Emergent material properties of developing epithelial tissues

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.

Peeking into the future: inferring mechanics in dynamical tissues

Cells exert forces on each other and their environment, shaping the tissue. The resulting mechanical stresses can be determined experimentally or estimated computationally using stress inference methods. Over the years, mechanical stress inference has become a non-invasive, low-cost computational method for estimating the relative intercellular stresses and intracellular pressures of tissues. This mini-review introduces and compares the static and dynamic modalities of stress inference, considering their advantages and limitations. To date, most software has focused on static inference, which requires only a single microscopy image as input. Although applicable in quasi-equilibrium states, this approach neglects the influence that cell rearrangements might have on the inference. In contrast, dynamic stress inference relies on a time series of microscopy images to estimate stresses and pressures. Here, we discuss both static and dynamic mechanical stress inference in terms of their physical, mathematical, and computational foundations and then outline what we believe are promising avenues for in silico inference of the mechanical states of tissues.

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.

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, the aspect ratio of amnioserosa cells increases 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 shrink-age 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.

Super-resolution microscopy reveals actomyosin dynamics in medioapical arrays

Arrays of actin filaments (F-actin) near the apical surface of epithelial cells (medioapical arrays) contribute to apical constriction and morphogenesis throughout phylogeny. Here, super-resolution approaches (grazing incidence structured illumination, GI-SIM and lattice light sheet, LLSM) microscopy resolve individual, fluorescently labeled F-actin and bipolar myosin filaments that drive amnioserosa cell shape changes during dorsal closure in Drosophila. In expanded cells, F-actin and myosin form loose, apically domed meshworks at the plasma membrane. The arrays condense as cells contract, drawing the domes into the plane of the junctional belts. As condensation continues, individual filaments are no longer uniformly apparent. As cells expand, arrays of actomyosin are again resolved - some F-actin turnover likely occurs, but a large fraction of existing filaments rearrange. In morphologically isotropic cells, actin filaments are randomly oriented and during contraction, are drawn together but remain essentially randomly oriented. In anisotropic cells, largely parallel actin filaments are drawn closer to one another. Our images offer unparalleled resolution of F-actin in embryonic tissue show that medioapical arrays are tightly apposed to the plasma membrane, are continuous with meshworks of lamellar F-actin and thereby constitute modified cell cortex. In concert with other tagged array components, super-resolution imaging of live specimens will offer new understanding of cortical architecture and function. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Shear-Driven Solidification and Nonlinear Elasticity in Epithelial Tissues

Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity observed in other soft matter systems. Interestingly, shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order critical point that governs the liquid-solid transition of the undeformed system. We further show that a solidlike tissue responds linearly only to small strains and but then switches to a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.

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.

Stress relaxation in epithelial monolayers is controlled by the actomyosin cortex

Epithelial monolayers are one-cell thick tissue sheets that line most of the body surfaces, separating internal and external environments. As part of their function, they must withstand extrinsic mechanical stresses applied at high strain rates. However, little is known about how monolayers respond to mechanical deformations. Here, by subjecting suspended epithelial monolayers to stretch, we find that they dissipate stresses on a minute timescale and that relaxation can be described by a power law with an exponential cut-off at timescales larger than ~10 s. This process involves an increase in monolayer length, pointing to active remodelling of cellular biopolymers at the molecular scale during relaxation. Strikingly, monolayers consisting of tens of thousands of cells relax stress with similar dynamics to single rounded cells and both respond similarly to perturbations of the actomyosin cytoskeleton. By contrast, cell-cell junctional complexes and intermediate filaments do not relax tissue stress, but form stable connections between cells, allowing monolayers to behave rheologically as single cells. Taken together our data show that actomyosin dynamics governs the rheological properties of epithelial monolayers, dissipating applied stresses, and enabling changes in monolayer length.

Oscillatory cortical forces promote three dimensional cell intercalations that shape the murine mandibular arch

Multiple vertebrate embryonic structures such as organ primordia are composed of confluent cells. Although mechanisms that shape tissue sheets are increasingly understood, those which shape a volume of cells remain obscure. Here we show that 3D mesenchymal cell intercalations are essential to shape the mandibular arch of the mouse embryo. Using a genetically encoded vinculin tension sensor that we knock-in to the mouse genome, we show that cortical force oscillations promote these intercalations. Genetic loss- and gain-of-function approaches show that Wnt5a functions as a spatial cue to coordinate cell polarity and cytoskeletal oscillation. These processes diminish tissue rigidity and help cells to overcome the energy barrier to intercalation. YAP/TAZ and PIEZO1 serve as downstream effectors of Wnt5a-mediated actomyosin polarity and cytosolic calcium transients that orient and drive mesenchymal cell intercalations. These findings advance our understanding of how developmental pathways regulate biophysical properties and forces to shape a solid organ primordium.

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.

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.

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.

Architecture shapes contractility in actomyosin networks

Myosin-driven contraction of the actin cytoskeleton is at the base of cell and tissue morphogenesis. At the molecular level, myosin motors drive contraction by sliding actin filaments past one another using energy produced by ATP hydrolysis. How this microscopic sliding activity gives rise to cell-scale contractions has been an active research question first in muscle cells, and over the last few decades in non-muscle cells. While many early investigations focused on myosin motor activity, increasingly, the nanoscale architecture of the actin network emerges as a key regulator of contractility. Here we review theoretical and in vitro reconstitution studies that have uncovered some of the key mechanisms by which actin network organization controls contractile tension generation. We then discuss recent findings indicating that similar principles apply in cells.

Taking the strain: quantifying the contributions of all cell behaviours to changes in epithelial shape

Computer-assisted tracking of the shapes of many cells over long periods of development has driven the exploration of novel ways to quantify the contributions of different cell behaviours to morphogenesis. A handful of similar methods have now been published that are used to calculate tissue deformations (strain rates) in epithelia. These methods are further used to quantify strain rates attributable to each of the cell behaviours in the tissue, such as cell shape change, cell rearrangement and cell division, that together sum to the tissue strain rates. In this review, aimed at developmental biologists, I will introduce the general approach, characterize differences in current approaches and highlight extensions of these methods that remain to be fully explored. The methods will make a major contribution to the emerging field of tissue mechanics. Precisely quantified strain rates are an essential first step towards exploring constitutive equations relating stress to strain via tissue mechanical properties.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Inferring cellular forces from image stacks

Although the importance of cellular forces to a wide range of embryogenesis and disease processes is widely recognized, measuring these forces is challenging, especially in three dimensions. Here, we introduce CellFIT-3D, a force inference technique that allows tension maps for three-dimensional cellular systems to be estimated from image stacks. Like its predecessors, video force microscopy and CellFIT, this cell mechanics technique assumes boundary-specific interfacial tensions to be the primary drivers, and it constructs force-balance equations based on triple junction (TJ) dihedral angles. The technique involves image processing, segmenting of cells, grouping of cell outlines, calculation of dihedral planes, averaging along three-dimensional TJs, and matrix equation assembly and solution. The equations tend to be strongly overdetermined, allowing indistinct TJs to be ignored and solution error estimates to be determined. Application to clean and noisy synthetic data generated using Surface Evolver gave tension errors of 1.6-7%, and analyses of eight-cell murine embryos gave estimated errors smaller than the 10% uncertainty of companion aspiration experiments. Other possible areas of application include morphogenesis, cancer metastasis and tissue engineering.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

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.

Integration of actomyosin contractility with cell-cell adhesion during dorsal closure

In this work, we combine genetic perturbation, time-lapse imaging and quantitative image analysis to investigate how pulsatile actomyosin contractility drives cell oscillations, apical cell contraction and tissue closure during morphogenesis of the amnioserosa, the main force-generating tissue during the dorsal closure in Drosophila We show that Myosin activity determines the oscillatory and contractile behaviour of amnioserosa cells. Reducing Myosin activity prevents cell shape oscillations and reduces cell contractility. By contrast, increasing Myosin activity increases the amplitude of cell shape oscillations and the time cells spend in the contracted phase relative to the expanded phase during an oscillatory cycle, promoting cell contractility and tissue closure. Furthermore, we show that in AS cells, Rok controls Myosin foci formation and Mbs regulates not only Myosin phosphorylation but also adhesion dynamics through control of Moesin phosphorylation, showing that Mbs coordinates actomyosin contractility with cell-cell adhesion during amnioserosa morphogenesis.

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.

Prediction of traction forces of motile cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

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.

The dynamic mechanical properties of cellularised aggregates

Cellularised materials are composed of cells interfaced through specialised intercellular junctions that link the cytoskeleton of one cell to that of its neighbours allowing for transmission of forces. Cellularised materials are common in early development and adult tissues where they can be found in the form of cell sheets, cysts, or amorphous aggregates and in pathophysiological conditions such as cancerous tumours. Given the growing realisation that forces can regulate cell physiology and developmental processes, understanding how cellularised materials deform under mechanical stress or dissipate stress appear as key biological questions. In this review, we will discuss the dynamic mechanical properties of cellularised materials devoid of extracellular matrix.