Topological structure and dynamics of three-dimensional active nematics

Scaling Transition of Active Turbulence from Two to Three Dimensions

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model we develop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organized systems.

Entangled nematic disclinations using multi-particle collision dynamics

Colloids dispersed in nematic liquid crystals form topological composites in which colloid-associated defects mediate interactions while adhering to fundamental topological constraints. Better realising the promise of such materials requires numerical methods that model nematic inclusions in dynamic and complex scenarios. We employ a mesoscale approach for simulating colloids as mobile surfaces embedded in a fluctuating nematohydrodynamic medium to study the kinetics of colloidal entanglement. In addition to reproducing far-field interactions, topological properties of disclination loops are resolved to reveal their metastable states and topological transitions during relaxation towards ground state. The intrinsic hydrodynamic fluctuations distinguish formerly unexplored far-from-equilibrium disclination states, including configurations with localised positive winding profiles. The adaptability and precision of this numerical approach offers promising avenues for studying the dynamics of colloids and topological defects in designed and out-of-equilibrium situations.

Topology-driven collective dynamics of nematic colloidal entanglement

Entanglement in a soft condensed matter system is enabled in the form of entangled disclination lines by using colloidal particles in nematic liquid crystals. These topological excitations are manifested as colloidal entanglement at equilibrium. How to further utilize nonequilibrium disclination lines to manipulate colloidal entanglement remains a nontrivial and challenging task. In this work, we use experiments and simulations to demonstrate the reconfigurations of nematic colloidal entanglement in light-driven spatiotemporal evolutions of disclination lines. Colloidal entanglement can sense subtle changes in the topological structures of disclination lines and realize chirality conversion. This conversion is manifested as the "domino effect" of the collective rotation of colloids in the disclination lines. By programming the topological patterns and the geometry of the disclination lines, colloidal entanglement can be assembled and split. More remarkably, a double-helix entangled structure can be formed by controlling the changes in the morphology of the disclination lines. Thus, this work will provide opportunities to program colloidal composites for smart materials and micromachines.

Diverse morphology and motility induced emergent order in bacterial collectives

Microbial communities exhibit complex behaviors driven by species interactions and individual characteristics. In this study, we delve into the dynamics of a mixed bacterial population comprising two distinct species with different morphology and motility aspects. Employing agent-based modeling and computer simulations, we analyze the impacts of size ratios and packing fractions on dispersal patterns, aggregate formation, clustering, and spatial ordering. Notably, we find that motility and anisotropy of elongated bacteria significantly influence the distribution and spatial organization of nonmotile spherical species. Passive spherical cells display a superdiffusive behavior, particularly at larger size ratios in the ballistic regime. As the size ratio increases, clustering of passive cells is observed, accompanied by enhanced alignment and closer packing of active cells in the presence of higher passive cell area fractions. In addition, we identify the pivotal role of passive cell area fraction in influencing the response of active cells toward nematicity, with its dependence on size ratio. These findings shed light on the significance of morphology and motility in shaping the collective behavior of microbial communities, providing valuable insights into complex microbial behaviors with implications for ecology, biotechnology, and bioengineering.

Designing turbulence with entangled vortices

Matter entanglement is a common chaotic structure found in both quantum and classical systems. For classical turbulence, viscous vortices are like sinews in fluid flows, storing and dissipating energy and accommodating strain and stress throughout a complex vortex network. However, to explain how the statistical properties of turbulence arise from elemental vortical structures remains challenging. Here, we use the quantum vortex tangle as a skeleton to generate an instantaneous classical turbulent field with intertwined vortex tubes. Combining the quantum skeleton and tunable vortex thickness makes the synthetic turbulence satisfy key statistical laws, offering valuable insights for elucidating energy cascade and extreme events. By manipulating the elemental structures, we customize turbulence with desired statistical features. This bottom-up approach of designing turbulence provides a testbed for analyzing and modeling turbulence.

The Casimir-like effect induced by active nematics

We consider an active nematic phase and use hydrodynamical equations of it to model the activity as an internal field. The interaction of this field with the nematic director in a confined geometry is included in the Hamiltonian of the system. Based on this model Hamiltonian and the standard field theoretical approach, the Casimir-like force induced between the boundaries of such a confined film is discussed. The force depends on the geometrical shape and the dynamical character of the constituents of our active phase, as well as the anchoring conditions. For homeotropically aligned rod-like particles which in principle tend to align along a planar flow field, extensile activity enhances the attraction present in a thin nematic film. As the film thickness increases the force reduces. Beyond a critical thickness, a planar flow field instantaneous to a bend distortion sets in. Near but below the threshold of this activity-induced instability, the force crosses zero and repulsively diverges right at the critical threshold of this so-called flow instability. For contractile rods, in the same geometry as above, the structure is stable and the Casimir-like force diminishes by an exponential factor as a function of the film thickness. On the other side for a planar director alignment, rod-like contractile particles can induce opposite shear flows at the boundaries creating a splay distortion for the director between the plates. In this configuration, we obtain the same universal pretransitional behavior for the force as above. Vice versa, for extensile rod-like particles in this geometry, the director fluctuations become massive and the Casimir-like force diminishes again by an exponential factor as the film thickness increases. The effect of the active field on thermal fluctuations of the director and the fluctuation-induced Casimir force per area is derived through a "semi"-dynamical approach as well. However, the results of the calculation due to a mathematical sum over the fluctuating modes do not lead to an approved closed form.

Structure and dynamics of motor-driven microtubule bundles

Connecting the large-scale emergent behaviors of active cytoskeletal materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems. We approach this problem by studying the impact of depletion attraction on bundles of microtubules and kinesin-14 molecular motors. For all depletant concentrations, kinesin-14 bundles generate comparable extensile dynamics. However, this invariable mesoscopic behavior masks the transition in the microscopic motion of microtubules. Specifically, with increasing attraction, we observe a transition from bi-directional sliding with extension to pure extension with no sliding. Small-angle X-ray scattering shows that the transition in microtubule dynamics is concurrent with a structural rearrangement of microtubules from an open hexagonal to a compressed rectangular lattice. These results demonstrate that bundles of microtubules and molecular motors can display the same mesoscopic extensile behaviors despite having different internal structures and microscopic dynamics. They provide essential information for developing multiscale models of active matter.

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Coexistence of Defect Morphologies in Three-Dimensional Active Nematics

We establish how active stress globally affects the morphology of disclination lines of a three-dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and that of long and tangled defect lines of fractal dimension 2. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the 3-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.

Moiré effect enables versatile design of topological defects in nematic liquid crystals

Recent advances in surface-patterning techniques of liquid crystals have enabled the precise creation of topological defects, which promise a variety of emergent applications. However, the manipulation and application of these defects remain limited. Here, we harness the moiré effect to engineer topological defects in patterned nematic liquid crystal cells. Specifically, we combine simulation and experiment to examine a nematic cell confined between two substrates of periodic surface anchoring patterns; by rotating one surface against the other, we observe a rich variety of highly tunable, novel topological defects. These defects are shown to guide the three-dimensional self-assembly of colloids, which can conversely impact defects by preventing the self-annihilation of loop-defects through jamming. Finally, we demonstrate that certain nematic moiré cells can engender arbitrary shapes represented by defect regions. As such, the proposed simple twist method enables the design and tuning of mesoscopic structures in liquid crystals, facilitating applications including defect-directed self-assembly, material transport, micro-reactors, photonic devices, and anti-counterfeiting materials.

A machine learning approach to robustly determine director fields and analyze defects in active nematics

Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.

Symmetry Breaking of Self-Propelled Topological Defects in Thin-Film Active Chiral Nematics

Active nematics represent a range of dense active matter systems which can engender spontaneous flows and self-propelled topological defects. Two-dimensional (2D) active nematic theory and simulation have been successful in explaining many quasi-2D experiments in which self-propelled +1/2 defects are observed to move along their symmetry axis. However, many active liquid crystals are essentially chiral nematic, but their twist mode becomes irrelevant under the 2D assumption. Here, we use theory and simulation to examine a three-dimensional active chiral nematic confined to a thin film, thus forming a quasi-2D system. We predict that the self-propelled +1/2 disclination in a curved thin film can break its mirror symmetry by moving circularly. Our prediction is confirmed by hydrodynamic simulations of thin spherical-shell and thin cylindrical-shell systems. In the spherical-shell confinement, the four emerged +1/2 disclinations exhibit rich dynamics as a function of activity and chirality. As such, we have proposed a new symmetry-breaking scenario in which self-propelled defects in quasi-2D active nematics can acquire an active angular velocity, greatly enriching their dynamics for finer control and emerging applications.

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Biofilms as self-shaping growing nematics

Active nematics are the nonequilibrium analogue of passive liquid crystals. They consist of anisotropic units that consume free energy to drive emergent behaviour. Like liquid crystal molecules in displays, ordering and dynamics in active nematics are sensitive to boundary conditions. However, unlike passive liquid crystals, active nematics have the potential to regulate their boundaries through self-generated stresses. Here, we show how a three-dimensional, living nematic can actively shape itself and its boundary to regulate its internal architecture through growth-induced stresses, using bacterial biofilms confined by a hydrogel as a model system. We show that biofilms exhibit a sharp transition in shape from domes to lenses upon changing environmental stiffness or cell-substrate friction, which is explained by a theoretical model that considers the competition between confinement and interfacial forces. The growth mode defines the progression of the boundary, which in turn determines the trajectories and spatial distribution of cell lineages. We further demonstrate that the evolving boundary and corresponding stress anisotropy define the orientational ordering of cells and the emergence of topological defects in the biofilm interior. Our findings may provide strategies for the development of programmed microbial consortia with emergent material properties.

Active nematic liquid crystals simulated by particle-based mesoscopic methods

Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.

Alcanivorax borkumensis biofilms enhance oil degradation by interfacial tubulation

During the consumption of alkanes, Alcanivorax borkumensis will form a biofilm around an oil droplet, but the role this plays during degradation remains unclear. We identified a shift in biofilm morphology that depends on adaptation to oil consumption: Longer exposure leads to the appearance of dendritic biofilms optimized for oil consumption effected through tubulation of the interface. In situ microfluidic tracking enabled us to correlate tubulation to localized defects in the interfacial cell ordering. We demonstrate control over droplet deformation by using confinement to position defects, inducing dimpling in the droplets. We developed a model that elucidates biofilm morphology, linking tubulation to decreased interfacial tension and increased cell hydrophobicity.

Local polar order controls mechanical stress and triggers layer formation in developing Myxococcus xanthus colonies

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are anomalously large due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.

Kinesin and myosin motors compete to drive rich multiphase dynamics in programmable cytoskeletal composites

The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable nonequilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton's versatile reconfigurability, programmed by interactions between its constituents, makes it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate-far from the composite cytoskeleton in cells. Here, we engineer actin-microtubule (MT) composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or MTs has an opposite effect. Our minimal advection-diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and demixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the nonequilibrium dynamics across all composites and timescales can be organized into three classes-slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.

Rectified Rotational Dynamics of Mobile Inclusions in Two-Dimensional Active Nematics

We investigate the dynamics of mobile inclusions embedded in 2D active nematics. The interplay between the inclusion shape, boundary-induced nematic order, and autonomous flows powers the inclusion motion. Disks and achiral gears exhibit unbiased rotational motion, but with distinct dynamics. In comparison, chiral gear-shaped inclusions exhibit long-term rectified rotation, which is correlated with dynamics and polarization of nearby +1/2 topological defects. The chirality of defect polarities and the active nematic texture around the inclusion correlate with the inclusion's instantaneous rotation rate. Inclusions provide a promising tool for probing the rheological properties of active nematics and extracting ordered motion from their inherently chaotic motion.

Atomic Aerogel Materials (or Single-Atom Aerogels): An Interesting New Paradigm in Materials Science and Catalysis Science

The concept of "single-atom catalysis" is first proposed by Tao Zhang, Jun Li, and Jingyue Liu in 2011. Single-atom catalysts (SACs) have a very high catalytic activity and greatly improved atom utilization ratio. At present, SACs have become frontier materials in the field of catalysis. Aerogels are highly porous materials with extremely low density and extremely high porosity. These pores play a key role in determining their surface reactivity and mechanical stability. The alliance of SACs and aerogels can fully reflect their structural advantages and lead to new enhancement effects. Herein, a general concept of "atomic aerogel materials" (AAMs) (or single-atom aerogels (SAAs)) is proposed to describe this interesting new paradigm in both material and catalysis fields. Based on the basic units of "gel," the AAMs can be divided into two categories: carrier-level AAMs (with micro-, nano-, or sub-nanometer pore structures) and atomic-level AAMs (with atomic-defective or oxygen-bridged sub-nanopore structures). The basic unit of the former (i.e., single-atom-functionalized aerogels) is the carrier materials in nanostructures, and the latter (i.e., single-atom-built aerogels) is the single metal atoms in atomic structures. The atomic-defective or oxygen-bridged AAMs will be important development directions in versatile heterogeneous catalytic or noncatalytic fields. The design proposals, latent challenges, and coping strategies of this new "atomic nanosystem" in applications are pointed out as well.

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. Using a combination of linear stability analysis and three-dimensional computational fluid dynamics, we demonstrate that such a coupling can in fact be tuned, depending on the type of liquid crystal order, the specific structure of the defect (i.e. asters or vortices) and the nature of the active forces. In polar systems, this can drive a spectacular transition from spherical to toroidal topology, in the presence of large extensile activity. Our analysis strengthens the idea that defects could serve as topological morphogens and provides a number of predictions that could be tested in in vitro studies, for instance in the context of organoids.

Collective transport and reconfigurable assembly of nematic colloids by light-driven cooperative molecular reorientations

Nanomotors in nature have inspired scientists to design synthetic molecular motors to drive the motion of microscale objects by cooperative action. Light-driven molecular motors have been synthesized, but using their cooperative reorganization to control the collective transport of colloids and to realize the reconfiguration of colloidal assembly remains a challenge. In this work, topological vortices are imprinted in the monolayers of azobenzene molecules which further interface with nematic liquid crystals (LCs). The light-driven cooperative reorientations of the azobenzene molecules induce the collective motion of LC molecules and thus the spatiotemporal evolutions of the nematic disclination networks which are defined by the controlled patterns of vortices. Continuum simulations provide physical insight into the morphology change of the disclination networks. When microcolloids are dispersed in the LC medium, the colloidal assembly is not only transported and reconfigured by the collective change of the disclination lines but also controlled by the elastic energy landscape defined by the predesigned orientational patterns. The collective transport and reconfiguration of colloidal assemblies can also be programmed by manipulating the irradiated polarization. This work opens opportunities to design programmable colloidal machines and smart composite materials.

Dissipation and energy propagation across scales in an active cytoskeletal material

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Defect Line Coarsening and Refinement in Active Nematics

Active matter is naturally out of equilibrium which results in the emergence of diverse dynamic steady states, including the omnipresent chaotic state known as the active turbulence. However, much less is known how active systems dynamically depart out of these configurations, such as get excited or damped to a different dynamic steady state. In this Letter, we demonstrate the coarsening and refinement dynamics of topological defect lines in three-dimensional active nematic turbulence. Specifically, using theory and numerical modeling, we are able to predict the evolution of the active defect density away from the steady state due to time-dependent activity or viscoelastic material properties, establishing a single length scale phenomenological description of defect line coarsening and refinement in a three-dimensional active nematic. The approach is first applied to growth dynamics of a single active defect loop, and then to a full three-dimensional active defect network. More generally, this Letter provides insight into the general coarsening phenomena between dynamical regimes in 3D active matter, with a possible analogy in other physical systems.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Polarity and chirality control of an active fluid by passive nematic defects

Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.

Individual consistency in the learning abilities of honey bees: cognitive specialization within sensory and reinforcement modalities

The question of whether individuals perform consistently across a variety of cognitive tasks is relevant for studies of comparative cognition. The honey bee (Apis mellifera) is an appropriate model to study cognitive consistency as its learning can be studied in multiple elemental and non-elemental learning tasks. We took advantage of this possibility and studied if the ability of honey bees to learn a simple discrimination correlates with their ability to solve two tasks of higher complexity, reversal learning and negative patterning. We performed four experiments in which we varied the sensory modality of the stimuli (visual or olfactory) and the type (Pavlovian or operant) and complexity (elemental or non-elemental) of conditioning to examine if stable correlated performances could be observed across experiments. Across all experiments, an individual's proficiency to learn the simple discrimination task was positively and significantly correlated with performance in both reversal learning and negative patterning, while the performances in reversal learning and negative patterning were positively, yet not significantly correlated. These results suggest that correlated performances across learning paradigms represent a distinct cognitive characteristic of bees. Further research is necessary to examine if individual cognitive consistency can be found in other insect species as a common characteristic of insect brains.

Data-Driven Discovery of Active Nematic Hydrodynamics

Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.

Topological defect-mediated morphodynamics of active-active interfaces

Physical interfaces widely exist in nature and engineering. Although the formation of passive interfaces is well elucidated, the physical principles governing active interfaces remain largely unknown. Here, we combine simulation, theory, and cell-based experiment to investigate the evolution of an active-active interface. We adopt a biphasic framework of active nematic liquid crystals. We find that long-lived topological defects mechanically energized by activity display unanticipated dynamics nearby the interface, where defects perform "U-turns" to keep away from the interface, push the interface to develop local fingers, or penetrate the interface to enter the opposite phase, driving interfacial morphogenesis and cross-interface defect transport. We identify that the emergent interfacial morphodynamics stems from the instability of the interface and is further driven by the activity-dependent defect-interface interactions. Experiments of interacting multicellular monolayers with extensile and contractile differences in cell activity have confirmed our predictions. These findings reveal a crucial role of topological defects in active-active interfaces during, for example, boundary formation and tissue competition that underlie organogenesis and clinically relevant disorders.

Motility of acoustically powered micro-swimmers in a liquid crystalline environment

Suspensions of microswimmers in liquid crystals demonstrate remarkably complex dynamics and serve as a model system for studying active nematics. So far, experimental realization of microswimmers suspended in liquid crystalline media has relied on biological microorganisms that impose strict limitations on the compatible media and makes it difficult to regulate activity. Here, we demonstrate that acoustically powered bubble microswimmers can efficiently self-propel in a lyotropic liquid crystal. The velocity of the swimmers is controlled by the amplitude of the acoustic field. Histograms of swimming directions with respect to the local nematic field reveal a bimodal distribution: the swimmers tend to either fully align with or swim perpendicular to the director field of the liquid crystal, occasionally switching between these two states. The bubble-induced streaming from a swimmer locally melts the liquid crystal and produces topological defects at the tail of the swimmer. We show that the defect proliferation rate increases with the angle between the swimmer's velocity and the local orientation of the director field.

Topological morphogenesis of neuroepithelial organoids

Animal organs exhibit complex topologies involving cavities and tubular networks, which underlie their form and function^1-3. However, how topology emerges during the development of organ shape, or morphogenesis, remains elusive. Here we combine tissue reconstitution and quantitative microscopy to show that tissue topology and shape is governed by two distinct modes of topological transitions^4,5. One mode involves the fusion of two separate epithelia and the other involves the fusion of two ends of the same epithelium. The morphological space is captured by a single control parameter that can be traced back to the relative rates of the two epithelial fusion modes. Finally, we identify a pharmacologically accessible pathway that regulates the frequency of two modes of epithelial fusion, and demonstrate the control of organoid topology and shape. The physical principles uncovered here provide fundamental insights into the self-organization of complex tissues⁶.

Continuous generation of topological defects in a passively driven nematic liquid crystal

Synthetic active matter is emerging as the prime route for the realisation of biological mechanisms such as locomotion, active mixing, and self-organisation in soft materials. In particular, passive nematic complex fluids are known to form out-of-equilibrium states with topological defects, but their locomotion, activation and experimental realization has been developed and understood to only a limited extent. Here, we report that the concentration-driven flow of small molecules triggers turbulent flow in the thin film of a nematic liquid crystal that continuously generates pairs of topological defects with an integer topological charge. The diffusion results in the formation of counter-rotating vortex rolls in the liquid crystal, which above a velocity threshold transform into a turbulent flow with continuous generation and annihilation of the defect pairs. The pairs of defects are created by the self-amplifying splay instability between the vortices, until a pair of oppositely charged defects is formed.

It has been known that spontaneous defect formation and annihilation can be triggered by turbulent flows in active nematic liquid crystals. Here, Mur et al. show a complementary mechanism induced by the flow of foreign organic molecules into the liquid crystal following the concentration gradient.

Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity

Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.

Competing instabilities reveal how to rationally design and control active crosslinked gels

How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.

Dispersion of activity at an active-passive nematic interface

Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems known as active nematics. However, the dynamics of this mixing is non-trivial as there is a coupling between nutrients concentration and velocity field. To address this question, we solve the hydrodynamic equation for active nematics to model the bacterial swarms coupled to an advection-diffusion equation for the activity field, which is proportional to the concentration of nutrients. At the interface between active and passive nematics the activity field is transported by the interfacial flows and in turn it modifies them through the generation of active stresses. We find that the dispersion of this conserved activity field is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects.

Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal

Topological defects-locations of local mismatch of order-are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even life phenomena. Among these, liquid crystal has been a platform for studying topological defects via visualization, yet it has been a challenge to resolve three-dimensional structures of dynamically evolving singular topological defects. Here, we report a direct confocal observation of nematic liquid crystalline defect lines, called disclinations, relaxing from an electrically driven turbulent state. We focus in particular on reconnections, characteristic of such line defects. We find a scaling law for in-plane reconnection events, by which the distance between reconnecting disclinations decreases by the square root of time to the reconnection. Moreover, we show that apparently asymmetric dynamics of reconnecting disclinations is actually symmetric in a comoving frame, in marked contrast to the two-dimensional counterpart whose asymmetry is established. We argue, with experimental supports, that this is because of energetically favorable symmetric twist configurations that disclinations take spontaneously, thanks to the topology that allows for rotation of the winding axis. Our work illustrates a general mechanism of such spontaneous symmetry restoring that may apply beyond liquid crystal, which can take place if topologically distinct asymmetric defects in lower dimensions become homeomorphic in higher dimensions and if the symmetric intermediate is energetically favorable.

Reconstituting and Characterizing Actin-Microtubule Composites with Tunable Motor-Driven Dynamics and Mechanics

The composite cytoskeleton, comprising interacting networks of semiflexible actin filaments and rigid microtubules, restructures and generates forces using motor proteins such as myosin II and kinesin to drive key processes such as migration, cytokinesis, adhesion, and mechanosensing. While actin-microtubule interactions are key to the cytoskeleton's versatility and adaptability, an understanding of their interplay with myosin and kinesin activity is still nascent. This work describes how to engineer tunable three-dimensional composite networks of co-entangled actin filaments and microtubules that undergo active restructuring and ballistic motion, driven by myosin II and kinesin motors, and are tuned by the relative concentrations of actin, microtubules, motor proteins, and passive crosslinkers. Protocols for fluorescence labeling of the microtubules and actin filaments to most effectively visualize composite restructuring and motion using multi-spectral confocal imaging are also detailed. Finally, the results of data analysis methods that can be used to quantitatively characterize non-equilibrium structure, dynamics, and mechanics are presented. Recreating and investigating this tunable biomimetic platform provides valuable insight into how coupled motor activity, composite mechanics, and filament dynamics can lead to myriad cellular processes from mitosis to polarization to mechano-sensation.

A soft active matter that can climb walls

Mechanical activity of an active fluid can be used to control its dynamics at the boundaries.

Activity gradients in two- and three-dimensional active nematics

We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.

Actin-microtubule dynamic composite forms responsive active matter with memory

Active cytoskeletal materials in vitro demonstrate self-organizing properties similar to those observed in their counterparts in cells. However, the search to emulate phenomena observed in living matter has fallen short of producing a cytoskeletal network that would be structurally stable yet possess adaptive plasticity. Here, we address this challenge by combining cytoskeletal polymers in a composite where self-assembling microtubules and actin filaments collectively self-organize due to the activity of microtubule-percolating molecular motors. We demonstrate that microtubules spatially organize actin filaments that in turn guide microtubules. The two networks align in an ordered fashion using this feedback loop. In this composite, actin filaments can act as structural memory and, depending on the concentration of the components, microtubules either write this memory or get guided by it. The system is sensitive to external stimuli, suggesting possible autoregulatory behavior in changing mechanochemical environments. We thus establish an artificial active actin-microtubule composite as a system demonstrating architectural stability and plasticity.

Crack patterns of drying dense bacterial suspensions

Drying of bacterial suspensions is frequently encountered in a plethora of natural and engineering processes. However, the evaporation-driven mechanical instabilities of dense consolidating bacterial suspensions have not been explored heretofore. Here, we report the formation of two different crack patterns of drying suspensions of Escherichia coli (E. coli) with distinct motile behaviors. Circular cracks are observed for wild-type E. coli with active swimming, whereas spiral-like cracks form for immotile bacteria. Using the elastic fracture mechanics and the poroelastic theory, we show that the formation of the circular cracks is determined by the tensile nature of the radial drying stress once the cracks are initiated by the local order structure of bacteria due to their collective swimming. Our study demonstrates the link between the microscopic swimming behaviors of individual bacteria and the mechanical instabilities and macroscopic pattern formation of drying bacterial films. The results shed light on the dynamics of active matter in a drying process and provide useful information for understanding various biological processes associated with drying bacterial suspensions.

Collective motion of epithelial cells along a wrinkled 3D-buckled hydrogel

Epithelial cells migrate autonomously by aligning and inducing a collective motion. Controlling the collective motion of epithelial cells in geometrically confined environments is important for understanding physiological processes such as wound healing and self-organized morphogenesis. However, collective migration under a three-dimensional (3D) curved surface resembling living epithelial tissue has not yet been explored. In this study, we investigated the collective motion of a 3D-buckled polyacrylamide (PAAm) gel that mimics the shape of folds and wrinkles of epithelial tissue to understand the geometric effects of collective motion. We found that the velocity correlation in the space near the hydrogel boundary showed a periodic change that correlated with the wrinkled folding of the hydrogel pattern. Furthermore, the characteristic length of the velocity correlation increased proportionally with the wavelength of wrinkled folding. These observations indicated that the hydrogel pattern could steer the collective motion of epithelial cells over long distances. Our study also suggests that the wrinkled design of the hydrogel is a versatile platform for studying the geometric effect of a curved surface on complex epithelial cell dynamics.

Nematic order condensation and topological defects in inertial active nematics

Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on the collective pattern formation in active nematics. We show that an incremental increase in inertial effects due to reduced viscosity results in gradual melting of nematic order with an increase in topological defect density before a discontinuous transition to a vortex-condensate state. The emergent vortex-condensate state at low enough viscosities coincides with nematic order condensation within the giant vortices and the drop in the density of topological defects. We further show flow field around topological defects is substantially affected by inertial effects. Moreover, we demonstrate the strong dependence of the kinetic energy spectrum on the inertial effects, recover the Kolmogorov scaling within the vortex-condensate phase, but find no evidence of universal scaling at higher viscosities. The findings reveal complexities in active nematic turbulence and emphasize the important cross-talk between active and inertial effects in setting flow and orientational organization of active particles.

Helical flow states in active nematics

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

Active transformations of topological structures in light-driven nematic disclination networks

SignificanceTopological defects are marvels of nature. Understanding their structures is important for their applications in, for example, directed self-assembly, sensing, and photonic devices. There is recent interest in active motion and transformation of topological defects in active nematics. In these nonequilibrium systems, however, the motion and transformation of disclinations are difficult to control, thereby hindering their applications. Here, we propose a surface-patterned system engendering periodic three-dimensional disclinations, which can be excited by light irradiation and undergo a programmable transformation between different topological states. Continuum simulations recapitulating these topological structures characterize the bending, breaking, and relinking events of the disclinations during the nonequilibrium process. Our work provides an alternative dynamic system in which active transformation of topological defects can be engineered.

Defect loops in three-dimensional active nematics as active multipoles

We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is nonzero only for nonplanar loops and generates a net "active torque," such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force- and torque-free geometries, suggesting a mechanism for generating an excess of twist loops. Finally, we determine the Stokesian flows created by defect loops and describe qualitatively their hydrodynamics.

Susceptibility of Polar Flocks to Spatial Anisotropy

We study the effect of spatial anisotropy on polar flocks by investigating active q-state clock models in two dimensions. In contrast to the equilibrium case, we find that any amount of anisotropy is asymptotically relevant, drastically altering the phenomenology from that of the rotationally invariant case. All of the well-known physics of the Vicsek model, from giant density fluctuations to microphase separation, is replaced by that of the active Ising model, with short-range correlations and complete phase separation. These changes appear beyond a length scale that diverges in the q→∞ limit, so that the Vicsek-model phenomenology is observed in finite systems for weak enough anisotropy, i.e., sufficiently high q. We provide a scaling argument which explains why anisotropy has such different effects in the passive and active cases.

Dynamic clustering of passive colloids in dense suspensions of motile bacteria

Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.

Assembling Microtubule-Based Active Matter

Studied for more than a century, equilibrium liquid crystals provided insight into the properties of ordered materials, and led to commonplace applications such as display technology. Active nematics are a new class of liquid crystal materials that are driven out of equilibrium by continuous motion of the constituent anisotropic units. A versatile experimental realization of active nematic liquid crystals is based on rod-like cytoskeletal filaments that are driven out of equilibrium by molecular motors. We describe protocols for assembling microtubule-kinesin based active nematic liquid crystals and associated isotropic fluids. We describe the purification of each protein and the assembly process of a two-dimensional active nematic on a water-oil interface. Finally, we show examples of nematic formation and describe methods for quantifying their non-equilibrium dynamics.