Gliding filament system giving both global orientational order and clusters in collective motion

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.

Collision-induced torque mediates the transition of chiral dynamic patterns formed by active particles

Controlling the patterns formed by self-propelled particles through dynamic self-organization is a challenging task. Although varieties of patterns associated with chiral self-propelled particles have been reported, essential factors that determine the morphology of the patterns have remained unclear. Here, we explore theoretically how torque formed upon collision of the particles affects the dynamic self-organization of the particles and determine the patterns. Based on a particle-based model with collision-induced torque and torque associated with self-propulsion, we find that introducing collision-induced torque turns the homogeneous bi-directionally aligned particles into rotating mono-polar flocks, which helps resolve a discrepancy in the earlier observations in microfilament gliding assays.

Programmable molecular transport achieved by engineering protein motors to move on DNA nanotubes

Intracellular transport is the basis of microscale logistics within cells and is powered by biomolecular motors. Mimicking transport for in vitro applications has been widely studied; however, the inflexibility in track design and control has hindered practical applications. Here, we developed protein-based motors that move on DNA nanotubes by combining a biomolecular motor dynein and DNA binding proteins. The new motors and DNA-based nanoarchitectures enabled us to arrange the binding sites on the track, locally control the direction of movement, and achieve multiplexed cargo transport by different motors. The integration of these technologies realized microscale cargo sorters and integrators that automatically transport molecules as programmed in DNA sequences on a branched DNA nanotube. Our system should provide a versatile, controllable platform for future applications.

Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity

Understanding how migrating cells can establish both dynamic structures and coherent dynamics may provide mechanistic insights to study how living systems acquire complex structures and functions. Recent studies revealed that intercellular contact communication plays a crucial role for establishing cellular dynamic self-organization (DSO) and provided a theoretical model of DSO for migrating solitary cells in a free space. However, to apply those understanding to situations in living organisms, we need to know the role of cell-cell communication for tissue dynamics under spatial confinements and epithelial integrity. Here, we expand the previous numerical studies on DSO to migrating cells subjected spatial confinement and/or epithelial integrity. An epithelial monolayer is simulated by combining the model of cellular DSO and the cellular vertex model in two dimensions for apical integrity. Under confinement to a small space, theoretical models of both solitary and epithelial cells exhibit characteristic coherent dynamics, including apparent swirling. We also find that such coherent dynamics can allow the cells to overcome the strong constraint due to spatial confinement and epithelial integrity. Furthermore, we demonstrate how epithelial cell clusters behave without spatial confinement and find various cluster dynamics, including spinning, migration and elongation.

Active nematic order and dynamic lane formation of microtubules driven by membrane-bound diffusing motors

Active nematics are ordered liquid crystalline fluids that exhibit spontaneous persistent flows and collective dynamics. The development of motile biopolymer systems inspired by nature has recently attracted considerable attention to out-of-equilibrium soft materials. We report the formation of an active nematic in which microtubules are propelled by kinesin motors coupled to a lipid membrane substrate. The system exhibits apolar order in a globally aligned nematic phase and locally ordered dynamic lanes. Use of a fluid substrate represents a significant advance for active matter as it allows for spatial re-organization of motors, which generate force, in response to the dynamics of the aligning microtubules. This self-organized feedback mechanism may have implications in vivo and for engineering efficient dynamic and reconfigurable materials.

Dynamic lane formation and long-range active nematic alignment are reported using a geometry in which kinesin motors are directly coupled to a lipid bilayer, allowing for in-plane motor diffusion during microtubule gliding. We use fluorescence microscopy to image protein distributions in and below the dense two-dimensional microtubule layer, revealing evidence of diffusion-enabled kinesin restructuring within the fluid membrane substrate as microtubules collectively glide above. We find that the lipid membrane acts to promote filament–filament alignment within the gliding layer, enhancing the formation of a globally aligned active nematic state. We also report the emergence of an intermediate, locally ordered state in which apolar dynamic lanes of nematically aligned microtubules migrate across the substrate. To understand this emergent behavior, we implement a continuum model obtained from coarse graining a collection of self-propelled rods, with propulsion set by the local motor kinetics. Tuning the microtubule and kinesin concentrations as well as active propulsion in these simulations reveals that increasing motor activity promotes dynamic nematic lane formation. Simulations and experiments show that, following fluid bilayer substrate mediated spatial motor restructuring, the total motor concentration becomes enriched below the microtubule lanes that they drive, with the feedback leading to more dynamic lanes. Our results have implications for membrane-coupled active nematics in vivo as well as for engineering dynamic and reconfigurable materials where the structural elements and power sources can dynamically colocalize, enabling efficient mechanical work.

Controlling Collective Motion of Kinesin-Driven Microtubules via Patterning of Topographic Landscapes

Biomolecular motor proteins that generate forces by consuming chemical energy obtained from ATP hydrolysis play pivotal roles in organizing cytoskeletal structures in living cells. An ability to control cytoskeletal structures would benefit programmable protein patterning; however, our current knowledge is limited because of the underdevelopment of engineering approaches for controlling pattern formation. Here, we demonstrate the controlling of self-assembled patterns of microtubules (MTs) driven by kinesin motors by designing the boundary shape in fabricated microwells. By manipulating the collision angle of gliding MTs defined by the boundary shape, the self-assembly of MTs can be controlled to form protruding bundle and bridge patterns. Corroborated by the theory of self-propelled rods, we further show that the alignment of MTs determines the transition between the assembled patterns, providing a blueprint to reconstruct bridge structures in microchannels. Our findings introduce the tailoring of the self-organization of cytoskeletons and motor proteins for nanotechnological applications.

Pattern formation and polarity sorting of driven actin filaments on lipid membranes

Pattern formation processes in active systems give rise to a plethora of collective structures. Predicting how the emergent structures depend on the microscopic interactions between the moving agents remains a challenge. By introducing a high-density actin gliding assay on a fluid membrane, we demonstrate the emergence of polar structures in a regime of nematic binary interactions dominated by steric repulsion. The transition from a microscopic nematic symmetry to a macroscopic polar structure is linked to microscopic polarity sorting mechanisms, including accumulation in wedge-like topological defects. Our results should be instrumental for a better understanding of pattern formation and polarity sorting processes in active matter.

Collective motion of active matter is ubiquitously observed, ranging from propelled colloids to flocks of bird, and often features the formation of complex structures composed of agents moving coherently. However, it remains extremely challenging to predict emergent patterns from the binary interaction between agents, especially as only a limited number of interaction regimes have been experimentally observed so far. Here, we introduce an actin gliding assay coupled to a supported lipid bilayer, whose fluidity forces the interaction between self-propelled filaments to be dominated by steric repulsion. This results in filaments stopping upon binary collisions and eventually aligning nematically. Such a binary interaction rule results at high densities in the emergence of dynamic collectively moving structures including clusters, vortices, and streams of filaments. Despite the microscopic interaction having a nematic symmetry, the emergent structures are found to be polar, with filaments collectively moving in the same direction. This is due to polar biases introduced by the stopping upon collision, both on the individual filaments scale as well as on the scale of collective structures. In this context, positive half-charged topological defects turn out to be a most efficient trapping and polarity sorting conformation.

Monopolar flocking of microtubules in collective motion

Flocking is a fascinating coordinated behavior of living organisms or self-propelled particles (SPPs). Particularly, monopolar flocking has been attractive due to its potential applications in various fields. However, the underlying mechanism behind flocking and emergence of monopolar motion in flocking of SPPs has remained obscured. Here, we demonstrate monopolar flocking of kinesin-driven microtubules, a self-propelled biomolecular motor system. Microtubules with an intrinsic structural chirality preferentially move towards counter-clockwise direction. At high density, the CCW motion of microtubules facilitates monopolar flocking and formation of a spiral pattern. The monopolar flocking of microtubules is accounted for by a torque generated when the motion of microtubules was obstructed due to collisions. Our results shed light on flocking and emergence of monopolar motion in flocking of chiral active matters. This work will help regulate the polarity in collective motion of SPPs which in turn will widen their applications in nanotechnology, materials science and engineering.

Long-Range Phase Order in Two Dimensions under Shear Flow

We theoretically and numerically investigate a two-dimensional O(2) model where an order parameter is convected by shear flow. We show that a long-range phase order emerges in two dimensions as a result of anomalous suppression of phase fluctuations by the shear flow. Furthermore, we use the finite-size scaling theory to demonstrate that a phase transition to the long-range ordered state from the disordered state is second order. At a transition point far from equilibrium, the critical exponents turn out to be close to the mean-field value for equilibrium systems.

Dynamic Self-Organization of Idealized Migrating Cells by Contact Communication

This Letter investigates what forms of cellular dynamic self-organization are caused through intercellular contact communication based on a theoretical model in which migrating cells perform contact following and contact inhibition and attraction of locomotion. Tuning those strengths causes varieties of dynamic patterns. This further includes a novel form of collective migration, snakelike dynamic assembly. Scrutinizing this pattern reveals that cells in this state can accurately respond to an external directional cue but have no spontaneous global polar order.

Kinesin-Recruiting Microtubules Exhibit Collective Gliding Motion while Forming Motor Trails

Microtubules gliding on surfaces coated with kinesin motors are minimalist experimental systems for studying collective behavior. Collective behavior in these systems arises from interactions between filaments, for example, from steric interactions, depletion forces, or cross-links. To maximize the utilization of system components and the production of work, it is desirable to achieve mutualistic interactions leading to the congregations of both types of agents, that is, cytoskeletal filaments and molecular motors. To this end, we used a microtubule-kinesin system, where motors reversibly bind to the surface via an interaction between a hexahistidine (His₆) tag on the motor and a Ni(II)-nitrilotriacetic acid (Ni-NTA) moiety on the surface. The surface density of binding sites for kinesin motors was increased relative to our earlier work, driving the motors from the solution to the surface. Characterization of the motor-surface interactions in the absence of microtubules yielded kinetic parameters consistent with previous data and revealed the capacity of the surface to support two-dimensional motor diffusion. The motor density gradually fell over 2 h, presumably due to the stripping of Ni(II) from the NTA moieties on the surface. Microtubules gliding on these reversibly bound motors were unable to cross each other and at high enough densities began to align and form long, dense bundles. The kinesin motors accumulated in trails surrounding the microtubule bundles and participated in microtubule transport.

Chiral Active Hexatics: Giant Number Fluctuations, Waves, and Destruction of Order

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behavior are thought to be confined to systems with polar or nematic asymmetry. In this Letter, we show that such departures are also displayed by more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large length scale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them nonmutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

Hohenberg-Mermin-Wagner-Type Theorems for Equilibrium Models of Flocking

We study a class of two-dimensional models of classical hard-core particles with Vicsek type "exchange interaction" that aligns the directions of motion of nearby particles. By extending the Hohenberg-Mermin-Wagner theorem for the absence of spontaneous magnetization and the McBryan-Spencer bound for correlation functions, we prove that the models do not spontaneously break the rotational symmetry in their equilibrium states at any nonzero temperature. This provides a counterexample to the well-known argument that the mobility of particles is the key origin of the spontaneous symmetry breaking in two-dimensional Vicsek type models. Our result suggests that the origin of the symmetry breaking should be sought in the absence of a detailed balance condition, or, equivalently, in nonequilibrium nature.

A particle-field approach bridges phase separation and collective motion in active matter

Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

Interacting self-propelled particles exhibit phase separation or collective motion depending on particle shape. A unified theory connecting these paradigms represents a major challenge in active matter, which the authors address here by modeling active particles as continuum fields.