The emergence of geometric order in proliferating metazoan epithelia

Activation of Topological Defects Induces a Brittle-to-Ductile Transition in Epithelial Monolayers

Epithelial monolayers are subjected to various mechanical forces, such as stretching, shearing, and compression. Thus, its mechanical response to external loadings is essential for its biological functions. However, the mechanism of the fracture failure of the epithelial monolayer remains poorly understood. Here, by introducing a new type of topological transition, i.e., detach transition or T4 transition, we develop a modified cellular vertex model to investigate the rupture of the cell monolayer. Interestingly, we find a brittle-to-ductile transition in epithelial monolayers, which is controlled by the mechanical properties of single cells and cell-cell contacts. We reveal that the external loadings can activate cell rearrangement in ductile cell monolayers. The plastic deformation results from the nucleation and propagation of "pentagon-heptagon defects" in analogy with the topological defects commonly seen in 2D materials. By using a simplified four-cell model, we further demonstrate that the brittle-to-ductile transition is induced by the competition between cell rearrangement and cell detachment. Our work provides a new theoretical framework to study the rupture of living tissues and may have important implications for many other biological processes, such as wound healing and tissue morphogenesis.

Emergence of a geometric pattern of cell fates from tissue-scale mechanics in the Drosophila eye

Pattern formation of biological structures involves the arrangement of different types of cells in an ordered spatial configuration. In this study, we investigate the mechanism of patterning the Drosophila eye epithelium into a precise triangular grid of photoreceptor clusters called ommatidia. Previous studies had led to a long-standing biochemical model whereby a reaction-diffusion process is templated by recently formed ommatidia to propagate a molecular prepattern across the eye. Here, we find that the templating mechanism is instead, mechanochemical in origin; newly born columns of differentiating ommatidia serve as a template to spatially pattern flows that move epithelial cells into position to form each new column of ommatidia. Cell flow is generated by a source and sink, corresponding to narrow zones of cell dilation and contraction respectively, that straddle the growing wavefront of ommatidia. The newly formed lattice grid of ommatidia cells are immobile, deflecting, and focusing the flow of other cells. Thus, the self-organization of a regular pattern of cell fates in an epithelium is mechanically driven.

Disorder in cellular packing can alter proliferation dynamics to regulate growth

The mechanisms by which an organ regulates its growth are not yet fully understood, especially when the cells are closely packed as in epithelial tissues. We explain growth arrest as a collective dynamical transition in coupled oscillators on disordered lattices. As the cellular morphologies become homogeneous over the course of development, the signals induced by cell-cell contact increase beyond a critical value that triggers coordinated cessation of the cell-cycle oscillators driving cell division. Thus, control of cell proliferation is causally related to the geometry of cellular packing.

Are cell jamming and unjamming essential in tissue development?

The last decade has seen a surge of evidence supporting the existence of the transition of the multicellular tissue from a collective material phase that is regarded as being jammed to a collective material phase that is regarded as being unjammed. The jammed phase is solid-like and effectively 'frozen', and therefore is associated with tissue homeostasis, rigidity, and mechanical stability. The unjammed phase, by contrast, is fluid-like and effectively 'melted', and therefore is associated with mechanical fluidity, plasticity and malleability that are required in dynamic multicellular processes that sculpt organ microstructure. Such multicellular sculpturing, for example, occurs during embryogenesis, growth and remodeling. Although unjamming and jamming events in the multicellular collective are reminiscent of those that occur in the inert granular collective, such as grain in a hopper that can flow or clog, the analogy is instructive but limited, and the implications for cell biology remain unclear. Here we ask, are the cellular jamming transition and its inverse --the unjamming transition-- mere epiphenomena? That is, are they dispensable downstream events that accompany but neither cause nor quench these core multicellular processes? Drawing from selected examples in developmental biology, here we suggest the hypothesis that, to the contrary, the graded departure from a jammed phase enables controlled degrees of malleability as might be required in developmental dynamics. We further suggest that the coordinated approach to a jammed phase progressively slows those dynamics and ultimately enables long-term mechanical stability as might be required in the mature homeostatic multicellular tissue.

Forced into shape: Mechanical forces in Drosophila development and homeostasis

Mechanical forces play a central role in shaping tissues during development and maintaining epithelial integrity in homeostasis. In this review, we discuss the roles of mechanical forces in Drosophila development and homeostasis, starting from the interplay of mechanics with cell growth and division. We then discuss several examples of morphogenetic processes where complex 3D structures are shaped by mechanical forces, followed by a closer look at patterning processes. We also review the role of forces in homeostatic processes, including cell elimination and wound healing. Finally, we look at the interplay of mechanics and developmental robustness and discuss open questions in the field, as well as novel approaches that will help tackle them in the future.

From apolar gastrula to polarized larva: Embryonic development of a marine hydroid, Dynamena pumila

BACKGROUND

In almost all metazoans examined to this respect, the axial patterning system based on canonical Wnt (cWnt) signaling operates throughout the course of development. In most metazoans, gastrulation is polar, and embryos develop morphological landmarks of axial polarity, such as blastopore under control/regulation from cWnt signaling. However, in many cnidarian species, gastrulation is morphologically apolar. The question remains whether сWnt signaling providing the establishment of a body axis controls morphogenetic processes involved in apolar gastrulation.

RESULTS

In this study, we focused on the embryonic development of Dynamena pumila, a cnidarian species with apolar gastrulation. We thoroughly described cell behavior, proliferation, and ultrastructure and examined axial patterning in the embryos of this species. We revealed that the first signs of morphological polarity appear only after the end of gastrulation, while molecular prepatterning of the embryo does exist during gastrulation. We have shown experimentally that in D. pumila, the direction of the oral-aboral axis is highly robust against perturbations in cWnt activity.

CONCLUSIONS

Our results suggest that morphogenetic processes are uncoupled from molecular axial patterning during gastrulation in D. pumila. Investigation of D. pumila might significantly expand our understanding of the ways in which morphological polarization and axial molecular patterning are linked in Metazoa.

Configurational fingerprints of multicellular living systems

Cells cooperate as groups to achieve structure and function at the tissue level, during which specific material characteristics emerge. Analogous to phase transitions in classical physics, transformations in the material characteristics of multicellular assemblies are essential for a variety of vital processes including morphogenesis, wound healing, and cancer. In this work, we develop configurational fingerprints of particulate and multicellular assemblies and extract volumetric and shear order parameters based on this fingerprint to quantify the system disorder. Theoretically, these two parameters form a complete and unique pair of signatures for the structural disorder of a multicellular system. The evolution of these two order parameters offers a robust and experimentally accessible way to map the phase transitions in expanding cell monolayers and during embryogenesis and invasion of epithelial spheroids.

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.

A multiscale analysis of early flower development in Arabidopsis provides an integrated view of molecular regulation and growth control

We have analyzed the link between the gene regulation and growth during the early stages of flower development in Arabidopsis. Starting from time-lapse images, we generated a 4D atlas of early flower development, including cell lineage, cellular growth rates, and the expression patterns of regulatory genes. This information was introduced in MorphoNet, a web-based platform. Using computational models, we found that the literature-based molecular network only explained a minority of the gene expression patterns. This was substantially improved by adding regulatory hypotheses for individual genes. Correlating growth with the combinatorial expression of multiple regulators led to a set of hypotheses for the action of individual genes in morphogenesis. This identified the central factor LEAFY as a potential regulator of heterogeneous growth, which was supported by quantifying growth patterns in a leafy mutant. By providing an integrated view, this atlas should represent a fundamental step toward mechanistic models of flower development.

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.

IVEN: A quantitative tool to describe 3D cell position and neighbourhood reveals architectural changes in FGF4-treated preimplantation embryos

Architectural changes at the cellular and organism level are integral and necessary to successful development and growth. During mammalian preimplantation development, cells reduce in size and the architecture of the embryo changes significantly. Such changes must be coordinated correctly to ensure continued development of the embryo and, ultimately, a successful pregnancy. However, the nature of such transformations is poorly defined during mammalian preimplantation development. In order to quantitatively describe changes in cell environment and organism architecture, we designed Internal Versus External Neighbourhood (IVEN). IVEN is a user-interactive, open-source pipeline that classifies cells into different populations based on their position and quantifies the number of neighbours of every cell within a dataset in a 3D environment. Through IVEN-driven analyses, we show how transformations in cell environment, defined here as changes in cell neighbourhood, are related to changes in embryo geometry and major developmental events during preimplantation mammalian development. Moreover, we demonstrate that modulation of the FGF pathway alters spatial relations of inner cells and neighbourhood distributions, leading to overall changes in embryo architecture. In conjunction with IVEN-driven analyses, we uncover differences in the dynamic of cell size changes over the preimplantation period and determine that cells within the mammalian embryo initiate growth phase only at the time of implantation.

Cell-scale biophysical determinants of cell competition in epithelia

How cells with different genetic makeups compete in tissues is an outstanding question in developmental biology and cancer research. Studies in recent years have revealed that cell competition can either be driven by short-range biochemical signalling or by long-range mechanical stresses in the tissue. To date, cell competition has generally been characterised at the population scale, leaving the single-cell-level mechanisms of competition elusive. Here, we use high time-resolution experimental data to construct a multi-scale agent-based model for epithelial cell competition and use it to gain a conceptual understanding of the cellular factors that governs competition in cell populations within tissues. We find that a key determinant of mechanical competition is the difference in homeostatic density between winners and losers, while differences in growth rates and tissue organisation do not affect competition end result. In contrast, the outcome and kinetics of biochemical competition is strongly influenced by local tissue organisation. Indeed, when loser cells are homogenously mixed with winners at the onset of competition, they are eradicated; however, when they are spatially separated, winner and loser cells coexist for long times. These findings suggest distinct biophysical origins for mechanical and biochemical modes of cell competition.

Competitive coordination of the dual roles of the Hedgehog co-receptor in homophilic adhesion and signal reception

Hedgehog (Hh) signaling patterns embryonic tissues and contributes to homeostasis in adults. In Drosophila, Hh transport and signaling are thought to occur along a specialized class of actin-rich filopodia, termed cytonemes. Here, we report that Interference hedgehog (Ihog) not only forms a Hh receptor complex with Patched to mediate intracellular signaling, but Ihog also engages in trans-homophilic binding leading to cytoneme stabilization in a manner independent of its role as the Hh receptor. Both functions of Ihog (trans-homophilic binding for cytoneme stabilization and Hh binding for ligand sensing) involve a heparin-binding site on the first fibronectin repeat of the extracellular domain. Thus, the Ihog-Ihog interaction and the Hh-Ihog interaction cannot occur simultaneously for a single Ihog molecule. By combining experimental data and mathematical modeling, we determined that Hh-Ihog heterophilic interaction dominates and Hh can disrupt and displace Ihog molecules involved in trans-homophilic binding. Consequently, we proposed that the weaker Ihog-Ihog trans interaction promotes and stabilizes direct membrane contacts along cytonemes and that, as the cytoneme encounters secreted Hh ligands, the ligands trigger release of Ihog from trans Ihog-Ihog complex enabling transport or internalization of the Hh ligand-Ihog-Patched -receptor complex. Thus, the seemingly incompatible functions of Ihog in homophilic adhesion and ligand binding cooperate to assist Hh transport and reception along the cytonemes.

Mechanical properties of external confinement modulate the rounding dynamics of cells

Many studies have demonstrated that mitotic cells can round up against external impediments. However, how the stiffness of external confinement affects the dynamics of rounding force/pressure and cell volume remains largely unknown. Here, we develop a theoretical framework to study the rounding of adherent cells confined between a substrate and a cantilever. We show that the rounding force and pressure increase exclusively with the effective confinement on the cell, which is related to the cantilever stiffness and the separation between cantilever and substrate. Remarkably, an increase of cantilever stiffness from 0.001 to 1 N/m can lead to a 100-fold change in rounding force. This model also predicts an active role of confinement stiffness in regulating the dynamics of cell volume and hydrostatic pressure. We find that the dynamic changes of cellular volume and hydrostatic pressure after osmotic shocks are opposite if the cantilever is soft, whereas the dynamic changes of cellular volume and pressure are the same if the cantilever is stiff. Taken together, this work demonstrates that confinement stiffness appears as a critical regulator in regulating the dynamics of rounding force and pressure. Our findings also indicate that the difference in cantilever stiffness need to be considered when comparing the measured rounding force and pressure from various experiments.

A mechanogenetic role for the actomyosin complex in branching morphogenesis of epithelial organs

The actomyosin complex plays crucial roles in various life processes by balancing the forces generated by cellular components. In addition to its physical function, the actomyosin complex participates in mechanotransduction. However, the exact role of actomyosin contractility in force transmission and the related transcriptional changes during morphogenesis are not fully understood. Here, we report a mechanogenetic role of the actomyosin complex in branching morphogenesis using an organotypic culture system of mouse embryonic submandibular glands. We dissected the physical factors arranged by characteristic actin structures in developing epithelial buds and identified the spatial distribution of forces that is essential for buckling mechanism to promote the branching process. Moreover, the crucial genes required for the distribution of epithelial progenitor cells were regulated by YAP and TAZ through a mechanotransduction process in epithelial organs. These findings are important for our understanding of the physical processes involved in the development of epithelial organs and provide a theoretical background for developing new approaches for organ regeneration.

The recycling endosome protein Rab25 coordinates collective cell movements in the zebrafish surface epithelium

In emerging epithelial tissues, cells undergo dramatic rearrangements to promote tissue shape changes. Dividing cells remain interconnected via transient cytokinetic bridges. Bridges are cleaved during abscission and currently, the consequences of disrupting abscission in developing epithelia are not well understood. We show that the Rab GTPase Rab25 localizes near cytokinetic midbodies and likely coordinates abscission through endomembrane trafficking in the epithelium of the zebrafish gastrula during epiboly. In maternal-zygotic Rab25a and Rab25b mutant embryos, morphogenic activity tears open persistent apical cytokinetic bridges that failed to undergo timely abscission. Cytokinesis defects result in anisotropic cell morphologies that are associated with a reduction of contractile actomyosin networks. This slows cell rearrangements and alters the viscoelastic responses of the tissue, all of which likely contribute to delayed epiboly. We present a model in which Rab25 trafficking coordinates cytokinetic bridge abscission and cortical actin density, impacting local cell shape changes and tissue-scale forces.

Nucleus-Cytoskeleton Crosstalk During Mitotic Entry

In preparation for mitosis, cells undergo extensive reorganization of the cytoskeleton and nucleus, so that chromosomes can be efficiently segregated into two daughter cells. Coordination of these cytoskeletal and nuclear events occurs through biochemical regulatory pathways, orchestrated by Cyclin-CDK activity. However, recent studies provide evidence that physical forces are also involved in the early steps of spindle assembly. Here, we will review how the crosstalk of physical forces and biochemical signals coordinates nuclear and cytoplasmic events during the G2-M transition, to ensure efficient spindle assembly and faithful chromosome segregation.

Cell cycle-dependent active stress drives epithelia remodeling

Epithelia have distinct cellular architectures which are established in development, reestablished after wounding, and maintained during tissue homeostasis despite cell turnover and mechanical perturbations. In turn, cell shape also controls tissue function as a regulator of cell differentiation, proliferation, and motility. Here, we investigate cell shape changes in a model epithelial monolayer. After the onset of confluence, cells continue to proliferate and change shape over time, eventually leading to a final architecture characterized by arrested motion and more regular cell shapes. Such monolayer remodeling is robust, with qualitatively similar evolution in cell shape and dynamics observed across disparate perturbations. Here, we quantify differences in monolayer remodeling guided by the active vertex model to identify underlying order parameters controlling epithelial architecture. When monolayers are formed atop an extracellular matrix with varied stiffness, we find the cell density at which motion arrests varies significantly, but the cell shape remains constant, consistent with the onset of tissue rigidity. In contrast, pharmacological perturbations can significantly alter the cell shape at which tissue dynamics are arrested, consistent with varied amounts of active stress within the tissue. Across all experimental conditions, the final cell shape is well correlated to the cell proliferation rate, and cell cycle inhibition immediately arrests cell motility. Finally, we demonstrate cell cycle variation in junctional tension as a source of active stress within the monolayer. Thus, the architecture and mechanics of epithelial tissue can arise from an interplay between cell mechanics and stresses arising from cell cycle dynamics.

From genes to shape during metamorphosis: a history

Metamorphosis (Greek for a state of transcending-form or change-in-shape) refers to a dramatic transformation of an animal's body structure that occurs after development of the embryo or larva in many species. The development of a fly (or butterfly) from a crawling larva (or caterpillar) that forms a pupa (or chrysalis) before eclosing as a flying adult is a classic example of metamorphosis that captures the imagination and has been immortalized in children's books. Powerful genetic experiments in the fruit fly Drosophila melanogaster have revealed how genes can instruct the behaviour of individual cells to control patterns of tissue growth, mechanical force, cell-cell adhesion and cell-matrix adhesion drive morphogenetic change in epithelial tissues. Together, the distribution of mass, force and resistance determines cell shape changes, cell-cell rearrangements, and/or the orientation of cell divisions to generate the final form of the tissue. In organising tissue shape, genes harness the power of self-organisation to determine the collective behaviour of molecules and cells, which can often be reproduced in computer simulations of cell polarity and/or tissue mechanics. This review highlights fundamental discoveries in epithelial morphogenesis made by pioneers who were fascinated by metamorphosis, including D'Arcy Thompson, Conrad Waddington, Dianne Fristrom and Antonio Garcia-Bellido.

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.

Ring structure of selected two-dimensional procrystalline lattices

Recent work has introduced the term "procrystalline" to define systems which lack translational symmetry but have an underlying high-symmetry lattice. The properties of five such two-dimensional (2D) lattices are considered in terms of the topologies of rings which may be formed from three-coordinate sites only. Parent lattices with full coordination numbers of four, five, and six are considered, with configurations generated using a Monte Carlo algorithm. The different lattices are shown to generate configurations with varied ring distributions. The different constraints imposed by the underlying lattices are discussed. Ring size distributions are obtained analytically for two of the simpler lattices considered (the square and trihexagonal nets). In all cases, the ring size distributions are compared to those obtained via a maximum entropy method. The configurations are analyzed with respect to the near-universal Lemaître curve (which connects the fraction of six-membered rings with the width of the ring size distribution) and three lattices are highlighted as rare examples of systems which generate configurations which do not map onto this curve. The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.

Apical stress fibers enable a scaling between cell mechanical response and area in epithelial tissue

Biological systems tailor their properties and behavior to their size throughout development and in numerous aspects of physiology. However, such size scaling remains poorly understood as it applies to cell mechanics and mechanosensing. By examining how the Drosophila pupal dorsal thorax epithelium responds to morphogenetic forces, we found that the number of apical stress fibers (aSFs) anchored to adherens junctions scales with cell apical area to limit larger cell elongation under mechanical stress. aSFs cluster Hippo pathway components, thereby scaling Hippo signaling and proliferation with area. This scaling is promoted by tricellular junctions mediating an increase in aSF nucleation rate and lifetime in larger cells. Development, homeostasis, and repair entail epithelial cell size changes driven by mechanical forces; our work highlights how, in turn, mechanosensitivity scales with cell size.

Unraveling spatial cellular pattern by computational tissue shuffling

Cell biology relies largely on reproducible visual observations. Unlike cell culture, tissues are heterogeneous, making difficult the collection of biological replicates that would spotlight a precise location. In consequence, there is no standard approach for estimating the statistical significance of an observed pattern in a tissue sample. Here, we introduce SET (for Synthesis of Epithelial Tissue), a method that can accurately reconstruct the cell tessellation formed by an epithelium in a microscopy image as well as thousands of alternative synthetic tessellations made of the exact same cells. SET can build an accurate null distribution to statistically test if any local pattern is necessarily the result of a process, or if it could be explained by chance in the given context. We provide examples in various tissues where visible, and invisible, cell and subcellular patterns are unraveled in a statistically significant manner using a single image and without any parameter settings.

3D alveolar in vitro model based on epithelialized biomimetically curved culture membranes

There is increasing evidence that surface curvature at a near-cell-scale influences cell behaviour. Epithelial or endothelial cells lining small acinar or tubular body lumens, as those of the alveoli or blood vessels, experience such highly curved surfaces. In contrast, the most commonly used culture substrates for in vitro modelling of these human tissue barriers, ion track-etched membranes, offer only flat surfaces. Here, we propose a more realistic culture environment for alveolar cells based on biomimetically curved track-etched membranes, preserving the mainly spherical geometry of the cells' native microenvironment. The curved membranes were created by a combination of three-dimensional (3D) micro film (thermo)forming and ion track technology. We could successfully demonstrate the formation, the growth and a first characterization of confluent layers of lung epithelial cell lines and primary alveolar epithelial cells on membranes shaped into an array of hemispherical microwells. Besides their application in submerged culture, we could also demonstrate the compatibility of the bioinspired membranes for air-exposed culture. We observed a distinct cellular response to membrane curvature. Cells (or cell layers) on the curved membranes reveal significant differences compared to cells on flat membranes concerning membrane epithelialization, areal cell density of the formed epithelial layers, their cross-sectional morphology, and proliferation and apoptosis rates, and the same tight barrier function as on the flat membranes. The presented 3D membrane technology might pave the way for more predictive barrier in vitro models in future.

EpiGraph: an open-source platform to quantify epithelial organization

Summary

Here we present EpiGraph, an image analysis tool that quantifies epithelial organization. Our method combines computational geometry and graph theory to measure the degree of order of any packed tissue. EpiGraph goes beyond the traditional polygon distribution analysis, capturing other organizational traits that improve the characterization of epithelia. EpiGraph can objectively compare the rearrangements of epithelial cells during development and homeostasis to quantify how the global ensemble is affected. Importantly, it has been implemented in the open-access platform Fiji. This makes EpiGraph very user friendly, with no programming skills required.

Availability and implementation

EpiGraph is available at https://imagej.net/EpiGraph and the code is accessible (https://github.com/ComplexOrganizationOfLivingMatter/Epigraph) under GPLv3 license.

Supplementary information

Supplementary data are available at Bioinformatics online.

DeepScratch: Single-cell based topological metrics of scratch wound assays

Changes in tissue architecture and multicellular organisation contribute to many diseases, including cancer and cardiovascular diseases. Scratch wound assay is a commonly used tool that assesses cells' migratory ability based on the area of a wound they cover over a certain time. However, analysis of changes in the organisational patterns formed by migrating cells following genetic or pharmacological perturbations are not well explored in these assays, in part because analysing the resulting imaging data is challenging. Here we present DeepScratch, a neural network that accurately detects the cells in scratch assays based on a heterogeneous set of markers. We demonstrate the utility of DeepScratch by analysing images of more than 232,000 lymphatic endothelial cells. In addition, we propose various topological measures of cell connectivity and local cell density (LCD) to characterise tissue remodelling during wound healing. We show that LCD-based metrics allow classification of CDH5 and CDC42 genetic perturbations that are known to affect cell migration through different biological mechanisms. Such differences cannot be captured when considering only the wound area. Taken together, single-cell detection using DeepScratch allows more detailed investigation of the roles of various genetic components in tissue topology and the biological mechanisms underlying their effects on collective cell migration.

Mechanobiology of leader-follower dynamics in epithelial cell migration

Collective cell migration is fundamental to biological form and function. It is also relevant to the formation and repair of organs and to various pathological situations, including metastatic propagation of cancer. Technological, experimental, and computational advancements have allowed the researchers to explore various aspects of collective migration, spanning from biochemical signalling to inter-cellular force transduction. Here, we summarize our current understanding of the mechanobiology of collective cell migration, limiting to epithelial tissues. On the basis of recent studies, we describe how cells sense and respond to guidance signals to orchestrate various modes of migration and identify the determining factors dictating leader-follower interactions. We highlight how the inherent mechanics of dense epithelial monolayers at multicellular length scale might instruct individual cells to behave collectively. On the basis of these findings, we propose that mechanical resilience, obtained by a certain extent of cell jamming, allows the epithelium to perform efficient collective migration during wound healing.

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.

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.

DE-cadherin and Myosin II balance regulates furrow length for onset of polygon shape in syncytial Drosophila embryos

Cell shape morphogenesis, from spherical to polygonal, occurs in epithelial cell formation in metazoan embryogenesis. In syncytial Drosophila embryos, the plasma membrane incompletely surrounds each nucleus and is organized as a polygonal epithelial-like array. Each cortical syncytial division cycle shows a circular to polygonal plasma membrane transition along with furrow extension between adjacent nuclei from interphase to metaphase. In this study, we assess the relative contribution of DE-cadherin (also known as Shotgun) and Myosin II (comprising Zipper and Spaghetti squash in flies) at the furrow to polygonal shape transition. We show that polygonality initiates during each cortical syncytial division cycle when the furrow extends from 4.75 to 5.75 μm. Polygon plasma membrane organization correlates with increased junctional tension, increased DE-cadherin and decreased Myosin II mobility. DE-cadherin regulates furrow length and polygonality. Decreased Myosin II activity allows for polygonality to occur at a lower length than controls. Increased Myosin II activity leads to loss of lateral furrow formation and complete disruption of the polygonal shape transition. Our studies show that DE-cadherin-Myosin II balance regulates an optimal lateral membrane length during each syncytial cycle for polygonal shape transition.This article has an associated First Person interview with the first author of the paper.

Cuticular reticulation replicates the pattern of epidermal cells in lowermost Cambrian scalidophoran worms

The cuticle of ecdysozoans (Panarthropoda, Scalidophora, Nematoida) is secreted by underlying epidermal cells and renewed via ecdysis. We explore here the relationship between epidermis and external cuticular ornament in stem-group scalidophorans from the early Cambrian of China (Kuanchuanpu Formation; ca 535 Ma) that had two types of microscopic polygonal cuticular networks with either straight or microfolded boundaries. Detailed comparisons with modern scalidophorans (priapulids) indicate that these networks faithfully replicate the cell boundaries of the epidermis. This suggests that the cuticle of early scalidophorans formed through the fusion between patches of extracellular material secreted by epidermal cells, as observed in various groups of present-day ecdysozoans, including arthropods. Key genetic, biochemical and mechanical processes associated with ecdysis and cuticle formation seem to have appeared very early (at least not later than 535 Ma) in the evolution of ecdysozoans. Microfolded reticulation is likely to be a mechanical response to absorbing contraction exerted by underlying muscles. The polygonal reticulation in early and extant ecdysozoans is clearly a by-product of the epidermal cell pavement and interacted with the sedimentary environment.

Crystal-like order and defects in metazoan epithelia with spherical geometry

Since Robert Hooke studied cork cell patterns in 1665, scientists have been puzzled by why cells form such ordered structures. The laws underlying this type of organization are universal, and we study them comparing the living and non-living two-dimensional systems self-organizing at the spherical surface. Such-type physical systems often possess trigonal order with specific elongated defects, scars and pleats, where the 5-valence and 7-valence vertices alternate. In spite of the fact that the same physical and topological rules are involved in the structural organization of biological systems, such topological defects were never reported in epithelia. We have discovered them in the follicular spherical epithelium of ascidians that are emerging models in developmental biology. Surprisingly, the considered defects appear in the epithelium even when the number of cells in it is significantly less than the previously known threshold value. We explain this result by differences in the cell sizes and check our hypothesis considering the self-assembly of different random size particles on the spherical surface. Scars, pleats and other complex defects found in ascidian samples can play an unexpected and decisive role in the permanent renewal and reorganization of epithelia, which forms or lines many tissues and organs in metazoans.

Control of cell colony growth by contact inhibition

Contact inhibition is a cell property that limits the migration and proliferation of cells in crowded environments. Here we investigate the growth dynamics of a cell colony composed of migrating and proliferating cells on a substrate using a minimal model that incorporates the mechanisms of contact inhibition of locomotion and proliferation. We find two distinct regimes. At early times, when contact inhibition is weak, the colony grows exponentially in time, fully characterised by the proliferation rate. At long times, the colony boundary moves at a constant speed, determined only by the migration speed of a single cell and independent of the proliferation rate. Further, the model demonstrates how cell-cell alignment speeds up colony growth. Our model illuminates how simple local mechanical interactions give rise to contact inhibition, and from this, how cell colony growth is self-organised and controlled on a local level.

Generalized network theory of physical two-dimensional systems

The properties of a wide range of two-dimensional network materials are investigated by developing a generalized network theory. The methods developed are shown to be applicable to a wide range of systems generated from both computation and experiment; incorporating atomistic materials, foams, fullerenes, colloidal monolayers, and geopolitical regions. The ring structure in physical networks is described in terms of the node degree distribution and the assortativity. These quantities are linked to previous empirical measures such as Lemaître's law and the Aboav-Weaire law. The effect on these network properties is explored by systematically changing the coordination environments, topologies, and underlying potential model of the physical system.

Cell-based simulations of biased epithelial lung growth

During morphogenesis, epithelial tubes elongate. In the case of the mammalian lung, biased elongation has been linked to a bias in cell shape and cell division, but it has remained unclear whether a bias in cell shape along the axis of outgrowth is sufficient for biased outgrowth and how it arises. Here, we use our 2D cell-based tissue simulation software [Formula: see text] to investigate the conditions for biased epithelial outgrowth. We show that the observed bias in cell shape and cell division can result in the observed bias in outgrowth only in the case of strong cortical tension, and comparison to biological data suggests that the cortical tension in epithelia is likely sufficient. We explore mechanisms that may result in the observed bias in cell division and cell shapes. To this end, we test the possibility that the surrounding tissue or extracellular matrix acts as a mechanical constraint that biases growth in the longitudinal direction. While external compressive forces can result in the observed bias in outgrowth, we find that they do not result in the observed bias in cell shapes. We conclude that other mechanisms must exist that generate the bias in lung epithelial outgrowth.

Neuronal differentiation influences progenitor arrangement in the vertebrate neuroepithelium

Cell division, movement and differentiation contribute to pattern formation in developing tissues. This is the case in the vertebrate neural tube, in which neurons differentiate in a characteristic pattern from a highly dynamic proliferating pseudostratified epithelium. To investigate how progenitor proliferation and differentiation affect cell arrangement and growth of the neural tube, we used experimental measurements to develop a mechanical model of the apical surface of the neuroepithelium that incorporates the effect of interkinetic nuclear movement and spatially varying rates of neuronal differentiation. Simulations predict that tissue growth and the shape of lineage-related clones of cells differ with the rate of differentiation. Growth is isotropic in regions of high differentiation, but dorsoventrally biased in regions of low differentiation. This is consistent with experimental observations. The absence of directional signalling in the simulations indicates that global mechanical constraints are sufficient to explain the observed differences in anisotropy. This provides insight into how the tissue growth rate affects cell dynamics and growth anisotropy and opens up possibilities to study the coupling between mechanics, pattern formation and growth in the neural tube.

Summary: A mechanical model of the vertebrate neuroepithelium, based on experimental observations, suggests that the rate of neuronal differentiation influences tissue growth and the shape of lineage-related clones.

Biomaterials and Advanced Biofabrication Techniques in hiPSCs Based Neuromyopathic Disease Modeling

Induced pluripotent stem cells (iPSCs) are reprogrammed somatic cells by defined factors, and have great application potentials in tissue regeneration and disease modeling. Biomaterials have been widely used in stem cell-based studies, and are involved in human iPSCs based studies, but they were not enough emphasized and recognized. Biomaterials can mimic the extracellular matrix and microenvironment, and act as powerful tools to promote iPSCs proliferation, differentiation, maturation, and migration. Many classic and advanced biofabrication technologies, such as cell-sheet approach, electrospinning, and 3D-bioprinting, are used to provide physical cues in macro-/micro-patterning, and in combination with other biological factors to support iPSCs applications. In this review, we highlight the biomaterials and fabrication technologies used in human iPSC-based tissue engineering to model neuromyopathic diseases, particularly those with genetic mutations, such as Duchenne Muscular Dystrophy (DMD), Congenital Heart Diseases (CHD) and Alzheimer's disease (AD).

Modeling the behavior of inclusions in circular plates undergoing shape changes from two to three dimensions

Growth of biological tissues and shape changes of thin synthetic sheets are commonly induced by stimulation of isolated regions (inclusions) in the system. These inclusions apply internal forces on their surroundings that, in turn, promote 2D layers to acquire complex 3D configurations. We focus on a fundamental building block of these systems, and consider a circular plate that contains an inclusion with dilative strains. Based on the Föppl-von Kármán (FvK) theory, we derive an analytical model that predicts the 2D-to-3D shape transitions in the system. Our findings are summarized in a phase diagram that reveals two distinct configurations in the post-buckling region. One is an extensive profile that holds close to the threshold of the instability, and the second is a localized profile, which preempts the extensive solution beyond the buckling threshold. While the former solution is derived as a perturbation around the flat configuration, assuming infinitesimal amplitudes, the latter solution is derived around a buckled state that is highly localized. We show that up to vanishingly small corrections that scale with the thickness, this localized configuration is equivalent to that expected for ultra-thin sheets, which completely relax compressive stresses. Our findings agree quantitatively with direct numerical minimization of the FvK energy. Furthermore, we extend the theory to describe shape transitions in polymeric gels, and compare the results with numerical simulations that account for the complete elastodynamic behavior of the gels. The agreement between the theory and these simulations indicates that our results are observable experimentally. Notably, our findings can provide guidelines to the analysis of more complicated systems that encompass interaction between several buckled inclusions.

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.

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

Topology of dividing planar tilings: Mitosis and order in epithelial tissues

We investigate a range of rule-based models of the in-plane structure of growing single-cell-thick epithelia represented by the distribution of frequencies of polygon classes. Within the Markovian framework introduced by Gibson et al. [Nature (London) 442, 1038 (2006)10.1038/nature05014], we discuss various topologically allowed cell division schemes assumed to control the structure of the tissue as well as a phenomenological Gaussian scheme, and we compute the stationary distributions for all of them. Some of the distributions reproduce those seen in tissues characterized by unbiased mitotic events but also in certain tissues with a preferred orientation of the mitotic plane or a cell-rearrangement process such as neighbor exchange. In addition, we propose the asynchronous-division variant of the model, which builds on the Lewis law and on the Aboav-Weaire law as well as on the fact that the dividing cells are larger than the resting cells. This generalization a posteriori validates the original model.

Topological traits of a cellular pattern versus growth rate anisotropy in radish roots

The topology of a cellular pattern, which means the spatial arrangement of cells, directly corresponds with cell packing, which is crucial for tissue and organ functioning. The topological features of cells that are typically analyzed are the number of their neighbors and the cell area. To date, the objects of most topological studies have been the growing cells of the surface tissues of plant and animal organs. Some of these researches also provide verification of Lewis's Law concerning the linear correlation between the number of neighboring cells and the cell area. Our aim was to analyze the cellular topology and applicability of Lewis's Law to an anisotropically growing plant organ. The object of our study was the root apex of radish. Based on the tensor description of plant organ growth, we specified the level of anisotropy in specific zones (the root proper, the columella of the cap and the lateral parts of the cap) and in specific types of both external (epidermis) and internal tissues (stele and ground tissue) of the apex. The strongest anisotropy occurred in the root proper, while both zones of the cap showed an intermediate level of anisotropy of growth. Some differences in the topology of the cellular pattern in the zones were also detected; in the root proper, six-sided cells predominated, while in the root cap columella and in the lateral parts of the cap, most cells had five neighbors. The correlation coefficient rL between the number of neighboring cells and the cell area was high in the apex as a whole as well as in all of the zones except the root proper and in all of the tissue types except the ground tissue. In general, Lewis's Law was fulfilled in the anisotropically growing radish root apex. However, the level of the applicability (rL value) of Lewis's Law was negatively correlated with the level of the anisotropy of growth, which may suggest that in plant organs in the regions of anisotropic growth, the number of neighboring cells is less dependent on the cell size.

Multicellular Systems Biology: Quantifying Cellular Patterning and Function in Plant Organs Using Network Science

Organ function is at least partially shaped and constrained by the organization of their constituent cells. Extensive investigation has revealed mechanisms explaining how these patterns are generated, with less being known about their functional relevance. In this paper, a methodology to discretize and quantitatively analyze cellular patterning is described. By performing global organ-scale cellular interaction mapping, the organization of cells can be extracted and analyzed using network science. This provides a means to take the developmental analysis of cellular organization in complex organisms beyond qualitative descriptions and provides data-driven approaches to inferring cellular function. The bridging of a structure-function relationship in hypocotyl epidermal cell patterning through global topological analysis provides support for this approach. The analysis of cellular topologies from patterning mutants further enables the contribution of gene activity toward the organizational properties of tissues to be linked, bridging molecular and tissue scales. This systems-based approach to investigate multicellular complexity paves the way to uncovering the principles of complex organ design and achieving predictive genotype-phenotype mapping.

Ellipse packing in two-dimensional cell tessellation: a theoretical explanation for Lewis's law and Aboav-Weaire's law

Background

Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear.

Methods

We used R software with the Conicfit package to fit ellipses based on the geometric parameters of polygonal cells of ten different kinds of natural and artificial 2D structures.

Results

Our results indicated that the cells could be classified as an ellipse’s inscribed polygon (EIP) and that they tended to form the ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law.

Conclusions

Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.

Multiple feedback mechanisms fine-tune Rho signaling to regulate morphogenetic outcomes

Rho signaling is a conserved mechanism for generating forces through activation of contractile actomyosin. How this pathway can produce different cell morphologies is poorly understood. In the Drosophila embryonic epithelium, we investigate how Rho signaling controls force asymmetry to drive morphogenesis. We study a distinct morphogenetic process termed 'alignment'. This process results in striking columns of rectilinear cells connected by aligned cell-cell contacts. We found that this is driven by contractile actomyosin cables that elevate tension along aligning interfaces. Our data show that polarization of Rho effectors, Rok and Dia, directs formation of these cables. Constitutive activation of these effectors causes aligning cells to instead invaginate. This suggests that moderating Rho signaling is essential to producing the aligned geometry. Therefore, we tested for feedback that could fine-tune Rho signaling. We discovered that F-actin exerts negative feedback on multiple nodes in the pathway. Further, we present evidence that suggests that Rok in part mediates feedback from F-actin to Rho in a manner independent of Myo-II. Collectively, our work suggests that multiple feedback mechanisms regulate Rho signaling, which may account for diverse morphological outcomes.

Statistics of noisy growth with mechanical feedback in elastic tissues

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow [Formula: see text] decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts.

Cdk1-mediated DIAPH1 phosphorylation maintains metaphase cortical tension and inactivates the spindle assembly checkpoint at anaphase

Animal cells undergo rapid rounding during mitosis, ensuring proper chromosome segregation, during which an outward rounding force abruptly increases upon prometaphase entry and is maintained at a constant level during metaphase. Initial cortical tension is generated by the actomyosin system to which both myosin motors and actin network architecture contribute. However, how cortical tension is maintained and its physiological significance remain unknown. We demonstrate here that Cdk1-mediated phosphorylation of DIAPH1 stably maintains cortical tension after rounding and inactivates the spindle assembly checkpoint (SAC). Cdk1 phosphorylates DIAPH1, preventing profilin1 binding to maintain cortical tension. Mutation of DIAPH1 phosphorylation sites promotes cortical F-actin accumulation, increases cortical tension, and delays anaphase onset due to SAC activation. Measurement of the intra-kinetochore length suggests that Cdk1-mediated cortex relaxation is indispensable for kinetochore stretching. We thus uncovered a previously unknown mechanism by which Cdk1 coordinates cortical tension maintenance and SAC inactivation at anaphase onset.

Cell rounding at mitosis is driven by cortical tension and maintained through metaphase, although the mechanism is unknown. Here, the authors demonstrate that Cdk1 phosphorylation of DIAPH1 is required for both cortical tension maintenance and inactivation of the spindle assembly checkpoint.