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.

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 states of two dimensional active gels driven by external shear.

Using a minimal hydrodynamic model, we theoretically and computationally study the Couette flow of active gels in straight and annular two-dimensional channels subject to an externally imposed shear. The gels are isotropic in the absence of externally- or activity-driven shear, but have nematic order that increases with shear rate. Using the finite element method, we determine the possible flow states for a range of activities and shear rates. Linear stability analysis of an unconfined gel in a straight channel shows that an externally imposed shear flow can stabilize an extensile fluid that would be unstable to spontaneous flow in the absence of the shear flow, and destabilize a contractile fluid that would be stable against spontaneous flow in the absence of shear flow. These results are in rough agreement with the stability boundaries between the base shear flow state and the nonlinear flow states that we find numerically for a confined active gel. For extensile fluids, we find three kinds of nonlinear flow states in the range of parameters we study: unidirectional flows, oscillatory flows, and dancing flows. To highlight the activity-driven spontaneous component of the nonlinear flows, we characterize these states by the average volumetric flow rate and the wall stress. For contractile fluids, we only find the linear shear flow and a nonlinear unidirectional flow in the range of parameters that we studied. For large magnitudes of the activity, the unidirectional contractile flow develops a boundary layer. Our analysis of annular channels shows how curvature of the streamlines in the base flow affects the transitions among flow states.

From disks to channels: dynamics of active nematics confined to an annulus.

Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require closed racetracks. Here, we computationally study 2D active nematics confined to such a geometry-an annulus. By systematically varying the annulus inner radius and channel width, we bridge the behaviors observed in the previously studied asymptotic limits of the annulus geometry: a disk and an infinite channel. We identify new steady-state behaviors, which reveal the influence of boundary curvature and its interplay with confinement. We also show that, below a threshold inner radius, the dynamics are insensitive to the presence of the inner hole. We explain this insensitivity through a simple scaling analysis. Our work sheds further light on design principles for using confinement to control the dynamics of active nematics.

Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids.

Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.

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.

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.

Vesicle shape transformations driven by confined active filaments.

In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

Nonreciprocity as a generic route to traveling states.

We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross-diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of nonreciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning nonreciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time-reversal symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit nonreciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with nonconservative dynamics, from reaction-diffusion and prey-predators models to multispecies mixtures of microorganisms with antagonistic interactions.

Topological structure and dynamics of three-dimensional active nematics.

Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms.

Confinement-Induced Self-Pumping in 3D Active Fluids.

Two dimensional active fluids display a transition from turbulent to coherent flow upon decreasing the size of the confining geometry. A recent experiment suggests that the behavior in three dimensions is remarkably different; emergent flows transition from turbulence to coherence upon increasing the confinement height to match the width. Using a simple hydrodynamic model of a suspension of extensile rodlike units, we provide the theoretical explanation for this puzzling behavior. Furthermore, using extensive numerical simulations supported by theoretical arguments, we map out the conditions that lead to coherent flows and elucidate the critical role played by the aspect ratio of the confining channel. The mechanism that we identify applies to a large class of symmetries and propulsion mechanisms, leading to a unified set of design principles for self-pumping 3D active fluids.

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.

Response of active Brownian particles to boundary driving.

We computationally study the behavior of underdamped active Brownian particles in a sheared channel geometry. Due to their underdamped dynamics, the particles carry momentum a characteristic distance away from the boundary before it is dissipated into the substrate. We correlate this distance with the persistence of particle trajectories, determined jointly by their friction and self-propulsion. Within this characteristic length, we observe counterintuitive phenomena stemming from the interplay of activity, interparticle interactions, and the boundary driving. Depending on the values of friction and self-propulsion, interparticle interactions can either aid or hinder momentum transport. More dramatically, in certain cases we observe a flow reversal near the wall, which we correlate with an induced polarization of the particle self-propulsion directions. We rationalize these results in terms of a simple kinetic picture of particle trajectories.

Reentrant Efficiency of Phototaxis in Chlamydomonas reinhardtii Cells.

Phototaxis is one of the most fundamental stimulus-response behaviors in biology wherein motile microorganisms sense light gradients to swim toward the light source. Apart from single-cell survival and growth, it plays a major role at the global scale of aquatic ecosystems and bioreactors. We study phototaxis of single-celled algae Chlamydomonas reinhardtii as a function of cell number density and light stimulus using high spatiotemporal video microscopy. Surprisingly, the phototactic efficiency has a minimum at a well-defined number density, for a given light gradient, above which the phototaxis behavior of a collection of cells can even exceed the performance obtainable from single isolated cells. We show that the origin of enhancement of performance above the critical concentration lies in the slowing down of the cells, which enables them to sense light more effectively. We also show that this steady-state phenomenology is well captured by modeling the phototactic response as a density-dependent torque acting on an active Brownian particle.

Conformational switching of chiral colloidal rafts regulates raft-raft attractions and repulsions.

Membrane-mediated particle interactions depend both on the properties of the particles themselves and the membrane environment in which they are suspended. Experiments have shown that chiral rod-like inclusions dissolved in a colloidal membrane of opposite handedness assemble into colloidal rafts, which are finite-sized reconfigurable droplets consisting of a large but precisely defined number of rods. We systematically tune the chirality of the background membrane and find that, in the achiral limit, colloidal rafts acquire complex structural properties and interactions. In particular, rafts can switch between 2 chiral states of opposite handedness, which alters the nature of the membrane-mediated raft-raft interactions. Rafts with the same chirality have long-ranged repulsions, while those with opposite chirality acquire attractions with a well-defined minimum. Both attractive and repulsive interactions are qualitatively explained by a continuum model that accounts for the coupling between the membrane thickness and the local tilt of the constituent rods. These switchable interactions enable assembly of colloidal rafts into intricate higher-order architectures, including stable tetrameric clusters and "ionic crystallites" of counter-twisting domains organized on a binary square lattice. Furthermore, the properties of individual rafts, such as their sizes, are controlled by their complexation with other rafts. The emergence of these complex behaviors can be rationalized purely in terms of generic couplings between compositional and orientational order of fluids of rod-like elements. Thus, the uncovered principles might have relevance for conventional lipid bilayers, in which the assembly of higher-order structures is also mediated by complex membrane-mediated interactions.

The interplay between activity and filament flexibility determines the emergent properties of active nematics.

Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by differences between previous simulations of active nematics based on rigid rods and experimental realizations based on semiflexible biopolymer filaments, we describe a large-scale simulation study of a particle-based computational model that explicitly incorporates filament semiflexibility. We find that energy injected into the system at the particle scale preferentially excites bend deformations, reducing the apparent filament bend modulus. The emergent characteristics of the active nematic depend on activity and flexibility only through this activity-renormalized bend 'modulus', demonstrating that apparent values of material parameters, such as the Frank 'constants', depend on activity. Thus, phenomenological parameters within continuum hydrodynamic descriptions of active nematics must account for this dependence. Further, we present a systematic way to estimate these parameters from observations of deformation fields and defect shapes in experimental or simulation data.

Insensitivity of active nematic liquid crystal dynamics to topological constraints.

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Noise and diffusion of a vibrated self-propelled granular particle.

Granular materials are an important physical realization of active matter. In vibration-fluidized granular matter, both diffusion and self-propulsion derive from the same collisional forcing, unlike many other active systems where there is a clean separation between the origin of single-particle mobility and the coupling to noise. Here we present experimental studies of single-particle motion in a vibrated granular monolayer, along with theoretical analysis that compares grain motion at short and long time scales to the assumptions and predictions, respectively, of the active Brownian particle (ABP) model. Our results show that despite the unique relation between noise and propulsion, a variety of granular particles are correctly described by the ABP model. Additionally, our scheme of analysis for validating the inputs and outputs of the model can be applied to other granular and non-granular active systems.

Equilibrium mappings in polar-isotropic confined active particles.

Despite their fundamentally nonequilibrium nature, the individual and collective behavior of active systems with polar propulsion and isotropic interactions (polar-isotropic active systems) are remarkably well captured by equilibrium mapping techniques. Here we examine two signatures of equilibrium systems --the existence of a local free energy function and the independence of the coarse-grained behavior on the details of the microscopic dynamics-- in polar-isotropic active particles confined by hard walls of arbitrary geometry at the one-particle level. We find that boundaries that possess concave regions make the density profile strongly dynamics-dependent and give it a nonlocal dependence on the geometry of the confining box. This in turn constrains the scope of equilibrium mapping techniques in polar-isotropic active systems.

Theory of microphase separation in bidisperse chiral membranes.

We present a Ginzburg-Landau theory of microphase separation in a bidisperse chiral membrane consisting of rods of opposite handedness. This model system undergoes a phase transition from an equilibrium state where the two components are completely phase separated to a state composed of microdomains of a finite size comparable to the twist penetration depth. Characterizing the phenomenology using linear stability analysis and numerical studies, we trace the origin of the discontinuous change in microdomain size that occurs during this phase transition to a competition between the cost of creating an interface and the gain in twist energy for small microdomains in which the twist penetrates deep into the center of the domain.