Buckling of an Epithelium Growing under Spherical Confinement

Timely neurogenesis drives the transition from nematic to crystalline nuclear packing during retinal morphogenesis

Correct organogenesis depends on the timely coordination of developmental processes, such as cell proliferation, differentiation, and migration. This coordination is particularly critical in crowded tissues, such as pseudostratified epithelia (PSE) that are often found as organ precursors. They are composed of elongated epithelial cells with densely packed nuclei aligned along the apicobasal axis. While cell cycle-dependent nuclear movements in PSE are well studied, less is known about how nuclear packing influences tissue morphogenesis. To investigate this, we analyzed nuclear shapes, sizes, and neighborhood statistics in zebrafish neuroepithelia, focusing on the retinal PSE. We found that nuclei exhibit elongated shapes and biaxial nematic-like orientational order but remain positionally disordered. During retinal development, nuclear packing density increases, approaching theoretical limits. This occurs when the tissue transitions to a laminated structure and nuclear shapes are remodeled. Timely neurogenesis is critical as failure to initiate neurogenesis leads to tissue deformations. These findings highlight the influence of nuclear shape and positioning for organ morphogenesis.

Epithelial Layer Fluidization by Curvature-Induced Unjamming

The transition of an epithelial layer from a stationary, quiescent state to a highly migratory, dynamic state is required for wound healing, development, and regeneration. This transition, known as the unjamming transition (UJT), is responsible for epithelial fluidization and collective migration. Previous theoretical models have primarily focused on the UJT in flat epithelial layers, neglecting the effects of strong surface curvature characteristic of the epithelium in vivo. In this Letter, we investigate the role of surface curvature on tissue plasticity and cellular migration using a vertex model embedded on a spherical surface. Our findings reveal that increasing curvature promotes the UJT by reducing the energy barriers to cellular rearrangements. Higher curvature favors cell intercalation, mobility, and self-diffusivity, resulting in epithelial structures that are malleable and migratory when small, but become more rigid and stationary as they grow. Together, these results provide a conceptual framework to better understand how cell shape, cell propulsion, and tissue geometry contribute to tissue malleability, remodeling, and stabilization.

Mechanochemical bistability of intestinal organoids enables robust morphogenesis

Reproducible pattern and form generation during embryogenesis is poorly understood. Intestinal organoid morphogenesis involves a number of mechanochemical regulators such as cell-type-specific cytoskeletal forces and osmotically driven lumen volume changes. It is unclear how these forces are coordinated in time and space to ensure robust morphogenesis. Here we show how mechanosensitive feedback on cytoskeletal tension gives rise to morphological bistability in a minimal model of organoid morphogenesis. In the model, lumen volume changes can impact the epithelial shape via both direct mechanical and indirect mechanosensitive mechanisms. We find that both bulged and budded crypt states are possible and dependent on the history of volume changes. We test key modelling assumptions via biophysical and pharmacological experiments to demonstrate how bistability can explain experimental observations, such as the importance of the timing of lumen shrinkage and robustness of the final morphogenetic state to mechanical perturbations. This suggests that bistability arising from feedback between cellular tensions and fluid pressure could be a general mechanism that coordinates multicellular shape changes in developing systems.

Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation

A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell-stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.

Topology changes of Hydra define actin orientation defects as organizers of morphogenesis

Hydra regenerates one head when cut, but how forces shaping the head are coordinated remains unclear. Soft compression of Hydra's head-regenerating tissues induces the formation of viable, two-headed animals. Compression creates new topological defects in the supracellular orientational order of muscular actin fibers, associated with additional heads. Theory supports that these defects organize muscle stresses required to shape the head. By compressing head-regenerating tissues along their body axis, we formed toroidal tissues, whose unique topology allows for the absence of defects. Toroids with no actin defects did not regenerate. Toroids with actin defects regenerated into viable toroidal animals with a bifurcated body. Topological defects in the actin orientational order are thus necessary for complete regeneration of Hydra, defining actin topological defects as mechanical organizers of morphogenesis.

Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids' morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.

Differential Effects of Confinement on the Dynamics of Normal and Tumor-Derived Pancreatic Ductal Organoids

Pancreatic ductal adenocarcinoma (PDAC) is a cancer of the epithelia comprising the ductal network of the pancreas. During disease progression, PDAC tumors recruit fibroblasts that promote fibrosis, increasing local tissue stiffness and subjecting epithelial cells to increased compressive forces. Previous in vitro studies have documented cytoskeletal and nuclear adaptation following compressive stresses in two-dimensional (2D) and three-dimensional (3D) environments. However, a comparison of the responses of normal and tumor-derived ductal epithelia to physiologically relevant confinement remains underexplored, especially in 3D organoids. Here we control confinement with an engineered 3D microenvironment composed of Matrigel mixed with a low yield stress granular microgel. Normal and tumor-derived murine pancreas organoids (normal and tumor) were cultured for 48 h within this composite 3D environment or in pure Matrigel to investigate the effects of confinement on morphogenesis and lumen expansion. In confinement, tumor organoids (mT) formed a lumen that expanded rapidly, whereas normal organoids (mN) expanded more slowly. Moreover, a majority of normal organoids in more-confined conditions exhibited an inverted apicobasal polarity compared to those in less-confined conditions. Tumor organoids exhibited a collective "pulsing" behavior that increased in confinement. These pulses generated forces sufficient to locally overcome the yield stress of the microgels in the direction of organoid expansion. Normal organoids more commonly exhibit unidirectional rotation. Our in vitro microgel confinement platform enabled the discovery of two distinct modes of collective force generation in organoids that may shed light on the mutual interactions between tumors and the microenvironment. These insights into in vitro dynamics may deepen our understanding of how the confinement of healthy cells within a fibrotic tumor niche disrupts tissue organization and function in vivo.

Luteinizing hormone-induced changes in the structure of mammalian preovulatory follicles

Ovulation of a mammalian oocyte from its follicle, which occurs in response to luteinizing hormone (LH), requires complex restructuring of the ∼20 layers of surrounding somatic cells. This chapter describes the cellular architecture of preovulatory follicles, the localization of the receptors for LH, and the LH-induced changes in follicular structure, focusing on mice and other small mammals. The multiple interrelated processes that result in ovulation include breakdown of existing extracellular matrix, generation of new extracellular matrix, thinning of the follicular apex where the oocyte will be released, invagination of the follicular surface, and responses of the vascular system to support these dynamic changes. However, much remains unknown about how these events function together to release a fertilizable egg.

Active curling of epithelial monolayers dominated by actin cytoskeleton mechanics

Active curling of epithelial tissues, as an indispensable component of developmental morphogenesis, occurs frequently both in vivo and in vitro microenvironments. Deciphering the mechanisms underlying the active curling of epithelial monolayers is crucial for understanding many physiological and pathological processes. Here, a multiscale structure-based cell monolayer model and an active constitutive relation are established to characterize this spontaneous curling of the epithelial tissue. It is shown that the asymmetric distribution of Myosin II along the apicobasal axis generates an active moment that drives spontaneous curling of the suspended epithelial tissue. The time-dependent deflection and rotation angle of the active curling are analytically solved, proving that the curling is driven by the active bending moment directly associated with the apicobasal asymmetric contractile force. Moreover, we demonstrate that the rotation angle is proportional to the apicobasal force ratio and inversely proportional to the thickness of epithelial tissues. In addition, we derive an approximate analytical relation between the out-of-plane curling behavior and in-plane stress, in good agreement with the experimental data and our simulation results. This study provides a pathway to elucidate the mechanical mechanism underlying complex morphological development as well as the physiological and pathological phenomena of epithelial tissues.

3D embedded bioprinting of large-scale intestine with complex structural organization and blood capillaries

Accurate reproduction of human intestinal structure and functionin vitrois of great significance for understanding the development and disease occurrence of the gut. However, mostin vitrostudies are often confined to 2D models, 2.5D organ chips or 3D organoids, which cannot fully recapitulate the tissue architecture, microenvironment and cell compartmentalization foundin vivo. Herein, a centimeter-scale intestine tissue that contains intestinal features, such as hollow tubular structure, capillaries and tightly connected epithelium with invivo-likering folds, crypt-villi, and microvilli is constructed by 3D embedding bioprinting. In our strategy, a novel photocurable bioink composed of methacrylated gelatin, methacrylated sodium alginate and poly (ethylene glycol) diacrylate is developed for the fabrication of intestinal model. The Caco-2 cells implanted in the lumen are induced by the topological structures of the model to derive microvilli, crypt-villi, and tight junctions, simulating the intestinal epithelial barrier. The human umbilical vein endothelial cells encapsulated within the model gradually form microvessels, mimicking the dense capillary network in the intestine. This intestine-like tissue, which closely resembles the structure and cell arrangement of the human gut, can act as a platform to predict the therapeutic and toxic side effects of new drugs on the intestine.

On mechanical phase and form

Epithelial folding is a fundamental biological process that requires epithelial interactions with the underlying mesenchyme. In this issue of Cell, Huycke et al. investigate intestinal villus formation. They discover that water-droplet-like behavior of mesenchymal cells drives their coalescence into uniformly patterned aggregates, which generate forces on the epithelium to initiate folding.

Endogenous OptoRhoGEFs reveal biophysical principles of epithelial tissue furrowing

During development, epithelia function as malleable substrates that undergo extensive remodeling to shape developing embryos. Optogenetic control of Rho signaling provides an avenue to investigate the mechanisms of epithelial morphogenesis, but transgenic optogenetic tools can be limited by variability in tool expression levels and deleterious effects of transgenic overexpression on development. Here, we use CRISPR/Cas9 to tag Drosophila RhoGEF2 and Cysts/Dp114RhoGEF with components of the iLID/SspB optogenetic heterodimer, permitting light-dependent control over endogenous protein activities. Using quantitative optogenetic perturbations, we uncover a dose-dependence of tissue furrow depth and bending behavior on RhoGEF recruitment, revealing mechanisms by which developing embryos can shape tissues into particular morphologies. We show that at the onset of gastrulation, furrows formed by cell lateral contraction are oriented and size-constrained by a stiff basal actomyosin layer. Our findings demonstrate the use of quantitative, 3D-patterned perturbations of cell contractility to precisely shape tissue structures and interrogate developmental mechanics.

Lumen expansion is initially driven by apical actin polymerization followed by osmotic pressure in a human epiblast model

Post-implantation, the pluripotent epiblast in a human embryo forms a central lumen, paving the way for gastrulation. Osmotic pressure gradients are considered the drivers of lumen expansion across development, but their role in human epiblasts is unknown. Here, we study lumenogenesis in a pluripotent-stem-cell-based epiblast model using engineered hydrogels. We find that leaky junctions prevent osmotic pressure gradients in early epiblasts and, instead, forces from apical actin polymerization drive lumen expansion. Once the lumen reaches a radius of ∼12 μm, tight junctions mature, and osmotic pressure gradients develop to drive further growth. Computational modeling indicates that apical actin polymerization into a stiff network mediates initial lumen expansion and predicts a transition to pressure-driven growth in larger epiblasts to avoid buckling. Human epiblasts show transcriptional signatures consistent with these mechanisms. Thus, actin polymerization drives lumen expansion in the human epiblast and may serve as a general mechanism of early lumenogenesis.

Cell proliferation and Notch signaling coordinate the formation of epithelial folds in the Drosophila leg

The formation of complex three-dimensional organs during development requires precise coordination between patterning networks and mechanical forces. In particular, tissue folding is a crucial process that relies on a combination of local and tissue-wide mechanical forces. Here, we investigate the contribution of cell proliferation to epithelial morphogenesis using the Drosophila leg tarsal folds as a model. We reveal that tissue-wide compression forces generated by cell proliferation, in coordination with the Notch signaling pathway, are essential for the formation of epithelial folds in precise locations along the proximo-distal axis of the leg. As cell numbers increase, compressive stresses arise, promoting the folding of the epithelium and reinforcing the apical constriction of invaginating cells. Additionally, the Notch target dysfusion plays a key function specifying the location of the folds, through the apical accumulation of F-actin and the apico-basal shortening of invaginating cells. These findings provide new insights into the intricate mechanisms involved in epithelial morphogenesis, highlighting the crucial role of tissue-wide forces in shaping a three-dimensional organ in a reproducible manner.

Topological balance of cell distributions in plane monolayers

Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.

Toward a predictive understanding of epithelial cell death

Epithelial cell death is highly prevalent during development and tissue homeostasis. While we have a rather good understanding of the molecular regulators of programmed cell death, especially for apoptosis, we still fail to predict when, where, how many and which specific cells will die in a tissue. This likely relies on the much more complex picture of apoptosis regulation in a tissular and epithelial context, which entails cell autonomous but also non-cell autonomous factors, diverse feedback and multiple layers of regulation of the commitment to apoptosis. In this review, we illustrate this complexity of epithelial apoptosis regulation by describing these different layers of control, all demonstrating that local cell death probability is a complex emerging feature. We first focus on non-cell autonomous factors that can locally modulate the rate of cell death, including cell competition, mechanical input and geometry as well as systemic effects. We then describe the multiple feedback mechanisms generated by cell death itself. We also outline the multiple layers of regulation of epithelial cell death, including the coordination of extrusion and regulation occurring downstream of effector caspases. Eventually, we propose a roadmap to reach a more predictive understanding of cell death regulation in an epithelial context.

Mechanical forces across compartments coordinate cell shape and fate transitions to generate tissue architecture

Morphogenesis and cell state transitions must be coordinated in time and space to produce a functional tissue. An excellent paradigm to understand the coupling of these processes is mammalian hair follicle development, which is initiated by the formation of an epithelial invagination-termed placode-that coincides with the emergence of a designated hair follicle stem cell population. The mechanisms directing the deformation of the epithelium, cell state transitions and physical compartmentalization of the placode are unknown. Here we identify a key role for coordinated mechanical forces stemming from contractile, proliferative and proteolytic activities across the epithelial and mesenchymal compartments in generating the placode structure. A ring of fibroblast cells gradually wraps around the placode cells to generate centripetal contractile forces, which, in collaboration with polarized epithelial myosin activity, promote elongation and local tissue thickening. These mechanical stresses further enhance compartmentalization of Sox9 expression to promote stem cell positioning. Subsequently, proteolytic remodelling locally softens the basement membrane to facilitate a release of pressure on the placode, enabling localized cell divisions, tissue fluidification and epithelial invagination into the underlying mesenchyme. Together, our experiments and modelling identify dynamic cell shape transformations and tissue-scale mechanical cooperation as key factors for orchestrating organ formation.

Friction forces determine cytoplasmic reorganization and shape changes of ascidian oocytes upon fertilization

Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole-a protuberance of the zygote's vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces.

Biomimetic growth in polymer gels

By modeling gels growing in confined environments, we uncover a biomimetic feedback mechanism between the evolving gel and confining walls that enables significant control over the properties of the grown gel. Our new model describes the monomer adsorption, polymerization and cross-linking involved in forming new networks and the resultant morphology and mechanical behavior of the grown gel. Confined between two hard walls, a thin, flat "parent" gel undergoes buckling; removal of the walls returns the gel to the flat structure. Polymerization and cross-linking in the confined parent generates the next stage of growth, forming a random copolymer network (RCN). When the walls are removed, the RCN remains in the buckled state, simultaneously "locking in" these patterns and increasing the Young's modulus by two orders of magnitude. Confinement of thicker gels between harder or softer 3D walls leads to controllable mechanical heterogeneities, where the Young's modulus between specific domains can differ by three orders of magnitude. These systems effectively replicate the feedback between mechanics and morphology in biological growth, where mechanical forces guide the structure formation throughout stages of growth. The findings provide new guidelines for shaping "growing materials" and introducing new approaches to matching form and function in synthetic systems.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Instabilities in a growing system of active particles: scalar and vectorial systems

The physics of micron-scale biological colonies usually benefits from different out-of-equilibrium sources. In bacterial colonies and cellular tissues, the growth process is among the important active sources that determine the dynamics. In this article, we study the generic dynamical instabilities associated with the growth phenomena that may arise in both scalar and vectorial systems. In vectorial systems, where the rotational degrees of particles play a role, a phenomenological growth-mediated torque can affect the rotational dynamics of individual particles. We show that such a growth-mediated torque can result in active traveling waves in the bulk of a growing system. In addition to the bulk properties, we analyze the instabilities in the shape of growing interfaces in both scalar and vectorial systems.

Transducing compressive forces into cellular outputs in cancer and beyond

In living organisms, cells sense mechanical forces (shearing, tensile, and compressive) and respond to those physical cues through a process called mechanotransduction. This process includes the simultaneous activation of biochemical signaling pathways. Recent studies mostly on human cells revealed that compressive forces selectively modulate a wide range of cell behavior, both in compressed and in neighboring less compressed cells. Besides participating in tissue homeostasis such as bone healing, compression is also involved in pathologies, including intervertebral disc degeneration or solid cancers. In this review, we will summarize the current scattered knowledge of compression-induced cell signaling pathways and their subsequent cellular outputs, both in physiological and pathological conditions, such as solid cancers.

Topological properties and shape of proliferative and nonproliferative cell monolayers

During embryonic development, structures with complex geometry can emerge from planar epithelial monolayers; studying these shape transitions is of key importance for revealing the biophysical laws involved in the morphogenesis of biological systems. Here, using the example of normal proliferative monkey kidney (COS) cell monolayers, we investigate global and local topological characteristics of this model system in dependence on its shape. The obtained distributions of cells by their valence demonstrate a difference between the spherical and planar monolayers. In addition, in both spherical and planar monolayers, the probability of observing a pair of neighboring cells with certain valences depends on the topological charge of the pair. The zero topological charge of the cell pair can increase the probability for the cells to be the nearest neighbors. We then test and confirm that analogous relationships take place in a more ordered spherical system with a larger fraction of 6-valent cells, namely, in the nonproliferative epithelium (follicular system) of ascidian species oocytes. However, unlike spherical COS cell monolayers, ascidian monolayers are prone to nonrandom agglomeration of 6-valent cells and have linear topological defects called scars and pleats. The reasons for this difference in morphology are discussed. The morphological peculiarities found are compared with predictions of the widely used vertex model of epithelium.

Sculpting with stiffness: rigidity as a regulator of morphogenesis

From a physical perspective, morphogenesis of tissues results from interplay between their material properties and the mechanical forces exerted on them. The importance of mechanical forces in influencing cell behaviour is widely recognised, whereas the importance of tissue material properties in vivo, like stiffness, has only begun to receive attention in recent years. In this mini-review, we highlight key themes and concepts that have emerged related to how tissue stiffness, a fundamental material property, guides various morphogenetic processes in living organisms.

Growth of a flexible fibre in a deformable ring

We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified geometry in which initially the container is a circular ring of radius R. Quasi-static growth is then studied by solving the equilibrium equations as the fibre length l increases, starting from l = 2R. Considering both the fibre and the ring as inextensible and unshearable, we find that beyond a critical length, which depends on the relative bending stiffness, the fibre buckles. Furthermore, as the fibre grows further it folds, distorting the ring until it induces a break in mirror symmetry at l > 2πR. We get that the equilibrium shapes depend only on two dimensionless parameters: the length ratio μ = l/R and the bending stiffnesses ratio κ. These findings are also supported by finite element simulation. Finally we experimentally validate the theoretical results showing a very good quantitative prediction of the observed buckling and folding regimes at variable geometrical parameters.

Universality in the buckling behavior of drying suspension drops

Fast evaporation of particle-suspension drops results in complex morphologies of the final dried granules. Understanding the morphological transformations is important to industrial processes such as spray drying where droplets of particulate suspensions are dried at a fast rate to produce granules of thermally sensitive materials. The transformation of an initial spherical shell to complex morphologies of the final dried granule has been attributed to the buckling of particle-packed shells. Here, we demonstrate a universal scaling law for buckling that depends on the particle size, hardness, particle packing and size of drying drop. The critical transition for buckling is set by a dimensionless number that measures the competition between the compressive stress generated by capillary forces and the elastic strength of the packing. The same dimensionless number is also responsible for cracking of drying colloidal films, suggesting a universality in the mechanical behaviour of particle packings saturated with a solvent. These results should enable design of hierarchically structured, buckle-free granules with varying porosity, surface composition and internal structure.

Size-dependent response of cells in epithelial tissue modulated by contractile stress fibers

Although cells with distinct apical areas have been widely observed in epithelial tissues, how the size of cells affects their behavior during tissue deformation and morphogenesis as well as key physical factors modulating such influence remains elusive. Here, we showed that the elongation of cells within the monolayer under anisotropic biaxial stretching increases with their size because the strain released by local cell rearrangement (i.e., T1 transition) is more significant for small cells that possess higher contractility. On the other hand, by incorporating the nucleation, peeling, merging, and breakage dynamics of subcellular stress fibers into classical vertex formulation, we found that stress fibers with orientations predominantly aligned with the main stretching direction will be formed at tricellular junctions, in good agreement with recent experiments. The contractile forces generated by stress fibers help cells to resist imposed stretching, reduce the occurrence of T1 transitions, and, consequently, modulate their size-dependent elongation. Our findings demonstrate that epithelial cells could utilize their size and internal structure to regulate their physical and related biological behaviors. The theoretical framework proposed here can also be extended to investigate the roles of cell geometry and intracellular contraction in processes such as collective cell migration and embryo development.

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.

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.

Homeotic compartment curvature and tension control spatiotemporal folding dynamics

Shape is a conspicuous and fundamental property of biological systems entailing the function of organs and tissues. While much emphasis has been put on how tissue tension and mechanical properties drive shape changes, whether and how a given tissue geometry influences subsequent morphogenesis remains poorly characterized. Here, we explored how curvature, a key descriptor of tissue geometry, impinges on the dynamics of epithelial tissue invagination. We found that the morphogenesis of the fold separating the adult Drosophila head and thorax segments is driven by the invagination of the Deformed (Dfd) homeotic compartment. Dfd controls invagination by modulating actomyosin organization and in-plane epithelial tension via the Tollo and Dystroglycan receptors. By experimentally introducing curvature heterogeneity within the homeotic compartment, we established that a curved tissue geometry converts the Dfd-dependent in-plane tension into an inward force driving folding. Accordingly, the interplay between in-plane tension and tissue curvature quantitatively explains the spatiotemporal folding dynamics. Collectively, our work highlights how genetic patterning and tissue geometry provide a simple design principle driving folding morphogenesis during development.

Mechanobiological approaches to synthetic morphogenesis: learning by building

Tissue morphogenesis occurs in a complex physicochemical microenvironment with limited experimental accessibility. This often prevents a clear identification of the processes that govern the formation of a given functional shape. By applying state-of-the-art methods to minimal tissue systems, synthetic morphogenesis aims to engineer the discrete events that are necessary and sufficient to build specific tissue shapes. Here, we review recent advances in synthetic morphogenesis, highlighting how a combination of microfabrication and mechanobiology is fostering our understanding of how tissues are built.

The dynamics along the biointerface between the epithelial and cancer mesenchymal cells: Modeling consideration

Epithelial cancer is the one of most lethal cancer type worldwide. Targeting the early stage of disease would allow dramatic improvements in the survival of cancer patients. The early stage of the disease is related to cancer cell spreading across surrounding healthy epithelium. Consequently, deeper insight into cell dynamics along the biointerface between epithelial and cancer (mesenchymal) cells is necessary in order to control the disease as soon as possible. Cell dynamics along this epithelial-cancer biointerface is the result of the interplay between various biological and physical mechanisms. Despite extensive research devoted to study cancer cell spreading across the epithelium, we still do not understand the physical mechanisms which influences the dynamics along the biointerface. These physical mechanisms are related to the interplay between physical parameters such as: (1) interfacial tension between cancer and epithelial subpopulations, (2) established interfacial tension gradients, (3) the bending rigidity of the biointerface and its impact on the interfacial tension, (4) surface tension of the subpopulations, (5) viscoelasticity caused by collective cell migration, and (6) cell residual stress accumulation. The main goal of this study is to review some of these physical parameters in the context of the epithelial/cancer biointerface elaborated on the model system such as the biointerface between breast epithelial MCF-10A cells and cancer MDA-MB-231 cells and then to incorporate these parameters into a new biophysical model that could describe the dynamics of the biointerface. We conclude by discussing three biophysical scenarios for cell dynamics along the biointerface, which can occur depending on the magnitude of the generated shear stress: a smooth biointerface, a slightly-perturbed biointerface and an intensively-perturbed biointerface in the context of the Kelvin-Helmholtz instability. These scenarios are related to the probability of cancer invasion.

Topological morphogenesis of neuroepithelial organoids

Animal organs exhibit complex topologies involving cavities and tubular networks, which underlie their form and function^1-3. However, how topology emerges during the development of organ shape, or morphogenesis, remains elusive. Here we combine tissue reconstitution and quantitative microscopy to show that tissue topology and shape is governed by two distinct modes of topological transitions^4,5. One mode involves the fusion of two separate epithelia and the other involves the fusion of two ends of the same epithelium. The morphological space is captured by a single control parameter that can be traced back to the relative rates of the two epithelial fusion modes. Finally, we identify a pharmacologically accessible pathway that regulates the frequency of two modes of epithelial fusion, and demonstrate the control of organoid topology and shape. The physical principles uncovered here provide fundamental insights into the self-organization of complex tissues⁶.

Cell fate decisions, transcription factors and signaling during early retinal development

The development of the vertebrate eyes is a complex process starting from anterior-posterior and dorso-ventral patterning of the anterior neural tube, resulting in the formation of the eye field. Symmetrical separation of the eye field at the anterior neural plate is followed by two symmetrical evaginations to generate a pair of optic vesicles. Next, reciprocal invagination of the optic vesicles with surface ectoderm-derived lens placodes generates double-layered optic cups. The inner and outer layers of the optic cups develop into the neural retina and retinal pigment epithelium (RPE), respectively. In vitro produced retinal tissues, called retinal organoids, are formed from human pluripotent stem cells, mimicking major steps of retinal differentiation in vivo. This review article summarizes recent progress in our understanding of early eye development, focusing on the formation the eye field, optic vesicles, and early optic cups. Recent single-cell transcriptomic studies are integrated with classical in vivo genetic and functional studies to uncover a range of cellular mechanisms underlying early eye development. The functions of signal transduction pathways and lineage-specific DNA-binding transcription factors are dissected to explain cell-specific regulatory mechanisms underlying cell fate determination during early eye development. The functions of homeodomain (HD) transcription factors Otx2, Pax6, Lhx2, Six3 and Six6, which are required for early eye development, are discussed in detail. Comprehensive understanding of the mechanisms of early eye development provides insight into the molecular and cellular basis of developmental ocular anomalies, such as optic cup coloboma. Lastly, modeling human development and inherited retinal diseases using stem cell-derived retinal organoids generates opportunities to discover novel therapies for retinal diseases.

A physical model for dynamic assembly of human salivary stem/progenitor microstructures

The in vitro reconstructions of human salivary glands in service of their eventual medical use represent a challenge for tissue engineering. Here, we present a theoretical approach to the dynamical formation of acinar structures from human salivary cells, focusing on observed stick-slip radial expansion as well as possible growth instabilities. Our findings demonstrate the critical importance of basement membrane remodeling in controlling the growth process.

Pressure and curvature control of the cell cycle in epithelia growing under spherical confinement

Morphogenesis requires spatiotemporal regulation of proliferation, both by biochemical and mechanical cues. In epithelia, this regulation is called contact inhibition of proliferation, but disentangling biochemical from mechanical cues remains challenging. Here, we show that epithelia growing under confinement accumulate pressure that inhibits proliferation above a threshold value. During growth, epithelia spontaneously buckle, and cell proliferation is transiently reactivated within the fold. Reactivation of proliferation within folds correlated with the local reactivation of the mechano-sensing YAP/TAZ pathway. At late time points, when the pressure is highest, β-catenin activity increases. The threshold pressure increases when β-catenin is overactivated and decreases when β-catenin is inhibited. Altogether, our results suggest that different mechanical cues resulting from pressure inhibition of proliferation are at play through different mechano-sensing pathways: the β-catenin pathway sustains cell division under high pressure, and the YAP pathway senses local curvature.

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Encapsulation of MDCK cells enables quantification of growth-induced pressure

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Confined epithelia reach a threshold pressure that inhibits cell-cycle progression

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Overactivation of β-catenin activity sustains cell division under high pressure

Mechanical forces directing intestinal form and function

The vertebrate intestine experiences a range of intrinsically generated and external forces during both development and adult homeostasis. It is increasingly understood how the coordination of these forces shapes the intestine through organ-scale folding and epithelial organization into crypt-villus compartments. Moreover, accumulating evidence shows that several cell types in the adult intestine can sense and respond to forces to regulate key cellular processes underlying adult intestinal functions and self-renewal. In this way, transduction of forces may direct both intestinal homeostasis as well as adaptation to external stimuli, such as food ingestion or injury. In this review, we will discuss recent insights from complementary model systems into the force-dependent mechanisms that establish and maintain the unique architecture of the intestine, as well as its homeostatic regulation and function throughout adult life.

Developmentally interdependent stretcher-compressor relationship between the embryonic brain and the surrounding scalp in the preosteogenic head

BACKGROUND

How developing brains mechanically interact with the surrounding embryonic scalp layers (ie, epidermal and mesenchymal) in the preosteogenic head remains unknown. Between embryonic day (E) 11 and E13 in mice, before ossification starts in the skull vault, the angle between the pons and the medulla decreases, raising the possibility that when the elastic scalp is directly pushed outward by the growing brain and thus stretched, it recoils inward in response, thereby confining and folding the brain.

RESULTS

Stress-release tests showed that the E11-13 scalp recoiled and that the in vivo prestretch prerequisite for this recoil was physically dependent on the brain (pressurization at 77-93 Pa) and on actomyosin and elastin within the scalp. In scalp-removed heads, brainstem folding was reduced, and the spreading of ink from the lateral ventricle to the spinal cord that occurred in scalp-intact embryos (with >5 μL injection) was lost, suggesting roles of the embryonic scalp in brain morphogenesis and cerebrospinal fluid homeostasis. Under nonstretched conditions, scalp cell proliferation declined, while the restretching of the shrunken scalp rescued scalp cell proliferation.

CONCLUSIONS

In the embryonic mouse head before ossification, a stretcher-compressor relationship elastically develops between the brain and the scalp, underlying their mechanically interdependent development.

Mechanical instability generated by Myosin 19 contributes to mitochondria cristae architecture and OXPHOS

The folded mitochondria inner membrane-cristae is the structural foundation for oxidative phosphorylation (OXPHOS) and energy production. By mechanically simulating mitochondria morphogenesis, we speculate that efficient sculpting of the cristae is organelle non-autonomous. It has long been inferred that folding requires buckling in living systems. However, the tethering force for cristae formation and regulation has not been identified. Combining electron tomography, proteomics strategies, super resolution live cell imaging and mathematical modeling, we reveal that the mitochondria localized actin motor-myosin 19 (Myo19) is critical for maintaining cristae structure, by associating with the SAM-MICOS super complex. We discover that depletion of Myo19 or disruption of its motor activity leads to altered mitochondria membrane potential and decreased OXPHOS. We propose that Myo19 may act as a mechanical tether for effective ridging of the mitochondria cristae, thus sustaining the energy homeostasis essential for various cellular functions.

The structure of the mitochondrial inner membrane, or cristae, is important for functional oxidative phosphorylation and energy production. Here, the authors show that loss of myosin 19 impairs cristae structure as well as energy production, connecting motor activity to membrane potential.

Epithelial cells adapt to curvature induction via transient active osmotic swelling

Generation of tissue curvature is essential to morphogenesis. However, how cells adapt to changing curvature is still unknown because tools to dynamically control curvature in vitro are lacking. Here, we developed self-rolling substrates to study how flat epithelial cell monolayers adapt to a rapid anisotropic change of curvature. We show that the primary response is an active and transient osmotic swelling of cells. This cell volume increase is not observed on inducible wrinkled substrates, where concave and convex regions alternate each other over short distances; and this finding identifies swelling as a collective response to changes of curvature with a persistent sign over large distances. It is triggered by a drop in membrane tension and actin depolymerization, which is perceived by cells as a hypertonic shock. Osmotic swelling restores tension while actin reorganizes, probably to comply with curvature. Thus, epithelia are unique materials that transiently and actively swell while adapting to large curvature induction.

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Rapid inward and outward epithelial rolling triggers cell volume increase

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Epithelial folding induces a mechano-osmotic feedback loop that involvs ion channels

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Cell volume regulation in curved tissues involves actin, membrane tension, and mTORC2

ARVCF catenin controls force production during vertebrate convergent extension

The design of an animal's body plan is encoded in the genome, and the execution of this program is a mechanical progression involving coordinated movement of proteins, cells, and whole tissues. Thus, a challenge to understanding morphogenesis is connecting events that occur across various length scales. Here, we describe how a poorly characterized adhesion effector, Arvcf catenin, controls Xenopus head-to-tail axis extension. We find that Arvcf is required for axis extension within the intact organism but not within isolated tissues. We show that the organism-scale phenotype results from a defect in tissue-scale force production. Finally, we determine that the force defect results from the dampening of the pulsatile recruitment of cell adhesion and cytoskeletal proteins to membranes. These results provide a comprehensive understanding of Arvcf function during axis extension and produce an insight into how a cellular-scale defect in adhesion results in an organism-scale failure of development.

Mechanobiology of Colorectal Cancer

In this review, the mechanobiology of colorectal cancer (CRC) are discussed. Mechanotransduction of CRC is addressed considering the relationship of several biophysical cues and biochemical pathways. Mechanobiology is focused on considering how it may influence epithelial cells in terms of motility, morphometric changes, intravasation, circulation, extravasation, and metastization in CRC development. The roles of the tumor microenvironment, ECM, and stroma are also discussed, taking into account the influence of alterations and surface modifications on mechanical properties and their impact on epithelial cells and CRC progression. The role of cancer-associated fibroblasts and the impact of flow shear stress is addressed in terms of how it affects CRC metastization. Finally, some insights concerning how the knowledge of biophysical mechanisms may contribute to the development of new therapeutic strategies and targeting molecules and how mechanical changes of the microenvironment play a role in CRC disease are presented.

Mechanical regulation of tissues that reproduces wrinkle patterns of gastrointestinal tracts

Gastrointestinal tracts exhibit a number of surface morphologies including zigzags, labyrinths, protrusions, and invaginations which are associated with digestive functions and are suggested to be formed by mechanical mechanisms. In this study, we investigate loading conditions and mechanical properties of tissues that reproduce different wrinkle patterning of gastrointestinal tracts on cell culture platforms. Numerical simulations of wrinkling dynamics are performed for a layered model consisting of an anisotropic epithelial layer resting on a bimodular soft substrate, which in turn adheres to a rigid foundation. Motivated by the patterning of intestinal villi of chicks and mice, we examine two-step compression, where the epithelial layer is subjected to uniaxial compression followed by biaxial compression, and one-step compression, where the epithelial layer is compressed in biaxial directions. Under different mechanical conditions of tissues, a wide variety of surface patterns are displayed that reproduce luminal patterns of digestive tracts. These results suggest possible conditions for mechanical regulation of tissues to duplicate gastrointestinal surface patterns in vitro and provide insight into mechanistic understandings of biological tissues.

Appreciating the role of cell shape changes in the mechanobiology of epithelial tissues

The wide range of epithelial cell shapes reveals the complexity and diversity of the intracellular mechanisms that serve to construct their morphology and regulate their functions. Using mechanosensitive steps, epithelial cells can sense a variety of different mechanochemical stimuli and adapt their behavior by reshaping their morphology. These changes of cell shape rely on a structural reorganization in space and time that generates modifications of the tensional state and activates biochemical cascades. Recent studies have started to unveil how the cell shape maintenance is involved in mechanical homeostatic tasks to sustain epithelial tissue folding, identity, and self-renewal. Here, we review relevant works that integrated mechanobiology to elucidate some of the core principles of how cell shape may be conveyed into spatial information to guide collective processes such as epithelial morphogenesis. Among many other parameters, we show that the regulation of the cell shape can be understood as the result of the interplay between two counteracting mechanisms: actomyosin contractility and intercellular adhesions, and that both do not act independently but are functionally integrated to operate on molecular, cellular, and tissue scales. We highlight the role of cadherin-based adhesions in force-sensing and mechanotransduction, and we report recent developments that exploit physics of liquid crystals to connect cell shape changes to orientational order in cell aggregates. Finally, we emphasize that the further intermingling of different disciplines to develop new mechanobiology assays will lead the way toward a unified picture of the contribution of cell shape to the pathophysiological behavior of epithelial tissues.

Cell Culture in Microfluidic Droplets

Cell manipulation in droplets has emerged as one of the great successes of microfluidic technologies, with the development of single-cell screening. However, the droplet format has also served to go beyond single-cell studies, namely by considering the interactions between different cells or between cells and their physical or chemical environment. These studies pose specific challenges linked to the need for long-term culture of adherent cells or the diverse types of measurements associated with complex biological phenomena. Here we review the emergence of droplet microfluidic methods for culturing cells and studying their interactions. We begin by characterizing the quantitative aspects that determine the ability to encapsulate cells, transport molecules, and provide sufficient nutrients within the droplets. This is followed by an evaluation of the biological constraints such as the control of the biochemical environment and promoting the anchorage of adherent cells. This first part ends with a description of measurement methods that have been developed. The second part of the manuscript focuses on applications of these technologies for cancer studies, immunology, and stem cells while paying special attention to the biological relevance of the cellular assays and providing guidelines on improving this relevance.

[3D Tumor organoid models produced by cellular capsules technology CCT]

Monolayer cultures of cell lines and derived-patient cells have long been the in vitro model of choice in oncology. In particular, these models have made it possible to decipher the mechanisms that determine tumor proliferation and invasion. However these 2D models are insufficient because they do not take into account the spatial organization of cells and their interactions with each other or with the extracellular matrix. In the context of cancer, there is a need to develop new 3D (tumoroid) models in order to gain a better understanding of the development of these pathologies but also to assess the penetration of drugs through a tissue and the associated cellular response. We present here the cell capsule technology (CCT), which allows the production of different tumoroid models: simple or more complex 3D culture models including co-culture of tumor cells with components of the microenvironment (fibroblasts, matrix, etc.). The development of these new 3D culture systems now makes it possible to propose refined physiopathological models that will allow the implementation of improved targeted therapeutic strategies.

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.

Extracellular hyaluronate pressure shaped by cellular tethers drives tissue morphogenesis

How tissues acquire complex shapes is a fundamental question in biology and regenerative medicine. Zebrafish semicircular canals form from invaginations in the otic epithelium (buds) that extend and fuse to form the hubs of each canal. We find that conventional actomyosin-driven behaviors are not required. Instead, local secretion of hyaluronan, made by the enzymes uridine 5'-diphosphate dehydrogenase (ugdh) and hyaluronan synthase 3 (has3), drives canal morphogenesis. Charged hyaluronate polymers osmotically swell with water and generate isotropic extracellular pressure to deform the overlying epithelium into buds. The mechanical anisotropy needed to shape buds into tubes is conferred by a polarized distribution of actomyosin and E-cadherin-rich membrane tethers, which we term cytocinches. Most work on tissue morphogenesis ascribes actomyosin contractility as the driving force, while the extracellular matrix shapes tissues through differential stiffness. Our work inverts this expectation. Hyaluronate pressure shaped by anisotropic tissue stiffness may be a widespread mechanism for powering morphological change in organogenesis and tissue engineering.

Direction of epithelial folding defines impact of mechanical forces on epithelial state

Cell shape dynamics during development is tightly regulated and coordinated with cell fate determination. Triggered by an interplay between biochemical and mechanical signals, epithelia form complex tissues by undergoing coordinated cell shape changes, but how such spatiotemporal coordination is controlled remains an open question. To dissect biochemical signaling from purely mechanical cues, we developed a microfluidic system that experimentally triggers epithelial folding to recapitulate stereotypic deformations observed in vivo. Using this system, we observe that the apical or basal direction of folding results in strikingly different mechanical states at the fold boundary, where the balance between tissue tension and torque (arising from the imposed curvature) controls the spread of folding-induced calcium waves at a short timescale and induces spatial patterns of gene expression at longer timescales. Our work uncovers that folding-associated gradients of cell shape and their resulting mechanical stresses direct spatially distinct biochemical responses within the monolayer.