Comparative study of non-invasive force and stress inference methods in tissue

The Geometric Basis of Epithelial Convergent Extension

Shape changes of epithelia during animal development, such as convergent extension, are achieved through concerted mechanical activity of individual cells. While much is known about the corresponding large scale tissue flow and its genetic drivers, fundamental questions regarding local control of contractile activity on cellular scale and its embryo-scale coordination remain open. To address these questions, we develop a quantitative, model-based analysis framework to relate cell geometry to local tension in recently obtained timelapse imaging data of gastrulating Drosophila embryos. This analysis provides a systematic decomposition of cell shape changes and T1-rearrangements into internally driven, active, and externally driven, passive, contributions. Our analysis provides evidence that germ band extension is driven by active T1 processes that self-organize through positive feedback acting on tensions. More generally, our findings suggest that epithelial convergent extension results from controlled transformation of internal force balance geometry which combines the effects of bottom-up local self-organization with the top-down, embryo-scale regulation by gene expression.

Numerical assessment of the applicability of geometry-based force inference on homogeneous and heterogeneous cells

The measurement of cellular forces, which reflect crucial biological attributes, has the potential to replace conventional cell assessment methods, such as morphology, proliferation, and molecular expression analysis, in medical cell diagnosis and cell culture studies. In medical cell evaluations, force inference techniques have gained prominence due to their non-invasiveness and lack of requirement for specialized equipment. Among those techniques, the method proposed by Ishihara et al., which estimates forces in densely packed cells based only on cell geometry, is a promising method. However, its applicability range of this method has not been fully established. In this study, we employed a two-dimensional vertex model to numerically assess the applicability of this method on homogeneous and heterogeneous cells. Our comparisons between the true values from numerical simulations and the estimated values from the inference method revealed a significant correlation between estimation accuracy and cell roundness in systems of homogeneous cell. Moreover, the method demonstrated efficient force estimations in heterogeneous-cell systems. These findings may be useful when the force inference method is employed to evaluate medical cells.

A Perspective on Developing Modeling and Image Analysis Tools to Investigate Mechanosensing Proteins

The shift of funding organizations to prioritize interdisciplinary work points to the need for workflow models that better accommodate interdisciplinary studies. Most scientists are trained in a specific field and are often unaware of the kind of insights that other disciplines could contribute to solving various problems. In this paper, we present a perspective on how we developed an experimental pipeline between a microscopy and image analysis/bioengineering lab. Specifically, we connected microscopy observations about a putative mechanosensing protein, obscurin, to image analysis techniques that quantify cell changes. While the individual methods used are well established (fluorescence microscopy; ImageJ WEKA and mTrack2 programs; MATLAB), there are no existing best practices for how to integrate these techniques into a cohesive, interdisciplinary narrative. Here, we describe a broadly applicable workflow of how microscopists can more easily quantify cell properties (e.g., perimeter, velocity) from microscopy videos of eukaryotic (MDCK) adherent cells. Additionally, we give examples of how these foundational measurements can create more complex, customizable cell mechanics tools and models.

Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy

Tissue morphogenesis results from a tight interplay between gene expression, biochemical signaling and mechanics. Although sequencing methods allow the generation of cell-resolved spatiotemporal maps of gene expression, creating similar maps of cell mechanics in three-dimensional (3D) developing tissues has remained a real challenge. Exploiting the foam-like arrangement of cells, we propose a robust end-to-end computational method called 'foambryo' to infer spatiotemporal atlases of cellular forces from fluorescence microscopy images of cell membranes. Our method generates precise 3D meshes of cells' geometry and successively predicts relative cell surface tensions and pressures. We validate it with 3D foam simulations, study its noise sensitivity and prove its biological relevance in mouse, ascidian and worm embryos. 3D force inference allows us to recover mechanical features identified previously, but also predicts new ones, unveiling potential new insights on the spatiotemporal regulation of cell mechanics in developing embryos. Our code is freely available and paves the way for unraveling the unknown mechanochemical feedbacks that control embryo and tissue morphogenesis.

Nature-inspired designs for disordered acoustic bandgap materials

We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self-assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides.

Revisiting the relationship between turgor pressure and plant cell growth

Growth is central to plant morphogenesis. Plant cells are encased in rigid cell walls, and they must overcome physical confinement to grow to specific sizes and shapes. Cell wall tension and turgor pressure are the main mechanical components impacting plant cell growth. Cell wall mechanics has been the focus of most plant biomechanical studies, and turgor pressure was often considered as a constant and largely passive component. Nevertheless, it is increasingly accepted that turgor pressure plays a significant role in plant growth. Numerous theoretical and experimental studies suggest that turgor pressure can be both spatially inhomogeneous and actively modulated during morphogenesis. Here, we revisit the pressure-growth relationship by reviewing recent advances in investigating the interactions between cellular/tissular pressure and growth.

Small hand-designed convolutional neural networks outperform transfer learning in automated cell shape detection in confluent tissues

Mechanical cues such as stresses and strains are now recognized as essential regulators in many biological processes like cell division, gene expression or morphogenesis. Studying the interplay between these mechanical cues and biological responses requires experimental tools to measure these cues. In the context of large scale tissues, this can be achieved by segmenting individual cells to extract their shapes and deformations which in turn inform on their mechanical environment. Historically, this has been done by segmentation methods which are well known to be time consuming and error prone. In this context however, one doesn't necessarily require a cell-level description and a coarse-grained approach can be more efficient while using tools different from segmentation. The advent of machine learning and deep neural networks has revolutionized the field of image analysis in recent years, including in biomedical research. With the democratization of these techniques, more and more researchers are trying to apply them to their own biological systems. In this paper, we tackle a problem of cell shape measurement thanks to a large annotated dataset. We develop simple Convolutional Neural Networks (CNNs) which we thoroughly optimize in terms of architecture and complexity to question construction rules usually applied. We find that increasing the complexity of the networks rapidly no longer yields improvements in performance and that the number of kernels in each convolutional layer is the most important parameter to achieve good results. In addition, we compare our step-by-step approach with transfer learning and find that our simple, optimized CNNs give better predictions, are faster in training and analysis and don't require more technical knowledge to be implemented. Overall, we offer a roadmap to develop optimized models and argue that we should limit the complexity of such models. We conclude by illustrating this strategy on a similar problem and dataset.

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.

Live 3D imaging and mapping of shear stresses within tissues using incompressible elastic beads

To investigate the role of mechanical constraints in morphogenesis and development, we have developed a pipeline of techniques based on incompressible elastic sensors. These techniques combine the advantages of incompressible liquid droplets, which have been used as precise in situ shear stress sensors, and of elastic compressible beads, which are easier to tune and to use. Droplets of a polydimethylsiloxane mix, made fluorescent through specific covalent binding to a rhodamin dye, are produced by a microfluidics device. The elastomer rigidity after polymerization is adjusted to the tissue rigidity. Its mechanical properties are carefully calibrated in situ, for a sensor embedded in a cell aggregate submitted to uniaxial compression. The local shear stress tensor is retrieved from the sensor shape, accurately reconstructed through an active contour method. In vitro, within cell aggregates, and in vivo, in the prechordal plate of the zebrafish embryo during gastrulation, our pipeline of techniques demonstrates its efficiency to directly measure the three dimensional shear stress repartition within a tissue.

Dynamic changes in epithelial cell packing during tissue morphogenesis

Cell packing - the spatial arrangement of cells - determines the shapes of organs. Recently, investigations of organ development in a variety of model organisms have uncovered cellular mechanisms that are used by epithelial tissues to change cell packing, and thereby their shapes, to generate functional architectures. Here, we review these cellular mechanisms across a wide variety of developmental processes in vertebrates and invertebrates and identify a set of common motifs in the morphogenesis toolbox that, in combination, appear to allow any change in tissue shape. We focus on tissue elongation, folding and invagination, and branching. We also highlight how these morphogenetic processes are achieved by cell-shape changes, cell rearrangements, and oriented cell division. Finally, we describe approaches that have the potential to engineer three-dimensional tissues for both basic science and translational purposes. This review provides a framework for future analyses of how tissues are shaped by the dynamics of epithelial cell packing.

Inferring cell junction tension and pressure from cell geometry

Recognizing the crucial role of mechanical regulation and forces in tissue development and homeostasis has stirred a demand for in situ measurement of forces and stresses. Among emerging techniques, the use of cell geometry to infer cell junction tensions, cell pressures and tissue stress has gained popularity owing to the development of computational analyses. This approach is non-destructive and fast, and statistically validated based on comparisons with other techniques. However, its qualitative and quantitative limitations, in theory as well as in practice, should be examined with care. In this Primer, we summarize the underlying principles and assumptions behind stress inference, discuss its validity criteria and provide guidance to help beginners make the appropriate choice of its variants. We extend our discussion from two-dimensional stress inference to three dimensional, using the early mouse embryo as an example, and list a few possible extensions. We hope to make stress inference more accessible to the scientific community and trigger a broader interest in using this technique to study mechanics in development.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Mechanical coordination is sufficient to promote tissue replacement during metamorphosis in Drosophila

During development, cells coordinate to organize in coherent structures. Although it is now well established that physical forces are essential for implementing this coordination, the instructive roles of mechanical inputs are not clear. Here, we show that the replacement of the larval epithelia by the adult one in Drosophila demands the coordinated exchange of mechanical signals between two cell types, the histoblasts (adult precursors) organized in nests and the surrounding larval epidermal cells (LECs). An increasing stress gradient develops from the center of the nests toward the LECs as a result of the forces generated by histoblasts as they proliferate and by the LECs as they delaminate (push/pull coordination). This asymmetric radial coordination of expansive and contractile activities contributes to epithelial replacement. Our analyses support a model in which cell-cell mechanical communication is sufficient for the rearrangements that implement epithelial morphogenesis.

DLITE Uses Cell-Cell Interface Movement to Better Infer Cell-Cell Tensions

Cell shapes and connectivities evolve over time as the colony changes shape or embryos develop. Shapes of intercellular interfaces are closely coupled with the forces resulting from actomyosin interactions, membrane tension, or cell-cell adhesions. Although it is possible to computationally infer cell-cell forces from a mechanical model of collective cell behavior, doing so for temporally evolving forces in a manner robust to digitization difficulties is challenging. Here, we introduce a method for dynamic local intercellular tension estimation (DLITE) that infers such evolution in temporal force with less sensitivity to digitization ambiguities or errors. This method builds upon previous work on single time points (cellular force-inference toolkit). We validate our method using synthetic geometries. DLITE's inferred cell colony tension evolutions correlate better with ground truth for these synthetic geometries as compared to tension values inferred from methods that consider each time point in isolation. We introduce cell connectivity errors, angle estimate errors, connection mislocalization, and connection topological changes to synthetic data and show that DLITE has reduced sensitivity to these conditions. Finally, we apply DLITE to time series of human-induced pluripotent stem cell colonies with endogenously expressed GFP-tagged zonulae occludentes-1. We show that DLITE offers improved stability in the inference of cell-cell tensions and supports a correlation between the dynamics of cell-cell forces and colony rearrangement.

Experimental validation of force inference in epithelia from cell to tissue scale

Morphogenesis relies on the active generation of forces, and the transmission of these forces to surrounding cells and tissues. Hence measuring forces directly in developing embryos is an essential task to study the mechanics of development. Among the experimental techniques that have emerged to measure forces in epithelial tissues, force inference is particularly appealing. Indeed it only requires a snapshot of the tissue, as it relies on the topology and geometry of cell contacts, assuming that forces are balanced at each vertex. However, establishing force inference as a reliable technique requires thorough validation in multiple conditions. Here we performed systematic comparisons of force inference with laser ablation experiments in four epithelial tissues from two animals, the fruit fly and the quail. We show that force inference accurately predicts single junction tension, tension patterns in stereotyped groups of cells, and tissue-scale stress patterns, in wild type and mutant conditions. We emphasize its ability to capture the distribution of forces at different scales from a single image, which gives it a critical advantage over perturbative techniques such as laser ablation. Overall, our results demonstrate that force inference is a reliable and efficient method to quantify the mechanical state of epithelia during morphogenesis, especially at larger scales when inferred tensions and pressures are binned into a coarse-grained stress tensor.

Mechanical Heterogeneity in Tissues Promotes Rigidity and Controls Cellular Invasion

We study the influence of cell-level mechanical heterogeneity in epithelial tissues using a vertex-based model. Heterogeneity is introduced into the cell shape index (p_{0}) that tunes the stiffness at a single-cell level. The addition of heterogeneity can always enhance the mechanical rigidity of the epithelial layer by increasing its shear modulus, hence making it more rigid. There is an excellent scaling collapse of our data as a function of a single scaling variable f_{r}, which accounts for the overall fraction of rigid cells. We identify a universal threshold f_{r}^{*} that demarcates fluid versus solid tissues. Furthermore, this rigidity onset is far below the contact percolation threshold of rigid cells. These results give rise to a separation of rigidity and contact percolation processes that leads to distinct types of solid states. We also investigate the influence of heterogeneity on tumor invasion dynamics. There is an overall impedance of invasion as the tissue becomes more rigid. Invasion can also occur in an intermediate heterogeneous solid state that is characterized by significant spatial-temporal intermittency.

[The irruption of mechanics in the chemistry of life]

Mechanical constraints are recognized as a key regulator of biological processes, from molecules to organisms, throughout embryonic development, tissue regeneration and in situations of physiological regulation and pathological disturbances. The study of the influence of these physical constraints on the living, in particular on the cells and the organisms of the animal kingdom, has been the object for a decade of important work carried out at the interface between biology, physics and mechanics, constituting a new discipline: mechanobiology. Here we briefly describe the remarkable advances in understanding how cells and tissues both generate and perceive mechanical stresses, and how these constrains dictate cell shape, migration, cell differentiation and finally adaptation of tissues to their environment during morphogenesis, injury and repair.

Kalman Inversion Stress Microscopy

Although mechanical cues are crucial to tissue morphogenesis and development, the tissue mechanical stress field remains poorly characterized. Given traction force time-lapse movies, as obtained by traction force microscopy of in vitro cellular sheets, we show that the tissue stress field can be estimated by Kalman filtering. After validation using numerical data, we apply Kalman inversion stress microscopy to experimental data. We combine the inferred stress field with velocity and cell-shape measurements to quantify the rheology of epithelial cell monolayers in physiological conditions, found to be close to that of an elastic and active material.

AIP1 and cofilin ensure a resistance to tissue tension and promote directional cell rearrangement

In order to understand how tissue mechanics shapes animal body, it is critical to clarify how cells respond to and resist tissue stress when undergoing morphogenetic processes, such as cell rearrangement. Here, we address the question in the Drosophila wing epithelium, where anisotropic tissue tension orients cell rearrangements. We found that anisotropic tissue tension localizes actin interacting protein 1 (AIP1), a cofactor of cofilin, on the remodeling junction via cooperative binding of cofilin to F-actin. AIP1 and cofilin promote actin turnover and locally regulate the Canoe-mediated linkage between actomyosin and the junction. This mechanism is essential for cells to resist the mechanical load imposed on the remodeling junction perpendicular to the direction of tissue stretching. Thus, the present study delineates how AIP1 and cofilin achieve an optimal balance between resistance to tissue tension and morphogenesis.

Coordination of Morphogenesis and Cell-Fate Specification in Development

During animal development, cell-fate-specific changes in gene expression can modify the material properties of a tissue and drive tissue morphogenesis. While mechanistic insights into the genetic control of tissue-shaping events are beginning to emerge, how tissue morphogenesis and mechanics can reciprocally impact cell-fate specification remains relatively unexplored. Here we review recent findings reporting how multicellular morphogenetic events and their underlying mechanical forces can feed back into gene regulatory pathways to specify cell fate. We further discuss emerging techniques that allow for the direct measurement and manipulation of mechanical signals in vivo, offering unprecedented access to study mechanotransduction during development. Examination of the mechanical control of cell fate during tissue morphogenesis will pave the way to an integrated understanding of the design principles that underlie robust tissue patterning in embryonic development.

Dynamic interplay of cell fate, polarity and force generation in ascidian embryos

A fundamental challenge in developmental biology is to understand how forces produced by individual cells are patterned in space and time and then integrated to produce stereotyped changes in tissue-level or embryo-level morphology. Ascidians offer a unique opportunity to address this challenge by studying how small groups of cells collectively execute complex, but highly stereotyped morphogenetic movements. Here we highlight recent progress and open questions in the study of ascidian morphogenesis, emphasizing the dynamic interplay of cell fate determination, cellular force generation and tissue-level mechanics.

A scheme for 3-dimensional morphological reconstruction and force inference in the early C. elegans embryo

In this study, we present a scheme for the reconstruction of cellular morphology and the inference of mechanical forces in the early C. elegans embryo. We have developed and bench-marked a morphological reconstruction scheme that transforms flourescence-based in vivo images of membranes into a point cloud of smoothed surface patches, which facilitates an accurate estimation of membrane curvatures and the angles between membranes. Assuming an isotropic and homogeneous distribution of tensions along individual membranes, we infer a pattern of forces that are 7% deviated from force balance at edges, and 10% deviated from the Young-Laplace relation across membranes. We demonstrate the stability of our inference scheme via a sensitivity analysis, and the reproducibility of our image-analysis and force inference pipelines.

Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

The growth and dynamics of epithelial tissues govern many morphogenetic processes in embryonic development. A recent quantitative transition in data acquisition, facilitated by advances in genetic and live-imaging techniques, is paving the way for new insights to these processes. Computational models can help us understand and interpret observations, and then make predictions for future experiments that can distinguish between hypothesised mechanisms. Increasingly, cell-based modelling approaches such as vertex models are being used to help understand the mechanics underlying epithelial morphogenesis. These models typically seek to reproduce qualitative phenomena, such as cell sorting or tissue buckling. However, it remains unclear to what extent quantitative data can be used to constrain these models so that they can then be used to make quantitative, experimentally testable predictions. To address this issue, we perform an in silico study to investigate whether vertex model parameters can be inferred from imaging data, and explore methods to quantify the uncertainty of such estimates. Our approach requires the use of summary statistics to estimate parameters. Here, we focus on summary statistics of cellular packing and of laser ablation experiments, as are commonly reported from imaging studies. We find that including data from repeated experiments is necessary to generate reliable parameter estimates that can facilitate quantitative model predictions.

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'.

Modeling and Identification of Amnioserosa Cell Mechanical Behavior by Using Mass-Spring Lattices

Various mechanical models of live amnioserosa cells during Drosophila melanogaster's dorsal closure are proposed. Such models account for specific biomechanical oscillating behaviors and depend on a different set of parameters. The identification of the parameters for each of the proposed models is accomplished according to a least-squares approach in such a way to best fit the cellular dynamics extracted from live images. For the purpose of comparison, the resulting models after identification are validated to allow for the selection of the most appropriate description of such a cell dynamics. The proposed methodology is general and it may be applied to other planar biological processes.

From cells to tissue: A continuum model of epithelial mechanics

A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangements, we elucidated dynamical behavior underlying passive relaxation, active contraction-elongation, and tissue shear flow, including a mechanism for contraction-elongation, whereby tissue flows perpendicularly to the axis of cell elongation. This study provides an integrated scheme for the understanding of the orchestration of morphogenetic processes in individual cells to achieve epithelial tissue morphogenesis.

Using cell deformation and motion to predict forces and collective behavior in morphogenesis

In multi-cellular organisms, morphogenesis translates processes at the cellular scale into tissue deformation at the scale of organs and organisms. To understand how biochemical signaling regulates tissue form and function, we must understand the mechanical forces that shape cells and tissues. Recent progress in developing mechanical models for tissues has led to quantitative predictions for how cell shape changes and polarized cell motility generate forces and collective behavior on the tissue scale. In particular, much insight has been gained by thinking about biological tissues as physical materials composed of cells. Here we review these advances and discuss how they might help shape future experiments in developmental biology.

Modelling apical columnar epithelium mechanics from circumferential contractile fibres

Simple columnar epithelia are formed by individual epithelial cells connecting together to form single cell high sheets. They are a main component of many important body tissues and are heavily involved in both normal and cancerous cell activities. Prior experimental observations have identified a series of contractile fibres around the circumference of a cross section located in the upper (apical) region of each cell. While other potential mechanisms have been identified in both the experimental and theoretical literature, these circumferential fibres are considered to be the most likely mechanism controlling movement of this cross section. Here, we investigated the impact of circumferential contractile fibres on movement of the cross section by creating an alternate model where movement is driven from circumferential contractile fibres, without any other potential mechanisms. In this model, we utilised a circumferential contractile fibre representation based on investigations into the movement of contractile fibres as an individual system, treated circumferential fibres as a series of units, and matched our model simulation to experimental geometries. By testing against laser ablation datasets sourced from existing literature, we found that circumferential fibres can reproduce the majority of cross-sectional movements. We also investigated model predictions related to various aspects of cross-sectional movement, providing insights into epithelium mechanics and demonstrating the usefulness of our modelling approach.

Vertex stability and topological transitions in vertex models of foams and epithelia

In computer simulations of dry foams and of epithelial tissues, vertex models are often used to describe the shape and motion of individual cells. Although these models have been widely adopted, relatively little is known about their basic theoretical properties. For example, while fourfold vertices in real foams are always unstable, it remains unclear whether a simplified vertex model description has the same behavior. Here, we study vertex stability and the dynamics of T1 topological transitions in vertex models. We show that, when all edges have the same tension, stationary fourfold vertices in these models do indeed always break up. In contrast, when tensions are allowed to depend on edge orientation, fourfold vertices can become stable, as is observed in some biological systems. More generally, our formulation of vertex stability leads to an improved treatment of T1 transitions in simulations and paves the way for studies of more biologically realistic models that couple topological transitions to the dynamics of regulatory proteins.

Inference of Internal Stress in a Cell Monolayer

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply Bayesian inversion stress microscopy to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi one-dimensional geometry.

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.

A toolbox to explore the mechanics of living embryonic tissues

The sculpting of embryonic tissues and organs into their functional morphologies involves the spatial and temporal regulation of mechanics at cell and tissue scales. Decades of in vitro work, complemented by some in vivo studies, have shown the relevance of mechanical cues in the control of cell behaviors that are central to developmental processes, but the lack of methodologies enabling precise, quantitative measurements of mechanical cues in vivo have hindered our understanding of the role of mechanics in embryonic development. Several methodologies are starting to enable quantitative studies of mechanics in vivo and in situ, opening new avenues to explore how mechanics contributes to shaping embryonic tissues and how it affects cell behavior within developing embryos. Here we review the present methodologies to study the role of mechanics in living embryonic tissues, considering their strengths and drawbacks as well as the conditions in which they are most suitable.

Measuring forces and stresses in situ in living tissues

Development, homeostasis and regeneration of tissues result from a complex combination of genetics and mechanics, and progresses in the former have been quicker than in the latter. Measurements of in situ forces and stresses appear to be increasingly important to delineate the role of mechanics in development. We review here several emerging techniques: contact manipulation, manipulation using light, visual sensors, and non-mechanical observation techniques. We compare their fields of applications, their advantages and limitations, and their validations. These techniques complement measurements of deformations and of mechanical properties. We argue that such approaches could have a significant impact on our understanding of the development of living tissues in the near future.

The organelle of differentiation in embryos: the cell state splitter

The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on "Embryogenesis Explained" (World Scientific Publishing, Singapore, 2016).

Unified quantitative characterization of epithelial tissue development

Understanding the mechanisms regulating development requires a quantitative characterization of cell divisions, rearrangements, cell size and shape changes, and apoptoses. We developed a multiscale formalism that relates the characterizations of each cell process to tissue growth and morphogenesis. Having validated the formalism on computer simulations, we quantified separately all morphogenetic events in the Drosophila dorsal thorax and wing pupal epithelia to obtain comprehensive statistical maps linking cell and tissue scale dynamics. While globally cell shape changes, rearrangements and divisions all significantly participate in tissue morphogenesis, locally, their relative participations display major variations in space and time. By blocking division we analyzed the impact of division on rearrangements, cell shape changes and tissue morphogenesis. Finally, by combining the formalism with mechanical stress measurement, we evidenced unexpected interplays between patterns of tissue elongation, cell division and stress. Our formalism provides a novel and rigorous approach to uncover mechanisms governing tissue development.

DOI:http://dx.doi.org/10.7554/eLife.08519.001

In animals, the final size and shape of each tissue is determined by the precise control of when, where and how much individual cells grow, divide, move and die. An important challenge in biology is to understand how the behaviors of each individual cell can act together to generate a large and reproducible change at the scale of entire tissues and organs. Here, Guirao et al. have developed a new approach to provide maps that reveal how much each cell process contributes to the development of tissues.

A caterpillar becoming a butterfly is a famous example of insect ‘metamorphosis’. The fruit fly offers another example of such tissue development: within five days, a rice grain-like maggot morphs into an adult fly with long antennae, legs and wings. Guirao et al. used a microscope to observe cells over a period of several hours during the metamorphosis of the adult fruit fly wings and thorax (the region between the neck and abdomen).

In both regions, Guirao et al. showed that all the cell processes participate in the formation of the adult tissue. Cell division, cell death, and changes in cell size affect the size of the tissue, while cell division, cell rearrangements, and changes in cell shape alter the shape of the tissue. The relative contributions of these cell processes varied a lot in both space and time. Further experiments then used mutant flies with defects in cell division to analyse the impact of cell division on the other cell processes and the eventual shape of the tissue. Finally, Guirao et al. showed that there are unexpected interactions between the patterns of tissue growth, cell division and the mechanical forces in the tissue.

These findings provide a new approach to uncover how animals from different species can have such a variety of shapes and sizes, even though they each start life as a single cell. Ultimately, this may also aid efforts to understand how certain diseases affect the development of tissues.

DOI:http://dx.doi.org/10.7554/eLife.08519.002

Mechanics of tissue compaction

During embryonic development, tissues deform by a succession and combination of morphogenetic processes. Tissue compaction is the morphogenetic process by which a tissue adopts a tighter structure. Recent studies characterized the respective roles of cells' adhesive and contractile properties in tissue compaction. In this review, we formalize the mechanical and molecular principles of tissue compaction and we analyze through the prism of this framework several morphogenetic events: the compaction of the early mouse embryo, the formation of the fly retina, the segmentation of somites and the separation of germ layers during gastrulation.

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.

Cell shapes and patterns as quantitative indicators of tissue stress in the plant epidermis

In a confluent, single-cell tissue layer, we show that cell shapes and statistics correlate directly with the tissue's mechanical properties, described by an energy functional with generic interfacial terms only. Upon increasing the cohesive component of the model, we observe a clear transition from a tense state with isotropic cells to a relaxed state with anisotropic cells. Signatures of the transition are present in the interfacial mechanics, the domain geometry, and the domain statistics, thus linking all three fields of study. This transition persists for all cell size distributions, but its exact position is crucially dependent on fluctuations in the parameter values of the functional (quenched disorder). The magnitude of fluctuations can be matched to the observed shape distribution of cells, so that visual observation of cell shapes and statistics provides information about the mechanical state of the tissue. Comparing with experimental data from the Cucumis epidermis, we find that the system is located right at the transition, allowing the tissue to relieve most of the local stress while maintaining integrity.

Robustness of force and stress inference in an epithelial tissue

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time (~minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.

Mechanical Forces and Growth in Animal Tissues

Mechanical forces shape biological tissues. They are the effectors of the developmental programs that orchestrate morphogenesis. A lot of effort has been devoted to understanding morphogenetic processes in mechanical terms. In this review, we focus on the interplay between tissue mechanics and growth. We first describe how tissue mechanics affects growth, by influencing the orientation of cell divisions and the signaling pathways that control the rate of volume increase and proliferation. We then address how the mechanical state of a tissue is affected by the patterns of growth. The forward and reverse interactions between growth and mechanics must be investigated in an integrative way if we want to understand how tissues grow and shape themselves. To illustrate this point, we describe examples in which growth homeostasis is achieved by feedback mechanisms that use mechanical forces.

Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model

Computational models of cell–cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell–cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. Keeping cell–cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force–inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature.

The mechanotransduction machinery at work at adherens junctions

The shaping of a multicellular body, and the maintenance and repair of adult tissues require fine-tuning of cell adhesion responses and the transmission of mechanical load between the cell, its neighbors and the underlying extracellular matrix. A growing field of research is focused on how single cells sense mechanical properties of their micro-environment (extracellular matrix, other cells), and on how mechanotransduction pathways affect cell shape, migration, survival as well as differentiation. Within multicellular assemblies, the mechanical load imposed by the physical properties of the environment is transmitted to neighboring cells. Force imbalance at cell-cell contacts induces essential morphogenetic processes such as cell-cell junction remodeling, cell polarization and migration, cell extrusion and cell intercalation. However, how cells respond and adapt to the mechanical properties of neighboring cells, transmit forces, and transform mechanical signals into chemical signals remain open questions. A defining feature of compact tissues is adhesion between cells at the specialized adherens junction (AJ) involving the cadherin super-family of Ca(2+)-dependent cell-cell adhesion proteins (e.g., E-cadherin in epithelia). Cadherins bind to the cytoplasmic protein β-catenin, which in turn binds to the filamentous (F)-actin binding adaptor protein α-catenin, which can also recruit vinculin, making the mechanical connection between cell-cell adhesion proteins and the contractile actomyosin cytoskeleton. The cadherin-catenin adhesion complex is a key component of the AJ, and contributes to cell assembly stability and dynamic cell movements. It has also emerged as the main route of propagation of forces within epithelial and non-epithelial tissues. Here, we discuss recent molecular studies that point toward force-dependent conformational changes in α-catenin that regulate protein interactions in the cadherin-catenin adhesion complex, and show that α-catenin is the core mechanosensor that allows cells to locally sense, transduce and adapt to environmental mechanical constrains.

Direct laser manipulation reveals the mechanics of cell contacts in vivo

Cell-generated forces produce a variety of tissue movements and tissue shape changes. The cytoskeletal elements that underlie these dynamics act at cell-cell and cell-ECM contacts to apply local forces on adhesive structures. In epithelia, force imbalance at cell contacts induces cell shape changes, such as apical constriction or polarized junction remodeling, driving tissue morphogenesis. The dynamics of these processes are well-characterized; however, the mechanical basis of cell shape changes is largely unknown because of a lack of mechanical measurements in vivo. We have developed an approach combining optical tweezers with light-sheet microscopy to probe the mechanical properties of epithelial cell junctions in the early Drosophila embryo. We show that optical trapping can efficiently deform cell-cell interfaces and measure tension at cell junctions, which is on the order of 100 pN. We show that tension at cell junctions equilibrates over a few seconds, a short timescale compared with the contractile events that drive morphogenetic movements. We also show that tension increases along cell interfaces during early tissue morphogenesis and becomes anisotropic as cells intercalate during germ-band extension. By performing pull-and-release experiments, we identify time-dependent properties of junctional mechanics consistent with a simple viscoelastic model. Integrating this constitutive law into a tissue-scale model, we predict quantitatively how local deformations propagate throughout the tissue.

Practical aspects of the cellular force inference toolkit (CellFIT)

If we are to fully understand the reasons that cells and tissues move and acquire their distinctive geometries during processes such as embryogenesis and wound healing, we will need detailed maps of the forces involved. One of the best current prospects for obtaining this information is noninvasive force-from-images techniques such as CellFIT, the Cellular Force Inference Toolkit, whose various steps are discussed here. Like other current quasistatic approaches, this one assumes that cell shapes are produced by interactions between interfacial tensions and intracellular pressures. CellFIT, however, allows cells to have curvilinear boundaries, which can significantly improve inference accuracy and reduce noise sensitivity. The quality of a CellFIT analysis depends on how accurately the junction angles and edge curvatures are measured, and a software tool we describe facilitates determination and evaluation of this information. Special attention is required when edges are crenulated or significantly different in shape from a circular arc. Because the tension and pressure equations are overdetermined, a select number of edges can be removed from the analysis, and these might include edges that are poorly defined in the source image, too short to provide accurate angles or curvatures, or noncircular. The approach works well for aggregates with as many as 1000 cells, and introduced errors have significant effects on only a few adjacent cells. An understanding of these considerations will help CellFIT users to get the most out of this promising new technique.

Bubbly vertex dynamics: A dynamical and geometrical model for epithelial tissues with curved cell shapes

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries

Mechanical forces play a key role in a wide range of biological processes, from embryogenesis to cancer metastasis, and there is considerable interest in the intuitive question, "Can cellular forces be inferred from cell shapes?" Although several groups have posited affirmative answers to this stimulating question, nagging issues remained regarding equation structure, solution uniqueness and noise sensitivity. Here we show that the mechanical and mathematical factors behind these issues can be resolved by using curved cell edges rather than straight ones. We present a new package of force-inference equations and assessment tools and denote this new package CellFIT, the Cellular Force Inference Toolkit. In this approach, cells in an image are segmented and equilibrium equations are constructed for each triple junction based solely on edge tensions and the limiting angles at which edges approach each junction. The resulting system of tension equations is generally overdetermined. As a result, solutions can be obtained even when a modest number of edges need to be removed from the analysis due to short length, poor definition, image clarity or other factors. Solving these equations yields a set of relative edge tensions whose scaling must be determined from data external to the image. In cases where intracellular pressures are also of interest, Laplace equations are constructed to relate the edge tensions, curvatures and cellular pressure differences. That system is also generally overdetermined and its solution yields a set of pressures whose offset requires reference to the surrounding medium, an open wound, or information external to the image. We show that condition numbers, residual analyses and standard errors can provide confidence information about the inferred forces and pressures. Application of CellFIT to several live and fixed biological tissues reveals considerable force variability within a cell population, significant differences between populations and elevated tensions along heterotypic boundaries.

Multiscale mathematical modeling and simulation of cellular dynamical process

Epidermal homeostasis is maintained by dynamic interactions among molecules and cells at different spatiotemporal scales. Mathematical modeling and simulation is expected to provide clear understanding and precise description of multiscaleness in tissue homeostasis under systems perspective. We introduce a stochastic process-based description of multiscale dynamics. Agent-based modeling as a framework of multiscale modeling to achieve consistent integration of definitive subsystems is proposed. A newly developed algorithm that particularly aims to perform stochastic simulations of cellular dynamical process is introduced. Finally we review applications of multiscale modeling and quantitative study to important aspects of epidermal and epithelial homeostasis.

The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing

Many epithelial tissues pack cells into a honeycomb pattern to support their structural and functional integrity. Developmental changes in cell packing geometry have been shown to be regulated by both mechanical and biochemical interactions between cells; however, it is largely unknown how molecular and cellular dynamics and tissue mechanics are orchestrated to realize the correct and robust development of hexagonal cell packing. Here, by combining mechanical and genetic perturbations along with live imaging and Bayesian force inference, we investigate how mechanical forces regulate cellular dynamics to attain a hexagonal cell configuration in the Drosophila pupal wing. We show that tissue stress is oriented towards the proximal-distal axis by extrinsic forces acting on the wing. Cells respond to tissue stretching and orient cell contact surfaces with the stretching direction of the tissue, thereby stabilizing the balance between the intrinsic cell junction tension and the extrinsic force at the cell-population level. Consequently, under topological constraints of the two-dimensional epithelial sheet, mismatches in the orientation of hexagonal arrays are suppressed, allowing more rapid relaxation to the hexagonal cell pattern. Thus, our results identify the mechanism through which the mechanical anisotropy in a tissue promotes ordering in cell packing geometry.