It is widely recognized that the shape of epithelial cells is determined by the tension generated by the actomyosin cortex and the adhesion of cells to the substrate and to each other. To account for these biological and structural contributions to cell shape, different physical models have been proposed. However, an experimental procedure that would allow a validation of a minimal physical model for the shape of epithelial cells in 3D has not yet been proposed. In this study, we cultured MDCK epithelial cells on substrates with a sinusoidal profile, allowing us to measure the shape of the cells on various positive and negative curvatures. We found that MDCK cells are thicker in the valleys than on the crests of sinusoidal substrates. The influence of curvature on the shape of epithelial cells could not be understood with a model using only differential apical, basal and lateral surface energies. However, the addition of an apical line tension was sufficient to quantitatively account for the experimental measurements. The model also accounts for the shape of MDCK cells that overexpress E-cadherin. On the other hand, when reducing myosin II activity with blebbistatin, we measured a saturation of the difference in cell thickness between valleys and crests, suggesting the need for a term limiting large cell deformations. Our results show that a minimal model that accounts for epithelial cell shape needs to include an apical line tension in addition to differential surface energies, highlighting the importance of structures that produce anisotropic tension in epithelial cells, such as the actin belt linking adherens junctions. In the future, our experimental procedure could be used to test a wider range of physical models for the shape of epithelia in curved environments, including, for example, continuous models.
Epithelial-substrate coupling strength regulates the landscape of the traction in cohesive monolayers: a parametric study and a revisit to "size effect"
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them on the vertex model. Thus, a model with the curvatures is constructed and its algorithm is given for simulation. Its possi…
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure of the extracellular matrix and nutrient concentration. We used the CellSim3D model, a kinetic division simulator, to investigate the growth kinetics and interface roughness dynamics of epithelial tissue growth on heterogeneous substrates with varying topologies. The results show that the presence of quenched disorder has a clear effect on the colony morphol…
Cell bulging and extrusion in a three-dimensional bubbly vertex model for curved epithelial sheets
Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）；BioQuant, Heidelberg University（海德堡大学生物定量研究中心）；Max Planck School Matter to Life, Heidelberg University（海德堡大学马克斯·普朗克生命物质学院）；Institute of Science and Technology Austria（奥地利科学技术研究所）；Division Signaling and Functional Genomics, German Cancer Research Center (DKFZ)（德国癌症研究中心信号与功能基因组学部）；Department of Molecular Human Genetics, Medical Faculty Heidelberg, Heidelberg University（海德堡大学医学院分子人类遗传学系）
We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell and cell-substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces and apical aspect ratios that decreased when moving f…
Morphogenesis, tissue regeneration and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon is considered on model system such as wetting of cell aggregate on rigid substrate which includes cell aggregate movement and isotropic/anisotropic spreading of cell monolayer around the aggregate depending on the substrate rigidity and aggregate size. This model system accounts for the transition between 3D epithelial aggregate and 2D cell monolayer as a pro…
Epithelial cell monolayers expand on substrates by forming finger-like protrusions, created by leader cells, in the monolayer boundary. Information transmission and communication between individual entities in the cohesive collective lead to long-range order, vortical structures, and disorder to ordered phase transitions. We ask the following questions: what makes a leader? What is the role of followers in leader cell formation? We used a particle-based model to simulate epithelial cell migrations on substrates of 9.4 kPa, 21 kPa and 33 kPa stiffness. The dynamics of cellular motion in the ens…
Collective cell migration plays a crucial role in many developmental processes that underlie morphogenesis, wound healing, or cancer progression. In such coordinated behaviours, cells are organised in coherent structures and actively migrate to serve different biological purposes. In some contexts, namely during epithelial wound healing, it is well known that a migrating free-edge monolayer develops finger-like instabilities, yet the onset is still under debate. Here, by means of theory and numerical simulations, we shed light on the main mechanisms driving the instability process, analysing t…
Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between 2D epithelial monolayers and 3D spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phe…
Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechano-chemical active feedback mechanism coupled to a substrate via friction. Robust convergent ext…
Epithelial tissues form physically integrated barriers against the external environment protecting organs from infection and invasion. Within each tissue, epithelial cells respond to different challenges that can potentially compromise tissue integrity. In particular, cells collectively respond by reorganizing their cell-cell junctions and migrating directionally towards the sites of injury. Notwithstanding, the mechanisms that define the spatiotemporal scales and driving forces of these collective responses remain poorly understood. To address this we first analyzed the collective response of…
A detailed understanding of the interface between living cells and substrate materials is of rising importance in many fields of medicine, biology and biotechnology. Cells at interfaces often form epithelia. The physical barrier that they form is one of their main functions. It is governed by the properties of the networks forming the cytoskeleton systems and by cell-to-cell contacts. Different substrates with varying surface properties modify the migration velocity of the cells. On the one hand one can change the materials composition. Organic and inorganic materials induce differing migratio…
Collective cell migration in cohesive units is vital for tissue morphogenesis, wound repair, and immune response. While the fundamental driving forces for collective cell motion stem from contractile and protrusive activities of individual cells, it remains unknown how their balance is optimized to maintain tissue cohesiveness and the fluidity for motion. Here we present a cell-based computational model for collective cell migration during wound healing that incorporates mechanochemical coupling of cell motion and adhesion kinetics with stochastic transformation of active motility forces. We s…
Viscous vertex model for active epithelial tissues
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院）；Interdisciplinary Research Center for Physical Mechanics in Complex Systems and Its Engineering Applications, School of Physics, Sun Yat-sen University（中山大学物理学院）；Aix Marseille Univ, IBDM (UMR 7288), Turing Centre for Living Systems（艾克斯-马赛大学）；Aix Marseille Univ, Université de Toulon, CPT (UMR 7332), Turing Centre for Living Systems（艾克斯-马赛大学）；Aix Marseille Univ, CNRS, LAI (UMR 7333), Turing Centre for Living Systems（艾克斯-马赛大学）
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the Jülicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interes…
How cells with diverse morphologies and cytoskeletal architectures modulate their mechanical behaviors to drive robust collective motion within tissues is poorly understood. During wound repair within epithelial monolayers in vitro, cells coordinate the assembly of branched and bundled actin networks to regulate the total mechanical work produced by collective cell motion. Using traction force microscopy, we show that the balance of actin network architectures optimizes the wound closure rate and the magnitude of the mechanical work. These values are constrained by the effective power exerted …
Epithelial tissues play a fundamental role in various morphogenetic events during development and early embryogenesis. Although epithelial monolayers are often modeled as two-dimensional (2D) elastic surfaces, they distinguish themselves from conventional thin elastic plates in three important ways - the presence of an apical-basal polarity, spatial variability of cellular thickness, and their nonequilibrium active nature. Here, we develop a minimal continuum model of a planar epithelial tissue as an active elastic material that incorporates all these features. We start from a full three-dimen…
Eukaryotic cells adhere to extracellular matrix during the normal development of the organism, forming static adhesion as well as during cell motility. We study this process by considering a simplified coarse-grained model of a vesicle that has uniform adhesion energy with a flat substrate, mobile curved membrane proteins and active forces. We find that a high concentration of curved proteins alone increases the spreading of the vesicle, by the self-organization of the curved proteins at the high curvature vesicle-substrate contact line, thereby reducing the bending energy penalty at the vesic…
Tissues are characterized by layers of functional units such as cells and extracellular matrix (ECM). Nevertheless, how dynamics at interlayer interfaces help transmit cellular forces in tissues remains overlooked. Here, we investigate a multi-layer system where a layer of epithelial cells is seeded upon an elastic substrate in contact with a hard surface. Our experiments show that, upon a cell extrusion event in the cellular layer, long-range wave propagation emerges in the substrate only when the two substrate layers were weakly attached to each other. We then derive a theoretical model whic…
Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating betwe…
Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation. These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are often confined to the edges of the cluster; there can exist density waves within the cluster; clusters can exhibit collective durotaxis when individual cells show no effect; and for cells in an annulus there is a transition between …
Collective cell migration is a key driver of embryonic development, wound healing, and some types of cancer invasion. Here we provide a physical perspective of the mechanisms underlying collective cell migration. We begin with a catalogue of the cell-cell and cell-substrate interactions that govern cell migration, which we classify into positional and orientational interactions. We then review the physical models that have been developed to explain how these interactions give rise to collective cellular movement. These models span the sub-cellular to the supracellular scales, and they include …
Key to collective cell migration is the ability of cells to rearrange their position with respect to their neighbors. Recent theory and experiments demonstrated that cellular rearrangements are facilitated by cell shape, with cells having more elongated shapes and greater perimeters more easily sliding past their neighbors within the cell layer. Though it is thought that cell perimeter is controlled primarily by cortical tension and adhesion at each cell's periphery, experimental testing of this hypothesis has produced conflicting results. Here we studied collective cell migration in an epithe…
Cell spreading requires a major reorganisation of the actin cytoskeleton, from a cortical structure to a lamellipodium where filaments are mostly parallel to the substrate. We propose a model inspired by the physics of nematic liquid crystals and fluid membranes, in which the coupling between actin mechanics, filaments orientation, and the local curvature of the cell membrane naturally yields the collective reorientation of actin filaments at the highly curved edge of a spreading cell. Filament orientation increases the traction force exerted by the frictional flow of polymerising actin on the…
Surface tension governed by differential adhesion can drive fluid particle mixtures to sort into separate regions, i.e., demix. Does the same phenomenon occur in confluent biological tissues? We begin to answer this question for epithelial monolayers with a combination of theory via a vertex model and experiments on keratinocyte monolayers. Vertex models are distinct from particle models in that the interactions between the cells are shape-based, as opposed to distance-dependent. We investigate whether a disparity in cell shape or size alone is sufficient to drive demixing in bidisperse vertex…
