Active Tensile Modulus of an Epithelial Monolayer

3D Micropatterned Traction Force Microscopy: A Technique to Control 3D Cell Shape While Measuring Cell-Substrate Force Transmission

Cell shape and function are intimately linked, in a way that is mediated by the forces exerted between cells and their environment. The relationship between cell shape and forces has been extensively studied for cells seeded on flat 2D substrates, but not for cells in more physiological 3D settings. Here, a technique called 3D micropatterned traction force microscopy (3D-µTFM) to confine cells in 3D wells of defined shape, while simultaneously measuring the forces transmitted between cells and their microenvironment is demonstrated. This technique is based on the 3D micropatterning of polyacrylamide wells and on the calculation of 3D traction force from their deformation. With 3D-µTFM, it is shown that MCF10A breast epithelial cells exert defined, reproducible patterns of forces on their microenvironment, which can be both contractile and extensile. Cells switch from a global contractile to extensile behavior as their volume is reduced are further shown. The technique enables the quantitative study of cell mechanobiology with full access to 3D cellular forces while having accurate control over cell morphology and the mechanical conditions of the microenvironment.

Modelling of Tissue Invasion in Epithelial Monolayers

Mathematical and computational models are used to describe biomechanical processes in multicellular systems. Here, we develop a model to analyse how two types of epithelial cell layers interact during tissue invasion depending on their cellular properties, i.e., simulating cancer cells expanding into a region of normal cells. We model the tissue invasion process using the cellular Potts model and implement our two-dimensional computational simulations in the software package CompuCell3D. The model predicts that differences in mechanical properties of cells can lead to tissue invasion, even if the division rates and death rates of the two cell types are the same. We also show how the invasion speed varies depending on the cell division and death rates and the mechanical properties of the cells.

Supracellular measurement of spatially varying mechanical heterogeneities in live monolayers

The mechanical properties of tissues have profound impacts on a wide range of biological processes such as embryo development (1,2), wound healing (3-6), and disease progression (7). Specifically, the spatially varying moduli of cells largely influence the local tissue deformation and intercellular interaction. Despite the importance of characterizing such a heterogeneous mechanical property, it has remained difficult to measure the supracellular modulus field in live cell layers with a high-throughput and minimal perturbation. In this work, we developed a monolayer effective modulus measurement by integrating a custom cell stretcher, light microscopy, and AI-based inference. Our approach first quantifies the heterogeneous deformation of a slightly stretched cell layer and converts the measured strain fields into an effective modulus field using an AI inference. This method allowed us to directly visualize the effective modulus distribution of thousands of cells virtually instantly. We characterized the mean value, SD, and correlation length of the effective cell modulus for epithelial cells and fibroblasts, which are in agreement with previous results. We also observed a mild correlation between cell area and stiffness in jammed epithelia, suggesting the influence of cell modulus on packing. Overall, our reported experimental platform provides a valuable alternative cell mechanics measurement tool that can be integrated with microscopy-based characterizations.

Mapping cell cortex rheology to tissue rheology and vice versa

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

Self-assembly of tessellated tissue sheets by expansion and collision

Tissues do not exist in isolation—they interact with other tissues within and across organs. While cell-cell interactions have been intensely investigated, less is known about tissue-tissue interactions. Here, we studied collisions between monolayer tissues with different geometries, cell densities, and cell types. First, we determine rules for tissue shape changes during binary collisions and describe complex cell migration at tri-tissue boundaries. Next, we propose that genetically identical tissues displace each other based on pressure gradients, which are directly linked to gradients in cell density. We present a physical model of tissue interactions that allows us to estimate the bulk modulus of the tissues from collision dynamics. Finally, we introduce TissEllate, a design tool for self-assembling complex tessellations from arrays of many tissues, and we use cell sheet engineering techniques to transfer these composite tissues like cellular films. Overall, our work provides insight into the mechanics of tissue collisions, harnessing them to engineer tissue composites as designable living materials.

Tissue boundaries in our body separate organs and enable healing, but boundary mechanics are not well known. Here, the authors define mechanical rules for colliding cell monolayers and use these rules to make complex, predictable tessellations.

Linear viscoelastic properties of the vertex model for epithelial tissues

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

Modelling the Collective Mechanical Regulation of the Structure and Morphology of Epithelial Cell Layers

The morphology and function of epithelial sheets play an important role in healthy tissue development and cancer progression. The maintenance of structure of closely packed epithelial layers requires the coordination of various mechanical forces due to intracellular activities and interactions with other cells and tissues. However, a general model for the combination of mechanical properties which determine the cell shape and the overall structure of epithelial layers remains elusive. Here, we propose a computational model, based on the Cellular Potts Model, to analyse the interplay between mechanical properties of cells and dynamical transitions in epithelial cell shapes and structures. We map out phase diagrams as functions of cellular properties and the orientation of cell division. Results show that monolayers of squamous, cuboidal, and columnar cells are formed when the axis of cell proliferation is perpendicular to the substrate or along the major axis of the cells. Monolayer-to-multilayer transition is promoted via cell extrusion, depending on the mechanical properties of cells and the orientation of cell division. The results and model predictions are discussed in the context of experimental observations.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Coordination of contractile tension and cell area changes in an epithelial cell monolayer

During tissue development and repair, cells contract and expand in coordination with their neighbors, giving rise to tissue deformations that occur on length scales far larger than that of a single cell. The biophysical mechanisms by which the contractile forces of each cell cause deformations on multicellular length scales are not fully clear. To investigate this question, we began with the principle of force equilibrium, which dictates a balance of tensile forces between neighboring cells. Based on this principle, we hypothesized that coordinated changes in cell area result from tension transmitted across the cell layer. To test this hypothesis, spatial correlations of both contractile tension and the divergence of cell velocities were measured as readouts of coordinated contractility and collective area changes, respectively. Experiments were designed to alter the spatial correlation of contractile tension using three different methods, including disrupting cell-cell adhesions, modulating the alignment of actomyosin stress fibers between neighboring cells, and changing the size of the cell monolayer. In all experiments, the spatial correlations of both tension and divergence increased or decreased together, in agreement with our hypothesis. To relate our findings to the intracellular mechanism connecting changes in cell area to contractile tension, we disrupted activation of extracellular signal-regulated kinase (ERK), which is known to mediate the intracellular relationship between cell area and contraction. Consistent with prior knowledge, a temporal cross-correlation between cell area and tension revealed that ERK was responsible for a proportional relationship between cell area and contraction. Inhibition of ERK activation reduced the spatial correlations of the divergence of cell velocity but not of tension. Together, our findings suggest that coordination of cell contraction and expansion requires transfer of cell tension over space and ERK-mediated coordination between cell area and contraction in time.

Integer topological defects of cell monolayers: Mechanics and flows

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.

Reversible elastic phase field approach and application to cell monolayers

Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells.

Migrating Epithelial Monolayer Flows Like a Maxwell Viscoelastic Liquid

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby canine kidney epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbor rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation, and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behavior (and not with a Kelvin-Voigt viscoelastic solid behavior). The value of the associated relaxation time is measured as τ=70±15  min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration.

Tug-of-war between stretching and bending in living cell sheets

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as monolayer stress microscopy (MSM) was suggested from which intercellular stresses could be computed for a given traction field. The core assumption of MSM is that intercellular stresses within the monolayer obey a linear and passive constitutive law. Examples of these include a Hookean solid (an elastic sheet) or a Newtonian fluid (thin fluid film), which imply a specific relation between the displacements or velocities and the tractions. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by a linear passive MSM model is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell-substrate tractions. Using the same assumptions as those underlying MSM, namely, a linear and passive constitutive law, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. Since the classical MSM and the Stokes approach both depend on the linear and passive constitutive law, it follows that some serious modification of the underling rheology is needed. One possible modification is the inclusion of an active force. In the special case where this is additive to the linear passive rheology, we have a new relationship between the active force density and the measured velocity (or displacement) field and tractions, which by Newton's laws, must be obeyed.

Multiscale modelling of motility wave propagation in cell migration

The collective motion of cell monolayers within a tissue is a fundamental biological process that occurs during tissue formation, wound healing, cancerous invasion, and viral infection. Experiments have shown that at the onset of migration, the motility is self-generated as a polarisation wave starting from the leading edge of the monolayer and progressively propagates into the bulk. However, it is unclear how the propagation of this motility wave is influenced by cellular properties. Here, we investigate this question using a computational model based on the Potts model coupled to the dynamics of intracellular polarisation. The model captures the propagation of the polarisation wave and suggests that the cells cortex can regulate the migration modes: strongly contractile cells may depolarise the monolayer, whereas less contractile cells can form swirling movement. Cortical contractility is further found to limit the cells motility, which (i) decelerates the wave speed and the leading edge progression, and (ii) destabilises the leading edge. Together, our model describes how different mechanical properties of cells can contribute to the regulation of collective cell migration.

Oriented Active Solids

We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.

Surface and Bulk Stresses Drive Morphological Changes in Fibrous Microtissues

Engineered fibrous tissues consisting of cells encapsulated within collagen gels are widely used three-dimensional in vitro models of morphogenesis and wound healing. Although cell-mediated matrix remodeling that occurs within these scaffolds has been extensively studied, less is known about the mesoscale physical principles governing the dynamics of tissue shape. Here, we show both experimentally and by using computer simulations how surface contraction through the development of surface stresses (analogous to surface tension in fluids) coordinates with bulk contraction to drive shape evolution in constrained three-dimensional microtissues. We used microelectromechanical systems technology to generate arrays of fibrous microtissues and robot-assisted microsurgery to perform local incisions and implantation. We introduce a technique based on phototoxic activation of a small molecule to selectively kill cells in a spatially controlled manner. The model simulations, which reproduced the experimentally observed shape changes after surgical and photochemical operations, indicate that fitting of only bulk and surface contractile moduli is sufficient for the prediction of the equilibrium shape of the microtissues. The computational and experimental methods we have developed provide a general framework to study and predict the morphogenic states of contractile fibrous tissues under external loading at multiple length scales.

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

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

Active Fingering Instability in Tissue Spreading

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

Curvature-dependent constraints drive remodeling of epithelia

Epithelial tissues function as barriers that separate the organism from the environment. They usually have highly curved shapes, such as tubules or cysts. However, the processes by which the geometry of the environment and the cell's mechanical properties set the epithelium shape are not yet known. In this study, we encapsulated two epithelial cell lines, MDCK and J3B1A, into hollow alginate tubes and grew them under cylindrical confinement forming a complete monolayer. MDCK monolayers detached from the alginate shell at a constant rate, whereas J3B1A monolayers detached at a low rate unless the tube radius was reduced. We showed that this detachment is driven by contractile stresses in the epithelium and can be enhanced by local curvature. This allows us to conclude that J3B1A cells exhibit smaller contractility than MDCK cells. Monolayers inside curved tubes detach at a higher rate on the outside of a curve, confirming that detachment is driven by contraction.

Continuum Models of Collective Cell Migration

Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.

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.

Active superelasticity in three-dimensional epithelia of controlled shape

Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour-which we term active superelasticity-that enables epithelial sheets to sustain extreme stretching under constant tension.

Collective cell migration without proliferation: density determines cell velocity and wave velocity

Collective cell migration contributes to embryogenesis, wound healing and tumour metastasis. Cell monolayer migration experiments help in understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length scales and time scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers, which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation.

Inverse tissue mechanics of cell monolayer expansion

Living tissues undergo deformation during morphogenesis. In this process, cells generate mechanical forces that drive the coordinated cell motion and shape changes. Recent advances in experimental and theoretical techniques have enabled in situ measurement of the mechanical forces, but the characterization of mechanical properties that determine how these forces quantitatively affect tissue deformation remains challenging, and this represents a major obstacle for the complete understanding of morphogenesis. Here, we proposed a non-invasive reverse-engineering approach for the estimation of the mechanical properties, by combining tissue mechanics modeling and statistical machine learning. Our strategy is to model the tissue as a continuum mechanical system and to use passive observations of spontaneous tissue deformation and force fields to statistically estimate the model parameters. This method was applied to the analysis of the collective migration of Madin-Darby canine kidney cells, and the tissue flow and force were simultaneously observed by the phase contrast imaging and traction force microscopy. We found that our monolayer elastic model, whose elastic moduli were reverse-engineered, enabled a long-term forecast of the traction force fields when given the tissue flow fields, indicating that the elasticity contributes to the evolution of the tissue stress. Furthermore, we investigated the tissues in which myosin was inhibited by blebbistatin treatment, and observed a several-fold reduction in the elastic moduli. The obtained results validate our framework, which paves the way to the estimation of mechanical properties of living tissues during morphogenesis.

In order to shape the body of a multicellular organism, cells generate mechanical forces and undergo deformation. Although these forces are being increasingly determined, quantitative characterization of the relation between the deformation and forces at the tissue level remains challenging. To estimate these properties, we developed a reverse-engineering method by combining tissue mechanics modeling and statistical machine learning, and then tested this method on a common model system, the expansion of cultured cell monolayer. This statistically sound framework uses the passive observations of spontaneous deformation and force dynamics in tissues, and enables us to elucidate unperturbed mechanical processes underlying morphogenesis.

Mechanical stress as a regulator of cell motility

The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can symmetrize and arrest moving cells. We show further that sufficiently strong squeezing can lead to the loss of cell integrity. The overall behavior of the system depends on the two dimensionless parameters characterizing internal driving (chemical activity) and external loading (applied stress). We construct a phase diagram in this parameter space distinguishing between static, motile, and collapsed states. The obtained results are relevant for the mechanical understanding of contact inhibition and the epithelial-to-mesenchymal transition.

Jamming transitions in cancer

The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patients.

Emergence of epithelial cell density waves

Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.

Hydrodynamic instabilities, waves and turbulence in spreading epithelia

We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.

Endogenous Sheet-Averaged Tension Within a Large Epithelial Cell Colony

Epithelial cells form quasi-two-dimensional sheets that function as contractile media to effect tissue shape changes during development and homeostasis. Endogenously generated intrasheet tension is a driver of such changes, but has predominantly been measured in the presence of directional migration. The nature of epithelial cell-generated forces transmitted over supracellular distances, in the absence of directional migration, is thus largely unclear. In this report, we consider large epithelial cell colonies which are archetypical multicell collectives with extensive cell-cell contacts but with a symmetric (circular) boundary. Using the traction force imbalance method (TFIM) (traction force microscopy combined with physical force balance), we first show that one can determine the colony-level endogenous sheet forces exerted at the midline by one half of the colony on the other half with no prior assumptions on the uniformity of the mechanical properties of the cell sheet. Importantly, we find that this colony-level sheet force exhibits large variations with orientation-the difference between the maximum and minimum sheet force is comparable to the average sheet force itself. Furthermore, the sheet force at the colony midline is largely tensile but the shear component exhibits significantly more variation with orientation. We thus show that even an unperturbed epithelial colony with a symmetric boundary shows significant directional variation in the endogenous sheet tension and shear forces that subsist at the colony level.

Actomyosin contractility and collective migration: may the force be with you

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Collective migration relies on the ability of a multicellular co-ordinated unit to efficiently respond to physical changes in their surrounding matrix.

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Conversely, migrating cohorts physically alter their microenvironment using mechanical forces.

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During collective migration, actomyosin contractility acts as a central hub coordinating mechanosensing and mechanotransduction responses.

Collective cell migration is essential during physiological processes such as development or wound healing and in pathological conditions such as cancer dissemination. Cells migrating within multicellular tissues experiment different forces which play an intricate role during tissue formation, development and maintenance. How cells are able to respond to these forces depends largely on how they interact with the extracellular matrix. In this review, we focus on mechanics and mechanotransduction in collective migration. In particular, we discuss current knowledge on how cells integrate mechanical signals during collective migration and we highlight actomyosin contractility as a central hub coordinating mechanosensing and mechanotransduction responses.

Single and collective cell migration: the mechanics of adhesions

Chemical and physical properties of the environment control cell proliferation, differentiation, or apoptosis in the long term. However, to be able to move and migrate through a complex three-dimensional environment, cells must quickly adapt in the short term to the physical properties of their surroundings. Interactions with the extracellular matrix (ECM) occur through focal adhesions or hemidesmosomes via the engagement of integrins with fibrillar ECM proteins. Cells also interact with their neighbors, and this involves various types of intercellular adhesive structures such as tight junctions, cadherin-based adherens junctions, and desmosomes. Mechanobiology studies have shown that cell-ECM and cell-cell adhesions participate in mechanosensing to transduce mechanical cues into biochemical signals and conversely are responsible for the transmission of intracellular forces to the extracellular environment. As they migrate, cells use these adhesive structures to probe their surroundings, adapt their mechanical properties, and exert the appropriate forces required for their movements. The focus of this review is to give an overview of recent developments showing the bidirectional relationship between the physical properties of the environment and the cell mechanical responses during single and collective cell migration.

Cellular Contraction and Polarization Drive Collective Cellular Motion

Coordinated motions of close-packed multicellular systems typically generate cooperative packs, swirls, and clusters. These cooperative motions are driven by active cellular forces, but the physical nature of these forces and how they generate collective cellular motion remain poorly understood. Here, we study forces and motions in a confined epithelial monolayer and make two experimental observations: 1) the direction of local cellular motion deviates systematically from the direction of the local traction exerted by each cell upon its substrate; and 2) oscillating waves of cellular motion arise spontaneously. Based on these observations, we propose a theory that connects forces and motions using two internal state variables, one of which generates an effective cellular polarization, and the other, through contractile forces, an effective cellular inertia. In agreement with theoretical predictions, drugs that inhibit contractility reduce both the cellular effective elastic modulus and the frequency of oscillations. Together, theory and experiment provide evidence suggesting that collective cellular motion is driven by at least two internal variables that serve to sustain waves and to polarize local cellular traction in a direction that deviates systematically from local cellular velocity.

Spatiotemporally Controlled Mechanical Cues Drive Progenitor Mesenchymal-to-Epithelial Transition Enabling Proper Heart Formation and Function

During early cardiogenesis, bilateral fields of mesenchymal heart progenitor cells (HPCs) move from the anterior lateral plate mesoderm to the ventral midline, undergoing a mesenchymal-to-epithelial transition (MET) en route to forming a single epithelial sheet. Through tracking of tissue-level deformations in the heart-forming region (HFR) as well as movement trajectories and traction generation of individual HPCs, we find that the onset of MET correlates with a peak in mechanical stress within the HFR and changes in HPC migratory behaviors. Small-molecule inhibitors targeting actomyosin contractility reveal a temporally specific requirement of bulk tissue compliance to regulate heart development and MET. Targeting mutant constructs to modulate contractility and compliance in the underlying endoderm, we find that MET in HPCs can be accelerated in response to microenvironmental stiffening and can be inhibited by softening. To test whether MET in HPCs was responsive to purely physical mechanical cues, we mimicked a high-stress state by injecting an inert oil droplet to generate high strain in the HFR, demonstrating that exogenously applied stress was sufficient to drive MET. MET-induced defects in anatomy result in defined functional lesions in the larval heart, implicating mechanical signaling and MET in the etiology of congenital heart defects. From this integrated analysis of HPC polarity and mechanics, we propose that normal heart development requires bilateral HPCs to undergo a critical behavioral and phenotypic transition on their way to the ventral midline, and that this transition is driven in response to the changing mechanical properties of their endoderm substrate.

Binding of ZO-1 to α5β1 integrins regulates the mechanical properties of α5β1-fibronectin links

Fundamental processes in cell adhesion, motility, and rigidity adaptation are regulated by integrin-mediated adhesion to the extracellular matrix (ECM). The link between the ECM component fibronectin (fn) and integrin α5β1 forms a complex with ZO-1 in cells at the edge of migrating monolayers, regulating cell migration. However, how this complex affects the α5β1-fn link is unknown. Here we show that the α5β1/ZO-1 complex decreases the resistance to force of α5β1-fn adhesions located at the edge of migrating cell monolayers while also increasing α5β1 recruitment. Consistently with a molecular clutch model of adhesion, this effect of ZO-1 leads to a decrease in the density and intensity of adhesions in cells at the edge of migrating monolayers. Taken together, our results unveil a new mode of integrin regulation through modification of the mechanical properties of integrin-ECM links, which may be harnessed by cells to control adhesion and migration.

Effective viscosity and dynamics of spreading epithelia: a solvable model

Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

Emergent structures and dynamics of cell colonies by contact inhibition of locomotion

Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing tissue phenotypes. These include regular distributions of cells, dynamic cell clusters, gel-like networks, collectively migrating monolayers, and 3D aggregates. We give analytical predictions for transitions between noncohesive, cohesive, and 3D cell arrangements. We explicitly show how CIL yields an effective repulsion that promotes cell dispersal, thereby hindering the formation of cohesive tissues. Yet, in continuous monolayers, CIL leads to collective cell motion, ensures tensile intercellular stresses, and opposes cell extrusion. Thus, our work highlights the prominent role of CIL in determining the emergent structures and dynamics of cell colonies.

Collective migration and cell jamming in asthma, cancer and development

Collective cellular migration within the epithelial layer impacts upon development, wound healing and cancer invasion, but remains poorly understood. Prevailing conceptual frameworks tend to focus on the isolated role of each particular underlying factor - taken one at a time or at most a few at a time - and thus might not be tailored to describe a cellular collective that embodies a wide palette of physical and molecular interactions that are both strong and complex. To bridge this gap, we shift the spotlight to the emerging concept of cell jamming, which points to only a small set of parameters that govern when a cellular collective might jam and rigidify like a solid, or instead unjam and flow like a fluid. As gateways to cellular migration, the unjamming transition (UJT) and the epithelial-to-mesenchymal transition (EMT) share certain superficial similarities, but their congruence - or lack thereof - remains unclear. In this Commentary, we discuss aspects of cell jamming, its established role in human epithelial cell layers derived from the airways of non-asthmatic and asthmatic donors, and its speculative but emerging roles in development and cancer cell invasion.

Strain Stiffening of Fibrillar Collagen during Individual and Collective Cell Migration Identified by AFM Nanoindentation

The multistep process of cell migration requires cells to dynamically couple to extracellular interfaces and generate traction force or friction for displacement of the cell body. When deformed, biopolymer networks, including fibrillar collagen and fibrin, undergo a nonlinear elasticity change that is termed strain stiffening and is commonly measured by bulk rheology. It remains poorly characterized, however, whether forces generated by moving cells suffice to induce strain stiffening. To detect strain stiffening at the leading edge of normal and tumor cells moving across fibrillar type I collagen, we combined AFM nanoindentation and differential field probing with confocal reflection microscopy. In different cell models, gradient-like fiber realignment, densification, and elevation of Young's modulus ahead of the leading edge were observed, with peak increases of up to 1.15 kPa near the leading edge. Moving fibroblasts generated a larger anterograde strain field with a higher amplitude and up to 6-fold increased cumulative strain stiffening (52 kPa) compared with mesenchymal HT1080 fibrosarcoma cells (8.8 kPa) and epithelial SCC38 cancer cells (9.8 kPa). Collectively moving SCC38 cells produced 4-fold increased cumulative strain stiffening (38 kPa) compared with individually moving SCC38 cells in a β1 integrin- and actomyosin-dependent manner. This indicates that the extent of strain stiffening by the leading edge of moving cells scales with cell type, multicellular cooperativity, integrin availability, and contractility. By straining, migrating cells realign and densify fibrillar extracellular matrix and thus adopt an autonomous strategy to move on a "traveling wave" of stiffened substrate, which reaches levels sufficient for mechanosensory activation and self-steering of migration.