Effects of Mg2+ on Ca2+ release from sarcoplasmic reticulum of skeletal muscle fibres from yabby (crustacean) and rat

1. The role of myoplasmic [Mg2+] on Ca2+ release from the sarcoplasmic reticulum (SR) was examined in the two major types of crustacean muscle fibres, the tonic, long sarcomere fibres and the phasic, short sarcomere fibres of the fresh mater decapod crustacean Cherax: destructor (yabby) and in the fast-twitch rat muscle fibres using the mechanically skinned muscle fibre preparation. 2. A robust Ca2+-induced Ca2+-release (CICR) mechanism was present in both long and short sarcomere fibres and 1 mM Mg2+ exerted a strong inhibitory action on the XR Ca2+ release in both fibre types. 3. The XR displayed different properties with respect to Ca2+ loading in the long and the short sarcomere fibres and marked functional differences were identified with respect to Mg2+ inhibition between the two crustacean fibre types. Thus, in long sarcomere fibres, the submaximally loaded XR was able to release Ca2+ when [Mg2+] was lowered from 1 to 0.01 mw in the presence of 8 mM ATP(total) and in the virtual absence of Ca2+ (< 5 nM) even when the CICR was suppressed. In contrast, negligible Ca2+ was released from the submaximally loaded SR of short sarcomere yabby fibres when [Mg2+] was lowered from 1. to 0.01 mM under the same conditions as for the long sarcomere fibres. Nevertheless, the rate of XR Ca2+ release in short sarcomere fibres increased markedly when [Mg2+] was lowered in the presence of [Ca2+] approaching the normal resting levels (50-100 nM). 4. Rat fibres were able to release SR Ca2+ at a faster rate than the long sarcomere yabby fibres when [Mg2+] was lowered from 1 to 0.01 mM in the virtual absence of Ca2+ but, unlike with yabby fibres, the net rate of Ca2+ release was actually increased for conditions that were considerably less favourable to CICR. 5. In summary it is concluded that crustacean skeletal muscles have more that one functional type of Ca2+-release channels, that these channels display properties that are intermediate between those of mammalian skeletal and cardiac isoforms, that the inhibition exerted by Mg2+ at rest on the crustacean SR Ca2+-release channels must be removed during excitation-contraction coupling and that, unlike in crustacean fibres, CICR cannot play the major role in the activation of XR Ca2+-release channels in the rat skeletal muscle.

Tubular system volume changes in twitch fibres from toad and rat skeletal muscle assessed by confocal microscopy

The volume of the extracellular compartment (tubular system) within intact muscle fibres from cane toad and rat was measured under various conditions using confocal microscopy. Under physiological conditions at rest, the fractional volume of the tubular system (t-sys(Vol)) was 1.38 +/- 0.09% (n = 17),1.41 +/- 0.09% (n = 12) and 0.83 +/- 0.07% (n = 12) of the total fibre volume in the twitch fibres from toad iliofibularis muscle, rat extensor digitorum longus muscle and rat soleus muscle, respectively. In toad muscle fibres, the t-sys(Vol) decreased by 30% when the tubular system was fully depolarized and decreased by 15% when membrane cholesterol was depleted from the tubular system with methyl-beta-cyclodextrin but did not change as the sarcomere length was changed from 1.93 to 3.30 mum. There was also an increase by 30% and a decrease by 25% in t-sys(Vol) when toad fibres were equilibrated in solutions that were 2.5-fold hypertonic and 50% hypotonic, respectively. When the changes in total fibre volume were taken into consideration, the t-sys(Vol) expressed as a percentage of the isotonic fibre volume did actually decrease as tonicity increased, revealing that the tubular system in intact fibres cannot be compressed below 0.9% of the isotonic fibre volume. The results can be explained in terms of forces acting at the level of the tubular wall. These observations have important physiological implications showing that the tubular system is a dynamic membrane structure capable of changing its volume in response to the membrane potential, cholesterol depletion and osmotic stress but not when the sarcomere length is changed in resting muscle.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

Evaluation of elastic modulus and hardness of thin films by nanoindentation

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

A numerical study of effect of grain boundaries on elastic and plastic properties in nanocomposite materials

Nanocomposite materials have received considerable attention in recent years due to their novel properties. Grain boundaries are considered to play an important role in nanostructured materials. This work focuses on the finite element analysis of the effect of grain boundaries on the overall mechanical properties of aluminium/alumina composites. A grain boundary is incorporated into the commonly used unit cell model to investigate its effect on material properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the ''effective'' plastic property of the grain boundary is estimated. In addition, the strengthening mechanism is also discussed based on the Estrin-Mecking model.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

The plausibility of long-wavelength stress correlation or stress magnitude as a mechanism for precursory seismicity: Results from two simple elastic models

Observations of accelerating seismic activity prior to large earthquakes in natural fault systems have raised hopes for intermediate-term eartquake forecasting. If this phenomena does exist, then what causes it to occur? Recent theoretical work suggests that the accelerating seismic release sequence is a symptom of increasing long-wavelength stress correlation in the fault region. A more traditional explanation, based on Reid's elastic rebound theory, argues that an accelerating sequence of seismic energy release could be a consequence of increasing stress in a fault system whose stress moment release is dominated by large events. Both of these theories are examined using two discrete models of seismicity: a Burridge-Knopoff block-slider model and an elastic continuum based model. Both models display an accelerating release of seismic energy prior to large simulated earthquakes. In both models there is a correlation between the rate of seismic energy release with the total root-mean-squared stress and the level of long-wavelength stress correlation. Furthermore, both models exhibit a systematic increase in the number of large events at high stress and high long-wavelength stress correlation levels. These results suggest that either explanation is plausible for the accelerating moment release in the models examined. A statistical model based on the Burridge-Knopoff block-slider is constructed which indicates that stress alone is sufficient to produce accelerating release of seismic energy with time prior to a large earthquake.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3(rd) and 5(th) order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.