Constituent Filaments Research Articles

Nonlinear Poisson effect in affine semiflexible polymer networks.

Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or, in the incompressible limit, remains constant as the material is stretched. However, in networks of semiflexible or stiff polymers, which are typically highly compressible yet stiffen significantly when stretched, one instead sees a significant reduction in specific volume under finite strains. This volume reduction is accompanied by increasing alignment of filaments along the strain axis and a nonlinear elastic response, with stiffening of the apparent Young's modulus. For semiflexible networks, in which entropic bending elasticity governs the linear elastic regime, the nonlinear Poisson effect is caused by the nonlinear force-extension relationship of the constituent filaments, which produces a highly asymmetric response of the constituent polymers to stretching and compression. The details of this relationship depend on the geometric and elastic properties of the underlying filaments, which can vary greatly in experimental systems. Here, we provide a comprehensive characterization of the nonlinear Poisson effect in an affine network model and explore the influence of filament properties on essential features of both microscopic and macroscopic response, including strain-driven alignment and volume reduction.

Nanocolloidal hydrogel mimics the structure and nonlinear mechanical properties of biological fibrous networks.

Fibrous networks formed by biological polymers such as collagen or fibrin exhibit nonlinear mechanical behavior. They undergo strong stiffening in response to weak shear and elongational strains, but soften under compressional strain, in striking difference with the response to the deformation of flexible-strand networks formed by molecules. The nonlinear properties of fibrous networks are attributed to the mechanical asymmetry of the constituent filaments, for which a stretching modulus is significantly larger than the bending modulus. Studies of the nonlinear mechanical behavior are generally performed on hydrogels formed by biological polymers, which offers limited control over network architecture. Here, we report an engineered covalently cross-linked nanofibrillar hydrogel derived from cellulose nanocrystals and gelatin. The variation in hydrogel composition provided a broad-range change in its shear modulus. The hydrogel exhibited both shear-stiffening and compression-induced softening, in agreement with the predictions of the affine model. The threshold nonlinear stress and strain were universal for the hydrogels with different compositions, which suggested that nonlinear mechanical properties are general for networks formed by rigid filaments. The experimental results were in agreement with an affine model describing deformation of the network formed by rigid filaments. Our results lend insight into the structural features that govern the nonlinear biomechanics of fibrous networks and provide a platform for future studies of the biological impact of nonlinear mechanical properties.

Bonded straight and helical flagellar filaments form ultra-low-density glasses

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semidilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are microns-long helical or straight filaments assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape-diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics. Consequently, the shape-diblock filaments become permanently jammed at exceedingly low densities. We also measure the rheological properties of semidilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semidilute fibrous suspensions.

Fibrous hydrogels under biaxial confinement

Confinement of fibrous hydrogels in narrow capillaries is of great importance in biological and biomedical systems. Stretching and uniaxial compression of fibrous hydrogels have been extensively studied; however, their response to biaxial confinement in capillaries remains unexplored. Here, we show experimentally and theoretically that due to the asymmetry in the mechanical properties of the constituent filaments that are soft upon compression and stiff upon extension, filamentous gels respond to confinement in a qualitatively different manner than flexible-strand gels. Under strong confinement, fibrous gels exhibit a weak elongation and an asymptotic decrease to zero of their biaxial Poisson’s ratio, which results in strong gel densification and a weak flux of liquid through the gel. These results shed light on the resistance of strained occlusive clots to lysis with therapeutic agents and stimulate the development of effective endovascular plugs from gels with fibrous structures for stopping vascular bleeding or suppressing blood supply to tumors.

Actively Driven Fluctuations in a Fibrin Network

Understanding force propagation through the fibrous extracellular matrix can elucidate how cells interact mechanically with their surrounding tissue. Presumably, due to elastic nonlinearities of the constituent filaments and their random connection topology, force propagation in fiber networks is quite complex, and the basic problem of force propagation in structurally heterogeneous networks remains unsolved. We report on a new technique to detect displacements through such networks in response to a localized force, using a fibrin hydrogel as an example. By studying the displacements of fibers surrounding a two-micron bead that is driven sinusoidally by optical tweezers, we develop maps of displacements in the network. Fiber movement is measured by fluorescence intensity fluctuations recorded by a laser scanning confocal microscope. We find that the Fourier magnitude of these intensity fluctuations at the drive frequency identifies fibers that are mechanically coupled to the driven bead. By examining the phase relation between the drive and the displacements, we show that the fiber displacements are, indeed, due to elastic couplings within the network. Both the Fourier magnitude and phase depend on the direction of the drive force, such that displacements typically propagate farther, but not exclusively, along the drive direction. This technique may be used to characterize the local mechanical response in 3-D tissue cultures, and to address fundamental questions about force propagation within fiber networks.

Mechanical properties of biofiber/glass reinforced hybrid composites produced by hand lay-up method: A review

Hybrid composites utilize more than one kind of strands within the same matrix to urge the synergistic impact of both fibers' properties on composites' general properties. Hybridization can be performed from artificial, natural, and a combination of both fibers. The constituent filaments can be altered in numerous ways, driving to the variety in composite properties. Partial substitution of glass fiber with natural ones offers an advantage compared with glass fiber composites while permitting to obtain a mechanical performance higher than using pure natural fiber composites. Recently, researchers are tending towards the development of hybrid composites which will provide good static properties. In this context, a concise review has been done on the recent developments of natural/glass fiber-reinforced composites made by hand lay-up method. It includes a survey of the past research already available involving the hybrid composites and the effect of various parameters on composites' performance studied by various researchers.

Water/moisture vapor permeabilities and thermal wear comfort of the Coolmax®/bamboo/tencel included PET and PP composite yarns and their woven fabrics

This study examined the water and moisture vapor permeabilities and the heat retention rate related to the wear comfort of the woven fabrics made from different types of composite yarn, the sheath/core composite yarn structure and non-circular cross-section of the constituent filaments (Coolmax®) in the core region played a very important role with high fabric porosity by including a capillary absorption in the wicking property. The fabric structures with high porosity composed of Coolmax® sheath/core yarns, and spun yarns with non-circular cross-sectional fibers (Coolmax®) affected strongly the fast drying rate due to moisture vapor diffusion of composite yarn fabrics. The moisture vapor permeability of the composite yarn fabrics was highly dependent on the porosity in the sheath/core yarn structures, In addition, the heat retention rate of the composite yarn fabric was strongly influenced by the high porosity due to the sheath/core and bulky staple yarn structures as well as the low thermal conductivity of the constituent fibers.

Dynamics of undulatory fluctuations of semiflexible filaments in a network.

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-De Dominicis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength sqrt[κ/τ_{R}], set by the filament's bending modulus κ and spring-renormalized tension τ_{R}, are changed by the boundary spring. This occurs near the crossover frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from ω^{1/2} to ω^{3/4}, but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.

Effect of Filament Configuration on Handle and Transmission Properties of Polyester Multifilament Fabrics

The configuration of constituent filaments in multifilament woven polyester fabrics plays very crucially to decide the low stress mechanical as well as transmission behaviour of shirting range fabrics. Intermingled, textured, and flat yarns (150/36/5, yarn of total denier 150, 36 filaments in that strand with 5 twist per meter) were used to produce different fabric samples. Twelve fabric samples using various combinations of warp and weft are manufactured with intermingled, textured, twisted, and flat configurations. Fabric samples were characterized to get low-stress mechanical properties by Kawabata Evaluation System (KES-FB) and transmission behaviour was tested by Permetest, air permeability tester, and wickability tester. The presence of textured configured multifilament yarn exhibits high bending elasticity with lower bending hysteresis. The compression behaviour of fabric consists of intermingled warp and textured weft shows the highest compressibility or fullness. The intermingled configuration offers higher total hand value for winter applications with a different combination of weft threads. The highest wicking potential is achieved in case of intermingled warp and textured weft combinations. The moisture transmission rate remains highest with twisted warp twisted weft fabrics.

Degradation study of polyester fiber in swimming pool water

The disinfection of swimming pool water is vital to maintain water quality. The chemicals used in this practice can damage the fabrics of bathing suits and shorten the shelf life of the textile substrate. The degradation of polyester, a polymer that is widely used in bathing suits for swimming pools, was investigated. For this, a 23 factorial design was employed for the experimental methodology. The effect of several variables was analyzed in a simulated swimming pool batch, such as textile-exposure time, concentration of the used disinfection product, and batch temperature. The response variables were enthalpy of fusion ΔHm, melting temperature and crystallinity (obtained by differential scanning calorimetry), percentage of weight loss, temperature of maximum rate of weight loss, onset temperature and endset temperature (measured through thermogravimetric analysis), and Young's modulus values (measured in strain-stress tests in the row and column directions). The factors of temperature, time, and the concentration of disinfectant were significant for melting temperature, crystallinity, onset temperature, and Young's modulus for columns. The analyses of variance were obtained using software Design-Expert DX7. Attenuated total reflectance-Fourier transform infrared spectroscopy analysis showed changes in band intensities at 695 cm−1, which were attributed to ester groups, as well as a decrease of the carbonyl band at 1712 cm−1, which was attributed to the hydrolysis of the material. Analysis through scanning electronic microscopy images showed the appearance of stretch marks in the constituent filaments of the tested textiles, which suggests a surface degradation occurred.

Tau (297-391) forms filaments that structurally mimic the core of paired helical filaments in Alzheimer's disease brain.

The constituent paired helical filaments (PHFs) in neurofibrillary tangles are insoluble intracellular deposits central to the development of Alzheimer’s disease (AD) and other tauopathies. Full‐length tau requires the addition of anionic cofactors such as heparin to enhance assembly. We have shown that a fragment from the proteolytically stable core of the PHF, tau 297‐391 known as ‘dGAE’, spontaneously forms cross‐β‐containing PHFs and straight filaments under physiological conditions. Here, we have analysed and compared the structures of the filaments formed by dGAE in vitro with those deposited in the brains of individuals diagnosed with AD. We show that dGAE forms PHFs that share a macromolecular structure similar to those found in brain tissue. Thus, dGAEs may serve as a model system for studying core domain assembly and for screening for inhibitors of tau aggregation.

Constant spacing in filament bundles

Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to the distance of closest approach between the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. In this paper, we consider two distinct notions of constant spacing in multi-filament packings in : equidistance, where the distance of closest approach is constant along the length of filament pairs; and isometry, where the distances of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in . The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while non-equidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three ‘almost equidistant’ ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness.

Buckling of filamentous actin bundles in filopodial protrusions

The mechanical behavior of filamentous actin bundles plays an essential role in filopodial protrusions at the leading edge of crawling cells. These bundles consist of parallel actin filaments that are hexagonally packed and interconnected via cross-linking proteins including α-actinin, filamin, and fascin. When pushing against the plasma membrane and/or external barriers, actin bundles in filopodial protrusions inevitably encounter a compressive load. The bending stiffness and buckling stability of actin bundles are therefore important in determining the filopodial architecture and subsequent cell morphology. In this work, we employ a coarse-grained molecular dynamics model to investigate the buckling behavior of cross-linked actin bundles under compression, explicitly accounting for the properties of the constituent filaments and the mechanical description of the cross-linkers. The bending stiffness of actin bundles exhibits a generic size effect depending on the number of filaments in the bundle, explicitly depending on the degree of interfilament coupling. The distinct buckling modes are analyzed for bundles with different coupling states and crosslinker strengths. This study could clarify the stability and buckling mechanisms of parallel packed actin bundles and the structure–function relations of mechanical components in filopodial protrusions.

Connecting macroscopic dynamics with microscopic properties in active microtubule network contraction

The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network’s constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled.

Nonaffine behavior of three-dimensional semiflexible polymer networks.

Three-dimensional semiflexible polymer networks are the structural building blocks of various biological and structural materials. Previous studies have primarily used two-dimensional models for understanding the behavior of these networks. In this paper, we develop a three-dimensional nonaffinity measure capable of providing direct comparison with continuum level homogenized quantities, i.e., strain field. The proposed nonaffinity measure is capable of capturing possible anisotropic microstructures of the filamentous networks. This strain-based nonaffinity measure is used to probe the mechanical behavior at different length scales and investigate the effects of network mechanical and microstructural properties. Specifically, it is found that although all nonaffinity measure components have a power-law variation with the probing length scale, the degree of nonaffinity decreases with increasing the length scale of observation. Furthermore, the amount of nonaffinity is a function of network fiber density, bending stiffness of the constituent filaments, and the network architecture. Finally, it is found that the two power-law scaling regimes previously reported for two-dimensional systems do not appear in three-dimensional networks. Also, unlike two-dimensional models, the exponent of the power-law relation depends weakly on the density of the three-dimensional networks.

Solid friction between soft filaments.

Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes's drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament's elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

Morphology Selection through Geometric Frustration in Twisted Filament Bundles and Fibers

Rope-like assemblies of twisted protein filaments constitute a common materials archetype appearing in a range of biological contexts from extracellular filament bundles to amyloid fibrils. Owing to the numerous distinctions in molecular structure and interactions underlying these diverse assemblies, a common framework to predict and classify the basic mechanisms of structure formation in twisted filament assemblies is still lacking. In this study, we exploit a recent and surprising connection between the assembly of self-twisting filaments and assembly on spherically-curved 2D surfaces to develop a universal theory of morphology selection in twisted fibers and bundles. This theory shows that the size and cross-sectional shape of self-assembled fibers is determined by competition between the elastic costs of inter-filament frustration, bending deformation of constituent filaments and surface energy of fibers. We find that for sufficiently large twist, isotropic (cylindrical) bundles are generically unstable to developing anisotropic cross-sections (helical tapes). Critically, the anisotropy of fiber cross-sections is found to give a direct measure of the anisotropy of inter-filament vs. intra-filament elasticity. We corroborate the universal predictions of our theory with numerical simulations of self-twisting fibers and compare the morphology diagram structural observations of anisotropy of micron-scale amyloid fibers assembled from hydrolyzed protein fragments.

Failure in anisotropic nonwoven materials at finite deformation

AbstractThe current work proposes a finite deformation strong discontinuity approach based modeling of failure in anisotropic materials with reorientation based micromechanical network model for the bulk response. These materials consist of randomly cross‐linked one dimensional filaments at their microstructure which undergo non‐affine deformation as well as reorientation upon loading before undergoing complete failure. The computationally efficient strong discontinuity approach allows to capture the failure kinematics by introducing a local problem where a strong discontinuity exists, thereby leading to an enhanced deformation gradient. A precise evaluation of the bulk response is done by homogenizing the physical microscopic response of constituent filaments where reorientation is introduced with an initial straightening effect of fiber undulations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Communication: Dominance of extreme statistics in a prototype many-body Brownian ratchet.

Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in filaments' spatial distribution.

Self-Assembly Enhances the Strength of Fibers Made from Vimentin Intermediate Filament Proteins

Hagfish slime threads were recently established as a promising biomimetic model for efforts to produce ecofriendly alternatives to petroleum polymers. Initial attempts to make fibers from solubilized slime thread proteins fell short of achieving the outstanding mechanics of native slime threads. Here we tested the hypothesis that the high strength and toughness of slime threads arise from the ability of constituent intermediate filaments to undergo a stress-induced α-to-β transition. To do this, we made fibers from human vimentin proteins that were first allowed to self-assemble into 10 nm intermediate filaments. Fibers made from assembled vimentin hydrogels underwent an α-to-β transition when strained and exhibited improved mechanical performance. Our data demonstrate that it is possible to make materials from intermediate filament hydrogels and that mimicking the secondary structure of native hagfish slime threads using intermediate filament self-assembly is a promising strategy for improving the mechanical performance of biomimetic protein materials.