Elastic Filaments Research Articles

Preclinical Evaluation of a New Hydroxypropyl-Guar Phospholipid Nanoemulsion-Based Artificial Tear Formulation in Models of Corneal Epithelium.

To evaluate the effect of hydroxypropyl-guar anionic phospholipid nanoemulsion (HP-guar nanoemulsion), a new artificial tear formulation for treatment of dry eye disease (DED), in corneal epithelium models. Cultured human corneal epithelial cells were used to assess (1) hydration protection and hydration retention protection against desiccation, and (2) cell recovery after benzalkonium chloride (BAC) damage. Corneal epithelium permeability was measured by 5,6-carboxyfluorescein (CF) uptake in intact rabbit eyes. Lubricity was determined using simulated blinking in bovine pericardium-pericardium tribological experiments; elastic filament strength was measured using an extensional rheometer. Comparator arms included vehicle/control and the microemulsion [Systane® Balance (SYSB)]. Cell hydration protection was 39.5%, 7.1%, and -0.1%, and surface hydration retention was 32.6%, 11.0%, and -1.2% with HP-guar nanoemulsion, SYSB, and vehicle, respectively, after desiccation. After 48 h, cell recovery from BAC exposure (relative fluorescence units ± SD) was faster with HP-guar nanoemulsion treatment (2.66 ± 0.2) than SYSB (2.76 ± 0.2) and vehicle (3.11 ± 0.4). The CF permeability (ng CF/g) decreased in rabbit cornea treated with HP-guar nanoemulsion (9.6 ± 2.3) than those with SYSB (13.12 ± 2.8) or BAC-exposed cornea (22.6 ± 5.1). HP-guar nanoemulsion demonstrated greater lubricity and polymer filament break-up time than SYSB and vehicle. In all assessments, HP-guar nanoemulsion showed significant improvement versus vehicle/control (P < 0.05); outcomes were better with HP-guar nanoemulsion versus microemulsion. The HP-guar nanoemulsion promotes greater moisture retention, protection, improved cell barrier function, and increased elastic filament strength in corneal epithelium models. The potential clinical benefits of HP-guar nanoemulsion needs to be evaluated in patients with DED, in future studies.

Well‐Posedness and Global Behavior of the Peskin Problem of an Immersed Elastic Filament in Stokes Flow

AbstractWe consider the problem of a one‐dimensional elastic filament immersed in a two‐dimensional steady Stokes fluid. Immersed boundary problems in which a thin elastic structure interacts with a surrounding fluid are prevalent in science and engineering, a class of problems for which Peskin has made pioneering contributions. Using boundary integrals, we first reduce the fluid equations to an evolution equation solely for the immersed filament configuration. We then establish local well‐posedness for this equation with initial data in low‐regularity Hölder spaces. This is accomplished by first extracting the principal linear evolution by a small‐scale decomposition and then establishing precise smoothing estimates on the nonlinear remainder. Higher regularity of these solutions is established via commutator estimates with error terms generated by an explicit class of integral kernels. Furthermore, we show that the set of equilibria consists of uniformly parametrized circles and prove nonlinear stability of these equilibria with explicit exponential decay estimates, the optimality of which we verify numerically. Finally, we identify a quantity that respects the symmetries of the problem and controls global‐in‐time behavior of the system. © 2018 Wiley Periodicals, Inc.

Morphological transitions of elastic filaments in shear flow

The morphological dynamics, instabilities, and transitions of elastic filaments in viscous flows underlie a wealth of biophysical processes from flagellar propulsion to intracellular streaming and are also key to deciphering the rheological behavior of many complex fluids and soft materials. Here, we combine experiments and computational modeling to elucidate the dynamical regimes and morphological transitions of elastic Brownian filaments in a simple shear flow. Actin filaments are used as an experimental model system and their conformations are investigated through fluorescence microscopy in microfluidic channels. Simulations matching the experimental conditions are also performed using inextensible Euler-Bernoulli beam theory and nonlocal slender-body hydrodynamics in the presence of thermal fluctuations and agree quantitatively with observations. We demonstrate that filament dynamics in this system are primarily governed by a dimensionless elasto-viscous number comparing viscous drag forces to elastic bending forces, with thermal fluctuations playing only a secondary role. While short and rigid filaments perform quasi-periodic tumbling motions, a buckling instability arises above a critical flow strength. A second transition to strongly deformed shapes occurs at a yet larger value of the elasto-viscous number and is characterized by the appearance of localized high-curvature bends that propagate along the filaments in apparent "snaking" motions. A theoretical model for the as yet unexplored onset of snaking accurately predicts the transition and explains the observed dynamics. We present a complete characterization of filament morphologies and transitions as a function of elasto-viscous number and scaled persistence length and demonstrate excellent agreement between theory, experiments, and simulations.

Torque driven ferromagnetic swimmers

Microscopic swimming devices hold promise for radically new applications in lab-on-a-chip and microfluidic technology, including diagnostics and drug delivery. In this paper, we realize a macroscopic single particle ferromagnetic swimmer experimentally and investigate its swimming properties. The flagella-based swimmer is comprised of a hard ferromagnetic head attached to a flexible tail. We investigate the dynamic performance of the swimmer on the air-liquid interface as a function of the external magnetic field parameters (frequency and amplitude of an applied magnetic field). We show that the speed of the swimmer can be controlled by manipulating the strength and frequency of the external magnetic field (&amp;lt;3.5 mT) and that the propagation direction has a dependence on parameters of the external magnetic field. The experimental results are compared to a theoretical model based on three beads, one of which having a fixed magnetic moment and the other two non-magnetic, connected via elastic filaments. The model shows sufficient complexity to satisfy the “non-reciprocity” condition and gives good agreement with experiment. Via a simple conversion, we also demonstrate a fluid pump and investigate the induced flow. This investigation paves the way to the fabrication of such swimmers and fluid pump systems on a micro-scale, promising a variety of microfluidic applications.

Hydrodynamic interactions of actuated elastic filaments near a planar wall with applications to sperm motility

Hydrodynamic interactions of actuated elastic filaments near a planar wall with applications to sperm motility

The effect of flexural stiffness on the sound of a hanging filament: From a membrane to a rigid body

We consider the acoustic field of a thin flexible filament subject to uniform mean flow and a ‘hanging chain’ tension force parallel to its unperturbed state. The filament is actuated via harmonic heaving motion at its upstream edge with prescribed frequency and small amplitude. To investigate the effect of filament flexural rigidity, we analyze the system acoustic radiation in the entire range of body structural stiffnesses. Assuming two-dimensional high Reynolds and low Mach number flow, we apply a near-field description based on potential thin airfoil theory. The near-field model is then used to formulate the source term in the Powell-Howe acoustic analogy. The far field sound is calculated applying a compact Green's function approach, yielding the leading order acoustic dipole field. In the limit of small flexural stiffness, we find that the acoustic field of a highly-elastic filament converges to the far field of a hanging membrane, dominated by the wake dipole sound. The wake sound component also dominates the system radiation in the limit of small actuation frequencies, where the filament deflects as a rigid body regardless of its structural stiffness. Sufficient increase in heaving frequency intensifies the relative contribution of filament motion dipole, resulting in significant differences between systems with different rigidities. Reflecting the impact of filament elasticity, these differences manifest the system's natural frequency response, leading to increased levels of sound for actuations at the system's eigenstates. In cases where the trailing edge wake and motion dipoles acquire similar amplitudes and opposite phases, significant sound reduction is found.

Titin-based mechanosensing modulates muscle hypertrophy.

BackgroundTitin is an elastic sarcomeric filament that has been proposed to play a key role in mechanosensing and trophicity of muscle. However, evidence for this proposal is scarce due to the lack of appropriate experimental models to directly test the role of titin in mechanosensing.MethodsWe used unilateral diaphragm denervation (UDD) in mice, an in vivo model in which the denervated hemidiaphragm is passively stretched by the contralateral, innervated hemidiaphragm and hypertrophy rapidly occurs.ResultsIn wildtype mice, the denervated hemidiaphragm mass increased 48 ± 3% after 6 days of UDD, due to the addition of both sarcomeres in series and in parallel. To test whether titin stiffness modulates the hypertrophy response, RBM20ΔRRM and TtnΔIAjxn mouse models were used, with decreased and increased titin stiffness, respectively. RBM20ΔRRM mice (reduced stiffness) showed a 20 ± 6% attenuated hypertrophy response, whereas the TtnΔIAjxn mice (increased stiffness) showed an 18 ± 8% exaggerated response after UDD. Thus, muscle hypertrophy scales with titin stiffness. Protein expression analysis revealed that titin‐binding proteins implicated previously in muscle trophicity were induced during UDD, MARP1 & 2, FHL1, and MuRF1.ConclusionsTitin functions as a mechanosensor that regulates muscle trophicity.

Persistence of Perfect Packing in Twisted Bundles of Elastic Filaments.

It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of twist due to a subtle counteraction of geometric expansion with elastic contraction. Using x-ray scanning and by locating each filament in the bundle, we show the remarkable persistence of order even as the twist is increased well above 360°, by measuring the spatial correlation function across the bundle cross section. We introduce a model which analyzes the combined effects of elasticity including filament stretching and radial and hoop compression necessary to explain this generic preservation of order observed with Hookean filaments.

Calculation of an flexible gently sloping filament using the generalized finite difference method

At the present time, in the construction industry hanging structures, such as, suspension bridges, ropeways, coverings of industrial and civil facilities are widely used. The thread can serve as a settlement scheme of some structural elements of such systems. The aim of the article is to create an algorithm for calculating an elastic flat filament that is convenient for practical application under the action of an arbitrary load. The article presents an algorithm for calculating an elastic flat thread on the effect of a vertical load, arbitrarily varying along its length, as well as vertical and horizontal concentrated forces. To solve this problem, we use the generalized method of final differences allowing to consider ruptures of function of displacement and her derivatives without special increase the number of points and without use the points lying behind the contour. The calculation is divided into two stages. First, we consider the equilibrium of the filament under the action of its own weight. The exact solution of this problem is known. Span of a thread is divided into a number of elements within which the distributed vertical load is continuous, and concentrated forces are applied at the boundaries The article gives an example of calculating a flexible flat thread based on the presented algorithm. Comparison of the calculation results for some types of loading with similar solutions obtained analytically showed the ease of use and effectiveness of this method with a small number of elements on which the system is divided.

Microtubules soften due to cross-sectional flattening.

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

Label-free sorting of soft microparticles using a bioinspired synthetic cilia array.

Isolating cells of interest from a heterogeneous population has been of critical importance in biological studies and clinical applications. In this study, a novel approach is proposed for utilizing an active ciliary system in microfluidic devices to separate particles based on their physical properties. In this approach, the bottom of the microchannel is covered with an equally spaced cilia array of various patterns which is actuated by an external stimuli. 3D simulations are carried out to study cilia-particle interaction and isolation dynamic in a microfluidic channel. It is observed that these elastic hair-like filaments can influence particle's trajectories differently depending on their biophysical properties. This modeling study utilizes immersed boundary method coupled with the lattice Boltzmann method. Soft particles and cilia are implemented through the spring connected network model and point-particle scheme, respectively. It is shown that cilia array with proper stimulation is able to continuously and non-destructively separate cells into subpopulations based on their size, shape, and stiffness. At the end, a design map for fabrication of a programmable microfluidic device capable of isolating various subpopulations of cells is developed. This biocompatible, label-free design can separate cells/soft microparticles with high throughput which can greatly complement existing separation technologies.

Do Optomechanical Metasurfaces Run Out of Time?

Artificially structured metasurfaces make use of specific configurations of subwavelength resonators to efficiently manipulate electromagnetic waves. Additionally, optomechanical metasurfaces have the desired property that their actual configuration may be tuned by adjusting the power of a pump beam, as resonators move to balance pump-induced electromagnetic forces with forces due to elastic filaments or substrates. Although the reconfiguration time of optomechanical metasurfaces crucially determines their performance, the transient dynamics of unit cells from one equilibrium state to another is not understood. Here, we make use of tools from nonlinear dynamics to analyze the transient dynamics of generic optomechanical metasurfaces based on a damped-resonator model with one configuration parameter. We show that the reconfiguration time of optomechanical metasurfaces is not only limited by the elastic properties of the unit cell but also by the nonlinear dependence of equilibrium states on the pump power. For example, when switching is enabled by hysteresis phenomena, the reconfiguration time is seen to increase by over an order of magnitude. To illustrate these results, we analyze the nonlinear dynamics of a bilayer cross-wire metasurface whose optical activity is tuned by an electromagnetic torque. Moreover, we provide a lower bound for the configuration time of generic optomechanical metasurfaces. This lower bound shows that optomechanical metasurfaces cannot be faster than state-of-the-art switches at reasonable powers, even at optical frequencies.

Propulsion and maneuvering of an artificial microswimmer by two closely spaced waving elastic filaments

We study the hydrodynamic interaction between two closely-spaced waving elastic cylinders immersed within a viscous liquid, at the creeping flow regime. The cylinders are actuated by a forced oscillation of the slope at their clamped end and are free at the opposite end. We obtain an expression for the interaction force and apply an asymptotic expansion based on a small parameter representing the ratio between the elastic deflections and the distance between the cylinders. The leading-order solution is an asymmetric oscillation pattern at the two frequencies ($\omega_1,\omega_2$) in which the cylinders are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first-order includes the $2\omega_1,2\omega_2,\omega_1+\omega_2$, and $\omega_1-\omega_2$ harmonics. For in-phase actuation with $\omega_1= \omega_2$, the deflection dynamics are identical to an isolated cylinder with a modified Sperm number. For configurations with $\omega_1\approx \omega_2$, the $\omega_1-\omega_2$ mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. Experiments are conducted to verify and illustrate the theoretical predictions.

Ordering of myosin II filaments driven by mechanical forces: experiments and theory

Myosin II filaments form ordered superstructures in both cross-striated muscle and non-muscle cells. In cross-striated muscle, myosin II (thick) filaments, actin (thin) filaments and elastic titin filaments comprise the stereotypical contractile units of muscles called sarcomeres. Linear chains of sarcomeres, called myofibrils, are aligned laterally in registry to form cross-striated muscle cells. The experimentally observed dependence of the registered organization of myofibrils on extracellular matrix elasticity has been proposed to arise from the interactions of sarcomeric contractile elements (considered as force dipoles) through the matrix. Non-muscle cells form small bipolar filaments built of less than 30 myosin II molecules. These filaments are associated in registry forming superstructures ('stacks') orthogonal to actin filament bundles. Formation of myosin II filament stacks requires the myosin II ATPase activity and function of the actin filament crosslinking, polymerizing and depolymerizing proteins. We propose that the myosin II filaments embedded into elastic, intervening actin network (IVN) function as force dipoles that interact attractively through the IVN. This is in analogy with the theoretical picture developed for myofibrils where the elastic medium is now the actin cytoskeleton itself. Myosin stack formation in non-muscle cells provides a novel mechanism for the self-organization of the actin cytoskeleton at the level of the entire cell.This article is part of the theme issue 'Self-organization in cell biology'.

Wall proximity effects on the flow past cylinder with flexible filament

The response of thin, elastic filament attached to a circular cylinder is numerically investigated under uniform flow at different wall proximities, GD (0.5, 0.6, 0.8, 1, 1.5, 2 and 2.5). The Reynolds number based on the diameter of the cylinder is 200. Numerical simulations were conducted for a range of reduced velocities Ur (3,4,5 and 6), where Ur = U∞fnD which appropriately captures the synchronization range of vortex-induced vibration(VIV) of the structure. Ur is varied by changing the density of the material. The force coefficients, the frequency of shedding/flapping are observed to be the function of GD and Ur. The positive vortices diffuses faster as GD decreases. The skewness in the amplitude attained by the flapping filament on either side of the cylinder causes unsteady shedding of vortices. Filament flaps in frequency that is closer to its natural frequency at higher GD and at lower GD, the frequency of flaps for all Ur is similar. For lower gap ratios, 0.5 and 0.6, the modulations in flapping amplitude is observed. The modulation is predominant as the Ur increases. During the growth and damping phase of the amplitudes in each modulation cycle, the vortex shedding is observed to be oblique towards the wall. The filament flaps in single mode shape. The frequency of the flapping depends on the Ur and GD. The frequency of the flapping is in resonance with shedding frequency.

Filamentary structures that self-organize due to adhesion.

We study the self-organization of random collections of elastic filaments that interact adhesively. The evolution from an initial fully random quasi-two-dimensional state is controlled by filament elasticity, adhesion and interfilament friction, and excluded volume. Three outcomes are possible: the system may remain locked in the initial state, may organize into isolated fiber bundles, or may form a stable, connected network of bundles. The range of system parameters leading to each of these states is identified. The network of bundles is subisostatic and is stabilized by prestressed triangular features forming at bundle-to-bundle nodes, similar to the situation in foams. Interfiber friction promotes locking and expands the parametric range of nonevolving systems.

SPHRINT – Printing Drug Delivery Microspheres from Polymeric Melts

This paper describes a simple, straightforward, and rapid method for producing microspheres from molten polymers by merely printing them in an inkjet-like manner onto a superoleophobic surface (microsphere printing, hence SPHRINT). Similar to 3D printing, a polymer melt is deposited onto a surface; however, in contrast to 2D or 3D printing, the surface is not wetted (i.e. exhibiting high contact angles with liquids, above 150°, due to its low surface energy), resulting in the formation of discrete spherical microspheres. In this study, microspheres were printed using polycaprolactone and poly(lactic-co-glycolic acid) loaded with a model active pharmaceutical ingredient—ibuprofen (IBU). The formation of microspheres was captured by high-speed imaging and was found to involve several physical phenomena characterized by non-dimensional numbers, including the thinning and breakup of highly viscous, weakly elastic filaments, which are first to be described in pure polymer melts. The resulting IBU-loaded microspheres had higher sphericity, reproducible sizes and shapes, and superior drug encapsulation efficiencies with a distinctly high process yield (>95%) as compared to the conservative solvent-based methods used presently. Furthermore, the microspheres showed sustained release profiles.

Development of instrumentation for measurements of two components of velocity with a single sensing element

A novel method of obtaining two orthogonal velocity components with high spatial and temporal resolution is investigated. Both components are obtained utilizing a single sensing nanoribbon by combining the two independent operating modes of classic hot wire anemometry and the newly discovered elastic filament velocimetry (EFV). In contrast to hot wire anemometry, EFV measures fluid velocity through correlating the fluid forcing with the internal strain of the wire. In order to utilize both modes of operation, a system that switches between the two operating modes is built and characterized, and the theoretically predicted sensing response time in water is compared to experimental results. The sensing system is capable of switching between the two modes of operation at a frequency of 100 kHz with minimal attenuation with an uncompensated repetition rate up to 3 kHz or up to 10 kHz utilizing modest signal compensation. While further characterization of the sensor performance in air is needed, this methodology enables a technique for obtaining well-resolved yet cost-efficient directional measurements of flow velocities which, for example, can be used for distributed measurements of velocity or measurements of turbulent stresses with excellent spatial resolution.

An historical perspective of the discovery of titin filaments -Part 2.

In 2017, a Special Issue of Biophysical Reviews was devoted to "Titin and Its Binding Partners. The issue contained a review: "An historical perspective of the discovery of titin filaments" by dos Remedios and Gilmour that was intended to be a history of the discovery of the giant protein titin, previously named connectin. The review took readers back to the earliest discovery of the so-called third filament component of skeletal and cardiac muscle sarcomeres and ended in 1969. Recently, my colleague Shin'ichi Ishiwata gently reminded me of two papers published in 1990 and 1993 that were unwittingly omitted from the original historical perspective. In the first paper (J Cell Biol 110:53-62, 1990), Funatsu et al. examined the elastic filaments in skeletal muscle using a combination of light and electron microscopy, but they also measured resting as well as passive stiffness mechanical measurements to establish that connectin (titin) is responsible for both stiffness and fiber tension. In the second paper (J Cell Biol 120:711-724, 1993), Funatsu et al. used permeabilised cardiac muscle myocytes (from rabbit papillary muscles) and focussed on filament ultrastructure using either freeze-substitution or deep-etched replica methods to visualise connectin/titin filaments in fibers with and without actin and myosin filaments.

Different bending models predict different dynamics of sedimenting elastic trumbbells.

The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.