A cell-level biomechanical model of Drosophila dorsal closure

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.

A Chemomechanical Model for Regulation of Contractility in the Embryonic Brain Tube

Morphogenesis is regulated by genetic, biochemical, and biomechanical factors, but the feedback controlling the interactions between these factors remains poorly understood. A previous study has found that compressing the brain tube of the early chick embryo induces changes in contractility and nuclear shape in the neuroepithelial wall. Assuming this response involves mechanical feedback, we use experiments and computational modeling to investigate a hypothetical mechanism behind the observed behavior. First, we measured nuclear circularity in embryonic chick brains subjected to transverse compression. Immediately after loading, the circularity varied regionally and appeared to reflect the local state of stress in the wall. After three hours of culture with sustained compression, however, the nuclei became rounder. Exposure to a gap junction blocker inhibited this response, suggesting that it requires intercellular diffusion of a biochemical signal. We speculate that the signal regulates the contraction that occurs near the lumen, altering stress distributions and nuclear geometry throughout the wall. Simulating compression using a chemomechanical finite-element model based on this idea shows that our hypothesis is consistent with most of the experimental data. This work provides a foundation for future investigations of chemomechanical feedback in epithelia during embryonic development.

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.

Elongated Cells Drive Morphogenesis in a Surface-Wrapped Finite-Element Model of Germband Retraction

During Drosophila embryogenesis, the germband first extends to curl around the posterior end of the embryo and then retracts back; however, retraction is not simply the reversal of extension. At a tissue level, extension is coincident with ventral furrow formation, and at a cellular level, extension occurs via convergent cell neighbor exchanges in the germband, whereas retraction involves only changes in cell shape. To understand how cell shapes, tissue organization, and cellular forces drive germband retraction, we investigate this process using a whole-embryo, surface-wrapped cellular finite-element model. This model represents two key epithelial tissues-amnioserosa and germband-as adjacent sheets of two-dimensional cellular finite elements that are wrapped around an ellipsoidal three-dimensional approximation of an embryo. The model reproduces the detailed kinematics of in vivo retraction by fitting just one free model parameter, the tension along germband cell interfaces; all other cellular forces are constrained to follow ratios inferred from experimental observations. With no additional parameter adjustments, the model also reproduces quantitative assessments of mechanical stress using laser dissection and failures of retraction when amnioserosa cells are removed via mutations or microsurgery. Surprisingly, retraction in the model is robust to changes in cellular force values but is critically dependent on starting from a configuration with highly elongated amnioserosa cells. Their extreme cellular elongation is established during the prior process of germband extension and is then used to drive retraction. The amnioserosa is the one tissue whose cellular morphogenesis is reversed from germband extension to retraction, and this reversal coordinates the forces needed to retract the germband back to its pre-extension position and shape. In this case, cellular force strengths are less important than the carefully established cell shapes that direct them. VIDEO ABSTRACT.

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.

Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer

Oscillatory morphodynamics provides necessary mechanical cues for many multicellular processes. Owing to their collective nature, these processes require robustly coordinated dynamics of individual cells, which are often separated too distantly to communicate with each other through biomaterial transportation. Although it is known that the mechanical balance generally plays a significant role in the systems' morphologies, it remains elusive whether and how the mechanical components may contribute to the systems' collective morphodynamics. Here, we study the collective oscillations in the Drosophila amnioserosa tissue to elucidate the regulatory roles of the mechanical components. We identify that the tensile stress is the key activator that switches the collective oscillations on and off. This regulatory role is shown analytically using the Hopf bifurcation theory. We find that the physical properties of the tissue boundary are directly responsible for synchronizing the oscillatory intensity and polarity of all inner cells and for orchestrating the spatial oscillation patterns inthe tissue.

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.

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.

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.

α-Catenin stabilises Cadherin-Catenin complexes and modulates actomyosin dynamics to allow pulsatile apical contraction

We have investigated how cell contractility and adhesion are functionally integrated during epithelial morphogenesis. To this end, we have analysed the role of α-Catenin, a key molecule linking E-Cadherin-based adhesion and the actomyosin cytoskeleton, during Drosophila embryonic dorsal closure, by studying a newly developed allelic series. We find that α-Catenin regulates pulsatile apical contraction in the amnioserosa, the main force-generating tissue driving closure of the embryonic epidermis. α-Catenin controls actomyosin dynamics by stabilising and promoting the formation of actomyosin foci, and also stabilises DE-Cadherin (Drosophila E-Cadherin, also known as Shotgun) at the cell membrane, suggesting that medioapical actomyosin contractility regulates junction stability. Furthermore, we uncover a genetic interaction between α-Catenin and Vinculin, and a tension-dependent recruitment of Vinculin to amniosersoa apical cell membranes, suggesting the existence of a mechano-sensitive module operating in this tissue.

Amnioserosa cell constriction but not epidermal actin cable tension autonomously drives dorsal closure

Tissue morphogenesis requires coordination of multiple force-producing components. During dorsal closure in fly embryogenesis, an epidermis opening closes. A tensioned epidermal actin/MyosinII cable, which surrounds the opening, produces a force that is thought to combine with another MyosinII force mediating apical constriction of the amnioserosa cells that fill the opening. A model proposing that each force could autonomously drive dorsal closure was recently challenged by a model in which the two forces combine in a ratchet mechanism. Acute force elimination via selective MyosinII depletion in one or the other tissue shows that the amnioserosa tissue autonomously drives dorsal closure while the actin/MyosinII cable cannot. These findings exclude both previous models, although a contribution of the ratchet mechanism at dorsal closure onset remains likely. This shifts the current view of dorsal closure being a combinatorial force-component system to a single tissue-driven closure event.

Myosin light-chain phosphatase regulates basal actomyosin oscillations during morphogenesis

Contractile actomyosin networks generate forces that drive tissue morphogenesis. Actomyosin contractility is controlled primarily by reversible phosphorylation of the myosin-II regulatory light chain through the action of myosin kinases and phosphatases. While the role of myosin light-chain kinase in regulating contractility during morphogenesis has been largely characterized, there is surprisingly little information on myosin light-chain phosphatase (MLCP) function in this context. Here, we use live imaging of Drosophila follicle cells combined with mathematical modelling to demonstrate that the MLCP subunit flapwing (flw) is a key regulator of basal myosin oscillations and cell contractions underlying egg chamber elongation. Flw expression decreases specifically on the basal side of follicle cells at the onset of contraction and flw controls the initiation and periodicity of basal actomyosin oscillations. Contrary to previous reports, basal F-actin pulsates similarly to myosin. Finally, we propose a quantitative model in which periodic basal actomyosin oscillations arise in a cell-autonomous fashion from intrinsic properties of motor assemblies.

Actomyosin contractility is regulated by phosphorylation of myosin regulatory light chain; much of the work in this area has focused on the kinase. Here the authors use Drosophila follicle cells and modelling to show that the phosphatase subunit Flapwing controls the initiation and dynamics of actomyosin oscillations.

Emergent material properties of developing epithelial tissues

BACKGROUND

Force generation and the material properties of cells and tissues are central to morphogenesis but remain difficult to measure in vivo. Insight is often limited to the ratios of mechanical properties obtained through disruptive manipulation, and the appropriate models relating stress and strain are unknown. The Drosophila amnioserosa epithelium progressively contracts over 3 hours of dorsal closure, during which cell apices exhibit area fluctuations driven by medial myosin pulses with periods of 1.5-6 min. Linking these two timescales and understanding how pulsatile contractions drive morphogenetic movements is an urgent challenge.

RESULTS

We present a novel framework to measure in a continuous manner the mechanical properties of epithelial cells in the natural context of a tissue undergoing morphogenesis. We show that the relationship between apicomedial myosin fluorescence intensity and strain during fluctuations is consistent with a linear behaviour, although with a lag. We thus used myosin fluorescence intensity as a proxy for active force generation and treated cells as natural experiments of mechanical response under cyclic loading, revealing unambiguous mechanical properties from the hysteresis loop relating stress to strain. Amnioserosa cells can be described as a contractile viscoelastic fluid. We show that their emergent mechanical behaviour can be described by a linear viscoelastic rheology at timescales relevant for tissue morphogenesis. For the first time, we establish relative changes in separate effective mechanical properties in vivo. Over the course of dorsal closure, the tissue solidifies and effective stiffness doubles as net contraction of the tissue commences. Combining our findings with those from previous laser ablation experiments, we show that both apicomedial and junctional stress also increase over time, with the relative increase in apicomedial stress approximately twice that of other obtained measures.

CONCLUSIONS

Our results show that in an epithelial tissue undergoing net contraction, stiffness and stress are coupled. Dorsal closure cell apical contraction is driven by the medial region where the relative increase in stress is greater than that of stiffness. At junctions, by contrast, the relative increase in the mechanical properties is the same, so the junctional contribution to tissue deformation is constant over time. An increase in myosin activity is likely to underlie, at least in part, the change in medioapical properties and we suggest that its greater effect on stress relative to stiffness is fundamental to actomyosin systems and confers on tissues the ability to regulate contraction rates in response to changes in external mechanics.

A biomechanical model for fluidization of cells under dynamic strain

Recent experiments have investigated the response of smooth muscle cells to transient stretch-compress (SC) and compress-stretch (CS) maneuvers. The results indicate that the transient SC maneuver causes a sudden fluidization of the cell while the CS maneuver does not. To understand this asymmetric behavior, we have built a biomechanical model to probe the response of stress fibers to the two maneuvers. The model couples the cross-bridge cycle of myosin motors with a viscoelastic Kelvin-Voigt element that represents the stress fiber. Simulation results point to the sensitivity of the myosin detachment rate to tension as the cause for the asymmetric response of the stress fiber to the CS and SC maneuvers. For the SC maneuver, the initial stretch increases the tension in the stress fiber and suppresses myosin detachment. The subsequent compression then causes a large proportion of the myosin population to disengage rapidly from actin filaments. This leads to the disassembly of the stress fibers and the observed fluidization. In contrast, the CS maneuver only produces a mild loss of myosin motors and no fluidization.

Spontaneous oscillations of elastic contractile materials with turnover

Single and collective cellular oscillations driven by the actomyosin cytoskeleton have been observed in numerous biological systems. Here, we propose that these oscillations can be accounted for by a generic oscillator model of a material turning over and contracting against an elastic element. As an example, we show that during dorsal closure of the Drosophila embryo, experimentally observed changes in actomyosin concentration and oscillatory cell shape changes can, indeed, be captured by the dynamic equations studied here. We also investigate the collective dynamics of an ensemble of such contractile elements and show that the relative contribution of viscous and friction losses yields different regimes of collective oscillations. Taking into account the diffusion of force-producing molecules between contractile elements, our theoretical framework predicts the appearance of traveling waves, resembling the propagation of actomyosin waves observed during morphogenesis.

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.

Apical oscillations in amnioserosa cells: basolateral coupling and mechanical autonomy

Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.

Bazooka inhibits aPKC to limit antagonism of actomyosin networks during amnioserosa apical constriction

Cell shape changes drive tissue morphogenesis during animal development. An important example is the apical cell constriction that initiates tissue internalisation. Apical constriction can occur through a phase of cyclic assembly and disassembly of apicomedial actomyosin networks, followed by stabilisation of these networks. Delayed negative-feedback mechanisms typically underlie cyclic behaviour, but the mechanisms regulating cyclic actomyosin networks remain obscure, as do mechanisms that transform overall network behaviour. Here, we show that a known inhibitor of apicomedial actomyosin networks in Drosophila amnioserosa cells, the Par-6-aPKC complex, is recruited to the apicomedial domain by actomyosin networks during dorsal closure of the embryo. This finding establishes an actomyosin-aPKC negative-feedback loop in the system. Additionally, we find that aPKC recruits Bazooka to the apicomedial domain, and phosphorylates Bazooka for a dynamic interaction. Remarkably, stabilising aPKC-Bazooka interactions can inhibit the antagonism of actomyosin by aPKC, suggesting that Bazooka acts as an aPKC inhibitor, and providing a possible mechanism for delaying the actomyosin-aPKC negative-feedback loop. Our data also implicate an increasing degree of Par-6-aPKC-Bazooka interactions as dorsal closure progresses, potentially explaining a developmental transition in actomyosin behaviour from cyclic to persistent networks. This later impact of aPKC inhibition is supported by mathematical modelling of the system. Overall, this work illustrates how shifting chemical signals can tune actomyosin network behaviour during development.

Local, cell-nonautonomous feedback regulation of myosin dynamics patterns transitions in cell behavior: a role for tension and geometry?

Signals, stresses, and myosin-dependent contractility influence cell geometry, tension, myosin dynamics, and pulsed constriction in the amnioserosa both cell-autonomously and -nonautonomously and feedback regulate cell behavior. Cell delamination is a locally patterned, nonautonomously regulated transition from pulsed to unpulsed constriction.

How robust patterns of tissue dynamics emerge from heterogeneities, stochasticities, and asynchronies in cell behavior is an outstanding question in morphogenesis. A clear understanding of this requires examining the influence of the behavior of single cells on tissue patterning. Here we develop single-cell manipulation strategies to uncover the origin of patterned cell behavior in the amnioserosa during Drosophila dorsal closure. We show that the formation and dissolution of contractile, medial actomyosin networks previously shown to underlie pulsed apical constrictions in the amnioserosa are apparently asynchronous in adjacent cells. We demonstrate for the first time that mechanical stresses and Rho1 GTPase control myosin dynamics qualitatively and quantitatively, in amplitude and direction, both cell autonomously and nonautonomously. We then demonstrate that interfering with myosin-dependent contractility in single cells also influences pulsed constrictions cell nonautonomously. Our results suggest that signals and stresses can feedback regulate the amplitude and spatial propagation of pulsed constrictions through their influence on tension and geometry. We establish the relevance of these findings to native closure by showing that cell delamination represents a locally patterned and collective transition from pulsed to unpulsed constriction that also relies on the nonautonomous feedback control of myosin dynamics.