Physical model of the dynamic instability in an expanding cell culture

Stability Transition in Gap Expansion-Driven Interfacial Flow

We investigate interfacial instability in a lifting Hele-Shaw cell by experiments and theory. We characterize the unexplored transition from stable to unstable patterns under a wide range of controlling parameters. Surprisingly, we find that the perturbation growth rate-based criterion for the onset of instability from linear stability theory is too strict by over 3 orders of magnitude. To reconcile this striking discrepancy, we propose a new criterion based on perturbation amplitude, which is in excellent agreement with the experimental results. We further show that the fingering pattern evolves to produce a hierarchical fluid structure and derive a theoretical equation to predict the fingering evolution.

[The Dynamic Model of the Active-Inactive Cell Interface]

Objective

To explore the morphodynamics of the active-inactive cell monolayer interfaces by using the active liquid crystal model.

Methods

A continuum mechanical model was established based on the active liquid crystal theory and the active-inactive cell monolayer interfaces were established by setting the activity difference of cell monolayers. The theoretical equations were solved numerically by the finite difference and the lattice Boltzmann method.

Results

The active-inactive cell interfaces displayed three typical morphologies, namely, flat interface, wavy interface, and finger-like interface. On the flat interfaces, the cells were oriented perpendicular to the interface, the -1/2 topological defects were clustered in the interfaces, and the interfaces were negatively charged. On the wavy interfaces, cells showed no obvious preference for orientation at the interfaces and the interfaces were neutrally charged. On the finger-like interfaces, cells were tangentially oriented at the interfaces, the +1/2 topological defects were collected at the interfaces, driving the growth of the finger-like structures, and the interfaces were positively charged.

Conclusion

The orientation of the cell alignment at the interface can significantly affect the morphologies of the active-inactive cell monolayer interfaces, which is closely associated with the dynamics of topological defects at the interfaces.

Fractal dimension to characterize interactions between blood and lymphatic endothelial cells

Spatial patterning of different cell types is crucial for tissue engineering and is characterized by the formation of sharp boundary between segregated groups of cells of different lineages. The cell-cell boundary layers, depending on the relative adhesion forces, can result in kinks in the border, similar to fingering patterns between two viscous partially miscible fluids which can be characterized by its fractal dimension. This suggests that mathematical models used to analyze the fingering patterns can be applied to cell migration data as a metric for intercellular adhesion forces. In this study, we develop a novel computational analysis method to characterize the interactions between blood endothelial cells (BECs) and lymphatic endothelial cells (LECs), which form segregated vasculature by recognizing each other through podoplanin. We observed indiscriminate mixing with LEC-LEC and BEC-BEC pairs and a sharp boundary between LEC-BEC pair, and fingering-like patterns with pseudo-LEC-BEC pairs. We found that the box counting method yields fractal dimension between 1 for sharp boundaries and 1.3 for indiscriminate mixing, and intermediate values for fingering-like boundaries. We further verify that these results are due to differential affinity by performing random walk simulations with differential attraction to nearby cells and generate similar migration pattern, confirming that higher differential attraction between different cell types result in lower fractal dimensions. We estimate the characteristic velocity and interfacial tension for our simulated and experimental data to show that the fractal dimension negatively correlates with capillary number (Ca), further indicating that the mathematical models used to study viscous fingering pattern can be used to characterize cell-cell mixing. Taken together, these results indicate that the fractal analysis of segregation boundaries can be used as a simple metric to estimate relative cell-cell adhesion forces between different cell types.

Dominant geometrical factors of collective cell migration in flexible 3D gelatin tube structures

Collective cell migration is a dynamic and interactive behavior of cell cohorts essential for diverse physiological developments in living organisms. Recent studies have revealed the importance of three-dimensional (3D) topographical confinements to regulate the migration modes of cell cohorts in tubular confinement. However, conventional in vitro assays fail to observe cells' behavior in response to 3D structural changes, which is necessary for examining the geometric regulation factors of collective migration. Here, we introduce a newly developed assay for fabricating flexible 3D structures of capillary microtunnels to examine the behavior of vascular endothelial cells (ECs) as they progress through the successive transition across wide or narrow tube structures. The microtunnels with altered diameters were formed inside gelatin-gel blocks by photo-thermal etching with micrometer-sized spot heating of the focused infrared laser absorption. The ECs migrated and spread two-dimensionally on the inner surface of gelatin capillary microtunnels as a monolayer instead of filling the entire capillary. In the straight cylindrical topographical constraint, leading ECs exhibited no apparent diameter dependence for the maximum peak migration velocity. However, widening the diameter in the narrow-wide structures caused a decrease in migration velocity following in direct proportion to the diameter increase ratio, whereas narrowing the diameter in wide-narrow microtunnels increased the speed without obvious correlation between velocity change and diameter change. The results demonstrated the ability of the newly developed flexible 3D gelatin tube structures for collective cell migration, and the findings provide insights into the dominant geometric factor of the emerging migratory modes for endothelial migration as asymmetric fluid flow-like behavior in the borderless cylindrical cell sheets.

A physical model for dynamic assembly of human salivary stem/progenitor microstructures

The in vitro reconstructions of human salivary glands in service of their eventual medical use represent a challenge for tissue engineering. Here, we present a theoretical approach to the dynamical formation of acinar structures from human salivary cells, focusing on observed stick-slip radial expansion as well as possible growth instabilities. Our findings demonstrate the critical importance of basement membrane remodeling in controlling the growth process.

p53 directs leader cell behavior, migration, and clearance during epithelial repair

Epithelial cells migrate across wounds to repair injured tissue. Leader cells at the front of migrating sheets often drive this process. However, it is unclear how leaders emerge from an apparently homogeneous epithelial cell population. We characterized leaders emerging from epithelial monolayers in cell culture and found that they activated the stress sensor p53, which was sufficient to initiate leader cell behavior. p53 activated the cell cycle inhibitor p21WAF1/CIP1, which in turn induced leader behavior through inhibition of cyclin-dependent kinase activity. p53 also induced crowding hypersensitivity in leader cells such that, upon epithelial closure, they were eliminated by cell competition. Thus, mechanically induced p53 directs emergence of a transient population of leader cells that drive migration and ensures their clearance upon epithelial repair.

Fingering instability in spreading epithelial monolayers: roles of cell polarisation, substrate friction and contractile stresses

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 the linear and nonlinear dynamics of a continuum compressible polar fluid. In particular, we assess the role of cell polarisation, substrate friction, and contractile stresses. Linear theory shows that it is crucial to analyse the perturbation transient dynamics, since we unravel a plethora of crossovers between different exponential growth rates during the linear regime. Numerical simulations suggest that cell-substrate friction could be the mechanism responsible for the formation of complex finger-like structures at the edge, since it triggers secondary fingering instabilities and tip-splitting phenomena. Finally, we obtain a critical contractile stress that depends on cell-substrate friction and the initial-to-nematic length ratio, characterising an active wetting-dewetting transition. In the dewetting scenario, the monolayer retracts and becomes stable without developing finger-like structures.

Cluster and conquer: the morphodynamics of invasion of a compliant substrate by active rods

The colonisation of a soft passive material by motile cells such as bacteria is common in biology. The resulting colonies of the invading cells are often observed to exhibit intricate patterns whose morphology and dynamics can depend on a number of factors, particularly the mechanical properties of the substrate and the motility of the individual cells. We use simulations of a minimal 2D model of self-propelled rods moving through a passive compliant medium consisting of particles that offer elastic resistance before being plastically displaced from their equilibrium positions. It is observed that the clustering of active (self-propelled) particles is crucial for understanding the morphodynamics of colonisation. Clustering enables motile colonies to spread faster than they would have as isolated particles. The colonisation rate depends non-monotonically on substrate stiffness with a distinct maximum at a non-zero value of substrate stiffness. This is observed to be due to a change in the morphology of clusters. Furrow networks created by the active particles have a fractal-like structure whose dimension varies systematically with substrate stiffness but is less sensitive to particle activity. The power-law growth exponent of the furrowed area is smaller than unity, suggesting that, to sustain such extensive furrow networks, colonies must regulate their overall growth rate.

Photothermal Agarose Microfabrication Technology for Collective Cell Migration Analysis

Agarose photothermal microfabrication technology is one of the micropatterning techniques that has the advantage of simple and flexible real-time fabrication even during the cultivation of cells. To examine the ability and limitation of the agarose microstructures, we investigated the collective epithelial cell migration behavior in two-dimensional agarose confined structures. Agarose microchannels from 10 to 211 micrometer width were fabricated with a spot heating of a focused 1480 nm wavelength infrared laser to the thin agarose layer coated on the cultivation dish after the cells occupied the reservoir. The collective cell migration velocity maintained constant regardless of their extension distance, whereas the width dependency of those velocities was maximized around 30 micrometer width and decreased both in the narrower and wider microchannels. The single-cell tracking revealed that the decrease of velocity in the narrower width was caused by the apparent increase of aspect ratio of cell shape (up to 8.9). In contrast, the decrease in the wider channels was mainly caused by the increase of the random walk-like behavior of component cells. The results confirmed the advantages of this method: (1) flexible fabrication without any pre-designing, (2) modification even during cultivation, and (3) the cells were confined in the agarose geometry.

Interfacial Curvature as a Potential Index for Prognosis of Colon Adenocarcinoma

Tumor invasion and metastasis are complex interfacial mechanical processes between the tumor and its surrounding tissue, with the interfacial curvature of tumor playing an important role in cancer progression. In this study, the potential role of interfacial curvature in the prognosis of patients with colon adenocarcinoma is investigated. The front edge interfacial curvature of adenocarcinoma from biopsies of patients in different tumor, lymph node, and metastasis (TNM) stages are calculated and compared, and prognosis assessment is conducted using Kaplan-Meier and Cox proportional hazards regression analyses. Results reveal that patients with larger interfacial curvature of adenocarcinoma are more likely to belong to higher TNM stages. Concomitantly, in the same TNM stage, patients with increased adenocarcinoma interfacial curvature show worse prognosis with higher recurrence and lower survival rates. Besides, interfacial curvature is an independent prognostic factor for cause-specific survival and relapse-free survival among all selected patients. Mechanical models of colon adenocarcinoma invasion and metastasis are established to better understand the close association between interfacial curvature and tumor progression. The results together with hematoxylin and eosin staining indicate that metastasis in stages T3N0M0 and T3N1M0 may be linked to large interfacial curvatures. Therefore, interfacial curvature may serve as a potential index for predicting prognosis in patients with colon adenocarcinoma.

Epithelial colonies in vitro elongate through collective effects

Epithelial tissues of the developing embryos elongate by different mechanisms, such as neighbor exchange, cell elongation, and oriented cell division. Since autonomous tissue self-organization is influenced by external cues such as morphogen gradients or neighboring tissues, it is difficult to distinguish intrinsic from directed tissue behavior. The mesoscopic processes leading to the different mechanisms remain elusive. Here, we study the spontaneous elongation behavior of spreading circular epithelial colonies in vitro. By quantifying deformation kinematics at multiple scales, we report that global elongation happens primarily due to cell elongations, and its direction correlates with the anisotropy of the average cell elongation. By imposing an external time-periodic stretch, the axis of this global symmetry breaking can be modified and elongation occurs primarily due to orientated neighbor exchange. These different behaviors are confirmed using a vertex model for collective cell behavior, providing a framework for understanding autonomous tissue elongation and its origins.

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent α=0.86 and the growth exponent β=0.73, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from (α=0.5,β=0.25) to (α=0.9,β=0.75), where the exponents α and β are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, α=0.74,β=0.68, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

Reversible elastic phase field approach and application to cell monolayers

Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells.

Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth

Epithelial branching morphogenesis drives the development of organs such as the lung, salivary gland, kidney and the mammary gland. It involves cell proliferation, cell differentiation and cell migration. An elaborate network of chemical and mechanical signals between the epithelium and the surrounding mesenchymal tissues regulates the formation and growth of branching organs. Surprisingly, when cultured in isolation from mesenchymal tissues, many epithelial tissues retain the ability to exhibit branching morphogenesis even in the absence of proliferation. In this work, we propose a simple, experimentally plausible mechanism that can drive branching morphogenesis in the absence of proliferation and cross-talk with the surrounding mesenchymal tissue. The assumptions of our mathematical model derive from in vitro observations of the behaviour of mammary epithelial cells. These data show that autocrine secretion of the growth factor TGF[Formula: see text]1 inhibits the formation of cell protrusions, leading to curvature-dependent inhibition of sprouting. Our hybrid cellular Potts and partial-differential equation model correctly reproduces the experimentally observed tissue-geometry-dependent determination of the sites of branching, and it suffices for the formation of self-avoiding branching structures in the absence and also in the presence of cell proliferation. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.

Active matter invasion

Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.

Interplay between surface and bending energy helps membrane protrusion formation

We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.

Motility-limited aggregation of mammary epithelial cells into fractal-like clusters

Migratory cells transition between dispersed individuals and multicellular collectives during development, wound healing, and cancer. These transitions are associated with coordinated behaviors as well as arrested motility at high cell densities, but remain poorly understood at lower cell densities. Here, we show that dispersed mammary epithelial cells organize into arrested, fractal-like clusters at low density in reduced epidermal growth factor (EGF). These clusters exhibit a branched architecture with a fractal dimension of [Formula: see text], reminiscent of diffusion-limited aggregation of nonliving colloidal particles. First, cells display diminished motility in reduced EGF, which permits irreversible adhesion upon cell-cell contact. Subsequently, leader cells emerge that guide collectively migrating strands and connect clusters into space-filling networks. Thus, this living system exhibits gelation-like arrest at low cell densities, analogous to the glass-like arrest of epithelial monolayers at high cell densities. We quantitatively capture these behaviors with a jamming-like phase diagram based on local cell density and EGF. These individual to collective transitions represent an intriguing link between living and nonliving systems, with potential relevance for epithelial morphogenesis into branched architectures.

Switch-like enhancement of epithelial-mesenchymal transition by YAP through feedback regulation of WT1 and Rho-family GTPases

Collective cell migration occurs in many patho-physiological states, including wound healing and invasive cancer growth. The integrity of the expanding epithelial sheets depends on extracellular cues, including cell-cell and cell-matrix interactions. We show that the nano-scale topography of the extracellular matrix underlying epithelial cell layers can strongly affect the speed and morphology of the fronts of the expanding sheet, triggering partial and complete epithelial-mesenchymal transitions (EMTs). We further demonstrate that this behavior depends on the mechano-sensitivity of the transcription regulator YAP and two new YAP-mediated cross-regulating feedback mechanisms: Wilms Tumor-1-YAP-mediated downregulation of E-cadherin, loosening cell-cell contacts, and YAP-TRIO-Merlin mediated regulation of Rho GTPase family proteins, enhancing cell migration. These YAP-dependent feedback loops result in a switch-like change in the signaling and the expression of EMT-related markers, leading to a robust enhancement in invasive cell spread, which may lead to a worsened clinical outcome in renal and other cancers.

Reorganisation of the extracellular matrix (ECM) controls processes involving epithelial-mesenchymal transition (EMT). Here, the authors show that EMT occurring in epithelial cells on a fabricated nano-engineered cell adhesion surface is triggered by mechanical cues from the ECM.

Neural crest streaming as an emergent property of tissue interactions during morphogenesis

A fundamental question in embryo morphogenesis is how a complex pattern is established in seemingly uniform tissues. During vertebrate development, neural crest cells differentiate as a continuous mass of tissue along the neural tube and subsequently split into spatially distinct migratory streams to invade the rest of the embryo. How these streams are established is not well understood. Inhibitory signals surrounding the migratory streams led to the idea that position and size of streams are determined by a pre-pattern of such signals. While clear evidence for a pre-pattern in the cranial region is still lacking, all computational models of neural crest migration published so far have assumed a pre-pattern of negative signals that channel the neural crest into streams. Here we test the hypothesis that instead of following a pre-existing pattern, the cranial neural crest creates their own migratory pathway by interacting with the surrounding tissue. By combining theoretical modeling with experimentation, we show that streams emerge from the interaction of the hindbrain neural crest and the neighboring epibranchial placodal tissues, without the need for a pre-existing guidance cue. Our model suggests that the initial collective neural crest invasion is based on short-range repulsion and asymmetric attraction between neighboring tissues. The model provides a coherent explanation for the formation of cranial neural crest streams in concert with previously reported findings and our new in vivo observations. Our results point to a general mechanism of inducing collective invasion patterns.

Active Fingering Instability in Tissue Spreading

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

Stability and Roughness of Interfaces in Mechanically Regulated Tissues

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface by analyzing a model of mechanically regulated tissue growth in the regime of small driving forces. For an interface driven by homeostatic pressure imbalance or leader-cell motility, long and intermediate-wavelength instabilities arise, depending, respectively, on an effective viscosity of cell number change, and on substrate friction. A further mechanism depends on the strength of directed motility forces acting in the bulk. We analyze the fluctuations of a stable interface subjected to cell-level stochasticity, and find that mechanical feedback can help preserve reproducibility at the tissue scale. Our results elucidate mechanisms that could be important for orderly interface motion in developing tissues.

Fingering instabilities in tissue invasion: an active fluid model

Metastatic tumours often invade healthy neighbouring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a two-dimensional circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model the evolution of a carcinoma in an epithelial layer. We find that our description can explain the propensity of tumour tissues to fingering instabilities, as conditioned by the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumour size at the onset of metastasis, and for the number of subsequent invasive fingers. Our active fluid model may help describe a wider range of biological processes, including wound healing and developmental patterning.

Dynamics phenotyping across length and time scales in collective cell migration

Processes in collective migration span many length and time scales. In this review, we focus on length scales ranging from tens of microns (single cells) to a few millimeters (cell clusters) and the motion of these cells and cell groups on time scales of minutes to hours. We focus on epithelial cell sheets and metrics of motion developed to measure migration phenotypes in this system. Comparisons between cell motion and fluid flows, facilitated by the popular image analysis technique particle image velocimetry, yield metrics that can be used to study migration across a range of length and time scales. Measuring collective cell migration across these scales provides a complex, quantitative phenotype useful for migration models, in particular those that compare and contrast collective cell migration to movement of particles near a transition to jamming. Contrasting the motion of epithelial cells and the jamming transition illustrates aspects of collective motion that can be attributed to the jammed character of cell clusters, and highlights aspects of collective behavior that likely involve active motility and cell-cell guidance. The application of multiple migration metrics, which span multiple scales of the system, thus allows us to link cell-scale signals and mechanics to collective behavior.

Mechanical interactions among followers determine the emergence of leaders in migrating epithelial cell collectives

Regulating the emergence of leaders is a central aspect of collective cell migration, but the underlying mechanisms remain ambiguous. Here we show that the selective emergence of leader cells at the epithelial wound-margin depends on the dynamics of the follower cells and is spatially limited by the length-scale of collective force transduction. Owing to the dynamic heterogeneity of the monolayer, cells behind the prospective leaders manifest locally increased traction and monolayer stresses much before these leaders display any phenotypic traits. Followers, in turn, pull on the future leaders to elect them to their fate. Once formed, the territory of a leader can extend only to the length up-to which forces are correlated, which is similar to the length up-to which leader cells can transmit forces. These findings provide mechanobiological insight into the hierarchy in cell collectives during epithelial wound healing.

During collective cell migration, how leader cells emerge is poorly understood. Here, the authors find that small groups of mechanically-interacting follower cells pull on the future leaders to stochastically elect them to their fate.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Symmetry-breaking in branching epithelia: cells on micro-patterns under flow challenge the hypothesis of positive feedback by a secreted autocrine inhibitor of motility

Branching morphogenesis of epithelia involves division of cells into leader (tip) and follower (stalk) cells. Published work on cell lines in culture has suggested that symmetry-breaking takes place via a secreted autocrine inhibitor of motility, the inhibitor accumulating more in concave regions of the culture boundary, slowing advance of cells there, and less in convex areas, allowing advance and a further exaggeration of the concave/convex difference. Here we test this hypothesis using a two-dimensional culture system that includes strong flow conditions to remove accumulating diffusible secretions. We find that, while motility does indeed follow boundary curvature in this system, flow makes no difference: this challenges the hypothesis of control by a diffusible secreted autocrine inhibitor.

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.

Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k₀. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

Seeds of Locally Aligned Motion and Stress Coordinate a Collective Cell Migration

We find how collective migration emerges from mechanical information transfer between cells. Local alignment of cell velocity and mechanical stress orientation-a phenomenon dubbed "plithotaxis"-plays a crucial role in inducing coordinated migration. Leader cells at the monolayer edge better align velocity and stress to migrate faster toward the open space. Local seeds of enhanced motion then generate stress on neighboring cells to guide their migration. Stress-induced motion propagates into the monolayer as well as along the monolayer boundary to generate increasingly larger clusters of coordinately migrating cells that move faster with enhanced alignment of velocity and stress. Together, our analysis provides a model of long-range mechanical communication between cells, in which plithotaxis translates local mechanical fluctuations into globally collective migration of entire tissues.

Active micromachines: Microfluidics powered by mesoscale turbulence

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.

Advancing Edge Speeds of Epithelial Monolayers Depend on Their Initial Confining Geometry

Collective cell migrations are essential in several physiological processes and are driven by both chemical and mechanical cues. The roles of substrate stiffness and confinement on collective migrations have been investigated in recent years, however few studies have addressed how geometric shapes influence collective cell migrations. Here, we address the hypothesis that the relative position of a cell within the confinement influences its motility. Monolayers of two types of epithelial cells--MCF7, a breast epithelial cancer cell line, and MDCK, a control epithelial cell line--were confined within circular, square, and cross-shaped stencils and their migration velocities were quantified upon release of the constraint using particle image velocimetry. The choice of stencil geometry allowed us to investigate individual cell motility within convex, straight and concave boundaries. Cells located in sharp, convex boundaries migrated at slower rates than those in concave or straight edges in both cell types. The overall cluster migration occurred in three phases: an initial linear increase with time, followed by a plateau region and a subsequent decrease in cluster speeds. An acto-myosin contractile ring, present in the MDCK but absent in MCF7 monolayer, was a prominent feature in the emergence of leader cells from the MDCK clusters which occurred every ~125 μm from the vertex of the cross. Further, coordinated cell movements displayed vorticity patterns in MDCK which were absent in MCF7 clusters. We also used cytoskeletal inhibitors to show the importance of acto-myosin bounding cables in collective migrations through translation of local movements to create long range coordinated movements and the creation of leader cells within ensembles. To our knowledge, this is the first demonstration of how bounding shapes influence long-term migratory behaviours of epithelial cell monolayers. These results are important for tissue engineering and may also enhance our understanding of cell movements during developmental patterning and cancer metastasis.

Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers

We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cell assemblies to change the flow and director patterns and the density of topological defects. Finally we model the evolution of the boundary of a cellular colony and compare the fingering instabilities induced by cell division to experimental observations on the expansion of MDCK cell cultures.

Regulation of epithelial cell organization by tuning cell-substrate adhesion

Collective migration of cells is of fundamental importance for a number of biological functions such as tissue development and regeneration, wound healing and cancer metastasis. The movement of cell groups consisting of multiple cells connected by cell-cell junctions depends on both extracellular and intercellular contacts. Epithelial cell assemblies are thus regulated by a cross-talk between cell-substrate and cell-cell interactions. Here, we investigated the onset of collective migration in groups of cells as they expand from a few cells into large colonies as a function of extracellular matrix (ECM) protein coating. By varying the amount of ECM presented to the cells, we observe that the mode of colony expansion, as well as their overall geometry, is strongly dependent on substrate adhesiveness. On high ECM protein coated surfaces, cells at the edges of the colonies are well spread exhibiting large outward-pointing protrusive activity, whereas cellular colonies display more circular and convex shapes on less adhesive surfaces. Actin structures at the edge of the colonies also show different organizations with the formation of lamellipodial structures on highly adhesive surfaces and a pluricellular actin cable on less adhesive ones. The analysis of traction forces and cell velocities within the cellular assemblies confirm these results. By increasing ECM protein density, cells exert higher traction forces together with a higher outward motility at the edges. Furthermore, tuning cell-cell adhesion of epithelial cells modified the mode of expansion of the colonies. Finally, we used a recently developed computational model to recapitulate the emergent experimental behaviors of expanding cell colonies and extract that the main effect of the different cell-substrate interactions is on the ability of edge cells to form outward lamellipodia-driven motility. Overall, our data suggest that switching behaviors of epithelial cell assemblies result in a tug-of-war between friction forces at the cell-substrate interface and cell-cell interactions.

Flow and diffusion in channel-guided cell migration

Collective migration of mechanically coupled cell layers is a notable feature of wound healing, embryonic development, and cancer progression. In confluent epithelial sheets, the dynamics have been found to be highly heterogeneous, exhibiting spontaneous formation of swirls, long-range correlations, and glass-like dynamic arrest as a function of cell density. In contrast, the flow-like properties of one-sided cell-sheet expansion in confining geometries are not well understood. Here, we studied the short- and long-term flow of Madin-Darby canine kidney (MDCK) cells as they moved through microchannels. Using single-cell tracking and particle image velocimetry (PIV), we found that a defined averaged stationary cell current emerged that exhibited a velocity gradient in the direction of migration and a plug-flow-like profile across the advancing sheet. The observed flow velocity can be decomposed into a constant term of directed cell migration and a diffusion-like contribution that increases with density gradient. The diffusive component is consistent with the cell-density profile and front propagation speed predicted by the Fisher-Kolmogorov equation. To connect diffusion-mediated transport to underlying cellular motility, we studied single-cell trajectories and occurrence of vorticity. We discovered that the directed large-scale cell flow altered fluctuations in cellular motion at short length scales: vorticity maps showed a reduced frequency of swirl formation in channel flow compared with resting sheets of equal cell density. Furthermore, under flow, single-cell trajectories showed persistent long-range, random-walk behavior superimposed on drift, whereas cells in resting tissue did not show significant displacements with respect to neighboring cells. Our work thus suggests that active cell migration manifests itself in an underlying, spatially uniform drift as well as in randomized bursts of short-range correlated motion that lead to a diffusion-mediated transport.

Emerging morphologies in round bacterial colonies: comparing volumetric versus chemotactic expansion

Biological experiments performed on living bacterial colonies have demonstrated the microbial capability to develop finger-like shapes and highly irregular contours, even starting from an homogeneous inoculum. In this work, we study from the continuum mechanics viewpoint the emergence of such branched morphologies in an initially circular colony expanding on the top of a Petri dish coated with agar. The bacterial colony expansion, based on either a source term, representing volumetric mitotic processes, or a nonconvective mass flux, describing chemotactic expansion, is modeled at the continuum scale. We demonstrate that the front of the colony is always linearly unstable, having similar dispersion curves to the ones characterizing branching instabilities. We also perform finite element simulations, which not only prove the emergence of branching, but also highlight dramatic differences between the two mechanisms of colony expansion in the nonlinear regime. Furthermore, the proposed combination of analytical and numerical analysis allowed studying the influence of different model parameters on the selection of specific patterns. A very good agreement has been found between the resulting simulations and the typical structures observed in biological assays. Finally, this work provides a new interpretation of the emergence of branched patterns in living aggregates, depicted as the results of a complex interplay among chemical, mechanical and size effects.

Gap geometry dictates epithelial closure efficiency

Closure of wounds and gaps in tissues is fundamental for the correct development and physiology of multicellular organisms and, when misregulated, may lead to inflammation and tumorigenesis. To re-establish tissue integrity, epithelial cells exhibit coordinated motion into the void by active crawling on the substrate and by constricting a supracellular actomyosin cable. Coexistence of these two mechanisms strongly depends on the environment. However, the nature of their coupling remains elusive because of the complexity of the overall process. Here we demonstrate that epithelial gap geometry in both in vitro and in vivo regulates these collective mechanisms. In addition, the mechanical coupling between actomyosin cable contraction and cell crawling acts as a large-scale regulator to control the dynamics of gap closure. Finally, our computational modelling clarifies the respective roles of the two mechanisms during this process, providing a robust and universal mechanism to explain how epithelial tissues restore their integrity.

Coherent motions in confluent cell monolayer sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.

Phenomenological approaches to collective behavior in epithelial cell migration

Collective cell migration in epithelial tissues resembles fluid-like behavior in time-lapse recordings. In the last years, hydrodynamic velocity fields in living matter have been studied intensely. The emergent properties were remarkably similar to phenomena known from active soft matter systems. Here, we review migration experiments of large cellular ensembles as well as of mesoscopic cohorts in micro-structured environments. Concepts such as diffusion, velocity correlations, swirl strength and polarization are metrics to quantify the cellular dynamics both in experiments as well as in computational simulations. We discuss challenges relating collective migration to single cell and oligocellular behavior as well as linking the phenotypic parameters to the underlying cytoskeleton dynamics and signaling networks. This article is part of a Special Issue entitled: Mechanobiology.

Collisions of deformable cells lead to collective migration

Collective migration of eukaryotic cells plays a fundamental role in tissue growth, wound healing and immune response. The motion, arising spontaneously or in response to chemical and mechanical stimuli, is also important for understanding life-threatening pathologies, such as cancer and metastasis formation. We present a phase-field model to describe the movement of many self-organized, interacting cells. The model takes into account the main mechanisms of cell motility - acto-myosin dynamics, as well as substrate-mediated and cell-cell adhesion. It predicts that collective cell migration emerges spontaneously as a result of inelastic collisions between neighboring cells: collisions lead to a mutual alignment of the cell velocities and to the formation of coherently-moving multi-cellular clusters. Small cell-to-cell adhesion, in turn, reduces the propensity for large-scale collective migration, while higher adhesion leads to the formation of moving bands. Our study provides valuable insight into biological processes associated with collective cell motility.

Modeling the finger instability in an expanding cell monolayer

Curvature-controlled cellular forces at the edge of an expanding monolayer are sufficient for the initiation and growth of finger-like instability.

Collective and individual migration following the epithelial-mesenchymal transition

During cancer progression, malignant cells in the tumour invade surrounding tissues. This transformation of adherent cells to a motile phenotype has been associated with the epithelial-mesenchymal transition (EMT). Here, we show that EMT-activated cells migrate through micropillar arrays as a collectively advancing front that scatters individual cells. Individual cells with few neighbours dispersed with fast, straight trajectories, whereas cells that encountered many neighbours migrated collectively with epithelial biomarkers. We modelled these emergent dynamics using a physical analogy to phase transitions during binary-mixture solidification, and validated it using drug perturbations, which revealed that individually migrating cells exhibit diminished chemosensitivity. Our measurements also indicate a degree of phenotypic plasticity as cells interconvert between individual and collective migration. The study of multicellular behaviours with single-cell resolution should enable further quantitative insights into heterogeneous tumour invasion.

Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells

The leading front of a collectively migrating epithelium often destabilizes into multicellular migration fingers where a cell initially similar to the others becomes a leader cell while its neighbours do not alter. The determinants of these leader cells include mechanical and biochemical cues, often under the control of small GTPases. However, an accurate dynamic cartography of both mechanical and biochemical activities remains to be established. Here, by mapping the mechanical traction forces exerted on the surface by MDCK migration fingers, we show that these structures are mechanical global entities with the leader cells exerting a large traction force. Moreover, the spatial distribution of RhoA differential activity at the basal plane strikingly mirrors this force cartography. We propose that RhoA controls the development of these fingers through mechanical cues: the leader cell drags the structure and the peripheral pluricellular acto-myosin cable prevents the initiation of new leader cells.

Galvanotactic control of collective cell migration in epithelial monolayers

Many normal and pathological biological processes involve the migration of epithelial cell sheets. This arises from complex emergent behaviour resulting from the interplay between cellular signalling networks and the forces that physically couple the cells. Here, we demonstrate that collective migration of an epithelium can be interactively guided by applying electric fields that bias the underlying signalling networks. We show that complex, spatiotemporal cues are locally interpreted by the epithelium, resulting in rapid, coordinated responses such as a collective U-turn, divergent migration, and unchecked migration against an obstacle. We observed that the degree of external control depends on the size and shape of the cell population, and on the existence of physical coupling between cells. Together, our results offer design and engineering principles for the rational manipulation of the collective behaviour and material properties of a tissue.

Polarizing cytoskeletal tension to induce leader cell formation during collective cell migration

The collective migration of cells is fundamental to epithelial biology. One of the hallmarks of collective behavior in migrating cohesive epithelial cell sheets is the emergence of so called leader cells. These cells exhibit a distinct morphology with a large and highly active lamellipodium. Although it is generally accepted that they play a crucial part in collective migration, the biophysical factors that regulate their formation remain unknown.Here we show that a geometry-based cue like local variation of curvature of the collective's perimeter is capable of triggering leader cell formation and promoting enhanced motility at defined positions. Remarkably, the extent of this effect scales with the magnitude of the curvature.Cytoskeletal tension was found to be important for geometry induced leader cell formation, as cells treated with tension reducing agents appeared less sensitive to local curvature variation. Accordingly, traction force microscopy revealed an increased level of shear stress at highly curved positions even before the cell migration had actually started, indicating the presence of a collective polarization induced by the geometry of the confinement.Together our findings suggest that high curvature leads to locally increased stress accumulation, mediated via cell-substrate interaction as well as via cytoskeleton tension. The stress accumulation in turn enhances the probability of leader cell formation as well as cell motility. This work defines the importance of geometric cue such as local curvature in the collective migration dynamics of epithelial cells and thus shows implications for the biophysical regulation of epithelium during wound healing, embryonic development, and oncogenesis.

Cell migration

Cell migration is fundamental to establishing and maintaining the proper organization of multicellular organisms. Morphogenesis can be viewed as a consequence, in part, of cell locomotion, from large-scale migrations of epithelial sheets during gastrulation, to the movement of individual cells during development of the nervous system. In an adult organism, cell migration is essential for proper immune response, wound repair, and tissue homeostasis, while aberrant cell migration is found in various pathologies. Indeed, as our knowledge of migration increases, we can look forward to, for example, abating the spread of highly malignant cancer cells, retarding the invasion of white cells in the inflammatory process, or enhancing the healing of wounds. This article is organized in two main sections. The first section is devoted to the single-cell migrating in isolation such as occurs when leukocytes migrate during the immune response or when fibroblasts squeeze through connective tissue. The second section is devoted to cells collectively migrating as part of multicellular clusters or sheets. This second type of migration is prevalent in development, wound healing, and in some forms of cancer metastasis.