Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure

Dynamics of PAR Proteins Explain the Oscillation and Ratcheting Mechanisms in Dorsal Closure

We present a vertex-based model for Drosophila dorsal closure that predicts the mechanics of cell oscillation and contraction from the dynamics of the PAR proteins. Based on experimental observations of how aPKC, Par-6, and Bazooka translocate from the circumference of the apical surface to the medial domain, and how they interact with each other and ultimately regulate the apicomedial actomyosin, we formulate a system of differential equations that captures the key features of dorsal closure, including distinctive behaviors in its early, slow, and fast phases. The oscillation in cell area in the early phase of dorsal closure results from an intracellular negative feedback loop that involves myosin, an actomyosin regulator, aPKC, and Bazooka. In the slow phase, gradual sequestration of apicomedial aPKC by Bazooka clusters causes incomplete disassembly of the actomyosin network over each cycle of oscillation, thus producing a so-called ratchet. The fast phase of rapid cell and tissue contraction arises when medial myosin, no longer antagonized by aPKC, builds up in time and produces sustained contraction. Thus, a minimal set of rules governing the dynamics of the PAR proteins, extracted from experimental observations, can account for all major mechanical outcomes of dorsal closure, including the transitions between its three distinct phases.

Mathematical models of dorsal closure

Dorsal closure is a model cell sheet movement that occurs midway through Drosophila embryogenesis. A dorsal hole, filled with amnioserosa, closes through the dorsalward elongation of lateral epidermal cell sheets. Closure requires contributions from 5 distinct tissues and well over 140 genes (see Mortensen et al., 2018, reviewed in Kiehart et al., 2017 and Hayes and Solon, 2017). In spite of this biological complexity, the movements (kinematics) of closure are geometrically simple at tissue, and in certain cases, at cellular scales. This simplicity has made closure the target of a number of mathematical models that seek to explain and quantify the processes that underlie closure's kinematics. The first (purely kinematic) modeling approach recapitulated well the time-evolving geometry of closure even though the underlying physical principles were not known. Almost all subsequent models delve into the forces of closure (i.e. the dynamics of closure). Models assign elastic, contractile and viscous forces which impact tissue and/or cell mechanics. They write rate equations which relate the forces to one another and to other variables, including those which represent geometric, kinematic, and or signaling characteristics. The time evolution of the variables is obtained by computing the solution of the model's system of equations, with optimized model parameters. The basis of the equations range from the phenomenological to biophysical first principles. We review various models and present their contribution to our understanding of the molecular mechanisms and biophysics of closure. Models of closure will contribute to our understanding of similar movements that characterize vertebrate morphogenesis.

Cell Sheet Morphogenesis: Dorsal Closure in Drosophila melanogaster as a Model System

Dorsal closure is a key process during Drosophila morphogenesis that models cell sheet movements in chordates, including neural tube closure, palate formation, and wound healing. Closure occurs midway through embryogenesis and entails circumferential elongation of lateral epidermal cell sheets that close a dorsal hole filled with amnioserosa cells. Signaling pathways regulate the function of cellular structures and processes, including Actomyosin and microtubule cytoskeletons, cell-cell/cell-matrix adhesion complexes, and endocytosis/vesicle trafficking. These orchestrate complex shape changes and movements that entail interactions between five distinct cell types. Genetic and laser perturbation studies establish that closure is robust, resilient, and the consequence of redundancy that contributes to four distinct biophysical processes: contraction of the amnioserosa, contraction of supracellular Actomyosin cables, elongation (stretching?) of the lateral epidermis, and zipping together of two converging cell sheets. What triggers closure and what the emergent properties are that give rise to its extraordinary resilience and fidelity remain key, extant questions.

Large, long range tensile forces drive convergence during Xenopus blastopore closure and body axis elongation

Indirect evidence suggests that blastopore closure during gastrulation of anamniotes, including amphibians such as Xenopus laevis, depends on circumblastoporal convergence forces generated by the marginal zone (MZ), but direct evidence is lacking. We show that explanted MZs generate tensile convergence forces up to 1.5 μN during gastrulation and over 4 μN thereafter. These forces are generated by convergent thickening (CT) until the midgastrula and increasingly by convergent extension (CE) thereafter. Explants from ventralized embryos, which lack tissues expressing CE but close their blastopores, produce up to 2 μN of tensile force, showing that CT alone generates forces sufficient to close the blastopore. Uniaxial tensile stress relaxation assays show stiffening of mesodermal and ectodermal tissues around the onset of neurulation, potentially enhancing long-range transmission of convergence forces. These results illuminate the mechanobiology of early vertebrate morphogenic mechanisms, aid interpretation of phenotypes, and give insight into the evolution of blastopore closure mechanisms.

Drosophila dorsal closure: An orchestra of forces to zip shut the embryo

Dorsal closure, a late-embryogenesis process, consists in the sealing of an epidermal gap on the dorsal side of the Drosophila embryo. Because of its similarities with wound healing and neural tube closure in humans, it has been extensively studied in the last twenty years. The process requires the coordination of several force generating mechanisms, that together will zip shut the epidermis. Recent works have provided a precise description of the cellular behavior at the origin of these forces and proposed quantitative models of the process. In this review, we will describe the different forces acting in dorsal closure. We will present our current knowledge on the mechanisms generating and regulating these forces and report on the different quantitative mathematical models proposed so far.

piragua encodes a zinc finger protein required for development in Drosophila

We isolated and characterized embryonic lethal mutations in piragua (prg). The prg locus encodes a protein with an amino terminus Zinc Finger-Associated-Domain (ZAD) and nine C₂H₂ zinc fingers (ZF). prg mRNA and protein expression during embryogenesis is dynamic with widespread maternal contribution, and subsequent expression in epithelial precursors. About a quarter of prg mutant embryos do not develop cuticle, and from those that do a small fraction have cuticular defects. Roughly half of prg mutants die during embryogenesis. prg mutants have an extended phenocritical period encompassing embryogenesis and first instar larval stage, since the other half of prg mutants die as first or second instar larvae. During dorsal closure, time-lapse high-resolution imaging shows defects arising out of sluggishness in closure, resolving at times in failures of closure. prg is expressed in imaginal discs, and is required for imaginal development. prg was identified in imaginal tissue in a cell super competition screen, together with other genes, like flower. We find that flower mutations are also embryonic lethal with a similar phenocritical period and strong embryonic mutant phenotypes (head involution defects, primarily). The two loci interact genetically in the embryo, as they increase embryonic mortality to close to 90% with the same embryonic phenotypes (dorsal closure and head involution defects, plus lack of cuticle). Mutant prg clones generated in developing dorsal thorax and eye imaginal tissue have strong developmental defects (lack of bristles and ommatidial malformations). prg is required in several developmental morphogenetic processes.

Quantifying dorsal closure in three dimensions

Dorsal closure is an essential stage of Drosophila embryogenesis and is a powerful model system for morphogenesis, wound healing, and tissue biomechanics. During closure, two flanks of lateral epidermis close an eye-shaped dorsal opening that is filled with amnioserosa. The two flanks of lateral epidermis are zipped together at each canthus ("corner" of the eye). Actomyosin-rich purse strings are localized at each of the two leading edges of lateral epidermis ("lids" of the eye). Here we report that each purse string indents the dorsal surface at each leading edge. The amnioserosa tissue bulges outward during the early-to-mid stages of closure to form a remarkably smooth, asymmetric dome indicative of an isotropic and uniform surface tension. Internal pressure of the embryo and tissue elastic properties help to shape the dorsal surface.

Remodeling Tissue Interfaces and the Thermodynamics of Zipping during Dorsal Closure in Drosophila

Dorsal closure during Drosophila embryogenesis is an important model system for investigating the biomechanics of morphogenesis. During closure, two flanks of lateral epidermis (with actomyosin-rich purse strings near each leading edge) close an eye-shaped opening that is filled with amnioserosa. At each canthus (corner of the eye) a zipping process remodels the tissue interfaces between the leading edges of the lateral epidermis and the amnioserosa. We investigated zipping dynamics and found that apposing leading edge cells come together at their apical ends and then square off basally to form a lateral junction. Meanwhile, the purse strings act as contractile elastic rods bent toward the embryo interior near each canthus. We propose that a canthus-localized force contributes to both bending the ends of the purse strings and the formation of lateral junctions. We developed a thermodynamic model for zipping based on three-dimensional remodeling of the tissue interfaces and the reaction dynamics of adhesion molecules in junctions and elsewhere, which we applied to zipping during unperturbed wild-type closure and to laser or genetically perturbed closure. We identified two processes that can contribute to the zipping mechanism, consistent with experiments, distinguished by whether amnioserosa dynamics do or do not augment canthus adhesion dynamics.

Cell Boundary Elongation by Non-autonomous Contractility in Cell Oscillation

Throughout development, tissues exhibit dynamic cell deformation, which is characterized by the integration of cell boundary contraction and/or elongation. Such changes ultimately establish tissue morphology and function [1-5]. In comparison to cell boundary contraction, which is predominantly driven by non-muscle myosin II (MyoII)-dependent contraction [6-9], the mechanisms of cell boundary elongation remain elusive. We explored the dynamics of the amnioserosa, which is known to exhibit cell shape oscillation [10-15], as a model system to study the subcellular-level mechanics that spatiotemporally evolve during Drosophila dorsal closure. Here we show that cell boundary elongation occurs through a combination of a non-autonomous active process and an autonomous process. The former is driven by a transient change in the level of MyoII in the neighboring cells that pull the vertices, whereas the latter is governed by the relaxation of junctional tension. By monitoring cell boundary deformation during live imaging, junctional tension at the specific phase of cell boundary oscillation, e.g., contraction or elongation, was probed by laser ablation. Junctional tension during boundary elongation is lower than during the other phase of oscillation. We extended our tension measurements to non-invasively estimate a tension map across the tissue, and found a correlation between junctional tension and vinculin dynamics at the cell junction. We propose that the medial actomyosin network is used as an entity to both contract and elongate the cell boundary. Moreover, our findings raise a possibility that the level of vinculin at the cell boundary could be used to approximate junctional tension in vivo.

Complete canthi removal reveals that forces from the amnioserosa alone are sufficient to drive dorsal closure in Drosophila

Drosophila's dorsal closure provides an excellent model system with which to analyze biomechanical processes during morphogenesis. During native closure, the amnioserosa, flanked by two lateral epidermal sheets, forms an eye-shaped opening with canthi at each corner. The dynamics of amnioserosa cells and actomyosin purse strings in the leading edges of epidermal cells promote closure, whereas the bulk of the lateral epidermis opposes closure. Canthi maintain purse string curvature (necessary for their dorsalward forces), and zipping at the canthi shortens leading edges, ensuring a continuous epithelium at closure completion. We investigated the requirement for intact canthi during closure with laser dissection approaches. Dissection of one or both canthi resulted in tissue recoil and flattening of each purse string. After recoil and a temporary pause, closure resumed at approximately native rates until slowing near the completion of closure. Thus the amnioserosa alone can drive closure after dissection of one or both canthi, requiring neither substantial purse string curvature nor zipping during the bulk of closure. How the embryo coordinates multiple, large forces (each of which is orders of magnitude greater than the net force) during native closure and is also resilient to multiple perturbations are key extant questions.

Growth and remodelling for profound circular wounds in skin

Wound healing studies both in vitro and in vivo have received a lot of attention recently. In vivo wound healing is a multi-step process involving physiological factors such as fibrinogen forming the clot, the infiltrated inflammatory cells, the recruited fibroblasts and the differentiated myofibroblasts as well as deposited collagens. All these actors play their roles at different times, aided by a cascade of morphogenetic agents and the result for the repair is approximatively successful but the imperfection is remained for large scars with fibrosis. Here, we want to study wound healing from the viewpoint of skin biomechanics, integrating the particular layered geometry of the skin, and the role of the neighbouring wound epidermis. After 2 days post-injury, it migrates towards the wound centre to cover the hole, the migration being coupled to proliferation at the wound border. Such a process is dominated by the skin properties which varies with ages, locations, pathologies, radiations, etc. It is also controlled by passive (actin, collagen) and active (myo-fibroblasts) fibres. We explore a growth model in finite elasticity of a bilayer surrounding a circular wound, only the interior one being proliferative and contractile. We discuss the occurrence of an irregular wound geometry generated by stresses and show quantitatively that it results from the combined effects of the stiffness, the size of the wound, eventually weakened by actin cables. Comparison of our findings is made with known observations or experiments in vivo.

Contractile and mechanical properties of epithelia with perturbed actomyosin dynamics

Mechanics has an important role during morphogenesis, both in the generation of forces driving cell shape changes and in determining the effective material properties of cells and tissues. Drosophila dorsal closure has emerged as a reference model system for investigating the interplay between tissue mechanics and cellular activity. During dorsal closure, the amnioserosa generates one of the major forces that drive closure through the apical contraction of its constituent cells. We combined quantitation of live data, genetic and mechanical perturbation and cell biology, to investigate how mechanical properties and contraction rate emerge from cytoskeletal activity. We found that a decrease in Myosin phosphorylation induces a fluidization of amnioserosa cells which become more compliant. Conversely, an increase in Myosin phosphorylation and an increase in actin linear polymerization induce a solidification of cells. Contrary to expectation, these two perturbations have an opposite effect on the strain rate of cells during DC. While an increase in actin polymerization increases the contraction rate of amnioserosa cells, an increase in Myosin phosphorylation gives rise to cells that contract very slowly. The quantification of how the perturbation induced by laser ablation decays throughout the tissue revealed that the tissue in these two mutant backgrounds reacts very differently. We suggest that the differences in the strain rate of cells in situations where Myosin activity or actin polymerization is increased arise from changes in how the contractile forces are transmitted and coordinated across the tissue through ECadherin-mediated adhesion. Altogether, our results show that there is an optimal level of Myosin activity to generate efficient contraction and suggest that the architecture of the actin cytoskeleton and the dynamics of adhesion complexes are important parameters for the emergence of coordinated activity throughout the tissue.

Ion channels contribute to the regulation of cell sheet forces during Drosophila dorsal closure

We demonstrate that ion channels contribute to the regulation of dorsal closure in Drosophila, a model system for cell sheet morphogenesis. We find that Ca(2+) is sufficient to cause cell contraction in dorsal closure tissues, as UV-mediated release of caged Ca(2+) leads to cell contraction. Furthermore, endogenous Ca(2+) fluxes correlate with cell contraction in the amnioserosa during closure, whereas the chelation of Ca(2+) slows closure. Microinjection of high concentrations of the peptide GsMTx4, which is a specific modulator of mechanically gated ion channel function, causes increases in cytoplasmic free Ca(2+) and actomyosin contractility and, in the long term, blocks closure in a dose-dependent manner. We identify two channel subunits, ripped pocket and dtrpA1 (TrpA1), that play a role in closure and other morphogenetic events. Blocking channels leads to defects in force generation via failure of actomyosin structures, and impairs the ability of tissues to regulate forces in response to laser microsurgery. Our results point to a key role for ion channels in closure, and suggest a mechanism for the coordination of force-producing cell behaviors across the embryo.

Computational and experimental study of the mechanics of embryonic wound healing

Wounds in the embryo show a remarkable ability to heal quickly without leaving a scar. Previous studies have found that an actomyosin ring (purse string) forms around the wound perimeter and contracts to close the wound over the course of several dozens of minutes. Here, we report experiments that reveal an even faster mechanism which remarkably closes wounds by more than 50% within the first 30s. Circular and elliptical wounds (~100μm in size) were made in the blastoderm of early chick embryos and allowed to heal, with wound area and shape characterized as functions of time. The closure rate displayed a biphasic behavior, with rapid constriction lasting about a minute, followed by a period of more gradual closure to complete healing. Fluorescent staining suggests that both healing phases are driven by actomyosin contraction, with relatively rapid contraction of fibers at cell borders within a relatively thick ring of tissue (several cells wide) around the wound followed by slower contraction of a thin supracellular actomyosin ring along the margin, consistent with a purse string mechanism. Finite-element modeling showed that this idea is biophysically plausible, with relatively isotropic contraction within the thick ring giving way to tangential contraction in the thin ring. In addition, consistent with experimental results, simulated elliptical wounds heal with little change in aspect ratio, and decreased membrane tension can cause these wounds to open briefly before going on to heal. These results provide new insight into the healing mechanism in embryonic epithelia.

A cell-level biomechanical model of Drosophila dorsal closure

We report a model describing the various stages of dorsal closure of Drosophila. Inspired by experimental observations, we represent the amnioserosa by 81 hexagonal cells that are coupled mechanically through the position of the nodes and the elastic forces on the edges. In addition, each cell has radial spokes representing actin filaments on which myosin motors can attach and exert contractile forces on the nodes, the attachment being controlled by a signaling molecule. Thus, the model couples dissipative cell and tissue motion with kinetic equations describing the myosin and signal dynamics. In the early phase, amnioserosa cells oscillate as a result of coupling among the chemical signaling, myosin attachment/detachment, and mechanical deformation of neighboring cells. In the slow phase, we test two ratcheting mechanisms suggested by experiments: an internal ratchet by the apical and junctional myosin condensates, and an external one by the supracellular actin cables encircling the amnioserosa. Within the range of parameters tested, the model predictions suggest the former as the main contributor to cell and tissue area reduction in this stage. In the fast phase of dorsal closure, cell pulsation is arrested, and the cell and tissue areas contract consistently. This is realized in the model by gradually shrinking the resting length of the spokes. Overall, the model captures the key features of dorsal closure through the three distinct phases, and its predictions are in good agreement with observations.

A mathematical model to study the dynamics of epithelial cellular networks

Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.

Classifying collective cancer cell invasion

Most invasive solid tumours display predominantly collective invasion, in which groups of cells invade the peritumoral stroma while maintaining cell-cell contacts. As the concepts and experimental models for functional analysis of collective cancer cell invasion are rapidly developing, we propose a framework for addressing potential mechanisms, experimental strategies and technical challenges to study this process.

Cell ingression and apical shape oscillations during dorsal closure in Drosophila

Programmed patterns of gene expression, cell-cell signaling, and cellular forces cause morphogenic movements during dorsal closure. We investigated the apical cell-shape changes that characterize amnioserosa cells during dorsal closure in Drosophila embryos with in vivo imaging of green-fluorescent-protein-labeled DE-cadherin. Time-lapsed, confocal images were assessed with a novel segmentation algorithm, Fourier analysis, and kinematic and dynamical modeling. We found two generic processes, reversible oscillations in apical cross-sectional area and cell ingression characterized by persistent loss of apical area. We quantified a time-dependent, spatially-averaged sum of intracellular and intercellular forces acting on each cell's apical belt of DE-cadherin. We observed that a substantial fraction of amnioserosa cells ingress near the leading edges of lateral epidermis, consistent with the view that ingression can be regulated by leading-edge cells. This is in addition to previously observed ingression processes associated with zipping and apoptosis. Although there is cell-to-cell variability in the maximum rate for decreasing apical area (0.3-9.5 μm(2)/min), the rate for completing ingression is remarkably constant (0.83 cells/min, r(2) > 0.99). We propose that this constant ingression rate contributes to the spatiotemporal regularity of mechanical stress exerted by the amnioserosa on each leading edge during closure.

Growing up is stressful: biophysical laws of morphogenesis

Would it not be nice to understand the rules that govern how a small and round zygote reforms itself into a full blown three-dimensional and structured organism? The past decades have provided us with a wealth of knowledge about molecular mechanisms, intracellular behaviors, and tissue organization. However, we still do not know how to systematically integrate molecular mechanisms into descriptions that operate at larger scales involving higher-order structures such as the actomyosin cell cortex or an entire tissue. For development, it is the biophysical laws by which these structures deform, move, and restructure that are essential for morphogenetic rearrangements at developmental length- and time-scales. Recent years have seen the advent of systematic approaches for identifying these laws and ways to determine associated physical behaviors. Here I attempt to paint an intuitive picture of the mechanical concepts that are important for large-scale developmental rearrangements, and I briefly review the technique of laser ablation for measuring associated physical quantities and testing physical models.

Modeling new conceptual interpretations of development

In April 2011, researchers from diverse background met at the Gulbenkian Institute (Oeiras, Portugal) to discuss the emerging input of biophysics into the field of developmental biology. The scope of the workshop was to bring together scientists working in different model systems and to discuss some of the most recent advances towards understanding how physical forces affect embryonic development. Discussions and talks highlighted two main trends: that many aspects of embryogenesis can be accurately quantified and translated into a limited number of physical forces and biochemical parameters; and that simulations and modeling provide new conceptual interpretations of classical developmental questions.