Spindles and active vortices in a model of confined filament-motor mixtures

Filamentous active matter: Band formation, bending, buckling, and defects

Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

Non-equilibrium effects of molecular motors on polymers

We present a generic coarse-grained model to describe molecular motors acting on polymer substrates, mimicking, for example, RNA polymerase on DNA or kinesin on microtubules. The polymer is modeled as a connected chain of beads; motors are represented as freely diffusing beads which, upon encountering the substrate, bind to it through a short-ranged attractive potential. When bound, motors and polymer beads experience an equal and opposite active force, directed tangential to the polymer; this leads to motion of the motors along the polymer contour. The inclusion of explicit motors differentiates our model from other recent active polymer models. We study, by means of Langevin dynamics simulations, the effect of the motor activity on both the conformational and dynamical properties of the substrate. We find that activity leads, in addition to the expected enhancement of polymer diffusion, to an effective reduction of its persistence length. We discover that this effective "softening" is a consequence of the emergence of double-folded branches, or hairpins, and that it can be tuned by changing the number of motors or the force they generate. Finally, we investigate the effect of the motors on the probability of knot formation. Counter-intuitively our simulations reveal that, even though at equilibrium a more flexible substrate would show an increased knotting probability, motor activity leads to a marked decrease in the occurrence of knotted conformations with respect to equilibrium.

Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization

Active networks composed of filaments and motor proteins can self-organize into a variety of architectures. Computer simulations in two or three spatial dimensions and including or omitting steric interactions between filaments can be used to model active networks. Here we examine how these modelling choices affect the state space of network self-organization. We compare the networks generated by different models of a system of dynamic microtubules and microtubule-crosslinking motors. We find that a thin 3D model that includes steric interactions between filaments is the most versatile, capturing a variety of network states observed in recent experiments. In contrast, 2D models either with or without steric interactions which prohibit microtubule crossings can produce some, but not all, observed network states. Our results provide guidelines for the most appropriate choice of model for the study of different network types and elucidate mechanisms of active network organization.

Cytoskeletal actin patterns shape mast cell activation

Activation of immune cells relies on a dynamic actin cytoskeleton. Despite detailed knowledge of molecular actin assembly, the exact processes governing actin organization during activation remain elusive. Using advanced microscopy, we here show that Rat Basophilic Leukemia (RBL) cells, a model mast cell line, employ an orchestrated series of reorganization events within the cortical actin network during activation. In response to IgE antigen-stimulation of FCε receptors (FCεR) at the RBL cell surface, we observed symmetry breaking of the F-actin network and subsequent rapid disassembly of the actin cortex. This was followed by a reassembly process that may be driven by the coordinated transformation of distinct nanoscale F-actin architectures, reminiscent of self-organizing actin patterns. Actin patterns co-localized with zones of Arp2/3 nucleation, while network reassembly was accompanied by myosin-II activity. Strikingly, cortical actin disassembly coincided with zones of granule secretion, suggesting that cytoskeletal actin patterns contribute to orchestrate RBL cell activation.

Huw Colin-York et al. use advanced microscopy techniques to show that the cortical actin network within a model mast cell line undergoes a series of reorganizational events at the basal interface during activation. They find that actin patterns co-localize with zones of Arp2/3 nucleation and myosin-II activity accompanies network reassembly.

A dynamic preferred direction model for the self-organization dynamics of bacterial microfluidic pumping

It is known that some flagellated bacteria like Serratia marcescens, when deposited and affixed onto a surface to form a "bacterial carpet", self-organize in a collective motion of the flagella that is capable of pumping fluid through microfluidic channels. We set up a continuum model comprising two macroscopic variables that is capable of describing this self-organization mechanism as well as quantifying it to the extent that an agreement with the experimentally observed channel width dependence of the pumping is reached. The activity is introduced through a collective angular velocity of the helical flagella rotation, which is an example of a dynamic macroscopic preferred direction. Our model supports and quantifies the view that the self-coordination is due to a positive feedback loop between the bacterial flagella and the local flow generated by their rotation. Moreover, our results indicate that this biological active system is operating close to the self-organization threshold.

Chronology of motor-mediated microtubule streaming

We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.

Determinants of Polar versus Nematic Organization in Networks of Dynamic Microtubules and Mitotic Motors

During cell division, mitotic motors organize microtubules in the bipolar spindle into either polar arrays at the spindle poles or a "nematic" network of aligned microtubules at the spindle center. The reasons for the distinct self-organizing capacities of dynamic microtubules and different motors are not understood. Using in vitro reconstitution experiments and computer simulations, we show that the human mitotic motors kinesin-5 KIF11 and kinesin-14 HSET, despite opposite directionalities, can both organize dynamic microtubules into either polar or nematic networks. We show that in addition to the motor properties the natural asymmetry between microtubule plus- and minus-end growth critically contributes to the organizational potential of the motors. We identify two control parameters that capture system composition and kinetic properties and predict the outcome of microtubule network organization. These results elucidate a fundamental design principle of spindle bipolarity and establish general rules for active filament network organization.

Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.

Self-organizing actin patterns shape membrane architecture but not cell mechanics

Cell-free studies have demonstrated how collective action of actin-associated proteins can organize actin filaments into dynamic patterns, such as vortices, asters and stars. Using complementary microscopic techniques, we here show evidence of such self-organization of the actin cortex in living HeLa cells. During cell adhesion, an active multistage process naturally leads to pattern transitions from actin vortices over stars into asters. This process is primarily driven by Arp2/3 complex nucleation, but not by myosin motors, which is in contrast to what has been theoretically predicted and observed in vitro. Concomitant measurements of mechanics and plasma membrane fluidity demonstrate that changes in actin patterning alter membrane architecture but occur functionally independent of macroscopic cortex elasticity. Consequently, tuning the activity of the Arp2/3 complex to alter filament assembly may thus be a mechanism allowing cells to adjust their membrane architecture without affecting their macroscopic mechanical properties.

In vitro models of actin organization show the formation of vortices, asters and stars. Here Fritzsche et al. show that such actin structures form in living cells in a manner dependent on the Arp2/3 complex but not myosin, and such structures influence membrane architecture but not cortex elasticity.

Physics of microswimmers--single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Nonequilibrium structure and dynamics in a microscopic model of thin-film active gels

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.