Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

A computer simulation study of a chiral active ring polymer

We investigate a ring polymer under the influence of chiral active Brownian forces in two dimensions using coarse-grained computer simulations. We observe a non-monotonic behavior of the radius of gyration of an active Brownian ring as a function of active force. However, the shrinkage of the ring in the intermediate strength of active forces becomes more pronounced in the presence of chiral active forces, and the shrinkage is monotonic at a given activity level as a function of the angular frequency controlling the direction of the active force. The distribution of radius of gyration, inter-monomer distance, and radial distribution suggest that the monomers come close to each other, eventually leading to the shrinkage of the ring. Moreover, the bond-correlation suggests that the chirality introduces a local folding of the monomers. Furthermore, using the diameter correlation function, we show that the ring performs tank-treading motion with a frequency following power-law relation with active force with exponent 3/2. The mean squared displacement of the monomers further assists the tank-treading dynamics by exhibiting oscillatory behavior.

Density and inertia effects on two-dimensional active semiflexible filament suspensions

We examine the influence of density on the transition between chain and spiral structures in planar assemblies of active semiflexible filaments, utilizing detailed numerical simulations. We focus on how increased density, and higher Péclet numbers, affect the activity-induced transition spiral state in a semiflexible, self-avoiding active chain. Our findings show that increasing the density causes the spiral state to break up, reverting to a motile chain-like shape. This results in a density-dependent reentrant phase transition from spirals back to open chains. We attribute this phenomenon to an inertial effect observed at the single polymer level, where increased persistence length due to inertia has been shown in recent three-dimensional studies to cause polymers to open up. Our two-dimensional simulations further reveal that a reduction in the damping coefficient leads to partial unwinding of the spirals, forming longer arms. In suspension, interactions among these extended arms can trigger a complete unwinding of the spirals, driven by the combined effects of density and inertia.

Constrained motion of self-propelling eccentric disks linked by a spring

It has been supposed that the interplay of elasticity and activity plays a key role in triggering the non-equilibrium behaviors in biological systems. However, the experimental model system is missing to investigate the spatiotemporally dynamical phenomena. Here, a model system of an active chain, where active eccentric-disks are linked by a spring, is designed to study the interplay of activity, elasticity, and friction. Individual active chain exhibits longitudinal and transverse motions; however, it starts to self-rotate when pinning one end and self-beat when clamping one end. In addition, our eccentric-disk model can qualitatively reproduce such behaviors and explain the unusual self-rotation of the first disk around its geometric center. Furthermore, the structure and dynamics of long chains were studied via simulations without steric interactions. It was found that a hairpin conformation emerges in free motion, while in the constrained motions, the rotational and beating frequencies scale with the flexure number (the ratio of self-propelling force to bending rigidity), χ, as ∼(χ)4/3. Scaling analysis suggests that it results from the balance between activity and energy dissipation. Our findings show that topological constraints play a vital role in non-equilibrium synergy behaviors.

Dynamics of active polar ring polymers

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equation of motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.

Effects of alignment activity on the collapse kinetics of a flexible polymer

The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.

Structure and dynamics of an active polymer adsorbed on the surface of a cylinder

The structure and dynamics of an active polymer on a smooth cylindrical surface are studied by Brownian dynamics simulations. The effect of an active force on the polymer adsorption behavior and the combined effect of chain mobility, length N, rigidity κ, and cylinder radius, R, on the phase diagrams are systemically investigated. We find that complete adsorption is replaced by the irregular alternative adsorption/desorption process at a large driving force. Three typical (spiral, helix-like, and rod-like) conformations of the active polymer are observed, dependent on N, κ, and R. Dynamically, the polymer shows rotational motion in the spiral state, snake-like motion in the intermediate state, and straight translational motion without turning back in the rod-like state. In the spiral state, we find that the rotation velocity ω and the chain length follow a power-law relation ω ∼ N^-0.42, consistent with the torque-balance theory of general Archimedean spirals. And the polymer shows super-diffusive behavior along the cylinder for a long time in the helix-like and rod-like states. Our results highlight that the mobility, rigidity, and curvature of surface can be used to regulate the polymer behavior.

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.

Hydrodynamics of polymers in an active bath

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

Mechanical Regulation of Neurite Polarization and Growth: A Computational Study

The densely packed microtubule (MT) array found in neuronal cell projections (neurites) serves two fundamental functions simultaneously: it provides a mechanically stable track for molecular motor-based transport and produces forces that drive neurite growth. The local pattern of MT polarity along the neurite shaft has been found to differ between axons and dendrites. In axons, the neurons' dominating long projections, roughly 90% of the MTs orient with their rapidly growing plus end away from the cell body, whereas in vertebrate dendrites, their orientations are locally mixed. Molecular motors are known to be responsible for cytoskeletal ordering and force generation, but their collective function in the dense MT cytoskeleton of neurites remains elusive. We here hypothesized that both the polarity pattern of MTs along the neurite shaft and the shaft's global extension are simultaneously driven by molecular motor forces and should thus be regulated by the mechanical load acting on the MT array as a whole. To investigate this, we simulated cylindrical bundles of MTs that are cross-linked and powered by molecular motors by iteratively solving a set of force-balance equations. The bundles were subjected to a fixed load arising from actively generated tension in the actomyosin cortex enveloping the MTs. The magnitude of the load and the level of motor-induced connectivity between the MTs have been varied systematically. With an increasing load and decreasing motor-induced connectivity between MTs, the bundles became wider in cross section and extended more slowly, and the local MT orientational order was reduced. These results reveal two, to our knowledge, novel mechanical factors that may underlie the distinctive development of the MT cytoskeleton in axons and dendrites: the cross-linking level of MTs by motors and the load acting on this cytoskeleton during growth.

Brownian Dynamics Simulations of Biological Molecules

Brownian dynamics (BD) is a technique for carrying out computer simulations of physical systems that are driven by thermal fluctuations. Biological systems at the macromolecular and cellular level, while falling in the gap between well-established atomic-level models and continuum models, are especially suitable for such simulations. We present a brief history, examples of important biological processes that are driven by thermal motion, and those that have been profitably studied by BD. We also present some of the challenges facing developers of algorithms and software, especially in the attempt to simulate larger systems more accurately and for longer times.

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.

Computational modeling of active deformable membranes embedded in three-dimensional flows

Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a three-dimensional flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an immersed-boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g., Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of Berthoumieux et al. [New J. Phys. 16, 065005 (2014)10.1088/1367-2630/16/6/065005] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a nonaxisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows.

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.

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.

Collective dynamics of self-propelled semiflexible filaments

The collective behavior of active semiflexible filaments is studied with a model of tangentially driven self-propelled worm-like chains. The combination of excluded-volume interactions and self-propulsion leads to several distinct dynamic phases as a function of bending rigidity, activity, and aspect ratio of individual filaments. We consider first the case of intermediate filament density. For high-aspect-ratio filaments, we identify a transition with increasing propulsion from a state of free-swimming filaments to a state of spiraled filaments with nearly frozen translational motion. For lower aspect ratios, this gas-of-spirals phase is suppressed with growing density due to filament collisions; instead, filaments form clusters similar to self-propelled rods. As activity increases, finite bending rigidity strongly effects the dynamics and phase behavior. Flexible filaments form small and transient clusters, while stiffer filaments organize into giant clusters, similarly to self-propelled rods, but with a reentrant phase behavior from giant to smaller clusters as activity becomes large enough to bend the filaments. For high filament densities, we identify a nearly frozen jamming state at low activities, a nematic laning state at intermediate activities, and an active-turbulence state at high activities. The latter state is characterized by a power-law decay of the energy spectrum as a function of wave number. The resulting phase diagrams encapsulate tunable non-equilibrium steady states that can be used in the organization of living matter.