Direct measurement of osmotic pressure of glycosaminoglycan solutions by membrane osmometry at room temperature

Articular cartilage is a hydrated soft tissue composed of negatively charged proteoglycans fixed within a collagen matrix. This charge gradient causes the tissue to imbibe water and swell, creating a net osmotic pressure that enhances the tissue's ability to bear load. In this study we designed and utilized an apparatus for directly measuring the osmotic pressure of chondroitin sulfate, the primary glycosaminoglycan found in articular cartilage, in solution with varying bathing ionic strength (0.015 M, 0.15 M, 0.5 M, 1 M, and 2 M NaCl) at room temperature. The osmotic pressure (pi) was found to increase nonlinearly with increasing chondroitin sulfate concentration and decreasing NaCl ionic bath environment. Above 1 M NaCl, pi changes negligibly with further increases in salt concentration, suggesting that Donnan osmotic pressure is negligible above this threshold, and the resulting pressure is attributed to configurational entropy. Results of the current study were also used to estimate the contribution of osmotic pressure to the stiffness of cartilage based on theoretical and experimental considerations. Our findings indicate that the osmotic pressure resulting from configurational entropy is much smaller in cartilage (based on an earlier study on bovine articular cartilage) than in free solution. The rate of change of osmotic pressure with compressive strain is found to contribute approximately one-third of the compressive modulus (H(A)(eff)) of cartilage (Pi approximately H(A)(eff)/3), with the balance contributed by the intrinsic structural modulus of the solid matrix (i.e., H(A) approximately 2H(A)(eff)/3). A strong dependence of this intrinsic modulus on salt concentration was found; therefore, it appears that proteoglycans contribute structurally to the magnitude of H(A), in a manner independent of osmotic pressure.     

Effects of polycationic drug carriers on the electromechanical and swelling properties of cartilage

Cationic nanocarriers offer a promising solution to challenges in delivering drugs to negatively charged connective tissues, such as to articular cartilage for the treatment of osteoarthritis (OA). However, little is known about the effects that cationic macromolecules may have on the mechanical properties of cartilage at high interstitial concentrations. We utilized arginine-rich cationic peptide carriers (CPCs) with varying net charge (from +8 to +20) to investigate the biophysical mechanisms of nanocarrier-induced alterations to cartilage biomechanical properties. We observed that CPCs increased the compressive modulus of healthy bovine cartilage explants by up to 70% and decreased the stiffness of glycosaminoglycan-depleted tissues (modeling OA) by 69%; in both cases, the magnitude of the change in stiffness correlated with the uptake of CPC charge variants. Next, we directly measured CPC-induced osmotic deswelling in cartilage tissue due to shielding of charge repulsions between anionic extracellular matrix constituents, with magnitudes of reductions between 36 and 64 kPa. We then demonstrated that electrostatic interactions were required for CPC-induced stiffening to occur, evidenced by no observed increase in tissue stiffness when measured in hypertonic bathing salinity. We applied a non-ideal Donnan osmotic model (under triphasic theory) to separate bulk modulus measurements into Donnan and non-Donnan components, which further demonstrated the conflicting charge-shielding and matrix-stiffening effects of CPCs. These results show that cationic drug carriers can alter tissue mechanical properties via multiple mechanisms, including the expected charge shielding as well as a novel stiffening phenomenon mediated by physical linkages. We introduce a model for how the magnitudes of these mechanical changes depend on tunable physical properties of the drug carrier, including net charge, size, and spatial charge distribution. We envision that the results and theory presented herein will inform the design of future cationic drug-delivery systems intended to treat diseases in a wide range of connective tissues.     

The influence of the fixed negative charges on mechanical and electrical behaviors of articular cartilage under unconfined compression

Unconfined compression test has been frequently used to study the mechanical behaviors of articular cartilage, both theoretically and experimentally. It has also been used in explant and gel-cell-complex studies in tissue engineering. In biphasic and poroelastic theories, the effect of charges fixed on the proteoglycan macromolecules in articular cartilage is embodied in the apparent compressive Young's modulus and the apparent Poisson's ratio of the tissue, and the fluid pressure is considered to be the portion above the osmotic pressure. In order to understand how proteoglycan fixed charges might affect the mechanical behaviors of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and the flow of ions within its porous interstices. In this paper, we used a finite element model based on the triphasic theory to study how fixed charges in the porous-permeable soft tissue can modulate its mechanical and electrochemical responses under a step displacement in unconfined compression. The results from finite element calculations showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young's modulus (the ratio of the equilibrium axial stress to the axial strain) is always greater than the intrinsic Young's modulus of an uncharged tissue. 3) The apparent Poisson's ratio (the negative ratio of the lateral strain to the axial strain) is always larger than the intrinsic Poisson's ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under the unconfined compression, the Donnan osmotic pressure can constitute between 13%-22% of the total load support at equilibrium. 5) During the stress-relaxation process following the initial instant of loading, the diffusion potential (due to the gradient of the fixed charge density and the associated gradient of ion concentrations) and the streaming potential (due to fluid convection) compete against each other. Within the physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and the fixed charge density (FCD) of the tissue. For softer tissues, the diffusion effects dominate the electromechanical response, while for stiffer tissues, the streaming potential dominates this response. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium osmotic pressure. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.     

Donnan potentials from striated muscle liquid crystals. Sarcomere length dependence.

Donnan potentials from A-bands and I-bands were measured as a function of sarcomere length in skinned long-tonic muscle fibers of the crayfish. These measurements were made using standard electrophysiological technique. Simultaneously, the relative cross-sectional area of the fibers was determined. Lattice plane spacings and hence unit-cell volumes were determined by low-angle x-ray diffraction. At a sarcomere length at which the myosin filaments and actin filaments nominally do not overlap, measurements of potential, relative cross-sectional area, and unit-cell volume were used in conjunction with Donnan equilibrium theory to calculate the effective linear charge densities along the myosin filament (6.6 X 10(4) e-/mu) and actin filament (6.8 X 10(3) e-/mu). Using these linear charge densities, unit-cell volumes and Donnan equilibrium theory, an algorithm was developed to predict A-band and I-band potentials at any sarcomere length. Over the range of sarcomere lengths investigated, the predicted values coincide with the experimental data. The ability of the model to predict the data demonstrates the applicability of Donnan equilibrium theory to measurements of electrochemical potential from liquid-crystalline systems.     

A Mechano-chemical Model for the Passive Swelling Response of an Isolated Chondron under Osmotic Loading

The chondron is a distinct structure in articular cartilage that consists of the chondrocyte and its pericellular matrix (PCM), a narrow tissue region surrounding the cell that is distinguished by type VI collagen and a high glycosaminoglycan concentration relative to the extracellular matrix. We present a theoretical mechano-chemical model for the passive volumetric response of an isolated chondron under osmotic loading in a simple salt solution at equilibrium. The chondrocyte is modeled as an ideal osmometer and the PCM model is formulated using triphasic mixture theory. A mechano-chemical chondron model is obtained assuming that the chondron boundary is permeable to both water and ions, while the chondrocyte membrane is selectively permeable to only water. For the case of a neo-Hookean PCM constitutive law, the model is used to conduct a parametric analysis of cell and chondron deformation under hyper- and hypo-osmotic loading. In combination with osmotic loading experiments on isolated chondrons, model predictions will aid in determination of pericellular fixed charge density and its relative contribution to PCM mechanical properties.     

Biphasic indentation of articular cartilage--I. Theoretical analysis

A mathematical solution has been obtained for the indentation creep and stress-relaxation behavior of articular cartilage where the tissue is modeled as a layer of linear KLM biphasic material of thickness h bonded to an impervious, rigid bony substrate. The circular (radius = a), plane-ended indenter is assumed to be rigid, porous, free-draining, and frictionless. Double Laplace and Hankel transform techniques were used to solve the partial differential equations. The transformed equations and boundary conditions yielded an integral equation of the Fredholm type which was analyzed asymptotically and solved numerically. Our asymptotic analyses showed that the linear KLM biphasic material behaves like an incompressible (v = 0.5) single-phase elastic solid at t = 0+; the instantaneous response of the material is governed by the shear modulus (mu s) of the solid matrix. The linear KLM biphasic material behaves like a compressible elastic solid with material properties defined by those of the solid matrix, i.e. (lambda s, mu s) or (mu s, v s) as t----infinity. The transient viscoelastic creep and stress-relaxation behavior, 0 less than t less than infinity, of this material is controlled by the frictional drag (which is inversely proportional to the permeability k) associated with the flow of the interstitial fluid through the porous-permeable solid matrix. For given values of the Poisson's ratio of the solid matrix v s and the aspect ratio a/h, where a is the radius of the indenter and h is the thickness of the layer, the creep behavior with respect to the dimensionless time H Akt/a2 is completely controlled by the load parameter P/2 mu sa2 and the stress relaxation behavior is completely controlled by the rate of compression parameter R0 = kH A/V0h where H A = lambda s + 2 mu s and the equilibrium strain u0/h. This mathematical solution may now be used to describe an indentation experiment on articular cartilage to determine the intrinsic material properties of the tissue, i.e. permeability k, and the elastic coefficients of the solid phase (lambda s, mu s) or (mu s, v s).     

THE INFLUENCE OF ELECTROLYTES ON THE SOLUTION AND PRECIPITATION OF CASEIN AND GELATIN

1. Colloids have been divided into two groups according to the ease with which their solutions or suspensions are precipitated by electrolytes. One group (hydrophilic colloids), e.g., solutions of gelatin or crystalline egg albumin in water, requires high concentrations of electrolytes for this purpose, while the other group (hydrophobic colloids) requires low concentrations. In the latter group the precipitating ion of the salt has the opposite sign of charge as the colloidal particle (Hardy''s rule), while no such relation exists in the precipitation of colloids of the first group. 2. The influence of electrolytes on the solubility of solid Na caseinate, which belongs to the first group (hydrophilic colloids), and of solid casein chloride which belongs to the second group (hydrophobic colloids), was investigated and it was found that the forces determining the solution are entirely different in the two cases. The forces which cause the hydrophobic casein chloride to go into solution are forces regulated by the Donnan equilibrium; namely, the swelling of particles. As soon as the swelling of a solid particle of casein chloride exceeds a certain limit it is dissolved. The forces which cause the hydrophilic Na caseinate to go into solution are of a different character and may be those of residual valency. Swelling plays no rôle in this case, and the solubility of Na caseinate is not regulated by the Donnan equilibrium. 3. The stability of solutions of casein chloride (requiring low concentrations of electrolytes for precipitation) is due, first, to the osmotic pressure generated through the Donnan equilibrium between the casein ions tending to form an aggregate, whereby the protein ions of the nascent micellum are forced apart again; and second, to the potential difference between the surface of a micellum and the surrounding solution (also regulated by the Donnan equilibrium) which prevents the further coalescence of micella already formed. This latter consequence of the Donnan effect had already been suggested by J. A. Wilson. 4. The precipitation of this group of hydrophobic colloids by salts is due to the diminution or annihilation of the osmotic pressure and the P.D. just discussed. Since low concentrations of electrolytes suffice for the depression of the swelling and P.D. of the micella, it is clear why low concentrations of electrolytes suffice for the precipitation of hydrophobic colloids, such as casein chloride. 5. This also explains why only that ion of the precipitating salt is active in the precipitation of hydrophobic colloids which has the opposite sign of charge as the colloidal ion, since this is always the case in the Donnan effect. Hardy''s rule is, therefore, at least in the precipitation of casein chloride, only a consequence of the Donnan effect. 6. For the salting out of hydrophilic colloids, like gelatin, from watery solution, sulfates are more efficient than chlorides regardless of the pH of the gelatin solution. Solution experiments lead to the result that while CaCl₂ or NaCl increase the solubility of isoelectric gelatin in water, and the more, the higher the concentration of the salt, Na₂SO₄ increases the solubility of isoelectric gelatin in low concentrations, but when the concentration of Na₂SO₄ exceeds M/32 it diminishes the solubility of isoelectric gelatin the more, the higher the concentration. The reason for this difference in the action of the two salts is not yet clear. 7. There is neither any necessity nor any room for the assumption that the precipitation of proteins is due to the adsorption of the ions of the precipitating salt by the colloid.     

Analysis of the permeation of cryoprotectants in cartilage

Some tissues, such as cartilage and cornea, carry an internal fixed negative charge, leading to a swelling pressure that is balanced by tensile stress in the tissue matrix. During the addition and removal of cryoprotectants the changes in osmotic pressure will cause the tissue to deform. Because of the fixed charge and osmotic deformation, the permeation process in such tissues differs from ordinary diffusion processes. In this paper a biomechanical multi-solute theory is introduced to describe this process in cartilage tissue. Typical values for the physiological and biomechanical properties are used in the simulation. Several parameters - the aggregate modulus, the fixed charge density and the frictional parameter - are analyzed to show their impact on the process. It is shown that friction between water and cryoprotectant has the greatest influence but the fixed charge density is also important. The aggregate modulus and the frictional parameter between the cryoprotectant and the solid matrix have the least influence. Both the new biomechanical model and the conventional diffusion model were fitted to published experimental data concerning the time course of mean tissue cryoprotectant concentration when cartilage is immersed in solutions of dimethyl sulphoxide or propylene glycol: in all cases and with both models a good fit was obtained only when a substantial amount of non-solvent water was assumed.     

Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.     

Donnan effect as measured by sedimentation equilibrium for the protein cytochrome c.

The protein turkey-heart cytochrome c is used as a model protein to study charge effects in sedimentation equilibrium experiments in three-component solutions. Data are given for the dependence of the apparent M (1–υ ρ) on ρ in solutions of KCl, RbCl, CsCl, and triethylamine hydrochloride. The results show the Donnan effect to have a significant influence on the apparent molecular weight, found by extrapolation of the data to a solution density of one. The apparent molecular weights are for protein at infinite dilution. A theoretical treatment is presented where the magnitude of this effect can be predicted accurately from the formal net charge of the protein as computed from the amino acid composition. The results are shown to be important in computing the preferential hydration of the protein in concentrated salt solutions. For such systems the Donnan effect should be subtracted from the total interaction coefficient for multicomponent system in order to obtain the preferential hydration.     

Application of polyelectrolyte limiting laws to virial and asymptotic expansions for the Donnan equilibrium

We have applied a general polyelectrolyte theory to an analysis of the Donnan equilibrium. The polyelectrolyte concentration is measured by a dimensionless parameter x, equal to the ratio of the equivalent polyelectrolyte concentration to the concentration of salt in the external compartment. For small x, virial series - expansions in powers of x - are developed for the Donnan salt-exclusion, osmotic pressure, and electromotive force. For large x, asymptotic expansions for these effects are presented. Polyion-polyion interactions are explicitly neglected, so that the physical significance of the virial series differs from its meaning in neutral polymer chemistry. Numerical results illustrate large deviations from ideal Donnan behavior as well as satisfactory agreement with published data on the salt-exclusion and emf effects. However, results for the Donnan osmotic pressure disagree with the data, except in the case of zero salt concentration in the external compartment, for which agreement is almost exact.     

Theoretical basis for an anomalous temperature coefficient in swelling pressure of rabbit corneal stroma.

In the rabbit corneal stroma, the swelling pressure, P, has been reported to have an anomalous (negative) temperature coefficient, alpha P, contradicting traditional Donnan swelling theory. A parallel-plate, diffuse double layer Gouy-Chapman model was used to resolve this discrepancy. The present model incorporates the possibility that surface charge, sigma, is temperature dependent. It is shown that negative, zero, or positive coefficients of swelling pressure change with temperature are not mutually exclusive conditions, but can be attributed to the same underlying mechanism. For likely values of alpha P(range -7 x 10(-3) K-1 to +3.2 x 10(-3)K-1), the effective stromal charge has a negative temperature dependency, or dln sigma/dT less than 0. The present formalism is robust against variation in assumed alpha P, and is able to simultaneously satisfy the known values of swelling pressure, its thermal dependency, and stromal charge. These results implicate significant coulombic forces behind P. Predicted stromal surface charge is approximately 0.01 Cm-2. The predictions were confirmed with macrocontinuum Donnan swelling theory, suggesting that Donnan osmotic swelling is the principal macroscopic component of P.     

ON THE INFLUENCE OF AGGREGATES ON THE MEMBRANE POTENTIALS AND THE OSMOTIC PRESSURE OF PROTEIN SOLUTIONS

1. It is shown that when part of the gelatin in a solution of gelatin chloride is replaced by particles of powdered gelatin (without change of pH) the membrane potential of the solution is influenced comparatively little. 2. A measurement of the hydrogen ion concentration of the gelatin chloride solution and the outside aqueous solution with which the gelatin solution is in osmotic equilibrium, shows that the membrane potential can be calculated from this difference of hydrogen ion concentration with an accuracy of half a millivolt. This proves that the membrane potential is due to the establishment of a membrane equilibrium and that the powdered particles participate in this membrane equilibrium. 3. It is shown that a Donnan equilibrium is established between powdered particles of gelatin chloride and not too strong a solution of gelatin chloride. This is due to the fact that the powdered gelatin particles may be considered as a solid solution of gelatin with a higher concentration than that of the weak gelatin solution in which they are suspended. It follows from the theory of membrane equilibria that this difference in concentration of protein ions must give rise to potential differences between the solid particles and the weaker gelatin solution. 4. The writer had shown previously that when the gelatin in a solution of gelatin chloride is replaced by powdered gelatin (without a change in pH), the osmotic pressure of the solution is lowered the more the more dissolved gelatin is replaced by powdered gelatin. It is therefore obvious that the powdered particles of gelatin do not participate in the osmotic pressure of the solution in spite of the fact that they participate in the establishment of the Donnan equilibrium and in the membrane potentials. 5. This paradoxical phenomenon finds its explanation in the fact that as a consequence of the participation of each particle in the Donnan equilibrium, a special osmotic pressure is set up in each individual particle of powdered gelatin which leads to a swelling of that particle, and this osmotic pressure is measured by the increase in the cohesion pressure of the powdered particles required to balance the osmotic pressure inside each particle. 6. In a mixture of protein in solution and powdered protein (or protein micellæ) we have therefore two kinds of osmotic pressure, the hydrostatic pressure of the protein which is in true solution, and the cohesion pressure of the aggregates. Since only the former is noticeable in the hydrostatic pressure which serves as a measure of the osmotic pressure of a solution, it is clear why the osmotic pressure of a protein solution must be diminished when part of the protein in true solution is replaced by aggregates.     

Polyelectrolyte Charge Corrected Molecular Weight and Effective Charge by Sedimentation

Ionic charge on a macromolecule complicates the determination of its molecular weight in solution due to the Donnan effect. Compensation for it can be made if one knows the value of the effective charge, which can be found by dialysis equilibrium across a semipermeable membrane. A moving boundary of molecules sedimenting in a centrifugal field can act as a membrane, obviating some of the disadvantages (such as selective adsorption) of a real membrane. Interference optics are used to monitor the reverse gradient of the salt due to the Donnan effect, hence facilitating the determination of the effective charge. The apparent molecular weight obtained from a conventional sedimentation equilibrium can then be corrected to yield the true molecular weight. The effective charge is valuable in revealing macromolecular structural features when related to the titratable charge through the Manning counter-ion condensation theory. Agreement between the values of the backbone molecular weights for the Na, Cs, and Ca salts of heparin indicated the validity of the approach. The effective charge ratio and the axial charge spacing for the Na and Ca heparin agreed with the literature, whereas the results for Cs indicated a degree of binding in excess of that due to counter-ion condensation.     

Distribution and diffusion of solutes in articular cartilage

An experimental study was made on the distribution of solutes between articular cartilage and external solution, and on their diffusivity in cartilage. The solutes were classed as small ions, small uncharged molecules, and uncharged molecules of increasing size ranging from glucose to hemoglobin. The distribution of sodium and chloride ions obeys the Donnan equilibrium when cartilage is equilibrated in physiological saline solution. However, in cartilage immersed in dilute solution the concentration of chloride ions is higher than predicted. This is probably due to the presence in cartilage of some microscopic regions depleted of mucopolysaccharide in which the Donnan exclusion does not operate. The molal distribution coefficients of small uncharged molecules like urea are close to unity, which indicates that all water in cartilage seems to behave as solvent water. For larger molecules the distribution as well as the diffusion coefficients decrease with increase in molecular weight and are very sensitive to variations in fixed charge density. The results have been interpreted on the basis of the “steric exclusion” principle. The largest molecules which can penetrate into cartilage are of the size of the hemoglobin molecule.     

THE RECIPROCAL RELATION BETWEEN THE OSMOTIC PRESSURE AND THE VISCOSITY OF GELATIN SOLUTIONS

1. These experiments confirm the conclusion that protein solutions are true solutions consisting of isolated ions and molecules, and that these solutions may or may not contain in addition solid submicroscopic particles capable of occluding water. 2. The typical influence of electrolytes on the osmotic pressure of protein solutions is due to the isolated protein ions since these alone are capable of causing a Donnan equilibrium across a membrane impermeable to the protein ions but permeable to most crystalloidal ions. 3. The similar influence of electrolytes on the viscosity of protein solutions is due to the submicroscopic solid protein particles capable of occluding water since the amount of water occluded by (or the amount of swelling of) these particles is regulated by the Donnan equilibrium. 4. These ideas are supported by the fact that the more the submicroscopic solid particles contained in a protein solution or suspension are transformed into isolated ions (e.g., by keeping gelatin solution for 1 hour or more at 45°C.) the more the viscosity of the solution is diminished while the osmotic pressure is increased, and vice versa.     

The influence of inorganic salts when staining with preformed metal complex dyes

Summary The influence of various inorganic salts on the staining of tissue sections by a variety of preformed metal complex dyes (MCDs) has been studied. The staining patterns resulting were found to be extremely complex, though certain generalisations are possible.Usually the staining of basophilic tissue components (e. g. cartilage matrix and cell nuclei) was reduced as the amount of salt in the dyebath was increased. On the other hand the staining of some acidophilic tissue components (especially elastic fibres) was increased as the salt concentration rose. Both these effects can be rationalised by use of the Donnan equilibrium.The limited occurrence of salt-induced increases in staining intensity may be attributed in part to the extremely low rates of staining observed with acidophilic substrates.The decreases and increases in staining seen were to some extent dependant on the particular salt used, and presented an extremely complex picture. One general effect seen was that salts of Al³⁺, Cr³⁺, and Mg²⁺ had a greater inhibitory effect on staining than salts of K⁺ and Na⁺. This is explicable in terms of coordinative binding of the polyvalent ions by tissue substrates.On the basis of the information obtained comments were possible on various topics of biological staining interest. Thus it was concluded that of the MCDs studied only the aluminon-chromium complex showed evidence of binding by a mordanting mechanism. Further, it was found that the Critical Electrolyte Concentration theory was commonly inapplicable when staining tissue sections with MCDs.     

A microstructural model of elastostatic properties of articular cartilage in confined compression

A microstructural model of cartilage was developed to investigate the relative contribution of tissue matrix components to its elastostatic properties. Cartilage was depicted as a tensed collagen lattice pressurized by the Donnan osmotic swelling pressure of proteoglycans. As a first step in modeling the collagen lattice, two-dimensional networks of tensed, elastic, interconnected cables were studied as conceptual models. The models were subjected to the boundary conditions of confined compression and stress-strain curves and elastic moduli were obtained as a function of a two-dimensional equivalent of swelling pressure. Model predictions were compared to equilibrium confined compression moduli of calf cartilage obtained at different bath concentrations ranging from 0.01 to 0.50 M NaCl. It was found that a triangular cable network provided the most consistent correspondence to the experimental data. The model showed that the cartilage collagen network remained tensed under large confined compression strains and could therefore support shear stress. The model also predicted that the elastic moduli increased with increasing swelling pressure in a manner qualitatively similar to experimental observations. Although the model did not preclude potential contributions of other tissue components and mechanisms, the consistency of model predictions with experimental observations suggests that the cartilage collagen network, prestressed by proteoglycan swelling pressure, plays an important role in supporting compression.     

Potential and K+ activity in skinned muscle fibers. Evidence against a simple Donnan equilibrium

It has been suggested that potentials measured with conventional microelectrodes in chemically or mechanically skinned muscle fibers arise from a Donnan equilibrium due to myofilament fixed charges. This hypothesis was tested in mechanically skinned frog (Rana pipiens) semitendinosus fibers by measuring the distribution potential (Ed) between fiber and bath with 3 M KCl-filled microelectrodes and the K+ activity gradient (aik/aok) with K+ ion-selective microelectrodes (KISE). If skinned fibers are a Donnan system, Ed should become more positive as pH is decreased, altering the fixed charge on the myofilaments. Consistent with this expectation, Ed was -4.4, -0.6, and +4.8 mV in ATP-containing solutions and -6.5, -2.2, and +8.4 mV in ATP-free solutions at pH 7, 6, and 5, respectively. Donnan equilibrium also requires that all mobile ionic species be in electrochemical equilibrium. In ATP-containing solutions, this was true for K+ at pH 7. At pH 5, however, KISE indicated that K+ was not in equilibrium; average Ed was 5.9 mV positive to the K+ equilibrium potential, and aik/aok was 1.04, while the Donnan prediction was 0.83. In contrast, KISE measurements in ATP-free solutions indicated that K+ was in equilibrium at all pH studied. Skinned fibers in ATP-containing media are not equilibrium systems because ATPase reactions occur. Under our conditions, frog myofibrils hydrolyze 0.4 and 0.08 mumol ATP/min X mg myofibrillar protein at pH 7 and 5, respectively. It is suggested that in the presence of ATP, Ed is a superposition of Donnan and diffusion potentials, the latter arising from differences in the mobilities of anionic substrate and products that diffuse through the charged myofilament lattice.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Donnan Equilibrium: A Theoretical Study of the Effects of Interionic Forces

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.