Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: A caprine in vitro study

The mechanical behaviour of the intervertebral disc highly depends on the content and transport of interstitial fluid. It is unknown, however, to what extent the time-dependent behaviour can be attributed to osmosis. Here we investigate the effect of both mechanical and osmotic loading on water content, nucleus pressure and disc height. Eight goat intervertebral discs, immersed in physiological saline, were subjected to a compressive force with a pressure needle inserted in the nucleus. The loading protocol was: 10 N (6 h); 150 N (42 h); 10 N (24 h). Half-way the 150 N-phase (24 h), we eliminated the osmotic gradient by adding 26% poly-ethylene glycol to the surrounding fluid. For 62 additional discs, we determined the water content of both nucleus and annulus after 6, 24, 48, or 72 h. The compressive load was initially counterbalanced by the hydrostatic pressure in the nucleus. The load forced 4.3% of the water out of the nucleus, which reduced nucleus pressure by 44(±6)%. Reduction of the osmotic gradient disturbed the equilibrium disc height, and a significant loss of annulus water content was found. Remarkably, pressure and water content of the nucleus pulposus remained unchanged. This shows that annulus water content is important in the response to axial loading. After unloading, in the absence of an osmotic gradient, there was substantial viscoelastic recovery of 53(±11)% of the disc height, without a change in water content. However, for restoration of the nucleus pressure and for full restoration of disc height, restoration of the osmotic gradient was needed.     

The effect of osmotic and mechanical pressures on water partitioning in articular cartilage

X-ray diffraction measurements on native and proteoglycan-free articular cartilage have been made in order to test the dependence of the lateral packing of the collagen molecules on the osmotic pressure gradient, either naturally occurring or externally applied, between the intra- and extrafibrillar compartments. From the information on collagen packing we have been able to calculate, albeit with several assumptions, the amount of intrafibrillar water as a function of pressure. In parallel with the above measurements, we have quantitated, using serum albumin partitioning, the intrafibrillar water in proteoglycan-free cartilage, as a function of mechanically applied pressure. The results of both sets of experiments lead to the conclusion that the molecular packing density, and hence the intrafibrillar water content, are a function of the osmotic pressure difference between the extrafibrillar and intrafibrillar spaces or the equivalent mechanically applied pressure. The determination of intrafibrillar water has enabled us to calculate, from measured values of fixed charge density, the internal osmotic pressure of cartilage specimens, both in compressed and uncompressed states.     

Studies of hydration and swelling pressure in normal and osteoarthritic cartilage

An experimental study was carried out which involved comparing cartilage from normal and osteoarthritic joints with respect to (a) swelling pressure and (b) variation of hydration with applied pressure. The main conclusion was that whilst osteoarthritic cartilage is undoubtedly less able to resist water loss under a given applied pressure than normal cartilage, this is not due to a change in the "quality" of the proteoglycans, resulting in a change in the osmotic pressure of the latter, but simply to a decreased fixed charge density. The latter decrease is either caused by an increase in the water content - and this we attribute to a weakened collagen network - and/or to a loss of part of the proteoglycans from the tissue.     

Osmotically induced helix-coil transition in poly(glutamic acid)

Protein folding and conformational changes are influenced by protein-water interactions and, as such, the energetics of protein function are necessarily linked to water activity. Here, we have chosen the helix-coil transition in poly(glutamic acid) as a model system to investigate the importance of hydration to protein structure by using the osmotic stress method combined with circular dichroism spectroscopy. Osmotic stress is applied using poly(ethylene glycol), molecular weight of 400, as the osmolyte. The energetics of the helix-coil transition under applied osmotic stress allows us to calculate the change in the number of preferentially included water molecules per residue accompanying the thermally induced conformational change. We find that osmotic stress raises the helix-coil transition temperature by favoring the more compact α-helical state over the more hydrated coil state. The contribution of other forces to α-helix stability also are explored by varying pH and studying a random copolymer, poly(glutamic acid-r-alanine). In this article, we clearly show the influence of osmotic pressure on the peptide folding equilibrium. Our results suggest that to study protein folding in vitro, the osmotic pressure, in addition to pH and salt concentration, should be controlled to better approximate the crowded environment inside cells.     

Energetics of a hexagonal-lamellar-hexagonal-phase transition sequence in dioleoylphosphatidylethanolamine membranes.

The phase diagram of DOPE/water dispersions was investigated by NMR and X-ray diffraction in the water concentration range from 2 to 20 water molecules per lipid and in the temperature range from -5 to +50 degrees C. At temperatures above 22 degrees C, the dispersions form an inverse (HII) phase at all water concentrations. Below 25 degrees C, an HII phase occurs at high water concentrations, an L alpha phase is formed at intermediate water concentrations, and finally the system switches back to an HII phase at low water concentrations. The enthalpy of the L alpha-HII-phase transition is +0.3 kcal/mol as measured by differential scanning calorimetry. Using 31P and 2H NMR and X-ray diffraction, we measured the trapped water volumes in HII and L alpha phases as a function of osmotic pressure. The change of the HII-phase free energy as a function of hydration was calculated by integrating the osmotic pressure vs trapped water volume curve. The phase diagram calculated on the basis of the known enthalpy of transition and the osmotic pressure vs water volume curves is in good agreement with the measured one. The HII-L alpha-HII double-phase transition at temperatures below 22 degrees C can be shown to be a consequence of (i) the greater degree of hydration of the HII phase in excess water and (ii) the relative sensitivities with which the lamellar and hexagonal phases dehydrate with increasing osmotic pressure. These results demonstrate the usefulness of osmotic stress measurements to understand lipid-phase diagrams.     

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.     

HYDRATION OF GELATIN IN SOLUTION

1. It was shown that the high viscosity of gelatin solutions as well as the character of the osmotic pressure-concentration curves indicates that gelatin is hydrated even at temperatures as high as 50°C. 2. The degree of hydration of gelatin was determined by means of viscosity measurements through the application of the formula See PDF for Equation. 3. When the concentration of gelatin was corrected for the volume of water of hydration as obtained from the viscosity measurements, the relation between the osmotic pressure of various concentrations of gelatin and the corrected concentrations became linear, thus making it possible to determine the apparent molecular weight of gelatin through the application of van''t Hoff''s law. The molecular weight of gelatin at 35°C. proved to be 61,500. 4. A study was made of the mechanism of hydration of gelatin and it was shown that the experimental data agree with the theory that the hydration of gelatin is a pure osmotic pressure phenomenon brought about by the presence in gelatin of a number of insoluble micellæ containing a definite amount of a soluble ingredient of gelatin. As long as there is a difference in the osmotic pressure between the inside of the micellæ and the outside gelatin solution the micellæ swell until an equilibrium is established at which the osmotic pressure inside of the micellæ is balanced by the total osmotic pressure of the gelatin solution and by the elasticity pressure of the micellæ. 5. On addition of HCl to isoelectric gelatin the total activity of ions inside of the micellæ is greater than in the outside solution due to a greater concentration of protein in the micellæ. This brings about a further swelling of the micellæ until a Donnan equilibrium is established in the ion distribution accompanied by an equilibrium in the osmotic pressure. Through the application of the theory developed here it was possible actually to calculate the osmotic pressure difference between the inside of the micellæ and the outside solution which was brought about by the difference in the ion distribution. 6. According to the same theory the effect of pH on viscosity of gelatin should diminish with increase in concentration of gelatin, since the difference in the concentration of the protein inside and outside of the micellæ also decreases. This was confirmed experimentally. At concentrations above 8 gm. per 100 gm. of H₂O there is very little difference in the viscosity of gelatin of various pH as compared with that of isoelectric gelatin.     

Measurement and modification of forces between lecithin bilayers.

We probe in two different ways the competing attractive and repulsive forces that create lamellar arrays of the phospholipid lecithin when in equilibrium with pure water. The first probe involves the addition of low molecular weight solutes, glucose and sucrose, to a system where the phospholipid is immersed in a large excess of water. Small solutes can enter the aqueous region between bilayers. Their effect is first to increase and then to decrease the separation between bilayers as sugar concentration increases. We interpret this waxing and waning of the lattice spacing in terms of the successive weakening and strengthening of the attractive van der Waals forces originally responsible for creation of a stable lattice. The second probe is an "osmotic stress method," in which very high molecular weight neutral polymer is added to the pure water phase but is unable to enter the multilayers. The polymer competes for water with the lamellar lattice, and thereby compresses it. From the resulting spacing (determined by X-ray diffraction) and the directly measured osmotic pressure, we find a force vs. distance curve for compressing the lattice (or, equivalently, the free energy of transfer to bulk water of water between bilayers. This method reveals a very strong, exponentially varying "hydration force" with a decay distance of about 2 A.     

A mechanical model for the human intervertebral disc

Stress relaxation experiments were performed on specimens from a human intervertebral disc. Specimens were made from the nucleus pulposus and from the external lamellae of the anulus fibrosus in two different orientations. Tests were run with varying moisture content so as to develop a relaxation master curve. A model was developed based on the experimental data. It was found that the short term master curve for the lamellae of the anulus and nucleus are similar, whereas the long term rubbery plateau is different between the lamellae and the nucleus. It was also established that the master curves for different lamellae and the nucleus were shifted relative to each other in the time domain due to changes in water content. The average relaxation modulus of the whole disc was obtained by averaging the properties between the anulus and nucleus. This model was then used for studies of Schmorl's nodes, of degenerated discs and for circumstances in which hydration is considered to be important.     

Hydration force and bilayer deformation: a reevaluation

The hydration repulsive force between lipid bilayers and the deformability of both gel and liquid-crystalline bilayers have been quantitated by an X-ray diffraction analysis of osmotically stressed liposomes. Both sampling theorem reconstructions and electron density distributions were calculated from diffraction data obtained from multilayers with applied osmotic pressures of 0-50 atm. The bilayer thickness and area per lipid molecule remain nearly constant (to within about 4%) in this pressure range, as adjacent bilayers move from their equilibrium separation in excess water to within 2-4 A of each other. This analysis indicates that the bilayers are relatively incompressible. This results differs from previously published X-ray diffraction studies of bilayer compressibility but agrees with direct mechanical measurements of the bilayer compressibility modulus. It is also found that the hydration repulsive force decays exponentially with separation between bilayers with a decay constant of 1.4 A for gel-state dipalmitoylphosphatidylcholine and 1.7 A for liquid-crystalline egg phosphatidylcholine bilayers. This implies that the exponential decay constant is not necessarily equal to the diameter of a water molecule, as has been previously suggested on experimental and theoretical grounds.     

Temperature dependence of the repulsive pressure between phosphatidylcholine bilayers.

Bilayer structure and interbilayer repulsive pressure were measured from 5 to 50 degrees C by the osmotic stress/x-ray diffraction method for both gel and liquid crystalline phase lipid bilayers. For gel phase dibehenoylphosphatidylcholine (DBPC) the bilayer thickness and pressure-distance relations were nearly temperature-independent, and at full hydration the equilibrium fluid spacing increased approximately 1 A, from 10 A at 5 degrees C to 11 A at 50 degrees C. In contrast, for liquid crystalline phase egg phosphatidylcholine (EPC), the bilayer thickness, equilibrium fluid spacing, and pressure-distance relation were all markedly temperature-dependent. As the temperature was increased from 5 to 50 degrees C the EPC bilayer thickness decreased approximately 4 A, and the equilibrium fluid spacing increased from 14 to 21 A. Over this temperature range there was little change in the pressure-distance relation for fluid spacings less than approximately 10 A, but a substantial increase in the total pressure for fluid spacings greater than 10 A. These data show that for both gel and liquid crystalline bilayers there is a short-range repulsive pressure that is nearly temperature-independent, whereas for liquid crystalline bilayers there is also a longer-range pressure that increases with temperature. From analysis of the energetics of dehydration we argue that the temperature-independent short-range pressure is consistent with a hydration pressure due to polarization or electrostriction of water molecules by the phosphorylcholine moiety. For the liquid crystalline phase, the 7 A increase in equilibrium fluid spacing with increasing temperature can be predicted by an increase in the undulation pressure as a consequence of a temperature-dependent decrease in bilayer bending modulus.     

Phloem water relations and translocation

Satisfactory measurements of phloem water potential of trees can be obtained with the Richards and Ogata psychrometer and the vapor equilibration techniques, although corrections for loss of dry weight and for heating by respiration are required for the vapor equilibrium values. The psychrometer technique is the more satisfactory of the 2 because it requires less time for equilibration, less tissue, and less handling of tissue. Phloem water potential of a yellow-poplar tree followed a diurnal pattern quite similar to that of leaves, except that the values were higher (less negative) and changed less than in the leaves.

The psychrometer technique permits a different approach to the study of translocation in trees. Measurements of water potential of phloem discs followed by freezing of samples and determination of osmotic potential allows estimation of turgor pressure in various parts of trees as the difference between osmotic potential and total water potential. This technique was used in evaluating gradients in water potential, osmotic potential, and turgor pressure in red maple trees. The expected gradients in osmotic potential were observed in the phloem, osmotic potential of the cell sap increasing (sap becoming more dilute) down the trunk. However, values of water potential were such that a gradient in turgor pressure apparently did not exist at a time when rate of translocation was expected to be high. These results do not support the mass flow theory of translocation favored by many workers.

     

Casein Micelle Dispersions under Osmotic Stress

Casein micelles dispersions have been concentrated and equilibrated at different osmotic pressures using equilibrium dialysis. This technique measured an equation of state of the dispersions over a wide range of pressures and concentrations and at different ionic strengths. Three regimes were found. i), A dilute regime in which the osmotic pressure is proportional to the casein concentration. In this regime, the casein micelles are well separated and rarely interact, whereas the osmotic pressure is dominated by the contribution from small residual peptides that are dissolved in the aqueous phase. ii), A transition range that starts when the casein micelles begin to interact through their κ-casein brushes and ends when the micelles are forced to get into contact with each other. At the end of this regime, the dispersions behave as coherent solids that do not fully redisperse when osmotic stress is released. iii), A concentrated regime in which compression removes water from within the micelles, and increases the fraction of micelles that are irreversibly linked to each other. In this regime the osmotic pressure profile is a power law of the residual free volume. It is well described by a simple model that considers the micelle to be made of dense regions separated by a continuous phase. The amount of water in the dense regions matches the usual hydration of proteins.     

Osmosensing by WNK Kinases

With No Lysine (K) WNK kinases regulate electro-neutral cotransporters that are controlled by osmotic stress and chloride. We showed previously that autophosphorylation of WNK1 is inhibited by chloride, raising the possibility that WNKs are activated by osmotic stress. Here we demonstrate that unphosphorylated WNK isoforms 3 and 1 autophosphorylate in response to osmotic pressure in vitro, applied with the crowding agent polyethylene glycol (PEG)400 or osmolyte ethylene glycol (EG), and that this activation is opposed by chloride. Small angle x-ray scattering of WNK3 in the presence and absence of PEG400, static light scattering in EG, and crystallography of WNK1 were used to understand the mechanism. Osmosensing in WNK3 and WNK1 appears to occur through a conformational equilibrium between an inactive, unphosphorylated, chloride-binding dimer and an autophosphorylation-competent monomer. An improved structure of the inactive kinase domain of WNK1, and a comparison with the structure of a monophosphorylated form of WNK1, suggests that large cavities, greater hydration, and specific bound water may participate in the osmosensing mechanism. Our prior work showed that osmolytes have effects on the structure of phosphorylated WNK1, suggestive of multiple stages of osmotic regulation in WNKs.     

Collagen Unfolding Accelerates Water Influx,Determining Hydration in the Interstitial Matrix

In the interstitial matrix, collagen unfolding at physiologic temperatures is thought to facilitate interactions with enzymes and scaffold molecules during inflammation, tissue remodeling, and wound healing. We tested the hypothesis that it also plays a role in modulating flows and matrix hydration potential. After progressively unfolding dermal collagen in situ, we measured the hydration parameters by osmotic stress techniques and modeled them as linear functions of unfolded collagen, quantified by differential scanning calorimetry after timed heat treatment. Consistent with the hypothetical model, the thermodynamic and flow parameters obtained experimentally were related linearly to the unfolded collagen fraction. The increases in relative humidity and intensity of T₂ maps were also consistent with interfacial energy contributions to the hydration potential and the hydrophobic character of the newly formed protein/water interfaces. As a plausible explanation, we propose that increased tension at interfaces formed during collagen unfolding generate local gradients in the matrix that accelerate water transfer in the dermis. This mechanism adds a convective component to interstitial transfer of biological fluids that, unlike diffusion, can speed the dispersion of water and large solutes within the matrix.     

Water of hydration in the intra- and extra-cellular environment of human erythrocytes

The proton nuclear magnetic resonance (NMR) titration method (which requires measurement of the relaxation rate at multiple measured levels of dehydration) was applied to the analysis of human erythrocytes, a hemoglobin solution, plasma, and serum. The results allowed identification of bulk water and four motionally perturbed water of hydration subfractions. Based on previous NMR studies of homopolypeptides we designated these subfractions as superbound, irrotationally bound, rotationally bound, and structured. The total water of hydration (sum of both structured and bound water subfractions) in plasma, serum, and hemoglobin ranged from 2.78 to 3.77 g H2O/g dry mass and the sum of the three bound water subfractions ranged from 1.23 to 1.72 g H2O/g dry mass. The total water of hydration on hemoglobin, as determined by (i) spin-lattice (T1) and spin-spin (T2) NMR data, (ii) quench ice-crystal imprint size, (iii) calculations based on osmotic pressure data, and (iv) two other methods, ranged from 2.26 to 3.45 g H2O/g dry mass. In contrast, the estimates of total water of hydration in the intact erythrocytes ranged from 0.34 to 1.44 g H2O/g dry mass, as determined by osmotic activity and spin-lattice titration, respectively. Studies on the magnetic-field dependence of the spin-lattice relaxation rate (1/T1 rho) of solvent water nuclei in protein solutions and in intact and disrupted erythrocytes indicated that hemoglobin aggregation exists in the intact erythrocytes and that erythrocyte disruption decreases the extent of hemoglobin aggregation. Together, the present and past data indicate that the extent of water of hydration associated with hemoglobin depends on the amount of salt present and the degree of aggregation of the hemoglobin molecules.     

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.     

Comparative studies of water sorption of hyaline cartilage

Vapor phase, water sorption isotherms were obtained for specimens of bovine, sturgeon and shark cartilage and for membranes composed of collagen and various proportions of cartilage proteoglycan. The data were interpreted in the light of an elementary model for swelling of gels which regards equilibrium swelling a resultant of a balance between contractile forces of an elastic matrix and expansive forces, principally osmotic in nature. Swelling ratios for bovine and sturgeon cartilage compared at the same water vapor pressure are nearly indentical, whereas the swelling ratios for shark cartilage are elevated. These high values are due principally to a higher ratio of glycosaminoglycan to collagen but also reflect a higher salt and urea content and possibly also a different type of collagen fibril network.