Myosin motors drive long range alignment of actin filaments

Phase separation kinetics and cluster dynamics in two-dimensional active dumbbell systems

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling properties of the structure factor, along with the averaged number of clusters and their radii of gyration. The growth observed is faster than in active disk models, and this effect is further enhanced under stronger activity. Next, we focused on studying the hexatic order of the clusters. The length associated with the orientational order increases algebraically with time and faster than for spherical active Brownian particles. Under weak active forces, most clusters exhibit a uniform internal orientational order. However, under strong forces, large clusters consist of domains with different orientational orders. We demonstrated that the latter configurations are not stable, and given sufficient time to evolve, they eventually achieve homogeneous configurations as well. No gas bubbles are formed within the clusters, even when there are patches of different hexatic order. Finally, attention was directed towards the geometry and motion of the clusters themselves. By employing a tracking algorithm, we showed that clusters smaller than the typical size at the observation time exhibit regular shapes, while larger ones display fractal characteristics. In between collisions or break-ups, the clusters behave as solid bodies. Their centers of mass undergo circular motion, with radii increasing with the cluster size. The angular velocity of the center of mass equals that of the constituents with respect to their center of mass. These observations were rationalised with a simple mechanical model.

Hierarchical defect-induced condensation in active nematics

Topological defects play a central role in the formation and organization of various biological systems. Historically, such nonequilibrium defects have been mainly studied in the context of homogeneous active nematics. Phase-separated systems, in turn, are known to form dense and dynamic nematic bands, but typically lack topological defects. In this paper, we use agent-based simulations of weakly aligning, self-propelled polymers and demonstrate that contrary to the existing paradigm phase-separated active nematics form -1/2 defects. Moreover, these defects, emerging due to interactions among dense nematic bands, constitute a novel second-order collective state. We investigate the morphology of defects in detail and find that their cores correspond to a strong increase in density, associated with a condensation of nematic fluxes. Unlike their analogs in homogeneous systems, such condensed defects form and decay in a different way and do not involve positively charged partners. We additionally observe and characterize lateral arc-like structures that separate from a band's bulk and move in transverse direction. We show that the key control parameters defining the route from stable bands to the coexistence of dynamic lanes and defects are the total density of particles and their path persistence length. We introduce a hydrodynamic theory that qualitatively recapitulates all the main features of the agent-based model, and use it to show that the emergence of both defects and arcs can be attributed to the same anisotropic active fluxes. Finally, we present a way to artificially engineer and position defects, and speculate about experimental verification of the provided model.

Emergence of diverse patterns driven by molecular motors in the motility assay

Actomyosin contractility originating from interactions between F-actin and myosin motors in the actin cytoskeleton generates mechanical forces and drives a wide range of cellular processes including cell migration and cytokinesis. To probe the interactions between F-actin and myosin motors, the myosin motility assay has been popularly employed, which consists of myosin heads attached to a glass surface and F-actins gliding on the surface via interactions with the heads. Several experiments have shown that F-actins move in a collective fashion due to volume-exclusion effects between neighboring F-actins. Furthermore, Computational models have shown how changes in key parameters lead to diverse pattern formation in motility assay. However, in most of the computational models, myosin motors were implicitly considered by applying a constant propulsion force to filaments to reduce computational cost. This simplification limits the physiological relevance of the insights provided by the models and potentially leads to artifacts. In this study, we employed an agent-based computational model for the motility assay with explicit immobile motors interacting with filaments. We rigorously account for the kinetics of myosin motors including the force-velocity relationship for walking and the binding and unbinding behaviors. We probed the effects of the length, rigidity, and concentration of filaments and repulsive strength on collective movements and pattern formation. It was found that four distinct types of structures-homogeneous networks, flocks, bands, and rings-emerged as a result of collisions between gliding filaments. We further analyzed the frequency and morphology of these structures and the curvature, alignment, and rotational motions of filaments. Our study provides better insights into the origin and properties of patterns formed by gliding filaments beyond what was shown before.

Characterization of Mechanical and Cellular Effects of Rhythmic Vertical Vibrations on Adherent Cell Cultures

This paper presents an innovative experimental setup that employs the principles of audio technology to subject adherent cells to rhythmic vertical vibrations. We employ a novel approach that combines three-axis acceleration measurements and particle tracking velocimetry to evaluate the setup's performance. This allows us to estimate crucial parameters such as root mean square acceleration, fluid flow patterns, and shear stress generated within the cell culture wells when subjected to various vibration types. The experimental conditions consisted of four vibrational modes: No Vibration, Continuous Vibration, Regular Pulse, and Variable Pulse. To evaluate the effects on cells, we utilized fluorescence microscopy and a customized feature extraction algorithm to analyze the F-actin filament structures. Our findings indicate a consistent trend across all vibrated cell cultures, revealing a reduction in size and altered orientation (2D angle) of the filaments. Furthermore, we observed cell accumulations in the G1 cell cycle phase in cells treated with Continuous Vibration and Regular Pulse. Our results demonstrate a negative correlation between the magnitude of mechanical stimuli and the size of F-actin filaments, as well as a positive correlation with the accumulations of cells in the G1 phase of the cell cycle. By unraveling these analyses, this study paves the way for future investigations and provides a compelling framework for comprehending the intricate cellular responses to rhythmic mechanical stimulation.

Fluctuation-induced dynamics of nematic topological defects

Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.

Activity-induced polar patterns of filaments gliding on a sphere

Active matter systems feature the ability to form collective patterns as observed in a plethora of living systems, from schools of fish to swimming bacteria. While many of these systems move in a wide, three-dimensional environment, several biological systems are confined by a curved topology. The role played by a non-Euclidean geometry on the self-organization of active systems is not yet fully understood, and few experimental systems are available to study it. Here, we introduce an experimental setup in which actin filaments glide on the inner surface of a spherical lipid vesicle, thus embedding them in a curved geometry. We show that filaments self-assemble into polar, elongated structures and that, when these match the size of the spherical geometry, both confinement and topological constraints become relevant for the emergent patterns, leading to the formation of polar vortices and jammed states. These results experimentally demonstrate that activity-induced complex patterns can be shaped by spherical confinement and topology.

Active matter exhibits a range of collective behaviors offering insights into how complex patterns can emerge at different length scales. Here, Hsu et al. confine active filaments on the spherical surface of a lipid vesicle and observe the formation of off-equator polar vortices and jammed patterns.

Noncentral forces mediated between two inclusions in a bath of active Brownian rods

Using Brownian Dynamics simulations, we study effective interactions mediated between two identical and impermeable disks (inclusions) immersed in a bath of identical, active (self-propelled), Brownian rods in two spatial dimensions, by assuming that the self-propulsion axis of the rods may generally deviate from their longitudinal axis. When the self-propulsion is transverse (perpendicular to the rod axis), the accumulation of active rods around the inclusions is significantly enhanced, causing a more expansive steric layering (ring formation) of the rods around the inclusions, as compared with the reference case of longitudinally self-propelling rods. As a result, the transversally self-propelling rods also mediate a significantly longer ranged effective interaction between the inclusions. The bath-mediated interaction arises due to the overlaps between the active-rod rings formed around the inclusions, as they are brought into small separations. When the self-propulsion axis is tilted relative to the rod axis, we find an asymmetric imbalance of active-rod accumulation around the inclusion dimer. This leads to a noncentral interaction, featuring an anti-parallel pair of transverse force components and, hence, a bath-mediated torque on the dimer.

Chiral self-sorting of active semiflexible filaments with intrinsic curvature

Many-body interactions in systems of active matter can cause particles to move collectively and self-organize into dynamic structures with long-range order. In cells, the self-assembly of cytoskeletal filaments is critical for cellular motility, structure, intracellular transport, and division. Semiflexible cytoskeletal filaments driven by polymerization or motor-protein interactions on a two-dimensional substrate, such as the cell cortex, can induce filament bending and curvature leading to interesting collective behavior. For example, the bacterial cell-division filament FtsZ is known to have intrinsic curvature that causes it to self-organize into rings and vortices, and recent experiments reconstituting the collective motion of microtubules driven by motor proteins on a surface have observed chiral symmetry breaking of the collective behavior due to motor-induced curvature of the filaments. Previous work on the self-organization of driven filament systems have not studied the effects of curvature and filament structure on collective behavior. In this work, we present Brownian dynamics simulation results of driven semiflexible filaments with intrinsic curvature and investigate how the interplay between filament rigidity and radius of curvature can tune the self-organization behavior in homochiral systems and heterochiral mixtures. We find a curvature-induced reorganization from polar flocks to self-sorted chiral clusters, which is modified by filament flexibility. This transition changes filament transport from ballistic to diffusive at long timescales.

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.

Polar pattern formation induced by contact following locomotion in a multicellular system

Biophysical mechanisms underlying collective cell migration of eukaryotic cells have been studied extensively in recent years. One mechanism that induces cells to correlate their motions is contact inhibition of locomotion, by which cells migrating away from the contact site. Here, we report that tail-following behavior at the contact site, termed contact following locomotion (CFL), can induce a non-trivial collective behavior in migrating cells. We show the emergence of a traveling band showing polar order in a mutant Dictyostelium cell that lacks chemotactic activity. We find that CFL is the cell-cell interaction underlying this phenomenon, enabling a theoretical description of how this traveling band forms. We further show that the polar order phase consists of subpopulations that exhibit characteristic transversal motions with respect to the direction of band propagation. These findings describe a novel mechanism of collective cell migration involving cell-cell interactions capable of inducing traveling band with polar order.

Synchronous operation of biomolecular engines

Biomolecular motor systems are the smallest natural machines with an ability to convert chemical energy into mechanical work with remarkably high efficiency. Such attractive features enabled biomolecular motors to become classic tools in soft matter research over the past decade. For designing suitably engineered biomimetic systems, the biomolecular motors can potentially be used as molecular engines that can transform energy and ensure great advantages for the construction of bio-nanodevices and molecular robots. From the optimization of their prolonged lifetime to coordinate them into highly complex and ordered structures, enormous efforts have been devoted to make them useful in the synthetic environment. Synchronous operation of the biomolecular engines is one of the key criteria to coordinate them into certain different patterns, which depends on the local interaction of biomolecular motors. Utilizing chemical and physical stimuli, synchronization of biomolecular motor systems has become possible, which allows them to coordinate into different higher ordered patterns with different modes of functionality. Recently, programmed synchronous operation of the biomolecular engines has also been demonstrated, using a smart biomaterial to build up swarms reminiscent of nature. Here, we review the recent progress in the synchronized operation of biomolecular motors in engineered systems to explicitly program their interaction and further their applications. Such developments in the coordination of biomolecular motors have opened a broad way to explore the construction of future autonomous molecular machines and robots based on synchronization of biomolecular engines.

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

Emergence and collapse of coherent motions of self-propelled particles are affected more by particle motions and interactions than by their material or biological details. In the reconstructed systems of biofilaments and molecular motors, several types of collective motion including a global-order pattern emerge due to the alignment interaction. Meanwhile, earlier studies show that the alignment interaction of a binary collision of biofilaments is too weak to form the global order. The multiple collision is revealed to be important to achieve global order, but it is still unclear what kind of multifilament collision is actually involved. In this study, we demonstrate that not only alignment but also crossing of two filaments is essential to produce an effective multiple-particle interaction and the global order. We design the reconstructed system of biofilaments and molecular motors to vary a probability of the crossing of biofilaments on a collision and thus control the effect of volume exclusion. In this system, biofilaments glide along their polar strands on the turf of molecular motors and can align themselves nematically when they collide with each other. Our experiments show the counterintuitive result, in which the global order is achieved only when the crossing is allowed. When the crossing is prohibited, the cluster pattern emerges instead. We also investigate the numerical model in which we can change the strength of the volume exclusion effect and find that the global orientational order and clusters emerge with weak and strong volume exclusion effects, respectively. With those results and simple theory, we conclude that not only alignment but also finite crossing probability are necessary for the effective multiple-particles interaction forming the global order. Additionally, we describe the chiral symmetry breaking of a microtubule motion which causes a rotation of global alignment.

Collective and contractile filament motions in the myosin motility assay

Cells require mechanical forces for their physiological functions. The forces are generated mainly from molecular interactions between actin filaments, cross-linking proteins, and myosin motors in the actin cytoskeleton. To better understand the molecular interactions, many studies employed myosin motility assays with actin filaments propelled by myosin heads fixed on a surface. Various interesting behaviors of actin filaments have been observed in the motility assay experiments. Despite the popularity of the motility assays, there were only a few computational models designed for simulating the motility assay systems. Most of the previous models have limitations which precluded full understanding of molecular origins for behaviors of actin filaments. In this study, we used an agent-based computational model based on Brownian dynamics for simulating the motility assay system. Our model rigorously describes the mechanics, dynamics, and interactions of actin filaments, cross-linking proteins, and molecular motors. Using the model, we first investigated how properties of actin filaments and motors affect gliding motions of actin filaments without volume-exclusion effects as a base study. We found that actin filaments can continuously glide at relative fast speed only when they are sufficiently longer than the average spacing between neighboring motors and that the gliding speed of F-actins shows a biphasic dependence on processivity of motors. Then, we showed that volume-exclusion effects between actin filaments can induce diverse collective movements and alignment of actin filaments, thus creating thick bundles and ring-like structures in the absence of cross-linking proteins. Lastly, we demonstrated that cross-linking proteins can lead to distinct contractile behaviors of actin networks depending on the density and kinetics of the cross-linking proteins. Results from our study show the ability of our model to simulate the motility assay system under various conditions and provide insights into understanding of different behaviors of actin filaments.

Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order

We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.

Effect of F-actin and Microtubules on Cellular Mechanical Behavior Studied Using Atomic Force Microscope and an Image Recognition-Based Cytoskeleton Quantification Approach

Cytoskeleton morphology plays a key role in regulating cell mechanics. Particularly, cellular mechanical properties are directly regulated by the highly cross-linked and dynamic cytoskeletal structure of F-actin and microtubules presented in the cytoplasm. Although great efforts have been devoted to investigating the qualitative relation between the cellular cytoskeleton state and cell mechanical properties, comprehensive quantification results of how the states of F-actin and microtubules affect mechanical behavior are still lacking. In this study, the effect of both F-actin and microtubules morphology on cellular mechanical properties was quantified using atomic force microscope indentation experiments together with the proposed image recognition-based cytoskeleton quantification approach. Young’s modulus and diffusion coefficient of NIH/3T3 cells with different cytoskeleton states were quantified at different length scales. It was found that the living NIH/3T3 cells sense and adapt to the F-actin and microtubules states: both the cellular elasticity and poroelasticity are closely correlated to the depolymerization degree of F-actin and microtubules at all measured indentation depths. Moreover, the significance of the quantitative effects of F-actin and microtubules in affecting cellular mechanical behavior is depth-dependent.

Dry active turbulence in a model for microtubule-motor mixtures

We study the dynamics and phase behaviour of a dry suspension of microtubules and molecular motors. We obtain a set of continuum equations by rigorously coarse graining a microscopic model where motor-induced interactions lead to parallel or antiparallel ordering. Through numerical simulations, we show that this model generically creates either stable stripes, or a never-settling pattern where stripes periodically form, rotate and then split up. We derive a minimal model which displays the same instability as the full model, and clarifies the underlying physical mechanism. The necessary ingredients are an extensile flux arising from microtubule sliding and an interfacial torque favouring ordering along density gradients. We argue that our minimal model unifies various previous observations of chaotic behaviour in dry active matter into a general universality class.

Neuroprotective Effects of Ginsenoside Rg1 against Hyperphosphorylated Tau-Induced Diabetic Retinal Neurodegeneration via Activation of IRS-1/Akt/GSK3β Signaling

We have recently demonstrated that tau hyperphosphorylation causes diabetic synaptic neurodegeneration of retinal ganglion cells (RGCs), which might be the earliest affair during the pathogenesis of diabetic retinopathy (DR). Thus, there is a pressing need to seek therapeutic agents possessing neuroprotective effects against tau hyperphosphorylation in RGCs for arresting the progression of DR. Here, using a well-characterized diabetes model of db/db mouse, we discovered that topical ocular application of 10 mg/kg/day of ginsenoside Rg1 (GRg1), one of the major active ingredients extracted from Panax ginseng and Panax notoginseng, ameliorated hyperphosphorylated tau-triggered RGCs synaptic neurodegeneration in diabetic mice. The neuroprotective effects of GRg1 on diabetic retinae were abrogated when retinal IRS-1 or Akt was suppressed by intravitreal injection with si-IRS-1 or topically coadministered with a specific inhibitor of Akt, respectively. However, selective repression of retinal GSK3β by intravitreal administration of si-GSK3β rescued the neuroprotective properties of GRg1 when Akt was inactivated. Therefore, the present study showed for the first time that GRg1 can prevent hyperphosphorylated tau-induced synaptic neurodegeneration of RGCs via activation of IRS-1/Akt/GSK3β signaling in the early phase of DR. Moreover, our data clarify the potential therapeutic significance of GRg1 for neuroprotective intervention strategies of DR.

Mobility of Molecular Motors Regulates Contractile Behaviors of Actin Networks

Cells generate mechanical forces primarily from interactions between F-actin, cross-linking proteins, myosin motors, and other actin-binding proteins in the cytoskeleton. To understand how molecular interactions between the cytoskeletal elements generate forces, a number of in vitro experiments have been performed but are limited in their ability to accurately reproduce the diversity of motor mobility. In myosin motility assays, myosin heads are fixed on a surface and glide F-actin. By contrast, in reconstituted gels, the motion of both myosin and F-actin is unrestricted. Because only these two extreme conditions have been used, the importance of mobility of motors for network behaviors has remained unclear. In this study, to illuminate the impacts of motor mobility on the contractile behaviors of the actin cytoskeleton, we employed an agent-based computational model based on Brownian dynamics. We find that if motors can bind to only one F-actin like myosin I, networks are most contractile at intermediate mobility. In this case, less motor mobility helps motors stably pull F-actins to generate tensile forces, whereas higher motor mobility allows F-actins to aggregate into larger clustering structures. The optimal intermediate motor mobility depends on the stall force and affinity of motors that are regulated by mechanochemical rates. In addition, we find that the role of motor mobility can vary drastically if motors can bind to a pair of F-actins. A network can exhibit large contraction with high motor mobility because motors bound to antiparallel pairs of F-actins can exert similar forces regardless of their mobility. Results from this study imply that the mobility of molecular motors may critically regulate contractile behaviors of actin networks in cells.

Rapid time-stamped analysis of filament motility

The in vitro motility assay is a valuable tool to understand motor protein mechanics, but existing algorithms are not optimized for accurate time resolution. We propose an algorithm that combines trace detection with a time-stamped analysis. By tracking filament ends, we minimize data loss from overlapping and crossing filaments. A movement trace formed by each filament end is created by time-stamping when the filament either first (filament tip) or last (filament tail) occupies a pixel. A frame number vs. distance curve is generated from this trace, which is segmented into regions by slope to detect stop-and-go movement. We show, using generated mock motility videos, accurate detection of velocity and motile fraction changes for velocities < 0.05 pixels per frame, without manual trace dropping and regardless of filament crossings. Compared with established algorithms we show greatly improved accuracy in velocity and motile fraction estimation, with greatly reduced user effort. We tested two actual motility experiments: (1) adenosine triphosphate (ATP) added to skeletal myosin in rigor; (2) myosin light chain phosphatase (MLCP) added to phasic smooth muscle myosin. Our algorithm revealed previously undetectable features: (1) rapid increase in motile fraction paralleled by a slow increase in velocity as ATP concentration increases; (2) simultaneous reductions in velocity and motile fraction as MLCP diffuses into the motility chamber at very low velocities. Our algorithm surpasses existing algorithms in the resolution of time dependent changes in motile fraction and velocity at a wide range of filament lengths and velocities, with minimal user input and CPU time.

Self-organization across scales: from molecules to organisms

Creating ordered structures from chaotic environments is at the core of biological processes at the subcellular, cellular and organismic level. In this perspective, we explore the physical as well as biological features of two prominent concepts driving self-organization, namely phase transition and reaction-diffusion, before closing with a discussion on open questions and future challenges associated with studying self-organizing systems.This article is part of the theme issue 'Self-organization in cell biology'.

Comparative analysis of widely used methods to remove nonfunctional myosin heads for the in vitro motility assay

The in vitro motility assay allows studies of muscle contraction through observation of actin filament propulsion by surface-adsorbed myosin motors or motor fragments isolated from muscle. A possible problem is that motility may be compromised by nonfunctional, “dead”, motors, obtained in the isolation process. Here we investigate the effects on motile function of two approaches designed to eliminate the effects of these dead motors. We first tested the removal of heavy meromyosin (HMM) molecules with ATP-insensitive “dead” heads by pelleting them with actin filaments, using ultracentrifugation in the presence of 1 mM MgATP (“affinity purification”). Alternatively we incubated motility assay flow cells, after HMM surface adsorption, with non-fluorescent “blocking actin” (1 µM) to block the dead heads. Both affinity purification and use of blocking actin increased the fraction of motile filaments compared to control conditions. However, affinity purification significantly reduced the actin sliding speed in five out of seven experiments on silanized surfaces and in one out of four experiments on nitrocellulose surfaces. Similar effects on velocity were not observed with the use of blocking actin. However, a reduced speed was also seen (without affinity purification) if HMM or myosin subfragment 1 was mixed with 1 mM MgATP before and during surface adsorption. We conclude that affinity purification can produce unexpected effects that may complicate the interpretation of in vitro motility assays and other experiments with surface adsorbed HMM, e.g. single molecule mechanics experiments. The presence of MgATP during incubation with myosin motor fragments is critical for the complicating effects.

Millimeter-sized belt-like pattern formation of actin filaments in solution by interacting with surface myosin in vitro

The movements of single actin filaments along a myosin-fixed glass surface were observed under a conventional fluorescence microscope. Although random at a low concentration, moving directions of filaments were aligned by the presence of over 1.0 mg/mL of unlabeled filaments. We found that actin filaments when at the intermediate concentrations ranging from 0.1 to 1.0 mg/mL, formed winding belt-like patterns and moved in a two-directional manner along the belts. These patterns were spread over a millimeter range and found to have bulged on the glass in a three-dimensional manner. Filaments did not get closer than about 37.5 nm to each other within each belt-pattern. The average width and the curvature radius of the pattern did not apparently change even when the range of actin concentrations was between 0.05 and 1.0 mg/mL or the sliding velocity between 1.2 and 3.2 μm/sec. However, when the length of filaments was shortened by ultrasonic treatments or the addition of gelsolin molecules, the curvature radius became small from 100 to 60 μm. These results indicate that this belt-forming nature of actin filaments may be due to some inter-filament interactions.

Myosin IIA Regulated Tight Junction in Oxygen Glucose-Deprived Brain Endothelial Cells Via Activation of TLR4/PI3K/Akt/JNK1/2/14-3-3ε/NF-κB/MMP9 Signal Transduction Pathway

Non-muscle myosin heavy chain IIA (NMMHC IIA), a member of Myosin II family, plays a critical role in various cellular physiological processes. Our previous research had suggested that NMMHC IIA could participate in regulating tight junction morphological changes induced by ischemia stroke. Thus, in the current study, we attempted to uncover the regulation pattern of NMMHC IIA on tight junction dysfunction in oxygen glucose-deprived (OGD) mouse brain bEND.3 endothelial cells. The regulation of NMMHC IIA on tight junction in OGD-stimulated bEND.3 cells was evaluated by western blotting assay. Morphologic change of occludin, claudin-5, and ZO-1 tight junction proteins was compared with pretreatment with NMMHC II inhibitor blebbistatin via immunohistochemical staining. Detection of activation of NMMHC IIA on OGD-mediated tight junction transduction pathway was investigated via Koch's postulate using corresponding protein inhibitor. Our results showed that NMMHC IIA was activated in OGD-stimulated bEND.3 endothelial cells. The inhibition of NMMHC IIA could attenuate the morphologic change of occludin, claudin-5, and ZO-1 tight junction proteins. NMMHC IIA participated in regulating downstream transduction pathway TLR4, phosphatidylinositol 3-kinase (PI3K), Akt, JNK1/2, 14-3-3ε, nuclear factor kappa B (NF-кB) and matrix metalloprotein 9 (MMP9). Blocking of these pathways using indicated inhibitors demonstrated that NMMHC IIA destroyed the connection of tight junction via the activation of TLR4/PI3K/Akt/JNK1/2/14-3-3ε/NF-κB/MMP9 pathway. Our study described the key role of NMMHC IIA in OGD-stimulated mouse brain bEND.3 endothelial cells, while also exhibited the molecule effect on tight junction dysfunction via TLR4/PI3K/Akt/JNK1/2/14-3-3ε/NF-κB/MMP9 signal transduction pathway.

Architectural Dynamics of CaMKII-Actin Networks

Calcium-calmodulin-dependent kinase II (CaMKII) has an important role in dendritic spine remodeling upon synaptic stimulation. Using fluorescence video microscopy and image analysis, we investigated the architectural dynamics of rhodamine-phalloidin stabilized filamentous actin (F-actin) networks cross-linked by CaMKII. We used automated image analysis to identify F-actin bundles and crossover junctions and developed a dimensionless metric to characterize network architecture. Similar networks were formed by three different CaMKII species with a 10-fold length difference in the linker region between the kinase domain and holoenzyme hub, implying linker length is not a primary determinant of F-actin cross-linking. Electron micrographs showed that at physiological molar ratios, single CaMKII holoenzymes cross-linked multiple F-actin filaments at random, whereas at higher CaMKII/F-actin ratios, filaments bundled. Light microscopy established that the random network architecture resisted macromolecular crowding with polyethylene glycol and blocked ATP-powered compaction by myosin-II miniature filaments. Importantly, the networks disassembled after the addition of calcium-calmodulin and were then spaced within 3 min into compacted foci by myosin motors or more slowly (30 min) aggregated by crowding. Single-molecule total internal reflection fluorescence microscopy showed CaMKII dissociation from surface-immobilized globular actin exhibited a monoexponential dwell-time distribution, whereas CaMKII bound to F-actin networks had a long-lived fraction, trapped at crossover junctions. Release of CaMKII from F-actin, triggered by calcium-calmodulin, was too rapid to measure with flow-cell exchange (<20 s). The residual bound fraction was reduced substantially upon addition of an N-methyl-D-aspartate receptor peptide analog but not ATP. These results provide mechanistic insights to CaMKII-actin interactions at the collective network and single-molecule level. Our findings argue that CaMKII-actin networks in dendritic spines maintain spine size against physical stress. Upon synaptic stimulation, CaMKII is disengaged by calcium-calmodulin, triggering network disassembly, expansion, and subsequent compaction by myosin motors with kinetics compatible with the times recorded for the poststimulus changes in spine volume.

Nanotopography-responsive myotube alignment and orientation as a sensitive phenotypic biomarker for Duchenne Muscular Dystrophy

Duchenne Muscular Dystrophy (DMD) is a fatal genetic disorder currently having no cure. Here we report that culture substrates patterned with nanogrooves and functionalized with Matrigel (or laminin) present an engineered cell microenvironment to allow myotubes derived from non-diseased, less-affected DMD, and severely-affected DMD human induced pluripotent stem cells (hiPSCs) to exhibit prominent differences in alignment and orientation, providing a sensitive phenotypic biomarker to potentially facilitate DMD drug development and early diagnosis. We discovered that myotubes differentiated from myogenic progenitors derived from non-diseased hiPSCs align nearly perpendicular to nanogrooves, a phenomenon not reported previously. We further found that myotubes derived from hiPSCs of a dystrophin-null DMD patient orient randomly, and those from hiPSCs of a patient carrying partially functional dystrophin align approximately 14° off the alignment direction of non-diseased myotubes. Substrates engineered with micron-scale grooves and/or cell adhesion molecules only interacting with integrins all guide parallel myotube alignment to grooves and lose the ability to distinguish different cell types. Disruption of the interaction between the Dystrophin-Associated-Protein-Complex (DAPC) and laminin by heparin or anti-α-dystroglycan antibody IIH6 disenables myotubes to align perpendicular to nanogrooves, suggesting that this phenotype is controlled by the DAPC-mediated cytoskeleton-extracellular matrix linkage.

Active nematics

Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.

Emergence of coexisting ordered states in active matter systems

Active systems can produce a far greater variety of ordered patterns than conventional equilibrium systems. In particular, transitions between disorder and either polar- or nematically ordered phases have been predicted and observed in two-dimensional active systems. However, coexistence between phases of different types of order has not been reported. We demonstrate the emergence of dynamic coexistence of ordered states with fluctuating nematic and polar symmetry in an actomyosin motility assay. Combining experiments with agent-based simulations, we identify sufficiently weak interactions that lack a clear alignment symmetry as a prerequisite for coexistence. Thus, the symmetry of macroscopic order becomes an emergent and dynamic property of the active system. These results provide a pathway by which living systems can express different types of order by using identical building blocks.

DNA-assisted swarm control in a biomolecular motor system

In nature, swarming behavior has evolved repeatedly among motile organisms because it confers a variety of beneficial emergent properties. These include improved information gathering, protection from predators, and resource utilization. Some organisms, e.g., locusts, switch between solitary and swarm behavior in response to external stimuli. Aspects of swarming behavior have been demonstrated for motile supramolecular systems composed of biomolecular motors and cytoskeletal filaments, where cross-linkers induce large scale organization. The capabilities of such supramolecular systems may be further extended if the swarming behavior can be programmed and controlled. Here, we demonstrate that the swarming of DNA-functionalized microtubules (MTs) propelled by surface-adhered kinesin motors can be programmed and reversibly regulated by DNA signals. Emergent swarm behavior, such as translational and circular motion, can be selected by tuning the MT stiffness. Photoresponsive DNA containing azobenzene groups enables switching between solitary and swarm behavior in response to stimulation with visible or ultraviolet light.

Compositional and expression analyses of the glideosome during the Plasmodium life cycle reveal an additional myosin light chain required for maximum motility

Myosin A (MyoA) is a Class XIV myosin implicated in gliding motility and host cell and tissue invasion by malaria parasites. MyoA is part of a membrane-associated protein complex called the glideosome, which is essential for parasite motility and includes the MyoA light chain myosin tail domain-interacting protein (MTIP) and several glideosome-associated proteins (GAPs). However, most studies of MyoA have focused on single stages of the parasite life cycle. We examined MyoA expression throughout the Plasmodium berghei life cycle in both mammalian and insect hosts. In extracellular ookinetes, sporozoites, and merozoites, MyoA was located at the parasite periphery. In the sexual stages, zygote formation and initial ookinete differentiation precede MyoA synthesis and deposition, which occurred only in the developing protuberance. In developing intracellular asexual blood stages, MyoA was synthesized in mature schizonts and was located at the periphery of segmenting merozoites, where it remained throughout maturation, merozoite egress, and host cell invasion. Besides the known GAPs in the malaria parasite, the complex included GAP40, an additional myosin light chain designated essential light chain (ELC), and several other candidate components. This ELC bound the MyoA neck region adjacent to the MTIP-binding site, and both myosin light chains co-located to the glideosome. Co-expression of MyoA with its two light chains revealed that the presence of both light chains enhances MyoA-dependent actin motility. In conclusion, we have established a system to study the interplay and function of the three glideosome components, enabling the assessment of inhibitors that target this motor complex to block host cell invasion.

The emergence and transient behaviour of collective motion in active filament systems

Most living systems, ranging from animal flocks, self-motile microorganisms to the cytoskeleton rely on self-organization processes to perform their own specific function. Despite its importance, the general understanding of how individual active constituents initiate the intriguing pattern formation phenomena on all these different length scales still remains elusive. Here, using a high density actomyosin motility assay system, we show that the observed collective motion arises from a seeding process driven by enhanced acute angle collisions. Once a critical size is reached, the clusters coarsen into high and low density phases each with fixed filament concentrations. The steady state is defined by a balance of collision induced randomization and alignment effects of the filaments by multi-filament collisions within ordered clusters.

Self-organization is observed in cytoskeletal systems but emergence of order from disorder is poorly understood. Using a high density actomyosin system, the authors capture the transition from disorder to order, which is driven by enhanced alignment effects caused by increase in multi-filament collisions.

Ginsenoside Rg1 Protects against Oxidative Stress-induced Neuronal Apoptosis through Myosin IIA-actin Related Cytoskeletal Reorganization

Oxidative stress-induced cytoskeletal dysfunction of neurons has been implicated as a crucial cause of cell apoptosis or death in the central nervous system (CNS) diseases, such as neurodegenerative and psychiatric diseases. The application of neuroprotectants rescuing the neurons from cytoskeletal damage and apoptosis can be a potential treatment for these CNS diseases. Ginsenoside Rg1 (Rg1), one of the major active components of ginseng, has been reported possessing notable neuroprotective activities. However, there is rare report about its effect on cytoskeleton and its undergoing mechanism. The current study is to reveal the regulatory effects of Rg1 on cytoskeletal and morphological lesion in oxidative stress-induced neuronal apoptosis. The results demonstrated that pre-treatment with Rg1 (0.1-10 μM) attenuated hydrogen peroxide (H₂O₂)-induced neuronal apoptosis and oxidative stress through reducing the intracellular reactive oxygen species (ROS) production and methane dicarboxylic aldehyde (MDA) level. The Rg1 treatment also abolished H₂O₂-induced morphological changes, including cell rounding, membrane blebbing, neurite retraction and nuclei condensation, which were generated by myosin IIA-actin interaction. These effects were mediated via the down-regulation of caspase-3, ROCK1 (Rho-associated kinase1) activation and myosin light chain (MLC, Ser-19) phosphorylation. Furthermore, inhibiting myosin II activity with blebbistatin partly blocked the neuroprotective effects of Rg1. The computer-aided homology modelling revealed that Rg1 preferentially positioned in the actin binding cleft of myosin IIA and might block the binding of myosin IIA to actin filaments. Accordingly, the neuroprotective mechanism of Rg1 is related to the activity that inhibits myosin IIA-actin interaction and the caspase-3/ROCK1/MLC signaling pathway. These findings put some insights into the unique neuroprotective properties of Rg1 associated with the regulation of myosin IIA-actin cytoskeletal structure under oxidative stress and provide experimental evidence for Rg1 in CNS diseases.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

Nonequilibrium phase transitions, fluctuations and correlations in an active contractile polar fluid

We study the patterning, fluctuations and correlations of an active polar fluid consisting of contractile polar filaments on a two-dimensional substrate, using a hydrodynamic description. The steady states generically consist of arrays of inward pointing asters and show a continuous transition from a moving lamellar phase, a moving aster street, to a stationary aster lattice with no net polar order. We next study the effect of spatio-temporal athermal noise, parametrized by an active temperature TA, on the stability of the ordered phases. In contrast to its equilibrium counterpart, we find that the active crystal shows true long range order at low TA. On increasing TA, the asters dynamically remodel, concomitantly we find novel phase transitions characterized by bond-orientational and polar order upon "heating".

Non-periodic oscillatory deformation of an actomyosin microdroplet encapsulated within a lipid interface

Active force generation in living organisms, which is mainly involved in actin cytoskeleton and myosin molecular motors, plays a crucial role in various biological processes. Although the contractile properties of actomyosin have been extensively investigated, their dynamic contribution to a deformable membrane remains unclear because of the cellular complexities and the difficulties associated with in vitro reconstitution. Here, by overcoming these experimental difficulties, we demonstrate the dynamic deformation of a reconstituted lipid interface coupled with self-organized structure of contractile actomyosin. Therein, the lipid interface repeatedly oscillates without any remarkable periods. The oscillatory deformation of the interface is caused by the aster-like three-dimensional hierarchical structure of actomyosin inside the droplet, which is revealed that the oscillation occurs stochastically as a Poisson process.

Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods

Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.

Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer

We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient Γ. Being controlled by Γ, our model provides a unified framework to describe the long-wavelength behavior of a variety of thin polar-ordered systems, ranging from wet to dry active matter and free-standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system that can depend sensitively on Γ. Based on our results, we discuss estimation of bounds on Γ in experimentally accessible systems.

Polar Pattern Formation in Driven Filament Systems Require Non-Binary Particle Collisions

Living matter has the extraordinary ability to behave in a concerted manner, which is exemplified throughout nature ranging from the self-organisation of the cytoskeleton to flocks of animals [1-4]. The microscopic dynamics of constituents have been linked to the system's meso- or macroscopic behaviour in silico via the Boltzmann equation for propelled particles [5-10]. Thereby, simplified binary collision rules between the constituents had to be assumed due to the lack of experimental data. We report here experimentally determined binary collision statistics by studying the recently introduced molecular system, the high density actomyosin motility assay [11-13]. We demonstrate that the alignment effect of the binary collision statistics is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, which indicates that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. The presented findings demonstrate that the unique properties of biological active matter systems require a description that goes well beyond a gas-like picture developed in the framework of kinetic theories.

Contractility of single cardiomyocytes differentiated from pluripotent stem cells depends on physiological shape and substrate stiffness

Single cardiomyocytes contain myofibrils that harbor the sarcomere-based contractile machinery of the myocardium. Cardiomyocytes differentiated from human pluripotent stem cells (hPSC-CMs) have potential as an in vitro model of heart activity. However, their fetal-like misalignment of myofibrils limits their usefulness for modeling contractile activity. We analyzed the effects of cell shape and substrate stiffness on the shortening and movement of labeled sarcomeres and the translation of sarcomere activity to mechanical output (contractility) in live engineered hPSC-CMs. Single hPSC-CMs were cultured on polyacrylamide substrates of physiological stiffness (10 kPa), and Matrigel micropatterns were used to generate physiological shapes (2,000-µm(2) rectangles with length:width aspect ratios of 5:1-7:1) and a mature alignment of myofibrils. Translation of sarcomere shortening to mechanical output was highest in 7:1 hPSC-CMs. Increased substrate stiffness and applied overstretch induced myofibril defects in 7:1 hPSC-CMs and decreased mechanical output. Inhibitors of nonmuscle myosin activity repressed the assembly of myofibrils, showing that subcellular tension drives the improved contractile activity in these engineered hPSC-CMs. Other factors associated with improved contractility were axially directed calcium flow, systematic mitochondrial distribution, more mature electrophysiology, and evidence of transverse-tubule formation. These findings support the potential of these engineered hPSC-CMs as powerful models for studying myocardial contractility at the cellular level.

Nanometric features of myosin filaments extracted from a single muscle fiber to uncover the mechanisms underlying organized motility

The single muscle fiber in vitro motility assay (SF-IVMA) is characterized by organized linear motility of actin filaments, i.e., actin filaments motility showing a parallel or anti-parallel direction with similar speed independent of direction in the central part of the flow-cell where density of myosin is high. In contrast, the low myosin density region in the flow-cell exhibits random filament movements, but the mechanisms underlying the organized motility remain unknown. Transmission electron microscopy (TEM) and atomic force microscopy (AFM) imaging techniques have been combined to investigate the morphological features of myosin extracted from single muscle fiber segments in the flow cell. Nanometric scale imaging of myosin filaments in the SF-IVMA showed intact spatial distances between myosin heads being essential for myosin filament function. However, angular spectrum analyses of myosin filaments in the high myosin density region showed organized myosin filament orientation only in small areas, while unorganized filament orientation were dominantly presented when larger areas were analyzed. Thus, parallel myosin filament organization is a less likely mechanism underlying the organized motility of actin filaments and the high myosin density per se is therefore forwarded as the primary "driver" that promotes organized linear motility.

Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

The spontaneous formation of vortices is a hallmark of collective cellular activity. Here, we study the onset and persistence of coherent angular motion as a function of the number of cells N confined in circular micropatterns. We find that the persistence of coherent angular motion increases with N but exhibits a pronounced discontinuity accompanied by a geometric rearrangement of cells to a configuration containing a central cell. Computer simulations based on a generalized Potts model reproduce the emergence of vortex states and show in agreement with experiment that their stability depends on the interplay of the spatial arrangement and internal polarization of neighboring cells. Hence, the distinct migrational states in finite size ensembles reveal significant insight into the local interaction rules guiding collective migration.

Collective dynamics of soft active particles

We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest-neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms, and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating between migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food.

Defect-mediated phase transitions in active soft matter

How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For strong alignment forces we find collectively moving polycrystalline states with fluctuating networks of grain boundaries. In the regime where repulsive forces dominate, the fluctuations generated by the active system give rise to quasi-long-range transitional order, but-unlike the thermal system-without creating topological defects.

Self-organized vortices of circling self-propelled particles and curved active flagella

Self-propelled pointlike particles move along circular trajectories when their translocation velocity is constant and the angular velocity related to their orientation vector is also constant. We investigate the collective behavior of ensembles of such circle swimmers by Brownian dynamics simulations. If the particles interact via a "velocity-trajectory coordination" rule within neighboring particles, a self-organized vortex pattern emerges. This vortex pattern is characterized by its particle-density correlation function Gρ, the density correlation function Gc of trajectory centers, and an order parameter S representing the degree of the aggregation of the particles. Here we systematically vary the system parameters, such as the particle density and the interaction range, in order to reveal the transition of the system from a light-vortex-dominated to heavy-vortex-dominated state, where vortices contain mainly a single and many self-propelled particles, respectively. We also study a semidilute solution of curved, sinusoidal-beating flagella, as an example of circling self-propelled particles with explicit propulsion mechanism and excluded-volume interactions. Our simulation results are compared with previous experimental results for the vortices in sea-urchin sperm solutions near a wall. The properties of the vortices in simulations and experiments are found to agree quantitatively.

Spiral and never-settling patterns in active systems

We present a combined numerical and analytical study of pattern formation in an active system where particles align, possess a density-dependent motility, and are subject to a logistic reaction. The model can describe suspensions of reproducing bacteria, as well as polymerizing actomyosin gels in vitro or in vivo. In the disordered phase, we find that motility suppression and growth compete to yield stable or blinking patterns, which, when dense enough, acquire internal orientational ordering to give asters or spirals. We predict these may be observed within chemotactic aggregates in bacterial fluids. In the ordered phase, the reaction term leads to previously unobserved never-settling patterns which can provide a simple framework to understand the formation of motile and spiral patterns in intracellular actin systems.

Critical assessment of the Boltzmann approach to active systems

Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of applicability of this equation remains elusive. We introduce a broad class of mesoscopic collision rules and analyze the prerequisites for the emergence of polar order in the framework of kinetic theory. Our findings suggest that a Boltzmann approach is appropriate for weakly aligning systems but is incompatible with experiments on cluster forming systems.