A biomechanical model for cell polarization and intercalation duringDrosophilagermband extension

PCP-dependent polarized mechanics in the cortex of individual cells during convergent extension

Convergent extension (CE) is a key process for tissue elongation during vertebrate development and is driven by polarized cell behaviors. Here, we used a novel image-based technique to investigate the mechanical properties of individual cells undergoing CE. Our results suggest a PCP- and Septin-dependent mechanical gradient, where cortical tension is higher at the anterior face of the cells compared with their posterior face. Disruption of PCP protein Vangl2 or its downstream effector Septin7 eliminates this mechanical polarity. These findings demonstrate a link between actin organization, PCP signaling, and mechanical polarization, providing new avenues into the mechanochemical regulation of cellular behaviors during CE.

A minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, both shape index and aspect ratio of amnioserosa cells increase markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts nonmonotonic junction tension that we confirm with laser ablation experiments.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster . During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, both shape index and aspect ratio of amnioserosa cells increase markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Significance Statement

During embryogenesis, cells in tissues can undergo significant shape changes. Many epithelial tissues fluidize, i.e. cells exchange neighbors, when the average cell shape index increases above a threshold value, consistent with the standard vertex model. During dorsal closure in Drosophila melanogaster , however, the amnioserosa tissue remains solid even as the average cell shape index increases well above threshold. We introduce perimeter polydispersity and allow the preferred cell perimeters, usually held fixed in vertex models, to decrease linearly with time as seen experimentally. With these extensions to the standard vertex model, we capture experimental observations quantitatively. Our results demonstrate that vertex models can describe the behavior of the amnioserosa in dorsal closure by allowing normally fixed parameters to vary with time.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

Interface extension is a continuum property suggesting a linkage between AP contractile and DV lengthening processes

In the early Drosophila embryo, the elongation of the anterior-posterior (AP) body axis is driven by cell intercalation in the germband epithelium. Neighboring cells intercalate through the contraction of AP interfaces (between AP neighbors) into higher-order vertices, which then resolve through the extension of new dorsal-ventral (DV) interfaces (between DV neighbors). Although interface contraction has been extensively studied, less is known about how new interfaces are established. Here we show that DV interface elongation behaviors initiate at the same time as AP contractions, and that DV interfaces which are newly created from resolution of higher-order vertices do not appear to possess a unique 'identity;' instead, all horizontal interfaces undergo lengthening, elongating through ratchetlike sliding behaviors analogous to those found in AP interfaces. Cortical F-actin networks are essential for high area oscillation amplitudes required for effective ratcheting. Our results suggest that, contrary to canonical models, the elongation of new DV interfaces is not produced by a mechanistically separate process. Instead, medial myosin populations drive oscillating radial forces in the cells to generate transient force asymmetries at all tricellular vertices, which-combined with planar polarized stabilization-produce directional ratcheted sliding to generate both AP interface contraction and DV interface elongation.

Powering morphogenesis: multiscale challenges at the interface of cell adhesion and the cytoskeleton

Among the defining features of the animal kingdom is the ability of cells to change shape and move. This underlies embryonic and postembryonic development, tissue homeostasis, regeneration, and wound healing. Cell shape change and motility require linkage of the cell's force-generating machinery to the plasma membrane at cell-cell and cell-extracellular matrix junctions. Connections of the actomyosin cytoskeleton to cell-cell adherens junctions need to be both resilient and dynamic, preventing tissue disruption during the dramatic events of embryonic morphogenesis. In the past decade, new insights radically altered the earlier simple paradigm that suggested simple linear linkage via the cadherin-catenin complex as the molecular mechanism of junction-cytoskeleton interaction. In this Perspective we provide a brief overview of our current state of knowledge and then focus on selected examples highlighting what we view as the major unanswered questions in our field and the approaches that offer exciting new insights at multiple scales from atomic structure to tissue mechanics.

Image-based parameter inference for epithelial mechanics

Measuring mechanical parameters in tissues, such as the elastic modulus of cell-cell junctions, is essential to decipher the mechanical control of morphogenesis. However, their in vivo measurement is technically challenging. Here, we formulated an image-based statistical approach to estimate the mechanical parameters of epithelial cells. Candidate mechanical models are constructed based on force-cell shape correlations obtained from image data. Substitution of the model functions into force-balance equations at the cell vertex leads to an equation with respect to the parameters of the model, by which one can estimate the parameter values using a least-squares method. A test using synthetic data confirmed the accuracy of parameter estimation and model selection. By applying this method to Drosophila epithelial tissues, we found that the magnitude and orientation of feedback between the junction tension and shrinkage, which are determined by the spring constant of the junction, were correlated with the elevation of tension and myosin-II on shrinking junctions during cell rearrangement. Further, this method clarified how alterations in tissue polarity and stretching affect the anisotropy in tension parameters. Thus, our method provides a novel approach to uncovering the mechanisms governing epithelial morphogenesis.

Linear viscoelastic properties of the vertex model for epithelial tissues

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

Forced into shape: Mechanical forces in Drosophila development and homeostasis

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

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.

Orchestrating morphogenesis: building the body plan by cell shape changes and movements

During embryonic development, a simple ball of cells re-shapes itself into the elaborate body plan of an animal. This requires dramatic cell shape changes and cell movements, powered by the contractile force generated by actin and myosin linked to the plasma membrane at cell-cell and cell-matrix junctions. Here, we review three morphogenetic events common to most animals: apical constriction, convergent extension and collective cell migration. Using the fruit fly Drosophila as an example, we discuss recent work that has revealed exciting new insights into the molecular mechanisms that allow cells to change shape and move without tearing tissues apart. We also point out parallel events at work in other animals, which suggest that the mechanisms underlying these morphogenetic processes are conserved.

Cellular, molecular, and biophysical control of epithelial cell intercalation

Convergent extension is a conserved mechanism for elongating tissues. In the Drosophila embryo, convergent extension is driven by planar polarized cell intercalation and is a paradigm for understanding the cellular, molecular, and biophysical mechanisms that establish tissue structure. Studies of convergent extension in Drosophila have provided key insights into the force-generating molecules that promote convergent extension in epithelial tissues, as well as the global systems of spatial information that systematically organize these cell behaviors. A general framework has emerged in which asymmetrically localized proteins involved in cytoskeletal tension and cell adhesion direct oriented cell movements, and spatial signals provided by the Toll, Tartan, and Teneurin receptor families break planar symmetry to establish and coordinate planar cell polarity throughout the tissue. In this chapter, we describe the cellular, molecular, and biophysical mechanisms that regulate cell intercalation in the Drosophila embryo, and discuss how research in this system has revealed conserved biological principles that control the organization of multicellular tissues and animal body plans.

Viscoelastic voyages - Biophysical perspectives on cell intercalation during Drosophila gastrulation

Developmental processes are driven by a combination of cytoplasmic, cortical, and surface-associated forces. However, teasing apart the contributions of these forces and how a viscoelastic cell responds has long been a key question in developmental biology. Recent advances in applying biophysical approaches to these questions is leading to a fundamentally new understanding of morphogenesis. In this review, we discuss how computational analysis of experimental findings and in silico modeling of Drosophila gastrulation processes has led to a deeper comprehension of the physical principles at work in the early embryo. We also summarize many of the emerging methodologies that permit biophysical analysis as well as those that provide direct and indirect measurements of force directions and magnitudes. Finally, we examine the multiple frameworks that have been used to model tissue and cellular behaviors.

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities such as restructuring of extracellular matrix (ECM), stress and force distribution profiles, and reorganization of the cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow "travelers". This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration as well as providing perspectives on future development toward eventually deciphering the key mechanisms behind the most lethal feature of cancer.

Apical and Basal Matrix Remodeling Control Epithelial Morphogenesis

Epithelial tissues can elongate in two dimensions by polarized cell intercalation, oriented cell division, or cell shape change, owing to local or global actomyosin contractile forces acting in the plane of the tissue. In addition, epithelia can undergo morphogenetic change in three dimensions. We show that elongation of the wings and legs of Drosophila involves a columnar-to-cuboidal cell shape change that reduces cell height and expands cell width. Remodeling of the apical extracellular matrix by the Stubble protease and basal matrix by MMP1/2 proteases induces wing and leg elongation. Matrix remodeling does not occur in the haltere, a limb that fails to elongate. Limb elongation is made anisotropic by planar polarized Myosin-II, which drives convergent extension along the proximal-distal axis. Subsequently, Myosin-II relocalizes to lateral membranes to accelerate columnar-to-cuboidal transition and isotropic tissue expansion. Thus, matrix remodeling induces dynamic changes in actomyosin contractility to drive epithelial morphogenesis in three dimensions.

The devil is in the mesoscale: Mechanical and behavioural heterogeneity in collective cell movement

Heterogeneity within cell populations can be an important aspect affecting their collective movement and tissue-mechanical properties, determining for example their effective viscoelasticity. Differences in cell-level properties and behaviour within a group of moving cells can give rise to unexpected and non-intuitive behaviours at the tissue level. Such emergent phenomena often manifest themselves through spatiotemporal patterns at an intermediate 'mesoscale' between cell and tissue scales, typically involving tens of cells. Focussing on the development of embryonic animal tissues, we review recent evidence for the importance of heterogeneity at the mesoscale for collective cell migration and convergence and extension movements. We further discuss approaches to incorporate heterogeneity into computational models to complement experimental investigations.

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Geometry can provide long-range mechanical guidance for embryogenesis

Downstream of gene expression, effectors such as the actomyosin contractile machinery drive embryo morphogenesis. During Drosophila embryonic axis extension, actomyosin has a specific planar-polarised organisation, which is responsible for oriented cell intercalation. In addition to these cell rearrangements, cell shape changes also contribute to tissue deformation. While cell-autonomous dynamics are well described, understanding the tissue-scale behaviour challenges us to solve the corresponding mechanical problem at the scale of the whole embryo, since mechanical resistance of all neighbouring epithelia will feedback on individual cells. Here we propose a novel numerical approach to compute the whole-embryo dynamics of the actomyosin-rich apical epithelial surface. We input in the model specific patterns of actomyosin contractility, such as the planar-polarisation of actomyosin in defined ventro-lateral regions of the embryo. Tissue strain rates and displacements are then predicted over the whole embryo surface according to the global balance of stresses and the material behaviour of the epithelium. Epithelia are modelled using a rheological law that relates the rate of deformation to the local stresses and actomyosin anisotropic contractility. Predicted flow patterns are consistent with the cell flows observed when imaging Drosophila axis extension in toto, using light sheet microscopy. The agreement between model and experimental data indicates that the anisotropic contractility of planar-polarised actomyosin in the ventro-lateral germband tissue can directly cause the tissue-scale deformations of the whole embryo. The three-dimensional mechanical balance is dependent on the geometry of the embryo, whose curved surface is taken into account in the simulations. Importantly, we find that to reproduce experimental flows, the model requires the presence of the cephalic furrow, a fold located anteriorly of the extending tissues. The presence of this geometric feature, through the global mechanical balance, guides the flow and orients extension towards the posterior end.

Forces directing germ-band extension in Drosophila embryos

Body axis elongation by convergent extension is a conserved developmental process found in all metazoans. Drosophila embryonic germ-band extension is an important morphogenetic process during embryogenesis, by which the length of the germ-band is more than doubled along the anterior-posterior axis. This lengthening is achieved by typical convergent extension, i.e. narrowing the lateral epidermis along the dorsal-ventral axis and simultaneous extension along the anterior-posterior axis. Germ-band extension is largely driven by cell intercalation, whose directionality is determined by the planar polarity of the tissue and ultimately by the anterior-posterior patterning system. In addition, extrinsic tensile forces originating from the invaginating endoderm induce cell shape changes, which transiently contribute to germ-band extension. Here, we review recent progress in understanding of the role of mechanical forces in germ-band extension.

Local mechanical forces promote polarized junctional assembly and axis elongation in Drosophila

Axis elongation is a conserved process in which the head-to-tail or anterior-posterior (AP) axis of an embryo extends. In Drosophila, cellular rearrangements drive axis elongation. Cells exchange neighbours by converging into transient multicellular vertices which resolve through the assembly of new cell interfaces parallel to the AP axis. We found that new interfaces elongate in pulses correlated with periodic contractions of the surrounding cells. Inhibiting actomyosin contractility globally, or specifically in the cells around multicellular vertices, disrupted the rate and directionality of new interface assembly. Laser ablation indicated that new interfaces sustained greater tension than non-elongating ones. We developed a method to apply ectopic tension and found that increasing AP tension locally increased the elongation rate of new edges by more than twofold. Increasing dorsal-ventral tension resulted in vertex resolution perpendicular to the AP direction. We propose that local, periodic contractile forces polarize vertex resolution to drive Drosophila axis elongation.

DOI:http://dx.doi.org/10.7554/eLife.10757.001

Tissues and organs form certain shapes that allow them to perform particular roles in the body. For example, the lungs form sacs that accommodate large volumes of air, while the skin forms a sheet to cover and protect our internal organs. One way to shape a tissue is for cells to swap places with their neighbours. During this rearrangement, the contacts between neighbouring cells break down before new contacts are formed with other cells. While the physical and molecular signals that guide the break down of cell contacts are well understood, less is known about how new contacts form.

Early in development, animal embryos establish a head-to-tail 'axis' that helps to guide where each tissue and organ will form in the body. In fruit fly embryos, the cell rearrangements that drive this process involve cells exchanging places with their neighbours by gathering around a single point. These temporary cell clusters are then organised via new cell contacts that form parallel to the head-to-tail axis.

Here, Yu and Fernandez-Gonzalez investigate the role of mechanical forces in forming new cell contacts as the head-tail axis elongates. The experiments show that disrupting the ability of the cells to generate mechanical forces inhibited the formation of new cell contacts and prevented cells from successfully swapping places. Conversely, when mechanical tension is applied at the rearrangement site, the assembly of new cell contacts happens faster. Furthermore, if the tension is applied in different orientations, new cell contacts form parallel to the direction of the mechanical force.

Yu and Fernandez-Gonzalez thus show that local mechanical forces direct the assembly of new cell contacts as the head-to-tail axis forms. These forces are most likely generated by cell contractions that appear to create mechanical tension at sites of cell rearrangement. How such physical forces are converted into molecular signals remains a question for future work.

DOI:http://dx.doi.org/10.7554/eLife.10757.002