Geometric constraints alter cell arrangements within curved epithelial tissues

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.

Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

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.

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.

Mapping and exploring the organoid state space using synthetic biology

The functional relevance of an organoid is dependent on the differentiation, morphology, cell arrangement and biophysical properties, which collectively define the state of an organoid. For an organoid culture, an individual organoid or the cells that compose it, these state variables can be characterised, most easily by transcriptomics and by high-content image analysis. Their states can be compared to their in vivo counterparts. Current evidence suggests that organoids explore a wider state space than organs in vivo due to the lack of niche signalling and the variability of boundary conditions in vitro. Using data-driven state inference and in silico modelling, phase diagrams can be constructed to systematically sort organoids along biochemical or biophysical axes. These phase diagrams allow us to identify control strategies to modulate organoid state. To do so, the biochemical and biophysical environment, as well as the cells that seed organoids, can be manipulated.

The impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. Here, we numerically determine the impact of the cell diameter, gradient length and the morphogen source on the variability of morphogen gradients. We show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show that they enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Curvature-Induced Cell Rearrangements in Biological Tissues

On a curved surface, epithelial cells can adapt to geometric constraints by tilting and by exchanging their neighbors from apical to basal sides, known as an apico-basal topological transition 1 (AB-T1). The relationship between cell tilt, AB-T1s, and tissue curvature still lacks a unified understanding. Here, we propose a general framework for cell packing in curved environments and explain the formation of AB-T1s from the perspective of strain anisotropy. We find that steep curvature gradients can lead to cell tilting and induce AB-T1s. Alternatively, pressure differences across the epithelial tissue can drive AB-T1s in regions of large curvature anisotropy. The two mechanisms compete to determine the impact of tissue geometry and mechanics on optimized cell rearrangements in three dimensions.

Membrane-actin interactions in morphogenesis: Lessons learned from Drosophila cellularization

During morphogenesis, changes in the shapes of individual cells are harnessed to mold an entire tissue. These changes in cell shapes require the coupled remodeling of the plasma membrane and underlying actin cytoskeleton. In this review, we highlight cellularization of the Drosophila embryo as a model system to uncover principles of how membrane and actin dynamics are co-regulated in space and time to drive morphogenesis.

Dynamics of changes in apical cell area during sex comb rotation in Drosophila melanogaster

Epithelia are highly dynamic tissues displaying various types of tissue rearrangements (Weliky and Oster, 1990; Taylor and Adler, 2008; Harris and Tepass, 2010; Lee et al. , 2013; Firmino et al. , 2016; Rupprecht et al. , 2017). Here, we describe the dynamics of changes in apical cell area (ACA) in an epithelial system displaying tissue rearrangement resulting in sex comb rotation on the forelegs of male Drosophila melanogaster . The sex comb is a row of leg bristles which rotates during morphogenesis (Atallah, 2008; Atallah et al. , 2009; Malagon, 2013). We quantified the ACA in the region proximal to the developing sex comb by tracing apical cell boundaries using ImageJ in pupal first leg imaginal discs. We found that cells display intricate irregular oscillations in size as the comb rotates. However, the net changes in ACA within most of the cells studied are subtle, only 0 to +/-15%. Our current working hypothesis suggests these irregular oscillations confer flexibility during tissue rearrangement and can be an important mechanism for tissue homeostasis.

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.

Collective motion of epithelial cells along a wrinkled 3D-buckled hydrogel

Epithelial cells migrate autonomously by aligning and inducing a collective motion. Controlling the collective motion of epithelial cells in geometrically confined environments is important for understanding physiological processes such as wound healing and self-organized morphogenesis. However, collective migration under a three-dimensional (3D) curved surface resembling living epithelial tissue has not yet been explored. In this study, we investigated the collective motion of a 3D-buckled polyacrylamide (PAAm) gel that mimics the shape of folds and wrinkles of epithelial tissue to understand the geometric effects of collective motion. We found that the velocity correlation in the space near the hydrogel boundary showed a periodic change that correlated with the wrinkled folding of the hydrogel pattern. Furthermore, the characteristic length of the velocity correlation increased proportionally with the wavelength of wrinkled folding. These observations indicated that the hydrogel pattern could steer the collective motion of epithelial cells over long distances. Our study also suggests that the wrinkled design of the hydrogel is a versatile platform for studying the geometric effect of a curved surface on complex epithelial cell dynamics.

Thickness of epithelia on wavy substrates: measurements and continuous models

We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys than on ridges. This is reminiscent of the so-called «healing length in the case of a thin liquid film wetting a rough solid substrate. We explore the ability of continuum mechanics models to account for these observations. Modeling the epithelium as a thin liquid film, with surface tension, does not fully account for the measurements. Neither does modeling the epithelium as a thin incompressible elastic film. On the contrary, the addition of an apical active stress gives satisfactory agreement with measurements, with one fitting parameter, the ratio between the active stress and the elastic modulus.

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.

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.

Effect of a Surfactant Mixture on Coalescence Occurring in Concentrated Emulsions: The Hole Nucleation Theory Revisited

By conducting both a bottle test and isolate drop-drop experiments, we determine the coalescence rates of water droplets within water-in-oil emulsions stabilized by a large amount of Span 80 in the presence of Tween 20, a surfactant that acts as a demulsifier. Using a microscopic model based on a theory of hole nucleation, we establish an analytical formula that quantitatively predicts the coalescence frequency per unit area of droplets whose interfaces are fully covered by surfactant molecules. Despite its simplicity and the strong assumptions made for its derivation, this formula captures our experimental findings on Span 80-stabilized emulsions as well as other results, found in the literature, remarkably well on a wide range of water-in-crude oil systems.

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.

Mechanical compartmentalization of the intestinal organoid enables crypt folding and collective cell migration

Intestinal organoids capture essential features of the intestinal epithelium such as crypt folding, cellular compartmentalization and collective movements. Each of these processes and their coordination require patterned forces that are at present unknown. Here we map three-dimensional cellular forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the extracellular matrix and folds through apical constriction, whereas the transit amplifying zone pulls the extracellular matrix and elongates through basal constriction. The size of the stem cell compartment depends on the extracellular-matrix stiffness and endogenous cellular forces. Computational modelling reveals that crypt shape and force distribution rely on cell surface tensions following cortical actomyosin density. Finally, cells are pulled out of the crypt along a gradient of increasing tension. Our study unveils how patterned forces enable compartmentalization, folding and collective migration in the intestinal epithelium.

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.

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.

Shape-Anisotropy-Induced Ordered Packings in Cylindrical Confinement

Densest possible packings of identical spheroids in cylindrical confinement have been obtained through Monte Carlo simulations. By varying the shape anisotropy of spheroids and also the cylinder-to-spheroid size ratio, a variety of densest possible crystalline structures have been discovered, including achiral structures with specific orientations of particles and chiral helical structures with rotating orientations of particles. Our findings reveal a transition between confinement-induced chiral ordering and shape-anisotropy-induced orientational ordering and would serve as a guide for the fabrication of crystalline wires using anisotropic particles.

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.

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

As animals develop, tissue bending contributes to shape the organs into complex three-dimensional structures. However, the architecture and packing of curved epithelia remains largely unknown. Here we show by means of mathematical modelling that cells in bent epithelia can undergo intercalations along the apico-basal axis. This phenomenon forces cells to have different neighbours in their basal and apical surfaces. As a consequence, epithelial cells adopt a novel shape that we term "scutoid". The detailed analysis of diverse tissues confirms that generation of apico-basal intercalations between cells is a common feature during morphogenesis. Using biophysical arguments, we propose that scutoids make possible the minimization of the tissue energy and stabilize three-dimensional packing. Hence, we conclude that scutoids are one of nature's solutions to achieve epithelial bending. Our findings pave the way to understand the three-dimensional organization of epithelial organs.