Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model.

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.

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.

Linear viscoelastic properties of the vertex model for epithelial tissues.

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.

Stratification relieves constraints from steric hindrance in the generation of compact actomyosin asters at the membrane cortex.

Recent in vivo studies reveal that several membrane proteins are driven to form nanoclusters by active contractile flows arising from localized dynamic patterning of F-actin and myosin at the cortex. Since myosin-II assemble as minifilaments with tens of myosin heads, one might worry that steric considerations would obstruct the emergence of nanoclustering. Using coarse-grained, agent-based simulations that account for steric constraints, we find that the patterns exhibited by actomyosin in two dimensions, do not resemble the steady-state patterns in our in vitro reconstitution of actomyosin on a supported bilayer. We perform simulations in a thin rectangular slab, separating the layer of actin filaments from myosin-II minifilaments. This recapitulates the observed features of in vitro patterning. Using super resolution microscopy, we find evidence for such stratification in our in vitro system. Our study suggests that molecular stratification may be an important organizing feature of the cortical cytoskeleton in vivo.

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.

Stiffening thermal membranes by cutting.

Two-dimensional crystalline membranes have recently been realized experimentally in systems such as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counterposed coupling of the lips of the slit to twist in the intact regions of the ribbon.

Effects of scars on icosahedral crystalline shell stability under external pressure.

We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically required defects to shells with extended defect arrays (grain boundary "scars" with nonvanishing net disclination charge). We perform both Monte Carlo and conjugate gradient simulations to compare how shells with and without scars deform quasistatically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally symmetric shell depend on the Föppl-von Kármán number.

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.

On the modeling of endocytosis in yeast.

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Results of experiments on endocytosis in yeast show general agreement that 1) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it, and 2) the large-scale membrane deformation is tubular in shape. In contrast, there are three competing proposals for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: 1) initiation, where clathrin interacts with the membrane via adaptor proteins; 2) elongation, where the membrane is then further deformed by polymerizing actin filaments; and 3) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

Defect dynamics in active nematics.

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behaviour of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals, topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article, we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals.

Optimal shapes and stresses of adherent cells on patterned substrates.

We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses. The build-up of tension from cortical actin bundles at the cell periphery is incorporated by introducing an energy cost for bending the cell boundary, resulting in a resistance to changes in the local curvature. Integrin-based adhesions are modeled as harmonic springs that pin the cell to adhesive patches of a predefined geometry. Using Monte Carlo simulations and analytical techniques we investigate the competing effects of bulk contractility and cortical bending rigidity in regulating cell shapes on non-adherent regions. We show that the crossover from convex to concave cell edges is controlled by the interplay between contractile stresses and boundary bending rigidity. In particular, the cell boundary becomes concave beyond a critical value of the contractile stress that is proportional to the cortical bending rigidity. Furthermore, the intracellular stresses are found to be largely concentrated at the concave edge of the cell. The model can be used to generate a cell-shape phase diagram for each specific adhesion geometry.

Thermally active hybridization drives the crystallization of DNA-functionalized nanoparticles.

The selectivity of DNA recognition inspires an elegant protocol for designing versatile nanoparticle (NP) assemblies. We use molecular dynamics simulations to analyze dynamic aspects of the assembly process and identify ingredients that are key to a successful assembly of NP superlattices through DNA hybridization. A scale-accurate coarse-grained model faithfully captures the relevant contributions to the kinetics of the DNA hybridization process and is able to recover all experimentally reported to date binary superlattices (BCC, CsCl, AlB2, Cr3Si, and Cs6C60). We study the assembly mechanism in systems with up to 10(6) degrees of freedom and find that the crystallization process is accompanied with a slight decrease of enthalpy. Furthermore, we find that the optimal range of the DNA linker interaction strengths for a successful assembly is 12-16kBT, and the optimal mean lifetime of a DNA hybridization event is 10(-4)-10(-3) of the total time it takes to form a crystal. We also obtain the optimal percentage of hybridized DNA pairs for different binary systems. On the basis of these results, we propose suitable linker sequences for future nanomaterials design.

Mechanical model of blebbing in nuclear lamin meshworks.

Much of the structural stability of the nucleus comes from meshworks of intermediate filament proteins known as lamins forming the inner layer of the nuclear envelope called the nuclear lamina. These lamin meshworks additionally play a role in gene expression. Abnormalities in nuclear shape are associated with a variety of pathologies, including some forms of cancer and Hutchinson-Gilford Progeria Syndrome, and often include protruding structures termed nuclear blebs. These nuclear blebs are thought to be related to pathological gene expression; however, little is known about how and why blebs form. We have developed a minimal continuum elastic model of a lamin meshwork that we use to investigate which aspects of the meshwork could be responsible for bleb formation. Mammalian lamin meshworks consist of two types of lamin proteins, A type and B type, and it has been reported that nuclear blebs are enriched in A-type lamins. Our model treats each lamin type separately and thus, can assign them different properties. Nuclear blebs have been reported to be located in regions where the fibers in the lamin meshwork have a greater separation, and we find that this greater separation of fibers is an essential characteristic for generating nuclear blebs. The model produces structures with comparable morphologies and distributions of lamin types as real pathological nuclei. Thus, preventing this opening of the meshwork could be a route to prevent bleb formation, which could be used as a potential therapy for the pathologies associated with nuclear blebs.

Molecular crystallization controlled by pH regulates mesoscopic membrane morphology.

Coassembled molecular structures are known to exhibit a large variety of geometries and morphologies. A grand challenge of self-assembly design is to find techniques to control the crystal symmetries and overall morphologies of multicomponent systems. By mixing +3 and -1 ionic amphiphiles, we assemble crystalline ionic bilayers in a large variety of geometries that resemble polyhedral cellular crystalline shells and archaea wall envelopes. We combine TEM with SAXS and WAXS to characterize the coassembled structures from the mesoscopic to nanometer scale. The degree of ionization of the amphiphiles and their intermolecular electrostatic interactions are controlled by varying pH. At low and high pH values, we observe closed, faceted vesicles with two-dimensional hexagonal molecular arrangements, and at intermediate pH, we observe ribbons with rectangular-C packing. Furthermore, as pH increases, we observe interdigitation of the bilayer leaflets. Accurate atomistic molecular dynamics simulations explain the pH-dependent bilayer thickness changes and also reveal bilayers of hexagonally packed tails at low pH, where only a small fraction of anionic headgroups is charged. Coarse-grained simulations show that the mesoscale geometries at low pH are faceted vesicles where liquid-like edges separate flat crystalline domains. Our simulations indicate that the curved-to-polyhedral shape transition can be controlled by tuning the tail density in regions where sharp bends can form the polyhedral edges. In particular, the pH acts to control the overall morphology of the ionic bilayers by changing the local crystalline order of the amphiphile tails.

Charge renormalization of bilayer elastic properties.

By combining molecular dynamics simulations and analytical arguments, we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity κ and the two-dimensional bulk modulus λ and Young's modulus Y are found to depend on the values of the charges assigned to the lipid head groups. To extract κ and λ, we fit the molecular dynamics data to a standard elastic model for lipid bilayers. Moreover, we analytically obtain the dependence of the Young modulus Y on the relative strengths of electrostatic and van der Waals interactions in the zero temperature limit.