Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices.

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations, and we develop a theoretical description based on mapping interactions onto a linear response model to describe the modes. Our results reveal the importance of entropic steric effects and can be used for developing reconfigurable materials at the colloidal length scale.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue.

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

Comparing individual-based models of collective cell motion in a benchmark flow geometry.

Collectively coordinated cell migration plays a role in tissue embryogenesis, cancer, homeostasis and healing. To study these processes, different cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended detailed cell shape contours. In the spirit of what Osborne et al. [PLOS Comput. Biol., 2017, 13, 1-34] did for cellular tissue structure simulation models, we here compare five simulation models of collective cell migration, chosen to be representatives in increasing order of included detail. They are Vicsek-Grégoire particles, Szabó-like particles, self-propelled Voronoi model, cellular Potts model, and multiparticle cells, where each model includes cell motility. We examine how these models compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. For this purpose, we use a benchmark that discriminates between complex material flow models, and that can be experimentally approached using cell cultures: the flow within a channel around a circular obstacle, that is, the geometry Stokes used in his historical 1851 experiment. For each model we explain how to best implement it; vary cell density, attraction force and alignment interaction; draw the resulting maps of velocity, density and deformation fields; and eventually discuss its respective advantages and limitations. We thus provide a recommendation on how to select a model to answer a given question, and we examine whether models of motile particles and motile cells display similar collective effects.

Generating active T1 transitions through mechanochemical feedback.

Convergence-extension in embryos is controlled by chemical and mechanical signalling. A key cellular process is the exchange of neighbours via T1 transitions. We propose and analyse a model with positive feedback between recruitment of myosin motors and mechanical tension in cell junctions. The model produces active T1 events, which act to elongate the tissue perpendicular to the main direction of tissue stress. Using an idealised tissue patch comprising several active cells embedded in a matrix of passive hexagonal cells, we identified an optimal range of mechanical stresses to trigger an active T1 event. We show that directed stresses also generate tension chains in a realistic patch made entirely of active cells of random shapes and leads to convergence-extension over a range of parameters. Our findings show that active intercalations can generate stress that activates T1 events in neighbouring cells, resulting in tension-dependent tissue reorganisation, in qualitative agreement with experiments on gastrulation in chick embryos.

The nonlinear motion of cells subject to external forces.

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop.

Spongelike Rigid Structures in Frictional Granular Packings.

We show how rigidity emerges in experiments on sheared two-dimensional frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a critical contact number z_{c}=2.4±0.1, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a spongelike morphology. While the pressure within rigid structures always exceeds the pressure outside the rigid structures, they are not identified with the force chains of shear jamming. These findings highlight the need to focus on mechanical stability arising through arch structures and hinges at the mesoscale.

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.

Confinement-Induced Transition between Wavelike Collective Cell Migration Modes.

The structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of long-range mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell monolayers to quasi-one-dimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multinodal wave, controlled by the confinement size. We confirm experimentally the existence of such a phase transition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level.

Dynamical patterns in nematic active matter on a sphere.

Using simulations of self-propelled agents with short-range repulsion and nematic alignment, we explore the dynamical phases of a dense active nematic confined to the surface of a sphere. We map the nonequilibrium phase diagram as a function of curvature, alignment strength, and activity. Our model reproduces several phases seen in recent experiments on active microtubule bundles confined the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a polar band wrapping around an equator, with large empty spherical caps corresponding to two +1 defects at the poles. Upon further increasing activity, the bands fold onto themselves, and the system eventually transitions to a turbulent state marked by the proliferation of pairs of topological defects. We highlight the key role of the nematic persistence length in controlling pattern formation in these confined systems with positive Gaussian curvature.

Dynamically generated patterns in dense suspensions of active filaments.

We use Langevin dynamics simulations to study dynamical behavior of a dense planar layer of active semiflexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several nonequilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that, for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterized by strong density fluctuations. Furthermore, we identify an activity-driven crossover from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analog in systems of active particles without internal degrees of freedom.

Active Vertex Model for cell-resolution description of epithelial tissue mechanics.

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.

Cell division and death inhibit glassy behaviour of confluent tissues.

We investigate the effects of cell division and apoptosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apoptosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phase, a gel-like phase, and a dense confluent (tissue) phase. Most striking is the observation that the tissue is self-melting through its own internal activity, ruling out the existence of any glassy phase.

Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming.

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. Our method suggests a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.

Active swarms on a sphere.

We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion-a consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

Freezing and phase separation of self-propelled disks.

We study numerically a model of soft polydisperse and non-aligning self-propelled particles interacting through elastic repulsion, which was recently shown to exhibit active phase separation in two dimensions in the absence of any attractive interaction or breaking of the orientational symmetry. We construct a phase diagram in terms of activity and packing fraction and identify three distinct regimes: a homogeneous liquid with anomalous cluster size distribution, a phase-separated state both at high and at low density, and a frozen phase. We provide a physical interpretation of the various regimes and develop scaling arguments for the boundaries separating them.

Soft-sphere packings at finite pressure but unstable to shear.

When are athermal soft-sphere packings jammed? Any experimentally relevant definition must, at the very least, require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols, in which particles are compressed together, can and do produce packings that are unstable to shear-and that the probability of generating such packings reaches one near jamming. We introduce a new protocol which, by allowing the system to explore different box shapes as it equilibrates, generates truly jammed packings with strictly positive shear moduli G. For these packings, the scaling of the average of G is consistent with earlier results, while the probability distribution P(G) exhibits novel and rich scalings.

Active jamming: self-propelled soft particles at high density.

We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction φ and high self-propulsion speed v(0) and a jammed phase at high φ and low v(0). The dynamics of the jammed phase is controlled by the low-frequency modes of the jammed packing.

Low-frequency vibrations of soft colloidal glasses.

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational properties are very similar to those predicted for zero-temperature sphere packings and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.

Statistical mechanics framework for static granular matter.

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.

Entropy and temperature of a static granular assembly: an ab initio approach.

We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman distribution for ensembles of grain packings. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks.