Glass-like dynamics of collective cell migration

How adherens junctions move cells during collective migration

In this review, we consider how the association between adherens junctions and the actomyosin cytoskeleton influences collective cell movement. We focus on recent findings which reveal different ways for adherens junctions to promote the locomotion of cells within tissues: through lamellipodia and junctional contraction. These contributions reflect how classic cadherins establish sites of cortical actin assembly and how adherens junctions couple to contractile actomyosin, respectively. The diverse interplay between cadherin adhesion and the cytoskeleton thus provides different ways for adherens junctions to support epithelial locomotion.

Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue

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 theoretical development difficult. The cellular Potts model (CPM) of confluent monolayers provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of the CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first-order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within the CPM is qualitatively similar to that in the VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P_{0} is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. The fragility of the system decreases with increasing P_{0} in the low-P_{0} regime, whereas the dynamics is independent of P_{0} in the other regime. The rigidity transition, found in the VM, is absent within the CPM; this difference seems to come from the nonequilibrium nature of the former. We show that the CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at subcellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

Topological data analysis of collective and individual epithelial cells using persistent homology of loops

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase transitions have been described based on local ordering, which may not capture structural features at larger length scales. Instead, topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology), and can compare different particle configurations based on the "cost" of reorganizing one configuration into another. Here, we demonstrate a topology-based machine learning approach for unsupervised profiling of individual and collective phases based on large-scale loops. We show that these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to map out phase diagrams for simulated particles with varying adhesion and propulsion, at constant population size as well as when proliferation is permitted. Next, we use this approach to profile our recent experiments on the clustering of epithelial cells in varying growth factor conditions, which are compared to our simulations. Finally, we characterize the robustness of this approach at varying length scales, with sparse sampling, and over time. Overall, we envision TDA will be broadly applicable as a model-agnostic approach to analyze active systems with varying population size, from cytoskeletal motors to motile cells to flocking or swarming animals.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

How to study a persistent active glassy system

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescaleτ_p, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times. We describe in detail a recently proposed scheme that allows one to study directly the dynamics in the large persistence time limit, on timescales around and well above the persistence time. We discuss the idea behind the proposed scheme, which we call 'activity-driven dynamics', as well as its numerical implementation. We establish that our prescription faithfully reproduces all dynamical quantities in the appropriate limitτ_p→ ∞. We deploy the approach to explore in detail the statistics of Eshelby-like plastic events in the steady state dynamics of a dense and intermittent active glass.

Glass-like characteristics of intracellular motion in human cells

The motion in the cytosol of microorganisms such as bacteria and yeast has been observed to undergo a dramatic slowing down upon cell energy depletion. These observations have been interpreted as the motion being "glassy," but whether this notion is useful also for active, motor-protein-driven transport in eukaryotic cells is less clear. Here, we use fluorescence microscopy of beads in human (HeLa) cells to probe the motion of membrane-surrounded structures that are carried along the cytoskeleton by motor proteins. Evaluating several hallmarks of glassy dynamics, we show that at short length scales, the motion is heterogeneous, is nonergodic, is well described by a model for the displacement distribution in glassy systems, and exhibits a decoupling of the exchange and persistence times. Overall, these results suggest that the short length scale behavior of objects that can be transported actively by motor proteins in human cells shares features with the motion in glassy systems.

Disentangling collective motion and local rearrangements in 2D and 3D cell assemblies

The accurate quantification of cellular motility and of the structural changes occurring in multicellular aggregates is critical in describing and understanding key biological processes, such as wound repair, embryogenesis and cancer invasion. Current methods based on cell tracking or velocimetry either suffer from limited spatial resolution or are challenging and time-consuming, especially for three-dimensional (3D) cell assemblies. Here we propose a conceptually simple, robust and tracking-free approach for the quantification of the dynamical activity of cells via a two-step procedure. We first characterise the global features of the collective cell migration by registering the temporal stack of the acquired images. As a second step, a map of the local cell motility is obtained by performing a mean squared amplitude analysis of the intensity fluctuations occurring when two registered image frames acquired at different times are subtracted. We successfully apply our approach to cell monolayers undergoing a jamming transition, as well as to monolayers and 3D aggregates that exhibit a cooperative unjamming-via-flocking transition. Our approach is capable of disentangling very efficiently and of assessing accurately the global and local contributions to cell motility.

Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.

Structural characterization and statistical properties of jammed soft ellipsoid packing

The jamming transition and jammed packing structures of hydrogel soft ellipsoids are studied using magnetic resonance imaging techniques. As the packing fraction increases, the fluctuation of local free volume decreases and the fluctuation of particle deformation increases. Effective thermodynamic quantities are obtained by characterizing these fluctuations using k-gamma distributions based on an underlying statistical model for granular materials. Surprisingly, the two granular temperatures measuring the relative fluctuations of both free volume and particle deformation remain basically unchanged as the packing fraction increases. The total configurational entropy is also approximately constant for packing with different packing fractions. The significantly different behaviors of these effective thermodynamic quantities compared with hard sphere systems are further attributed to a statistically affine structural transformation of the packing structures along with particle deformations when the packing fraction changes.

Cell cycle-dependent active stress drives epithelia remodeling

Epithelia have distinct cellular architectures which are established in development, reestablished after wounding, and maintained during tissue homeostasis despite cell turnover and mechanical perturbations. In turn, cell shape also controls tissue function as a regulator of cell differentiation, proliferation, and motility. Here, we investigate cell shape changes in a model epithelial monolayer. After the onset of confluence, cells continue to proliferate and change shape over time, eventually leading to a final architecture characterized by arrested motion and more regular cell shapes. Such monolayer remodeling is robust, with qualitatively similar evolution in cell shape and dynamics observed across disparate perturbations. Here, we quantify differences in monolayer remodeling guided by the active vertex model to identify underlying order parameters controlling epithelial architecture. When monolayers are formed atop an extracellular matrix with varied stiffness, we find the cell density at which motion arrests varies significantly, but the cell shape remains constant, consistent with the onset of tissue rigidity. In contrast, pharmacological perturbations can significantly alter the cell shape at which tissue dynamics are arrested, consistent with varied amounts of active stress within the tissue. Across all experimental conditions, the final cell shape is well correlated to the cell proliferation rate, and cell cycle inhibition immediately arrests cell motility. Finally, we demonstrate cell cycle variation in junctional tension as a source of active stress within the monolayer. Thus, the architecture and mechanics of epithelial tissue can arise from an interplay between cell mechanics and stresses arising from cell cycle dynamics.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Dynamic heterogeneity flow promotes binding reactions in a dense system of hard annular sector particles

We perform molecular dynamics simulations on a system of hard annular sector particles (ASPs) to investigate the reaction-dynamics relationship. The dimerization reaction zone, mixing reaction zone including dimerization and n-merization (n > 2), and arrested region are observed successively as area fraction φ_A increases from low to high. In this work, we focus on the properties of the concentrated arrested region (φ_A≥ 0.400). The results show that for systems at φ_A≥ 0.400, the ratio of n-merization increases with φ_A and n-merization finally becomes the dominant reaction in the system; dynamic heterogeneity (DH) is observed and is demonstrated to originate from the divergent size of clusters consisting of high-mobility particles; the particles with a high translational or rotational mobility are found to have a high ability to react with other particles at φ_A > 0.400; more interestingly, binding reactions are found to correlate spatially with DH at φ_A > 0.400. Our work sheds new light on understanding the role of DH in binding reactions or specific-site recognition assembly in a crowded environment.

Connecting relaxation time to a dynamical length scale in athermal active glass formers

Supercooled liquids display dynamics that are inherently heterogeneous in space. This essentially means that at temperatures below the melting point, particle dynamics in certain regions of the liquid can be orders of magnitude faster than other regions. Often dubbed dynamical heterogeneity, this behavior has fascinated researchers involved in the study of glass transition for over two decades. A fundamentally important question in all glass transition studies is whether one can connect the growing relaxation time to a concomitantly growing length scale. In this paper, we go beyond the realm of ordinary glass forming liquids and study the origin of a growing dynamical length scale ξ in a self-propelled "active" glass former. This length scale, which is constructed using structural correlations, agrees well with the average size of the clusters of slow-moving particles that are formed as the liquid becomes spatially heterogeneous. We further report that the concomitantly growing α-relaxation time exhibits a simple scaling law, τ_{α}∼exp(μξ/T_{eff}), with μ as an effective chemical potential, T_{eff} as the effective temperature, and μξ as the growing free energy barrier for cluster rearrangements. The findings of our study are valid over four decades of persistence times, and hence they could be very useful in understanding the slow dynamics of a generic active liquid such as an active colloidal suspension, or a self-propelled granular medium.

Observation of liquid glass in suspensions of ellipsoidal colloids

Despite the omnipresence of colloidal suspensions, little is known about the influence of colloid shape on phase transformations, especially in nonequilibrium. To date, real-space imaging results at high concentrations have been limited to systems composed of spherical colloids. In most natural and technical systems, however, particles are nonspherical, and their structural dynamics are determined by translational and rotational degrees of freedom. Using confocal microscopy of fluorescently labeled core-shell particles, we reveal that suspensions of ellipsoidal colloids form an unexpected state of matter, a liquid glass in which rotations are frozen while translations remain fluid. Image analysis unveils hitherto unknown nematic precursors as characteristic structural elements of this state. The mutual obstruction of these ramified clusters prevents liquid crystalline order. Our results give insight into the interplay between local structures and phase transformations. This helps to guide applications such as self-assembly of colloidal superstructures and also gives evidence of the importance of shape on the glass transition in general.

Multiple dynamic regimes in a coarsening foam

Intermittent dynamics driven by internal stress imbalances in disordered systems is a fascinating yet poorly understood phenomenon. Here, we study it for a coarsening foam. By exploiting differential dynamic microscopy and particle tracking we determine the dynamical characteristics of the foam at different ages in reciprocal and direct space, respectively. At all wavevectors q investigated, the intermediate scattering function exhibits a compressed exponential decay. However, the access to unprecedentedly small values of q highlights the existence of two distinct regimes for the q-dependence of the foam relaxation rate Γ(q). At high q, Γ(q) ∼ q consistent with directionally-persistent and intermittent bubble displacements. At low q, we find the surprising scaling Γ(q) ∼ q ^δ , with δ = 1.6 ± 0.2. The analysis of the bubble displacement distribution in real space reveals the existence of a displacement cut-off of the order of the bubble diameter. Introducing such cut-off length in an existing model, describing stress-driven dynamics in disordered systems, fully accounts for the observed behavior in direct and reciprocal space.

Highly strained mixtures of bidimensional soft and rigid grains: an experimental approach from the local scale

Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D bidisperse systems made of both soft and rigid grains. By means of a recently developed experimental set-up, from the measurement of the displacementfield we can follow all the mechanical observables of this granular medium from the inside of each particle up-to the whole system scale. We are able to detect the jamming transition from these observables and study their evolution deep in the jammed state for packing fractions as high as 0.915. We show the uniqueness of the behavior of such a system, in which way it is similar to purely soft or rigid systems and how it is different from them. This study constitutes thefirst step toward a better understanding of mechanical behavior of granular materials that are polydisperse in terms of grain rheology.

Tracking collective cell motion by topological data analysis

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

Caveolin-1 influences epithelial collective cell migration via FMNL2 formin

BACKGROUND INFORMATION

Epithelial collective cell migration requires the intrinsic locomotor activity of cells to be coordinated across populations. This coordination is governed by the presence of cell-cell adhesions as well as the cooperative behaviour of cells within the monolayer.

RESULTS

Here, we report a role for Caveolin-1 (CAV1) in epithelial collective cell migration. CAV1 depletion reduced the migratory behaviour of AML12 liver epithelial cells when grown as monolayers, but not as individual cells. This suggested that CAV1 is a component of the process by which multicellular collectivity regulates epithelial motility. The correlation length for migration velocity was increased by CAV1 RNAi, a possible sign of epithelial jamming. However, CAV1 RNAi reduced migration, even when monolayers were allowed to migrate into unconfined spaces. The migratory defect was ameliorated by simultaneous depletion of the FMNL2 formin, whose cortical recruitment is increased in CAV1 RNAi cells.

CONCLUSIONS

We therefore suggest that CAV1 modulates intraepithelial motility by controlling the cortical availability of FMNL2.

SIGNIFICANCE

Although epithelial collective cell migration has been observed in multiple contexts both in vivo and in vitro, the inherent coupling and coordination of activity between cells within the monolayer remain incompletely understood. Our study highlights a role for CAV1 in regulating intraepithelial motility, an effect that involves the formin FMNL2.

Multiple Types of Aging in Active Glasses

Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids. This leads to a fundamental question: how do these nonequilibrium (active) amorphous materials differ from conventional passive glasses, created by lowering temperature or increasing density? To address this we investigate the aging after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behavior of this dense active matter system: short persistence times of the active forcing give effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times and activity-driven aging at late times. We develop a dedicated simulation method that gives access to this longtime scaling regime for highly persistent active forces.

Lipid Dynamics in Membranes Slowed Down by Transmembrane Proteins

Lipids and proteins, as essential components of biological cell membranes, exhibit a significant degree of freedom for different kinds of motions including lateral long-range mobility. Due to their interactions, they not only preserve the cellular membrane but also contribute to many important cellular functions as e.g., signal transport or molecular exchange of the cell with its surrounding. Many of these processes take place on a short time (up to some nanoseconds) and length scale (up to some nanometers) which is perfectly accessible by quasielastic neutron scattering (QENS) experiments and molecular dynamics (MD) simulations. In order to probe the influence of a peptide, a transmembrane sequence of the transferrin receptor (TFRC) protein, on the dynamics of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) large unilamellar vesicles (LUVs) on a nanosecond time scale, high-resolution QENS experiments and complementary MD simulations have been utilized. By using different scattering contrasts in the experiment (chain-deuterated lipids and protonated lipids, respectively), a model could be developed which allows to examine the lipid and peptide dynamics separately. The experimental results revealed a restricted lipid lateral mobility in the presence of the TFRC transmembrane peptides. Also the apparent self-diffusion coefficient of the lateral movement of the peptide molecules could be determined quantitatively for the probed short-time regime. The findings could be confirmed very precisely by MD simulations. Furthermore, the article presents an estimation for the radius of influence of the peptides on the lipid long-range dynamics which could be determined by consistently combining results from experiment and simulation.

Epithelial layer unjamming shifts energy metabolism toward glycolysis

In development of an embryo, healing of a wound, or progression of a carcinoma, a requisite event is collective epithelial cellular migration. For example, cells at the advancing front of a wound edge tend to migrate collectively, elongate substantially, and exert tractions more forcefully compared with cells many ranks behind. With regards to energy metabolism, striking spatial gradients have recently been reported in the wounded epithelium, as well as in the tumor, but within the wounded cell layer little is known about the link between mechanical events and underlying energy metabolism. Using the advancing confluent monolayer of MDCKII cells as a model system, here we report at single cell resolution the evolving spatiotemporal fields of cell migration speeds, cell shapes, and traction forces measured simultaneously with fields of multiple indices of cellular energy metabolism. Compared with the epithelial layer that is unwounded, which is non-migratory, solid-like and jammed, the leading edge of the advancing cell layer is shown to become progressively more migratory, fluid-like, and unjammed. In doing so the cytoplasmic redox ratio becomes progressively smaller, the NADH lifetime becomes progressively shorter, and the mitochondrial membrane potential and glucose uptake become progressively larger. These observations indicate that a metabolic shift toward glycolysis accompanies collective cellular migration but show, further, that this shift occurs throughout the cell layer, even in regions where associated changes in cell shapes, traction forces, and migration velocities have yet to penetrate. In characterizing the wound healing process these morphological, mechanical, and metabolic observations, taken on a cell-by-cell basis, comprise the most comprehensive set of biophysical data yet reported. Together, these data suggest the novel hypothesis that the unjammed phase evolved to accommodate fluid-like migratory dynamics during episodes of tissue wound healing, development, and plasticity, but is more energetically expensive compared with the jammed phase, which evolved to maintain a solid-like non-migratory state that is more energetically economical.

3D alveolar in vitro model based on epithelialized biomimetically curved culture membranes

There is increasing evidence that surface curvature at a near-cell-scale influences cell behaviour. Epithelial or endothelial cells lining small acinar or tubular body lumens, as those of the alveoli or blood vessels, experience such highly curved surfaces. In contrast, the most commonly used culture substrates for in vitro modelling of these human tissue barriers, ion track-etched membranes, offer only flat surfaces. Here, we propose a more realistic culture environment for alveolar cells based on biomimetically curved track-etched membranes, preserving the mainly spherical geometry of the cells' native microenvironment. The curved membranes were created by a combination of three-dimensional (3D) micro film (thermo)forming and ion track technology. We could successfully demonstrate the formation, the growth and a first characterization of confluent layers of lung epithelial cell lines and primary alveolar epithelial cells on membranes shaped into an array of hemispherical microwells. Besides their application in submerged culture, we could also demonstrate the compatibility of the bioinspired membranes for air-exposed culture. We observed a distinct cellular response to membrane curvature. Cells (or cell layers) on the curved membranes reveal significant differences compared to cells on flat membranes concerning membrane epithelialization, areal cell density of the formed epithelial layers, their cross-sectional morphology, and proliferation and apoptosis rates, and the same tight barrier function as on the flat membranes. The presented 3D membrane technology might pave the way for more predictive barrier in vitro models in future.

In primary airway epithelial cells, the unjamming transition is distinct from the epithelial-to-mesenchymal transition

The epithelial-to-mesenchymal transition (EMT) and the unjamming transition (UJT) each comprises a gateway to cellular migration, plasticity and remodeling, but the extent to which these core programs are distinct, overlapping, or identical has remained undefined. Here, we triggered partial EMT (pEMT) or UJT in differentiated primary human bronchial epithelial cells. After triggering UJT, cell-cell junctions, apico-basal polarity, and barrier function remain intact, cells elongate and align into cooperative migratory packs, and mesenchymal markers of EMT remain unapparent. After triggering pEMT these and other metrics of UJT versus pEMT diverge. A computational model attributes effects of pEMT mainly to diminished junctional tension but attributes those of UJT mainly to augmented cellular propulsion. Through the actions of UJT and pEMT working independently, sequentially, or interactively, those tissues that are subject to development, injury, or disease become endowed with rich mechanisms for cellular migration, plasticity, self-repair, and regeneration.

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Cell-cell adhesion and 3D matrix confinement determine jamming transitions in breast cancer invasion

Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single-cell dissemination, controlled by cadherin-mediated cell-cell junctions. In clinical samples, E-cadherin-expressing and -deficient tumours both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Here, using spatially defined organotypic culture, intravital microscopy of mammary tumours in mice and in silico modelling, we identify cell density regulation by three-dimensional tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions by downregulation of E-cadherin and p120-catenin resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas single-cell escape depended on locally free tissue space. These results indicate that cadherins and extracellular matrix confinement cooperate to determine unjamming transitions and stepwise epithelial fluidization towards, ultimately, cell individualization.

Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia

The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.

Introduction to Active Matter

Moumita Das, Michael Murrell and Christoph Schmidt introduce the Soft Matter collection on active matter.

The Role of Tricellulin in Epithelial Jamming and Unjamming via Segmentation of Tricellular Junctions

Collective cellular behavior in confluent monolayers supports physiological and pathological processes of epithelial development, regeneration, and carcinogenesis. Here, the attainment of a mature and static tissue configuration or the local reactivation of cell motility involve a dynamic regulation of the junctions established between neighboring cells. Tricellular junctions (tTJs), established at vertexes where three cells meet, are ideally located to control cellular shape and coordinate multicellular movements. However, their function in epithelial tissue dynamic remains poorly defined. To investigate the role of tTJs establishment and maturation in the jamming and unjamming transitions of epithelial monolayers, a semi-automatic image-processing pipeline is developed and validated enabling the unbiased and spatially resolved determination of the tTJ maturity state based on the localization of fluorescent reporters. The software resolves the variation of tTJ maturity accompanying collective transitions during tissue maturation, wound healing, and upon the adaptation to osmolarity changes. Altogether, this work establishes junctional maturity at tricellular contacts as a novel biological descriptor of collective responses in epithelial monolayers.

Dynamic heterogeneity influences the leader-follower dynamics during epithelial wound closure

Cells of epithelial tissue proliferate and pack together to attain an eventual density homeostasis. As the cell density increases, spatial distribution of velocity and force show striking similarity to the dynamic heterogeneity observed elsewhere in dense granular matter. While the physical nature of this heterogeneity is somewhat known in the epithelial cell monolayer, its biological relevance and precise connection to cell density remain elusive. Relevantly, we had demonstrated how large-scale dynamic heterogeneity in the monolayer stress field in the bulk could critically influence the emergence of leader cells at the wound margin during wound closure, but did not connect the observation to the corresponding cell density. In fact, numerous previous reports had essentially associated long-range force and velocity correlation with either cell density or dynamic heterogeneity, without any generalization. Here, we attempted to unify these two parameters under a single framework and explored their consequence on the dynamics of leader cells, which eventually affected the efficacy of collective migration and wound closure. To this end, we first quantified the dynamic heterogeneity by the peak height of four-point susceptibility. Remarkably, this quantity showed a linear relationship with cell density over many experimental samples. We then varied the heterogeneity, by changing cell density, and found this change altered the number of leader cells at the wound margin. At low heterogeneity, wound closure was slower, with decreased persistence, reduced coordination and disruptive leader-follower interactions. Finally, microscopic characterization of cell-substrate adhesions illustrated how heterogeneity influenced orientations of focal adhesions, affecting coordinated cell movements. Together, these results demonstrate the importance of dynamic heterogeneity in epithelial wound healing. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Solid-Liquid Transition of Deformable and Overlapping Active Particles

Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.

Mechanobiology of leader-follower dynamics in epithelial cell migration

Collective cell migration is fundamental to biological form and function. It is also relevant to the formation and repair of organs and to various pathological situations, including metastatic propagation of cancer. Technological, experimental, and computational advancements have allowed the researchers to explore various aspects of collective migration, spanning from biochemical signalling to inter-cellular force transduction. Here, we summarize our current understanding of the mechanobiology of collective cell migration, limiting to epithelial tissues. On the basis of recent studies, we describe how cells sense and respond to guidance signals to orchestrate various modes of migration and identify the determining factors dictating leader-follower interactions. We highlight how the inherent mechanics of dense epithelial monolayers at multicellular length scale might instruct individual cells to behave collectively. On the basis of these findings, we propose that mechanical resilience, obtained by a certain extent of cell jamming, allows the epithelium to perform efficient collective migration during wound healing.

The role of extracellular matrix in normal and pathological pregnancy: Future applications of microphysiological systems in reproductive medicine

IMPACT STATEMENT

Extracellular matrix in the womb regulates the initiation, progression, and completion of a healthy pregnancy. The composition and physical properties of extracellular matrix in the uterus and at the maternal-fetal interface are remodeled at each gestational stage, while maladaptive matrix remodeling results in obstetric disease. As in vitro models of uterine and placental tissues, including micro-and milli-scale versions of these organs on chips, are developed to overcome the inherent limitations of studying human development in vivo, we can isolate the influence of cellular and extracellular components in healthy and pathological pregnancies. By understanding and recreating key aspects of the extracellular microenvironment at the maternal-fetal interface, we can engineer microphysiological systems to improve assisted reproduction, obstetric disease treatment, and prenatal drug safety.

Active microrheology of a bulk metallic glass

The glass transition remains unclarified in condensed matter physics. Investigating the mechanical properties of glass is challenging because any global deformation that might result in shear rejuvenation would require a prohibitively long relaxation time. Moreover, glass is well known to be heterogeneous, and a global perturbation would prevent exploration of local mechanical/transport properties. However, investigation based on a local probe, i.e., microrheology, may overcome these problems. Here, we establish active microrheology of a bulk metallic glass, via a probe particle driven into host medium glass. This technique is amenable to experimental investigations via nanoindentation tests. We provide distinct evidence of a strong relationship between the microscopic dynamics of the probe particle and the macroscopic properties of the host medium glass. These findings establish active microrheology as a promising technique for investigating the local properties of bulk metallic glass.

Spatiotemporal force and motion in collective cell migration

Cells move in collective groups in biological processes such as wound healing, morphogenesis, and cancer metastasis. How active cell forces produce the motion in collective cell migration is still unclear. Many theoretical models have been introduced to elucidate the relationship between the cell's active forces and different observations about the collective motion such as collective swirls, oscillations, and rearrangements. Though many models share the common feature of balancing forces in the cell layer, the specific relationships between force and motion vary among the different models, which can lead to different conclusions. Simultaneous experimental measurements of force and motion can aid in testing assumptions and predictions of the theoretical models. Here, we provide time-lapse images of cells in 1 mm circular islands, which are used to compute cell velocities, cell-substrate tractions, and monolayer stresses. Additional data are included from experiments that perturbed cell number density and actomyosin contractility. We expect this data set to be useful to researchers interested in force and motion in collective cell migration.

Engineering slit-like channels for studying the growth of epithelial tissues in 3D-confined spaces

The development of epithelial lumens in ducts is essential to the functioning of various organs and in organogenesis. Ductal elongation requires the collective migration of cell cohorts in three-dimensional (3D) confined spaces, while maintaining their epithelial integrity. Epithelial lumens generally adopt circular morphologies, however abnormalities in complex physiological environments can lead to the narrowing of glandular spaces that adopt elongated and slit-like morphologies. Here, we describe a simple method to form epithelial tissues in microchannels of various widths (100-300 µm) with a constant height of 25 µm that mimic elongated geometries of glandular spaces. The significance of this biomimetic platform has been evidenced by studying the migration of epithelial cell sheets inside these narrow slits of varying dimensions. We show that the growth of epithelial tissues in 3D-confined slits leads to a gradient of cell density along the slit axis and that the migration cell velocity depends on the extent of the spatial confinement. Our findings indicate that nuclear orientation is higher for leader cells and depends on the slit width, whereas YAP protein was predominantly localized in the nucleus of leader cells. This method will pave the way to studies aiming at understanding how 3D-confined spaces, which are reminiscent of in vivo pathological conditions, can affect the growth and the homeostasis of epithelial tissues.

Cell jamming, stratification and p63 expression in cultivated human corneal epithelial cell sheets

Corneal limbal epithelial stem cell transplantation using cultivated human corneal epithelial cell sheets has been used successfully to treat limbal stem cell deficiencies. Here we report an investigation into the quality of cultivated human corneal epithelial cell sheets using time-lapse imaging of the cell culture process every 20 minutes over 14 days to ascertain the level of cell jamming, a phenomenon in which cells become smaller, more rounded and less actively expansive. In parallel, we also assessed the expression of p63, an important corneal epithelial stem cell marker. The occurrence of cell jamming was variable and transient, but was invariably associated with a thickening and stratification of the cell sheet. p63 was present in all expanding cell sheets in the first 9 days of culture, but it's presence did not always correlate with stratification of the cell sheet. Nor did p63 expression necessarily persist in stratified cell sheets. An assessment of cell jamming, therefore, can shed significant light on the quality and regenerative potential of cultivated human corneal epithelial cell sheets.

Extreme active matter at high densities

We study the remarkable behaviour of dense active matter comprising self-propelled particles at large Péclet numbers, over a range of persistence times, from τ_p → 0, when the active fluid undergoes a slowing down of density relaxations leading to a glass transition as the active propulsion force f reduces, to τ_p → ∞, when as f reduces, the fluid jams at a critical point, with stresses along force-chains. For intermediate τ_p, a decrease in f drives the fluid through an intermittent phase before dynamical arrest at low f. This intermittency is a consequence of periods of jamming followed by bursts of plastic yielding associated with Eshelby deformations. On the other hand, an increase in f leads to an increase in the burst frequency; the correlated plastic events result in large scale vorticity and turbulence. Dense extreme active matter brings together the physics of glass, jamming, plasticity and turbulence, in a new state of driven classical matter.

While active matter exhibits unusual dynamics at low density, high density behavior has not been explored. Mandal et al. show that extreme dense active matter, shows a rich spectrum of behaviour from intermittent plastic bursts and turbulence, to glassy states and jamming in the limit of infinite persistence time.

Control of cell colony growth by contact inhibition

Contact inhibition is a cell property that limits the migration and proliferation of cells in crowded environments. Here we investigate the growth dynamics of a cell colony composed of migrating and proliferating cells on a substrate using a minimal model that incorporates the mechanisms of contact inhibition of locomotion and proliferation. We find two distinct regimes. At early times, when contact inhibition is weak, the colony grows exponentially in time, fully characterised by the proliferation rate. At long times, the colony boundary moves at a constant speed, determined only by the migration speed of a single cell and independent of the proliferation rate. Further, the model demonstrates how cell-cell alignment speeds up colony growth. Our model illuminates how simple local mechanical interactions give rise to contact inhibition, and from this, how cell colony growth is self-organised and controlled on a local level.

Mechanochemical Feedback Loops in Development and Disease

There is increasing evidence that both mechanical and biochemical signals play important roles in development and disease. The development of complex organisms, in particular, has been proposed to rely on the feedback between mechanical and biochemical patterning events. This feedback occurs at the molecular level via mechanosensation but can also arise as an emergent property of the system at the cellular and tissue level. In recent years, dynamic changes in tissue geometry, flow, rheology, and cell fate specification have emerged as key platforms of mechanochemical feedback loops in multiple processes. Here, we review recent experimental and theoretical advances in understanding how these feedbacks function in development and disease.

Solid-fluid transition and cell sorting in epithelia with junctional tension fluctuations

Tissues transition between solid-like and fluid-like behavior, which has major implications for morphogenesis and disease. These transitions can occur due to changes in the intrinsic shape of constituent cells and cell motility. We consider an alternative mechanism by studying tissues that explore the energy landscape through stochastic dynamics, driven by turnover of junctional molecular motors. To identify the solid-fluid transition, we start with single-component tissues and show that the mean cell-shape index uniquely describes the effective diffusion coefficient of cell movements, which becomes finite at the transition. We generalize our approach to two-component tissues, and explore cell-sorting dynamics both due to differential adhesion and due to differential degree of junctional fluctuations. We recover some known characteristic scaling relations describing the sorting kinetics, and discover some discrepancies from these relations in the case of differential-fluctuations-driven sorting. Finally, we show that differential fluctuations efficiently sort two solid-like tissues with a fluid intercompartmental boundary.

Collective dynamics of coherent motile cells on curved surfaces

Cellular dynamic behaviors in organ morphogenesis and embryogenesis are affected by geometrical constraints. In this paper, we investigate how the surface topology and curvature of the underlying substrate tailor collective cell migration. An active vertex model is developed to explore the collective dynamics of coherent cells crawling on curved surfaces. We show that cells can self-organize into rich dynamic patterns including local swirling, global rotation, spiral crawling, serpentine crawling, and directed migration, depending on the interplay between cell-cell interactions and geometric constraints. Increasing substrate curvature results in higher cell-cell bending energy and thus tends to suppress local swirling and enhance density fluctuations. Substrate topology is revealed to regulate both the collective migration modes and density fluctuations of cell populations. In addition, upon increasing noise intensity, a Kosterlitz-Thouless-like ordering transition can emerge on both undevelopable and developable surfaces. This study paves the way to investigate various in vivo morphomechanics that involve surface curvature and topology.

Dense active matter model of motion patterns in confluent cell monolayers

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 simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

Microscopic pathways for stress relaxation in repulsive colloidal glasses

Residual stresses are well-known companions of all glassy materials. They affect and, in many cases, even strongly modify important material properties like the mechanical response and the optical transparency. The mechanisms through which stresses affect such properties are, in many cases, still under study, and their full understanding can pave the way to a full exploitation of stress as a primary control parameter. It is, for example, known that stresses promote particle mobility at small length scales, e.g., in colloidal glasses, gels, and metallic glasses, but this connection still remains essentially qualitative. Exploiting a preparation protocol that leads to colloidal glasses with an exceptionally directional built-in stress field, we characterize the stress-induced dynamics and show that it can be visualized as a collection of "flickering," mobile regions with linear sizes of the order of ≈20 particle diameters (≈2 μm here) that move cooperatively, displaying an overall stationary but locally ballistic dynamics.

Fragile-to-strong crossover, growing length scales, and dynamic heterogeneity in Wigner glasses

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition theories. In these systems glassy behavior arises as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass-forming properties, observed normally in molecular glasses. Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions show that tuning the softness of the interaction potential, achievable by changing the monovalent salt concentration results in a continuous transition from fragile to strong behavior. Remarkably, this is found in a system where the well characterized interaction potential between the colloidal particles is isotropic. We also show that the predictions of the random first-order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, ξ∼(ϕ_{K}/ϕ-1)^{-ν} with ν=2/3 where ϕ_{K}, the analog of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity as the system is compressed. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular and polymer glasses. The large variations in the fragility are normally found only when the temperature dependence of the viscosity is examined for a large class of diverse glass-forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses.