Statistical properties of autonomous flows in 2D active nematics

Heterogeneous distribution of kinesin-streptavidin complexes revealed by mass photometry

Kinesin-streptavidin complexes are widely used in microtubule-based active-matter studies. The stoichiometry of the complexes is empirically tuned but experimentally challenging to determine. Here, mass photometry measurements reveal heterogenous distributions of kinesin-streptavidin complexes. Our binding model indicates that heterogeneity arises from both the kinesin-streptavidin mixing ratio and the kinesin-biotinylation efficiency.

Emerging Mesoscale Flows and Chaotic Advection in Dense Active Matter

We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Both models support active mesoscale flows, leading to chaotic advection and transport over large length scales in their homogeneous dense fluid states, away from dynamical arrest. They form streams and vortices reminiscent of multiscale flow patterns in turbulence. We show that the characteristics of these flows do not depend on the specific details of the active fluids, and result from the competition between crowding effects and persistent propulsions. This observation suggests that dense active suspensions of self-propelled particles present a type of "active turbulence" distinct from collective flows reported in other types of active systems.

Motor crosslinking augments elasticity in active nematics

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Controlling active turbulence by activity patterns

By patterning activity in space, one can control active turbulence. To show this, we use Doi's hydrodynamic equations of a semidilute solution of active rods. A linear stability analysis reveals the resting isotropic fluid to be unstable above an absolute pusher activity. The emergent activity-induced paranematic state displays active turbulence, which we characterize by different quantities including the energy spectrum, which shows the typical power-law decay with exponent -4. Then, we control the active turbulence by a square lattice of circular spots where activity is switched off. In the parameter space lattice constant versus surface-to-surface distance of the spots, we identify different flow states. Most interestingly, for lattice constants below the vorticity correlation length and for spot distances smaller than the nematic coherence length, we observe a multi-lane flow state, where flow lanes with alternating flow directions are separated by a street of vortices. The flow pattern displays pronounced multistability and also appears transiently at the transition to the isotropic active-turbulence state. At larger lattice constants a trapped vortex state is identified with a non-Gaussian vorticity distribution due to the low flow vorticity at the spots. It transitions to conventional active turbulence for increasing spot distance.

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.

Maximally mixing active nematics

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

Measuring response functions of active materials from data

From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so-called active systems generally aim to extract important length or time scales from experimental fields. Because such methods focus on extracting scalar values, they do not wring maximal information from experimental data. We introduce a method to overcome these limitations. We extend the framework of correlation functions by taking into account the internal headings of displacement fields. The functions we construct represent the material response to specific types of active perturbation within the system. Utilizing these response functions we query the material response of disparate active systems composed of actin filaments and myosin motors, from model fluids to living cells. We show we can extract critical length scales from the turbulent flows of an active nematic, anticipate contractility in an active gel, distinguish viscous from viscoelastic dissipation, and even differentiate modes of contractility in living cells. These examples underscore the vast utility of this method which measures response functions from experimental observations of complex active systems.

Light-activated microtubule-based two-dimensional active nematic

We assess the ability of two light responsive kinesin motor clusters to drive dynamics of microtubule-based active nematics: opto-K401, a processive motor, and opto-K365, a non-processive motor. Measurements reveal an order of magnitude improvement in the contrast of nematic flow speeds between maximally- and minimally-illuminated states for opto-K365 motors when compared to opto-K401 construct. For opto-K365 nematics, we characterize both the steady-state flow and defect density as a function of applied light. We also examine the transient behavior as the system switches between steady-states upon changes in light intensities. Although nematic flows reach a steady state within tens of seconds, the defect density exhibits transient behavior for up to 10 minutes, showing a separation between small-scale active flows and system-scale structural states. Our work establishes an experimental platform that can exploit spatiotemporally-heterogeneous patterns of activity to generate targeted dynamical states.

Physically informed data-driven modeling of active nematics

A continuum description is essential for understanding a variety of collective phenomena in active matter. However, building quantitative continuum models of active matter from first principles can be extremely challenging due to both the gaps in our knowledge and the complicated structure of nonlinear interactions. Here, we use a physically informed data-driven approach to construct a complete mathematical model of an active nematic from experimental data describing kinesin-driven microtubule bundles confined to an oil-water interface. We find that the structure of the model is similar to the Leslie-Ericksen and Beris-Edwards models, but there are appreciable and important differences. Rather unexpectedly, elastic effects are found to play no role in the experiments considered, with the dynamics controlled entirely by the balance between active stresses and friction stresses.

Flow patterns and defect dynamics of active nematic liquid crystals under an electric field

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics with simultaneous creation of two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.

Defect self-propulsion in active nematic films with spatially varying activity

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

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.

Active boundary layers in confined active nematics

The role of boundary layers in conventional liquid crystals is commonly related to the mesogen anchoring on confining walls. In the classical view, anchoring enslaves the orientational field of the passive material under equilibrium conditions. In this work, we show that an active nematic can develop active boundary layers that topologically polarize the confining walls. We find that negatively-charged defects accumulate in the boundary layer, regardless of the wall curvature, and they influence the overall dynamics of the system to the point of fully controlling the behavior of the active nematic in situations of strong confinement. Further, we show that wall defects exhibit behaviors that are essentially different from those of their bulk counterparts, such as high motility or the ability to recombine with another defect of like-sign topological charge. These exotic behaviors result from a change of symmetry induced by the wall in the director field around the defect. Finally, we suggest that the collective dynamics of wall defects might be described in terms of a model equation for one-dimensional spatio-temporal chaos.

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.

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion

Collective motion is a ubiquitous phenomenon in nature. The collective motion of cytoskeleton filaments results mainly from dynamic collisions and alignments; however, the detailed mechanism of pattern formation still needs to be clarified. In particular, the influence of persistence length, which is a measure of filament flexibility, on collective motion is still unclear and lacks experimental verifications although it is likely to directly affect the orientational flexibility of filaments. Here, we investigated the collective motion of microtubules with different persistence lengths using a microtubule-kinesin motility system. We showed that local interactions between microtubules significantly vary depending on their persistence length. We demonstrated that the bundling of microtubules is enhanced by more durable alignment, rather than by greater likelihood of alignment. An agent-based computational model confirmed that the rigidity-dependent durability of microtubule alignment dominates their collective behavior.

Mesoscopic simulations of active nematics

Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a substantial role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarse-grained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multiparticle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active nematic MPCD (AN-MPCD) simulations not only exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing simulations of composite active-passive systems.

Hydrodynamic theory of p-atic liquid crystals

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p=2) and hexatics (p=6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p>2. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any p-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates.

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.

Engineering stability, longevity, and miscibility of microtubule-based active fluids

Microtubule-based active matter provides insight into the self-organization of motile interacting constituents. We describe several formulations of microtubule-based 3D active isotropic fluids. Dynamics of these fluids is powered by three types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. Another modification uses a specific microtubule crosslinker to induce bundle formation instead of a non-specific polymer depletant. In comparison to the already established system, each formulation exhibits distinct properties. These developments reveal the temporal stability of microtubule-based active fluids while extending their reach and the applicability.

Extensile to contractile transition in active microtubule-actin composites generates layered asters with programmable lifetimes

We study a reconstituted composite system consisting of an active microtubule network interdigitated with a passive network of entangled F-actin filaments. Increasing the concentration of filamentous actin controls the emergent dynamics, inducing a transition from turbulent-like flows to bulk contractions. At intermediate concentrations, where the active stresses change their symmetry from anisotropic extensile to isotropic contracting, the composite separates into layered asters that coexist with the background turbulent fluid. Contracted onion-like asters have a radially extending microtubule-rich cortex that envelops alternating layers of microtubules and F-actin. These self-regulating structures undergo internal reorganization, which appears to minimize the surface area and maintain the ordered layering, even when undergoing aster merging events. Finally, the layered asters are metastable structures. Their lifetime, which ranges from minutes to hours, is encoded in the material properties of the composite. These results challenge the current models of active matter. They demonstrate self-organized dynamical states and patterns evocative of those observed in the cytoskeleton do not require precise biochemical regulation, but can arise from purely mechanical interactions of actively driven filamentous materials.

Active Extensile Stress Promotes 3D Director Orientations and Flows

We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist type in extensile or wedge type in contractile materials.

Flow around topological defects in active nematic films

We study the active flow around isolated defects and the self-propulsion velocity of +1/2 defects in an active nematic film with both viscous dissipation (with viscosity η) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓd=η/Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R. In the presence of friction that leads to a finite value of ℓd, the vorticity field decays to zero on the lengthscales larger than ℓd. We show that the self-propulsion velocity of +1/2 defects grows with R in small systems where R<ℓd, while in the infinite system limit or when R≫ℓd, it approaches a constant value determined by ℓd.

Orientational Correlations in Active and Passive Nematic Defects

We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from antialigning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are insensitive to material properties and qualitatively similar to what is found for defects in passive nematic liquid crystals.

Effects of confinement on the dynamics and correlation scales in kinesin-microtubule active fluids

We study the influence of solid boundaries on dynamics and structure of kinesin-driven microtubule active fluids as the height of the container, H, increases from hundreds of micrometers to several millimeters. By three-dimensional tracking of passive tracers dispersed in the active fluid, we observe that the activity level, characterized by velocity fluctuations, increases as system size increases and retains a small-scale isotropy. Concomitantly, as the confinement level decreases, the velocity-velocity temporal correlation develops a strong positive correlation at longer times, suggesting the establishment of a "memory". We estimate the characteristic size of the flow structures from the spatial correlation function and find that, as the confinement becomes weaker, the correlation length, l_{c}, saturates at approximately 400 microns. This saturation suggests an intrinsic length scale which, along with the small-scale isotropy, demonstrates the multiscale nature of this kinesin-driven bundled microtubule active system.

Multiscale Microtubule Dynamics in Active Nematics

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

Modeling spatiotemporally varying protein-protein interactions in CyLaKS, the Cytoskeleton Lattice-based Kinetic Simulator

Interaction of cytoskeletal filaments, motor proteins, and crosslinking proteins drives important cellular processes such as cell division and cell movement. Cytoskeletal networks also exhibit nonequilibrium self-assembly in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding, obstacles along the filament, motor interactions and direction switching, and changes, defects, or heterogeneity in the filament binding lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) to investigate such problems. The simulation model builds on previous work by incorporating motor mechanochemistry into a simulation with many interacting motors and/or associated proteins on a discretized lattice. CyLaKS also includes detailed balance in binding kinetics, movement, and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work and is available on GitHub for others to freely use or build upon. Here we illustrate the use of CyLaKS to study long-range motor interactions, microtubule lattice heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.

Flow coupling between active and passive fluids across water-oil interfaces

Active fluid droplets surrounded by oil can spontaneously develop circulatory flows. However, the dynamics of the surrounding oil and their influence on the active fluid remain poorly understood. To investigate interactions between the active fluid and the passive oil across their interface, kinesin-driven microtubule-based active fluid droplets were immersed in oil and compressed into a cylinder-like shape. The droplet geometry supported intradroplet circulatory flows, but the circulation was suppressed when the thickness of the oil layer surrounding the droplet decreased. Experiments with tracers and network structure analyses and continuum models based on the dynamics of self-elongating rods demonstrated that the flow transition resulted from flow coupling across the interface between active fluid and oil, with a millimeter-scale coupling length. In addition, two novel millifluidic devices were developed that could trigger and suppress intradroplet circulatory flows in real time: one by changing the thickness of the surrounding oil layer and the other by locally deforming the droplet. This work highlights the role of interfacial dynamics in the active fluid droplet system and shows that circulatory flows within droplets can be affected by millimeter-scale flow coupling across the interface between the active fluid and the oil.

Fractal generation in a two-dimensional active-nematic fluid

Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k^-β for large wavenumbers k. The parameter β is measured for several experimental realizations. Though β is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k^-β seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between β and a single dimensionless quantity r, which characterizes the compressibility.

Crowder and surface effects on self-organization of microtubules

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Alignment of a topological defect by an activity gradient

As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single defect of topological charge +1/2, moving in an activity gradient. This modeling uses three methods: (1) approximate analytic solution of hydrodynamic equations, (2) macroscopic, symmetry-based theory of the defect as an effective oriented particle, and (3) numerical simulation. All three methods show that an activity gradient aligns the defect orientation, and hence should be useful to control defect motion.

Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics

We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive limit, we show that, as the friction is increased, memory effects become more prominent and +1/2 topological defects leave increasingly persistent trails in the director field as they pass. The trails are preferential sites for defect formation and they tend to impose polar order on any new +1/2 defects. In the absence of noise and for high friction, it becomes very difficult to create defects, but trails formed by any defects present at the beginning of the simulations persist and organise into parallel arch-like patterns in the director field. We show aligned arches of equal width are approximate steady state solutions of the equations of motion which co-exist with the nematic state. We compare our results to other models in the literature, in particular dry systems with no hydrodynamics, where trails, arches and polar defect ordering have also been observed.

Machine learning active-nematic hydrodynamics

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Machine learning forecasting of active nematics

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.

Confinement-induced self-organization in growing bacterial colonies

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

Confinement Controls the Bend Instability of Three-Dimensional Active Liquid Crystals

Spontaneous growth of long-wavelength deformations is a defining feature of active liquid crystals. We investigate the effect of confinement on the instability of 3D active liquid crystals in the isotropic phase composed of extensile microtubule bundles and kinesin molecular motors. When shear aligned, such fluids exhibit finite-wavelength self-amplifying bend deformations. By systematically changing the channel size we elucidate how the instability wavelength and its growth rate depend on the channel dimensions. Experimental findings are qualitatively consistent with a minimal hydrodynamic model, where the fastest growing deformation is set by a balance of active driving and elastic relaxation. Our results demonstrate that confinement determines the structure and dynamics of active fluids on all experimentally accessible length scales.

Collective motion of driven semiflexible filaments tuned by soft repulsion and stiffness

In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins form complex structures important for cell mechanics, motility, and division. Collective dynamics of cytoskeletal systems can be reconstituted using filament gliding experiments, in which cytoskeletal filaments are propelled by surface-bound motor proteins. These experiments have observed diverse dynamical states, including flocks, polar streams, swirling vortices, and single-filament spirals. Recent experiments with microtubules and kinesin motor proteins found that the collective behavior of gliding filaments can be tuned by altering the concentration of the crowding macromolecule methylcellulose in solution. Increasing the methylcellulose concentration reduced filament crossing, promoted alignment, and led to a transition from active, isotropically oriented filaments to locally aligned polar streams. This emergence of collective motion is typically explained as an increase in alignment interactions by Vicsek-type models of active polar particles. However, it is not yet understood how steric interactions and bending stiffness modify the collective behavior of active semiflexible filaments. Here we use simulations of driven filaments with tunable soft repulsion and rigidity in order to better understand how the interplay between filament flexibility and steric effects can lead to different active dynamic states. We find that increasing filament stiffness decreases the probability of filament alignment, yet increases collective motion and long-range order, in contrast to the assumptions of a Vicsek-type model. We identify swirling flocks, polar streams, buckling bands, and spirals, and describe the physics that govern transitions between these states. In addition to repulsion and driving, tuning filament stiffness can promote collective behavior, and controls the transition between active isotropic filaments, locally aligned flocks, and polar streams.

Shear-Induced Gelation of Self-Yielding Active Networks

An enticing feature of active materials is the possibility of controlling macroscale rheological properties through the activity of the microscopic constituents. Using a unique combination of microscopy and rheology we study three dimensional microtubule-based active materials whose autonomous flows are powered by a continually rearranging connected network. We quantify the relationship between the microscopic dynamics and the bulk mechanical properties of these nonequilibrium networks. Experiments reveal a surprising nonmonotonic viscosity that strongly depends on the relative magnitude of the rate of internally generated activity and the externally applied shear. A simple two-state mechanical model that accounts for both the solidlike and yielded fluidlike elements of the network accurately describes the rheological measurements.

Driven topological transitions in active nematic films

The topological properties of many materials are central to their behavior. In intrinsically out-of-equilibrium active materials, the dynamics of topological defects can be particularly important. In this paper, local manipulation of the order, dynamics, and topological properties of microtubule-based active nematic films is demonstrated in a joint experimental and simulation study. Hydrodynamic stresses created by magnetically actuated rotation of disk-shaped colloids in proximity to the films compete with internal stresses in the active nematic, influencing the local motion of +1/2 charge topological defects that are intrinsic to the nematic order in the spontaneously turbulent active films. Sufficiently large applied stresses drive the formation of +1 charge topological vortices through the merger of two +1/2 defects. The directed motion of the defects is accompanied by ordering of the vorticity and velocity of the active flows within the film that is qualitatively unlike the response of passive viscous films. Many features of the film's response to the stress are captured by lattice Boltzmann simulations, providing insight into the anomalous viscoelastic nature of the active nematic. The topological vortex formation is accompanied by a rheological instability in the film that leads to significant increase in the flow velocities. Comparison of the velocity profile in vicinity of the vortex with fluid-dynamics calculations provides an estimate of the film viscosity.

Active microfluidic transport in two-dimensional handlebodies

Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.

Wrinkling Instability in 3D Active Nematics

In nature, interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviors. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors, and depleting agent. It shows a rich behavior evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For high accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B+  as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Andersen potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.