Motion Of Filament Research Articles

Bacterial Cell Division: A Swirling Ring to Rule Them All?

FtsZ, a tubulin homologue and the major constituent of the bacterial Z ring, hasbeen shown to assemble into curved filament bundles, which exhibit GTP-hydrolysis-dependent turnover. Surprisingly, the presence of its membrane adaptor FtsA renders this turnover directional, inducing treadmilling and collective circular motion of filaments invitro.

Comment on “Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation” [Phys. Fluids 25, 085101 (2013)

We comment on the paper by Van Gorder [“Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation,” Phys. Fluids 25, 085101 (2013)]. We point out that the flow of the normal fluid component parallel to the vortex will often lead into the Donnelly–Glaberson instability, which will cause the amplification of the Kelvin wave. We explain why the comparison to local nonlinear equation is unreasonable, and remark that neglecting the motion in the x-direction is not reasonable for a Kelvin wave with an arbitrary wavelength and amplitude. The correct equations in the general case are also derived.

Simulation of Fluid-Structure and Fluid-Mediated Structure-Structure Interactions in Stokes Regime Using Immersed Boundary Method

The Stokes flow induced by the motion of an elastic massless filament immersed in a two-dimensional fluid is studied. Initially, the filament is deviated from its equilibrium state and the fluid is at rest. The filament will induce fluid motion while returning to its equilibrium state. Two different test cases are examined. In both cases, the motion of a fixed-end massless filament induces the fluid motion inside a square domain. However, in the second test case, a deformable circular string is placed in the square domain and its interaction with the Stokes flow induced by the filament motion is studied. The interaction between the fluid and deformable body/bodies can become very complicated from the computational point of view. An immersed boundary method is used in the present study. In order to substantiate the accuracy of the numerical method employed, the simulated results associated with the Stokes flow induced by the motion of an extending star string are compared well with those obtained by the immersed interface method. The results show the ability and accuracy of the IBM method in solving the complicated fluid-structure and fluid-mediated structure-structure interaction problems happening in a wide variety of engineering and biological systems.

Response to “Comment on ‘Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation”’ [Phys. Fluids 26, 019101 (2014)

I agree with the authors regarding their comments on the Donnelly-Glaberson instability for such helical filaments as those obtained in my paper. I also find merit in their derivation of the quantum LIA (local induction approximation) in the manner of the LIA of Boffetta et al. However, I disagree with the primary criticisms of Hietala and Hänninen. In particular, though they suggest LIA and local nonlinear equation modes are not comparable since the former class of models contains superfluid friction parameters, note that since these parameters are small one may take them to zero and consider a qualitative comparison of the models (which is what was done in my paper). Second, while Hietala and Hänninen criticize certain assumptions made in my paper (and the paper of Shivamoggi where the model comes from) since the results break-down when Ak → ∞, note that in my paper I state that any deviations from the central axis along which the filament is aligned must be sufficiently bounded in variation. Therefore, it was already acknowledged that Ak(=|Φx|) should be sufficiently bounded, precluding the Ak → ∞ case. I also show that, despite what Hietala and Hänninen claim, the dispersion relation obtained in my paper is consistent with LIA, where applicable. Finally, while Hietala and Hänninen claim that the dispersion parameter should be complex valued, I show that their dispersion relation is wrong, since it was derived incorrectly (they assume the complex modulus of the potential function is constant, yet then use this to obtain a potential function with non-constant modulus).

Dimensional Reduction of a Multiscale Continuum Model of Microtubule Gliding Assays

Microtubule gliding assays, in which molecular motors anchored to a plate drive the gliding motion of filaments in a quasi--two-dimensional fluid layer, have been shown to organize into a variety of large-scale patterns. We derive a fully three-dimensional multiscale coarse-grained model of a gliding assay including the evolution of densities of rigid filaments, bound motors, and free motors, coupled to fluid equations. Our model combines continuum theories of polymeric liquids with the force spreading approach of the immersed boundary method. We use dimensional and asymptotic analysis to derive a reduced two-dimensional model and show that, to leading order, the filaments evolve in a plane, similar to what is experimentally observed. We simulate our model numerically with a GPU-based implementation and observe the same qualitative behavior as in experimental work.

The Minimal Group Size for Globally Coordinated Stepping of Muscle Myosins Depends on ATP Hydrolysis Free Energy

In motility assays of muscle myosins, a distinct motile state emerges with increasing number of mechanically coupled myosin binding sites (N). This is explicable by coordinated myosin stepping (CMS): build-up of pre power stroke (PS) myosins is followed by a whole group PS and detachment cascade [1]. At low N, singular infrequent detachment cascades occur; at intermediate N, cascades group into bursts; for high N, interruptions between bursts disappear [1]. Here, we investigate how changing ATP hydrolysis free energy (ΔG) affects N-dependent emergence of CMS. We executed motility assays of muscle myosins and changed Pi concentration ([Pi]=0,1,2.5,5,15,30 mM, ionic strength adjusted by [KCl], [ATP]=2 mM, [ADP]=0.2 mM). Resolving actin sliding velocities by N [2] showed that increasing [Pi] increased the N at which bursts and continuous filament motion emerge. Lowering the rate of Pi release reproduced these observations in our detailed mechanochemical model of linearly elastic myosins mechanically coupled via an actin filament [1]. In this model, the rate of myosins' mechanical steps increases monotonically by ∼6 orders of magnitude dependent on the skew in myosin crossbridge strains (S). Plotting S and the fraction of myosin in the pre and the post PS state (n1,n2) reveals globally coordinated behavior that changes with N. N∼5: a quiescent state with high n1 dominates; N∼15: a quiescent state and cascading behavior with lowered n1 alternate; N∼30: cascading behavior dominates. An according continuous model shows two N-dependent stable steady states representing quiescence and cascading. Adding stochastic fluctuations in S lead to N-dependent cascade-like cycles. This suggests global coordination of myosins, which occurs above a minimal myosin group size that depends on ΔG.[1] Hilbert et al., Biophys J, 105(6):1466(2013) [2] Hilbert et al., PLoS Comp Biol, (2013).

Biomechanical Cell Model by Liquid-Crystal Elastomers

AbstractIn this work, a soft matter cell model is proposed to simulate the cellular cytoskeleton network and motions of intermediate filaments during cell contact and adhesion, in an attempt to explain mechanical information exchange between cells and their extracellular environment. In particular, the cell is modeled as liquid-crystal elastomers. A microscale adhesive model has been introduced to describe the interaction between receptors and ligands. A Lagrange-type mesh-free Galerkin formulation and related computational algorithms for the proposed cell and adhesive contact model have been developed and implemented. A comparison study with experimental data has been conducted to validate the parameters of the cell model. By using the soft matter cell model, the soft adhesive contact process between cells and extracellular substrates with different stiffness has been simulated. The simulation shows that cell motion includes gliding as well as rolling forward along the substrate during the spreading process.

Molecular Mechanical Differences between Isoforms of Contractile Actin in the Presence of Isoforms of Smooth Muscle Tropomyosin

The proteins involved in smooth muscle's molecular contractile mechanism – the anti-parallel motion of actin and myosin filaments driven by myosin heads interacting with actin – are found as different isoforms. While their expression levels are altered in disease states, their relevance to the mechanical interaction of myosin with actin is not sufficiently understood. Here, we analyzed in vitro actin filament propulsion by smooth muscle myosin for -actin (A), -actin-tropomyosin- (A-Tm), -actin-tropomyosin- (A-Tm), -actin (A), -actin-tropomyosin- (A-Tm), and -actin-tropomoysin- (A-Tm). Actin sliding analysis with our specifically developed video analysis software followed by statistical assessment (Bootstrapped Principal Component Analysis) indicated that the in vitro motility of A, A, and A-Tm is not distinguishable. Compared to these three ‘baseline conditions’, statistically significant differences () were: A-Tm – actin sliding velocity increased 1.12-fold, A-Tm – motile fraction decreased to 0.96-fold, stop time elevated 1.6-fold, A-Tm – run time elevated 1.7-fold. We constructed a mathematical model, simulated actin sliding data, and adjusted the kinetic parameters so as to mimic the experimentally observed differences: A-Tm – myosin binding to actin, the main, and the secondary myosin power stroke are accelerated, A-Tm – mechanical coupling between myosins is stronger, A-Tm – the secondary power stroke is decelerated and mechanical coupling between myosins is weaker. In summary, our results explain the different regulatory effects that specific combinations of actin and smooth muscle tropomyosin have on smooth muscle actin-myosin interaction kinetics.

Motion of a vortex filament with axial flow in the half space

We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of initial–boundary value problems as an attempt to analyze the motion of a tornado.

Orbital Stability for Rotating Planar Vortex Filaments in the Cartesian and Arclength Forms of the Local Induction Approximation

The local induction approximation (LIA) is commonly used to study the motion of a vortex filament in a fluid. The fully nonlinear form of the LIA is equivalent to a type of derivative nonlinear Schrödinger (NLS) equation, and stationary solutions of this equation correspond to rotating planar vortex filaments. Such solutions were first discussed in the plane by Hasimoto [J. Phys. Soc. Jpn. 31 (1971) 293], and have been described both in Cartesian three-space and in the arclength formulation in subsequent works. Despite their interest, fully analytical stability results have been elusive. In the present paper, we present elegant and simple proofs of the orbital stability for the stationary solutions to the derivative nonlinear Schrödinger equations governing the self-induced motion of a vortex filament under the LIA, in both the extrinsic (Cartesian) and intrinsic (arclength) coordinate representations. Such results constitute an exact criterion for the orbital stability of rotating planar vortex filament solutions for the vortex filament problem under the LIA.

Self-similar vortex dynamics in superfluid 4He under the Cartesian representation of the Hall-Vinen model including superfluid friction

We determine conditions under which the fully nonlinear form of the local induction approximation (LIA) governing the motion of a vortex filament in superfluid 4He (that is, the Hall-Vinen model) in the Cartesian frame of reference permits the existence of self-similar solutions, even in the presence of superfluid friction parameters. Writing the Cartesian Hall-Vinen LIA in potential form for the motion of a vortex filament, we find that a necessary condition for self-similarity is that the normal-fluid component vanishes (which makes sense in the low temperature limit), and we reduce the potential form of the Hall-Vinen LIA to a complex nonlinear ordinary differential equation governing the behavior of a similarity solution. In the limit where superfluid friction parameters are negligible, we provide some analytical and asymptotic results for various regimes. While such analytical results are useful for determining the qualitative behavior of the vortex filament in the limit where superfluid friction parameters vanish, numerical simulations are needed to determine the true behavior of the filaments in the case of non-zero superfluid friction parameters. While the superfluid friction parameters are small, the numerical results demonstrate that the influence of the superfluid friction parameters on the self-similar vortex structures can be strong. We classify two types of filaments from the numerical results: singular filaments (which demonstrate growing oscillations and hold kink-type solutions as a special case) and bounded filaments (whose behavior is a bounded function of x). We also comment on how to include the case where there is a non-zero normal fluid, and we find a transformation of the self-similar solutions into non-similar solutions that can account for this.

Spatiotemporal Dynamics of Actomyosin Networks

Rhodamine–phalloidin-labeled actin filaments were visualized gliding over a skeletal heavy meromyosin (HMM)-coated surface. Experiments at low filament densities showed that when two filaments collided, their paths were affected in a manner that depended on collision angle. Some collisions resulted in complete alignment of the filament paths; in others, the filaments crossed over one another. Filament crossover or alignment was equally probable at ∼40° contact angle. Filaments often underwent significant bending during collision and analysis of filament shape indicated an energy requirement of ∼13 kBT. Experiments were performed over a wide range of HMM surface density and actin filament bulk concentration. Actin filament gliding speed and path persistence plateaued above a critical HMM surface density, and at high (micromolar) actin filament concentrations, filament motion became dramatically aligned in a common direction. Spatiotemporal features of alignment behavior were determined by correlation analysis, supported by simulations. The thermal drift of individual filament tracks was suppressed as the population became more oriented. Spatial correlation analysis revealed that long-range alignment was due to incremental recruitment rather than fusion of locally ordered seed domains. The global alignment of filament movement, described by an “order parameter,” peaked at optimal actin concentrations and myosin surface densities, in contrast to previous predictions of a critical phase transition. Either hydrodynamic coupling or exchange of filaments between the surface bound and adjacent bulk phase layers might degrade order at high actin filament concentration, and high HMM surface densities might decrease alignment probability during collisions. Our results are compatible with generation of long-range order from mechanical interaction between individual actin filaments. Furthermore, we show that randomly oriented myosin motors align relatively short, submicrometer actin filaments into motile surface domains that extend over many tens of micrometers and these patterns persist for several minutes.

Proper motions of Hα filaments in the supernova remnant RCW 86

We present a proper motion study of the eastern shock-region of the supernova remnant RCW 86 (MSH 14-63, G315.4-2.3), based on optical observations carried out with VLT/FORS2 in 2007 and 2010. For both the northeastern and southeastern regions, we measure an average proper motion of H-alpha filaments of 0.10 +/- 0.02 arcsec/yr, corresponding to 1200 +/- 200 km/s at 2.5kpc. There is substantial variation in the derived proper motions, indicating shock velocities ranging from just below 700 km/s to above 2200 km/s. The optical proper motion is lower than the previously measured X-ray proper motion of northeastern region. The new measurements are consistent with the previously measured proton temperature of 2.3 +/- 0.3 keV, assuming no cosmic-ray acceleration. However, within the uncertainties, moderately efficient (< 27 per cent) shock acceleration is still possible. The combination of optical proper motion and proton temperature rule out the possibility that RCW 86 has a distance less than 1.5kpc. The similarity of the proper motions in the northeast and southeast is peculiar, given the different densities and X-ray emission properties of the regions. The northeastern region has lower densities and the X-ray emission is synchrotron dominated, suggesting that the shock velocities should be higher than in the southeastern, thermal X-ray dominated, region. A possible solution is that the H-alpha emitting filaments are biased toward denser regions, with lower shock velocities. Alternatively, in the northeast the shock velocity may have decreased rapidly during the past 200yr, and the X-ray synchrotron emission is an afterglow from a period when the shock velocity was higher.

Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation

Very recently, Shivamoggi [“Vortex motion in superfluid 4He: Reformulation in the extrinsic vortex-filament coordinate space,” Phys. Rev. B 84, 012506 (2011)]10.1103/PhysRevB.84.012506 studied the extrinsic form of the local induction approximation (LIA) for the motion of a Kelvin wave on a vortex filament in superfluid 4He, and obtained some results in a cubic approximation. Presently, we study the motion of helical vortex filaments in superfluid 4He under the exact fully nonlinear LIA considered in potential form by Van Gorder [“Fully nonlinear local induction equation describing the motion of a vortex filament in superfluid 4He,” J. Fluid Mech. 707, 585 (2012)]10.1017/jfm.2012.308 and obtained from the Biot-Savart law through the equations of Hall and Vinen [“The rotation of liquid helium II. I. Experiments on the propagation of second sound in uniformly rotating helium II,” Proc. R. Soc. London, Ser. A 238, 204 (1956)]10.1098/rspa.1956.0214 including superfluid friction terms. Nonlinear dispersion relations governing the helical Kelvin wave on such a vortex filament are derived in exact form, from which we may exactly calculate the phase and group velocity of the Kelvin wave. With this, we classify the motion of a helical Kelvin wave on a vortex filament under the LIA. The dispersion relations and results, which follow are exact in nature, in contrast to most results in the literature, which are usually numerical approximations. As such, our results accurately capture the qualitative behavior of the Kelvin waves under the LIA. Extensions to other frameworks are discussed.

Motion of variable-length MreB filaments at the bacterial cell membrane influences cell morphology

The maintenance of rod-cell shape in many bacteria depends on actin-like MreB proteins and several membrane proteins that interact with MreB. Using superresolution microscopy, we show that at 50-nm resolution, Bacillus subtilis MreB forms filamentous structures of length up to 3.4 μm underneath the cell membrane, which run at angles diverging up to 40° relative to the cell circumference. MreB from Escherichia coli forms at least 1.4-μm-long filaments. MreB filaments move along various tracks with a maximal speed of 85 nm/s, and the loss of ATPase activity leads to the formation of extended and static filaments. Suboptimal growth conditions lead to formation of patch-like structures rather than extended filaments. Coexpression of wild-type MreB with MreB mutated in the subunit interface leads to formation of shorter MreB filaments and a strong effect on cell shape, revealing a link between filament length and cell morphology. Thus MreB has an extended-filament architecture with the potential to position membrane proteins over long distances, whose localization in turn may affect the shape of the cell wall.

Measuring the regulation of keratin filament network dynamics

The organization of the keratin intermediate filament cytoskeleton is closely linked to epithelial function. To study keratin network plasticity and its regulation at different levels, tools are needed to localize and measure local network dynamics. In this paper, we present image analysis methods designed to determine the speed and direction of keratin filament motion and to identify locations of keratin filament polymerization and depolymerization at subcellular resolution. Using these methods, we have analyzed time-lapse fluorescence recordings of fluorescent keratin 13 in human vulva carcinoma-derived A431 cells. The fluorescent keratins integrated into the endogenous keratin cytoskeleton, and thereby served as reliable markers of keratin dynamics. We found that increased times after seeding correlated with down-regulation of inward-directed keratin filament movement. Bulk flow analyses further revealed that keratin filament polymerization in the cell periphery and keratin depolymerization in the more central cytoplasm were both reduced. Treating these cells and other human keratinocyte-derived cells with EGF reversed all these processes within a few minutes, coinciding with increased keratin phosphorylation. These results highlight the value of the newly developed tools for identifying modulators of keratin filament network dynamics and characterizing their mode of action, which, in turn, contributes to understanding the close link between keratin filament network plasticity and epithelial physiology.

Observation and simulation of a filament eruption associated with the contraction of the overlying coronal loops and the filament rotation

AbstractBy using the data of Solar Dynamics Observatory (SDO), we present a case study of the contraction of the overlying coronal loop and the rotation motion of a sigmoid filament on 2012 May 22. At the beginning of the filament eruption, the overlying coronal loop experienced a significant contraction. In the following, the filament started to rotate counterclockwise. We also carried the simulation to investigate the process of the filament eruption.

Vortex motion in superfluid 4He: effects of normal fluid flow

The motion of a vortex filament in superfluid 4He is considered by using the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) [H.E. Hall, W.F. Vinen, Proc. Roy. Soc. Lond. A 238, 204 (1956); H.E. Hall, W.F. Vinen, Proc. Roy. Soc. Lond. A 238, 215 (1956); I.L. Bekarevich, I.M. Khalatnikov, Sov. Phys. J. Exp. Theor. Phys. 13, 643 (1961)] phenomenological model for the scattering process between the vortex and thermal excitations in liquid 4He. The HVBK equations are analytically formulated first in the intrinsic geometric parameter space to obtain insights into the physical implications of the friction terms, associated with the friction coefficients α and α′ (in the Hall-Vinen notation) as well as the previous neglect of the friction term associated with the friction coefficient α′. The normal fluid velocity components both along and transverse to the vortex filament are included. This analytical development also serves to highlight the difficulties arising in making further progress on this route. A reformulation of the HVBK equation in the extrinsic vortex filament coordinate space is then given which is known [B.K. Shivamoggi, Phys. Rev. B 84, 012506 (2011)] to provide a useful alternative analytical approach in this regard. A nonlinear Schrodinger equation for the propagation of nonlinear Kelvin waves on a vortex filament in a superfluid is given taking into account the generalized normal fluid flow. The friction term associated with α′, even in the presence of the normal fluid velocity components transverse to the vortex filament, is shown to produce merely an algebraic growth of the Kelvin waves hence providing further justification for the neglect of this term. On the other hand, the instability produced by the friction term associated with α via the normal fluid velocity component along the vortex filament is shown to manifest itself as a parametric amplification on considering the problem of a rotating planar vortex filament in a superfluid.

THE CONTRACTION OF OVERLYING CORONAL LOOP AND THE ROTATING MOTION OF A SIGMOID FILAMENT DURING ITS ERUPTION

We present an observation of overlying coronal loop contraction and rotating motion of the sigmoid filament during its eruption on 2012 May 22 observed by the Solar Dynamics Observatory (SDO). Our results show that the twist can be transported into the filament from the lower atmosphere to the higher atmosphere. The successive contraction of the coronal loops was due to a suddenly reduced magnetic pressure underneath the filament, which was caused by the rising of the filament. Before the sigmoid filament eruption, there was a counterclockwise flow in the photosphere at the right feet of the filament and the contraction loops and a convergence flow at the left foot of the filament. The hot and cool materials have inverse motion along the filament before the filament eruption. Moreover, two coronal loops overlying the filament first experienced brightening, expansion, and contraction successively. At the beginning of the rising and rotation of the left part of the filament, the second coronal loop exhibited rapid contraction. The top of the second coronal loop also showed counterclockwise rotation during the contraction process. After the contraction of the second loop, the left part of the filament rotated counterclockwise and expanded toward the right of NOAA AR 11485. During the filament expansion, the right part of the filament also exhibited counterclockwise rotation like a tornado.

Scaling laws and accurate small-amplitude stationary solution for the motion of a planar vortex filament in the Cartesian form of the local induction approximation

We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.