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-dimensional (3D)description of the tissue and derive an effective 2D model that captures, through the curvature of the apical surface, both the apical-basal asymmetry and the spatial geometry of the tissue. Crucially, variations of active stresses across the apical-basal axis lead to active torques that can drive curvature transitions. By identifying four distinct sources of activity, we find that bulk active stresses arising from actomyosin contractility and growth compete with boundary active tensions due to localized actomyosin cables and lamellipodial activity to generate the various states spanning the morphospace of a planar epithelium. Our treatment hence unifies 3D shape deformations through the coupled mechanics of apical curvature change and in-plane expansion/contraction of substrate-adhered tissues. Finally, we discuss the implications of our results for some biologically relevant processes such as tissue folding at the onset of lumen formation.
Elasticity and plasticity of epithelial gap closure
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）
The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension …
We derive a continuum mechanical model to capture the morphological changes occurring at the pretumoral stage of epithelial tissues. The proposed model aims to investigate the competition between the bulk elasticity of the epithelium and the surface tensions of the apical and basal sides. According to this model, when the apico-basal tension imbalance reaches a critical value, a subcritical bifurcation is triggered and the epithelium attains its physiological folded shape. Based on data available in the literature, our model predicts that pretumoral cells are softer than healthy cells.
Macroscopic properties and shapes of biological tissues depend on the remodelling of cell-cell junctions at the microscopic scale. We propose a theoretical framework that couples a vertex model of solid confluent tissues with the dynamics describing generation of local force dipoles in the junctional actomyosin. Depending on the myosin-turnover rate, junctions either preserve stable length or collapse to initiate cell rearrangements. We find that noise can amplify and sustain transient oscillations to the fixed point, giving rise to quasi-periodic junctional dynamics. We also discover that jun…
The optimal shapes attained by contractile cells on adhesive substrates are determined by the interplay between intracellular forces and adhesion with the extracellular matrix. We model the cell as a contractile film bounded by an elastic cortex and connected to the substrate via elastic links. When the adhesion sites are continuously distributed, optimal cell shape is constrained by the adhesion geometry, with a spread area sensitively dependent on the substrate stiffness and contractile tension. For discrete adhesion sites, equilibrium cell shape is convex at weak contractility, while develo…
Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity o…
Adhesive contact between a thin elastic sheet and a substrate in a liquid environment arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long wavelength elastic deformations and microscopic adhesion, and solving the resulting partial differential equation numerically, we uncover the short-time dynamics of the onset of adhesion and the long-time dynamics of a steady propagating adhesion front. Simple scaling laws corroborate our results for characteristic waiting-time for adhesive contact, as w…
We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses. The build-up of tension from cortical actin bundles at the cell periphery is incorporated by introducing an energy cost for bending of the cell boundary, resulting to a resistance to changes in local curvature. Integrin-based adhesions are modeled as harmonic springs, that pin the cell to adhesive patches of a predefined geometry. Using Monte Carlo simulation…
Cell divisions imprint long lasting elastic strain fields in epithelial tissues
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Excellence Cluster, Physics of Life, Technische Universität Dresden（德累斯顿工业大学生命物理卓越集群）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）
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 present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. We show that a viscous fluid model explains a variety of observations on the slow dynamics of epithelial monolayers, in particular those that had been interpreted before as signatures of elasticity. The non-elastic nature of the waves can b…
Epithelial-substrate coupling strength regulates the landscape of the traction in cohesive monolayers: a parametric study and a revisit to "size effect"
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…
Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorpo…
We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support by an elastic theory of T1 transformations. Using a 3D vertex model, we show that the degree of active noise driving forced cell rearrangements governs the stress-relaxation time-scale of the tissue. We study tissue response to in-plane shear at different time scales. At short time, the tissue behaves as a solid, whereas its long-time fluid behavior can be as…
Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical sim…
Princeton University（普林斯顿大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
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 be…
Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-prop…
Solid-to-solid transition in dense assemblies of elongated cells
Sun Yat-sen University（中山大学）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院磁电物理与器件广东省重点实验室）；Interdisciplinary Research Center for Physical Mechanics in Complex Systems and Its Engineering Applications, School of Physics, Sun Yat-sen University（中山大学物理学院复杂系统力学及其工程应用交叉研究中心）；Aix Marseille Univ, CNRS and Turing Centre for Living Systems, CPT (UMR 7332)（艾克斯-马赛大学、法国国家科学研究中心及图灵生命系统中心，CPT（UMR 7332））；Aix Marseille Univ, Université de Toulon, CNRS, LAI (UMR 7333), Turing Centre for Living Systems（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、LAI（UMR 7333）及图灵生命系统中心）
Coordinated and cooperative motion of cells is essential for embryonic development, tissue morphogenesis, wound healing and cancer invasion. A predictive understanding of the emergent mechanical behaviors in collective cell motion is challenging due to the complex interplay between cell-cell interactions, cell-matrix adhesions and active cell behaviors. To overcome this challenge, we develop a predictive cellular vertex model that can delineate the relative roles of substrate rigidity, tissue mechanics and active cell properties on the movement of cell collectives. We apply the model to the sp…
