Topology and dynamics of active nematic vesicles

Cortical actin and the plasma membrane: inextricably intertwined

The plasma membrane serves as a barrier, separating the cell from its external environment. Simultaneously it acts as a site for information transduction, entry of nutrients, receptor signaling, and adapts to the shape of the cell. This requires local control of organization at multiple scales in this heterogeneous fluid lipid bilayer with a plethora of proteins and a closely juxtaposed dynamic cortical cytoskeleton. New membrane models highlight the influence of the underlying cortical actin on the diffusion of membrane components. Myosin motors as well as proteins that remodel actin filaments have additionally been implicated in defining the organization of many membrane constituents. Here we provide a perspective of the intimate relationship of the membrane lipid matrix and the underlying cytoskeleton.

Microscopic origins of anisotropic active stress in motor-driven nematic liquid crystals

The cytoskeleton, despite comprising relatively few building blocks, drives an impressive variety of cellular phenomena ranging from cell division to motility. These building blocks include filaments, motor proteins, and static crosslinkers. Outside of cells, these same components can form novel materials exhibiting active flows and nonequilibrium contraction or extension. While dipolar extensile or contractile active stresses are common in nematic motor-filament systems, their microscopic origin remains unclear. Here we study a minimal physical model of filaments, crosslinking motors, and static crosslinkers to dissect the microscopic mechanisms of stress generation in a two-dimensional system of orientationally aligned rods. We demonstrate the essential role of filament steric interactions which have not previously been considered to significantly contribute to active stresses. With this insight, we are able to tune contractile or extensile behavior through the control of motor-driven filament sliding and crosslinking. This work provides a roadmap for engineering stresses in active liquid crystals. The mechanisms we study may help explain why flowing nematic motor-filament mixtures are extensile while gelled systems are contractile.

Actomyosin dynamics drive local membrane component organization in an in vitro active composite layer

The surface of a living cell provides a platform for receptor signaling, protein sorting, transport, and endocytosis, whose regulation requires the local control of membrane organization. Previous work has revealed a role for dynamic actomyosin in membrane protein and lipid organization, suggesting that the cell surface behaves as an active composite composed of a fluid bilayer and a thin film of active actomyosin. We reconstitute an analogous system in vitro that consists of a fluid lipid bilayer coupled via membrane-associated actin-binding proteins to dynamic actin filaments and myosin motors. Upon complete consumption of ATP, this system settles into distinct phases of actin organization, namely bundled filaments, linked apolar asters, and a lattice of polar asters. These depend on actin concentration, filament length, and actin/myosin ratio. During formation of the polar aster phase, advection of the self-organizing actomyosin network drives transient clustering of actin-associated membrane components. Regeneration of ATP supports a constitutively remodeling actomyosin state, which in turn drives active fluctuations of coupled membrane components, resembling those observed at the cell surface. In a multicomponent membrane bilayer, this remodeling actomyosin layer contributes to changes in the extent and dynamics of phase-segregating domains. These results show how local membrane composition can be driven by active processes arising from actomyosin, highlighting the fundamental basis of the active composite model of the cell surface, and indicate its relevance to the study of membrane organization.

Stabilization of active matter by flow-vortex lattices and defect ordering

Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate both theoretically and through numerical simulations, that the crossover between wet active systems, whose behaviour is dominated by hydrodynamics, and dry active matter where any flow is screened, can be achieved by using friction as a control parameter. Moreover, we discover unexpected vortex ordering at this wet-dry crossover. We show that the self organization of vortices into lattices is accompanied by the spatial ordering of topological defects leading to active crystal-like structures. The emergence of vortex lattices, which leads to the positional ordering of topological defects, suggests potential applications in the design and control of active materials.

Soft spherical nanostructures with a dodecagonal quasicrystal-like order

We develop a theory which predicts curvature-related structural peculiarities of soft spherical nanostructures with a dodecagonal local arrangement of subunits. Spherical templates coated with a thin film of a soft quasicrystal (QC)-forming material constitute the most promising direction to realize these nanostructures. Disordered and perfect spherical nanostructures are simulated using two approaches. The first of them models a random QC-like spherical nanostructure with extended curvature-induced topological defects similar to scars in colloidal spherical crystals. The second approach is inspired by the physics of viral capsids. It deals with the most regular spherical nanostructures with a local QC-like order derived from three well-known planar dodecagonal tilings. We explain how the additional QC-like degrees of freedom assist the nanostructure stabilization and determine the point defect number and location without extended scar formation. Unusual for nanoassemblies snub cube geometry is shown to be the most energetically favorable global organization of these spherical QC nanostructures.

Multiscale modeling and simulation of microtubule-motor-protein assemblies

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Motility of active fluid drops on surfaces

Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez et al., Nature 491, 431 (2013)]. Here, we study the onset and different aspects of motility of a three-dimensional drop of active fluid on a planar surface. We analyze theoretically how motility is affected by orientation profiles with defects of various types and locations, by the shape of the drop, and by surface friction at the substrate. In the scope of a thin drop approximation, we derive exact expressions for the flow in the drop that is generated by a given orientation profile. The flow has a natural decomposition into terms that depend entirely on the geometrical properties of the orientation profile, i.e., its bend and splay, and a term coupling the orientation to the shape of the drop. We find that asymmetric splay or bend generates a directed bulk flow and enables the drop to move, with maximal speeds achieved when the splay or bend is induced by a topological defect in the interior of the drop. In motile drops the direction and speed of self-propulsion is controlled by friction at the substrate.

Deformation and failure of curved colloidal crystal shells

Designing and controlling particle self-assembly into robust and reliable high-performance smart materials often involves crystalline ordering in curved spaces. Examples include carbon allotropes like graphene, synthetic materials such as colloidosomes, or biological systems like lipid membranes, solid domains on vesicles, or viral capsids. Despite the relevance of these structures, the irreversible deformation and failure of curved crystals is still mostly unexplored. Here, we report simulation results of the mechanical deformation of colloidal crystalline shells that illustrate the subtle role played by geometrically necessary topological defects in controlling plastic yielding and failure. We observe plastic deformation attributable to the migration and reorientation of grain boundary scars, a collective process assisted by the intermittent proliferation of disclination pairs or abrupt structural failure induced by crack nucleating at defects. Our results provide general guiding principles to optimize the structural and mechanical stability of curved colloidal crystals.

Orientational order of motile defects in active nematics

The study of liquid crystals at equilibrium has led to fundamental insights into the nature of ordered materials, as well as to practical applications such as display technologies. Active nematics are a fundamentally different class of liquid crystals, driven away from equilibrium by the autonomous motion of their constituent rod-like particles. This internally generated activity powers the continuous creation and annihilation of topological defects, which leads to complex streaming flows whose chaotic dynamics seem to destroy long-range order. Here, we study these dynamics in experimental and computational realizations of active nematics. By tracking thousands of defects over centimetre-scale distances in microtubule-based active nematics, we identify a non-equilibrium phase characterized by a system-spanning orientational order of defects. This emergent order persists over hours despite defect lifetimes of only seconds. Similar dynamical structures are observed in coarse-grained simulations, suggesting that defect-ordered phases are a generic feature of active nematics.

Trains, tails and loops of partially adsorbed semi-flexible filaments

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials.

Superstructures of chiral nematic microspheres as all-optical switchable distributors of light

Light technology is based on generating, detecting and controlling the wavelength, polarization and direction of light. Emerging applications range from electronics and telecommunication to health, defence and security. In particular, data transmission and communication technologies are currently asking for increasingly complex and fast devices, and therefore there is a growing interest in materials that can be used to transmit light and also to control the distribution of light in space and time. Here, we design chiral nematic microspheres whose shape enables them to reflect light of different wavelengths and handedness in all directions. Assembled in organized hexagonal superstructures, these microspheres of well-defined sizes communicate optically with high selectivity for the colour and chirality of light. Importantly, when the microspheres are doped with photo-responsive molecular switches, their chiroptical communication can be tuned, both gradually in wavelength and reversibly in polarization. Since the kinetics of the "on" and "off" switching can be adjusted by molecular engineering of the dopants and because the photonic cross-communication is selective with respect to the chirality of the incoming light, these photo-responsive microspheres show potential for chiroptical all-optical distributors and switches, in which wavelength, chirality and direction of the reflected light can be controlled independently and reversibly.

Nematic liquid crystals confined in microcapillaries for imaging phenomena at liquid-liquid interfaces

Here, we report the development of an experimental system based on liquid crystals (LCs) confined in microcapillaries for imaging interfacial phenomena. The inner surfaces of the microcapillaries were modified with octadecyltrichlorosilane to promote an escaped-radial configuration of LCs. We checked the optical appearance of the capillary-confined LCs under a crossed polarizing microscope and determined their arrangement based on side and top views. We then placed the capillary-confined LCs in contact with non-surfactant and surfactant solutions, producing characteristic textures of two bright lines and a four-petal shape, respectively. We also evaluated the sensitivity, stability, and reusability of the system. Our imaging system was more sensitive than previously reported LC thin film systems. The textures formed in microcapillaries were stable for more than 120 h and the capillaries could be reused at least 10 times. Finally, we successfully applied our system to image the interactions of phospholipids and bivalent metal ions. In summary, we developed a simple, small, portable, sensitive, stable, and reusable experimental system that can be broadly applied to monitor liquid-liquid interfacial phenomena. These results provide valuable information for designs using confined LCs as chemoresponsive materials in optical sensors.

Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime

Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic state, consisting of discrete 1d banded or 2d cellular patterns depending on nanorod volume fraction. Increasing activation strength further induces a sequence of attractor bifurcations, including oscillations superimposed on the 1d and 2d stationary patterns, a uniform translational motion of 1d and 2d oscillating patterns, and periodic switching between 1d and 2d patterns. These results imply that active macromolecular suspensions are capable of long-range spatial and dynamic organization at isotropic equilibrium concentrations, provided particle-scale activation is sufficiently strong.

Shape control and compartmentalization in active colloidal cells

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core-shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble-crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non-momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier-Stokes equation.

Emergent vortices in populations of colloidal rollers

Coherent vortical motion has been reported in a wide variety of populations including living organisms (bacteria, fishes, human crowds) and synthetic active matter (shaken grains, mixtures of biopolymers), yet a unified description of the formation and structure of this pattern remains lacking. Here we report the self-organization of motile colloids into a macroscopic steadily rotating vortex. Combining physical experiments and numerical simulations, we elucidate this collective behaviour. We demonstrate that the emergent-vortex structure lives on the verge of a phase separation, and single out the very constituents responsible for this state of polar active matter. Building on this observation, we establish a continuum theory and lay out a strong foundation for the description of vortical collective motion in a broad class of motile populations constrained by geometrical boundaries.

Confined populations of interacting motile particles often display collective motion in the form of large-scale vortices, such as fish groups and bacteria colonies. Bricard et al. study a model system with self-propelled colloidal rollers and identify the constituents responsible for emergent vortices.

Self-assembly of active attractive spheres

We study the self-assembly of a system of self-propelled, Lennard-Jones particles using Brownian dynamics simulations. We examine the state diagrams of the system for different rotational diffusion coefficients of the self-propelled motion of the particles. For fast rotational diffusion, the state diagram exhibits a strong similarity to that of the equilibrium Lennard-Jones fluid. As we decrease the rotational diffusion coefficient, the state diagram is slowly transformed. Specifically, the liquid-gas coexistence region is gradually replaced by a highly dynamic percolating network state. We find significant local alignment of the particles in the percolating network state despite the absence of aligning interactions, and propose a simple mechanism to justify the formation of this novel state.

Molecular behavior of DNA in a cell-sized compartment coated by lipids

The behavior of long DNA molecules in a cell-sized confined space was investigated. We prepared water-in-oil droplets covered by phospholipids, which mimic the inner space of a cell, following the encapsulation of DNA molecules with unfolded coil and folded globule conformations. Microscopic observation revealed that the adsorption of coiled DNA onto the membrane surface depended on the size of the vesicular space. Globular DNA showed a cell-size-dependent unfolding transition after adsorption on the membrane. Furthermore, when DNA interacted with a two-phase membrane surface, DNA selectively adsorbed on the membrane phase, such as an ordered or disordered phase, depending on its conformation. We discuss the mechanism of these trends by considering the free energy of DNA together with a polyamine in the solution. The free energy of our model was consistent with the present experimental data. The cooperative interaction of DNA and polyamines with a membrane surface leads to the size-dependent behavior of molecular systems in a small space. These findings may contribute to a better understanding of the physical mechanism of molecular events and reactions inside a cell.

Active cell mechanics: Measurement and theory

Living cells are active mechanical systems that are able to generate forces. Their structure and shape are primarily determined by biopolymer filaments and molecular motors that form the cytoskeleton. Active force generation requires constant consumption of energy to maintain the nonequilibrium activity to drive organization and transport processes necessary for their function. To understand this activity it is necessary to develop new approaches to probe the underlying physical processes. Active cell mechanics incorporates active molecular-scale force generation into the traditional framework of mechanics of materials. This review highlights recent experimental and theoretical developments towards understanding active cell mechanics. We focus primarily on intracellular mechanical measurements and theoretical advances utilizing the Langevin framework. These developing approaches allow a quantitative understanding of nonequilibrium mechanical activity in living cells. This article is part of a Special Issue entitled: Mechanobiology.

Self-organization of motors and microtubules in lipid-monolayered droplets

In living cells, the architecture of the microtubule cytoskeleton is intimately linked to its function. The principles determining how microtubules arrange in space are, however, still not fully understood. Biochemical activities controlling microtubule nucleation and dynamics as well as mechanochemical activities exerted by molecular motors and the dynamic microtubules themselves are known to be critical for the correct spatial organization of the microtubule cytoskeleton. In vitro reconstitution approaches have revealed the morphogenetic properties of these activities in minimal systems. In most cases, such in vitro experiments were performed in experimental chambers of spatial dimensions that exceeded typical cell sizes by orders of magnitude. Here, we describe a method for the fluorescence microscopic study of the effects of spatial confinement on the self-organization of purified motors and microtubules that are encapsulated in micrometer-sized lipid-monolayered droplets emulsified in oil. In the future, this experimental setup can be extended in several ways. Additional proteins can be added, either to the lumen or to the boundary of the microcontainers, and the droplets can be transformed into liposomes. Such more complex in vitro reconstitutions would be another step closer to mimicking intracellular cytoskeleton organization.

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.