The role of geometrical confinement on collective cell migration has been recognized but has not been elucidated yet. Here, we show that the geometrical properties of the environment regulate the formation of collective cell migration patterns through cell-cell interactions. Using microfabrication techniques to allow epithelial cell sheets to migrate into strips whose width was varied from one up to several cell diameters, we identified the modes of collective migration in response to geometrical constraints. We observed that a decrease in the width of the strips is accompanied by an overall increase in the speed of the migrating cell sheet. Moreover, largescale vortices over tens of cell lengths appeared in the wide strips whereas a contraction-elongation type of motion is observed in the narrow strips. Velocity fields and traction force signatures within the cellular population revealed migration modes with alternative pulling and/or pushing mechanisms that depend on extrinsic constraints. Force transmission through intercellular contacts plays a key role in this process because the disruption of cell-cell junctions abolishes directed collective migration and passive cell-cell adhesions tend to move the cells uniformly together independent of the geometry. Altogether, these findings not only demonstrate the existence of patterns of collective cell migration depending on external constraints but also provide a mechanical explanation for how large-scale interactions through cell-cell junctions can feed back to regulate the organization of migrating tissues.cell traction forces | collective dynamics | madin darby canine kidney epithelial cells | particle image velocimetry C ollective behavior is a fundamental phenomenon exhibited by a wide variety of systems such as flows in granular matter (1), collective movements of animals (2), self-organization of bacteria (3), and morphogenesis of biological tissues (4). Although collective behaviors have been observed across diverse physical and biological systems, it is increasingly clear that there are broad unifying and common parameters that govern the emergence of this phenomenon such as the density of the constituent particles, the boundary conditions within which the movements occur, and the nature of coupling between the individual particles. In this context, collective behavior in migrating cells is of particular interest as a highly out-of-equilibrium process where cells passively interact with each other and exert active forces in response to their mechanical environment (4). Such collective behavior drives many biological processes such as embryonic development (5), tissue morphogenesis (6), wound healing (7), and tumor metastasis (8, 9). Although single cell dynamics has been extensively studied (10-12), the movement of multicellular structures could not be simply explained by cell autonomous behaviors (13-16). Instead, intercellular interactions and large-scale propagation of mechanical signals (over several cell sizes) are necessary to understand the emergen...

One-cell-thick monolayers are the simplest tissues in multicellular organisms, yet they fulfill critical roles in development and normal physiology. In early development, embryonic morphogenesis results largely from monolayer rearrangement and deformation due to internally generated forces. Later, monolayers act as physical barriers separating the internal environment from the exterior and must withstand externally applied forces. Though resisting and generating mechanical forces is an essential part of monolayer function, simple experimental methods to characterize monolayer mechanical properties are lacking. Here, we describe a system for tensile testing of freely suspended cultured monolayers that enables the examination of their mechanical behavior at multi-, uni-, and subcellular scales. Using this system, we provide measurements of monolayer elasticity and show that this is two orders of magnitude larger than the elasticity of their isolated cellular components. Monolayers could withstand more than a doubling in length before failing through rupture of intercellular junctions. Measurement of stress at fracture enabled a first estimation of the average force needed to separate cells within truly mature monolayers, approximately ninefold larger than measured in pairs of isolated cells. As in single cells, monolayer mechanical properties were strongly dependent on the integrity of the actin cytoskeleton, myosin, and intercellular adhesions interfacing adjacent cells. High magnification imaging revealed that keratin filaments became progressively stretched during extension, suggesting they participate in monolayer mechanics. This multiscale study of monolayer response to deformation enabled by our device provides the first quantitative investigation of the link between monolayer biology and mechanics.cell mechanics | tissue mechanics | intermediate filaments M any of the cavities and free surfaces of the human body are lined by a layer of cells one cell thick. Cells within these monolayers are tightly connected to one another by intercellular junctions. Tight junctions form barriers restricting the passage of solutes while others, such as adherens junctions and desmosomes, integrate the cytoskeletons of constituent cells into a mechanical syncitium. Exposure to mechanical stresses is a normal part of physiology for monolayers: intestinal epithelia are stretched during peristaltic movements in the gut, lung alveoli deform during breathing, and endothelia are exposed to pulsatile fluid shear stresses in blood flow (1-3). The mechanical function of monolayers is particularly apparent in disease where mutations or pathogens affecting the cytoskeleton, adherens junctions, or desmosomes result in increased fragility of tissues (4). Development offers perhaps the most vivid illustration of the role of epithelia in withstanding and exerting mechanical stresses. Indeed, embryonic epithelial tissues are under a constant tension generated by spatially restricted cellular actomyosin contractions (5). When cadherin interce...

Collagen is the most abundant extracellular-network-forming protein in animal biology and is important in both natural and artificial tissues, where it serves as a material of great mechanical versatility. This versatility arises from its almost unique ability to remodel under applied loads into anisotropic and inhomogeneous structures. To explore the origins of this property, we develop a set of analysis tools and a novel experimental setup that probes the mechanical response of fibrous networks in a geometry that mimics a typical deformation profile imposed by cells in vivo. We observe strong fiber alignment and densification as a function of applied strain for both uncrosslinked and crosslinked collagenous networks. This alignment is found to be irreversibly imprinted in uncrosslinked collagen networks, suggesting a simple mechanism for tissue organization at the microscale. However, crosslinked networks display similar fiber alignment and the same geometrical properties as uncrosslinked gels, but with full reversibility. Plasticity is therefore not required to align fibers. On the contrary, our data show that this effect is part of the fundamental non-linear properties of fibrous biological networks.

Collective behavior refers to the emergence of complex migration patterns over scales larger than those of the individual elements constituting a system. It plays a pivotal role in biological systems in regulating various processes such as gastrulation, morphogenesis and tissue organization. Here, by combining experimental approaches and numerical modeling, we explore the role of cell density ('crowding'), strength of intercellular adhesion ('cohesion') and boundary conditions imposed by extracellular matrix (ECM) proteins ('constraints') in regulating the emergence of collective behavior within epithelial cell sheets. Our results show that the geometrical confinement of cells into well-defined circles induces a persistent, coordinated and synchronized rotation of cells that depends on cell density. The speed of such rotating large-scale movements slows down as the density increases. Furthermore, such collective rotation behavior depends on the size of the micropatterned circles: we observe a rotating motion of the overall cell population in the same direction for sizes of up to 200 μm. The rotating cells move as a solid body, with a uniform angular velocity. Interestingly, this upper limit leads to length scales that are similar to the natural correlation length observed for unconfined epithelial cell sheets. This behavior is strongly altered in cells that present a downregulation of adherens junctions and in cancerous cell types. We anticipate that our system provides a simple and easy approach to investigate collective cell behavior in a well-controlled and systematic manner.

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network δz; a floppy network has δz < 0, while a stiff network has δz > 0. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of nonaffine displacements, and the network stiffening as a function of δz, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks. The mechanics of crystalline solids is a fairly well understood subject owing to the simplicity of the underlying lattice which is periodic. In contrast, an understanding of the mechanics of amorphous solids is complicated by the presence of quenched disorder, often on multiple scales. Two structural properties affecting the elasticity of disordered solids are their coordination, and the presence of different types of interactions between the constituents of vastly dissimilar strengths. In the case of weaklycoordinated covalent glass such as amorphous selenium, the backbone is floppy, i.e. it is continuously deformable with almost no energy cost, but weak interactions such as van der Waals are responsible for the non-vanishing elastic moduli. On the other hand, highly-coordinated covalent glasses such as silica, or amorphous particle assemblies where the main interaction is radial, such as emulsions, metallic glasses or granular matter, the backbone is stiff. In foams and fibrous networks which are made of low-dimensional structures such as filaments and membranes, there is a wide separation of energetic scales between stretching and bending modes. This leads to a range of curious mechanical responses in these materials including strongly non-affine deformations [1,2,3,4,5,6] and elastic moduli that can be quite sensitive to the applied stress [1,7]. Despite several theoretical advances [8,9,10,11,12], a unified descriptions of these behaviors remains to be given. Here we study the mechanical response of simple floppy and rigid systems as the coordination is continuously varied and propose such a unifying approach.We start by recalling Maxwell's criterion for rigidity in a central force network [13] by considering a set of N points in d dimensions, subject to N c constraints in the form of bonds that connect these points. This network has N d − N c effective degrees of freedom (ignoring the d(d + 1)/2 rigid motions of the entire system), and an average coordination number z = 2N c /N . The system is said to be isostatic when the system is just rigid, i.e. the number of constraints and the number of degrees of freedom are just balanced, so that N d = N c , and z = 2d. W...

A number of biological processes, such as embryo development, cancer metastasis or wound healing, rely on cells moving in concert. The mechanisms leading to the emergence of coordinated motion remain however largely unexplored. Although biomolecular signalling is known to be involved in most occurrences of collective migration, the role of physical and mechanical interactions has only been recently investigated. In this study, a versatile framework for cell motility is implemented in silico in order to study the minimal requirements for the coordination of a group of epithelial cells. We find that cell motility and cell -cell mechanical interactions are sufficient to generate a broad array of behaviours commonly observed in vitro and in vivo. Cell streaming, sheet migration and susceptibility to leader cells are examples of behaviours spontaneously emerging from these simple assumptions, which might explain why collective effects are so ubiquitous in nature. The size of the population and its confinement appear, in particular, to play an important role in the coordination process. In all cases, the complex response of the population can be predicted from the knowledge of the correlation length of the velocity field measured in the bulk of the epithelial layer. This analysis provides also new insights into cancer metastasis and cell sorting, suggesting, in particular, that collective invasion might result from an emerging coordination in a system where single cells are mechanically unable to invade.

The dynamic reshaping of tissues during morphogenesis results from a combination of individual cell behaviours and collective cell rearrangements. However, a comprehensive framework to unambiguously measure and link cell behaviour to tissue morphogenesis is lacking. Here we introduce such a kinematic framework, bridging cell and tissue behaviours at an intermediate, mesoscopic, level of cell clusters or domains. By measuring domain deformation in terms of the relative motion of cell positions and the evolution of their shapes, we characterize the basic invariant quantities that measure fundamental classes of cell behaviour, namely tensorial rates of cell shape change and cell intercalation. In doing so we introduce an explicit definition of cell intercalation as a continuous process. We demonstrate how spatiotemporal mapping of strain rates in three models of tissue morphogenesis leads to new insight into morphogenetic mechanisms. Our quantitative approach has broad relevance for the precise characterisation and comparison of morphogenetic phenotypes.

Drosophila germ-band extension (GBE) is an example of the convergence and extension movements that elongate and narrow embryonic tissues. To understand the collective cell behaviours underlying tissue morphogenesis, we have continuously quantified cell intercalation and cell shape change during GBE. We show that the fast, early phase of GBE depends on cell shape change in addition to cell intercalation. In antero-posterior patterning mutants such as those for the gap gene Krüppel, defective polarized cell intercalation is compensated for by an increase in antero-posterior cell elongation, such that the initial rate of extension remains the same. Spatio-temporal patterns of cell behaviours indicate that an antero-posterior tensile force deforms the germ band, causing the cells to change shape passively. The rate of antero-posterior cell elongation is reduced in twist mutant embryos, which lack mesoderm. We propose that cell shape change contributing to germ-band extension is a passive response to mechanical forces caused by the invaginating mesoderm.