Bundle Stiffness Research Articles

LHFPL5 is a key element in force transmission from the tip link to the hair cell mechanotransducer channel.

During auditory transduction, sound-evoked vibrations of the hair cell stereociliary bundles open mechanotransducer (MET) ion channels via tip links extending from one stereocilium to its neighbor. How tension in the tip link is delivered to the channel is not fully understood. The MET channel comprises a pore-forming subunit, transmembrane channel-like protein (TMC1 or TMC2), aided by several accessory proteins, including LHFPL5 (lipoma HMGIC fusion partner-like 5). We investigated the role of LHFPL5 in transduction by comparing MET channel activation in outer hair cells of Lhfpl5-/- knockout mice with those in Lhfpl5+/- heterozygotes. The 10 to 90 percent working range of transduction in Tmc1+/+; Lhfpl5+/- was 52 nm, from which the single-channel gating force, Z, was evaluated as 0.34 pN. However, in Tmc1+/+; Lhfpl5-/- mice, the working range increased to 123 nm and Z more than halved to 0.13 pN, indicating reduced sensitivity. Tip link tension is thought to activate the channel via a gating spring, whose stiffness is inferred from the stiffness change on tip link destruction. The gating stiffness was ~40 percent of the total bundle stiffness in wild type but was virtually abolished in Lhfpl5-/-, implicating LHFPL5 as a principal component of the gating spring. The mutation Tmc1 p.D569N reduced the LHFPL5 immunolabeling in the stereocilia and like Lhfpl5-/- doubled the MET working range, but other deafness mutations had no effect on the dynamic range. We conclude that tip-link tension is transmitted to the channel primarily via LHFPL5; residual activation without LHFPL5 may occur by direct interaction between PCDH15 and TMC1.

Collagenase treatment decreases muscle stiffness in cerebral palsy: A preclinical ex vivo biomechanical analysis of hip adductor muscle fiber bundles.

To determine the dose-response relationship of collagenase Clostridium histolyticum (CCH) on collagen content and the change in muscle fiber bundle stiffness after ex vivo treatment of adductor longus biopsies with CCH in children with cerebral palsy (CP). Biopsy samples of adductor longus from children with CP (classified in Gross Motor Function Classification System levels IV and V) were treated with 0 U/mL, 200 U/mL, 350 U/mL, or 500 U/mL CCH; percentage collagen reduction was measured to determine the dose-response. Peak and steady-state stresses were determined at 1%, 2.5%, 5%, and 7.5% strain increments; Young's modulus was calculated. Eleven patients were enrolled (nine males, two females, mean age at surgery 6 years 5 months; range: 2-16 years). A linear CCH dose-response relationship was determined. Peak and steady-state stress generation increased linearly at 5.9/2.3mN/mm2 , 12.4/5.3mN/mm2 , 22.2/9.7mN/mm2 , and 33.3/15.5mN/mm2 at each percentage strain increment respectively. After CCH treatment, peak and steady-state stress generation decreased to 3.2/1.2mN/mm2 , 6.5/2.9mN/mm2 , 12.2/5.7mN/mm2 , and 15.4/7.7mN/mm2 respectively (p < 0.004). Young's modulus decreased from 205 kPa to 100 kPa after CCH (p = 0.003). Steady-state Young's elastic modulus decreased from median (IQR) 205.4 (118.5) to 100.3 (64.0) after CCH treatment (p = 0.003). This preclinical ex vivo study provides proof of concept for the use of collagenase to decrease muscle stiffness in individuals with CP.

Elucidating the molecular determinants of force transmission in myosin ensembles using QCM-D.

Myosin II motors collectively produce force to facilitate muscle contraction via an ATP-mediated mechanochemical process, causing the motors to step along actin filaments. Such myosin II ensembles have been shown to display environment-based mechanosensitive abilities, where ensemble motor duty ratio can change in response to external signals, including force and local rigidity. However, at the single-molecule level, myosin II is non-processive; as such, it is becoming increasingly clear that myosin II motor ensembles do not behave as the sum of their single molecule properties. Interrogation of myosin motors within cytoskeletal filament networks in vitro is needed to understand how motors that crosslink multiple filaments know whether to be in a low duty ratio, non-processive mode as an individual molecule or in a high duty ratio, processive mode within ensembles. A quartz crystal microbalance with dissipation monitoring (QCM-D) is a powerful biophysical tool that can measure the kinetics and viscoelastic properties of protein complexes, films, and surface interactions. Here, we adapt in vitro cytoskeleton reconstitution assays to QCM-D experiments to investigate the assembly kinetics and viscoelastic properties of actomyosin bundles consisting of multiple myosin II motors acting between actin filaments. Actively monitoring the binding kinetics and stiffness of such bundles in real-time with the QCM-D as each element of the bundle assembles into the higher order actomyosin architecture will provide insight into the molecular-level drivers of mechanosensation and communication within the local cytoskeletal environment.

Fatigue life prediction of 3D braided carbon/carbon composites with braided angle variation at elevated temperature

The braiding angle of 3D braided carbon/carbon composites (C/CCs) will change during high temperature fatigue loading, which will affect the fatigue properties of 3D braided C/CCs. In order to realize this dynamic simulation in the high temperature fatigue life prediction of 3D braided C/CCs and further improve the prediction accuracy of high temperature fatigue life of 3D braided C/CCs, a high temperature fatigue life prediction model of 3D braided C/CCs considering the change of braiding angle with fatigue cycle number was established. The establishment of the prediction model mainly includes: a meso-scale representative volume elements (RVEs) of 3D braided C/CCs considering yarn direction and fiber bundle cross-section shape is established at the meso-scale; the high temperature residual stiffness and residual strength models of fiber bundles considering high temperature and stress level are established. Based on the experimental data characteristics of high temperature fatigue residual stiffness of 3D braided C/CCs, a mathematical model of cycle number/braided angles (CN/BAs) is established. The fatigue life prediction model was used to predict the 3D braided C/CCs at 700°C and stress levels of 87% and 85%. The results showed that the prediction error of single flower node was less than 5%. The fatigue life prediction error is less than two times the tolerance.

Morphometric Analysis of Anatomy of Anterior Cruciate Ligament of Knee and its Attachments - a Cadaveric Study in Indian Population.

Introduction:The Anterior Cruciate Ligament tends to stabilise the knee in various range of extension and flexion. Precise study of anatomy, attachments and position of bundles is important for successful ACL reconstruction. In our study, we attempt to assess general anatomy of ACL, determine and compare its morphometric data pertaining to length and width and its tibio-femoral foot prints in different gender and secondarily determine changes in the same during ACL dynamics witnessed during knee flexion changes.Materials and methods:A total of 19 knees from 10 cadavers were used in the research with mean age of 61±7 years. After dissecting the skin, muscles, patellar and articular capsule were removed and bundle attachments were studied. Thereafter the relative length, width and stiffness of ACL bundles at 0, 90, 140 (maximum) angles of knee flexion were measured along with maximum horizontal and vertical bundle footprints at tibio-femoral attachments were recorded.Results:Mean length and width of insertion of anteromedial (AM) bundle on the tibial surface was 8.8mm and 9.0mm in males and 8.1mm and 8.8mm in females. Furthermore, that of PL bundle was 9.1mm and 7.8mm in males and 8.9mm and 7.1mm in females.Conclusion:The anteromedial (AM) bundle and posterolateral (PL) bundle of ACL were found to be most relaxed at full extension and were most taut at maximum flexion of 140°. AM bundle underwent greater stretching and change of length in comparison to the PL bundle, indicating that it is comparatively a more dominant bundle.

The Effect of Posterior Lumbar Spinal Surgery on Biomechanical Properties of Rat Paraspinal Muscles 13 Weeks After Surgery.

Preclinical study in rodents. To investigate changes in biomechanical properties of paraspinal muscles following a posterior spinal surgery in an animal model. Posterior spine surgery damages paraspinal musculature per histological and imaging studies. The biomechanical effects of these changes are unknown. 12 Sprague-Dawley rats were divided equally into sham and surgical injury (SI) groups. For sham, the skin and lumbodorsal fascia were incised at midline. For SI, the paraspinal muscles were detached from the vertebrae, per normal procedure. Thirteen weeks postsurgery, multifidus and longissimus biopsies at L1, L3, and L5 levels were harvested on the right. From each biopsy, three fibers and three to six bundles of fibers (∼10-20 fibers ensheathed in their extracellular matrix) were tested mechanically to measure their passive elastic modulus. The collagen content and fatty infiltration of each biopsy were also examined histologically by immunofluorescence staining. Nonparametric statistical methods were used with a 1.25% level of significance. A total of 220 fibers and 279 bundles of fibers were tested. The elastic moduli of the multifidus and longissimus fibers and longissimus fiber bundles were not significantly different between the SI and sham groups. However, the elastic modulus of multifidus fiber bundles was significantly greater in the SI group compared to sham (SI median 82 kPa, range 23-284; sham median 38 kPa, range 23-50, P = 0.0004). The elastic modulus of multifidus fiber bundles in the SI group was not statistically different between spinal levels (P = 0.023). For histology, only collagen I deposition in multifidus was significantly greater in the SI group (median 20.8% vs. 5.8% for sham, P < 0.0001). The surgical injury increased the passive stiffness of the multifidus fiber bundles. Increased collagen content in the extracellular matrix is the likely reason and these changes may be important in the postoperative compensation of the spine.Level of Evidence: N/A.

An energy‐momentum space‐time discretization of a constrained micropolar continuum for 3D fiber‐reinforced composites

AbstractIn 2D fiber‐reinforced composites, single fibers with a diameter in the range of micrometers are embedded in a matrix material. 3D fiber‐reinforced composites consist of fiber bundles (rovings) with diameters of millimeters. Therefore, 3D fiber‐reinforced composites require an extended material modelling, because a fiber bundle has to be considered as a beam‐like structure with curvature‐twist (twisting and bending) stiffness. By means of an extended continuum formulation, we modell a micro inertia and a curvature‐twist stiffness. We introduce these secondary effects by means of independent drilling degrees of freedom. The resulting constrained micropolar continuum is derived by a mixed principle of virtual power. In the discrete setting, this variational principle generates a mixed B‐bar method and an energy‐momentum scheme. We show transient numerical examples, which demonstrate the effect of micro inertia as well as the twisting and bending stiffness of the fiber bundles.

Oligoether grafting on cellulose microfibers for dispersion in poly(propylene glycol) and fabrication of reinforced polyurethane composite

Application of cellulose microfibers as a reinforcing agent for high-performance polyurethane composites is rarely mentioned because the inherent hydrophilicity combined with the adverse aspect ratio of the fibers cause difficulties in dispersion within and compatibility with the polymer matrix. Here, we propose a feasible approach to graft oligoethers synthesized by ring-opening polymerization in a heterogeneous reaction to the cellulose microfiber surface. The oligomers composed of ether linkages and flexible hydroxyl groups provide cellulose fibers with good dispersity in poly(propylene glycol) and potential physical and chemical cross-linking points in reaction with isocyanates to form good interfacial adhesion between the fibers and the polyurethane matrix. Consequently, the tensile properties and viscoelasticity of the oligomer-grafted cellulose-filled polyurethane composite were enhanced compared with those of the neat elastomer and composite containing pristine cellulose microfibers. This reinforcement effect is attributed to the natural stiffness of the fiber bundles and the cross-linking network generated by the oligomers grafted on the fiber surface.

Fast recovery of disrupted tip links induced by mechanical displacement of hair bundles

Hearing and balance rely on the capacity of mechanically sensitive hair bundles to transduce vibrations into electrical signals that are forwarded to the brain. Hair bundles possess tip links that interconnect the mechanosensitive stereocilia and convey force to the transduction channels. A dimer of dimers, each of these links comprises two molecules of protocadherin 15 (PCDH15) joined to two of cadherin 23 (CDH23). The "handshake" that conjoins the four molecules can be disrupted in vivo by intense stimulation and in vitro by exposure to Ca2+ chelators. Using hair bundles from the rat's cochlea and the bullfrog's sacculus, we observed that extensive recovery of mechanoelectrical transduction, hair bundle stiffness, and spontaneous bundle oscillation can occur within seconds after Ca2+ chelation, especially if hair bundles are deflected toward their short edges. Investigating the phenomenon in a two-compartment ionic environment that mimics natural conditions, we combined iontophoretic application of a Ca2+ chelator to selectively disrupt the tip links of individual frog hair bundles with displacement clamping to control hair bundle motion and measure forces. Our observations suggest that, after the normal Ca2+ concentration has been restored, mechanical stimulation facilitates the reconstitution of functional tip links.

Growing Old Too Early: Skeletal Muscle Single Fiber Biomechanics in Ageing R349P Desmin Knock-in Mice Using the MyoRobot Technology.

Muscle biomechanics relies on active motor protein assembly and passive strain transmission through cytoskeletal structures. The desmin filament network aligns myofibrils at the z-discs, provides nuclear–sarcolemmal anchorage and may also serve as memory for muscle repositioning following large strains. Our previous analyses of R349P desmin knock-in mice, an animal model for the human R350P desminopathy, already depicted pre-clinical changes in myofibrillar arrangement and increased fiber bundle stiffness. As the effect of R349P desmin on axial biomechanics in fully differentiated single muscle fibers is unknown, we used our MyoRobot to compare passive visco-elasticity and active contractile biomechanics in single fibers from fast- and slow-twitch muscles from adult to senile mice, hetero- or homozygous for the R349P desmin mutation with wild type littermates. We demonstrate that R349P desmin presence predominantly increased axial stiffness in both muscle types with a pre-aged phenotype over wild type fibers. Axial viscosity and Ca-mediated force were largely unaffected. Mutant single fibers showed tendencies towards faster unloaded shortening over wild type fibers. Effects of aging seen in the wild type appeared earlier in the mutant desmin fibers. Our single-fiber experiments, free of extracellular matrix, suggest that compromised muscle biomechanics is not exclusively attributed to fibrosis but also originates from an impaired intermediate filament network.

Non-isothermal energy–momentum time integrations with drilling degrees of freedom of composites with viscoelastic fiber bundles and curvature–twist stiffness

3D fiber-reinforced composites demand for a special simulation technique, because they consist of fiber bundles. Therefore, in the corresponding representative volume element of these metamaterials, secondary effects as a micro inertia and a curvature–twist stiffness have to bear in mind. The latter increases the strength-to-weight ratio of thin-walled lightweight structures due to a separate twisting and bending stiffness of the fiber bundles. In this paper, these secondary effects are introduced in a continuum formulation by means of independent drilling degrees of freedom. The resulting non-isothermal constrained micropolar continuum is derived by a principle of virtual power, which simultaneously generates in the discrete setting a mixed B-bar method and a Galerkin-based energy–momentum scheme of higher order. This work also takes into account viscoelastic material behavior in the fiber bundles, which arises from a mixture of organic and inorganic fibers. Here, the viscous evolution equation is solved elementwise by using a mixed field as viscous internal variable. Representative numerical examples demonstrate the inelastic material behavior, the effect of micro inertia on the physical properties of the continuum as well as on its space and time discretization and, finally, the twisting and bending stiffness of the fiber bundles. Further, non-standard boundary conditions are applied in the dynamic simulations performed by higher order energy–momentum schemes.

Tks5 and Dynamin-2 enhance actin bundle rigidity in invadosomes to promote myoblast fusion.

Skeletal muscle development requires the cell-cell fusion of differentiated myoblasts to form muscle fibers. The actin cytoskeleton is known to be the main driving force for myoblast fusion; however, how actin is organized to direct intercellular fusion remains unclear. Here we show that an actin- and dynamin-2-enriched protrusive structure, the invadosome, is required for the fusion process of myogenesis. Upon differentiation, myoblasts acquire the ability to form invadosomes through isoform switching of a critical invadosome scaffold protein, Tks5. Tks5 directly interacts with and recruits dynamin-2 to the invadosome and regulates its assembly around actin filaments to strengthen the stiffness of dynamin-actin bundles and invadosomes. These findings provide a mechanistic framework for the acquisition of myogenic fusion machinery during myogenesis and reveal a novel structural function for Tks5 and dynamin-2 in organizing actin filaments in the invadosome to drive membrane fusion.

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.

Cochlear outer hair cell horizontal top connectors mediate mature stereocilia bundle mechanics.

Outer hair cell (OHC) stereocilia bundle deflection opens mechanoelectrical transduction channels at the tips of the stereocilia from the middle and short rows, while bundle cohesion is maintained owing to the presence of horizontal top connectors. Here, we used a quantitative noncontact atomic force microscopy method to investigate stereocilia bundle stiffness and damping, when stimulated at acoustic frequencies and nanometer distances from the bundle. Stereocilia bundle mechanics were determined in stereocilin-deficient mice lacking top connectors and with detached tectorial membrane (Strc -/-/Tecta -/- double knockout) and heterozygous littermate controls (Strc +/-/Tecta -/-). A substantial decrease in bundle stiffness and damping by ~60 and ~74% on postnatal days P13 to P15 was observed when top connectors were absent. Additionally, we followed bundle mechanics during OHC top connectors development between P9 and P15 and quantified the observed increase in OHC bundle stiffness and damping in Strc +/-/Tecta -/- mice while no significant change was detected in Strc -/-/Tecta -/- animals.

Atomistic Modeling of F-Actin Mechanical Responses and Determination of Mechanical Properties.

A molecular structural mechanics (MSM) model was developed for F-actins in cells, where the force constants describing the monomer interaction were achieved using molecular dynamics simulations. The MSM was then employed to predict the mechanical properties of F-actin. The obtained Young's modulus (1.92 GPa), torsional rigidity (2.36 × 10-26 Nm2), and flexural rigidity (10.84 × 10-26 Nm2) were found to be in good agreement with existing experimental data. Subsequently, the tension-induced bending was studied for F-actins as a result of their helical structure. Mechanical instability was also investigated for the actin filaments in filopodial protrusion by considering the reinforcing effect of the actin-binding proteins. The predicted buckling load agreed well with the experimentally obtained stall force, showing a pivotal role of the actin-binding protein in regulating the stiffness of F-actin bundles during the formation of filopodia protrusion. Herein, it is expected that the MSM model can be extended to the mechanics of more complex filamentous systems such as stress fibers and actin meshwork.

Mammalian Auditory Hair Cell Bundle Stiffness Affects Frequency Tuning by Increasing Coupling along the Length of the Cochlea

SUMMARYThe stereociliary bundles of cochlear hair cells convert mechanical vibrations into the electrical signals required for auditory sensation. While the stiffness of the bundles strongly influences mechanotransduction, its influence on the vibratory response of the cochlear partition is unclear. To assess this, we measured cochlear vibrations in mutant mice with reduced bundle stiffness or with a tectorial membrane (TM) that is detached from the sensory epithelium. We found that reducing bundle stiffness decreased the high-frequency extent and sharpened the tuning of vibratory responses obtained postmortem. Detaching the TM further reduced the high-frequency extent of the vibrations but also lowered the partition’s resonant frequency. Together, these results demonstrate that the bundle’s stiffness and attachment to the TM contribute to passive longitudinal coupling in the cochlea. We conclude that the stereociliary bundles and TM interact to facilitate passive wave propagation to more apical locations, possibly enhancing active wave amplification in vivo.

Cations Modulate Actin Bundle Mechanics, Assembly Dynamics, and Structure.

Actin bundles are key factors in the mechanical support and dynamic reorganization of the cytoskeleton. High concentrations of multivalent counterions promote bundle formation through electrostatic attraction between actin filaments that are negatively charged polyelectrolytes. In this study, we evaluate how physiologically relevant divalent cations affect the mechanical, dynamic, and structural properties of actin bundles. Using a combination of total internal reflection fluorescence microscopy, transmission electron microscopy, and dynamic light scattering, we demonstrate that divalent cations modulate bundle stiffness, length distribution, and lateral growth. Molecular dynamics simulations of an all-atom model of the actin bundle reveal specific actin residues coordinate cation-binding sites that promote the bundle formation. Our work suggests that specific cation interactions may play a fundamental role in the assembly, structure, and mechanical properties of actin bundles.

Elucidating the mechanism of the considerable mechanical stiffening of DNA induced by the couple Zn2+/Calix[4]arene-1,3-O-diphosphorous acid

The couple Calix[4]arene-1,3-O-diphosphorous acid (C4diP) and zinc ions (Zn2+) acts as a synergistic DNA binder. Silicon NanoTweezer (SNT) measurements show an increase in the mechanical stiffness of DNA bundles by a factor of >150, at Zn2+ to C4diP ratios above 8, as compared to Zinc alone whereas C4diP alone decreases the stiffness of DNA. Electroanalytical measurements using 3D printed devices demonstrate a progression of events in the assembly of C4diP on DNA promoted by zinc ions. A mechanism at the molecular level can be deduced in which C4diP initially coordinates to DNA by phosphate-phosphate hydrogen bonds or in the presence of Zn2+ by Zn2+ bridging coordination of the phosphate groups. Then, at high ratios of Zn2+ to C4diP, interdigitated dimerization of C4diP is followed by cross coordination of DNA strands through Zn2+/C4diP inter-strand interaction. The sum of these interactions leads to strong stiffening of the DNA bundles and increased inter-strand binding.

Single Actin Bundle Rheology.

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory.

Geometric Requirements for Tectorial Membrane Traveling Waves in the Presence of Cochlear Loads

Recent studies suggest that wave motions of the tectorial membrane (TM) play a critical role in determining the frequency selectivity of hearing. However, frequency tuning is also thought to be limited by viscous loss in subtectorial fluid. Here, we analyze effects of this loss and other cochlear loads on TM traveling waves. Using a viscoelastic model, we demonstrate that hair bundle stiffness has little effect on TM traveling waves calculated with physiological parameters, that the limbal attachment can cause small (<20%) increases in TM wavelength, and that viscous loss in the subtectorial fluid can cause small (<20%) decreases in TM wave decay constants. However, effects of viscous loss in the subtectorial fluid are significantly increased if TM thickness is decreased. In contrast, increasing TM thickness above its physiological range has little effect on the wave, suggesting that the TM is just thick enough to maximize the spatial extent of the TM traveling wave.