Mechanobiology of collective cell behaviours.

The way in which cells coordinate their behaviours during various biological processes, including morphogenesis, cancer progression and tissue remodelling, largely depends on the mechanical properties of the external environment. In contrast to single cells, collective cell behaviours rely on the cellular interactions not only with the surrounding extracellular matrix but also with neighbouring cells. Collective dynamics is not simply the result of many individually moving blocks. Instead, cells coordinate their movements by actively interacting with each other. These mechanisms are governed by mechanosensitive adhesion complexes at the cell-substrate interface and cell-cell junctions, which respond to but also further transmit physical signals. The mechanosensitivity and mechanotransduction at adhesion complexes are important for regulating tissue cohesiveness and thus are important for collective cell behaviours. Recent studies have shown that the physical properties of the cellular environment, which include matrix stiffness, topography, geometry and the application of external forces, can alter collective cell behaviours, tissue organization and cell-generated forces. On the basis of these findings, we can now start building our understanding of the mechanobiology of collective cell movements that span over multiple length scales from the molecular to the tissue level.

Deposited footprints let cells switch between confined, oscillatory, and exploratory migration.

For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.

A minimal physical model for curvotaxis driven by curved protein complexes at the cell's leading edge.

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

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.

Polarization and motility of one-dimensional multi-cellular trains.

Collective cell migration, whereby cells adhere to form multi-cellular clusters that move as a single entity, play an important role in numerous biological processes, such as during development and cancer progression. Recent experimental work focused on migration of one-dimensional cellular clusters, confined to move along adhesive lanes, as a simple geometry in which to systematically study this complex system. One-dimensional migration also arises in the body when cells migrate along blood vessels, axonal projections, and narrow cavities between tissues. We explore here the modes of one-dimensional migration of cellular clusters ("trains") by implementing cell-cell interactions in a model of cell migration that contains a mechanism for spontaneous cell polarization. We go beyond simple phenomenological models of the cells as self-propelled particles by having the internal polarization of each cell depend on its interactions with the neighboring cells that directly affect the actin polymerization activity at the cell's leading edges. Both contact inhibition of locomotion and cryptic lamellipodia interactions between neighboring cells are introduced. We find that this model predicts multiple motility modes of the cell trains, which can have several different speeds for the same polarization pattern. Compared to experimental data, we find that Madin-Darby canine kidney cells are poised along the transition region where contact inhibition of locomotion and cryptic lamellipodia roughly balance each other, where collective migration speed is most sensitive to the values of the cell-cell interaction strength.

Topological defects in epithelia govern cell death and extrusion.

Epithelial tissues (epithelia) remove excess cells through extrusion, preventing the accumulation of unnecessary or pathological cells. The extrusion process can be triggered by apoptotic signalling, oncogenic transformation and overcrowding of cells. Despite the important linkage of cell extrusion to developmental, homeostatic and pathological processes such as cancer metastasis, its underlying mechanism and connections to the intrinsic mechanics of the epithelium are largely unexplored. We approach this problem by modelling the epithelium as an active nematic liquid crystal (that has a long range directional order), and comparing numerical simulations to strain rate and stress measurements within monolayers of MDCK (Madin Darby canine kidney) cells. Here we show that apoptotic cell extrusion is provoked by singularities in cell alignments in the form of comet-shaped topological defects. We find a universal correlation between extrusion sites and positions of nematic defects in the cell orientation field in different epithelium types. The results confirm the active nematic nature of epithelia, and demonstrate that defect-induced isotropic stresses are the primary precursors of mechanotransductive responses in cells, including YAP (Yes-associated protein) transcription factor activity, caspase-3-mediated cell death, and extrusions. Importantly, the defect-driven extrusion mechanism depends on intercellular junctions, because the weakening of cell-cell interactions in an α-catenin knockdown monolayer reduces the defect size and increases both the number of defects and extrusion rates, as is also predicted by our model. We further demonstrate the ability to control extrusion hotspots by geometrically inducing defects through microcontact printing of patterned monolayers. On the basis of these results, we propose a mechanism for apoptotic cell extrusion: spontaneously formed topological defects in epithelia govern cell fate. This will be important in predicting extrusion hotspots and dynamics in vivo, with potential applications to tissue regeneration and the suppression of metastasis. Moreover, we anticipate that the analogy between the epithelium and active nematic liquid crystals will trigger further investigations of the link between cellular processes and the material properties of epithelia.

Cell response to substrate rigidity is regulated by active and passive cytoskeletal stress.

Morphogenesis, tumor formation, and wound healing are regulated by tissue rigidity. Focal adhesion behavior is locally regulated by stiffness; however, how cells globally adapt, detect, and respond to rigidity remains unknown. Here, we studied the interplay between the rheological properties of the cytoskeleton and matrix rigidity. We seeded fibroblasts onto flexible microfabricated pillar arrays with varying stiffness and simultaneously measured the cytoskeleton organization, traction forces, and cell-rigidity responses at both the adhesion and cell scale. Cells adopted a rigidity-dependent phenotype whereby the actin cytoskeleton polarized on stiff substrates but not on soft. We further showed a crucial role of active and passive cross-linkers in rigidity-sensing responses. By reducing myosin II activity or knocking down α-actinin, we found that both promoted cell polarization on soft substrates, whereas α-actinin overexpression prevented polarization on stiff substrates. Atomic force microscopy indentation experiments showed that this polarization response correlated with cell stiffness, whereby cell stiffness decreased when active or passive cross-linking was reduced and softer cells polarized on softer matrices. Theoretical modeling of the actin network as an active gel suggests that adaptation to matrix rigidity is controlled by internal mechanical properties of the cytoskeleton and puts forward a universal scaling between nematic order of the actin cytoskeleton and the substrate-to-cell elastic modulus ratio. Altogether, our study demonstrates the implication of cell-scale mechanosensing through the internal stress within the actomyosin cytoskeleton and its coupling with local rigidity sensing at focal adhesions in the regulation of cell shape changes and polarity.

Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers.

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell-substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.

Direct measurement of near-nano-Newton forces developed by self-organizing actomyosin fibers bound α-catenin.

BACKGROUND INFORMATION: Actin cytoskeleton contractility plays a critical role in morphogenetic processes by generating forces that are then transmitted to cell-cell and cell-ECM adhesion complexes. In turn, mechanical properties of the environment are sensed and transmitted to the cytoskeleton at cell adhesion sites, influencing cellular processes such as cell migration, differentiation and survival. Anchoring of the actomyosin cytoskeleton to adhesion sites is mediated by adaptor proteins such as talin or α-catenin that link F-actin to transmembrane cell adhesion receptors, thereby allowing mechanical coupling between the intracellular and extracellular compartments. Thus, a key issue is to be able to measure the forces generated by actomyosin and transmitted to the adhesion complexes. Approaches developed in cells and those probing single molecule mechanical properties of α-catenin molecules allowed to identify α-catenin, an F-actin binding protein which binds to the cadherin complexes as a major player in cadherin-based mechanotransduction. However, it is still very difficult to bridge intercellular forces measured at cellular levels and those measured at the single-molecule level. RESULTS: Here, we applied an intermediate approach allowing reconstruction of the actomyosin-α-catenin complex in acellular conditions to probe directly the transmitted forces. For this, we combined micropatterning of purified α-catenin and spontaneous actomyosin network assembly in the presence of G-actin and Myosin II with microforce sensor arrays used so far to measure cell-generated forces. CONCLUSIONS: Using this method, we show that self-organizing actomyosin bundles bound to micrometric α-catenin patches can apply near-nano-Newton forces. SIGNIFICANCE: Our results pave the way for future studies on molecular/cellular mechanotransduction and mechanosensing.

Mechanical forces in cell monolayers.

In various physiological processes, the cell collective is organized in a monolayer, such as seen in a simple epithelium. The advances in the understanding of mechanical behavior of the monolayer and its underlying cellular and molecular mechanisms will help to elucidate the properties of cell collectives. In this Review, we discuss recent in vitro studies on monolayer mechanics and their implications on collective dynamics, regulation of monolayer mechanics by physical confinement and geometrical cues and the effect of tissue mechanics on biological processes, such as cell division and extrusion. In particular, we focus on the active nematic property of cell monolayers and the emerging approach to view biological systems in the light of liquid crystal theory. We also highlight the mechanosensing and mechanotransduction mechanisms at the sub-cellular and molecular level that are mediated by the contractile actomyosin cytoskeleton and cell-cell adhesion proteins, such as E-cadherin and α-catenin. To conclude, we argue that, in order to have a holistic understanding of the cellular response to biophysical environments, interdisciplinary approaches and multiple techniques - from large-scale traction force measurements to molecular force protein sensors - must be employed.

A subtle relationship between substrate stiffness and collective migration of cell clusters.

The physical cues from the extracellular environment mediates cell signaling spatially and temporally. Cells respond to physical cues from their environment in a non-monotonic fashion. Despite our understanding of the role of substrate rigidity on single cell migration, how cells respond collectively to increasing extracellular matrix stiffness is not well established. Here we patterned multicellular epithelial Madin-Darby canine kidney (MDCK) islands on polyacrylamide gels of varying stiffness and studied their expansion. Our findings show that the MDCK islands expanded faster with increasing stiffness only up to an optimum stiffness, over which the expansion plateaued. We then focused on the expansion of the front of the assemblies and the formation of leader cells. We observed cell front destabilization only above substrate stiffness of a few kPa. The extension of multicellular finger-like structures at the edges of the colonies for intermediate and high stiffnesses from 6 to 60 kPa responded to higher substrate stiffness by increasing focal adhesion areas and actin cable assembly. Additionally, the number of leader cells at the finger-like protrusions increased with stiffness in correlation with an increase of the area of these multicellular protrusions. Consequently, the force profile along the epithelial fingers in the parallel and transverse directions of migration showed an unexpected relationship leading to a global force decrease with the increase of stiffness. Taken together, our findings show that epithelial cell colonies respond to substrate stiffness but in a non-trivial manner that may be of importance to understand morphogenesis and collective cell invasion during tumour progression.

Sustained Oscillations of Epithelial Cell Sheets.

Morphological changes during development, tissue repair, and disease largely rely on coordinated cell movements and are controlled by the tissue environment. Epithelial cell sheets are often subjected to large-scale deformation during tissue formation. The active mechanical environment in which epithelial cells operate have the ability to promote collective oscillations, but how these cellular movements are generated and relate to collective migration remains unclear. Here, combining in vitro experiments and computational modeling, we describe a form of collective oscillations in confined epithelial tissues in which the oscillatory motion is the dominant contribution to the cellular movements. We show that epithelial cells exhibit large-scale coherent oscillations when constrained within micropatterns of varying shapes and sizes and that their period and amplitude are set by the smallest confinement dimension. Using molecular perturbations, we then demonstrate that force transmission at cell-cell junctions and its coupling to cell polarity are pivotal for the generation of these collective movements. We find that the resulting tissue deformations are sufficient to trigger osillatory mechanotransduction of YAP within cells, potentially affecting a wide range of cellular processes.

Influence of proliferation on the motions of epithelial monolayers invading adherent strips.

Biological systems integrate dynamics at many scales, from molecules, protein complexes and genes, to cells, tissues and organisms. At every step of the way, mechanics, biochemistry and genetics offer complementary approaches to understand these dynamics. At the tissue scale, in vitro monolayers of epithelial cells provide a model to capture the influence of various factors on the motions of the tissue, in order to understand in vivo processes from morphogenesis, cancer progression and tissue remodelling. Ongoing efforts include research aimed at deciphering the roles of the cytoskeleton, of cell-substrate and cell-cell adhesions, and of cell proliferation-the point we investigate here. We show that confined to adherent strips, and on the time scale of a day or two, monolayers move with a characteristic front speed independent of proliferation, but that the motion is accompanied by persistent velocity waves, only in the absence of cell divisions. Here we show that the long-range transmission of physical signals is strongly coupled to cell density and proliferation. We interpret our results from a kinematic and mechanical perspective. Our study provides a framework to understand density-driven mechanisms of collective cell migration.

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.

Coordination between Intra- and Extracellular Forces Regulates Focal Adhesion Dynamics.

Focal adhesions (FAs) are important mediators of cell-substrate interactions. One of their key functions is the transmission of forces between the intracellular acto-myosin network and the substrate. However, the relationships between cell traction forces, FA architecture, and molecular forces within FAs are poorly understood. Here, by combining Förster resonance energy transfer (FRET)-based molecular force biosensors with micropillar-based traction force sensors and high-resolution fluorescence microscopy, we simultaneously map molecular tension across vinculin, a key protein in FAs, and traction forces at FAs. Our results reveal strong spatiotemporal correlations between vinculin tension and cell traction forces at FAs throughout a wide range of substrate stiffnesses. Furthermore, we find that molecular tension within individual FAs follows a biphasic distribution from the proximal (toward the cell nucleus) to distal end (toward the cell edge). Using super-resolution imaging, we show that such a distribution relates to that of FA proteins. On the basis of our experimental data, we propose a model in which FA dynamics results from tension changes along the FAs.

Modeling collective cell migration in geometric confinement.

Monolayer expansion has generated great interest as a model system to study collective cell migration. During such an expansion the culture front often develops 'fingers', which we have recently modeled using a proposed feedback between the curvature of the monolayer's leading edge and the outward motility of the edge cells. We show that this model is able to explain the puzzling observed increase of collective cellular migration speed of a monolayer expanding into thin stripes, as well as describe the behavior within different confining geometries that were recently observed in experiments. These comparisons give support to the model and emphasize the role played by the edge cells and the edge shape during collective cell motion.

Actomyosin bundles serve as a tension sensor and a platform for ERK activation.

Tensile forces generated by stress fibers drive signal transduction events at focal adhesions. Here, we report that stress fibers per se act as a platform for tension-induced activation of biochemical signals. The MAP kinase, ERK is activated on stress fibers in a myosin II-dependent manner. In myosin II-inhibited cells, uniaxial stretching of cell adhesion substrates restores ERK activation on stress fibers. By quantifying myosin II- or mechanical stretch-mediated tensile forces in individual stress fibers, we show that ERK activation on stress fibers correlates positively with tensile forces acting on the fibers, indicating stress fibers as a tension sensor in ERK activation. Myosin II-dependent ERK activation is also observed on actomyosin bundles connecting E-cadherin clusters, thus suggesting that actomyosin bundles, in general, work as a platform for tension-dependent ERK activation.