A triphasic theory for the swelling and deformation behaviors of articular cartilage

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single-salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by mu i = mu io + (RT/Mi)ln[gamma 2 +/- c(c + cF)] and mu w = mu wo + [p-RT phi (2c + cF) + Bwe]/pwT, where R, T, Mi, gamma +/-, phi, pwT and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI-TcI + lambda s(trE)I + 2 musE, where E is the strain tensor and (lambda s, mu s) are the Lamé constants of the elastic solid matrix. The chemical-expansion stress (-Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.     

Structural theory of the swelling pressure of corneal stroma in saline

The swelling pressure of the corneal stroma is discussed in terms of a stromal model of collagen fibrils interconnected via protein-mucopolysaccharide molecular complexes. The analysis leads to an expression for the swelling pressure in terms of molecular parameters of the complexes regarded as polymeric chains. Assigning reasonable values to these parameters we find that the model is consistent with the swelling pressure experiments. These parameters indicate the electrostatic (Donnan) pressure component accounts for most of the swelling pressure at normal thickness in 0.174 M NaCl, while the pressure components deriving from a free energy of mixing account for most of the swelling pressure at normal thickness in 1.74 M NaCl.     

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.     

Application of catastrophe theory to corneal swelling

Stromal swelling in human, cat, and rabbit cornea is biphasic, interpretable as an elementary cusp catastrophe proposed by Thom, with t* = log t and Q* = log Q (stromal charge Q, time t) as control parameters, and H0.5 (hydration H) as the state variable. A thermodynamic potential with two attractor regions, each with a local minimum, governs corneal stromal swelling. Transitions follow a 'saturation convention' whereby the second minimum is preferred upon availability. Corneal swelling is an example of a space-equivalent unfolding, where the transition plane moves in time. It is proposed that the transition plane coincides with the uncoupling of interfibrillary linkages or 'springs' in the corneal stroma, and is associated with a critical hydration of ca. 10 kg H2O per kilogram dry mass, and stromal charge ca. 1 x 10(-7) mol electrons.     

The Donnan effect in tobacco mosaic virus and its components

Osmotic pressure studies were carried on tobacco mosaic virus (TMV) and its components, protein and RNA, as well as on bis(3,3′-aminopropyl)amine, reported to be present in TMV preparations. Solvents were phosphate and barbital buffers at different values of pH and ionic strength. Measurements were made at room temperature. The Donnan effect was exhibited by TMV protein in phosphate buffer of 0.01 ionic strength at pH values ranging between 5.8 and 7.5. The observed values of the Donnan effect at pH 5.8 and 5.97 were in reasonable agreement with theoretical values calculated from the charge obtained by hydrogen ion titration. TMV-RNA in phosphate buffer at pH 7.5 and ionic strength 0.01 did not exhibit more than 1% of the expected Donnan effect. This is explained tentatively as the result of firm binding of metal ions. Negative values of osmotic pressure were observed with bis(3,3′-aminopropyl)amine. Similar anomalous osmosis was sometimes observed with TMV protein and with TMV. In agreement with earlier observations, TMV did not exhibit the Donnan effect in phosphate buffer of 0.01 ionic strength at pH values ranging from 5.5 to 8.0. However, TMV dialysed extensively in the presence of EDTA at pH 8.5 and TMV produced by reconstitution of purified protein and RNA did exhibit the Donnan effect in both phosphate and barbital buffers. The magnitude was of the same order as that calculated from the net charge determined by hydrogen ion titration. When reconstituted TMV, which did exhibit Donnan effect, was treated with calcium ions, the effect was abolished.     

Water and electrolyte content of the myofilament phase in the chemically skinned barnacle fiber

Muscle fibers from the giant barnacle, Balanus nubilus, were placed inside the lumen of a porous glass capillary and equilibrated for 48 h in an electrolyte solution containing 2% Tween. The glass capillary prevented the chemically "skinned" fiber from swelling with a water content beyond 80%. Isotope exchange studies using 22Na, 42K, and 36Cl indicated the existence of an intermediate rate constant and compartment which varied with pH. This intermediate rate was attributed to counter-ions and co-ions in the myofilament phase. Analysis of the electrolyte composition of the fiber at pH 8 predicts that the myofilaments contain about 0.3 of the fiber water, and that a -15 mV Donnan potential exists at the myofilament surface. An open-tipped (1- micrometer) microelectrode in the skinned fiber measured a potential (similar in magnitude to the Donnan potential), which decreased and reversed sign as the pH was lowered. The measured cation contents of the fiber between pH 5 and 8 were found to be similar to the cation contents predicted from the measured Donnan potentials. The net negative charge of the myofilaments at pH 7.5 and at ionic strength 0.56 is estimated to be 41 eq per 10(5) g of dry weight.     

Relationship among the surface potential, Donnan potential and charge density of ion-penetrable membranes

Calculation of the potential distribution across a uniformly charged ion-penetrable membrane that we developed previously is extended to derive a relationship among the surface potential, Donnan potential and charge density of an ion-penetrable membrane in a mixed solution of 2-1 and 1-1 electrolytes. We also present an approximate method for calculating the surface potential/Donnan potential/charge density relationship for membranes with an arbitrary distribution of membrane-fixed charges.     

Light-scattering studies on supercoil unwinding

It has been shown previously that supercoiled [unk]X174 bacteriophage intracellular DNA (mol.wt. 3.2x10(6)) with superhelix density, sigma=-0.025 (-12 superhelical turns) at 25 degrees C is best represented as a Y shape. In this work two techniques have been used to unwind the supercoil and study the changes in tertiary structure which result from changes in the secondary structure. The molecular weights from all experiments were in the range 3.2x10(6)+/-0.12x10(6). In experiments involving temperature change little change in the Y shape was observed between sigma=-0.027 (-13 superhelical turns, 14.9 degrees C) and sigma=-0.021 (-10 superhelical turns, 53.4 degrees C) as evidenced by the root-mean-square radius and the particle-scattering factor P(theta). However, at sigma=-0.0176 (-8 superhelical turns, 74.5 degrees C) the root-mean-square radius fell to between 60 and 70nm from 90nm indicating a large structural change, as did alterations in the P(theta) function. In experiments with the intercalating dye proflavine from values of bound proflavine of 0-0.06mol of dye/mol equiv. of nucleotide which correspond to values of sigma from -0.025 to -0.0004 (-12 to 0 superhelical turns) a similar transition was found when the superhelix density was changed by the same amount, and the molecule was shown to go through a further structural change as the unwinding of the duplex proceeded. At sigma=-0.018 (-9 superhelical turns) the structure was compatible with a toroid, and at sigma=-0.0004 it was compatible with a circle but at no point in the sequence of structure transitions was the structure compatible with the conventional straight interwound model normally visualized as the shape of supercoiled DNA.     

A fixed charge model of the transverse tubular system of frog sartorius

Volume changes of the transverse tubular system (T system) of frog sartorius in different solutions can be explained by a model which assumes fixed negative charges in the T system lumen, an open T system mouth, and a Donnan equilibrium between the T system and external solution. The T system volume is regulated by the osmotic pressure difference between the lumen and external solution, as well as by constraining forces whose nature is as yet unclear. The decreased swelling tendency produced by hypotonic solutions and increased tendency produced by some hypertonic solutions are ascribed to changes in the pressure constraint from the sarcoplasm. Fixed charge concentration was estimated tentatively from swelling and resistivity data to be between 0.1 and 0.4 M.     

Donnan potentials from striated muscle liquid crystals. Lattice spacing dependence.

Electrochemical potentials were measured as a function of myofilament packing density in crayfish striated muscle. The A-band striations are supramolecular smectic B1 lattice assemblies of myosin filaments and the I-band striations are nematic liquid crystals of actin filaments. Both A- and I-bands generate potentials derived from the fixed charge that is associated with structural proteins. In the reported experiments, filament packing density was varied by osmotically reducing lattice volume. The electrochemical potentials were measured from the A- and I-bands in the relaxed condition over a range of lattice volumes. From the measurements of relative cross-sectional area, unit-cell volume (obtained by low-angle x-ray diffraction) and previously determined effective linear charge densities (Aldoroty, R.A., N.B. Garty, and E.W. April, 1985, Biophys. J., 47:89-96), Donnan potentials can be predicted for any amount of compression. In the relaxed condition, the predicted Donnan potentials correspond to the measured electrochemical potentials. In the rigor condition, however, a net increase in negative charge associated with the myosin filament is observed. The predictability of the data demonstrates the applicability of Donnan equilibrium theory to the measurement of electrochemical potentials from liquid-crystalline systems. Moreover, the relationship between filament spacing and the Donnan potential is consistent with the concept that surface charge provides the necessary electrostatic force to stabilize the myofilament lattice.     

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.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.     

Isolation and Characterization of a New Generalized Transducing Bacteriophage Different from Pl in Escherichia coli

A new generalized transducing bacteriophage in the Escherichia coli system was isolated and characterized. This phage, designated D108, makes clear plaques on E. coli K-10, K-12, K-12(P1kc), K-12(D6), B/r, C, and 15 T(-), and Shigella dysenteriae. The plaque of phage D108 is larger in size than that of phage P1kc. Electron-microscopic observation revealed that phages D108 and P1kc are morphologically different from each other, suggesting that phage D108 belongs to a phage group different from phage P1. The fact that all of the 10 markers tested were transduced by phage D108 indicates that this phage is a generalized transducing phage in the E. coli system. The transduction frequency by phage D108 of chromosomal markers and of a drug resistance factor (R factor) ranged from 2 x 10(-6) to 3 x 10(-8) and 3 x 10(-9) to 6 x 10(-10) per phage, respectively. The cotransduction frequency of the thr and leu markers was 2.8% for phage P1kc and 1.5% for phage D108. The CM and TC markers (chloramphenicol-resistant and tetracycline-resistant markers, respectively) of the R factor were not cotransduced by phage D108, but the markers were generally cotransduced by phage P1kc. The results suggest that the transducing particle of phage D108 contains a smaller amount of host deoxyribonucleic acid than does phage P1kc.     

Electroosmotic Characteristics of Canine Aorta and Vena Cava Wall

Experiments in which canine aorta and vena cava walls are subjected to electroosmosis in an open system at constant pressure are described. Electroosmosis reveals that the blood vessel walls studied have a negative zeta potential. The calculated zeta potentials are different for aorta and vena cava, -9.0 +/- 5.0 mv compared with -4.7 +/- 1.2 mv, respectively, and again of different magnitude with different bathing solutions. The calculated membrane pore charge per centimeter of effective pore surface in statcoulombs is approximately 6.2 x 10(3) for aorta compared with 3.5 x 10(3) for vena cava. The implications of the negative electroosmotic zeta potential in terms of the surrounding electric double layer, ion transport, and thrombosis are briefly discussed.     

Diffusion and consumption of oxygen in the resting frog sartorius muscle

Adaptations of the method of Takahashi et al. (1966. J. Gen. Physiol. 50:317-333) were used to test the validity of the one-dimensional diffusion equation for O2 in the resting excised frog sartorius muscle. This equation is: (formula: see text) where x is the distance perpendicular to the muscle surface. t is time, P(x, t) is the partial pressure of O2,D and alpha are the diffusion coefficient and solubility for O2 in the tissue, and Q is the rate of O2 consumption. P(O, t), the time-course of PO2 at one muscle surface, was measured by a micro-oxygen electrode. Transients in the PO2 profile of the muscle were induced by two methods: (a) after an equilibration period, one surface was sealed off by a disc in which the O2 electrode was embedded; (b) when PO2 at this surface reached a steady state, a step change was made in the PO2 at the other surface. With either method, the agreement between the measured P(O, t) and that predicted by the diffusion equation was excellent, making possible the calculation of D and Q. These two methods yielded statistically indistinguishable results, with the following pooled means (+/- SEM): (formula: see text) At each temperature, D was independent of muscle thickness (range, 0.67-1.34 mm). The activation energy (EA) for diffusion of oxygen in muscle was -3.85 kcal/mol, which closely matches the corresponding value in water. Together with absolute values of D in water taken from the literature, the present data imply that (Dmuscle/DH2O) is in the range 0.59-0.69. This value, and that of EA, are in agreement with the theory of Wang (1954, J. Am. Chem. Soc. 76:4755-4763), suggesting that with respects to the diffusion of O2, to a useful approximation, frog skeletal muscle may be considered simply as a homogeneous protein solution.     

Survismeter--type I and II for surface tension, viscosity measurements of liquids for academic, and research and development studies

For centuries surface tension (gamma) and viscosity (eta) data have been measured with individual instruments consuming much time and materials. Thus the two different types of survismeters have been designed and made of borosil glass material for surface tension and viscosity data to rationalize frictional and cohesive forces, respectively. Friccohesity (sigma (sm(-1), second per meter)) is derived from Fric of frictional and cohesity of cohesive forces of the liquid respectively, and denoted by rational coefficient a eta/gamma (sigma). The values of the friccohesity are correlated to the dipole moment of liquids and their plot gives a standard calibration curve along with an equation of the curve with definite values of the coefficients, the friccohesity values are put on the calibration curve to retrieve the dipole moment values. Here, the sigma values for each of dimethylformamide, dimethylsulfoxide and acetronitrile solvents along with their 0.05, 0.10 and 0.20 mol kg(-1) aqueous solutions, respectively, were determined at 293.15K and plotted against their dipole moment values for standard calibration curve. The range of the dipole moment values for calibration curve is pre-decided and the sigma values for homogenous solutions of compositions below their saturation point can be measured with +/-1 x 10(-5)sm(-1).     

A transmural pressure gradient induces mechanical and biological adaptive responses in endothelial cells

A sudden increase in the transmural pressure gradient across endothelial monolayers reduces hydraulic conductivity (L(p)), a phenomenon known as the sealing effect. To further characterize this endothelial adaptive response, we measured bovine aortic endothelial cell (BAEC) permeability to albumin and 70-kDa dextran, L(p), and the solvent-drag reflection coefficients (sigma) during the sealing process. The diffusional permeability coefficients for albumin (1.33 +/- 0.18 x 10(-6) cm/s) and dextran (0.60 +/- 0.16 x 10(-6) cm/s) were measured before pressure application. The effective permeabilities (measured when solvent drag contributes to solute transport) of albumin and dextran (P(ealb) and P(edex)) were measured after the application of a 10 cmH(2)O pressure gradient; during the first 2 h of pressure application, P(ealb), P(edex), and L(p) were significantly reduced by 2.0 +/- 0.3-, 2.1 +/- 0.3-, and 3.7 +/- 0.3-fold, respectively. Immunostaining of the tight junction (TJ) protein zonula occludens-1 (ZO-1) was significantly increased at cell-cell contacts after the application of transmural pressure. Cytochalasin D treatment significantly elevated transport but did not inhibit the adaptive response, whereas colchicine treatment had no effect on diffusive permeability but inhibited the adaptive response. Neither cytoskeletal inhibitor altered sigma despite significantly elevating both L(p) and effective permeability. Our data suggest that BAECs actively adapt to elevated transmural pressure by mobilizing ZO-1 to intercellular junctions via microtubules. A mechanical (passive) component of the sealing effect appears to reduce the size of a small pore system that allows the transport of water but not dextran or albumin. Furthermore, the structures of the TJ determine transport rates but do not define the selectivity of the monolayer to solutes (sigma).     

Localization of conserved and variable segments in amino acid sequences of homologous proteins using a personal computer]

A set of aligned homologous protein sequences is divided into two groups consisting of the most related sequences m and k. The value of the position variability of homologous protein sequences is defined as a number of failures to coincide in the intergroup comparison of all possible k x m pairs of amino acid residues in that position divided by k x m. The position variability value plotted vs the sequence position number with a window of 10 positions gives the intergroup local variability profile. The area S of the figure included between the local variability profile and the straight line corresponding to the mean local variability value is compared with the average area S(r) for 1000 random homologous protein families. If S is greater than S(r) by more than 2 standard deviation units sigma r the local variability profile is assumed to contain peaks and hollows corresponding to significant variable and conservative regions of the sequences. The profile extrema containing the area surplus delta S = S-(S(r) + 2 sigma r) are cut off by two straight lines to locate significant regions. The numerical experiment on the family of homologous phospholipases A2 revealed the linear dependence of the values S(r) and sigma r upon the position variability standard deviation sigma v of the homologous sequences. Furthermore, it was shown for protein families of various length (rhodopsins, aspartate aminotransferases, cytochromes b, L- and M-subunits of photosynthetic bacteria photoreaction centre and alpha-subunits of Na, K-ATPase), that delta S = S - n(S'r + 2 sigma r), where S - the area of the local variability profile, n = L/l (L - the length of the given protein family and l - the length of the hypothetical protein domain). If l = 250 then S'r = -1.42 + 62.56 sigma v and sigma'r = -0.14 + 7.46 sigma v.     

A triphasic analysis of corneal swelling and hydration control.

Physiological studies strongly support the view that hydration control in the cornea is dependent on active ion transport at the corneal endothelium. However, the mechanism by which endothelial ion transport regulates corneal thickness has not been elaborated in detail. In this study, the corneal stroma is modeled as a triphasic material under steady-state conditions. An ion flux boundary condition is developed to represent active transport at the endothelium. The equations are solved in cylindrical coordinates for confined compression and in spherical coordinates to represent an intact cornea. The model provides a mechanism by which active ion transport at the endothelium regulates corneal hydration and provides a basis for explaining the origin of the "imbibition pressure" and stromal "swelling pressure." The model encapsulates the Donnan view of corneal swelling as well as the "pump-leak hypothesis."