The emergence of collective motion exhibited by systems ranging from flocks of animals to self-propelled microorganisms to the cytoskeleton is a ubiquitous and fascinating self-organization phenomenon. Similarities between these systems, such as the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of very large density fluctuations, suggest universal principles underlying pattern formation. This idea is followed by theoretical models at all levels of description: micro- or mesoscopic models directly map local forces and interactions using only a few, preferably simple, interaction rules, and more macroscopic approaches in the hydrodynamic limit rely on the systems' generic symmetries. All these models characteristically have a broad parameter space with a manifold of possible patterns, most of which have not yet been experimentally verified. The complexity of interactions and the limited parameter control of existing experimental systems are major obstacles to our understanding of the underlying ordering principles. Here we demonstrate the emergence of collective motion in a high-density motility assay that consists of highly concentrated actin filaments propelled by immobilized molecular motors in a planar geometry. Above a critical density, the filaments self-organize to form coherently moving structures with persistent density modulations, such as clusters, swirls and interconnected bands. These polar nematic structures are long lived and can span length scales orders of magnitudes larger than their constituents. Our experimental approach, which offers control of all relevant system parameters, complemented by agent-based simulations, allows backtracking of the assembly and disassembly pathways to the underlying local interactions. We identify weak and local alignment interactions to be essential for the observed formation of patterns and their dynamics. The presented minimal polar-pattern-forming system may thus provide new insight into emerging order in the broad class of active fluids and self-propelled particles.

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells.Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of 1 intracellular dynamics.

Even simple active systems can show a plethora of intriguing phenomena and often we find complexity where we would have expected simplicity. One striking example is the occurrence of a quiescent or absorbing state with frozen fluctuations that at first sight seems to be impossible for active matter driven by the incessant input of energy. While such states were reported for externally driven systems through macroscopic shear or agitation, the investigation of frozen active states in inherently active systems like cytoskeletal suspensions or active gels is still at large. Using high-density motility assay experiments, we demonstrate that frozen steady states can arise in active systems if active transport is coupled to growth processes. The experiments are complemented by agent-based simulations which identify the coupling between self-organization, growth, and mechanical properties to be responsible for the pattern formation process.active fluids | cytoskeleton | actin networks

Ensembles of collectively moving particles like flocks of birds, bacteria, or filamentous polymers show a broad range of intriguing phenomena, yet seem to obey very similar physical principles. These generic principles have been predicted to lead to characteristic density fluctuations, which are in sharp contrast to normal fluctuations determining the properties of ordered systems in thermal equilibrium. Using high-density motility assays of driven filaments, we characterize here the origin and nature of giant fluctuations that emerge in this class of systems. By showing that these unique statistical properties result from the coupling between particle density and the topology of the velocity field of the particles, we provide insight in the physics of collective motion.active fluids | nonequilibrium T he composition of active systems that show collective motion is quite generic: They consist of a sufficiently high density of "particles" like birds (1), insects (2), or fish (3), vibrated granules (4, 5), bacteria and cells (6-10), or filamentous proteins (11-17) that are either self-propelled or actively driven. However, the dynamics that results from mostly local interactions among the driven constituents (18) is anything but simple: Apart from collective motion and nematic or polar order, these systems can show such intriguing phenomena as swirling motion (5,6,12,15), spontaneous and collective changes in the direction of motion (1, 3, 11), and persistent density inhomogeneities (7,11,12,16) and can generate macroscopic fluid flow (17). The theoretical description of these systems proves exceedingly difficult. To elucidate the underlying physical principles and to assess whether these systems rely on unifying organizing principles, numerous theoretical studies have been devoted to model (self-)propelled particle systems. Pioneered by the work of Vicsek et al. (19), they approach the problem on all levels of description ranging from agent-based simulations (20-24) and mesoscopic models coarsegraining microscopic interaction rules (25-29) to mean field models in the hydrodynamic limit (10,(30)(31)(32).The dynamic properties of all these models are strikingly similar to the phenomena observed in this broad class of systems. However, due to the lack of adequate and well-controlled experimental systems, a quantitative comparison with experimental results so far proved difficult. Of particular interest are certain key properties of collective motion that were first identified by Toner and Tu (30). These hallmarks of collective motility include the occurrence of abnormally large fluctuations in the particle density, the so-called giant number fluctuations (4,7,16,24,30,31,33) and correlations that are anisotropic with respect to the direction of collective motion (7,20,30,34).Despite the utmost importance of these unifying observables for a sound understanding of the physics of collective motion, most experimental systems studied to date defy their unambiguous measurement. On the one hand, this can be attributed to t...

How order can emerge spontaneously from a disordered system has always fascinated scientists from numerous disciplines. Especially in active systems like flocks animals, self-propelled microorganisms or the cytoskeleton, a unifying understanding of the pattern formation remains elusive. This is attributed to the inherent complexity of most model systems that prevents a thorough identification of the fundamental mechanisms that are responsible for the intriguing self-organizing phenomena in active systems. Here we show that long ranged hydrodynamic interactions play a crucial role in the pattern forming mechanisms in the high density motility assay, a precisely controllable minimal model system consisting of highly concentrated filaments that are driven on the nanoscale. Stability and size of the patterns depend on long ranged hydrodynamic interactions that are self-induced by the coherently moving filaments. The hydrodynamic interactions not only influence the spatial and temporal scale of the patterns but also affect the dynamics of a particular cluster in close proximity to confining boundaries or other surrounding clusters.

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. active filaments | nonthermal statistics | molecular motors | gliding assay | kinetic model I n active systems, perpetual local energy input prevents relaxation into a thermal equilibrium state (1-3). Examples are living matter (4-10) or appropriately reconstituted or synthetic model systems (11)(12)(13)(14)(15)(16)(17). It is widely accepted that nonthermal fluctuations play a crucial role for the dynamics of active systems (8,9,(18)(19)(20)(21)(22)(23)(24) and may even cause an apparent violation of the fluctuation-dissipation theorem (11). The physical origin of the violation can be attributed to local tensile stresses generated by myosin minifilaments, as shown by rheological measurements of 3D actin networks consisting of myosin II, actin filaments, and cross-linkers (11). Although this study focused on how the macroscopic properties of the active filament network are altered with respect to its equilibrium counterpart, we consider how local stresses generated by motors mesoscopically affect the dynamics and the conformational statistics of individual filaments. To this end, we use the actin gliding assay (25,26), which has become a paradigm of active systems. In this assay, actin filaments are moved by individual nonprocessive myosin motors, which are bound to a substrate. We find that motile filaments in this assay display a nonthermal distribution of curvatures with an exponential shape, which is essentially different from its equilibrium counterpart. Based on our observations, we were able to elucidate the origin of the nonthermal fluctuations in the gliding assay and introduce a mechanism that explains how nonthermal distributions may emerge in active matter systems. The mechanism relies on the interplay between local and random input of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes due to sudden jumplike changes in the system's dynamic variables. We perform stochastic simulations of the filament's dynamics and provide a rationale drawn from kinetic theory. Both approaches quantitatively reproduce the experimental curvature distribution...

Self organization mechanisms are essential for the cytoskeleton to adapt to the requirements of living cells. They rely on the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors. Here we present an in vitro minimal model system consisting of actin filaments, fascin and myosin-II filaments exhibiting pulsatile collective dynamics and superdiffusive transport properties. Both phenomena rely on the complex competition of crosslinking molecules and motor filaments in the network. They are only observed if the relative strength of the binding of myosin-II filaments to the actin network allows exerting high enough forces to unbind actin/fascin crosslinks. This is shown by varying the binding strength of the acto-myosin bond and by combining the experiments with phenomenological simulations based on simple interaction rules.

While the existence of polar ordered states in active systems is well established, the dynamics of the selfassembly processes are still elusive. We study a lattice gas model of self-propelled elongated particles interacting through excluded volume and alignment interactions, which shows a phase transition from an isotropic to a polar ordered state. By analyzing the ordering process we find that the transition is driven by the formation of a critical nucleation cluster and a subsequent coarsening process. Moreover, the time to establish a polar ordered state shows a power-law divergence. Understanding collective motion in driven or self-propelled particle systems is a topic of recent interdisciplinary interest [1][2][3]. Coherently moving groups have been observed over a broad range of scales, spanning from micrometer-sized systems [4-10] over millimeter-large granules [11][12][13] to large cooperative animal groups [14]. The ubiquity of this phenomenon raises the questions of how these coherently moving and ordered clusters arise. Coarse-grained particlebased models [15][16][17][18][19][20][21][22] have shown that interactions favoring the alignment of the particles' direction of motion is sufficient for the emergence of large scale order. As possible origins for the alignment, excluded volume interactions [23], dissipative collisions [24], and hydrodynamic interactions [25,26] have been discussed. Complementary to these coarse-grained agent-based models, hydrodynamic models have been derived from mesoscopic collision rules [27][28][29][30][31], or by means of microscopic interactions [32][33][34][35][36]. These approaches allow to determine the kinetic coefficients, and thereby to analyze pattern-forming instabilities. Furthermore, hydrodynamic equations based on symmetry arguments [37][38][39][40][41][42] were derived, enabling to show that collections of self-propelled particles exhibit a true, long-range ordered, spontaneously broken symmetry state. In addition, scaling exponents have been calculated analytically [37,38], and validated by agent-based simulations [39]. Moreover, these studies revealed the existence of giant number fluctuations and long-lived density correlations, which have also been found experimentally [10,11,43].While previous approaches on propelled particle systems focused on the long-time dynamics, the assembly processes leading to collective motion remain elusive. To close this gap, we present an agent-based model of (self-)propelled particles interacting via an effective excluded volume interaction and a local polar alignment field. In the absence of excluded volume interactions, we find a phase transition to collective motion above a critical packing fraction. Strong excluded volume interactions increase this critical packing fraction or even inhibit the development of collective motion. Analyzing the dynamics of the pattern-forming processes we find that collective motion is accompanied by a gain in free volume. Close to the critical packing fraction, the onset of collective motion ...