Relaxing Medium Research Articles

Fourier series solution of Burger’s equation for nonlinear acoustics in relaxing media

This paper modifies Burger’s equation, presented by previous authors, for nonlinear acoustics in relaxing media. Based on the forms of the Fourier series solution of the equation in the case of lossless media, the author solves successfully the extended Burger’s equation including various types of relaxation mechanisms. The solutions are obtained in the separate cases—before and after shock formation. It has been found that the results of previous authors can be derived from our solutions if certain approximations are made.

Myosin heavy chain and actin fractional rates of synthesis in normal and overload rat heart ventricles

The rates of synthesis (in per cent per day) of the total protein (ks) and myosin heavy chains (ke HC) and actin (ke A), isolated by preparative electrophoresis from myofibrils prepared in a relaxing medium, have been measured in rat heart ventricles after a continuous infusion of 50 microCi of (14C) Tyrosine (0.5 ml/h during 6 h). Normal values, in the sham-operated group, were for ks 19%, ke HC 23% and ke A 11%. Two to 4 days after an abdominal aortic stenosis there was an increase in the specific radioactivity of free plasma and intra-cellular tyrosine and of protein-bound tyrosine. The rate of synthesis also increased up to 37% for ks, 41% for ke HC and 21% for ke A but the ratio ke HC/ke A remained unchanged. We conclude that the normal heterogeneity of the rate of synthesis of the two main contractile proteins, at least when measured on myofibrils free from easily releasable myofilaments, was unmodified by cardiac overload, although both of these rates of synthesis were stimulated.

Damping of strong shocks in relaxing media

Damping of strong shocks in relaxing media

Effect of sodium gradient on the rate of relaxation of rat mesenteric small arteries from potassium contractures.

We have measured the relaxation of rat mesenteric small arteries (internal diameter ca. 200 micron) from a potassium contracture under conditions where the transplasmalemmal sodium gradient was altered. Adjustment of the sodium gradient was made either by exposing vessels to ouabain (1 mM) for different periods to vary the intracellular sodium concentration (Nai), or by varying the sodium concentrations of the relaxation solutions (Nao). Under normal conditions (where we have previously shown Nai is about 19 mM), vessels relaxed completely within 1 min in low sodium solutions (Nao = 25 mM) using either sucrose, choline-Cl or MgCl2 as substitutes. However, the relaxation (measured after 1 min) was reduced when sucrose substitution was used, and further experiments were made using this substitute. Here it was found that exposing vessels to ouabain, for example 90 min (thus increasing Nai to about 73 mM) and then performing the relaxation in a low sodium solution gave only about 50% relaxation after 1 min. Experiments with intermediate sodium concentrations in the relaxation medium showed that reduction to 100 mM had no significant effect on the relaxation, and that it was only below 50 mM that effects were most marked. The effects of altered sodium gradient were eliminated if the calcium concentration of the relaxation medium was zero. The results indicate that under normal physiological conditions, small changes in sodium gradient have little effect on calcium metabolism of rat mesenteric small arteries, but also that under extreme conditions net calcium extrusion does appear to be reduced by a reduced sodium gradient.

Propagation of small disturbances in concentrated dispersed systems

The mechanism of elastic pressure waves in concentrated dispersed systems is discussed. It is shown that the continuously relaxing medium model is valid for describing acoustic effects in a fluidized vibrating layer.

Non-uniform staining of myofibrila bands by a monoclonal antibody to skeletal muscle myosin S1 heavy chain

A monoclonal antibody specific for the S1 fragment of skeletal muscle myosin has been identified. The antibody does not inhibit actin-activated Mg 2+-ATPase or K +-EDTA-activated ATPase of myosin, indicating that it is not related to the portion of the S1 which carries the ATPase activity. In the absence of relaxing medium, antibody binding to the myosin filament is restricted to narrow regions on each side of the bare zone region of the filament, and to a narrow region at the tapered ends of the filament. This restricted antibody binding is not altered by the attachment of the myosin cross-bridges to the actin filaments. In the presence of relaxing medium, antibody binding occurs along the entire length of the cross-bridge-bearing region of the filament. The restricted binding to only small regions of the filament in the absence of relaxing medium suggests that the molecular packing of the myosin in different portions of the filament may be different, resulting in differences in the availability of the antigenic site on the S1 for antibody binding. The change in availability of the antigenic sites along the filament in the presence of relaxing medium may reflect a perturbation in the molecular packing of the filament, or a conformational change resulting from the binding of MgATP, both of which could affect the availability of the antigenic sites on the S1 for antibody.

Heat generation by ultrasound in a relaxing medium

It is shown that at any point P in a continuous sound field the time-averaged rate of heat generation by relaxational absorption per unit volume is given by αp02/ρc. Here p0 is the pressure amplitude at P while α is the absorption coefficient arising from relaxation when the coefficient of shear viscosity η is zero; ρ and c are, respectively, the density and velocity of sound in the medium. The result, a familiar one for plane traveling waves, is shown here to apply generally when η = 0.

Nonlinear dispersive waves in a relaxing medium

The dispersion of nonlinear waves in a relaxing medium is analysed by making use of the evolution equations for longitudinal waves. The dispersion relations are obtained and the behaviour of the waves compared to those that arise when they are governed by the well-known Korteweg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations that describe unidirectional motion and also by the time regularized long wave (TRLW) equation that describes bi-directional motion. The nonlinear steady wave solutions are obtained. The general mathematical model used throughout this paper is obtained by the theory of nonlinear elasticity with weak relaxation effects (standard viscoelasticity). A further generalization using a four-element model is also discussed briefly.

Hyperbolic diffusion equation in a relaxational and dispersed medium

Using an operator representation of the effective diffusion coefficient we obtain a hyperbolic diffusion equation in a relaxational medium.

Stretch and radial compression studies on relaxed skinned muscle fibers of the frog

The influence of stretch and radial compression on the width of mechanically skinned fibers from the semitendinosus muscle of the frog (R. pipiens) was examined in relaxing solutions with high-power light microscopy. Fibers were skinned under mineral oil. We find that, after correcting for water uptake in the oil, fiber width increased by an average of 28% upon transfer from oil to relaxing medium, with some tendency for greater swelling at longer sarcomere lengths. Subsequently, fibers were compressed by addition of the long-chain polymer polyvinylpyrrolidone (PVP-40, number average molecular weight 40,000) to relaxing solutions. Sarcomere length does not appear to be affected by addition of PVP. At any PVP concentration, the inverse square of the fiber width increased smoothly and linearly with increasing stretch for sarcomere lengths between 2.10 and 4.60 micrometer. At any fixed sarcomere length, fiber width decreased linearly with the logarithm of the osmotic compressive pressure exerted by PVP (2-10% concentration). From this logarithmic relation we estimate that the swelling pressure of the intact fiber is 3.40 x 10(3) N/m2, between that of a 2 and a 3% PVP solution. The pressure giving rise to fiber swelling is not due to dilation of the sarcoplasmic reticulum (SR), since the experimental results above were not significantly different after treatment with 0.5% BRIJ-58, a nonionic detergent that disrupts the SR. Swelling may be due simply to elastic structures within the fiber that are constrained in the intact cell. Values of bulk moduli of fibers, calculated from the compression experiments, and preliminary measurements of Young's modulus from stretch experiments, are quantitatively consistent with the idea that skinned fibers behave as nonisotropic elastic bodies.

Asymptotic solutions of model equations in nonlinear acoustics

This paper uses the method of matched asymptotic expansions to derive asymptotic solutions to various problems in nonlinear acoustics. Model equations, generalizing the well known Burgers equation to include effects of cylindrical or spherical spreading and of non-equilibrium relaxation, are given and regarded as governing the propagation. Solutions are sought for initial or boundary conditions of N-wave or harmonic wave form. For a thermoviscous medium, the small parameter upon which the asymptotic expansions are predicated is an inverse acoustic Reynolds number; for a relaxing medium it is the product of wave frequency and relaxation time. The complete asymptotic solution for N-waves in a thermoviscous fluid is known, in the case of plane motion, from the Cole—Hopf solution of Burgers’s equation. Here a similarly complete solution is found for spherical N-waves, with the exception of one region of space—time in which an irreducible nonlinear problem remains unsolved. In this region the outer limiting behaviour is, nevertheless, determined, so that the solutions in all other regions are completely fixed. For cylindrical N-waves an irreducible problem again results, but the motion can be followed right through into its ‘old age’ phase aside from an undetermined purely numerical constant. Correct results are obtained here for the ‘correction due to diffusivity' to the weak-shock theory prediction of shock centre location for plane, cylindrical and spherical N-waves. These results indicate a non-uniformity in weak shock theory at large times, and also, in the case of spherical N-waves, reveal a large time non-uniformity in the Taylor shock solution. Harmonic waves, plane, cylindrical and spherical, in thermoviscous fluids and relaxing fluids are considered, and the asymptotic solutions are found to leading order in most of the many overlapping asymptotic regions of space-time. A single dimensionless function remains undetermined in the important case of spherical harmonic waves. We have also been unable to find scalings and differential equations describing precisely how a discontinuity is formed at the front of a partly dispersed shock in a relaxing gas, though the shock centre is located for both fully and partly dispersed shocks. The harmonic wave solutions unify and extend certain solutions (the Fay, Fubini and old-age solutions) which are well known in the nonlinear acoustics literature, and the amplitude saturation and scaling laws for the old age regime are in accord with experiments on high amplitude spherical waves in water.

Structure of shock waves in elastoplastic relaxing media

Structure of shock waves in elastoplastic relaxing media

Aerodynamic sound in a relaxing medium

In this paper we formulate the aerodynamic sound problem for a relaxing medium in a rather general way, independent of the details of the relaxation process. The medium is characterized by an appropriate relaxation time τ0and by a frozen (af0) and an equilibrium (ae0) sound speed. The equation describing aerodynamic sound in such a medium is the familiar one describing acoustic waves in a non-equilibrium medium but subjected to aerodynamic sound sources expressed in terms of a frozen and an equilibrium form of the Lighthill stress tensor. The far-field result for both compact and non-compact sources in the frequency range ω [Gt ] τ0−1can be expressed as the ratio of far-field densities for the relaxing and non-relaxing propagation medium:\[ \frac{\rho}{\rho_L} = \exp\left[-\left(1-\frac{a^2_{e_0}}{a^2_{f_0}}\right)\frac{x}{2a_{f0}\tau_0}\right], \]wherexis the observation distance and the subscriptLstands for ‘Lighthill’. The result for the main radiated aerodynamic sound, which comes from sources in the range ω [Lt ] τ0−1, essentially propagates in a manner described by the lower-order equilibrium waves, the diffusive effects from the higher-order waves being small, and the result for compact sources is a restatement of Lighthill's result in terms of the equilibrium propagation speed with the source region identically in equilibrium. For non-compact sources the propagation is still given byae0but the source region is now understood to encompass relaxation effects, the details of which are left unspecified.

Swelling of Skinned Muscle Fibers of the Frog: Experimental Observations

Frog skeletal muscle fibers, mechanically skinned under water-saturated silicone oil, swell upon transfer to aqueous relaxing medium (60 mM KCl; 3 mM MgCl(2); 3 mM ATP; 4 mM EGTA; 20 mM Tris maleate; pH = 7.0; ionic strength 0.15 M). Their cross-sectional areas, estimated with an elliptical approximation, increase 2.32-fold (+/-0.54 SD). Sarcomere spacing is unaffected by this swelling. Addition of 200 mM sucrose to relaxing medium had no effect on fiber dimensions, whereas decreasing pH to 5.0 caused fibers to shrink nearly to their original (oil) size. Decreasing MgCl(2) to 0.3 mM caused fibers to swell 10%, and increasing MgCl(2) to 9 mM led to an 8% shrinkage. Increasing ionic strength to 0.29 M with KCl caused a 26% increase in cross-sectional area; decreasing ionic strength to 0.09 M had no effect. Swelling pressure was estimated with long-chain polymers, which are probably excluded from the myofilament lattice. Shrinkage in dextran T10 (number average mol wt 6,200) was transient, indicating that this polymer may penetrate into the fibers. Shrinkage in dextran T40 (number average mol wt 28,000), polyvinylpyrrolidone (PVP) K30 (number average mol wt 40,000) and dextran T70 (number average mol wt 40,300) was not transient, indicating exclusion. Maximal calcium-activated tension is decreased by 21% in PVP solutions and by 31% in dextran T40 solutions. Fibers were shrunk to their original size with 8 x 10(-2) g/cm(3) PVP K30, a concentration which, from osmometric data, corresponds to an osmotic pressure (II/RT) of 10.5 mM. As discussed in the text, we consider this our best estimate of the swelling pressure. We find that increasing ionic strength to 0.39 M with KCl decreases swelling pressure slightly, whereas decreasing ionic strength to 0.09 M has no effect. We feel these data are consistent with the idea that swelling arises from the negatively charged nature of the myofilaments, from either mutual filamentary repulsion or a Donnan-osmotic mechanism.

Rayleigh stability of shear flow in relaxing media

The stability of steady-state flow is considered in a medium with a nonlocal coupling between pressure and density. The equations for perturbations in such a medium are derived in the linear approximation. The results of numerical integration are given for shear motion. The stability of parallel layered flow in an inviscid homogeneous fluid has been studied for a hundred years. The mathematics for investigating an inviscid instability has been developed, and it has been given a physical interpretation. The first important results in flow stability of an incompressible fluid were obtained in the papers of Helmholtz, Rayleigh, and Kelvin [1] in the last century. Heisenberg [2] worked on this problem in the 1920's, and a series of interesting papers by Tollmien [3] appeared subsequently. Apparently one of the first problems in the stability of a compressible fluid was solved by Landau [4]. The first investigations on the boundary-layer stability of an ideal gas were carried out by Lees and Lin [5], and Dunn and Lin [6]. Mention should be made of a series of papers which have appeared quite recently [7–9]. In all the papers mentioned flow stability is investigated in the framework of classical single-phase hydrodynamics. Meanwhile, in recent years, the processes by which perturbations propagate in media with relaxation have been intensively studied [10–12].

Thick filaments and paramyosin of annelid muscles

Thick filaments from annelid muscle were observed by positive and negative staining of the glycerinated sample, which was homogenized in a relaxing medium containing ATP. The preservation of myosin on the filament surface was strictly related to very high concentration of ATP (12 m M .). The 144 A periodicity was scarcely visible. When the ATP in the homogenate was at low concentration (less than 3 m M ), the underlyng periodic structure of paramyosin appeared. Purified paramyosin cores (at low pH and high ionic strength) presented a striation with a 144 A pitch. The Bear-Selby net pattern was also present, even in a small number of filaments. Paramyosin was extracted and purified from fresh muscles of Lumbricus terrestris and Sipunculus nudus . The purified protein exibited a single peak in the ultracentrifuge, and the intrinsic sedimentation constant was 3.29 S for Lumbricus and 3.19 S for Sipunculus . After dialysis with divalent cations, paracrystals were obtained, most of which showed a 144 A periodicity; sometimes, paracrystals with a different band pattern appeared. In all tactoids observed a 48 A subperiod was evident, as in the native isolated cores.

Scanning Secondary Electron Microscopy of Myofibrils Using Transmission Techniques

When observing small objects such as cellular organelles by scanning electron microscopy, it is often valuable to use the techniques of transmission electron microscopy. The common practice of mounting and coating for SEM may not always be necessary. These possibilities are illustrated using vertebrate skeletal muscle myofibrils.Micrographs for this study were made using a Hitachi HFS-2 scanning electron microscope, with photographic recording usually done at 60 seconds per frame. The instrument was operated at 25 kV, with a specimen chamber vacuum usually better than 10-7 torr. Myofibrils were obtained from rabbit back muscle using the method of Zak et al. To show the component filaments of this contractile organelle, the myofibrils were partially disrupted by agitation in a relaxing medium. A brief centrifugation was done to clear the solution of most of the undisrupted myofibrils before a drop was placed on the grid. Standard 3 mm transmission electron microscope grids covered with thin carbon films were used in this study.

Fine structure of the thick filament in molluscan catch muscle

1. (1) Intact profiles of the thick filament from molluscan smooth muscle were observed by negative staining of the fresh sample, which was homogenized in a modified relaxing medium containing a high concentration of ATP. The surface of the thick filament showed clear projections of myosin heads in samples negatively stained immediately after homogenization. 2. (2) When the ATP in the homogenate was exhausted, myosin molecules bound to the surface of the thick filament were gradually removed and bound to suspended thin filaments, and the underlying periodic structure of the paramyosin core previously covered by the myosin molecules appeared. 3. (3) The profiles of the paramyosin core after complete elimination of surface myosin molecules were of two different types; the Bear-Selby net pattern type and the striated type with 14.5 run pitch. 4. (4) The thick filament was reconstructed under special conditions; myosin molecules bound to the surface of the paramyosin core or to paramyosin para-crystals appeared as projections. 5. (5) The actin-activated myosin ATPase activity, which was initiated by the addition of a mixture of ATP and actin to the myosin-paramyosin core complex, was increased slightly by increasing the ratio of paramyosin to actin plus myosin. 6. (6) The underlying striated pattern of the thick filament was revealed in sectioned material as a result of removal of myosin molecules from the surface of the core on exhaustion of ATP.

Nonlinear physical stress - strain relationship of cellular polymers and glass plastics under conditions of attenuating creep

The coupling equations of hard cellular polymers and glass plastics based on these are analyzed. The material is considered as an elastically relaxing medium for the case of small deformations. The physical relationship between the rubber-elastic stresses and strains is derived in explicit form for the case of attenuating creep and a uniform three-dimensional stressed state. The total deformations are described by the one-dimensional rheological model of a "typical body" with a reduced stress and an instantaneous elastic modulus, having the appropriately chosen viscosity of a non-Newtonian liquid.

Isolation and composition of thick filaments from rabbit skeletal muscle

A method has been developed for the isolation of thick filaments from rabbit skeletal muscle. We found that the thick filaments of this muscle are readily dispersed in the presence of a relaxing medium if the M and Z-line structures are first extracted in a low-salt solvent system. Thick filaments were separated from thin filaments by zone sedimentation in a 10% to 30% glycerol density gradient. The isolated filaments are homogeneous in length (1.5 to 1.6 μm) and retain the physical characteristics of these structures observed in sectioned muscle. Gel electrophoresis of thick filaments in the presence of sodium dodecyl sulfate showed a band of C-protein as well as bands with mobilities characteristic of the heavy and light chains of myosin. No other protein species was detected in these experiments. Thus our results provide evidence against the presence of a special protein component which would serve as the core of the skeletal thick filament structure. From the relative stain density of bands, the molar ratio of C-protein to myosin was estimated to be 1 to 5.8.