Self-organization in systems of treadmilling filaments

The cytoskeleton is an important substructure of living cells, playing essential roles in cell division, cell locomotion, and the internal organization of subcellular components. Physically, the cytoskeleton is an active polar gel, that is, a system of polar filamentous polymers, which is intrinsically out of thermodynamic equilibrium. Active processes are notably involved in filament growth and can lead to net filament assembly at one end and disassembly at the other, a phenomenon called treadmilling. Here, we develop a framework for describing collective effects in systems of treadmilling filaments in the presence of agents regulating filament assembly. We find that such systems can self-organize into asters and moving filament blobs. We discuss possible implications of our findings for subcellular processes.     

Steady state dynamics of a moving model cell

Crawling cell motility results due to treadmilling of a polymerized actin network at the leading edge. Steady state dynamics of a moving cell are governed by actin concentration profiles across the cell. Branching of new filaments implicating Arp2/3 and capping of existing filaments with capZ or Gelsolin are central to the robust functioning of the actin network. Using computer simulations, steady state concentration profiles of globular actin (G actin) and filamentous actin (F actin) are computed. The profiles are in agreement with experimentally observed ones. Simulations unveil that there is an optimal capping and branching rate for which the velocity of the model cell is maximum. Our simulations also indicate that the capping of actin filaments results in an increase in nucleation of new filaments by Arp2/3-induced branching and is in agreement with a recently observed monomer gating model. We observe that Arp2/3 and capping protein exhibit a functional antagonism with respect to the actin network treadmilling.     

Cytoskeleton Dynamics: A Continuum Cooperative Hydrolysis Model

Cytoskeleton is a network of filamentous proteins, such as actin filaments and microtubules. We propose a continuum cooperative hydrolysis model which possesses exactly analytical solution to describe the dynamics of filament.The results show that the cooperativity leads to non negative-exponential distribution of T(ATP or GTP) subunits.As an application, we investigate the treadmilling phenomenon using our model. It is shown that the cooperativity remarkably affects the length of filament.     

Dielectric-barrier discharges in two-dimensional lattice potentials

We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or underfill the lattice are reminiscent of those observed in other physical systems involving 2D lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles.     

Driven Diffusive Systems of Active Filament Bundles

The cytoskeleton is an important subsystem of cells that is involved for example in cell division and locomotion. It consists of filaments that are cross-linked by molecular motors that can induce relative sliding between filaments and generate stresses in the network. In order to study the effects of fluctuations on the dynamics of such a system we introduce here a new class of driven diffusive systems mimicking the dynamics of active filament bundles where the filaments are aligned with respect to a common axis. After introducing the model class we first analyze an exactly solvable case and find condensation. For the general case we perform a mean-field analysis and study the behavior on large length scales by coarse-graining. We determine conditions for condensation and establish a relation between the hopping rates and the tension generated in the bundle.     

Twisted vortex filaments in the three-dimensional complex Ginzburg-Landau equation

The structure and dynamics of vortex filaments that form the cores of scroll waves in three-dimensional oscillatory media described by the complex Ginzburg-Landau equation are investigated. The study focuses on the role that twist plays in determining the bifurcation structure in various regions of the (alpha,beta) parameter space of this equation. As the degree of twist increases, initially straight filaments first undergo a Hopf bifurcation to helical filaments; further increase in the twist leads to a secondary Hopf bifurcation that results in supercoiled helices. In addition, localized states composed of superhelical segments interspersed with helical segments are found. If the twist is zero, zigzag filaments are found in certain regions of the parameter space. In very large systems disordered states comprising zigzag and helical segments with positive and negative senses exist. The behavior of vortex filaments in different regions of the parameter space is explored in some detail. In particular, an instability for nonzero twist near the alpha=beta line suggests the existence of a nonsaturating state that reduces the stability domain of straight filaments. The results are obtained through extensive simulations of the complex Ginzburg-Landau equation on large domains for long times, in conjunction with simulations on equivalent two-dimensional reductions of this equation and analytical considerations based on topological concepts.     

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.     

Statistical physics of active processes in cells

Simple concepts from statistical physics are discussed to describe the transduction of chemical energy of a fuel to mechanical work on the molecular level. Such approaches can characterize general physical features of motor proteins that generate forces in the cell cytoskeleton. In integrated cellular systems such as cilia and hair bundles, cytoskeletal filaments and motors form complex structures and interact in large numbers. In such systems the interplay of filaments and motors can lead to emergent dynamic behaviors such as oscillating collective modes or to wave-like patterns. We discuss general aspects of such dynamic states and relate them to the dynamics of cytoskeletal structures in cells.     

Chaotic Quantum Vortices in He II: Thermodynamic Equilibrium and Turbulence

The use of superfluid helium as a refrigerant in cryogenic systems is governed by the presence of a chaotic tangle of quantum filaments in the superfluid component of helium. Therefore, to describe any hydrodynamic phenomena (in particular, heat transfer) in quantumliquids containing vortex tangles, it is necessary to have information on their structure and statistics. The paper discusses two possible statistical configurations of chaotic vortices: the thermodynamic equilibrium and the highly nonequilibrium turbulent state, as well as the transition between them. Basing on the Langevin approach, we discuss the mechanism of establishment of thermodynamic equilibrium for a chaotic set of quantum vortex filaments. The corresponding Fokker–Planck equation for the probability density functional has a solution in the form of the Gibbs distribution. Basing on the above analysis, we discuss the possible causes and mechanisms of violation of thermodynamic equilibrium and transition to the turbulent regime.     

Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect

We report the quantized superfluid vortex filaments induced by the axial flow effect, which exhibit intriguing loop structures on helical vortexes. Such new vortex filaments correspond to a series of soliton excitations including the multipeak soliton, W-shaped soliton, and anti-dark soliton, which have no analogue when the axial flow effect is absent. In particular, we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex, while the vortex filament induced by the anti-dark soliton is caused only by the bending action, which is consistent with the case of the standard bright soliton. These results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices.     

Spontaneous pattern formation in an effectively one-dimensional dielectric-barrier discharge system

In a dielectric-barrier discharge between diametrically opposite sides of a narrow tube, discharge filaments stabilize at regular intervals along the tube's length. Three types of periodic patterns are observed, as is a disordered state in which filaments fire at apparently random positions and times. Time-resolved current measurements indicate that for each spatial pattern, a particular number of discharge stages occur during the voltage half-cycle. A preliminary model of the pattern-formation dynamics is described, motivating further work on time-resolved imaging and investigations of surface charge distributions.     

Rheology of active-particle suspensions

We study the interplay of activity, order, and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration, and stress fields in a suspension of active, energy-dissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis, and active mechanosensing find natural explanations within our model.     

Actively contracting bundles of polar filaments

We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics in the unstable regime, and the tensile stress generated in the bundle are discussed. We find that the interaction of parallel filaments can induce unstable behavior and is responsible for active contraction and tension in the bundle. The interaction between antiparallel filaments leads to filament sorting. Our model could apply to simple contractile structures in cells such as stress fibers.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.     

Wetting of liquid droplets on two parallel filaments

Droplet wetting on two parallel filaments may assume a barrel-shaped morphology or a liquid bridge depending upon the filament diameter and spacing, droplet volume, and contact angle. This paper is aimed to examine the dependency of droplet wetting length upon the above parameters. In the process, morphology of either a barrel-shaped droplet or a liquid bridge sitting on two parallel filaments is determined numerically by using surface finite element method (SFEM). Variation of wetting length with contact angle is examined at varying droplet volume, filament spacing, and droplet morphology. It is found that the droplet wetting length increases with decreasing filament spacing ratio as well as contact angle while it also increases with the growth of droplet volume. The dependency of wetting length upon contact angle behaves sensitive to filament spacing in the case of stable liquid bridges, while it exhibits nearly constant sensitivity to the contact angle in the case of barrel-shaped droplets. The quantitative relations yielded in this study can be considered as characteristic curves applicable for a variety of droplet-on-filament systems, particularly useful to wetting property characterization of filaments, micro liquid delivery, biological cell manipulation, etc.     

Active dynamics of filaments in motility assays

We study the active dynamics of single and interacting cytoskeletal filaments in motility assays, in which immobilized motor proteins bind the filaments to a surface and actively pull them along this surface. We present a model which couples the overdamped dynamics of filaments, the active dynamics of motor heads, and the elasticity of motor stalks and which can be used for Langevin dynamics simulations. Single filaments perform a persistent random walk, which we characterize by several simulation results. For interacting filaments with a repulsive interaction of filaments, the motor-driven dynamics of filaments leads to a non-equilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations and analytical theory show that the motor activity enhances the tendency for nematic ordering.     

From limit cycles to periodic orbits through ultradiscretisation

We examine the transition between discrete and ultradiscrete (cellular-automaton-like) systems, the dynamics of which exhibit limit cycles. Motivated by results obtained previously for three-dimensional systems, we consider here a more manageable two-dimensional model. We show that one can follow the changes in dynamics of the system when a parameter that tunes the discrete-ultradiscrete transition is varied. In particular we explain the phenomenon of the splitting of a discrete limit cycle to a profusion of periodic orbits at the ultradiscrete limit.     

Decrease of magnetic AC loss in twisted-filament Bi-2223 tapes

In AC power-engineering applications, a large part of the AC loss in the superconductor is due to magnetization by the external field. This magnetic AC loss has been well described for the low-T_c conductors. In Bi-2223 tapes the picture is different due to strong anisotropy, granularity and flux creep. Magnetic AC loss in various twisted and non-twisted Bi-2223 tapes has been measured at power frequencies by a pickup method. The results are compared to theoretical models of magnetization loss. When the field is parallel to the tape plane, the filaments in twisted tapes can be decoupled and the AC loss is decreased even when the matrix is pure silver. The extra effect of higher-resistance matrix materials is studied. In perpendicular field it is more difficult to decouple the filaments, due to the particular tape geometry. Contrary to a wire, there are essential differences between the AC loss mechanisms in a long twisted tape and those in a short piece of non-twisted tape. Finally, the dynamic resistance caused by the AC magnetic field is examined.     

Semi-flexible polymers with attractive interactions

The delocalization and unbinding transitions of two semi-flexible polymers which experience attractive interactions are studied by a variety of theoretical methods. In two-dimensional systems, one has to distinguish four different universality classes for the interaction potentials. In particular, the delocalization transitions from a potential well and the unbinding transitions from such a well in the presence of a hard wall exhibit distinct critical behavior governed by different critical exponents. In three-dimensional systems, we predict first-order transitions with a jump in the energy density but with critical or self-similar fluctuations leading to distribution functions with power law tails. The predicted critical behavior is confirmed numerically by transfer matrix calculations in two dimensions and by Monte Carlo simulations in three dimensions. This behavior should be accessible to experiments on biopolymers such as actin filaments or microtubuli. Received 15 December 1999 and Received in final form 19 May 2000