Elastic Extension Research Articles

Proline Periodicity Modulates the Self-Assembly Properties of Elastin-Like Polypeptides

Elastin is a self-assembling protein of the extracellular matrix that provides tissues with elastic extensibility and recoil. The monomeric precursor, tropoelastin, is highly hydrophobic yet remains substantially disordered and flexible in solution, due in large part to a high combined threshold of proline and glycine residues within hydrophobic sequences. In fact, proline-poor elastin-like sequences are known to form amyloid-like fibrils, rich in β-structure, from solution. On this basis, it is clear that hydrophobic elastin sequences are in general optimized to avoid an amyloid fate. However, a small number of hydrophobic domains near the C-terminus of tropoelastin are substantially depleted of prolines. Here we investigated the specific contribution of proline number and spacing to the structure and self-assembly propensities of elastin-like polypeptides. Increasing the spacing between proline residues significantly decreased the ability of polypeptides to reversibly self-associate. Characterization of the assembly process revealed the presence of smaller colloidal droplets with enhanced propensity to cluster into dense networks, enriched in β-structure. These data strongly support a model where proline-poor regions of the elastin monomer provide a unique contribution to assembly, and suggest a role for localized β-sheet in mediating self-assembly interactions.

Proline Periodicity Modulates the Self-assembly Properties of Elastin-like Polypeptides

Elastin is a self-assembling protein of the extracellular matrix that provides tissues with elastic extensibility and recoil. The monomeric precursor, tropoelastin, is highly hydrophobic yet remains substantially disordered and flexible in solution, due in large part to a high combined threshold of proline and glycine residues within hydrophobic sequences. In fact, proline-poor elastin-like sequences are known to form amyloid-like fibrils, rich in β-structure, from solution. On this basis, it is clear that hydrophobic elastin sequences are in general optimized to avoid an amyloid fate. However, a small number of hydrophobic domains near the C terminus of tropoelastin are substantially depleted of proline residues. Here we investigated the specific contribution of proline number and spacing to the structure and self-assembly propensities of elastin-like polypeptides. Increasing the spacing between proline residues significantly decreased the ability of polypeptides to reversibly self-associate. Real-time imaging of the assembly process revealed the presence of smaller colloidal droplets that displayed enhanced propensity to cluster into dense networks. Structural characterization showed that these aggregates were enriched in β-structure but unable to bind thioflavin-T. These data strongly support a model where proline-poor regions of the elastin monomer provide a unique contribution to assembly and suggest a role for localized β-sheet in mediating self-assembly interactions.

A highly elastic tissue sealant based on photopolymerised gelatin

Gelatin is widely used as a medical biomaterial because it is readily available, cheap, biodegradable and demonstrates favourable biocompatibility. Many applications require stabilisation of the biomaterial by chemical crosslinking, and this often involves derivatisation of the protein or treatment with cytotoxic crosslinking agents. We have previously shown that a facile photochemical method, using blue light, a ruthenium catalyst and a persulphate oxidant, produces covalent di-tyrosine crosslinks in resilin and fibrinogen to form stable hydrogel biomaterials. Here we show that various gelatins can also be rapidly crosslinked to form highly elastic (extension to break >650%) and adhesive (stress at break >100 kPa) biomaterials. Although the method does not require derivatisation of the protein, we show that when the phenolic (tyrosine-like) content of gelatin is increased, the crosslinked material becomes resistant to swelling, yet retains considerable elasticity and high adhesive strength. The reagents are not cytotoxic at the concentration used in the photopolymerisation reaction. When tested in vivo in sheep lung, the photopolymerised gelatin effectively sealed a wound in lung tissue from blood and air leakage, was not cytotoxic and did not produce an inflammatory response. The elastic properties, thermal stability, speed of curing and high tissue adhesive strength of this photopolymerised gelatin, offer considerable improvement over current surgical tissue sealants.

Morphogenetic bases and parametric system of trichome evolution in plants of the genus Draba L.

Using quantitative morphological analysis of light microscopy data, the normal variation of trichome morphogenesis is studied in six whitlow grass species (Draba L.) and the morphological variation of adult trichomes in 11 species. The evolution consists in the transition from a radial morphogenesis pattern to bilateral and replacement of complex (branched) trichome rays with simple (unbranched) rays. A parametric system is constructed for classification of the ray morphology; this system includes two parameters-the ratio of the numbers of complex to simple rays, characterizing the probability of secondary branching of primary buds, and the number of primary buds, characterizing the probability of primary branching on the surface of the trichome cell. In this parametric space, all of the studied species fit well a third-order curve consisting of two ascending branches displaying a positive correlation between the primary and secondary branchings and a descending branch, located between them, where the primary and secondary branches are negatively correlated. The deduced evolutionary direction is almost independent of the size of the trichome cells and is explained exclusively by the mechanics of morphogenesis: acceleration in the development of the primary bud of the ray decreases the probability of its own branching and creates additional elastic extension of the cell surface, preventing other buds from branching. The morphogenesis itself appears to be a mechanically nonholonomic system, filtering in a selective manner the fluctuations of the same sign, which explains the directed pattern of its evolution. In the evolutionarily initial state, trichome ontogenesis is absent because its modules (primary buds) are formed by a mirror duplication. The ontogenesis commences when mirror symmetry in the formation of modules is lost and replaced with an axial pattern; thus, the change in the morphological type of buds is a direct consequence of the emergence of ontogenesis and its further evolution. Its main material is intraindividual variation, the only source of which is the mechanics of morphogenesis itself. It is found that morphological evolution can take place at an initially zero heritability and zero adaptive value of morphological differences.

Elasticity and Rupture of a Multi-Domain Neural Cell Adhesion Molecule Complex

The neural cell adhesion molecule (NCAM) plays an important role in nervous system development. NCAM forms a complex between its terminal domains Ig1 and Ig2. When NCAM of cell A and of cell B connect to each other through complexes Ig12(A)/Ig12(B), the relative mobility of cells A and B and membrane tension exerts a force on the Ig12(A)/Ig12(B) complex. In this study, we investigated the response of the complex to force, using steered molecular dynamics. Starting from the structure of the complex from the Ig1-Ig2-Ig3 fragment, we first demonstrated that the complex, which differs in dimensions from a previous structure from the Ig1-Ig2 fragment in the crystal environment, assumes the same extension when equilibrated in solvent. We then showed that, when the Ig12(A)/Ig12(B) complex is pulled apart with forces 30–70 pN, it exhibits elastic behavior (with a spring constant of ∼0.03 N/m) because of the relative reorientation of domains Ig1 and Ig2. At higher forces, the complex ruptures; i.e., Ig12(A) and Ig12(B) separate. The interfacial interactions between Ig12(A) and Ig12(B), monitored throughout elastic extension and rupture, identify E16, F19, K98, and L175 as key side chains stabilizing the complex.

A novel methodology to explore the viscoelasticity of spider major ampullate silk.

Even before material science was a recognized discipline, the amazing mechanical properties of spider silk were documented and became the object of much study. In addition to the exceptional material properties of spider silk and the reported low immunogenicity, its concatenated amino acid motif arrangement facilitates a distinct possibility of manipulating the silk to create a designer biomaterial for medical applications. Crystalline protein regions imbedded in a mobile protein matrix give it a distinct set of viscoelastic abilities. Consequently, elasticity cannot be simply quantified by only measuring extensibility. To understand how the sequence of the major ampullate proteins affects elasticity, the hysteresis of single fibers from two different species, Argiope aurantia and Nephila clavipes, were examined using cyclic loading and unloading. The yield point that discriminates a transition from elastic extension to a plastic extension was analyzed by examining three different properties: Young's modulus, energy recovery and slack in the fiber after recovery. Young's modulus remained relatively constant regardless of the cycle. However, the energy recovered decreased as the slack and cycle number increased. Large standard deviations masked any quantitative differences between species and substantiated the necessity of developing synthetic silk to harness the amazing mechanical properties of spider silk.

Suppression of oscillations of piston-aided wind tunnels

The method chosen to compensate for the forces acting on the barrel in the course of compression and confinement of the test gas in the settling chamber of a hypersonic wind tunnel with a free locking piston is justified. A method is proposed to compensate for the effect of adverse factors by optimizing the mass of an auxiliary piston introduced into the system. The effectiveness of the method is validated experimentally. As a result, for the case of gas compression to 200 MPa, the displacement of the center of mass of the barrel is reduced from 50 to 0.25 mm, which is smaller than the amplitude of elastic axial extension corresponding to the maximum pressure of the gas.

A NEW REGISTRATION METHOD BASED ON LOG-EUCLIDEAN TENSOR METRICS AND ITS APPLICATION TO GENETIC STUDIES.

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation (or strain) tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

Energetics of Hydrophobic Matching in Lipid-Protein Interactions

Lipid chain length modulates the activity of transmembrane proteins by mismatch between the hydrophobic span of the protein and that of the lipid membrane. Relative binding affinities of lipids with different chain lengths are used to estimate the excess free energy of lipid-protein interaction that arises from hydrophobic mismatch. For a wide range of integral proteins and peptides, the energy cost is much less than the elastic penalty of fully stretching or compressing the lipid chains to achieve complete hydrophobic matching. The chain length dependences of the free energies of lipid association are described by a model that combines elastic chain extension with a free energy term that depends linearly on the extent of residual mismatch. The excess free energy densities involved lie in the region of 0.5–2.0kBT.nm−2. Values of this size could arise from exposure of hydrophobic groups to polar portions of the lipid or protein, but not directly to water, or alternatively from changes in tilt of the transmembrane helices that are energetically comparable to those activating mechanosensitive channels. The influence of hydrophobic mismatch on dimerization of transmembrane helices and their transfer between lipid vesicles, and on shifts in chain-melting transitions of lipid bilayers by incorporated proteins, is analyzed by using the same thermodynamic model. Segmental order parameters confirm that elastic lipid chain distortions are insufficient to compensate fully for the mismatch, but the dependence on chain length with tryptophan-anchored peptides requires that the free energy density of hydrophobic mismatch should increase with increasing extent of mismatch.

STRESS RELAXATION BEHAVIOR OF MICROWAVE‐VACUUM‐DRIED ALGINATE GELS

ABSTRACT Swelling of alginate polymer matrix in water involves a build up of network pressure due to an elastic extension of the polymeric matrix. When this network pressure undergoes relaxation by means of dehydration, shrinkage may take place. Three different types of wet alginate gels were prepared and dried using microwave‐vacuum‐drying technique. Dried alginate gel solids had a porous structure. To understand the stress relaxation behavior of alginate gel‐based porous solid structures, uniaxial compressive relaxation studies were performed at selected strain rates, preloads and relaxation times Experimental relaxation curves were normalized and fitted to an empirical relationship, and relaxation behavior was explained. Stress relaxation data were also fitted to another empirical model. All three types of gels had similar elastic components. At lower strain rate, all samples had more resistance to elastic deformation. Stress relaxation information of the dried gel was related to its microstructure. Type 2 gel had more stiffness than type 1 and type 3 gels. The mechanism involved in stress relaxation was entanglement coupling of larger polymer chains in covalently cross‐linked alginate gels.

Biophysical constraints on leaf expansion in a tall conifer

The physiological mechanisms responsible for reduced extension growth as trees increase in height remain elusive. We evaluated biophysical constraints on leaf expansion in old-growth Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) trees. Needle elongation rates, plastic and elastic extensibility, bulk leaf water (Psi(L)) and osmotic (Psi(pi)) potential, bulk tissue yield threshold and final needle length were characterized along a height gradient in crowns of > 50-m-tall trees during the period between bud break and full expansion (May to June). Although needle length decreased with increasing height, there was no height-related trend in leaf plastic extensibility, which was highest immediately after bud break (2.9%) and declined rapidly to a stable minimum value (0.3%) over a 3-week period during which leaf expansion was completed. There was a significant positive linear relationship between needle elongation rates and plastic extensibility. Yield thresholds were consistently lower at the upper and middle crown sampling heights. The mean yield threshold across all sampling heights was 0.12 +/- 0.03 MPa on June 8, rising to 0.34 +/- 0.03 MPa on June 15 and 0.45 +/- 0.05 MPa on June 24. Bulk leaf Psi(pi) decreased linearly with increasing height at a rate of 0.004 MPa m(-1) during the period of most rapid needle elongation, but the vertical osmotic gradient was not sufficient to fully compensate for the 0.015 MPa m(-1) vertical gradient in Psi(L), implying that bulk leaf turgor declined at a rate of about 0.011 MPa m(-1) increase in height. Although height-dependent reductions in turgor appeared to constrain leaf expansion, it is possible that the impact of reduced turgor was mitigated by delayed phenological development with increasing height, which resulted in an increase with height in the temperature during leaf expansion.

Least‐squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity

AbstractThe objective of this work is to discuss a least‐squares finite element method with applications to physically nonlinear and anisotropic constitutive equations at small strains. The L2‐norm minimization of the residuals of the given first order system of differential equations leads to a functional, which is a two field formulation in the displacements and the stresses, see e.g. Cai & Starke [1]. These functionals provide the foundation for the formulations of the related least‐squares mixed finite elements. A main focus of the presentation lies on the extension of plane elasticity to anisotropic or nonlinear material behavior. In this context transversely isotropic elasticity and viscoplasticity is considered. Finally a numerical example is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Antitrust and Competition in Two-Sided Markets

This article extends antitrust analysis to two-sided markets in which a virtual monopolist competes with local bricks-and-mortar dealers. The discussion examines the market power of an Internet market maker as well as an Internet matchmaker. The analysis shows that equilibrium in a two-sided market can be characterized as a one-sided market in which transaction demand depends on the bid-ask spread of the central market maker. This allows for a straightforward extension of critical demand elasticity and critical loss analysis from one-sided markets to two-sided markets, with antitrust tests based on the hypothetical monopolist's bid-ask spread. Antitrust analysis of a one-sided market also carries over to a two-sided market with a matchmaker where antitrust tests are based on the sum of participation fees.

Determinants of force rise time during isometric contraction of frog muscle fibres.

Force-velocity (F-V) relationships were determined for single frog muscle fibres during the rise of tetanic contraction. F-V curves obtained using isotonic shortening early in a tetanic contraction were different from those obtained at equivalent times with isovelocity shortening, apparently because changing activation early in the contraction leads, in isovelocity experiments, to changing force and changing series elastic extension. F-V curves obtained with isotonic and with isovelocity shortening are similar if the shortening velocity in the isovelocity trials is corrected for series elastic extension. There is a progressive shift in the scaling of force-velocity curves along the force axis during the course of the tetanic rise, reflecting increasing fibre activation. The time taken for F-V curves to reach the steady-state position was quite variable, ranging from about 50 ms after the onset of contraction (1-3 degrees C) to well over 100 ms in different fibres. The muscle force at a fixed, moderately high shortening velocity relative to the force at this velocity during the tetanic plateau was taken as a measure of muscle activation. The reference velocity used was 60% of the maximum shortening velocity (V(max)) at the tetanic plateau. The estimated value of the fractional activation at 40 ms after the onset of contraction was used as a measure of the rate of activation. The rate of rise of isometric tension in different fibres was correlated with the rate of fibre activation and with V(max) during the plateau of the tetanus. Together differences in rate of activation and in V(max) accounted for 60-80% of the fibre-to-fibre variability in the rate of rise of isometric tension, depending on the measure of the force rise time used. There was not a significant correlation between the rate of fibre activation and V(max). The steady-state F-V characteristics and the rate at which these characteristics are achieved early in contraction are seemingly independent. A simulation study based on F-V properties and series compliance in frog muscle fibres indicates that if muscle activation were instantaneous, the time taken for force to rise to 50% of the plateau value would be about 60% shorter than that actually measured from living fibres. Thus about 60% of the force rise time is a consequence of the time course of activation processes and about 40% represents time taken to stretch series compliance by activated contractile material.

Steady mechanics of layered, multi-band belt drives used in continuously variable transmissions (CVT)

The steady mechanics of multi-layered metal belts used in metal-pushing continuously variable transmissions (CVT) are examined where the thin individual bands are modeled as axially moving strings. For each band, the main characteristics of classic flat belt models, such as band inertia, tension/speed constitutive law and elastic extension, are retained. Relative speeds between the layered bands and between the innermost band and the pulleys transfer the driving torque via friction between the contacting surfaces. The friction, tension and speed distributions in the individual bands are obtained by a boundary value problem (BVP) solver-based method. Load sharing among the multiple bands is investigated. This model is useful for belt fatigue life analysis and to guide the design of such multi-layered belts, given that one of the main failure modes of metal-pushing CVT is premature breakage of one or more of the layered steel bands.

Wedge and twist disclinations in second strain gradient elasticity

The aim of this paper is to study disclinations in the framework of a second strain gradient elasticity theory. This second strain gradient elasticity has been proposed based on the first and second gradients of the strain tensor by Lazar et al. [Lazar, M., Maugin, G.A., Aifantis, E.C., 2006. Dislocations in second strain gradient elasticity. Int. J. Solids Struct. 43, 1787–1817]. Such a theory is an extension of the first strain gradient elasticity [Lazar, M., Maugin, G.A., 2005. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int. J. Eng. Sci. 43, 1157–1184] with triple stress. By means of the stress function method, the exact analytical solutions for stress and strain fields of straight disclinations in an infinitely extended linear isotropic medium have been found. An important result is that the force stress, double stress and triple stress produced by wedge and twist disclinations are nonsingular. Meanwhile, the corresponding elastic strain and its gradients are also nonsingular. Analytical results indicate that the second strain gradient theory has the capacity of eliminating all unphysical singularities of physical fields.

Identifying cytoplasmic input to the cell wall of growing Chara corallina

Plants enlarge mostly because the walls of certain cells enlarge, with accompanying input of wall constituents and other factors from the cytoplasm. However, the enlargement can occur without input, suggesting an uncertain relationship between cytoplasmic input and plant growth. Therefore, the role of the input was investigated by quantitatively comparing growth in isolated walls (no input) with that in living cells (input occurring). Cell walls were isolated from growing internodes of Chara corallina and filled with pressurized oil to control turgor pressure while elongation was monitored. Turgor pressure in living cells was similarly controlled and monitored by adding/removing cell solution. Temperature was varied in some experiments. At all pressures and temperatures, isolated walls displayed turgor-driven growth indistinguishable in every respect from that in living cells, except the rate decelerated in the isolated walls while the living cells grew rapidly. The growth in the isolated walls was highly responsive to temperature, in contrast to the elastic extension that has been shown to be insensitive to similar temperatures. Consequently, strong intermolecular bonds were responsible for growth and weak bonds for elastic extension. Boiling the walls gave the same results, indicating that enzyme activities were not controlling these bonds. However, pectin added to isolated walls reversed their growth deceleration and returned the rate to that in the living cells. The pectin was similar to that normally produced by the cytoplasm and deposited in the wall, suggesting that continued cytoplasmic input of pectin may play a role in sustaining turgor-driven growth in Chara.

Fibrin Fibers Have Extraordinary Extensibility and Elasticity

Blood clots perform an essential mechanical task, yet the mechanical behavior of fibrin fibers, which form the structural framework of a clot, is largely unknown. By using combined atomic force-fluorescence microscopy, we determined the elastic limit and extensibility of individual fibers. Fibrin fibers can be strained 180% (2.8-fold extension) without sustaining permanent lengthening, and they can be strained up to 525% (average 330%) before rupturing. This is the largest extensibility observed for protein fibers. The data imply that fibrin monomers must be able to undergo sizeable, reversible structural changes and that deformations in clots can be accommodated by individual fiber stretching.

Ultrastructural pathology of aortic dissections in patients with Marfan syndrome:: Comparison with dissections in patients without Marfan syndrome

Despite the discovery in 1990 that mutations in the fibrillin-1 gene cause the Marfan syndrome, the pathogenesis of the life-threatening dissections associated with this disease is far from elucidated. Both the massive number of known fibrillin-1 mutations that result in a heterogeneous patient population and the strongly heterogeneous histology of patients' aortae presumably contribute to this lack of knowledge. We performed a detailed ultrastructural immunoelectron microscopic and histochemical analysis of the dissected media of ascending aortae of 10 patients with Marfan syndrome and compared them with those of 6 patients without Marfan syndrome and 77 individuals without known aortic disease. Relatively similar abnormalities were found in both patient groups, although they were more numerous and more diffusely spread in the patients with Marfan syndrome than in the patients without Marfan syndrome. The most conspicuous ultrastructural defects were the formation of abrupt transverse tears in thick and compact elastic lamellae and the local breaking up of smooth muscle cell–elastic lamella connections (that largely consist of microfibrils and elastic extensions, protruding from the elastic lamellae). This breaking up was characterized by a strongly reduced number of microfibrils and a severe shortening of the elastic extensions. Finally, the elastic extensions detached from the lamellae to ultimately degenerate and disappear. These changes were found mainly in the oldest group of patients with Marfan syndrome, indicating that they represented a loss of previously normally developed structures. We also compared our findings with those from a recently developed murine Marfan model (Pereira L, Lee SY, Gayraud B, Andrilopoulos K, Shapiro SD, Bunton T, Biery NJ, Dietz HC, Sakai LY, Ramirez F. Pathogenetic sequence for aneurysm revealed in mice underexpressing fibrillin-1. Proc Natl Acad Sci. U. S. A. 1999: 96: 3819–3823). Next to similarities, several striking differences existed, demonstrating that this model is not fully representative of the human Marfan syndrome.

Orthodontic latex elastics: a force relaxation study.

The objectives of this study were to assess the force relaxation of latex elastics occurring within 24 hours of extension and to estimate the extension required to reach the reported force. Five specimens of various manufacturers' latex elastics size and force levels were mounted on a custom-made setup capable of monitoring force levels in real time with a continuous mode and without operator intervention. The percentage of force relaxation was estimated from the initial and 24-hour levels, and the results were analyzed with one-way analysis of variance and the Tukey test at alpha = 0.05 level of significance. The elastics showed force relaxation in the order of 25%, which consisted of an initial high slope component and a latent part of decreased rate. Most relaxation occurred within the first 3-5 hours after extension, regardless of size, manufacturer, or force level of the elastic. The overall as well as the initial relaxation curves were fitted to equations, which described the variation of force with time. Elastic extension to achieve the reported force was found to range between 2.7 and five times the original length. Latex elastics show force relaxation in the order of 25%, which consists of an initial high slope component and a latent part of decreased rate. Most relaxation occurs within the first 3-5 hours after extension, regardless of size, manufacturer, or force level of the elastic. The empirical rule of "3" shows remarkable variation, ranging from 2.7 to five.