Confined cell migration along extracellular matrix space in vivo.

Collective migration of cancer cells is often interpreted using concepts derived from the physics of active matter, but the experimental evidence is mostly restricted to observations made in vitro. Here, we study collective invasion of metastatic cancer cells injected into the mouse deep dermis using intravital multiphoton microscopy combined with a skin window technique and three-dimensional quantitative image analysis. We observe a multicellular but low-cohesive migration mode characterized by rotational patterns which self-organize into antiparallel persistent tracks with orientational nematic order.

Lipid membranes supported by polydimethylsiloxane substrates with designed geometry.

The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes is challenging because of the biochemical and geometrical complexity as well as the short time and small length scales involved in cellular processes. By contrast, model membranes with engineered curvature would provide a versatile platform for this investigation and applications to biosensing and biocomputing.

Designing highly efficient interlocking interactions in anisotropic active particles.

Cluster formation of microscopic swimmers is key to the formation of biofilms and colonies, efficient motion and nutrient uptake, but, in the absence of other interactions, requires high swimmer concentrations to occur. Here we experimentally and numerically show that cluster formation can be dramatically enhanced by an anisotropic swimmer shape. We analyze a class of model microswimmers with a shape that can be continuously tuned from spherical to bent and straight rods.

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.

Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density.

Changes in tissue geometry during developmental processes are associated with collective migration of cells. Recent experimental and numerical results suggest that these changes could leverage on the coexistence of nematic and hexatic orientational order at different length scales. How this multiscale organization is affected by the material properties of the cells and their substrate is presently unknown.

Tuneable defect-curvature coupling and topological transitions in active shells.

Recent experimental observations have suggested that topological defects can facilitate the creation of sharp features in developing embryos. Whereas these observations echo established knowledge about the interplay between geometry and topology in two-dimensional passive liquid crystals, the role of activity has mostly remained unexplored. In this article we focus on deformable shells consisting of either polar or nematic active liquid crystals and demonstrate that activity renders the mechanical coupling between defects and curvature much more involved and versatile than previously thought.

Hydrodynamic Enhancement of p-atic Defect Dynamics.

We investigate numerically and analytically the effects of hydrodynamics on the dynamics of topological defects in p-atic liquid crystals, i.e., two-dimensional liquid crystals with p-fold rotational symmetry.

Hydrodynamic theory of p-atic liquid crystals.

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p=2) and hexatics (p=6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p>2.

Long-Ranged Order and Flow Alignment in Sheared p-atic Liquid Crystals.

We formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of p-atic phases, allows us to unveil several unknown aspects of flowing p-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

Statistics and topology of fluctuating ribbons.

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques.

Theory of defect-mediated morphogenesis.

Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations.

Self-Assembly Dynamics of Reconfigurable Colloidal Molecules.

Colloidal molecules are designed to mimic their molecular analogues through their anisotropic shape and interactions. However, current experimental realizations are missing the structural flexibility present in real molecules thereby restricting their use as model systems. We overcome this limitation by assembling reconfigurable colloidal molecules from silica particles functionalized with mobile DNA linkers in high yields.

Orientational Correlations in Active and Passive Nematic Defects.

We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from antialigning to aligning at scales that are smaller than the typical distance between like-sign defects.

Faceting and Flattening of Emulsion Droplets: A Mechanical Model.

When cooled down, emulsion droplets stabilized by a frozen interface of alkane molecules and surfactants have been observed to undergo a spectacular sequence of morphological transformations: from spheres to faceted liquid icosahedra, down to flattened liquid platelets. While generally ascribed to the interplay between the elasticity of the frozen interface and surface tension, the physical mechanisms underpinning these transitions have remained elusive, despite different theoretical pictures having been proposed in recent years. In this Letter, we introduce a comprehensive mechanical model of morphing emulsion droplets, which quantitatively accounts for various experimental observations, including the size scaling behavior of the faceting transition.

Confinement-induced self-organization in growing bacterial colonies.

We investigate the emergence of global alignment in colonies of dividing rod-shaped cells under confinement. Using molecular dynamics simulations and continuous modeling, we demonstrate that geometrical anisotropies in the confining environment give rise to an imbalance in the normal stresses, which, in turn, drives a collective rearrangement of the cells. This behavior crucially relies on the colony's solid-like mechanical response at short time scales and can be recovered within the framework of active hydrodynamics upon modeling bacterial colonies as growing viscoelastic gels characterized by Maxwell-like stress relaxation.

Measuring Gaussian Rigidity Using Curved Substrates.

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here, we consider such membranes supported by curved substrates that thereby control the membrane curvatures.

Geometric pinning and antimixing in scaffolded lipid vesicles.

Previous studies on the phase behaviour of multicomponent lipid bilayers found an intricate interplay between membrane geometry and its composition, but a fundamental understanding of curvature-induced effects remains elusive. Thanks to a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work, we demonstrate that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids. In the mixed phase, a strong geometrical anisotropy can give rise to an antimixed state, where the lipids are mixed, but their relative concentration varies across the membrane.

Dislocation screening in crystals with spherical topology.

Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes, or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated either by a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as "scars.

Mechanical interplay between cell shape and actin cytoskeleton organization.

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses.

Lipid exchange enhances geometric pinning in multicomponent membranes on patterned substrates.

Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate.

Topotaxis of active Brownian particles.

Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, has been extensively studied for topographical gradients at the subcellular scale, but can also occur in the presence of a spatially varying density of cell-sized features. Such a large-scale topotaxis has recently been observed in highly motile cells that persistently crawl within an array of obstacles with smoothly varying lattice spacing.

Chiral stresses in nematic cell monolayers.

Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains.

Mono- to Multilayer Transition in Growing Bacterial Colonies.

The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial microcolonies comprising a few hundred cells. Using a combination of numerical simulations and analytical modeling, here we demonstrate that this transition originates from the competition between growth-induced in-plane active stresses and vertical restoring forces, due to the cell-substrate interactions.