show how ideas and hypotheses in the field have been revisited, developed, and/or rejected and what are the open questions that need to be tackled by future research.

Morphologies of compressed active epithelial monolayers

Using a three-dimensional active vertex model, we numerically study the shapes of strained unsupported epithelial monolayers subject to active junctional noise due to stochastic binding and unbinding of myosin. We find that while uniaxial, biaxial, and isotropic in-plane compressive strains do lead to the formation of longitudinal, herringbone pattern, and labyrinthine folds, respectively, the villus morphology characteristic of, e.g., the small intestine appears only if junctional tension fluctuations are strong enough to fluidize the tissue. Moreover, the fluidized epithelium features villi even in the absence of compressive strain provided that the apico-basal differential surface tension is large enough. We analyze several details of the different epithelial forms including the role of strain rate and the modulation of tissue thickness across folds. Our results show that even unsupported, non-patterned epithelia can form nontrivial morphologies.

The early Drosophila embryo as a model system for quantitative biology

With the rise of new tools, from controlled genetic manipulations and optogenetics to improved microscopy, it is now possible to make clear, quantitative and reproducible measurements of biological processes. The humble fruit fly Drosophila melanogaster, with its ease of genetic manipulation combined with excellent imaging accessibility, has become a major model system for performing quantitative in vivo measurements. Such measurements are driving a new wave of interest from physicists and engineers, who are developing a range of testable dynamic models of active systems to understand fundamental biological processes. The reproducibility of the early Drosophila embryo has been crucial for understanding how biological systems are robust to unavoidable noise during development. Insights from quantitative in vivo experiments in the Drosophila embryo are having an impact on our understanding of critical biological processes, such as how cells make decisions and how complex tissue shape emerges. Here, to highlight the power of using Drosophila embryogenesis for quantitative biology, I focus on three main areas: (1) formation and robustness of morphogen gradients; (2) how gene regulatory networks ensure precise boundary formation; and (3) how mechanical interactions drive packing and tissue folding. I further discuss how such data has driven advances in modelling.

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

The Voronoi theory of the normal liver lobular architecture and its applicability in hepatic zonation

The precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed. Our aim was to evaluate whether Voronoi diagrams can be used to describe the classic liver lobular architecture. We examined the histology of normal porcine and human livers and analyzed the geometric relationships of various microanatomic structures utilizing digital tools. The Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy nearly 90% based on known histologic landmarks. We have also designed a Voronoi-based algorithm of hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. Therefore, we have presented evidence that Voronoi diagrams represent the basis of the two-dimensional organization of the normal liver and that this concept may have wide applicability in liver pathology and research.

A two-tier junctional mechanism drives simultaneous tissue folding and extension

During embryo development, tissues often undergo multiple concomitant changes in shape. It is unclear which signaling pathways and cellular mechanisms are responsible for multiple simultaneous tissue shape transformations. We focus on the process of concomitant tissue folding and extension that is key during gastrulation and neurulation. We use the Drosophila embryo as model system and focus on the process of mesoderm invagination. Here, we show that the prospective mesoderm simultaneously folds and extends. We report that mesoderm cells, under the control of anterior-posterior and dorsal-ventral gene patterning synergy, establish two sets of adherens junctions at different apical-basal positions with specialized functions: while apical junctions drive apical constriction initiating tissue bending, lateral junctions concomitantly drive polarized cell intercalation, resulting in tissue convergence-extension. Thus, epithelial cells devise multiple specialized junctional sets that drive composite morphogenetic processes under the synergistic control of apparently orthogonal signaling sources.

Morphometric Analysis of Retinal Pigment Epithelial Cells From C57BL/6J Mice During Aging

Purpose

To quantitatively evaluate the changes in orientation and morphometric features of mouse retinal pigment epithelial (RPE) cells in different regions of the eye during aging.

Methods

We segmented individual RPE cells from whole RPE flatmount images of C57BL/6J mice (postnatal days 30 to 720) using a machine-learning method and evaluated changes in morphometric features, including our newly developed metric combining alignment and shape of RPE cells during aging.

Results

Mainly, the anterior part of the RPE sheet grows during aging, while the posterior part remains constant. Changes in size and shape of the peripheral RPE cells are prominent with aging as cells become larger, elongated, and concave. Conversely, the central RPE cells maintain relatively constant size and numbers with aging. Cell count in the central area and the overall cell count (approximately 50,000) were relatively constant over different age groups. RPE cells also present a specific orientation concordance that matches the shape of the specific region of the eyeball. Those cells near the optic disc or equator have a circumferential orientation to cover the round shape of the eyeball, whereas those cells in the periphery have a radial orientation and corresponding radial elongation, the extent of which increases with aging and matches with axial elongation of the eyeball.

Conclusions

These results suggest that the fluid RPE morphology reflects various growth rates of underlying eyeball, and RPE cells could be classified into four regional classes (near the optic disc, central, equatorial, and peripheral) according to their morphometric features.

The complex three-dimensional organization of epithelial tissues

Understanding the cellular organization of tissues is key to developmental biology. In order to deal with this complex problem, researchers have taken advantage of reductionist approaches to reveal fundamental morphogenetic mechanisms and quantitative laws. For epithelia, their two-dimensional representation as polygonal tessellations has proved successful for understanding tissue organization. Yet, epithelial tissues bend and fold to shape organs in three dimensions. In this context, epithelial cells are too often simplified as prismatic blocks with a limited plasticity. However, there is increasing evidence that a realistic approach, even from a reductionist perspective, must include apico-basal intercalations (i.e. scutoidal cell shapes) for explaining epithelial organization convincingly. Here, we present an historical perspective about the tissue organization problem. Specifically, we analyze past and recent breakthroughs, and discuss how and why simplified, but realistic, in silico models require scutoidal features to address key morphogenetic events.

Establishment of a morphological atlas of the Caenorhabditis elegans embryo using deep-learning-based 4D segmentation

The invariant development and transparent body of the nematode Caenorhabditis elegans enables complete delineation of cell lineages throughout development. Despite extensive studies of cell division, cell migration and cell fate differentiation, cell morphology during development has not yet been systematically characterized in any metazoan, including C. elegans. This knowledge gap substantially hampers many studies in both developmental and cell biology. Here we report an automatic pipeline, CShaper, which combines automated segmentation of fluorescently labeled membranes with automated cell lineage tracing. We apply this pipeline to quantify morphological parameters of densely packed cells in 17 developing C. elegans embryos. Consequently, we generate a time-lapse 3D atlas of cell morphology for the C. elegans embryo from the 4- to 350-cell stages, including cell shape, volume, surface area, migration, nucleus position and cell-cell contact with resolved cell identities. We anticipate that CShaper and the morphological atlas will stimulate and enhance further studies in the fields of developmental biology, cell biology and biomechanics.

The systematic characterization of C. elegans morphology during development has yet to be performed. Here, the authors produce a 3D atlas of C. elegans morphology from 17 embryos and 54 developmental stages, using an automated pipeline, CShaper (combining segmentation of fluorescently labeled membranes with automated cell lineage tracing).

Asymmetry in the frequency and position of mitosis in the mouse embryo epiblast at gastrulation

At gastrulation, a subpopulation of epiblast cells constitutes a transient posteriorly located structure called the primitive streak, where cells that undergo epithelial-mesenchymal transition make up the mesoderm and endoderm lineages. Mouse embryo epiblast cells were labelled ubiquitously or in a mosaic fashion. Cell shape, packing, organization and division were recorded through live imaging during primitive streak formation. Posterior epiblast displays a higher frequency of rosettes, some of which associate with a central cell undergoing mitosis. Cells at the primitive streak, in particular delaminating cells, undergo mitosis more frequently than other epiblast cells. In pseudostratified epithelia, mitosis takes place at the apical side of the epithelium. However, mitosis is not restricted to the apical side of the epiblast, particularly on its posterior side. Non-apical mitosis occurs specifically in the streak even when ectopically located. Posterior non-apical mitosis results in one or two daughter cells leaving the epiblast layer. Cell rearrangement associated with mitotic cell rounding in posterior epiblast, in particular when non-apical, might thus facilitate cell ingression and transition to a mesenchymal phenotype.

Neuronal immunoglobulin superfamily cell adhesion molecules in epithelial morphogenesis: insights from Drosophila

In this review, we address the function of immunoglobulin superfamily cell adhesion molecules (IgCAMs) in epithelia. Work in the Drosophila model system in particular has revealed novel roles for calcium-independent adhesion molecules in the morphogenesis of epithelial tissues. We review the molecular composition of lateral junctions with a focus on their IgCAM components and reconsider the functional roles of epithelial lateral junctions. The epithelial IgCAMs discussed in this review have well-defined roles in the nervous system, particularly in the process of axon guidance, suggesting functional overlap and conservation in mechanism between that process and epithelial remodelling. We expand on the hypothesis that epithelial occluding junctions and synaptic junctions are compositionally equivalent and present a novel hypothesis that the mechanism of epithelial cell (re)integration and synaptic junction formation are shared. We highlight the importance of considering non-cadherin-based adhesion in our understanding of the mechanics of epithelial tissues and raise questions to direct future work. This article is part of the discussion meeting issue 'Contemporary morphogenesis'.

Cell intercalation in a simple epithelium

Cell intercalation is a key topological transformation driving tissue morphogenesis, homeostasis and diseases such as cancer cell invasion. In recent years, much work has been undertaken to better elucidate the fundamental mechanisms controlling intercalation. Cells often use protrusions to propel themselves in between cell neighbours, resulting in topology changes. Nevertheless, in simple epithelial tissues, formed by a single layer of densely packed prism-shaped cells, topology change takes place in an astonishing fashion: cells exchange neighbours medio-laterally by conserving their apical-basal architecture and by maintaining an intact epithelial layer. Medio-lateral cell intercalation in simple epithelia is thus an exemplary case of both robustness and plasticity. Interestingly, in simple epithelia, cells use a combinatory set of mechanisms to ensure a topological transformation at the apical and basal sides. This article is part of the discussion meeting issue 'Contemporary morphogenesis'.

TiFoSi: an efficient tool for mechanobiology simulations of epithelia

MOTIVATION

Emerging phenomena in developmental biology and tissue engineering are the result of feedbacks between gene expression and cell biomechanics. In that context, in silico experiments are a powerful tool to understand fundamental mechanisms and to formulate and test hypotheses.

RESULTS

Here, we present TiFoSi, a computational tool to simulate the cellular dynamics of planar epithelia. TiFoSi allows to model feedbacks between cellular mechanics and gene expression (either in a deterministic or a stochastic way), the interaction between different cell populations, the custom design of the cell cycle and cleavage properties, the protein number partitioning upon cell division, and the modeling of cell communication (juxtacrine and paracrine signaling).

AVAILABILITY AND IMPLEMENTATION

http://tifosi.thesimbiosys.com.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Self-sustained planar intercalations due to mechanosignaling feedbacks lead to robust axis extension during morphogenesis

Tissue elongation is a necessary process in metazoans to implement their body plans that is not fully understood. Here we propose a mechanism based on the interplay between cellular mechanics and primordia patterning that results in self-sustained planar intercalations. Thus, we show that a location-dependent modulation of the mechanical properties of cells leads to robust axis extension. To illustrate the plausibility of this mechanism, we test it against different patterning models by means of computer simulations of tissues where we implemented mechano-signaling feedbacks. Our results suggest that robust elongation relies on a trade-off between cellular and tissue strains that is orchestrated through the cleavage orientation. In the particular context of axis extension in Turing-patterned tissues, we report that different directional cell activities cooperate synergetically to achieve elongation. Altogether, our findings help to understand how the axis extension phenomenon emerges from the dynamics of individual cells.

Cell-type-specific mechanical response and myosin dynamics during retinal lens development in Drosophila

During organogenesis, different cell types need to work together to generate functional multicellular structures. To study this process, we made use of the genetically tractable fly retina, with a focus on the mechanisms that coordinate morphogenesis between the different epithelial cell types that make up the optical lens. Our work shows that these epithelial cells present contractile apical-medial MyosinII meshworks, which control the apical area and junctional geometry of these cells during lens development. Our study also suggests that these MyosinII meshworks drive cell shape changes in response to external forces, and thus they mediate part of the biomechanical coupling that takes place between these cells. Importantly, our work, including mathematical modeling of forces and material stiffness during lens development, raises the possibility that increased cell stiffness acts as a mechanism for limiting this mechanical coupling. We propose this might be required in complex tissues, where different cell types undergo concurrent morphogenesis and where averaging out of forces across cells could compromise individual cell apical geometry and thereby organ function.

Mechanical Adaptations of Epithelial Cells on Various Protruded Convex Geometries

The shape of epithelial tissue supports physiological functions of organs such as intestinal villi and corneal epithelium. Despite the mounting evidence showing the importance of geometry in tissue microenvironments, the current understanding on how it affects biophysical behaviors of cells is still elusive. Here, we cultured cells on various protruded convex structure such as triangle, square, and circle shape fabricated using two-photon laser lithography and quantitatively analyzed individual cells. Morphological data indicates that epithelial cells can sense the sharpness of the corner by showing the characteristic cell alignments, which was caused by actin contractility. Cell area was mainly influenced by surface convexity, and Rho-activation increased cell area on circle shape. Moreover, we found that intermediate filaments, vimentin, and cytokeratin 8/18, play important roles in growth and adaptation of epithelial cells by enhancing expression level on convex structure depending on the shape. In addition, microtubule building blocks, α-tubulin, was also responded on geometric structure, which indicates that intermediate filaments and microtubule can cooperatively secure mechanical stability of epithelial cells on convex surface. Altogether, the current study will expand our understanding of mechanical adaptations of cells on out-of-plane geometry.

Development of a New 3D Hybrid Model for Epithelia Morphogenesis

Many epithelial developmental processes like cell migration and spreading, cell sorting, or T1 transitions can be described as planar deformations. As such, they can be studied using two-dimensional tools and vertex models that can properly predict collective dynamics. However, many other epithelial shape changes are characterized by out-of-plane mechanics and three-dimensional effects, such as bending, cell extrusion, delamination, or invagination. Furthermore, during planar cell dynamics or tissue repair in monolayers, spatial intercalation between the apical and basal sides has even been detected. Motivated by this lack of symmetry with respect to the midsurface, we here present a 3D hybrid model that allows us to model differential contractility at the apical, basal or lateral sides. We use the model to study the effects on wound closure of solely apical or lateral contractile contributions and show that an apical purse-string can be sufficient for full closure when it is accompanied by volume preservation.

A Mechanical Instability in Planar Epithelial Monolayers Leads to Cell Extrusion

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or precancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken because of an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation in which cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers in vivo and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes.

Substrate curvature as a cue to guide spatiotemporal cell and tissue organization

Recent evidence clearly shows that cells respond to various physical cues in their environments, guiding many cellular processes and tissue morphogenesis, pathology, and repair. One aspect that is gaining significant traction is the role of local geometry as an extracellular cue. Elucidating how geometry affects cell and tissue behavior is, indeed, crucial to design artificial scaffolds and understand tissue growth and remodeling. Perhaps the most fundamental descriptor of local geometry is surface curvature, and a growing body of evidence confirms that surface curvature affects the spatiotemporal organization of cells and tissues. While well-defined in differential geometry, curvature remains somewhat ambiguously treated in biological studies. Here, we provide a more formal curvature framework, based on the notions of mean and Gaussian curvature, and summarize the available evidence on curvature guidance at the cell and tissue levels. We discuss the involved mechanisms, highlighting the interplay between tensile forces and substrate curvature that forms the foundation of curvature guidance. Moreover, we show that relatively simple computational models, based on some application of curvature flow, are able to capture experimental tissue growth remarkably well. Since curvature guidance principles could be leveraged for tissue regeneration, the implications for geometrical scaffold design are also discussed. Finally, perspectives on future research opportunities are provided.

The tricellular vertex-specific adhesion molecule Sidekick facilitates polarised cell intercalation during Drosophila axis extension

In epithelia, tricellular vertices are emerging as important sites for the regulation of epithelial integrity and function. Compared to bicellular contacts, however, much less is known. In particular, resident proteins at tricellular vertices were identified only at occluding junctions, with none known at adherens junctions (AJs). In a previous study, we discovered that in Drosophila embryos, the adhesion molecule Sidekick (Sdk), well-known in invertebrates and vertebrates for its role in the visual system, localises at tricellular vertices at the level of AJs. Here, we survey a wide range of Drosophila epithelia and establish that Sdk is a resident protein at tricellular AJs (tAJs), the first of its kind. Clonal analysis showed that two cells, rather than three cells, contributing Sdk are sufficient for tAJ localisation. Super-resolution imaging using structured illumination reveals that Sdk proteins form string-like structures at vertices. Postulating that Sdk may have a role in epithelia where AJs are actively remodelled, we analysed the phenotype of sdk null mutant embryos during Drosophila axis extension using quantitative methods. We find that apical cell shapes are abnormal in sdk mutants, suggesting a defect in tissue remodelling during convergence and extension. Moreover, adhesion at apical vertices is compromised in rearranging cells, with apical tears in the cortex forming and persisting throughout axis extension, especially at the centres of rosettes. Finally, we show that polarised cell intercalation is decreased in sdk mutants. Mathematical modelling of the cell behaviours supports the notion that the T1 transitions of polarised cell intercalation are delayed in sdk mutants, in particular in rosettes. We propose that this delay, in combination with a change in the mechanical properties of the converging and extending tissue, causes the abnormal apical cell shapes in sdk mutant embryos.

This study identifies the adhesion molecule Sidekick as a resident protein of tricellular vertices between cells, at the level of adherens junctions. A combination of quantitative methods and modelling provides evidence that Sidekick facilitates polarised cell intercalation during Drosophila axis extension.

Convergent extension in mammalian morphogenesis

Convergent extension is a fundamental morphogenetic process that underlies not only the generation of the elongated vertebrate body plan from the initially radially symmetrical embryo, but also the specific shape changes characteristic of many individual tissues. These tissue shape changes are the result of specific cell behaviors, coordinated in time and space, and affected by the physical properties of the tissue. While mediolateral cell intercalation is the classic cellular mechanism for producing tissue convergence and extension, other cell behaviors can also provide similar tissue-scale distortions or can modulate the effects of mediolateral cell intercalation to sculpt a specific shape. Regulation of regional tissue morphogenesis through planar polarization of the variety of underlying cell behaviors is well-recognized, but as yet is not well understood at the molecular level. Here, we review recent advances in understanding the cellular basis for convergence and extension and its regulation.

Cell-Size Pleomorphism Drives Aberrant Clone Dispersal in Proliferating Epithelia

As epithelial tissues develop, groups of cells related by descent tend to associate in clonal populations rather than dispersing within the cell layer. While this is frequently assumed to be a result of differential adhesion, precise mechanisms controlling clonal cohesiveness remain unknown. Here we employ computational simulations to modulate epithelial cell size in silico and show that junctions between small cells frequently collapse, resulting in clone-cell dispersal among larger neighbors. Consistent with similar dynamics in vivo, we further demonstrate that mosaic disruption of Drosophila Tor generates small cells and results in aberrant clone dispersal in developing wing disc epithelia. We propose a geometric basis for this phenomenon, supported in part by the observation that soap-foam cells exhibit similar size-dependent junctional rearrangements. Combined, these results establish a link between cell-size pleomorphism and the control of epithelial cell packing, with potential implications for understanding tumor cell dispersal in human disease.