Glass-like dynamics of collective cell migration

Structural fluctuations in active glasses

The glassy dynamics of dense active matter have recently become a topic of interest due to their importance in biological processes such as wound healing and tissue development. However, while the liquid-state properties of dense active matter have been studied in relation to the glass transition of active matter, the solid-state properties of active glasses have yet to be understood. In this work, we study the structural fluctuations in the active glasses composed of self-propelled particles. We develop a formalism to describe the solid-state properties of active glasses in the harmonic approximation limit and use it to analyze the displacement fields in the active glasses. Our findings reveal that the dynamics of high-frequency normal modes become quasi-static with respect to the active forces, and consequently, excitations of these modes are significantly suppressed. This leads to a violation of the equipartition law, suppression of particle displacements, and the apparent collective motion of active glasses. Overall, our results provide a fundamental understanding of the solid-state properties of active glasses.

The cellular Potts model on disordered lattices

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Cell-substrate distance fluctuations of confluent cells enable fast and coherent collective migration

Collective cell migration is an emergent phenomenon, with long-range cell-cell communication influenced by various factors, including transmission of forces, viscoelasticity of individual cells, substrate interactions, and mechanotransduction. We investigate how alterations in cell-substrate distance fluctuations, cell-substrate adhesion, and traction forces impact the average velocity and temporal-spatial correlation of confluent monolayers formed by either wild-type (WT) MDCKII cells or zonula occludens (ZO)-1/2-depleted MDCKII cells (double knockdown [dKD]) representing highly contractile cells. The data indicate that confluent dKD monolayers exhibit decreased average velocity compared to less contractile WT cells concomitant with increased substrate adhesion, reduced traction forces, a more compact shape, diminished cell-cell interactions, and reduced cell-substrate distance fluctuations. Depletion of basal actin and myosin further supports the notion that short-range cell-substrate interactions, particularly fluctuations driven by basal actomyosin, significantly influence the migration speed of the monolayer on a larger length scale.

Motility driven glassy dynamics in confluent epithelial monolayers

As wounds heal, embryos develop, cancer spreads, or asthma progresses, the cellular monolayer undergoes a glass transition between solid-like jammed and fluid-like flowing states. During some of these processes, the cells undergo an epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and become motile. Thus, how motility drives the glassy dynamics in epithelial systems is critical for the EMT process. However, no analytical framework that is indispensable for deeper insights exists. Here, we develop such a theory inspired by a well-known glass theory. One crucial result of this work is that the confluency affects the effective persistence time-scale of active force, described by its rotational diffusivity, Deffr. Deffr differs from the bare rotational diffusivity, Dr, of the motile force due to cell shape dynamics, which acts to rectify the force dynamics: Deffr is equal to Dr when Dr is small and saturates when Dr is large. We test the theoretical prediction of Deffr and how it affects the relaxation dynamics in our simulations of the active Vertex model. This novel effect of Deffr is crucial to understanding the new and previously published simulation data of active glassy dynamics in epithelial monolayers.

A two-dimensional vertex model for curvy cell-cell interfaces at the subcellular scale

Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date, two-dimensional vertex models predicting the structure and mechanics of cell monolayers have been mostly limited to convex polygons. To overcome this limitation, we introduce a framework to study curvy cell-cell interfaces at the subcellular scale within vertex models by using a parametrized curve between vertices that is expanded in a Fourier series and whose coefficients represent additional degrees of freedom. This extension to non-convex polygons allows for cells with the same shape index, or dimensionless perimeter, to be, for example, either elongated or globular with lobes. In the presence of applied, anisotropic stresses, we find that local, subcellular curvature or buckling can be energetically more favourable than larger scale deformations involving groups of cells. Inspired by recent experiments, we also find that local, subcellular curvature at cell-cell interfaces emerges in a group of cells in response to the swelling of additional cells surrounding the group. Our framework, therefore, can account for a wider array of multicellular responses to constraints in the tissue environment.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Multicell-Fold: geometric learning in folding multicellular life

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology. However, it remains a major challenge to understand and predict the behavior of every cell within the living tissue over time during such intricate processes. Here we present a geometric deep-learning model that can accurately capture the highly convoluted interactions among cells. We demonstrate that multicellular data can be represented with both granular and foam-like physical pictures through a unified graph data structure, considering both cellular interactions and cell junction networks. Using this model, we achieve interpretable 4-D morphological sequence alignment, and predicting cell rearrangements before they occur at single-cell resolution. Furthermore, using neural activation map and ablation studies, we demonstrate cell geometries and cell junction networks together regulate morphogenesis at single-cell precision. This approach offers a pathway toward a unified dynamic atlas for a variety of developmental processes.

Learning Dynamics from Multicellular Graphs with Deep Neural Networks

Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell migratory dynamics from their static configuration is valuable for both understanding and predicting these complex processes. However, the identification of structural features that can indicate multicellular motion has been difficult, and existing metrics largely rely on physical instincts. Here we show that using a graph neural network (GNN), the motion of multicellular collectives can be inferred from a static snapshot of cell positions, in both experimental and synthetic datasets.

A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics

Many critical biological processes, like wound healing, require densely packed cell monolayers/tissues to transition from a jammed solid-like to a fluid-like state. Although numerical studies anticipate changes in the cell shape alone can lead to unjamming, experimental support for this prediction is not definitive because, in living systems, fluidization due to density changes cannot be ruled out. Additionally, a cell's ability to modulate its motility only compounds difficulties since even in assemblies of rigid active particles, changing the nature of self-propulsion has non-trivial effects on the dynamics. Here, we design and assemble a monolayer of synthetic cell-mimics and examine their collective behaviour. By systematically increasing the persistence time of self-propulsion, we discovered a cell shape-driven, density-independent, re-entrant jamming transition. Notably, we observed cell shape and shape variability were mutually constrained in the confluent limit and followed the same universal scaling as that observed in confluent epithelia. Dynamical heterogeneities, however, did not conform to this scaling, with the fast cells showing suppressed shape variability, which our simulations revealed is due to a transient confinement effect of these cells by their slower neighbors. Our experiments unequivocally establish a morphodynamic link, demonstrating that geometric constraints alone can dictate epithelial jamming/unjamming.

Multiple aspects of matrix stiffness in cancer progression

The biophysical and biomechanical properties of the extracellular matrix (ECM) are crucial in the processes of cell differentiation and proliferation. However, it is unclear to what extent tumor cells are influenced by biomechanical and biophysical changes of the surrounding microenvironment and how this response varies between different tumor forms, and over the course of tumor progression. The entire ensemble of genes encoding the ECM associated proteins is called matrisome. In cancer, the ECM evolves to become highly dysregulated, rigid, and fibrotic, serving both pro-tumorigenic and anti-tumorigenic roles. Tumor desmoplasia is characterized by a dramatic increase of α-smooth muscle actin expressing fibroblast and the deposition of hard ECM containing collagen, fibronectin, proteoglycans, and hyaluronic acid and is common in many solid tumors. In this review, we described the role of inflammation and inflammatory cytokines, in desmoplastic matrix remodeling, tumor state transition driven by microenvironment forces and the signaling pathways in mechanotransduction as potential targeted therapies, focusing on the impact of qualitative and quantitative variations of the ECM on the regulation of tumor development, hypothesizing the presence of matrisome drivers, acting alongside the cell-intrinsic oncogenic drivers, in some stages of neoplastic progression and in some tumor contexts, such as pancreatic carcinoma, breast cancer, lung cancer and mesothelioma.

Emergence of bacterial glass

Densely packed, motile bacteria can adopt collective states not seen in conventional, passive materials. These states remain in many ways mysterious, and their physical characterization can aid our understanding of natural bacterial colonies and biofilms as well as materials in general. Here, we overcome challenges associated with generating uniformly growing, large, quasi-two-dimensional bacterial assemblies by a membrane-based microfluidic device and report the emergence of glassy states in two-dimensional suspension of Escherichia coli. As the number density increases by cell growth, populations of motile bacteria transition to a glassy state, where cells are packed and unable to move. This takes place in two steps, the first one suppressing only the orientational modes and the second one vitrifying the motion completely. Characterizing each phase through statistical analyses and investigations of individual motion of bacteria, we find not only characteristic features of glass such as rapid slowdown, dynamic heterogeneity, and cage effects, but also a few properties distinguished from those of thermal glass. These distinctive properties include the spontaneous formation of micro-domains of aligned cells with collective motion, the appearance of an unusual signal in the dynamic susceptibility, and the dynamic slowdown with a density dependence generally forbidden for thermal systems. Our results are expected to capture general characteristics of such active rod glass, which may serve as a physical mechanism underlying dense bacterial aggregates.

Perspectives in collective cell migration - moving forward

Collective cell migration, where cells move as a cohesive unit, is a vital process underlying morphogenesis and cancer metastasis. Thanks to recent advances in imaging and modelling, we are beginning to understand the intricate relationship between a cell and its microenvironment and how this shapes cell polarity, metabolism and modes of migration. The use of biophysical and mathematical models offers a fresh perspective on how cells migrate collectively, either flowing in a fluid-like state or transitioning to more static states. Continuing to unite researchers in biology, physics and mathematics will enable us to decode more complex biological behaviours that underly collective cell migration; only then can we understand how this coordinated movement of cells influences the formation and organisation of tissues and directs the spread of metastatic cancer. In this Perspective, we highlight exciting discoveries, emerging themes and common challenges that have arisen in recent years, and possible ways forward to bridge the gaps in our current understanding of collective cell migration.

Rotational inertia-induced glassy transition in chiral particle systems

The dense active matter exhibits characteristics reminiscent of traditional glassy phenomena, yet the role of rotational inertia in glass dynamics remains elusive. In this study, we investigate the glass dynamics of chiral active particles influenced by rotational inertia. Rotational inertia endows exponential memory to particle orientation, restricting its alteration and amplifying the effective persistence time. At lower spinning frequencies, the diffusion coefficient exhibits a peak function relative to rotational inertia for shorter persistence times, while it steadily increases with rotational inertia for longer persistence times. In the realm of high-frequency spinning, the impact of rotational inertia on diffusion behavior becomes more pronounced, resulting in a nonmonotonic and intricate relationship between the diffusion coefficient and rotational inertia. Consequently, the introduction of rotational inertia significantly alters the glassy dynamics of chiral active particles, allowing for the control over transitions between fluid and glassy states by modulating rotational inertia. Moreover, our findings indicate that at a specific spinning temperature, there exists an optimal spinning frequency at which the diffusion coefficient attains its maximum value.

Extinction and coexistence in a binary mixture of proliferating motile disks

A binary mixture of two-different-size proliferating motile disks is studied. As growth is space limited, we focus on the conditions such that there is a coexistence of both large and small disks, or dominance of the larger disks. The study involves systematically varying some system parameters, such as diffusivities, growth rates, and self-propulsion velocities. In particular, we demonstrate that diffusing faster confers a competitive advantage, so that larger disks can in the long time coexist or even dominate the smaller ones. In the case of self-propelled disks, a coexistence regime is induced by the activity where the two types of disks show the same spatial distribution: both particles are phase separated or both are homogeneously distributed in the whole system.

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

The ability of cells to organize into tissues with proper structure and function requires the effective coordination of proliferation, migration, polarization, and differentiation across length scales. Skeletal muscle is innately anisotropic; however, few biomaterials can emulate mechanical anisotropy to determine its influence on tissue patterning without introducing confounding topography. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topography, C2C12 myoblasts collectively polarize in the stiffest direction. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of the same chemical formulation. These findings provide valuable insights for designing biomaterials that mimic anisotropic microenvironments and underscore the importance of stiffness anisotropy in orchestrating tissue morphogenesis.

A novel strategy to facilitate uniform epithelial cell maturation using liquid-liquid interfaces

Epithelial tissue forms and maintains a critical barrier function in the body. A novel culture design aimed at promoting uniform maturation of epithelial cells using liquid materials is described. Culturing Madin-Darby canine kidney (MDCK) cells at the liquid-liquid interface yielded reduced migration and stimulated active cell growth. Similar to solid-liquid interfaces, cells cultured on a fibronectin-coated liquid-liquid interface exhibited active migration and growth, ultimately reaching a confluent state. These cells exhibited reduced stress fiber formation and adopted a cobblestone-like shape, which led to their even distribution in the culture vessel. To inhibit stress fiber formation and apoptosis, the exposure of cells on liquid-liquid interfaces to Y27632, a specific inhibitor of the Rho-associated protein kinase (ROCK), facilitated tight junction formation (frequency of ZO-2-positive cells, FZ = 0.73). In Y27632-exposed cells on the liquid-liquid interface, the value obtained by subtracting the standard deviation of the ratio of nucleus densities in each region that compartmentalized a culture vessel from 1, denoted as HLN, was 0.93 ± 0.01, indicated even cell distribution in the culture vessel at t = 72 h. The behavior of epithelial cells on liquid-liquid interfaces contributes to the promotion of their uniform maturation.

Cell Division and Motility Enable Hexatic Order in Biological Tissues

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

Confinement induces internal flows in adherent cell aggregates

During mesenchymal migration, F-actin protrusion at the leading edge and actomyosin contraction determine the retrograde flow of F-actin within the lamella. The coupling of this flow to integrin-based adhesions determines the force transmitted to the extracellular matrix and the net motion of the cell. In tissues, motion may also arise from convection, driven by gradients in tissue-scale surface tensions and pressures. However, how migration coordinates with convection to determine the net motion of cellular ensembles is unclear. To explore this, we study the spreading of cell aggregates on adhesive micropatterns on compliant substrates. During spreading, a cell monolayer expands from the aggregate towards the adhesive boundary. However, cells are unable to stabilize the protrusion beyond the adhesive boundary, resulting in retraction of the protrusion and detachment of cells from the matrix. Subsequently, the cells move upwards and rearwards, yielding a bulk convective flow towards the centre of the aggregate. The process is cyclic, yielding a steady-state balance between outward (protrusive) migration along the surface, and 'retrograde' (contractile) flows above the surface. Modelling the cell aggregates as confined active droplets, we demonstrate that the interplay between surface tension-driven flows within the aggregate, radially outward monolayer flow and conservation of mass leads to an internal circulation.

Microscopic theory for nonequilibrium correlation functions in dense active fluids

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is the so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here, we present a fully microscopic method to calculate nonequilibrium correlations in two-dimensional systems of thermal active Brownian particles (ABPs). We use the integration through transients formalism together with (active) mode-coupling theory and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations.

Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

Regulation of Chromatin Modifications through Coordination of Nucleus Size and Epithelial Cell Morphology Heterogeneity

Cell morphology heterogeneity within epithelial collectives is a pervasive phenomenon intertwined with tissue mechanical properties. Despite its widespread occurrence, the underlying mechanisms driving cell morphology heterogeneity and its consequential biological ramifications remain elusive. Here, we investigate the dynamic evolution of epithelial cell morphology and nucleus morphology during crowding, unveiling a consistent correlation between the two. Our investigation reveals a persistent log-normal probability distribution characterizing both cell and nucleus areas across diverse crowding stages and epithelial model systems. We showed that this morphological diversity arises from asymmetric partitioning during cell division and is perpetuated through actomyosin-mediated regulation of cell-nucleus size coordination. Moreover, we provide insights into the impact of nucleus morphology on chromatin dynamics, demonstrating that constraining nucleus area leads to downregulation of the euchromatic mark H3K9ac and upregulation of the heterochromatic mark H3K27me3 through modulation of histone demethylase UTX expression. These findings under-score the significance of cell morphology heterogeneity as a driver of chromatin state diversity, shaping functional variability within epithelial tissues.

Unraveling Endothelial Cell Migration: Insights into Fundamental Forces, Inflammation, Biomaterial Applications, and Tissue Regeneration Strategies

Cell migration is vital for many fundamental biological processes and human pathologies throughout our life. Dynamic molecular changes in the tissue microenvironment determine modifications of cell movement, which can be reflected either individually or collectively. Endothelial cell (EC) migratory adaptation occurs during several events and phenomena, such as endothelial injury, vasculogenesis, and angiogenesis, under both normal and highly inflammatory conditions. Several advantageous processes can be supported by biomaterials. Endothelial cells are used in combination with various types of biomaterials to design scaffolds promoting the formation of mature blood vessels within tissue engineered structures. Appropriate selection, in terms of scaffolding properties, can promote desirable cell behavior to varying degrees. An increasing amount of research could lead to the creation of the perfect biomaterial for regenerative medicine applications. In this review, we summarize the state of knowledge regarding the possible systems by which inflammation may influence endothelial cell migration. We also describe the fundamental forces governing cell motility with a specific focus on ECs. Additionally, we discuss the biomaterials used for EC culture, which serve to enhance the proliferative, proangiogenic, and promigratory potential of cells. Moreover, we introduce the mechanisms of cell movement and highlight the significance of understanding these mechanisms in the context of designing scaffolds that promote tissue regeneration.

Using a probabilistic approach to derive a two-phase model of flow-induced cell migration

Interstitial fluid flow is a feature of many solid tumors. In vitro experiments have shown that such fluid flow can direct tumor cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis (cell migration up stress gradients) and autologous chemotaxis (downstream cell movement in response to flow-induced gradients of self-secreted chemoattractants). In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow. We use a kinetic description for the cell velocity probability density function, and model the flow-dependent mechanical and chemical stimuli as forcing terms that bias cell migration upstream and downstream. Using velocity-space averaging, we reformulate the model as a system of continuum equations for the spatiotemporal evolution of the cell volume fraction and flux in response to forcing terms that depend on the local direction and magnitude of the mechanochemical cues. We specialize our model to describe a one-dimensional cell layer subject to fluid flow. Using a combination of numerical simulations and asymptotic analysis, we delineate the parameter regime where transitions from downstream to upstream cell migration occur. As has been observed experimentally, the model predicts downstream-oriented chemotactic migration at low cell volume fractions, and upstream-oriented tensotactic migration at larger volume fractions. We show that the locus of the critical volume fraction, at which the system transitions from downstream to upstream migration, is dominated by the ratio of the rate of chemokine secretion and advection. Our model also predicts that, because the tensotactic stimulus depends strongly on the cell volume fraction, upstream, tensotaxis-dominated migration occurs only transiently when the cells are initially seeded, and transitions to downstream, chemotaxis-dominated migration occur at later times due to the dispersive effect of cell diffusion.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Trapping of deformable active particles by a periodic background potential

The dynamic behaviors, specifically trapping and sorting, of active particles interacting with periodic substrates have garnered significant attention. This study investigates numerically the trapping of soft, deformable particles on a periodic potential substrate, which can be experimentally verified through optical tweezers. The research demonstrates that multiple factors, including the relative size of traps, self-propelled velocity, shape parameters, ratio of particles to traps, and translational diffusion, can influence the trapping effect. Within certain parameter boundaries, it is shown that all particles can be consistently trapped. The research reveals that stable trapping typically occurs at median values of the relative trap size. An increase in the self-propelled velocity, the shape parameter, and the translational diffusion coefficient tends to facilitate the escapement of the particles from the traps. It is noteworthy that particles with larger shape parameters can escape even when the restoring force exceeds the self-propelled force. In addition, as the ratio of particles to traps grows, the fraction of trapped particles steadily reduces. Notably, rigid particles are consistently divided and trapped by traps closely approximating an integer multiple of the particles' area, up until the ratio reaches the aforesaid integer value. These findings can potentially enhance the understanding of the interactive effects between active deformable particles and periodic substrates. Moreover, this work suggests a different experimental approach to sort active particles based on rigidity disparities.

PIEZO1 regulates leader cell formation and cellular coordination during collective keratinocyte migration

The collective migration of keratinocytes during wound healing requires both the generation and transmission of mechanical forces for individual cellular locomotion and the coordination of movement across cells. Leader cells along the wound edge transmit mechanical and biochemical cues to ensuing follower cells, ensuring their coordinated direction of migration across multiple cells. Despite the observed importance of mechanical cues in leader cell formation and in controlling coordinated directionality of cell migration, the underlying biophysical mechanisms remain elusive. The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during the reepithelialization of wounds. Here, through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1's contributions to collective migration. Time-lapse microscopy reveals that PIEZO1 activity inhibits leader cell formation at the wound edge. To probe the relationship between PIEZO1 activity, leader cell formation and inhibition of reepithelialization, we developed an integrative 2D continuum model of wound closure that links observations at the single cell and collective cell migration scales. Through numerical simulations and subsequent experimental validation, we found that coordinated directionality plays a key role during wound closure and is inhibited by upregulated PIEZO1 activity. We propose that PIEZO1-mediated retraction suppresses leader cell formation which inhibits coordinated directionality between cells during collective migration.

Topological defects in self-assembled patterns of mesenchymal stromal cells in vitro are predictive attributes of condensation and chondrogenesis

Mesenchymal stromal cells (MSCs) are promising therapeutic agents for cartilage regeneration, including the potential of cells to promote chondrogenesis in vivo. However, process development and regulatory approval of MSCs as cell therapy products benefit from facile in vitro approaches that can predict potency for a given production run. Current standard in vitro approaches include a 21 day 3D differentiation assay followed by quantification of cartilage matrix proteins. We propose a novel biophysical marker that is cell population-based and can be measured from in vitro monolayer culture of MSCs. We hypothesized that the self-assembly pattern that emerges from collective-cell behavior would predict chondrogenesis motivated by our observation that certain features in this pattern, namely, topological defects, corresponded to mesenchymal condensations. Indeed, we observed a strong predictive correlation between the degree-of-order of the pattern at day 9 of the monolayer culture and chondrogenic potential later estimated from in vitro 3D chondrogenic differentiation at day 21. These findings provide the rationale and the proof-of-concept for using self-assembly patterns to monitor chondrogenic commitment of cell populations. Such correlations across multiple MSC donors and production batches suggest that self-assembly patterns can be used as a candidate biophysical attribute to predict quality and efficacy for MSCs employed therapeutically for cartilage regeneration.

Mechanical convergence in mixed populations of mammalian epithelial cells

Tissues consist of cells with different molecular and/or mechanical properties. Measuring the forces and stresses in mixed-cell populations is essential for understanding the mechanisms by which tissue development, homeostasis, and disease emerge from the cooperation of distinct cell types. However, many previous studies have primarily focused their mechanical measurements on dissociated cells or aggregates of a single-cell type, leaving the mechanics of mixed-cell populations largely unexplored. In the present study, we aimed to elucidate the influence of interactions between different cell types on cell mechanics by conducting in situ mechanical measurements on a monolayer of mammalian epithelial cells. Our findings revealed that while individual cell types displayed varying magnitudes of traction and intercellular stress before mixing, these mechanical values shifted in the mixed monolayer, becoming nearly indistinguishable between the cell types. Moreover, by analyzing a mixed-phase model of active tissues, we identified physical conditions under which such mechanical convergence is induced. Overall, the present study underscores the importance of in situ mechanical measurements in mixed-cell populations to deepen our understanding of the mechanics of multicellular systems.

A Hierarchical Mechanotransduction System: From Macro to Micro

Mechanotransduction is a strictly regulated process whereby mechanical stimuli, including mechanical forces and properties, are sensed and translated into biochemical signals. Increasing data demonstrate that mechanotransduction is crucial for regulating macroscopic and microscopic dynamics and functionalities. However, the actions and mechanisms of mechanotransduction across multiple hierarchies, from molecules, subcellular structures, cells, tissues/organs, to the whole-body level, have not been yet comprehensively documented. Herein, the biological roles and operational mechanisms of mechanotransduction from macro to micro are revisited, with a focus on the orchestrations across diverse hierarchies. The implications, applications, and challenges of mechanotransduction in human diseases are also summarized and discussed. Together, this knowledge from a hierarchical perspective has the potential to refresh insights into mechanotransduction regulation and disease pathogenesis and therapy, and ultimately revolutionize the prevention, diagnosis, and treatment of human diseases.

Self-enhanced mobility enables vortex pattern formation in living matter

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Effect of non-linear strain stiffening in eDAH and unjamming

In cell clusters, the prominent factors at play encompass contractility-based enhanced tissue surface tension and cell unjamming transition. The former effect pertains to the boundary effect, while the latter constitutes a bulk effect. Both effects share outcomes of inducing significant elongation in cells. This elongation is so substantial that it surpasses the limits of linear elasticity, thereby giving rise to additional effects. To investigate these effects, we employ atomic force microscopy (AFM) to analyze how the mechanical properties of individual cells change under such considerable elongation. Our selection of cell lines includes MCF-10A, chosen for its pronounced demonstration of the extended differential adhesion hypothesis (eDAH), and MDA-MB-436, selected due to its manifestation of cell unjamming behavior. In the AFM analyses, we observe a common trend in both cases: as elongation increases, both cell lines exhibit strain stiffening. Notably, this effect is more prominent in MCF-10A compared to MDA-MB-436. Subsequently, we employ AFM on a dynamic range of 1-200 Hz to probe the mechanical characteristics of cell spheroids, focusing on both surface and bulk mechanics. Our findings align with the results from single cell investigations. Specifically, MCF-10A cells, characterized by strong contractile tissue tension, exhibit the greatest stiffness on their surface. Conversely, MDA-MB-436 cells, which experience significant elongation, showcase their highest stiffness within the bulk region. Consequently, the concept of single cell strain stiffening emerges as a crucial element in understanding the mechanics of multicellular spheroids (MCSs), even in the case of MDA-MB-436 cells, which are comparatively softer in nature.

Pulling the strings on solid-to-liquid phase transitions in cell collectives

Cell collectives must dynamically adapt to different biological contexts. For instance, in homeostatic conditions, epithelia must establish a barrier between body compartments and resist external stresses, while during development, wound healing or cancer invasion, these tissues undergo extensive remodeling. Using analogies from inert, passive materials, changes in cellular density, shape, rearrangements and/or migration were shown to result in collective transitions between solid and fluid states. However, what biological mechanisms govern these transitions remains an open question. In particular, the upstream signaling pathways and molecular effectors controlling the key physical axes determining tissue rheology and dynamics remain poorly understood. In this perspective, we focus on emerging evidence identifying the first biological signals determining the collective state of living tissues, with an emphasis on how these mechanisms are exploited for functionality across biological contexts.

Hydrodynamics and multiscale order in confluent epithelia

We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) orders, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power-law scaling regimes, reflecting both the hexagonal geometry of small cells clusters and the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocityv0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case ofv0polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Interfacial Organization and Forces Arising from Epithelial-Cancerous Monolayer Interactions

The interfacial interactions between epithelia and cancer cells have profound relevance for tumor development and metastasis. Through monolayer confrontation of MCF10A (nontumorigenic human breast epithelial cells) and MDA-MB-231 (human epithelial breast cancer cells) cells, we investigate the epithelial-cancerous interfacial interactions at the tissue level. We show that the monolayer interaction leads to competitive interfacial morphodynamics and drives an intricate spatial organization of MCF10A cells into multicellular finger-like structures, which further branch into multiple subfinger-like structures. These hierarchical interfacial structures penetrate the cancer monolayer and can spontaneously segregate or even envelop cancer cell clusters, consistent with our theoretical prediction. By tracking the substrate displacements via embedded fluorescent nanobeads and implementing nanomechanical modeling that combines atomic force microscopy and finite element simulations, we computed mechanical force patterns, including traction forces and monolayer stresses, caused by the monolayer interaction. It is found that the heterogeneous mechanical forces accumulated in the monolayers are able to squeeze cancer cells, leading to three-dimensional interfacial bulges or cell extrusion, initiating the p53 apoptosis signaling pathways of cancer cells. We reveal that intercellular E-cadherin and P-cadherin of epithelial cells differentially regulate the interfacial organization including migration speed, directionality, spatial correlation, F-actin alignment, and subcellular protrusions of MCF10A cells; whereas E-cadherin governs interfacial geometry that is relevant to force localization and cancer cell extrusion, P-cadherin maintains interfacial integrity that enables long-range force transmission. Our findings suggest that the collaborative molecular and mechanical behaviors are crucial for preventing epithelial tissues from undergoing tumor invasion.

On the origins of developmental robustness: modeling buffering mechanisms against cell-level noise

During development, cells are subject to stochastic fluctuations in their positions (i.e. cell-level noise) that can potentially lead to morphological noise (i.e. stochastic differences between morphologies that are expected to be equal, e.g. the right and left sides of bilateral organisms). In this study, we explore new and existing hypotheses on buffering mechanisms against cell-level noise. Many of these hypotheses focus on how the boundaries between territories of gene expression remain regular and well defined, despite cell-level noise and division. We study these hypotheses and how irregular territory boundaries lead to morphological noise. To determine the consistency of the different hypotheses, we use a general computational model of development: EmbryoMaker. EmbryoMaker can implement arbitrary gene networks regulating basic cell behaviors (contraction, adhesion, etc.), signaling and tissue biomechanics. We found that buffering mechanisms based on the orientation of cell divisions cannot lead to regular boundaries but that other buffering mechanisms can (homotypic adhesion, planar contraction, non-dividing boundaries, constant signaling and majority rule hypotheses). We also explore the effects of the shape and size of the territories on morphological noise.

Bridging the gap between collective motility and epithelial-mesenchymal transitions through the active finite voronoi model

We introduce an active version of the recently proposed finite Voronoi model of epithelial tissue. The resultant Active Finite Voronoi (AFV) model enables the study of both confluent and non-confluent geometries and transitions between them, in the presence of active cells. Our study identifies six distinct phases, characterized by aggregation-segregation, dynamical jamming-unjamming, and epithelial-mesenchymal transitions (EMT), thereby extending the behavior beyond that observed in previously studied vertex-based models. The AFV model with rich phase diagram provides a cohesive framework that unifies the well-observed progression to collective motility via unjamming with the intricate dynamics enabled by EMT. This approach should prove useful for challenges in developmental biology systems as well as the complex context of cancer metastasis. The simulation code is also provided.

Polarization and motility of one-dimensional multi-cellular trains

Collective cell migration, whereby cells adhere to form multi-cellular clusters that move as a single entity, play an important role in numerous biological processes, such as during development and cancer progression. Recent experimental work focused on migration of one-dimensional cellular clusters, confined to move along adhesive lanes, as a simple geometry in which to systematically study this complex system. One-dimensional migration also arises in the body when cells migrate along blood vessels, axonal projections, and narrow cavities between tissues. We explore here the modes of one-dimensional migration of cellular clusters ("trains") by implementing cell-cell interactions in a model of cell migration that contains a mechanism for spontaneous cell polarization. We go beyond simple phenomenological models of the cells as self-propelled particles by having the internal polarization of each cell depend on its interactions with the neighboring cells that directly affect the actin polymerization activity at the cell's leading edges. Both contact inhibition of locomotion and cryptic lamellipodia interactions between neighboring cells are introduced. We find that this model predicts multiple motility modes of the cell trains, which can have several different speeds for the same polarization pattern. Compared to experimental data, we find that Madin-Darby canine kidney cells are poised along the transition region where contact inhibition of locomotion and cryptic lamellipodia roughly balance each other, where collective migration speed is most sensitive to the values of the cell-cell interaction strength.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

A toolbox to analyze collective cell migration, proliferation and cellular organization simultaneously

BACKGROUND

Analyses of collective cell migration and orientation phenomena are needed to assess the behavior of multicellular clusters. While some tools to the authors' knowledge none is capable to analyze collective migration, cellular orientation and proliferation in phase contrast images simultaneously.

METHODS

We provide a tool based to analyze phase contrast images of dense cell layers. PIV is used to calculatevelocity fields, while the structure tensor provides cellular orientation. An artificial neural network is used to identify cell division events, allowing to correlate migratory and organizational phenomena with cell density.

CONCLUSION

The presented tool allows the simultaneous analysis of collective cell behavior from phase contrast images in terms of migration, (self-)organization and proliferation.

Tumor-Derived Membrane Vesicles Restrain Migration in Gliomas By Altering Collective Polarization

Mechanobiology is a cornerstone in physiology. However, its role in biomedical applications remains considerably undermined. In this study, we employed cell membrane vesicles (CMVs), which are currently being used as nanodrug carriers, as tactile cues for mechano-regulation of collective cell behaviors. Gliomas, which are among the most resilient brain tumors and have a low patient survival rate, were used as the cell model. We observed that mechanical responses due to the application of glioma- or microglia-derived CMVs resulted in the doubling of the traction stress of glioma cell collectives with a 10-fold increase in the CMV concentration. Glioma-CMVs constrained cell protrusions and hindered their collective migration, with the migration speed of such cells declining by almost 40% compared to the untreated cells. We speculated that the alteration of collective polarization leads to migration speed changes, and this phenomenon was elucidated using the cellular Potts model. In addition to intracellular force modulation and cytoskeletal reorganization, glioma-CMVs altered drug diffusion within glioma spheroids by downregulating the mechano-signaling protein YAP-1 while also marginally enhancing the associated apoptotic events. Our results suggest that glioma-CMVs can be applied as an adjuvant to current treatment approaches to restrict tumor invasion and enhance the penetration of reagents within tumors. Considering the broad impact of mechano-transduction on cell functions, the regulation of cell mechanics through CMVs can provide a foundation for alternative therapeutic strategies.

Shape-driven confluent rigidity transition in curved biological tissues

Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those tissue-scale dynamics derive from local cell-level properties. Specifically, there has been little consideration of the interplay between local tissue geometry and cellular properties influencing larger-scale tissue behaviors. Here, we consider a simple two-dimensional computational vertex model for confluent tissue monolayers, which exhibits a rigidity phase transition controlled by the shape index (ratio of perimeter to square root area) of cells, on surfaces of constant curvature. We show that the critical point for the rigidity transition is a function of curvature such that positively curved systems are likely to be in a less rigid, more fluid, phase. Likewise, negatively curved systems (saddles) are likely to be in a more rigid, less fluid, phase. A phase diagram we generate for the curvature and shape index constitutes a testable prediction from the model. The curvature dependence is interesting because it suggests a natural explanation for more dynamic tissue remodeling and facile growth in regions of higher surface curvature. Conversely, we would predict stability at the base of saddle-shaped budding structures without invoking the need for biochemical or other physical differences. This concept has potential ramifications for our understanding of morphogenesis of budding and branching structures.

Different glassy characteristics are related to either caging or dynamical heterogeneity

Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.

Random Traction Yielding Transition in Epithelial Tissues

We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude F_{c}. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.

Soliton approximation in continuum models of leader-follower behavior

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.

Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles

We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.

A geometry-enhanced graph neural network for learning the smoothness of glassy dynamics from static structure

Modeling the dynamics of glassy systems has been challenging in physics for several decades. Recent studies have shown the efficacy of Graph Neural Networks (GNNs) in capturing particle dynamics from the graph structure of glassy systems. However, current GNN methods do not take the dynamic patterns established by neighboring particles explicitly into account. In contrast to these approaches, this paper introduces a novel dynamical parameter termed "smoothness" based on the theory of graph signal processing, which explores the dynamic patterns from a graph perspective. Present graph-based approaches encode structural features without considering smoothness constraints, leading to a weakened correlation between structure and dynamics, particularly on short timescales. To address this limitation, we propose a Geometry-enhanced Graph Neural Network (Geo-GNN) to learn the smoothness of dynamics. Results demonstrate that our method outperforms state-of-the-art baselines in predicting glassy dynamics. Ablation studies validate the effectiveness of each proposed component in capturing smoothness within dynamics. These findings contribute to a deeper understanding of the interplay between glassy dynamics and static structure.

Collective heterogeneity of mitochondrial potential in contact inhibition of proliferation

In the epithelium, cell density and cell proliferation are closely connected to each other through contact inhibition of proliferation (CIP). Depending on cell density, CIP proceeds through three distinct stages: the free-growing stage at low density, the pre-epithelial transition stage at medium density, and the post-epithelial transition stage at high density. Previous studies have elucidated how cell morphology, motion, and mechanics vary in these stages. However, it remains unknown whether cellular metabolism also has a density-dependent behavior. By measuring the mitochondrial membrane potential at different cell densities, here we reveal a heterogeneous landscape of metabolism in the epithelium, which appears qualitatively distinct in three stages of CIP and did not follow the trend of other CIP-associated parameters, which increases or decreases monotonically with increasing cell density. Importantly, epithelial cells established a collective metabolic heterogeneity exclusively in the pre-epithelial transition stage, where the multicellular clusters of high- and low-potential cells emerged. However, in the post-epithelial transition stage, the metabolic potential field became relatively homogeneous. Next, to study the underlying dynamics, we constructed a system biology model, which predicted the role of cell proliferation in metabolic potential toward establishing collective heterogeneity. Further experiments indeed revealed that the metabolic pattern spatially correlated with the proliferation capacity of cells, as measured by the nuclear localization of a pro-proliferation protein, YAP. Finally, experiments perturbing the actomyosin contractility revealed that, while metabolic heterogeneity was maintained in the absence of actomyosin contractility, its ab initio emergence depended on the latter. Taken together, our results revealed a density-dependent collective heterogeneity in the metabolic field of a pre-epithelial transition-stage epithelial monolayer, which may have significant implications for epithelial form and function.

Long-term, real-time and label-free live cell image processing and analysis based on a combined algorithm of CellPose and watershed segmentation

Developing a rapid and quantitative method to accurately evaluate the physiological abilities of living cells is critical for tumor control. Many experiments have been conducted in the field of biology in an attempt to measure the proliferation and movement abilities of cells, but existing methods cannot provide real-time and objective data for label-free cells. The quantitative imaging technique, including an automatic segmentation algorithm for individual label-free cells, has been a breakthrough in this regard. In this study, we develop a combined automatic image processing algorithm of CellPose and watershed segmentation for the long-term and real-time imaging of label-free cells. This method shows strong reliability in cell identification regardless of cell densities, allowing us to obtain accurate information about the number and proliferation ability of the target cells. Additionally, our results also suggest that this method is a reliable way to assess real-time data on drug cytotoxicity, cell morphology, and cell movement ability.