Passive mechanical forces control cell-shape change during Drosophila ventral furrow formation

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their "space" and "time") as well as their effective parameters are all emergent, i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the "space," the "time" and the "parameter" axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection-diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

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.

Viscous shear is a key force in Drosophila ventral furrow morphogenesis

Ventral furrow (VF) formation in Drosophila melanogaster is an important model of epithelial folding. Previous models of VF formation require cell volume conservation to convert apically localized constriction forces into lateral cell elongation and tissue folding. Here, we have investigated embryonic morphogenesis in anillin knockdown (scra RNAi) embryos, where basal cell membranes fail to form and therefore cells can lose cytoplasmic volume through their basal side. Surprisingly, the mesoderm elongation and subsequent folding that comprise VF formation occurred essentially normally. We hypothesized that the effects of viscous shear may be sufficient to drive membrane elongation, providing effective volume conservation, and thus driving tissue folding. Since this hypothesis may not be possible to test experimentally, we turned to a computational approach. To test whether viscous shear is a dominant force for morphogenesis in vivo, we developed a 3D computational model incorporating both accurate cell and tissue geometry, and experimentally measured material parameters. Results from this model demonstrate that viscous shear generates sufficient force to drive cell elongation and tissue folding in vivo.

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.

HIF-1α-dependent upregulation of angiogenic factors by mechanical stimulation in retinal pigment epithelial cells

Mechanical stimulation as a mimic of drusen formation in the eye increases the expression of angiogenic factors in retinal pigment epithelial (RPE) cells, but the underlying molecular mechanisms remain unclear. We investigated and characterized the effects of mechanical stimulation on the expression of angiogenic factors in RPE cells both in vitro and in a mouse model. Mechanical stimulation increased the expression of vascular endothelial growth factor (VEGF, encoded by VEGFA) and other angiogenesis-related genes in cultured RPE1 cells. The presence of hypoxia-inducible factor 1α (HIF-1α, encoded by HIF1A) was also increased, and both knockdown of HIF-1α and treatment with the HIF-1α inhibitor CAY10585 attenuated the effect of mechanical stimulation on angiogenesis factor gene expression. Signaling by the tyrosine kinase SRC and p38 mitogen-activated protein kinase was involved in HIF-1α activation and consequent angiogenesis-related gene expression induced by mechanical stimulation. Our results suggest that SRC-p38 and HIF-1α signaling are involved in the upregulation of angiogenic factors in RPE cells by mechanical stimulation. Such in vivo suppression of upregulated expression of angiogenesis-related genes by pharmacological inhibitors of HIF-1α suggests a new potential approach to the treatment of age-related macular degeneration.

The mechanical influence of densification on epithelial architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayered epithelial tissue-whether protective, secretory, absorptive, or filtrative-relies on the side-by-side arrangement of its component cells. The mechanical parameters that determine the shape of epithelial cells in the apical-basal plane are not well-understood. Epithelial tissue architecture in culture is intimately connected to cell density, and cultured layers transition between architectures as they proliferate. This prompted us to ask to what extent epithelial architecture emerges from two mechanical considerations: A) the constraints of densification and B) cell-cell adhesion, a hallmark feature of epithelial cells. To address these questions, we developed a novel polyline cell-based computational model and used it to make theoretical predictions about epithelial architecture upon changes to density and cell-cell adhesion. We tested these predictions using cultured cell experiments. Our results show that the appearance of extended lateral cell-cell borders in culture arises as a consequence of crowding-independent of cell-cell adhesion. However, cadherin-mediated cell-cell adhesion is associated with a novel architectural transition. Our results suggest that this transition represents the initial appearance of a distinctive epithelial architecture. Together our work reveals the distinct mechanical roles of densification and adhesion to epithelial layer formation and provides a novel theoretical framework to understand the less well-studied apical-basal plane of epithelial tissues.

A mechanical wave travels along a genetic guide to drive the formation of an epithelial furrow during Drosophila gastrulation

Epithelial furrowing is a fundamental morphogenetic process during gastrulation, neurulation, and body shaping. A furrow often results from a fold that propagates along a line. How fold formation and propagation are controlled and driven is poorly understood. To shed light on this, we study the formation of the cephalic furrow, a fold that runs along the embryo dorsal-ventral axis during Drosophila gastrulation and the developmental role of which is still unknown. We provide evidence of its function and show that epithelial furrowing is initiated by a group of cells. This cellular cluster works as a pacemaker, triggering a bidirectional morphogenetic wave powered by actomyosin contractions and sustained by de novo medial apex-to-apex cell adhesion. The pacemaker's Cartesian position is under the crossed control of the anterior-posterior and dorsal-ventral gene patterning systems. Thus, furrow formation is driven by a mechanical trigger wave that travels under the control of a multidimensional genetic guide.

Evo-Devo Mechanobiology: The Missing Link

While the modern framework of evolutionary development (evo-devo) has been decidedly genetic, historic analyses have also considered the importance of mechanics in the evolution of form. With the aid of recent technological advancements in both quantifying and perturbing changes in the molecular and mechanical effectors of organismal shape, how molecular and genetic cues regulate the biophysical aspects of morphogenesis is becoming increasingly well studied. As a result, this is an opportune time to consider how the tissue-scale mechanics that underlie morphogenesis are acted upon through evolution to establish morphological diversity. Such a focus will enable a field of evo-devo mechanobiology that will serve to better elucidate the opaque relations between genes and forms by articulating intermediary physical mechanisms. Here, we review how the evolution of shape is measured and related to genetics, how recent strides have been made in the dissection of developmental tissue mechanics, and how we expect these areas to coalesce in evo-devo studies in the future.

The mechanics of cephalic furrow formation in the Drosophila embryo

Cephalic furrow formation (CFF) is a major morphogenetic movement during gastrulation in Drosophila melanogaster embryos that gives rise to a deep, transitory epithelial invagination. Recent studies have identified the individual cell shape changes that drive the initiation and progression phases of CFF; however, the underlying mechanics are not yet well understood. During the progression phase, the furrow deepens as columnar cells from both the anterior and posterior directions fold inwards rotating by 90°. To analyze the mechanics of this process, we have developed an advanced two-dimensional lateral vertex model that includes multinode representation of cellular membranes and allows us to capture the membrane curvature associated with pressure variation. Our investigations reveal some key potential mechanical features of CFF, as follows. When cells begin to roll over the cephalic furrow cleft, they become wedge shaped as their apical cortices and overlying membranes expand, lateral cortices and overlying membranes release tension, internal pressures drop, and basal cortices and membranes contract. Then, cells reverse this process by shortening apical cortices and membranes, increasing lateral tension, and causing internal pressures to rise. Since the basal membranes expand, the cells recover their rotated columnar shape once in the furrow. Interestingly, our findings indicate that the basal membranes may be passively reactive throughout the progression phase. We also find that the smooth rolling of cells over the cephalic furrow cleft necessitates that internalized cells provide a solid base through high levels of membrane tension and internal pressure, which allows the transmission of tensile force that pulls new cells into the furrow. These results lead us to suggest that CFF helps to establish a baseline tension across the apical surface of the embryo to facilitate cellular coordination of other morphogenetic movements via mechanical stress feedback mechanisms.

A comprehensive model of Drosophila epithelium reveals the role of embryo geometry and cell topology in mechanical responses

In order to understand morphogenesis, it is necessary to know the material properties or forces shaping the living tissue. In spite of this need, very few in vivo measurements are currently available. Here, using the early Drosophila embryo as a model, we describe a novel cantilever-based technique which allows for the simultaneous quantification of applied force and tissue displacement in a living embryo. By analyzing data from a series of experiments in which embryonic epithelium is subjected to developmentally relevant perturbations, we conclude that the response to applied force is adiabatic and is dominated by elastic forces and geometric constraints, or system size effects. Crucially, computational modeling of the experimental data indicated that the apical surface of the epithelium must be softer than the basal surface, a result which we confirmed experimentally. Further, we used the combination of experimental data and comprehensive computational model to estimate the elastic modulus of the apical surface and set a lower bound on the elastic modulus of the basal surface. More generally, our investigations revealed important general features that we believe should be more widely addressed when quantitatively modeling tissue mechanics in any system. Specifically, different compartments of the same cell can have very different mechanical properties; when they do, they can contribute differently to different mechanical stimuli and cannot be merely averaged together. Additionally, tissue geometry can play a substantial role in mechanical response, and cannot be neglected.

An integrated vertex model of the mesoderm invagination during the embryonic development of Drosophila

The mesoderm invagination of the Drosophila embryo is known as an archetypal morphogenic process. To explore the roles of the active cellular forces and the regulation of these forces, we developed an integrated vertex model that combines the regulation of morphogen expression with cell movements and tissue mechanics. Our results suggest that a successful furrow formation requires an apical tension gradient, decreased basal tension, and increased lateral tension, which corresponds to apical constriction, basal expansion, and apicobasal shortening respectively. Our model also considers the mechanical feedback which leads to an ectopic twist expression with external compression as observed in experiments. Our model predicts that ectopic invagination could happen if an external compressive gradient is applied.

Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation

Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation.

Drosophila mesoderm invagination begins with the formation of a furrow. Here they show that a long-range mechanism, powered by actomyosin contraction between the embryo polar caps, works like a ‘cheese-cutter wire’ indenting the tissue surface and folding it into a propagating furrow.

Evidence for a Role of the Lateral Ectoderm in Drosophila Mesoderm Invagination

The folding of two-dimensional epithelial sheets into specific three-dimensional structures is a fundamental tissue construction mechanism in animal development. A common mechanism that mediates epithelial folding is apical constriction, the active shrinking of cell apices driven by actomyosin contractions. It remains unclear whether cells outside of the constriction domain also contribute to folding. During Drosophila mesoderm invagination, ventrally localized mesoderm epithelium undergoes apical constriction and subsequently folds into a furrow. While the critical role of apical constriction in ventral furrow formation has been well demonstrated, it remains unclear whether, and if so, how the laterally localized ectodermal tissue adjacent to the mesoderm contributes to furrow invagination. In this study, we combine experimental and computational approaches to test the potential function of the ectoderm in mesoderm invagination. Through laser-mediated, targeted disruption of cell formation prior to gastrulation, we found that the presence of intact lateral ectoderm is important for the effective transition between apical constriction and furrow invagination in the mesoderm. In addition, using a laser-ablation approach widely used for probing tissue tension, we found that the lateral ectodermal tissues exhibit signatures of tissue compression when ablation was performed shortly before the onset of mesoderm invagination. These observations led to the hypothesis that in-plane compression from the surrounding ectoderm facilitates mesoderm invagination by triggering buckling of the mesoderm epithelium. In support of this notion, we show that the dynamics of tissue flow during mesoderm invagination displays characteristic of elastic buckling, and this tissue dynamics can be recapitulated by combining local apical constriction and global compression in a simulated elastic monolayer. We propose that Drosophila mesoderm invagination is achieved through epithelial buckling jointly mediated by apical constriction in the mesoderm and compression from the neighboring ectoderm.

The cell polarity determinant Dlg1 facilitates epithelial invagination by promoting tissue-scale mechanical coordination

Epithelial folding mediated by apical constriction serves as a fundamental mechanism to convert flat epithelial sheets into multilayered structures. It remains unknown whether additional mechanical inputs are required for apical constriction-mediated folding. Using Drosophila mesoderm invagination as a model, we identified an important role for the non-constricting, lateral mesodermal cells adjacent to the constriction domain ('flanking cells') in facilitating epithelial folding. We found that depletion of the basolateral determinant Dlg1 disrupts the transition between apical constriction and invagination without affecting the rate of apical constriction. Strikingly, the observed delay in invagination is associated with ineffective apical myosin contractions in the flanking cells that lead to overstretching of their apical domain. The defects in the flanking cells impede ventral-directed movement of the lateral ectoderm, suggesting reduced mechanical coupling between tissues. Specifically disrupting the flanking cells in wild-type embryos by laser ablation or optogenetic depletion of cortical actin is sufficient to delay the apical constriction-to-invagination transition. Our findings indicate that effective mesoderm invagination requires intact flanking cells and suggest a role for tissue-scale mechanical coupling during epithelial folding.

Optogenetic inhibition of actomyosin reveals mechanical bistability of the mesoderm epithelium during Drosophila mesoderm invagination

Apical constriction driven by actin and non-muscle myosin II (actomyosin) provides a well-conserved mechanism to mediate epithelial folding. It remains unclear how contractile forces near the apical surface of a cell sheet drive out-of-the-plane bending of the sheet and whether myosin contractility is required throughout folding. By optogenetic-mediated acute inhibition of actomyosin, we find that during Drosophila mesoderm invagination, actomyosin contractility is critical to prevent tissue relaxation during the early, 'priming' stage of folding but is dispensable for the actual folding step after the tissue passes through a stereotyped transitional configuration. This binary response suggests that Drosophila mesoderm is mechanically bistable during gastrulation. Computer modeling analysis demonstrates that the binary tissue response to actomyosin inhibition can be recapitulated in the simulated epithelium that undergoes buckling-like deformation jointly mediated by apical constriction in the mesoderm and in-plane compression generated by apicobasal shrinkage of the surrounding ectoderm. Interestingly, comparison between wild-type and snail mutants that fail to specify the mesoderm demonstrates that the lateral ectoderm undergoes apicobasal shrinkage during gastrulation independently of mesoderm invagination. We propose that Drosophila mesoderm invagination is achieved through an interplay between local apical constriction and mechanical bistability of the epithelium that facilitates epithelial buckling.

Generation, Transmission, and Regulation of Mechanical Forces in Embryonic Morphogenesis

Embryonic morphogenesis is a biological process which depicts shape forming of tissues and organs during development. Unveiling the roles of mechanical forces generated, transmitted, and regulated in cells and tissues through these processes is key to understanding the biophysical mechanisms governing morphogenesis. To this end, it is imperative to measure, simulate, and predict the regulation and control of these mechanical forces during morphogenesis. This article aims to provide a comprehensive review of the recent advances on mechanical properties of cells and tissues, generation of mechanical forces in cells and tissues, the transmission processes of these generated forces during cells and tissues, the tools and methods used to measure and predict these mechanical forces in vivo, in vitro, or in silico, and to better understand the corresponding regulation and control of generated forces. Understanding the biomechanics and mechanobiology of morphogenesis will not only shed light on the fundamental physical mechanisms underlying these concerted biological processes during normal development, but also uncover new information that will benefit biomedical research in preventing and treating congenital defects or tissue engineering and regeneration.

Toll-Dorsal signaling regulates the spatiotemporal dynamics of yolk granule tubulation during Drosophila cleavage

The Toll-Dorsal signaling pathway controls dorsal-ventral (DV) patterning in early Drosophila embryos, which defines specific cell fates along the DV axis and controls morphogenetic behavior of cells during gastrulation and beyond. The extent by which DV patterning information regulates subcellular organization in pre-gastrulation embryos remains unclear. We find that during Drosophila cleavage, the late endosome marker Rab7 is increasingly recruited to the yolk granules and promotes the formation of dynamic membrane tubules. The biogenesis of yolk granule tubules is positively regulated by active Rab7 and its effector complex HOPS, but negatively regulated by the Rab7 effector retromer. The occurrence of tubules is strongly biased towards the ventral side of the embryo, which we show is controlled by the Toll-Dorsal signaling pathway. Our work provides the first evidence for the formation and regulation of yolk granule tubulation in oviparous embryos and elucidates an unexpected role of Toll-Dorsal signaling in regulating this process.

Vesicle shape transformations driven by confined active filaments

In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

Mechanical competition alters the cellular interpretation of an endogenous genetic program

The intrinsic genetic program of a cell is not sufficient to explain all of the cell's activities. External mechanical stimuli are increasingly recognized as determinants of cell behavior. In the epithelial folding event that constitutes the beginning of gastrulation in Drosophila, the genetic program of the future mesoderm leads to the establishment of a contractile actomyosin network that triggers apical constriction of cells and thereby tissue folding. However, some cells do not constrict but instead stretch, even though they share the same genetic program as their constricting neighbors. We show here that tissue-wide interactions force these cells to expand even when an otherwise sufficient amount of apical, active actomyosin is present. Models based on contractile forces and linear stress-strain responses do not reproduce experimental observations, but simulations in which cells behave as ductile materials with nonlinear mechanical properties do. Our models show that this behavior is a general emergent property of actomyosin networks in a supracellular context, in accordance with our experimental observations of actin reorganization within stretching cells.

Pinching and pushing: fold formation in the Drosophila dorsal epidermis

Epithelial folding is a fundamental morphogenetic process that shapes planar epithelial sheets into complex three-dimensional structures. Multiple mechanisms can generate epithelial folds, including apical constriction, which acts locally at the cellular level, differential growth on the tissue scale, or buckling because of compression from neighboring tissues. Here, we investigate the formation of dorsally located epithelial folds at segment boundaries during the late stages of Drosophila embryogenesis. We found that the fold formation at the segment boundaries occurs through the juxtaposition of two key morphogenetic processes: local apical constriction and tissue-level compressive forces from posterior segments. Further, we found that epidermal spreading and fold formation are accompanied by spatiotemporal pulses of Hedgehog (Hh) signaling. A computational model that incorporates the local forces generated from the differential tensions of the apical, basal, and lateral sides of the cell and active forces generated within the whole tissue recapitulates the overall fold formation process in wild-type and Hh overexpression conditions. In sum, this work demonstrates how epithelial folding depends on multiple, separable physical mechanisms to generate the final morphology of the dorsal epidermis. This work illustrates the modularity of morphogenetic unit operations that occur during epithelial morphogenesis.

Orchestration of Force Generation and Nuclear Collapse in Apoptotic Cells

Apoptosis, or programmed cell death, is a form of cell suicide that is extremely important for ridding the body of cells that are no longer required, to protect the body against hazardous cells, such as cancerous ones, and to promote tissue morphogenesis during animal development. Upon reception of a death stimulus, the doomed cell activates biochemical pathways that eventually converge on the activation of dedicated enzymes, caspases. Numerous pieces of information on the biochemical control of the process have been gathered, from the successive events of caspase activation to the identification of their targets, such as lamins, which constitute the nuclear skeleton. Yet, evidence from multiple systems now shows that apoptosis is also a mechanical process, which may even ultimately impinge on the morphogenesis of the surrounding tissues. This mechanical role relies on dramatic actomyosin cytoskeleton remodelling, and on its coupling with the nucleus before nucleus fragmentation. Here, we provide an overview of apoptosis before describing how apoptotic forces could combine with selective caspase-dependent proteolysis to orchestrate nucleus destruction.

Physical basis for the determination of lumen shape in a simple epithelium

The formation of a hollow lumen in a formerly solid mass of cells is a key developmental process whose dysregulation leads to diseases of the kidney and other organs. Hydrostatic pressure has been proposed to drive lumen expansion, a view that is supported by experiments in the mouse blastocyst. However, lumens formed in other tissues adopt irregular shapes with cell apical faces that are bowed inward, suggesting that pressure may not be the dominant contributor to lumen shape in all cases. Here we use live-cell imaging to study the physical mechanism of lumen formation in Madin-Darby Canine Kidney cell spheroids, a canonical cell-culture model for lumenogenesis. We find that in this system, lumen shape reflects basic geometrical considerations tied to the establishment of apico-basal polarity. A physical model incorporating both cell geometry and intraluminal pressure can account for our observations as well as cases in which pressure plays a dominant role.

Condensation tendency and planar isotropic actin gradient induce radial alignment in confined monolayers

A monolayer of highly motile cells can establish long-range orientational order, which can be explained by hydrodynamic theory of active gels and fluids. However, it is less clear how cell shape changes and rearrangement are governed when the monolayer is in mechanical equilibrium states when cell motility diminishes. In this work, we report that rat embryonic fibroblasts (REF), when confined in circular mesoscale patterns on rigid substrates, can transition from the spindle shapes to more compact morphologies. Cells align radially only at the pattern boundary when they are in the mechanical equilibrium. This radial alignment disappears when cell contractility or cell-cell adhesion is reduced. Unlike monolayers of spindle-like cells such as NIH-3T3 fibroblasts with minimal intercellular interactions or epithelial cells like Madin-Darby canine kidney (MDCK) with strong cortical actin network, confined REF monolayers present an actin gradient with isotropic meshwork, suggesting the existence of a stiffness gradient. In addition, the REF cells tend to condense on soft substrates, a collective cell behavior we refer to as the 'condensation tendency'. This condensation tendency, together with geometrical confinement, induces tensile prestretch (i.e. an isotropic stretch that causes tissue to contract when released) to the confined monolayer. By developing a Voronoi-cell model, we demonstrate that the combined global tissue prestretch and cell stiffness differential between the inner and boundary cells can sufficiently define the cell radial alignment at the pattern boundary.

Composite morphogenesis during embryo development

Morphogenesis drives the formation of functional living shapes. Gene expression patterns and signaling pathways define the body plans of the animal and control the morphogenetic processes shaping the embryonic tissues. During embryogenesis, a tissue can undergo composite morphogenesis resulting from multiple concomitant shape changes. While previous studies have unraveled the mechanisms that drive simple morphogenetic processes, how a tissue can undergo multiple and simultaneous changes in shape is still not known and not much explored. In this chapter, we focus on the process of concomitant tissue folding and extension that is vital for the animal since it is key for embryo gastrulation and neurulation. Recent pioneering studies focus on this problem highlighting the roles of different spatially coordinated cell mechanisms or of the synergy between different patterns of gene expression to drive composite morphogenesis.

The origin and the mechanism of mechanical polarity during epithelial folding

Epithelial tissues are sheet-like tissue structures that line the inner and outer surfaces of animal bodies and organs. Their remarkable ability to actively produce, or passively adapt to, complex surface geometries has fascinated physicists and biologists alike for centuries. The most simple and yet versatile process of epithelial deformation is epithelial folding, through which curved shapes, tissue convolutions and internal structures are produced. The advent of quantitative live imaging, combined with experimental manipulation and computational modeling, has rapidly advanced our understanding of epithelial folding. In particular, a set of mechanical principles has emerged to illustrate how forces are generated and dissipated to instigate curvature transitions in a variety of developmental contexts. Folding a tissue requires that mechanical loads or geometric changes be non-uniform. Given that polarity is the most distinct and fundamental feature of epithelia, understanding epithelial folding mechanics hinges crucially on how forces become polarized and how polarized differential deformation arises, for which I coin the term 'mechanical polarity'. In this review, five typical modules of mechanical processes are distilled from a diverse array of epithelial folding events. Their mechanical underpinnings with regard to how forces and polarity intersect are analyzed to accentuate the importance of mechanical polarity in the understanding of epithelial folding.

A three-dimensional vertex model forDrosophilasalivary gland invagination

During epithelial morphogenesis, force generation at the cellular level not only causes cell deformation, but may also produce coordinated cell movement and rearrangement on the tissue level. In this paper, we use a novel three-dimensional vertex model to explore the roles of cellular forces during the formation of the salivary gland in theDrosophilaembryo. Representing the placode as an epithelial sheet of initially columnar cells, we focus on the spatial and temporal patterning of contractile forces due to three actomyosin pools: the apicomedial actomyosin in the pit of the placode, junctional actomyosin arcs outside the pit, and a supracellular actomyosin cable along the circumference of the placode. In anin silico'wild type' model, these pools are activated at different times according to experimental data. To identify the role of each myosin pool, we have also simulated variousin silico'mutants' in which only one or two of the myosin pools are activated. We find that the apicomedial myosin initiates a small dimple in the pit, but this is not essential for the overall invagination of the placode. The myosin arcs are the main driver of invagination and are responsible for the internalization of the apical surface. The circumferential actomyosin cable acts to constrict the opening of the developing tube, and is responsible for forming a properly shaped lumen. Cell intercalation tends to facilitate the invagination, but the geometric constraints of our model only allow a small number of intercalations, and their effect is minor. The placode invagination predicted by the model is in general agreement with experimental observations. It confirms some features of the current 'belt-and-braces' model for the process, and provides new insights on the separate roles of the various myosin pools and their spatio-temporal coordination.

Actin-based force generation and cell adhesion in tissue morphogenesis

The generation of organismal form - morphogenesis - arises from forces produced at the cellular level. In animal cells, much of this force is produced by the actin cytoskeleton. Here, we review how mechanisms of actin-based force generation are deployed during animal morphogenesis to sculpt organs and organisms. Furthermore, we consider how cytoskeletal forces are coupled through cell adhesions to propagate across tissues, and discuss cases where cytoskeletal force or adhesion is patterned across a tissue to direct shape changes. Together, our review provides a conceptual framework that reflects our current understanding of animal morphogenesis and gives perspectives on future opportunities for study.

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.

Self-organized cytoskeletal alignment during Drosophila mesoderm invagination

During tissue morphogenesis, mechanical forces are propagated across tissues, resulting in tissue shape changes. These forces in turn can influence cell behaviour, leading to a feedback process that can be described as self-organizing. Here, I discuss cytoskeletal self-organization and point to evidence that suggests its role in directing force during morphogenesis. During Drosophila mesoderm invagination, the shape of the region of cells that initiates constriction creates a mechanical pattern that in turn aligns the cytoskeleton with the axis of greatest resistance to contraction. The wild-type direction of the force controls the shape and orientation of the invaginating mesoderm. Given the ability of the actomyosin cytoskeleton to self-organize, these types of feedback mechanisms are likely to play important roles in a range of different morphogenetic events. This article is part of the discussion meeting issue 'Contemporary morphogenesis'.

On folding morphogenesis, a mechanical problem

Tissue folding is a fundamental process that sculpts a simple flat epithelium into a complex three-dimensional organ structure. Whether it is the folding of the brain, or the looping of the gut, it has become clear that to generate an invagination or a fold of any form, mechanical asymmetries must exist in the epithelium. These mechanical asymmetries can be generated locally, involving just the invaginating cells and their immediate neighbours, or on a more global tissue-wide scale. Here, we review the different mechanical mechanisms that epithelia have adopted to generate folds, and how the use of precisely defined mathematical models has helped decipher which mechanisms are the key driving forces in different epithelia. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

The Physical Mechanisms of Drosophila Gastrulation: Mesoderm and Endoderm Invagination

A critical juncture in early development is the partitioning of cells that will adopt different fates into three germ layers: the ectoderm, the mesoderm, and the endoderm. This step is achieved through the internalization of specified cells from the outermost surface layer, through a process called gastrulation. In Drosophila, gastrulation is achieved through cell shape changes (i.e., apical constriction) that change tissue curvature and lead to the folding of a surface epithelium. Folding of embryonic tissue results in mesoderm and endoderm invagination, not as individual cells, but as collective tissue units. The tractability of Drosophila as a model system is best exemplified by how much we know about Drosophila gastrulation, from the signals that pattern the embryo to the molecular components that generate force, and how these components are organized to promote cell and tissue shape changes. For mesoderm invagination, graded signaling by the morphogen, Spätzle, sets up a gradient in transcriptional activity that leads to the expression of a secreted ligand (Folded gastrulation) and a transmembrane protein (T48). Together with the GPCR Mist, which is expressed in the mesoderm, and the GPCR Smog, which is expressed uniformly, these signals activate heterotrimeric G-protein and small Rho-family G-protein signaling to promote apical contractility and changes in cell and tissue shape. A notable feature of this signaling pathway is its intricate organization in both space and time. At the cellular level, signaling components and the cytoskeleton exhibit striking polarity, not only along the apical-basal cell axis, but also within the apical domain. Furthermore, gene expression controls a highly choreographed chain of events, the dynamics of which are critical for primordium invagination; it does not simply throw the cytoskeletal "on" switch. Finally, studies of Drosophila gastrulation have provided insight into how global tissue mechanics and movements are intertwined as multiple tissues simultaneously change shape. Overall, these studies have contributed to the view that cells respond to forces that propagate over great distances, demonstrating that cellular decisions, and, ultimately, tissue shape changes, proceed by integrating cues across an entire embryo.

The Epithelial-to-Mesenchymal Transition (EMT) in Development and Cancer

Epithelial-to-mesenchymal transitions (EMTs) are complex cellular processes where cells undergo dramatic changes in signaling, transcriptional programming, and cell shape, while directing the exit of cells from the epithelium and promoting migratory properties of the resulting mesenchyme. EMTs are essential for morphogenesis during development and are also a critical step in cancer progression and metastasis formation. Here we provide an overview of the molecular regulation of the EMT process during embryo development, focusing on chick and mouse gastrulation and neural crest development. We go on to describe how EMT regulators participate in the progression of pancreatic and breast cancer in mouse models, and discuss the parallels with developmental EMTs and how these help to understand cancer EMTs. We also highlight the differences between EMTs in tumor and in development to arrive at a broader view of cancer EMT. We conclude by discussing how further advances in the field will rely on in vivo dynamic imaging of the cellular events of EMT.

Principles and applications of optogenetics in developmental biology

The development of multicellular organisms is controlled by highly dynamic molecular and cellular processes organized in spatially restricted patterns. Recent advances in optogenetics are allowing protein function to be controlled with the precision of a pulse of laser light in vivo, providing a powerful new tool to perturb developmental processes at a wide range of spatiotemporal scales. In this Primer, we describe the most commonly used optogenetic tools, their application in developmental biology and in the nascent field of synthetic morphogenesis.

Planar Differential Growth Rates Initiate Precise Fold Positions in Complex Epithelia

Tissue folding is a fundamental process that shapes epithelia into complex 3D organs. The initial positioning of folds is the foundation for the emergence of correct tissue morphology. Mechanisms forming individual folds have been studied, but the precise positioning of folds in complex, multi-folded epithelia is less well-understood. We present a computational model of morphogenesis, encompassing local differential growth and tissue mechanics, to investigate tissue fold positioning. We use the Drosophila wing disc as our model system and show that there is spatial-temporal heterogeneity in its planar growth rates. This differential growth, especially at the early stages of development, is the main driver for fold positioning. Increased apical layer stiffness and confinement by the basement membrane drive fold formation but influence positioning to a lesser degree. The model successfully predicts the in vivo morphology of overgrowth clones and wingless mutants via perturbations solely on planar differential growth in silico.

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Drosophila wing discs grow with spatial and temporal heterogeneity

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This differential growth determines the positions of epithelial folds

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Constriction from the basement membrane is necessary for correct fold initiation

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Our computational model correctly predicts the shape of growth mutants

Structural Redundancy in Supracellular Actomyosin Networks Enables Robust Tissue Folding

Tissue morphogenesis is strikingly robust. Yet, how tissues are sculpted under challenging conditions is unknown. Here, we combined network analysis, experimental perturbations, and computational modeling to determine how network connectivity between hundreds of contractile cells on the ventral side of the Drosophila embryo ensures robust tissue folding. We identified two network properties that mechanically promote robustness. First, redundant supracellular cytoskeletal network paths ensure global connectivity, even with network degradation. By forming many more connections than are required, morphogenesis is not disrupted by local network damage, analogous to the way redundancy guarantees the large-scale function of vasculature and transportation networks. Second, directional stiffening of edges oriented orthogonal to the folding axis promotes furrow formation at lower contractility levels. Structural redundancy and directional network stiffening ensure robust tissue folding with proper orientation.

Mechanical impact of epithelial-mesenchymal transition on epithelial morphogenesis in Drosophila

Epithelial-mesenchymal transition (EMT) is an essential process both in physiological and pathological contexts. Intriguingly, EMT is often associated with tissue invagination during development; however, the impact of EMT on tissue remodeling remain unexplored. Here, we show that at the initiation of the EMT process, cells produce an apico-basal force, orthogonal to the surface of the epithelium, that constitutes an important driving force for tissue invagination in Drosophila. When EMT is ectopically induced, cells starting their delamination generate an orthogonal force and induce ectopic folding. Similarly, during mesoderm invagination, cells undergoing EMT generate an apico-basal force through the formation of apico-basal structures of myosin II. Using both laser microdissection and in silico physical modelling, we show that mesoderm invagination does not proceed if apico-basal forces are impaired, indicating that they constitute driving forces in the folding process. Altogether, these data reveal the mechanical impact of EMT on morphogenesis.

Biomechanical regulation of EMT and epithelial morphogenesis in amniote epiblast

Epiblast is composed of pluripotent cells which will give rise to all cell lineages in a human body. It forms a single-cell layered epithelium conserved among all amniotic vertebrates (birds, reptiles and mammals) and undergoes complex morphogenesis both before and during gastrulation. Our knowledge of the amniote epiblast is based on data acquired through cellular and molecular analyses of early chick and mouse embryos in vivo and mammalian pluripotent stem cells (PSCs) in vitro. Very few studies have been published on biomechanical characteristics of the amniote epiblast, largely due to lack of experimental tools for measuring and perturbing biomechanical properties. Also missing is a conceptual framework that can integrate both biomechanical and molecular parameters of the epiblast. This review is aimed at providing a background based on which epiblast morphogenesis, including its transition between the epithelial and mesenchymal states, can be understood from a biomechanical perspective. This simple developmental biology system is suitable for testing a multitude of theoretical models in biomechanics, leading to a better understanding of biomechanical logics and constraints governing multicellular organization.

Mathematical Modeling of Tissue Folding and Asymmetric Tissue Flow during Epithelial Morphogenesis

Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to induce tissue deformation was unclear, because there was no experimental method with which to verify it in vivo. In such cases, mathematical modeling can be effective for verifying whether a locally generated force can propagate through an entire tissue and induce deformation. Moreover, the mathematical model sometimes provides potential mechanistic insight beyond the information obtained from biological experimental results. Here, we present two examples of modeling tissue morphogenesis driven by cell deformation or cell interaction. In the first example, a mathematical study on tissue-autonomous folding based on a two-dimensional vertex model revealed that active modulations of cell mechanics along the basal–lateral surface, in addition to the apical side, can induce tissue-fold formation. In the second example, by applying a two-dimensional vertex model in an apical plane, a novel mechanism of tissue flow caused by asymmetric cell interactions was discovered, which explained the mechanics behind the collective cellular movement observed during epithelial morphogenesis.

Optogenetic control of morphogenesis goes 3D

The generation of form in living embryos, a process termed “morphogenesis” from the Greek word μορφογένεση, is one of the most fascinating unsolved problems in biology. In embryonic epithelia, most attention has been paid to events occurring at the apical surface of epithelia, particularly the regulation of actomyosin contractility during morphogenetic change. In a new report, De Renzis and colleagues demonstrate a key role for regulated actomyosin contractility at the basal surface of the epithelium during formation of the first epithelial fold in Drosophila (the “ventral furrow”) (Krueger et al, 2018).

Theoretical tool bridging cell polarities with development of robust morphologies

Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development – gastrulation and the origins of folds and tubes – our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.

Cells have the power to organise themselves to form complex and stable structures, whether it is to create a fully shaped baby from a single egg, or to allow adult salamanders to grow a new limb after losing a leg. This ability has been scrutinised at many different levels. For example, researchers have looked at the chemical messages exchanged by cells, or they have recorded the different shapes an embryo goes through during development. However, it is still difficult to reconcile the information from these approaches into a description that makes sense at multiple scales.

When an embryo develops, sheets of cells fold and unfold to create complex 3D shapes, like the tubes that make our lungs. Moulding sheets into tubes relies on interactions between cells that are not the same in all directions. In fact, two types of asymmetry (or polarity) guide these interactions. Apical-basal polarity runs across a sheet of cells, which means that the top surface of the sheet differs from the bottom. Planar cell polarity runs along the sheet and distinguishes one end from the other. For instance, apical-basal polarity marks the inner and outer surfaces of our skin, while planar cell polarity controls the direction in which our hair grows.

Nissen et al. set out to investigate how these polarities help cells in an embryo organise themselves to form complicated folds and tubes. To do this, simple mathematical representations of both apical-basal and planar cell polarities were designed. The representations were then combined to create computer simulations of groups of cells as these divide and interact with each other.

Simulations of ‘cells’ with only apical-basal polarity were able to generate different shapes in the ‘tissues’ produced, including many found in living organisms. External conditions, such as how cells were arranged to start with, determined the resulting shape. With both apical-basal and planar cell polarities, the simulations reproduced an important change that occurs during early development. They also replicated how the tubes that transport nutrients and oxygen form.

These results show that simple properties of individual cells, such as polarities, can produce different shapes in developing tissues and organs, without the need for a complicated overarching program. Abnormal changes in cell polarity are also associated with diseases such as cancer. The mathematical model developed by Nissen et al. could therefore be a useful tool to study these events.

Downregulation of basal myosin-II is required for cell shape changes and tissue invagination

Tissue invagination drives embryo remodeling and assembly of internal organs during animal development. While the role of actomyosin‐mediated apical constriction in initiating inward folding is well established, computational models suggest relaxation of the basal surface as an additional requirement. However, the lack of genetic mutations interfering specifically with basal relaxation has made it difficult to test its requirement during invagination so far. Here we use optogenetics to quantitatively control myosin‐II levels at the basal surface of invaginating cells during Drosophila gastrulation. We show that while basal myosin‐II is lost progressively during ventral furrow formation, optogenetics allows the maintenance of pre‐invagination levels over time. Quantitative imaging demonstrates that optogenetic activation prior to tissue bending slows down cell elongation and blocks invagination. Activation after cell elongation and tissue bending has initiated inhibits cell shortening and folding of the furrow into a tube‐like structure. Collectively, these data demonstrate the requirement of myosin‐II polarization and basal relaxation throughout the entire invagination process.

Three-dimensional forces beyond actomyosin contraction: lessons from fly epithelial deformation

Epithelium undergoes complex deformations during morphogenesis. Many of these deformations rely on the remodelling of apical cell junctions by actomyosin-based contractile force and this has been a major research interest for many years. Recent studies have shown that cells can use additional mechanisms that are not directly driven by actomyosin contractility to alter cell shape and movement, in three-dimensional (3D) space and time. In this review, we focus on a number of these mechanisms, including basolateral cellular protrusion, lateral shift of cell polarity, cytoplasmic flow, regulation of cell volume, and force transmission between cell-cell adhesion and cell-extracellular matrix adhesion, and describe how they underlie Drosophila epithelia deformations.

Guided morphogenesis through optogenetic activation of Rho signalling during early Drosophila embryogenesis

During organismal development, cells undergo complex changes in shape whose causal relationship to individual morphogenetic processes remains unclear. The modular nature of such processes suggests that it should be possible to isolate individual modules, determine the minimum set of requirements sufficient to drive tissue remodeling, and re-construct morphogenesis. Here we use optogenetics to reconstitute epithelial folding in embryonic Drosophila tissues that otherwise would not undergo invagination. We show that precise spatial and temporal activation of Rho signaling is sufficient to trigger apical constriction and tissue folding. Induced furrows can occur at any position along the dorsal–ventral or anterior–posterior embryo axis in response to the spatial pattern and level of optogenetic activation. Thus, epithelial folding is a direct function of the spatio-temporal organization and strength of Rho signaling that on its own is sufficient to drive tissue internalization independently of any pre-determined condition or differentiation program associated with endogenous invagination processes.

Optogenetics is opening the possibility to not only perturb morphogenesis, but also to guide it. Here, the authors use this technique to reconstruct epithelial folding in Drosophila embryos and study the relationship between strength of Rho activation, apical constrictions, and tissue invagination.

Global morphogenetic flow is accurately predicted by the spatial distribution of myosin motors

During embryogenesis tissue layers undergo morphogenetic flow rearranging and folding into specific shapes. While developmental biology has identified key genes and local cellular processes, global coordination of tissue remodeling at the organ scale remains unclear. Here, we combine in toto light-sheet microscopy of the Drosophila embryo with quantitative analysis and physical modeling to relate cellular flow with the patterns of force generation during the gastrulation process. We find that the complex spatio-temporal flow pattern can be predicted from the measured meso-scale myosin density and anisotropy using a simple, effective viscous model of the tissue, achieving close to 90% accuracy with one time dependent and two constant parameters. Our analysis uncovers the importance of a) spatial modulation of myosin distribution on the scale of the embryo and b) the non-locality of its effect due to mechanical interaction of cells, demonstrating the need for the global perspective in the study of morphogenetic flow.

Tension, contraction and tissue morphogenesis

D'Arcy Thompson was a proponent of applying mathematical and physical principles to biological systems, an approach that is becoming increasingly common in developmental biology. Indeed, the recent integration of quantitative experimental data, force measurements and mathematical modeling has changed our understanding of morphogenesis - the shaping of an organism during development. Emerging evidence suggests that the subcellular organization of contractile cytoskeletal networks plays a key role in force generation, while on the tissue level the spatial organization of forces determines the morphogenetic output. Inspired by D'Arcy Thompson's On Growth and Form, we review our current understanding of how biological forms are created and maintained by the generation and organization of contractile forces at the cell and tissue levels. We focus on recent advances in our understanding of how cells actively sculpt tissues and how forces are involved in specific morphogenetic processes.