Topology and dynamics of active nematic vesicles

Direct Observation of Topological Defects in Striped Block Copolymer Discs and Polymersomes

Topology and defects are of fundamental importance for ordered structures on all length scales. Despite extensive research on block copolymer self-assembly in solution, knowledge about topological defects and their effect on nanostructure formation has remained limited. Here, we report on the self-assembly of block copolymer discs and polymersomes with a cylinder line pattern on the surface that develops specific combinations of topological defects to satisfy the Euler characteristics for closed spheres as described by Gauss-Bonnet theorem. The dimension of the line pattern allows the direct visualization of defect emergence, evolution, and annihilation. On discs, cylinders either form end-caps that coincide with λ^+1/2 disclinations or they bend around τ^+1/2 disclinations in 180° turns (hairpin loops). On polymersomes, two λ^+1/2 defects connect into three-dimensional (3D) Archimedean spirals, while two τ^+1/2 defects form 3D Fermat spirals. Electron tomography reveals two complementary line patterns on the inside and outside of the polymersome membrane, where λ^+1/2 and τ^+1/2 disclinations always eclipse on opposing sides ("defect communication"). Attractive defects are able to annihilate with each other into +1 disclinations and stabilize anisotropic polymersomes with sharp tips through screening of high-energy curvature. This study fosters our understanding of the behavior of topological defects in self-assembled polymer materials and aids in the design of polymersomes with preprogrammed shapes governed by synthetic block length and topological rules.

Topological Defect Arrays in Nematic Liquid Crystals Assisted by Polymeric Pillar Arrays: Effect of the Geometry of Pillars

Topological defects that spontaneously occur in condensed matter and structured fluids such as liquid crystals are useful for their elastic and optical properties, but often the applicability of defect arrays to optics and photonic devices relies on the regularity and tunability of the system. In our recent work [Adv. Opt. Mater. 8, 1900991 (2020)], we showed the formation of regular, reconfigurable, and scalable patterns by exploiting the elastic response of a defect array in liquid crystals in the presence of a polymeric pillar array. In this work, we experimentally investigate the role of size and shape of the pillars on the defect array. We find that the pillar size and geometry provide additional means to regulate the response time, the threshold voltage for the defects’ formation, and the spatial arrangement of the defects.

Radial alignment of microtubules through tubulin polymerization in an evaporating droplet

We report the formation of spherulites from droplets of highly concentrated tubulin solution via nucleation and subsequent polymerization to microtubules (MTs) under water evaporation by heating. Radial alignment of MTs in the spherulites was confirmed by the optical properties of the spherulites observed using polarized optical microscopy and fluorescence microscopy. Temperature and concentration of tubulins were found as important parameters to control the spherulite pattern formation of MTs where evaporation plays a significant role. The alignment of MTs was regulated reversibly by temperature induced polymerization and depolymerization of tubulins. The formation of the MTs patterns was also confirmed at the molecular level from the small angle X-ray measurements. This work provides a simple method for obtaining radially aligned arrays of MTs.

Reversal of contractility as a signature of self-organization in cytoskeletal bundles

Bundles of cytoskeletal filaments and molecular motors generate motion in living cells, and have internal structures ranging from very organized to apparently disordered. The mechanisms powering the disordered structures are debated, and existing models predominantly predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay between three well-characterized internal dynamical processes in cytoskeletal bundles: filament assembly and disassembly, the attachement-detachment dynamics of motors and that of crosslinking proteins. The resulting self-organization is easily understood in terms of motor and crosslink localization, and allows for an extensive control of the active bundle mechanics, including reversals of the filaments’ apparent velocities and the possibility of generating extension instead of contraction. This reversal mirrors some recent experimental observations, and provides a robust criterion to experimentally elucidate the underpinnings of both actomyosin activity and the dynamics of microtubule/motor assemblies in vitro as well as in diverse intracellular structures ranging from contractile bundles to the mitotic spindle.

Three-Dimensional Active Defect Loops

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions.

Active nematics with anisotropic friction: the decisive role of the flow aligning parameter

We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.

Clusterization of self-propelled particles in a two-component system

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Bacteria driving droplets

We confine a dense suspension of motile Escherichia coli inside a spherical droplet in a water-in-oil emulsion, creating a "bacterially" propelled droplet. We show that droplets move in a persistent random walk, with a persistence time τ∼ 0.3 s, a long-time diffusion coefficient D∼ 0.5 μm² s^-1, and an average instantaneous speed V∼ 1.5 μm s^-1 when the bacterial suspension is at the maximum studied concentration. Several droplets are analyzed, varying the drop radius and bacterial concentration. We show that the persistence time, diffusion coefficient and average speed increase with the bacterial concentration inside the drop, but are largely independent of the droplet size. By measuring the turbulent-like motion of the bacteria inside the drop, we demonstrate that the mean velocity of the bacteria near the bottom of the drop, which is separated from a glass substrate by a thin lubrication oil film, is antiparallel to the instantaneous velocity of the drop. This suggests that the driving mechanism is a slippery rolling of the drop over the substrate, caused by the collective motion of the bacteria. Our results show that microscopic organisms can transfer useful mechanical energy to their confining environment, opening the way to the assembly of mesoscopic motors composed of microswimmers.

Spontaneous helical flows in active nematics lying on a cylindrical surface

Within the framework of the two-dimensional Ericksen-Leslie model, we explore the effect of geometric confinement on the spontaneous flow of active nematic gels. The nematic particles are assumed to flow on a cylindrical surface, while a degenerate tangential anchoring is enforced. Using the linear approximation of the motion equations, we show that there is a close interplay among extrinsic curvature, flow, director alignment, and activity. We find that the extrinsic curvature promotes the director alignment parallel to the cylindrical axis and is responsible for raising the critical threshold with respect to the flat case. Our analysis reveals a very rich scenario where the key quantities are the activity coefficient, the tumbling parameter, and the anisotropic viscosity ratio. Thus, solutions can exhibit a double periodicity in both the azimuthal and axial variables. As a consequence, the velocity field can make a finite angle with the cylinder axis and the active flow winds on the surface with a helical pattern, while the director oscillates around the cylinder generators. Our results can be validated on thin layers of nematic gels placed between two concentric cylinders and suggest which material properties are most suited for the design of active microfluidic devices.

Ion transportation by Prussian blue nanoparticles embedded in a giant liposome

A new type of artificial giant liposome incorporating ion transport channels and using nanoparticles of metal organic frameworks was demonstrated. The micropores of Prussian blue nanoparticles served as ion transport channels between the outer and inner phases of liposomes.

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. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation.

Active glasses

Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.

Rotating oil droplets driven by motile bacteria at interfaces

We show that oil droplets suspended near a liquid-solid interface can be driven to rotate by motile bacteria adhered to the droplet surface. Droplets rotate clockwise when viewed from the liquid side, due to symmetry-breaking hydrodynamic interactions of bacteria with the interface. The angular speed of rotation for droplets decreases as their size is increased. Differences in the speed of rotation driven by Escherichia coli, Shewanella haliotis, and Halomonas titanicae bacteria reflects differences in the number of bacteria adhered at the droplet surface and their interfacial affinity. Adding surfactant reduces the number of adherent bacteria and hence lowers the speed of rotation. Together, these results demonstrate that bacterial activity can be used to manipulate suspended droplets.

Formation of phase separated vesicles by double layer cDICE

Recently, continuous droplet interface crossing encapsulation (cDICE) was developed, which allows fast and efficient production of giant unilamellar vesicles (GUVs) under high salt conditions, at low temperature and with low consumption of the encapsulated proteins. Unfortunately, cholesterol encapsulation within the lipid bilayer was not efficient for the cDICE protocol so far and thus the formation of phase separated vesicles was limited. Here we present a modified version of cDICE that allows incorporation of cholesterol into lipid bilayers and enables the reproducible formation of phase-separated vesicles. We show that cholesterol incorporation relies on the amount of mineral oil in the lipid-oil emulsions, which is essential for protein encapsulation inside GUVs by cDICE. The possibility of creating phase separated vesicles by cDICE will enable the study of the interdependence between phase separation and cytoskeletal proteins under confinement.

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

We develop and implement a finite difference lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. The standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focusing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of the torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our finite difference lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

Functional Coiled-Coil-like Assembly by Knob-into-Hole Packing of Single Heptad Repeat

Coiled-coil peptides represent the principal building blocks for structure-based design of bionanomaterials. The sequence-structure relationship and precise nanoscale ordering of the coiled-coil helices originate from the knob-into-hole (KIH) packing of side chains. The helical interface stabilized by the KIH interaction is known to have chain lengths ranging from 30 to 1000 residues. Yet the shortest peptide required for oligomerization through KIH assembly is still unknown. Here, we report that through atomic resolution a minimal seven-residue amphipathic helix forms a different type of KIH motif, termed "supramolecular KIH packing", which confers an exceptional stability to the helical dimers. Significantly, at a low pH, the peptide self-assembles into nanofibers with coiled-coil architecture resembling the natural fibrous proteins. Furthermore, hierarchical ordering of the nanofibers affords lyotropic liquid crystals composed of a shortest natural helical sequence. Thus, this study expands the sequence space for a coiled-coil folding manifold and provides another paradigm for designer nanomaterials from minimal helical sequences.

Topology and Morphology of Self-Deforming Active Shells

We present a generic framework for modeling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding environment. We find that the cross talk between the self-induced flows of active particles and dynamic reshaping of the shell can result in conformations that are tunable by varying the form and magnitude of active stresses. We further demonstrate and explain how self-induced topological defects in the active layer can direct the morphodynamics of the shell. These findings are relevant to understanding morphological changes during organ development and the design of bioinspired materials that are capable of self-organization.

Tunable corrugated patterns in an active nematic sheet

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

De novo synthesized Min proteins drive oscillatory liposome deformation and regulate FtsA-FtsZ cytoskeletal patterns

The Min biochemical network regulates bacterial cell division and is a prototypical example of self-organizing molecular systems. Cell-free assays relying on purified proteins have shown that MinE and MinD self-organize into surface waves and oscillatory patterns. In the context of developing a synthetic cell from elementary biological modules, harnessing Min oscillations might allow us to implement higher-order cellular functions. To convey hereditary information, the Min system must be encoded in a DNA molecule that can be copied, transcribed, and translated. Here, the MinD and MinE proteins are synthesized de novo from their genes inside liposomes. Dynamic protein patterns and accompanying liposome shape deformation are observed. When integrated with the cytoskeletal proteins FtsA and FtsZ, the synthetic Min system is able to dynamically regulate FtsZ patterns. By enabling genetic control over Min protein self-organization and membrane remodeling, our methodology offers unique opportunities towards directed evolution of bacterial division processes in vitro.

The Min biochemical network regulates bacterial cell division and is a prototypical example of self-organizing molecular systems. Here authors synthesize Min proteins from their genes inside liposomes and observe dynamic protein patterns and liposome shape deformation.

Encapsulation of the cytoskeleton: towards mimicking the mechanics of a cell

The cytoskeleton of a cell controls all the aspects of cell shape changes and motility from its physiological functions for survival to reproduction to death. The structure and dynamics of the cytoskeletal components: actin, microtubules, intermediate filaments, and septins - recently regarded as the fourth member of the cytoskeleton family - are conserved during evolution. Such conserved and effective control over the mechanics of the cell makes the cytoskeletal components great candidates for in vitro reconstitution and bottom-up synthetic biology studies. Here, we review the recent efforts in reconstitution of the cytoskeleton in and on membrane-enclosed biomimetic systems and argue that co-reconstitution and synergistic interplay between cytoskeletal filaments might be indispensable for efficient mechanical functionality of active minimal cells. Further, mechanical equilibrium in adherent eukaryotic cells is achieved by the formation of integrin-based focal contacts with extracellular matrix (ECM) and the transmission of stresses generated by actomyosin contraction to ECM. Therefore, a minimal mimic of such balance of forces and quasi-static kinetics of the cell by bottom-up reconstitution requires a careful construction of contractile machineries and their link with adhesive contacts. In this review, in addition to cytoskeletal crosstalk, we provide a perspective on reconstruction of cell mechanical equilibrium by reconstitution of cortical actomyosin networks in lipid membrane vesicles adhered on compliant substrates and also discuss future perspectives of this active research area.

Rotation and propulsion in 3D active chiral droplets

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, actomyosin filaments, and microtubule bundles are active systems that are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, many features of intrinsically chiral systems still need to be explored and explained. To address this gap in knowledge, here we study the effects of internal active forces and torques on a 3-dimensional (3D) droplet of cholesteric liquid crystal (CLC) embedded in an isotropic liquid. We consider tangential anchoring of the liquid crystal director at the droplet surface. Contrary to what happens in nematics, where moderate extensile activity leads to droplet rotation, cholesteric active droplets exhibit more complex and variegated behaviors. We find that extensile force dipole activity stabilizes complex defect configurations, in which orbiting dynamics couples to thermodynamic chirality to propel screw-like droplet motion. Instead, dipolar torque activity may either tighten or unwind the cholesteric helix and if tuned, can power rotations with an oscillatory angular velocity of 0 mean.

A simulation algorithm for Brownian dynamics on complex curved surfaces

Brownian dynamics of colloidal particles on complex curved surfaces has found important applications in diverse physical, chemical, and biological processes. However, most Brownian dynamics simulation algorithms focus on relatively simple curved surfaces that can be analytically parameterized. In this work, we develop an algorithm to enable Brownian dynamics simulation on extremely complex curved surfaces. We approximate complex curved surfaces with triangle mesh surfaces and employ a novel scheme to perform particle simulation on these triangle mesh surfaces. Our algorithm computes forces and velocities of particles in global coordinates but updates their positions in local coordinates, which combines the strengths from both global and local simulation schemes. We benchmark the proposed algorithm with theory and then simulate Brownian dynamics of both single and multiple particles on torus and knot surfaces. The results show that our method captures well diffusion, transport, and crystallization of colloidal particles on complex surfaces with nontrivial topology. This study offers an efficient strategy for elucidating the impact of curvature, geometry, and topology on particle dynamics and microstructure formation in complex environments.

Osmotic-engine-driven liposomes in microfluidic channels

Self-propelled underwater microrobots that locomote without external sources of energy have potential application as drug carriers and probes in narrow spaces. In this study, we focused on an osmotic engine model, which is a migration mechanism, and applied it as a negative chemotaxis mechanism to induce liposome displacement. First, we confirmed the osmotic flow across the lipid bilayer and calculated the osmotic flow velocity to be 8.5 fL min-1 μm-2 when a salt concentration difference was applied to the lipid bilayer. Next, we designed and fabricated a microchannel that can trap a giant liposome and apply a salt concentration difference to the front and rear of the liposome. Then, we demonstrated the movement of the liposome by flowing it to the microchannel. The liposome successfully moved in the direction of the lower ion concentration at a speed of 0.6 μm min-1 owing to the osmotic pressure difference. Finally, we visualized the inner flow in the liposome by encapsulating microbeads in the liposome and observed the movement of the microbeads to verify that an osmotic flow was generated on the liposome. As a result, we observed the circulation of the microbeads in the liposome when the concentration difference was applied to the front and rear of the liposome, suggesting that the movement of the liposome was driven by the osmotic flow generated by the osmotic pressure difference. These results indicate that the osmotic-pressure-based migration mechanism has the potential to be utilized as the actuator of molecular robots.

Shape Transformations of Vesicles Induced by Swim Pressure

While the behavior of vesicles in thermodynamic equilibrium has been studied extensively, how active forces control vesicle shape transformations is not understood. Here, we combine theory and simulations to study the shape behavior of vesicles containing active Brownian particles. We show that the combination of active forces, dimensionality, and membrane bending free energy creates a plethora of novel phase transitions. At low swim pressure, the vesicle exhibits a discontinuous transition from a spherical to a prolate shape, which has no counterpart in two dimensions. At high swim pressure it exhibits stochastic spatiotemporal oscillations. Our work helps researchers to understand and control the shape dynamics of membranes in active-matter systems.

Soft matter from liquid crystals

Liquid crystals (LCs) are fluids within which molecules exhibit long-range orientational order, leading to anisotropic properties such as optical birefringence and curvature elasticity. Because the ordering of molecules within LCs can be altered by weak external stimuli, LCs have been widely used to create soft matter systems that respond optically to electric fields (LC display), temperature (LC thermometer) or molecular adsorbates (LC chemical sensor). More recent studies, however, have moved beyond investigations of optical responses of LCs to explore the design of complex LC-based soft matter systems that offer the potential to realize more sophisticated functions (e.g., autonomous, self-regulating chemical responses to mechanical stimuli) by directing the interactions of small molecules, synthetic colloids and living cells dispersed within the bulk of LCs or at their interfaces. These studies are also increasingly focusing on LC systems driven beyond equilibrium states. This review presents one perspective on these advances, with an emphasis on the discovery of fundamental phenomena that may enable new technologies. Three areas of progress are highlighted; (i) directed assembly of amphiphilic molecules either within topological defects of LCs or at aqueous interfaces of LCs, (ii) templated polymerization in LCs via chemical vapor deposition, an approach that overcomes fundamental challenges related to control of LC phase behavior during polymerization, and (iii) studies of colloids in LCs, including chiral colloids, soft colloids that are strained by LCs, and active colloids that are driven into organized states by dissipation of energy (e.g. bacteria). These examples, and key unresolved issues discussed at the end of this perspective, serve to convey the message that soft matter systems that integrate ideas from LC, surfactant, polymer and colloid sciences define fertile territory for fundamental studies and creation of future transformative technologies.

Optical motion control of liquid crystalline droplets by host-guest molecular interaction

Photo-induced motion is demonstrated for a photo-responsive dye-doped liquid crystal (LC) droplet in a surfactant solution. The LC droplets started rolling on a substrate during UV irradiation and moved either toward or away from the UV light, depending on the functional groups of the guest dyes. The mechanism is explained by the Marangoni flow caused by the photo-isomerization-induced adsorption and desorption of the dye molecules to and from the LC/solution interfaces.

Dynamic clustering and re-dispersion in concentrated colloid-active gel composites

We study the dynamics of quasi-two-dimensional concentrated suspensions of colloidal particles in active gels by computer simulations. Remarkably, we find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites. Our quasi-two-dimensional "inverse" dispersions of passive particles in active fluids (as opposed to the more common "direct" suspensions of active particles in passive fluids) provide a promising route towards the self-assembly of new soft materials.

Molecular Orientation Change Nearby Topological Defects Observed by Photo-Induced Polarization/Phase Microscopy

Topological defects in liquid crystals (LCs) have been intensively studied and intentionally generated in an organized way recently because they could control the alignment and motion of LCs. We studied how the topological defects could change the molecular orientation/alignment from the observation of photo-induced orientation change of a photo-responsive LC. The photo-induced dynamics was observed by an LED-induced time-resolved polarization/phase microscopy with white light illumination. From the color image sequence, we found that the molecular orientation change started from the topological defects and the orientation change propagated as a pair of defects and was connected, and further disordering was induced as a next step after the initial orientation change finished.

Controlling organization and forces in active matter through optically defined boundaries

Living systems are capable of locomotion, reconfiguration and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, 'active' molecules that create and manipulate non-equilibrium structures and force fields of up to millimetre length scales1-3. Experimental active-matter systems of biological or synthetic molecules are capable of spontaneously organizing into structures4,5 and generating global flows6-9. However, these experimental systems lack the spatiotemporal control found in cells, limiting their utility for studying non-equilibrium phenomena and bioinspired engineering. Here we uncover non-equilibrium phenomena and principles of boundary-mediated control by optically modulating structures and fluid flow in an engineered system of active biomolecules. Our system consists of purified microtubules and light-activatable motor proteins that crosslink and organize the microtubules into distinct structures upon illumination. We develop basic operations-defined as sets of light patterns-to create, move and merge the microtubule structures. By combining these operations, we create microtubule networks that span several hundred micrometres in length and contract at speeds up to an order of magnitude higher than the speed of an individual motor protein. We manipulate these contractile networks to generate and sculpt persistent fluid flows. The principles of boundary-mediated control that we uncover may be used to study emergent cellular structures and forces and to develop programmable active-matter devices.

Nonsphere Drop Impact Assembly of Graphene Oxide Liquid Crystals

Creating long-lived topological textured liquid crystals (LCs) in confined nonspherical space is of significance in both generations of structures and fundamental studies of topological physics. However, it remains a great challenge due to the fluid character of LCs and the unstable tensional state of transient nonspheres. Here, we realize a rich series of topological textures confined in nonspherical geometries by drop impact assembly (DIA) of graphene oxide (GO) aqueous LCs. Various highly curved nonspherical morphologies of LCs were captured by gelator bath, generating distinct out-of-equilibrium yet long-lived macroscopic topological textures in 3D confinement. Our hydrodynamic investigations on DIA processes reveal that the shear-thinning fluid behavior of LCs and the arrested GO alignments mainly contribute to the topological richness in DIA. Utilizing the shaping behavior of GO LCs compared to other conventional linear polymers such as alginate, we further extend the DIA methodology to design more complex yet highly controllable functional composites and hybrids. This work thus reveals the potential to scale production of uniform yet anisotropic materials with rich topologic textures and tailored composition.

Fabrication of elastomer pillar arrays with elasticity gradient for cell migration, elongation and patterning

The elasticity of the cell and that of the supporting extracellular matrices (ECMs) in tissue are correlated. In some cases, the modulus of the ECM varies with a high spatial gradient. To study the effect of such a modulus gradient on the cell culture behavior, we proposed a novel yet straightforward method to fabricate elastomeric micropillar substrates with different height gradients, which could provide a large range of elasticity gradient from 2.4 kPa to 60 kPa. The micropillars were integrated into a microfluidic chip to demonstrate the elasticity variation, with the theoretical results proving that the elasticity of the two micropillar substrates was in the same range but with distinguished gradient strengths. Fibroblast seeded on the micropillar substrates showed migration toward the stiffer area but their elongation highly depended on the strength of the elasticity gradient. In the case of high gradient strength, cells could easily migrate to the stiffer area and then elongated perpendicularly to their migration direction. Otherwise, cells were mostly elongated in the direction of the gradient. Our results also showed that when the cell density was sufficiently high, cells tended to be oriented in the same direction locally, which was affected by both underneath pillars and cell-cell contact. The elasticity gradients could also be generated in a ripple shape, and the cell behavior showed the feasibility of using the micropillars for cell patterning applications. Moreover, the gradient pillar substrates were further used for the aggregate formation of induced pluripotent stem cells, thus providing an alternative substrate to study the effect of substrate elasticity on stem cell behavior and differentiation.

Command of Collective Dynamics by Topological Defects in Spherical Crystals

Directing individual motions of many constituents to a coherent dynamical state is a fundamental challenge in multiple fields. Here, based on the spherical crystal model, we show that topological defects in particle arrays can be a crucial element in regulating collective dynamics. Specifically, we highlight the defect-driven synchronized breathing modes around disclinations and collective oscillations with strong connection to disruption of crystalline order. This work opens the promising possibility of an organizational principle based on topological defects, and may inspire new strategies for harnessing intriguing collective dynamics in extensive nonequilibrium systems.

Activity Driven Orientational Order in Active Nematic Liquid Crystals on an Anisotropic Substrate

We investigate the effect of an anisotropic substrate on the turbulent dynamics of a simulated two-dimensional active nematic. This is introduced as an anisotropic friction and an effective anisotropic viscosity, with the orientation of the anisotropy being defined by the substrate. In this system, we observe the emergence of global nematic order of topological defects that is controlled by the degree of anisotropy in the viscosity and the magnitude of the active stress. No global defect alignment is seen in passive liquid crystals with anisotropic viscosity or friction confirming that ordering is driven by the active stress. We then closely examine the active flow generated by a single defect to show that the net kinetic energy of the flow is dependent on the orientation of the defect relative to the substrate, resulting in a torque on the defect to align it with the anisotropy in the substrate.

Computational modeling of active deformable membranes embedded in three-dimensional flows

Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a three-dimensional flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an immersed-boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g., Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of Berthoumieux et al. [New J. Phys. 16, 065005 (2014)10.1088/1367-2630/16/6/065005] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a nonaxisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows.

Active fluid with Acidithiobacillus ferrooxidans: correlations between swimming and the oxidation route

To explore engineering platforms towards 'active bacterial baths', we grow and characterize native and commercial strains of Acidithiobacillus ferrooxidans to promote swimming locomotion. Three different energy sources were used, namely elemental sulfur, ferrous sulfate, and pyrite. The characteristics of the culture, such as pH, Eh, and the concentration of cells and ions, are monitored to seek correlations between the oxidation route and the transport mechanism. We found that only elemental sulfur induces swimming mobility in the commercial DSMZ - 24,419 strain, while ferrous sulfate and the sulfide mineral, pyrite, did not activate swimming on any strain. The bacterial mean squared displacement and the mean velocity are measured to provide a quantitative description of the bacterial mobility. We found that, even if the A. ferrooxidans strain is grown in a sulfur-rich environment, it preferentially oxidizes iron when an iron-based material is included in the media. Similar to other species, once the culture pH decreases below 1.2, the active locomotion is inhibited. The engineering control and activation of swimming in bacterial cultures offer fertile grounds towards applications of active suspensions such as energy-efficient bioleaching, mixing, drug delivery, and bio-sensing.

Self-propelled particle in a nonconvex external potential: Persistent limit in one dimension

Equilibrium mapping techniques for nonaligning self-propelled particles have made it possible to predict the density profile of an active ideal gas in a wide variety of external potentials. However, they fail when the self-propulsion is very persistent and the potential is nonconvex, which is precisely when the most uniquely active phenomena occur. Here, we show how to predict the density profile of a 1D active Ornstein-Uhlenbeck particle in an arbitrary external potential in the persistent limit and discuss the consequences of the potential's nonconvexity on the structure of the solution, including the central role of the potential's inflection points and the nonlocal dependence of the density profile on the potential.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Building Reconfigurable Devices Using Complex Liquid-Fluid Interfaces

Liquid-fluid interfaces provide a platform both for structuring liquids into complex shapes and assembling dimensionally confined, functional nanomaterials. Historically, attention in this area has focused on simple emulsions and foams, in which surface-active materials such as surfactants or colloids stabilize structures against coalescence and alter the mechanical properties of the interface. In recent decades, however, a growing body of work has begun to demonstrate the full potential of the assembly of nanomaterials at liquid-fluid interfaces to generate functionally advanced, biomimetic systems. Here, a broad overview is given, from fundamentals to applications, of the use of liquid-fluid interfaces to generate complex, all-liquid devices with a myriad of potential applications.

Geometrical Control of Active Turbulence in Curved Topographies

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.

Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization

Active networks composed of filaments and motor proteins can self-organize into a variety of architectures. Computer simulations in two or three spatial dimensions and including or omitting steric interactions between filaments can be used to model active networks. Here we examine how these modelling choices affect the state space of network self-organization. We compare the networks generated by different models of a system of dynamic microtubules and microtubule-crosslinking motors. We find that a thin 3D model that includes steric interactions between filaments is the most versatile, capturing a variety of network states observed in recent experiments. In contrast, 2D models either with or without steric interactions which prohibit microtubule crossings can produce some, but not all, observed network states. Our results provide guidelines for the most appropriate choice of model for the study of different network types and elucidate mechanisms of active network organization.

Statistical properties of autonomous flows in 2D active nematics

We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs the motion of individual kinesin motors.

Creation of Artificial Cell-Like Structures Promoted by Microfluidics Technologies

The creation of artificial cells is an immensely challenging task in science. Artificial cells contribute to revealing the mechanisms of biological systems and deepening our understanding of them. The progress of versatile biological research fields has clarified many biological phenomena, and various artificial cell models have been proposed in these fields. Microfluidics provides useful technologies for the study of artificial cells because it allows the fabrication of cell-like compartments, including water-in-oil emulsions and giant unilamellar vesicles. Furthermore, microfluidics also allows the mimicry of cellular functions with chip devices based on sophisticated chamber design. In this review, we describe contributions of microfluidics to the study of artificial cells. Although typical microfluidic methods are useful for the creation of artificial-cell compartments, recent methods provide further benefits, including low-cost fabrication and a reduction of the sample volume. Microfluidics also allows us to create multi-compartments, compartments with artificial organelles, and on-chip artificial cells. We discuss these topics and the future perspective of microfluidics for the study of artificial cells and molecular robotics.

Active matter invasion of a viscous fluid: Unstable sheets and a no-flow theorem

We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities, governed at small times by an equation that also describes the Saffman-Taylor instability in a Hele-Shaw cell, or the Rayleigh-Taylor instability in a two-dimensional flow through a porous medium. Thin sheets of aligned pusher particles are always unstable, while sheets of aligned puller particles can either be stable (immotile particles), or unstable (motile particles) with a growth rate that is nonmonotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow everywhere and for all time.