Elastic Filaments Research Articles

A pendulum in a flowing soap film

We consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the added-mass. Although the system is an infinite-dimensional, we can explain many of our results in terms of a one degree-of-freedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system.

Elasticity of biopolymer filaments

Within the general one-dimensional theory of nonlinear elasticity we analyze the elasticity of biopolymer filaments. The approach adopted is purely mechanical but is reconciled with statistical physics approaches and allows for a proper formulation of boundary-value problems. By specializing the general framework we obtain force–extension relations for inextensible filaments and show how previous work on the biophysics of filaments fits within the framework. On the other hand, within the same framework, the theory of extensible filaments, which is appropriate for semi-flexible filaments such as F-actin, enables us to fit representative F-actin data. The specific formulas derived are relatively simple and the parameters involved have direct mechanical interpretations and are immediately related to the filament properties, including the initial end-to-end length, contour length and persistence length.

ПОЧАТКОВО-КРАЙОВА ЗАДАЧА ВИЗНАЧЕННЯ ДИНАМІЧНИХ НАПРУЖЕНЬ У ШАХТНИХ ПІДЙОМНИХ МЕХАНІЗМАХ З УРІВНОВАЖЕНИМ ГОЛОВНЫМ КАНАТОМ

Initial boundary value problem definition for a steel rope of lifting installation is considered in the article.The solution of initial-boundary problem for elastic filament as the area with mobile border is found.Program realization of results of influence of the reflected waves on stress in rope sections is presented.

Microscopic theory of the glassy dynamics of passive and active network materials

Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements within the random first order transition theory of escape from a local energy minimum. The influence of crosslinking on the fragility of inorganic network glass formers is recapitulated by the model. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells: Highly connected tense networks behave as strong glass formers; intense motor action promotes reconfiguration. The fact that our model assuming a negative motor susceptibility predicts the latter suggests that on average the motorized processes in living cells do resist the imposed mechanical load. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.

Force Spectroscopy of Complex Biopolymers with Heterogeneous Elasticity

Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.

Force spectroscopy of complex biopolymers with heterogeneous elasticity

Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of individual complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.

Contorting a heavy and naturally curved elastic rod

We investigate how the configurations obtained from the writhing of a heavy elastic rod are influenced by its intrinsic natural curvature. To this end, we perform a combination of numerics and precision model experiments on the compression or twisting of a thin rod. The ‘softness’ of these single elastic filaments stems from their slenderness (high aspect ratio), which allow for geometrically nonlinear compliant modes that can accommodate large deformations. We uncover the original mechanism that the presence of a body force (gravity in our case) delays the effect of natural curvature, which results from the complex interplay between geometrical constraints, elasticity and weight. We rationalize our experimental results by coupling the predictive power of a numerical method of our own, with classic theory for elastic rods under large deformations. This preponderance of geometry is relevant in systems over a wide range of length scales where curvature and body-forces often co-exist; from engineered rod-like structures such as wires, cables, and pipelines, to natural macromolecules, flagella, fibers and tendrils.

On the optimal shape of magnetic swimmers

Magnetic actuation of elasto-magnetic devices has long been proposed as a simple way to propel fluid and achieve locomotion in environments dominated by viscous forces. Under the action of an oscillating magnetic field, a permanent magnet, when attached to an elastic tail, is able to generate bending waves and sufficient thrust for propulsion. We study the hydrodynamical effects of the magnetic head geometry using a geometrically exact formulation for the elastic tail elastohydrodynamics.We show that the spherical head geometry fails to take full advantage of the propulsive potential from the flexible tail. Nevertheless, while elongated prolate spheroids demonstrate a superior swimming performance, this is still regulated by the nature of the imposed magnetic field. Interestingly, the highest swimming speed is observed when the magnitude of the magnetic field is weak due to delays between the orientation of the magnetic moment and the oscillating magnetic field. This allows the stored elastic energy from the deformed tail to relax during the phase lag between the imposed magnetic field and the swimmer’s magnetic moment, favouring in this way the net propulsion. In particular, this result suggests the existence of optimal magnetic actuations that are non-smooth, and even discontinuous in time, in order to fully explore the propulsive potential associated with the relaxation dynamics of periodically deformed elastic filaments.

Thermal Properties of the Polyolefin Based Elastic Filament DOW XLA<sup>TM</sup>

Thermal properties of the elastic filament DOW XLATMwere analyzed by differential scanning calorimetry (DSC) and thermogravimetry analysis (TG). Besides, the elastic recovery characteristics after heat treatment were also discussed. The DSC scan shows typical endotherms and its melting temperature (Tm) ranges from 28 °C- 65 °C. TG analysis indicates that the thermal degradation begins at 285 °C and the highest weight loss rate occurs at 461.9 oC. When the filaments are heat treated under relaxation or at constant elongatiSuperscript texton, their elastic recovery ratios all decrease with the increase of the heat treatment temperature except for 50 °C.

Buckling transitions of an elastic filament in a viscous stagnation point flow

The interplay of viscous and elastic stresses is relevant to a number of flow problems involving slender elastic fibers. These range from the swimming of microorganisms to the transport of pulp fibers in processing flow as well as from nanotube and nanocarpet applications to semi-flexible polymer behavior. In some applications, slender fibers are attached to walls where they experience externally applied flows. In this paper, we focus on the model problem of a wall mounted filament in a (compressive) extensional flow and characterize the flow-induced bending and buckling of the fiber. Using a combination of stability analysis and numerical simulations (with the latter based on a discretized beam model), we show that, for a critical value of the ratio between viscous and elastic forces, the filament is susceptible to bending and buckling instabilities at supercritical bifurcation points.

Swimming dynamics of the lyme disease spirochete.

The Lyme disease spirochete, Borrelia burgdorferi, swims by undulating its cell body in the form of a traveling flat wave, a process driven by rotating internal flagella. We study B. burgdorferi's swimming by treating the cell body and flagella as linearly elastic filaments. The dynamics of the cell are then determined from the balance between elastic and resistive forces and moments. We find that planar, traveling waves only exist when the flagella are effectively anchored at both ends of the bacterium and that these traveling flat waves rotate as they undulate. The model predicts how the undulation frequency is related to the torque from the flagellar motors and how the stiffness of the cell body and flagella affect the undulations and morphology.

Wrapping transition and wrapping-mediated interactions for discrete binding along an elastic filament: An exact solution

The wrapping equilibria of one and two adsorbing cylinders are studied along a semi-flexible filament (polymer) due to the interplay between elastic rigidity and short-range adhesive energy between the cylinder and the filament. We show that statistical mechanics of the system can be solved exactly using a path integral formalism which gives access to the full effect of thermal fluctuations, going thus beyond the usual Gaussian approximations which take into account only the contributions from the minimal energy configuration and small fluctuations about this minimal energy solution. We obtain the free energy of the wrapping-unwrapping transition of the filament around the cylinders as well as the effective interaction between two wrapped cylinders due to thermal fluctuations of the elastic filament. A change of entropy due to wrapping of the filament around the adsorbing cylinders as they move closer together is identified as an additional source of interactions between them. Such entropic wrapping effects should be distinguished from the usual entropic configuration effects in semi-flexible polymers. Our results may be relevant to the problem of adsorption of oriented nano-rods on semi-flexible polymers.

Autonomous Motility of Active Filaments due to Spontaneous Flow-Symmetry Breaking

We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry, can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles, or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment.

Stress relaxation through crosslink unbinding in cytoskeletal networks

The mechanical properties of cells are dominated by the cytoskeleton, an interconnected network of long elastic filaments. The connections between the filaments are provided by crosslinking proteins, which constitute, next to the filaments, the second important mechanical element of the network. An important aspect of cytoskeletal assemblies is their dynamic nature, which allows remodeling in response to external cues. The reversible nature of crosslink binding is an important mechanism that underlies these dynamical processes. Here, we develop a theoretical model that provides us insight into how the mechanical properties of cytoskeletal networks may depend on their underlying constituting elements. We incorporate three important ingredients: non-affine filament deformations in response to network strain; the interplay between filament and crosslink mechanical properties; and reversible crosslink (un)binding in response to the imposed stress. With this we are able to self-consistently calculate the nonlinear modulus of the network as a function of deformation amplitude and crosslink as well as filament stiffnesses. During loading, crosslink unbinding processes lead to a relaxation of stress and therefore to a reduction of the network modulus and eventually to network failure, when all crosslinks are unbound. This softening due to crosslink unbinding generically competes with an inherent stiffening response, which may be due to either filament or crosslink nonlinear elasticity.

Constant force elongational flow of polymer melts: Experiment and modelling

Characterizing elongational behavior of polymer melts in constant elongation rate or constant tensile stress experiments is hampered by the onset of “necking” instabilities according to the Considère criterion: For an elastic filament, homogeneous uniaxial extension is not guaranteed for strains larger than the strain at which a maximum occurs in the force versus extension curve. Although simulations and experiments seem to indicate that in viscoelastic fluids viscosity effects delay the onset of necking to higher strains, integral measurements of elongational viscosities in Meissner- or Münstedt-type elongational rheometers are often affected by inhomogeneous deformations. A simple means of avoiding the consequences of the Considère criterion consists in operating at constant tensile force, but little attention has been paid so far to constant force elongational rheometry since the pioneering work of Raible et al. [J. Non-Newtonian Fluid Mech. 11, 239 (1982)]. Constant force elongation is also of great industrial relevance, since it is the correct analog of steady fiber spinning, as, e.g., exemplified by the so-called Rheotens test. We present experimental data for two long-chain branched polyethylene melts obtained in constant elongation rate and constant tensile force modes by use of a Sentmanat extensional rheometer in combination with an Anton Paar MCR301 rotational rheometer. The accessible experimental window and experimental limitations are discussed. Constant force elongation can be subdivided into three distinct deformation regimes: At small deformations (regime 1), constant force elongation is equivalent to creep at constant tensile stress. This is followed by regime 2, which is characterized by a steep increase in tensile stress at roughly constant strain rate, while regime 3 corresponds to elongation of a viscous power-law fluid. All three regimes can be modelled quantitatively by a single integral constitutive equation, and a constitutive analysis reveals substantial underestimation of the effective strain-hardening effect observed in constant strain-rate elongation in comparison to constant tensile force extension, which may be indicative of the effect of necking under constant elongation-rate conditions.

Kinematics of the Most Efficient Cilium

In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although cilia have a remarkably conserved internal molecular structure, experimental observations report very diverse kinematics. To address this diversity, we determine numerically the kinematics and energetics of the most efficient cilium. Specifically, we compute the time-periodic deformation of a wall-bound elastic filament leading to transport of a surrounding fluid at minimum energetic cost, where the cost is taken to be the positive work done by all internal molecular motors. The optimal kinematics are found to strongly depend on the cilium bending rigidity through a single dimensionless number, the Sperm number, and closely resemble the two-stroke ciliary beating pattern observed experimentally.

Tensegrity and motor-driven effective interactions in a model cytoskeleton

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity, and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.

Superhelical Architecture of the Myosin Filament-Linking Protein Myomesin with Unusual Elastic Properties

Author SummaryThe contraction and relaxation cycles of active muscles generate substantial mechanical forces, both axially and radially, that place extraordinary stress on the molecular structures within the muscle fibers. These forces are sensed and buffered by unusually long and elastic filament proteins with highly repetitive domain structures. Myomesin is one such repetitive filament protein that is thought to form bridges between the main contractile filaments of the muscle, providing the muscle structure with resistance in the radial dimension. To investigate how the repetitive structure of myomesin contributes to muscle elasticity, we determined the overall architecture of its complete repetitive domain array using a combination of four complementary structural biology methods. Our study reveals a long, dimeric tail-to-tail filament structure folded into an irregular superhelical coil arrangement of almost identical domain modules separated by short linkers. When we applied tension to these myomesin filaments, we found they could stretch to about 2.5 times their original length by unfolding these linkers, and then return to their original state when the tension was removed. Our findings explain how myomesin might adapt its overall length in response to the changing dimensions of the contracting and relaxing muscle, so acting as a highly elastic ribbon that maintains the overall structural organization of the muscle fibers. More generally, these findings demonstrate how repetitive domain modules, such as those in myomesin, can provide elasticity to highly organized biological structures.

Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an "equation of state." From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

Beating synthetic cilia enhance heat transport in microfluidic channels

Using computational modeling, we probed the utility of actuated synthetic cilia for enhancing heat transport in microfluidic channels. Cilia are elastic filaments that are attached to the bottom channel wall with a constant tilt and actuated by a periodical vertical force applied to their free ends. We show that periodical oscillations of elastic cilia mix the heated fluid and create secondary flows in the microchannel that facilitate heat transport between channel walls. The magnitude of the secondary flows and the cilium deformation pattern are controlled by the frequency and amplitude of the periodic driving force. Thus, by varying the force parameters one can effectively regulate the local heat transport in ciliated microchannels.