Elastic behavior of zymogen granule membranes in response to changes in pH and pCa.

In the process of secretion, the membrane of secretory granules is expected to change its elastic behavior. Elastic modulus of the membrane of zymogen granules, prepared from the rat pancreas acinar cell, was measured by an osmotic swelling method. The elastic modulus of the granule membrane at pCa 8 reduced from the maximal value of 230 dyn/cm at pH 6.0 to almost zero at pH 7.5. In a cytosol of an acinar cell, calcium ions play an important role as a second messenger in secretion. The elastic modulus of the granule membrane reduced in a sigmoidal fashion at pCa between 7.0 and 6.0. This range of pCa corresponds to a physiological rise of free Ca2+ concentrations in the cell cytosol when stimulated by external secretagogues. Reduction of the elastic modulus indicates that the state of the granule membrane switches to a more flexible one in which the granule is easy to appose to the cell plasma membrane and then swell as a final step of exocytosis.     

Effect of solute permeability in determination of elastic modulus using the vesicular swelling method.

The modulus of elasticity of artificial and biological membranes can be determined in membrane vesicles by monitoring the limitation of vesicular swelling during a slow decrease in medium tonicity. The higher the elastic modulus of the membrane, the more effectively the vesicles will resist swelling. This method assumes that the solutes in the system are impermeant, so that the final volume of the vesicles is determined solely by a balance of osmotic and hydrostatic forces. In this paper, we present the results of computer simulation of vesicular swelling in which the solute permeability of the membrane was varied. We find that even a small permeability will lead to a loss of solute from the vesicle that will retard the increase in vesicular volume during dilution of the medium, and thereby cause the apparent modulus of elasticity to be much greater than the true value. For example, if one takes the mannitol permeability in brush border membrane vesicles from small intestine to be 0.004 micron/s (a reasonable estimate), one finds that a vesicular swelling study using mannitol as the principal solute will show the apparent elastic modulus of the vesicles to be greater than 10 times larger than the true value. With higher permeabilities, the effect is even more dramatic. We conclude that determination of impermeance of solutes is a critical prerequisite for making valid determinations of membrane elastic modulus using the vesicular swelling method.     

Hypotonic Challenge of Endothelial Cells Increases Membrane Stiffness with No Effect on Tether Force

Regulation of cell volume is a fundamental property of all mammalian cells. Multiple signaling pathways are known to be activated by cell swelling and to contribute to cell volume homeostasis. Although cell mechanics and membrane tension have been proposed to couple cell swelling to signaling pathways, the impact of swelling on cellular biomechanics and membrane tension have yet to be fully elucidated. In this study, we use atomic force microscopy under isotonic and hypotonic conditions to measure mechanical properties of endothelial membranes including membrane stiffness, which reflects the stiffness of the submembrane cytoskeleton complex, and the force required for membrane tether formation, reflecting membrane tension and membrane-cytoskeleton attachment. We find that hypotonic swelling results in significant stiffening of the endothelial membrane without a change in membrane tension/membrane-cytoskeleton attachment. Furthermore, depolymerization of F-actin, which, as expected, results in a dramatic decrease in the cellular elastic modulus of both the membrane and the deeper cytoskeleton, indicating a collapse of the cytoskeleton scaffold, does not abrogate swelling-induced stiffening of the membrane. Instead, this swelling-induced stiffening of the membrane is enhanced. We propose that the membrane stiffening should be attributed to an increase in hydrostatic pressure that results from an influx of solutes and water into the cells. Most importantly, our results suggest that increased hydrostatic pressure, rather than changes in membrane tension, could be responsible for activating volume-sensitive mechanisms in hypotonically swollen cells.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

The existence of molecular water pumps in the nervous system: a review of the evidence

Recently, the presence if both influx and efflux molecular water pumps (MWP's) in vertebrate cells has been reported. These appear to use a common mechanism; the intercompartmental cotransport of water uphill against a gradient as a hydrophylic osmolyte is transported down its own gradient, in a regulated fashion, by a membrane spanning cotransporter protein. In each case, the dwell time of the transported osmolyte is short in that it is metabolically converted and its products either eliminated or recycled, thereby maintaining the required high intercompartmental gradient. An influx water pump osmolyte has been identified as a sodium-glucose complex, and an efflux water pump osmolyte as N-acetylhistidine. These osmolytes may also be archetypal representatives of many other osmolytes with similar functions in a variety of cells. When recycled, the osmolyte metabolites appear to be dewatered during high affinity binding that is associated with their active transport back across the membrane prior to intracellular resynthesis of the osmolyte. Since these cyclical systems result in the pumping of water, they also appear to create a previously unrecognized motive force which results in the establishment of unidirectional transcellular water flows between apical and basolateral cell membranes. As neurons represent highly specialized forms of animal cells, and cells which are also extremely sensitive to changes in osmotic pressure, the presence of these water pumps in the CNS could be significant. There would be connotations with regard to how neurons regulate water balance and transaxonal flow as well as to how these factors affect the integrated function of the nervous system. In this article, evidence of the presence of MWP's in the nervous system, and how they might relate to aspects of both normal and abnormal brain function is reviewed.     

Comparison of the Osmolyte Transport Properties Induced by trAE1 versus IClswell in Xenopus Oocytes

During cell swelling, cells release organic osmolytes via a volume-activated channel as part of the regulatory volume decrease. The erythrocyte membrane protein AE1 (band 3), has been shown to be involved in regulatory volume responses of fish erythrocytes. Previous studies showed that the expression of trout AE1 in Xenopus laevis oocytes induces band 3 anion exchange activity and organic osmolyte channel activity. However, an endogenous swelling-activated anion channel, IClswell, is present in Xenopus oocyte membranes. Therefore, it is not yet known whether a new organic osmolyte channel is formed or whether the endogenous channel, IClswell, is activated when trout AE1 is expressed in the oocytes. The purpose of this study was to determine whether the expression of trout AE1 in Xenopus oocytes leads to the formation and membrane insertion of a new organic osmolyte channel or activates IClswell. To differentiate between the two possibilities, we compared the time courses, pH profiles and inhibitor sensitivities of both trout AE1 and IClswell. The results of taurine-uptake experiments show that the time courses and pH levels for optimum expression of trout AE1 and IClswell differ significantly. The inhibitor sensitivities of the organic osmolyte channel mediated by trout AE1 and IClswell are also significantly different, strongly suggesting that the expression of trout AE1 in Xenopus oocytes does not activate IClswell, but rather forms a new organic osmolyte channel.     

Regulation of cell volume via microvillar ion channels

A novel mechanism of cellular volume regulation is presented, which ensues from the recently introduced concept of transport and ion channel regulation via microvillar structures (Lange K, 1999, J Cell Physiol 180:19-35). According to this notion, the activity of ion channels and transporter proteins located on microvilli of differentiated cells is regulated by changes in the structural organization of the bundle of actin filaments in the microvillar shaft region. Cells with microvillar surfaces represent two-compartment systems consisting of the cytoplasm on the one side and the sum of the microvillar tip (or, entrance) compartments on the other side. The two compartments are separated by the microvillar actin filament bundle acting as diffusion barrier ions and other solutes. The specific organization of ion and water channels on the surface of microvillar cell types enables this two-compartment system to respond to hypo- and hyperosmotic conditions by activation of ionic fluxes along electrochemical gradients. Hypotonic exposure results in swelling of the cytoplasmic compartment accompanied by a corresponding reduction in the length of the microvillar diffusion barrier, allowing osmolyte efflux and regulatory volume decrease (RVD). Hypertonic conditions, which cause shortening of the diffusion barrier via swelling of the entrance compartment, allow osmolyte influx for regulatory volume increase (RVI). Swelling of either the cytoplasmic or the entrance compartment, by using membrane portions of the microvillar shafts for surface enlargement, activates ion fluxes between the cytoplasm and the entrance compartment by shortening of microvilli. The pool of available membrane lipids used for cell swelling, which is proportional to length and number of microvilli per cell, represents the sensor system that directly translates surface enlargements into activation of ion channels. Thus, the use of additional membrane components for osmotic swelling or other types of surface-expanding shape changes (such as the volume-invariant cell spreading or stretching) directly regulates influx and efflux activities of microvillar ion channels. The proposed mechanism of ion flux regulation also applies to the physiological main functions of epithelial cells and the auxiliary action of swelling-induced ATP release. Furthermore, the microvillar entrance compartment, as a finely dispersed ion-accessible peripheral space, represents a cellular sensor for environmental ionic/osmotic conditions able to detect concentration gradients with high lateral resolution. Volume regulation via microvillar surfaces is only one special aspect of the general property of mechanosensitivity of microvillar ionic pathways.     

Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman-Hodgkin-Katz equation

Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling’s adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.     

Change in membrane elastic modulus on activation of glucose transport system of brush border membrane vesicles studied by osmotic swelling and dynamic light scattering.

The cell membrane having a transport system is inferred to be flexible when its function is being activated. For the brush border membrane vesicles prepared from rat small intestine, which have the co-transport system of Na+ and glucose, the membrane elasticity was measured as a function of the d-glucose concentration in the presence of Na+ ions. The elastic modulus of the vesicle membrane was obtained by an osmotic swelling method. Osmolality was changed by diluting the extravesicular d-mannitol concentration. The change in the diameter of the membrane vesicle in response to an osmolality change was measured by the dynamic light-scattering method. The elastic modulus of the vesicle membrane decreased from 150 dyn/cm to 80 (45) dyn/cm with the increase of d-glucose, from 0 mM to 10(30) mM in the presence of 10 mM Na+ ions. On the other hand, in the presence of 1 mM phlorizin, a glucose-transport inhibitor, the elastic modulus remained at a constant value of 160 dyn/cm in the same range of the d-glucose concentration. This indicates that the vesicle membrane becomes flexible when its transport function is activated. In a broad osmolality range, the brush border membrane vesicle showed cycles of "swell-burst-reseal". The vesicle membrane became flexible after every cycle, namely, the modulus was 150, 120, and 55 in units of dyn/cm in the presence of 1 mM d-glucose and 50 mM Na+ ions.     

Temperature dependence of the viscoelastic recovery of red cell membrane.

The time-dependent recovery of an elongated red cell is studied as a function of temperature. Before release, the elongated cell is in static equilibrium where external forces are balanced by surface elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of a viscoelastic solid material undergoing large ("finite") deformation. The recovery process is characterized by a time constant, tc, that decreases from approximately 0.27 s at 6 degrees C to 0.06 s at 37 degrees C. From this measurement of the time constant and an independent measurement of the shear modulus of surface elasticity for red cell membrane, the value for the membrane surface viscosity as a function of temperature can be calculated.     

Statistical-mechanical theory of passive transport through partially sieving or leaky membranes

The basic equations for multicomponent transport through partially sieving or leaky membranes are discussed from a statistical-mechanical viewpoint. They have the same mathematical form as the corresponding equations for open membranes, but differ in a discontinuous way from the equations for semipermeable membranes (since a "leak" in a semipermeable membrane constitutes a discontinuous or singular perturbation). Partially sieving membranes can be made to mimic semipermeable behavior through the introduction of characteristic time scales. They may approximate semipermeable behavior at short times, but always deviate at longer times.     

Theoretical and experimental exclusion of errors in the determination of the elasticity and water transport parameters of plant cells by the pressure probe technique

The volumetric elastic modulus of the cell wall and the hydraulic conductivity of the cell membranes were measured on ligatured compartments of different sizes of Chara corallina internodes using the pressure probe technique. The ratio between intact cell surface area and the area of puncture in the cell wall and membrane introduced by the microcapillary of the pressure probe was varied over a large range by inserting microcapillaries of widely varying diameters in different sized compartments. The relationship of the elastic modulus and the hydraulic conductivity to turgor pressure was independent of the ratio of intact cell surface area to the area of injury. The increase in the hydraulic conductivity below 2 bar turgor pressure and the volume dependence of the elastic modulus were shown to be the same as those observed in intact nonligatured cells. Theoretical considerations of the possible influence of injury of the cell wall and cell membrane around the inserted microcapillary on the measurement of the water transport and cell wall parameters do not explain the experimental findings. Thus, mechanical artifacts, if at all present, are too small to account for the observed dependence of the hydraulic conductivity and the elastic modulus on turgor pressure. The pressure probe technique thus represents an accurate method for measuring water transport parameters in both giant algal cells and in tissue cells of higher plants.     

Epithelial cell volume modulation and regulation

Summary Epithelial cell volume is a sensitive indicator of the balance between solute entry into the cell and solute exit. Solute accumulation in the cell leads to cell swelling because the water permeability of the cell membranes is high. Similarly, solute depletion leads to cell shrinkage. The rate of volume change under a variety of experimental conditions may be utilized to study the rate and direction of solute transport by an epithelial cell. The pathways of water movement across an epithelium may also be deduced from the changes in cellular volume. A technique for the measurement of the volume of living epithelial cells is described, and a number of experiments are discussed in which cell volume determination provided significant new information about the dynamic behavior of epithelia. The mechanism of volume regulation of epithelial cells exposed to anisotonic bathing solution is discussed and shown to involve the transient stimulation of normally dormant ion exchangers in the cell membrane.     

Osmotic flow in membrane pores of molecular size

Water transfer by osmosis through pores occurs either by viscous flow or diffusion depending on whether the driving osmolyte is able to enter the pore. Analysis of osmotic permeabilities (P _os )measured in antibiotic and cellular pore systems supports this distinction, showing that P _os approaches either the viscous value (P _f ) or the diffusive value (P _d )depending on the size of the osmolyte in relation to the pore radius. Macroscopic hydrodynamics and diffusion theory, when used with drag and steric coefficients within an appropriate osmotic model, apply with remarkable accuracy to channels of molecular dimensions where water molecules cannot pass each other, without the need to postulate any special flow regimes. It becomes apparent that the true viscous to diffusive flow ratio, P _f /P _d , can be separated from the effects of tracer filing by osmotic measurements alone. It does not monotonically decrease with the pore radius but rises steeply at the smaller radii which would apply to pores in cell membranes. Consequently, the application of the theory to osmotic and diffusive flow data for the red cell predicts a pore radius of 0.2 nm in agreement with other recent measurements on isolated components of the system, showing that the viscous-diffusive distinction applies even in molecular pores.     

Adhesivity and rigidity of erythrocyte membrane in relation to wheat germ agglutinin binding

Binding of the plant lectin wheat germ agglutinin (WGA) to erythrocyte membranes causes membrane rigidification. One of our objectives has been to directly measure the effects of WGA binding on membrane rigidity and to relate rigidification to the kinetics and levels of WGA binding. Our other objective has been to measure the strength of adhesion and mechanics of cell separation for erythrocytes bound together by WGA. The erythrocyte membrane rigidity was measured on single cells by micropipette aspiration. The slope of the suction pressure-length data for entry into the pipette provided the measure of the membrane extensional modulus. Data were collected for cells equilibrated with WGA solutions in the range of concentrations of 0.01- 10 micrograms/ml. Erythrocyte-erythrocyte adherence properties were studied by micropipette separation of two-cell aggregates. First, a "test" cell was selected from a WGA solution by aspiration into a small micropipette, then transferred to a separate chamber that contained erythrocytes in WGA-free buffer. Here, a second cell was aspirated with another pipette and maneuvered into close proximity of the test cell surface, and adhesive contact was produced. The flaccid cell was separated from the test cell surface in steps at which the force of attachment was derived from the pipette suction pressure and cell geometry. In addition, we measured the time-dependent binding and release of fluorescently labeled WGA to single erythrocytes with a laser microfluorometry system. The results showed that the stiffening of the erythrocyte membrane and binding of fluorescently labeled WGA to the membrane surface followed the same concentration and time dependencies. The threshold concentration for membrane stiffening was at approximately 0.1 microgram/ml where the time course to reach equilibrium was close to 1 h. The maximal stiffening (almost 30-fold over the normal membrane elastic modulus) occurred in concentrations greater than 2 micrograms/ml where the time to reach equilibrium took less than 1 min. The WGA binding also altered the normal elastic membrane behavior into an inelastic, plastic-like response which indicated that mechanical extension of the membrane caused an increase in cross-linking within the surface plane. Similar to the stiffening effect, we observed that the membrane adhesivity of cells equilibrated with WGA solutions greatly increased with concentration greater than 0.1 microgram/ml.(ABSTRACT TRUNCATED AT 400 WORDS)     

Osmotic flow caused by polyelectrolytes

Osmotic flow of water caused by high concentrations of anionic polyelectrolytes across semipermeable membranes, permeable only to solvent and simple electrolyte, has been measured in a newly designed flow cell. The flow cell features small solution and solvent compartments and an efficient stirring mechanism. We have demonstrated that, while the osmotic pressure of the anionic polyelectrolytes is determined primarily by micro-counterions, the osmotic flow is determined by solution-dependent properties as embodied in the hydrodynamic frictional coefficient which is determined by the polymer backbone segment of the polyelectrolyte. The variation of the osmotic permeability coefficient, L(p)(o), with concentration and osmotic pressure closely correlated with the concentration dependence of this frictional coefficient. These studies confirm previous work that the kinetics of osmotic flow across a membrane impermeable to the osmotically active solute is primarily determined by the diffusive mobility of the solute.     

The Structure of the Mitochondrial Membrane: Inferences from Permeability Properties

Mitochondria possess a semipermeable membrane with properties similar to the cell membrane. Despite the presence of a limiting membrane, mitochondria swell approximately 4 to 5 times their original volume without lysis or loss of internal solute. For this reason, it has been argued that the membrane might be convoluted. The present kinetic study of the permeability of isolated mitochondria was undertaken to clarify this question. A photometric method described previously was used. In the case of highly lipid soluble penetrants, the results suggest that neither the permeability nor the surface area available for penetration varies significantly during considerable swelling. These results may be interpreted to mean that the mitochondrial membrane is convoluted. For highly polar compounds, the permeability of the membrane also remains unchanged during swelling, but the surface area available to penetration increases. These results may be interpreted to mean that in this latter case, the surface of the convolutions becomes available only after they are unfolded by swelling. The simplest model that can explain the permeability properties of this membrane consists of a bimolecular lipid layer where the inner monomolecular layer is convoluted.     

Elasticity of synthetic phospholipid vesicles and submitochondrial particles during osmotic swelling

A rapid and accurate method has been developed for measuring the elastic response of vesicle bilayer membranes to an applied osmotic pressure. The technique of dynamic light scattering is used to measure both the elastic constant and the elastic limit of dioleoylphosphatidic acid (DOPA) and DOPA-cholesterol vesicles and of submitochondrial particles derived from the inner membrane of bovine heart mitochondria. The vesicles prepared by the pH-adjustment method are unilamellar and of uniform size between 240 and 460 nm in diameter. The vesicles swell uniformly upon dilution. The observed change in size is not due to any change in the shape of the vesicles. The data also indicate that the vesicles are spherical and not flaccid. The total vesicle swelling in these studies resulted in a 3-4% increase in surface area for vesicles swollen in 0.15 M KCl and a 5-10% increase in surface area for vesicles swollen in 0.25 M sucrose. This maximum represents the elastic limit of the vesicles. Evidence is presented to show that the vesicles release contents after swelling to this maximum, reseal immediately, and reswell according to the osmotic pressure. For DOPA vesicles in a 0.15 M KCl-tris(hydroxymethyl)aminomethane hydrochloride (Tris-HCl) buffer (pH 7.55), the observed membrane modulus is found to be in the range of 10(8) dyn/cm2. The modulus was found to be in the order of 10(7) dyn/cm2 for DOPA vesicles in a 0.25 M sucrose-Tris-HCl buffer (pH 7.55). This is comparable to that of submitochondrial particles in the same sucrose-Tris-HCl buffer. The observed membrane modulus also decreases with vesicle size. Its magnitude and its variation with ionic strength indicate that the major component of bilayer elasticity is neither the inherent elasticity of the bilayer nor the bending modulus. The variation of the membrane modulus with respect to curvature suggests that its principal component may be related to surface tension effects including the negative charges on the vesicle surface. There is considerable variation between vesicles swollen in sucrose and those swollen in KCl in the membrane modulus, in the elastic limit at which the vesicles burst, and in the transbilayer pressure difference at bursting. The latter was found to be 4-6 mosM (10(5) dyn/cm2) in sucrose solution and 20-4 mosM (10(6) dyn/cm2) in KCl solution.     

A biophysical analysis of stem and root diameter variations in woody plants

A comprehensive model of stem and root diameter variation was developed. The stem (or root) was represented using two coaxial cylinders corresponding with the mature xylem and the extensible tissues. The extensible tissues were assumed to behave as a single cell separated from the mature xylem by a virtual membrane. The mature xylem and the extensible tissues are able to dilate with temperature and grow. Moreover, the extensible tissues are able to shrink and swell according to water flow intensity. The model is mainly based on the calculation of water volume flows in the "single cell" that are described using the principles of irreversible thermodynamics. The elastic response to storage volume and plastic extension accompanying growth are described. The model simulates diameter variation due to temperature, solute accumulation, and xylem, water potential. The model was applied to the peach (Prunus persica) stem and to the plum (Prunus domestica x Prunus spinosa) root. The simulation outputs corresponded well with the diameter variation observed. The model predicts that variations of turgor pressure and osmotic potential are smaller than the variations of xylem water potential. It also demonstrates correlations between the xylem water potential, the turgor pressure, the elastic modulus, and the osmotic potential. The relationship between the diameter and the xylem water potential exhibits a substantial hysteresis, as observed in field data. A sensitivity analysis using the model parameters showed that growth and shrinkage were highly sensitive to the initial values of the turgor pressure and to the reflection coefficient of solutes. Shrinkage and growth were sensitive to elastic modulus and wall-yielding threshold pressure, respectively. The model was not sensitive to changes in temperature.     

Red cell extensional recovery and the determination of membrane viscosity.

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.