A closed-form structural model of planar fibrous tissue mechanics

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress–strain law.     

Nebulin Alters Cross-bridge Cycling Kinetics and Increases Thin Filament Activation: A NOVEL MECHANISM FOR INCREASING TENSION AND REDUCING TENSION COST*

Nebulin is a giant filamentous F-actin-binding protein (∼800 kDa) that binds along the thin filament of the skeletal muscle sarcomere. Nebulin is one of the least well understood major muscle proteins. Although nebulin is usually viewed as a structural protein, here we investigated whether nebulin plays a role in muscle contraction by using skinned muscle fiber bundles from a nebulin knock-out (NEB KO) mouse model. We measured force-pCa (−log[Ca²⁺]) and force-ATPase relations, as well as the rate of tension re-development (k_tr) in tibialis cranialis muscle fibers. To rule out any alterations in troponin (Tn) isoform expression and/or status of Tn phosphorylation, we studied fiber bundles that had been reconstituted with bacterially expressed fast skeletal muscle recombinant Tn. We also performed a detailed analysis of myosin heavy chain, myosin light chain, and myosin light chain 2 phosphorylation, which showed no significant differences between wild type and NEB KO. Our mechanical studies revealed that NEB KO fibers had increased tension cost (5.9 versus 4.4 pmol millinewtons⁻¹ mm⁻¹ s⁻¹) and reductions in k_tr (4.7 versus 7.3 s⁻¹), calcium sensitivity (pCa₅₀ 5.74 versus 5.90), and cooperativity of activation (n_H 3.64 versus 4.38). Our findings indicate the following: 1) in skeletal muscle nebulin increases thin filament activation, and 2) through altering cross-bridge cycling kinetics, nebulin increases force and efficiency of contraction. These novel properties of nebulin add a new level of understanding of skeletal muscle function and provide a mechanism for the severe muscle weakness in patients with nebulin-based nemaline myopathy.     

Sparse Solution of Fiber Orientation Distribution Function by Diffusion Decomposition

Fiber orientation is the key information in diffusion tractography. Several deconvolution methods have been proposed to obtain fiber orientations by estimating a fiber orientation distribution function (ODF). However, the L ₂ regularization used in deconvolution often leads to false fibers that compromise the specificity of the results. To address this problem, we propose a method called diffusion decomposition, which obtains a sparse solution of fiber ODF by decomposing the diffusion ODF obtained from q-ball imaging (QBI), diffusion spectrum imaging (DSI), or generalized q-sampling imaging (GQI). A simulation study, a phantom study, and an in-vivo study were conducted to examine the performance of diffusion decomposition. The simulation study showed that diffusion decomposition was more accurate than both constrained spherical deconvolution and ball-and-sticks model. The phantom study showed that the angular error of diffusion decomposition was significantly lower than those of constrained spherical deconvolution at 30° crossing and ball-and-sticks model at 60° crossing. The in-vivo study showed that diffusion decomposition can be applied to QBI, DSI, or GQI, and the resolved fiber orientations were consistent regardless of the diffusion sampling schemes and diffusion reconstruction methods. The performance of diffusion decomposition was further demonstrated by resolving crossing fibers on a 30-direction QBI dataset and a 40-direction DSI dataset. In conclusion, diffusion decomposition can improve angular resolution and resolve crossing fibers in datasets with low SNR and substantially reduced number of diffusion encoding directions. These advantages may be valuable for human connectome studies and clinical research.     

Microanatomy and ultrastructure of the foot of the infaunal bivalve Tegillarca granosa (Bivalvia: Arcidae)

In this study, the morphology and ultrastructure of the foot of Tegillarca granosa was compared with the bivalves from different habitats. The sediment of habitat of T. granosa is mostly a mixture of sand (68.93%) and mud (24.12%). The foot is wedge-shaped with multiple projections on the surface and covered with ciliary tufts. The epithelial layer is simple and composed of ciliated columnar epithelia and mucous cells. Although the mucous cells are distributed mostly in the epithelial layer, they are developed even in the connective tissues and muscle layers, and the mucous cells mostly contain acidic carboxylated mucosubstances. From the TEM observation, secretory cells are classified into three types. Type A secretory cell has a goblet form and is most widely distributed among the three types. Type B secretory cell has an oval form and the secretory granule has fibrous substance. Type C secretory cell has an elongated elliptic form and membrane-bounded secretory granules. The muscle fiber bundles are composed mainly of smooth muscle fibers. The smooth muscle fibers can be divided into two types. Type A muscle fibers have evenly distributed thick microfilaments between the thin microfilaments of cytoplasm. Type B muscle fiber has cluster of condensed microfilaments in the medulla cytoplasm while the cortical cytoplasm has loose distribution of thin microfilaments.     

Reduction of dimensionality in Bayesian nonlinear regression with a pharmacokinetic application

Application of Bayes's theorem to the analysis of nonlinear regression models is limited by numerical problems associated with calculation of integrals of functions of several variables. For k-parameter models that are linear in l of the parameters, a dimension-reduction procedure is described for factoring the posterior distribution into the product of a multivariate normal density and a function of k-l nonlinear parameters. Integrals can then be calculated with (k-l)-dimensional numerical integration. A four-parameter, two-compartment pharmacokinetic model of lidocaine disposition is analyzed using a change of variables in order to obtain a model that is linear in two parameters. It is shown that a Bayesian analysis, with reduction of dimensionality, applied to this model produces appropriate results with reasonable CPU-time requirements.     

A rapid assay for the binding of actinomycin to DNA.

The theory of countercurrent distribution (CCD) was reviewed and extended. The separation function for the fundamental distribution of CCD was presented in the form n = t²(αk₁+β)²/αk₁(β?1)² where n is the number of transfers, t the abscissa of the standard normal distribution, α = v_m/v₈ the phase ratio, β = k₁/k₂≥ 1 the separation factor, and k₁ the partition coefficient of the more radidly moving component; n was found to be minimal on the condition αk₁ = β. The separation function for the single withdrawal of CCD was obtained in the form N = u + 1 = t²{(αk₁ + 1)^1/2 + [β(αk₁ + β)]^1/2}²/(β ? 1)²+ 1, where N is the number of partition units. From this equation it appears that N is minimal when αk₁ = 0. Compared with the former separation functions presented in the literature, these separation functions have the advantage of giving directly the relationships among the phase ratio, the absolute partition coefficient, the separation factor, the resolution degree, and the number of transfers or partition units required. In addition, the dependencies of the elution volumes and the widths of the elution curves on α, β, and the partition coefficients were considered mathematically by means of differential calculus. The elution volumes were found to have minima at certain αk₁ values. The standard deviations, on the contrary, did not have minima in respect to αk₁. The theory presented can be used for selecting proper operating conditions while separating chemical compounds.     

Stochastic processes in particle-number fluctuations in an electron-photon shower

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k ₁,G(∞,¦α?β¦)=k ₂ (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled.     

Computational and experimental investigation of local stress fiber orientation in uniaxially and biaxially constrained microtissues

The orientation of cells and associated F-actin stress fibers is essential for proper tissue functioning. We have previously developed a computational model that qualitatively describes stress fiber orientation in response to a range of mechanical stimuli. In this paper, the aim is to quantitatively validate the model in a static, heterogeneous environment. The stress fiber orientation in uniaxially and biaxially constrained microscale tissues was investigated using a recently developed experimental system. Computed and experimental stress fiber orientations were compared, while accounting for changes in orientation with location in the tissue. This allowed for validation of the model, and additionally, it showed how sensitive the stress fiber orientation in the experimental system is to the location where it is measured, i.e., the heterogeneity of the stress fiber orientation. Computed and experimental stress fiber orientations showed good quantitative agreement in most regions. A strong local alignment near the locations where boundary conditions were enforced was observed for both uniaxially and biaxially constrained tissues. Excepting these regions, in biaxially constrained tissues, no preferred orientation was found and the distribution was independent of location. The stress fiber orientation in uniaxially constrained tissues was more heterogeneous, and stress fibers mainly oriented in the constrained direction or along the free edge. These results indicate that the stress fiber orientation in these constrained microtissues is mainly determined by the local mechanical environment, as hypothesized in our model, and also that the model is a valid tool to predict stress fiber orientation in heterogeneously loaded tissues.     

Cerebral microvessels contain a beta 2-adrenergic receptor

Cerebral microvessels isolated from cat forebrain contain a specific β-adrenergic-sensitive adenylate cyclase. Among various compounds tested, the most potent activator of enzyme activity is isoproterenol (k_a = 1.4 × 10^?7M), followed in order by epinephrine (k_a= 1.5 × 10^?6M), norepinephrine (k_a= 1.4 × 10^?5M) and phenylephrine (k_a> 3 × 10^?4M). Isoproterenol-stimulated enzyme activity is blocked by propranolol (k_i= 2.4 × 10^?9M, IPS 339 (k_i= 4 × 10^?9M), H35/25 (k_i = 1.2 × 10^?7M), atenolol (k_i= 5.9 × 10^?6M) and practolol (k_i= 1.8 × 10^?5M). These agonist and antagonist properties are quite similar to those demonstrated by β₂-adrenergic receptors and β₂-stimulated adenylate cyclase present in other tissues and indicate that the majority of adenylate cyclase-associated adrenergic receptors in cerebral microvessels are β₂. The findings are relevant to physiological studies of cerebral blood flow and vascular permeability.     

Quantitative analysis of single-molecule force spectroscopy on folded chromatin fibers

Single-molecule techniques allow for picoNewton manipulation and nanometer accuracy measurements of single chromatin fibers. However, the complexity of the data, the heterogeneity of the composition of individual fibers and the relatively large fluctuations in extension of the fibers complicate a structural interpretation of such force-extension curves. Here we introduce a statistical mechanics model that quantitatively describes the extension of individual fibers in response to force on a per nucleosome basis. Four nucleosome conformations can be distinguished when pulling a chromatin fiber apart. A novel, transient conformation is introduced that coexists with single wrapped nucleosomes between 3 and 7 pN. Comparison of force-extension curves between single nucleosomes and chromatin fibers shows that embedding nucleosomes in a fiber stabilizes the nucleosome by 10 k_BT. Chromatin fibers with 20- and 50-bp linker DNA follow a different unfolding pathway. These results have implications for accessibility of DNA in fully folded and partially unwrapped chromatin fibers and are vital for understanding force unfolding experiments on nucleosome arrays.     

Anisotropic microsphere-based approach to damage in soft fibered tissue

An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi-scale scheme and focusing on the directionally dependent behavior of these materials. For this purpose, a micro-structural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and discussed herein in order to test the model features. Finally, a clinical application with the material behavior obtained from actual experimental data is also presented.     

Molecular Modeling of the Misfolded Insulin Subunit and Amyloid Fibril

Insulin, a small hormone protein comprising 51 residues in two disulfide-linked polypeptide chains, adopts a predominantly α-helical conformation in its native state. It readily undergoes protein misfolding and aggregates into amyloid fibrils under a variety of conditions. Insulin is a unique model system in which to study protein fibrillization, since its three disulfide bridges are retained in the fibrillar state and thus limit the conformational space available to the polypeptide chains during misfolding and fibrillization. Taking into account this unique conformational restriction, we modeled possible monomeric subunits of the insulin amyloid fibrils using β-solenoid folds, namely, the β-helix and β-roll. Both models agreed with currently available biophysical data. We performed molecular dynamics simulations, which allowed some limited insights into the relative structural stability, suggesting that the β-roll subunit model may be more stable than the β-helix subunit model. We also constructed β-solenoid-based insulin fibril models and conducted fiber diffraction simulation to identify plausible fibril architectures of insulin amyloid. A comparison of simulated fiber diffraction patterns of the fibril models to the experimental insulin x-ray fiber diffraction data suggests that the model fibers composed of six twisted β-roll protofilaments provide the most reasonable fit to available experimental diffraction patterns and previous biophysical studies.     

Mechanical Response of Silk Crystalline Units from Force-Distribution Analysis

The outstanding mechanical toughness of silk fibers is thought to be caused by embedded crystalline units acting as cross links of silk proteins in the fiber. Here, we examine the robustness of these highly ordered β-sheet structures by molecular dynamics simulations and finite element analysis. Structural parameters and stress-strain relationships of four different models, from spider and Bombyx mori silk peptides, in antiparallel and parallel arrangement, were determined and found to be in good agreement with x-ray diffraction data. Rupture forces exceed those of any previously examined globular protein many times over, with spider silk (poly-alanine) slightly outperforming Bombyx mori silk ((Gly-Ala)_n). All-atom force distribution analysis reveals both intrasheet hydrogen-bonding and intersheet side-chain interactions to contribute to stability to similar extent. In combination with finite element analysis of simplified β-sheet skeletons, we could ascribe the distinct force distribution pattern of the antiparallel and parallel silk crystalline units to the difference in hydrogen-bond geometry, featuring an in-line or zigzag arrangement, respectively. Hydrogen-bond strength was higher in antiparallel models, and ultimately resulted in higher stiffness of the crystal, compensating the effect of the mechanically disadvantageous in-line hydrogen-bond geometry. Atomistic and coarse-grained force distribution patterns can thus explain differences in mechanical response of silk crystals, opening up the road to predict full fiber mechanics.     

Cotton Fiber Cell Walls of Gossypium hirsutum and Gossypium barbadense Have Differences Related to Loosely-Bound Xyloglucan

Cotton fiber is an important natural textile fiber due to its exceptional length and thickness. These properties arise largely through primary and secondary cell wall synthesis. The cotton fiber of commerce is a cellulosic secondary wall surrounded by a thin cuticulated primary wall, but there were only sparse details available about the polysaccharides in the fiber cell wall of any cotton species. In addition, Gossypium hirsutum (Gh) fiber was known to have an adhesive cotton fiber middle lamella (CFML) that joins adjacent fibers into tissue-like bundles, but it was unknown whether a CFML existed in other commercially important cotton fibers. We compared the cell wall chemistry over the time course of fiber development in Gh and Gossypium barbadense (Gb), the two most important commercial cotton species, when plants were grown in parallel in a highly controlled greenhouse. Under these growing conditions, the rate of early fiber elongation and the time of onset of secondary wall deposition were similar in fibers of the two species, but as expected the Gb fiber had a prolonged elongation period and developed higher quality compared to Gh fiber. The Gb fibers had a CFML, but it was not directly required for fiber elongation because Gb fiber continued to elongate rapidly after CFML hydrolysis. For both species, fiber at seven ages was extracted with four increasingly strong solvents, followed by analysis of cell wall matrix polysaccharide epitopes using antibody-based Glycome Profiling. Together with immunohistochemistry of fiber cross-sections, the data show that the CFML of Gb fiber contained lower levels of xyloglucan compared to Gh fiber. Xyloglucan endo-hydrolase activity was also higher in Gb fiber. In general, the data provide a rich picture of the similarities and differences in the cell wall structure of the two most important commercial cotton species.     

Biaxial tensile testing and constitutive modeling of human supraspinatus tendon

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon's two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R(2) ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.     

Galα1→4Gal-glycans are expressed on myofibrillar associated proteins

There is evidence that glycans carrying terminal galactose residues are differently expressed in the sarcoplasm of different muscle fiber types. In this study monoclonal antibodies directed against P blood group antigens P^k: Galα1–4Galβ1–4Glcβ- and P₁: Galα1–4Galβ1–4GlcNAcβ- were used to detect terminal α-galactosylated glycoconjugates on muscle proteins. Electrotransfer of proteins, extracted from human masseter and biceps muscles, to nitrocellulose after polyacrylamide gel electrophoresis (PAGE) and incubation with anti-P^k (CD77) consistently showed two bands with apparent molecular weights of 66 kDa and 64 kDa. In fresh frozen muscle sections from some humans there was endothelial reaction with anti-CD77 in capillaries, venules and veins but not in arterioles and arteries. In muscle samples from other humans there was no staining of endothelial cells. Formalin-fixed human muscle displayed a CD77 reaction with highest accumulation of reaction product at the periphery of the fibers. This may be explained by the presence of P^k glycoconjugates on intermediate filaments in muscle fibers. In preparations of cat masseter muscle proteins the antibodies against P₁P^k antigens reacted with a 170 kDa and a 55 kDa band while in preparations of cat biceps brachii only a 55 kDa band was reactive. The specificities of the antibodies were investigated by fluorescence-activated cell sorter (FACS), α- and β-galactosidase digestion and inhibitory sugars. This study indicates that glycans carrying Galα1–4Galβ1- epitopes are expressed on myofibrillar associated proteins.