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.