In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic tension at the interface between two distinct cell types in a fully 3D model for confluent tissues. We find that cells rapidly sort and self-organize to generate a tissue-scale interface between cell types, and cells adjacent to this interface exhibit signature geometric features including nematic-like ordering, bimodal facet areas, and registration, or alignment, of cell centers on either side of the two-tissue interface. The magnitude of these features scales directly with the magnitude of imposed tension, suggesting that biologists can estimate the magnitude of tissue surface tension between two tissue types simply by segmenting a 3D tissue. To uncover the underlying physical mechanisms driving these geometric features, we develop two minimal, ordered models using two different underlying lattices that identify an energetic competition between bulk cell shapes and tissue interface area. When the interface area dominates, changes to neighbor topology are costly and occur less frequently, which generates the observed geometric features.
In vivo and in vitro cells rely on the support of an underlying biocompatible substrate, such as the extracellular matrix or a culture substrate, to spread and proliferate. The mechanical and chemical properties of such structures play a central role in the dynamical and statistical properties of the tissue. At the cell scale, these substrates are highly disordered. Here, we investigate how spatial heterogeneities of the cell-substrate interaction influence the motility of the cells in a model confluent tissue. We use the Self-Propelled Voronoi model and describe the disorder as a spatially de…
The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and size, and the interaction between adjacent cells is a byproduct of this additive energy. We generalize this model so as to allow zero or partial contact between cells. We identify several phases, two of which (solid confluent and liquid confluent) were found in previous studies that imposed confluency but others that are novel. Transitions in this model may be r…
How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue-level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions o…
We investigate the effects of cell division and apopotosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apopotosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phas…
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the ability of cells to independently regulate adhesivity and tension, together with neighbor-based interaction rules, lets them support strikingly unusual interfaces. In particular, we show that mechanical- and fluctuation-based measurements of the effective surface tension of a cellular aggregate yield different results, leading to mechanically soft interfaces t…
Recent work on particle-based models of tissues has suggested that any finite rate of cell division and cell death is sufficient to fluidize an epithelial tissue. At the same time, experimental evidence has indicated the existence of glassy dynamics in some epithelial layers despite continued cell cycling. To address this discrepancy, we quantify the role of cell birth and death on glassy states in confluent tissues using simulations of an active vertex model that includes cell motility, cell division, and cell death. Our simulation data is consistent with a simple ansatz in which the rate of …
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This impli…
In development and homeostasis, multi-cellular systems exhibit spatial and temporal heterogeneity in their biochemical and mechanical properties. Nevertheless, it remains unclear how spatiotemporally heterogeneous forces affect the dynamical and mechanical properties of confluent tissue. To address this question, we study the dynamical behavior of the two-dimensional cellular vertex model for epithelial monolayers in the presence of fluctuating cell-cell interfacial tensions, which is a biologically relevant source of mechanical spatiotemporal heterogeneity. In particular, we investigate the e…
Collective cell migration underlies important biological processes, such as embryonic development, wound healing and cancer invasion. While many aspects of single cell movements are now well established, the mechanisms leading to displacements of cohesive cell groups are still poorly understood. To elucidate the emergence of collective migration in mechanosensitive cells, we examine a self-propelled Voronoi (SPV) model of confluent tissues with an orientational feedback that aligns a cell's polarization with its local migration velocity. While shape and motility are known to regulate a density…
Models of 3D confluent tissue as under-constrained glasses
Department of Physics, Emory University（埃默里大学物理系）；Aix Marseille Univ, Université de Toulon, CNRS, CPT (UMR 7332), 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、CPT（UMR 7332）、图灵生命系统中心）
Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes it difficult for theoretical development. Cellular Potts model (CPM) of confluent monolayer provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of CPM and an analytical study based on one of the m…
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…
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…
Collective cell migration is a highly regulated process involved in wound healing, cancer metastasis and morphogenesis. Mechanical interactions among cells provide an important regulatory mechanism to coordinate such collective motion. Using a Self-Propelled Voronoi (SPV) model that links cell mechanics to cell shape and cell motility, we formulate a generalized mechanical inference method to obtain the spatio-temporal distribution of cellular stresses from measured traction forces in motile tissues and show that such traction-based stresses match those calculated from instantaneous cell shape…
Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 tr…
The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that specifies cell shapes. Here, we generalize this model to 3D and find a rigidity transition that is similarly controlled by the preferred surface area: the model is solid-like below a dimensionless surface area of $s_0^\ast\approx5.413$, and fluid-like above this value. We demonstrate that, unlike jamming in soft spheres, residual stresses are necessary to create r…
Cell migration is important in many biological processes, including embryonic development, cancer metastasis, and wound healing. In these tissues, a cell's motion is often strongly constrained by its neighbors, leading to glassy dynamics. While self-propelled particle models exhibit a density-driven glass transition, this does not explain liquid-to-solid transitions in confluent tissues, where there are no gaps between cells and therefore the density is constant. Here we demonstrate the existence of a new type of rigidity transition that occurs in the well-studied vertex model for confluent ti…
Various multicellular tissues show chiral morphology. Experimental studies have shown this can originate from cell chirality. However, no theory has been proposed to connect the cellular chiral torque and multicellular chiral morphogenesis. We propose a model of confluent tissue dynamics with cellular chiral torque. We found that cells migrate unidirectionally under a gradient of cellular chiral torque. While the migration speed varies depending on the tissue's mechanical parameters, it is scaled solely by a structural order parameter for liquid-to-solid transition in confluent tissues.
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.
We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural de…
Mechanical characterization of brain tissue at high loading velocities is crucial for modeling Traumatic Brain Injury (TBI). During severe impact conditions, brain tissue experiences compression, tension and shear. Limited experimental data is available for brain tissue in extension at dynamic strain rates. In this research, a High Rate Tension Device (HRTD) was developed to obtain dynamic properties of brain tissue in extension at strain rates of < 90/s. In vitro tensile tests were performed to obtain properties of brain tissue at strain rates of 30, 60 and 90/s up to 30% strain. The brain ti…
The mechanical properties of cells, which influence the properties of the tissue they belong to, are controlled by various mechanisms. Bi et al. theoretically demonstrated that density-independent rigidity transition occurs in two-dimensional confluent tissues that consist of mechanically uniform cells. They also analyzed the dynamical behavior of tissues near the critical point, which is geometrically controlled by `shape parameter'. To investigate whether the behavior of three-dimensional tissues is similar to that of two-dimensional ones, we extend the model proposed by Bi et al. to a three…
Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher order vertices or multicellular rosettes are prevalent in developmental and {\it in vitro} processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and effective medium theory we find a …
In this paper, we examine the emergence of cell flow induced by a tension gradient on a tissue interface as in the case of the Marangoni flow on liquid interface. We consider the molecule density polarity of the heterophilic adhesion between tissues as the origin of the tension gradient. By applying the cellular Potts model, we demonstrate that polarization in concentration (i.e., intracellular localization) of heterophilic adhesion molecules can induce a cell flow similar to the Marangoni flow. In contrast to the ordinary Marangoni flow, this flow is oriented in the opposite direction to that…
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）
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…
The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the cells remain mechanically stable remains unknown. Here, we used computer simulations of deformable particles to develop a purely mechanical model for the development of…
In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell polarization and motility might be governed by the internal shear stiffness of nearby tissue, deemed "plithotaxis". Meanwhile, other work has demonstrated that there is a direct relationship between cell shapes and tissue shear modulus in confluent tissues. Joining these two ideas, we develop a hydrodynamic model that couples cell shape, and therefore tissue …
Confluent cell monolayers and epithelia tissues show remarkable patterns and correlations in structural arrangements and actively-driven collective flows. We simulate these properties using multiphase field models. The models are based on cell deformations and cell-cell interactions and we investigate the influence of microscopic details to incorporate active forces on emerging phenomena. We compare four different approaches, one in which the activity is determined by a random orientation, one where the activity is related to the deformation of the cells and two models with subcellular details…
Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounti…
The surface tension of living cells and tissues originates from the generation of nonequilibrium active stresses within the cell cytoskeleton. Here, using laser ablation, we generate gradients in the surface tension of cellular aggregates as models of simple tissues. These gradients of active surface stress drive large-scale and rapid toroidal motion. Subsequently, the motions spontaneously reverse as stresses reaccumulate and cells return to their original positions. Both forward and reverse motions resemble Marangoni flows in viscous fluids. However, the motions are faster than the timescale…
It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects mechanical properties at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the ins…
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…
Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which may affect their respective rigidities. To study this interaction, we consider a vertex model with interfacial tension (a spheroid) embedded in a spring network in two dimensions. We identify two regimes with different global spheroid shapes, governed by the pressure resulting from competition between interfacial tension and tension in the network. In the first regime, the tissue remains compact, while in the s…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by executing a series of cell rearrangements, or T1 transitions. In a disordered 2D vertex model, the tissue fluidizes when the T1 energy barriers disappear as the target shape index approaches a critical value ($s^*_{0} \sim 3.81$), and the shear modulus describing the linear response also vanishes at this same critical point. However, the ordered ground states of…
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 …
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 behaviour. 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 f…
We propose two toy-models to describe, predict, and interpret the wrinkles appearing on the surface of skin when it is sheared. With the first model, we account for the lines of greatest tension present in human skin by subjecting a layer of soft tissue to a pre-stretch, and for the epidermis by endowing one of the layer's faces with a surface tension. For the second model, we consider an anisotropic model for the skin, to reflect the presence of stiff collagen fibres in a softer elastic matrix. In both cases, we find an explicit bifurcation criterion, linking geometrical and material paramete…
Convergence-extension in embryos is controlled by chemical and mechanical signalling. A key cellular process is the exchange of neighbours via T1 transitions. We propose and analyse a model with positive feedback between recruitment of myosin motors and mechanical tension in cell junctions. The model produces active T1 events, which act to elongate the tissue perpendicular to external pulling. Using an idealized tissue patch comprising several active cells embedded in a matrix of passive hexagonal cells we identified an optimal range of pulling forces to trigger an active T1 event. We show tha…
Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlle…
