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.     

Extrafibrillar proteoglycans osmotically regulate the molecular packing of collagen in cartilage

The molecular packing density of collagen and hence the intrafibrillar water content appears to be regulated in cartilage by the osmotic pressure gradient existing between the extrafibrillar and the intrafibrillar compartments.     

The distribution of water in arterial elastin: Effects of mechanical stress,osmotic pressure,and temperature

Using gravimetric and radiotracer techniques, we investigated the effects of mechanical stress, osmotic pressure, and temperature on the volumes of the intra- and extrafibrillar water spaces in arterial elastin. We also investigated the effects of temperature on water flow through elastin membranes and on dynamic mechanical properties of elastin rings. Compression by mechanical or osmotic loading reduced the hydration of the elastin in an identical manner. Two distinct stages were evident; at low loads there was extensive water removal from the extrafibrillar space while high loads were required to remove water from the intrafibrillar space. Conversely, dehydration caused by mechanical extension of the matrix was associated with a much smaller loss from the extrafibrillar compartment and a large fractional decrease in the intrafibrillar space. Contraction of the matrix as a result of increased temperature had similar effects on hydration to those produced by extension. Water flux across elastin membranes, corrected for changes in viscosity, and specific hydraulic conductivity both increased as a result of temperature-induced contraction. This effect was attributed to increases in both the fractional volume of the extrafibrillar space and the fiber radius. The elastic modulus decreased with increasing temperature, but there was an increase in viscoelasticity. Previous studies have determined that viscoelasticity depends on the rate of redistribution of intrafibrillar water, so this finding provides additional evidence that heating affects primarily the volume of the intrafibrillar space. © 1995 John Wiley & Sons, Inc.     

Mechanical properties of mineralized collagen fibrils as influenced by demineralization

Dentin and bone derive their mechanical properties from a complex arrangement of collagen type-I fibrils reinforced with nanocrystalline apatite mineral in extra- and intrafibrillar compartments. While mechanical properties have been determined for the bulk of the mineralized tissue, information on the mechanics of the individual fibril is limited. Here, atomic force microscopy was used on individual collagen fibrils to study structural and mechanical changes during acid etching. The characteristic 67 nm periodicity of gap zones was not observed on the mineralized fibril, but became apparent and increasingly pronounced with continuous demineralization. AFM-nanoindentation showed a decrease in modulus from 1.5 GPa to 50 MPa during acid etching of individual collagen fibrils and revealed that the modulus profile followed the axial periodicity. The nanomechanical data, Raman spectroscopy and SAXS support the hypothesis that intrafibrillar mineral etches at a substantially slower rate than the extrafibrillar mineral. These findings are relevant for understanding the biomechanics and design principles of calcified tissues derived from collagen matrices.     

A study of dense mineralized tissue by neutron diffraction

Neutron diffraction studies of mineralized tissue show a close relationship between the wet state equatorial diffraction spacing and wet tissue density expressable as a second-order polynomial. The molecular fractional shrinkage when the tissue is dried shows a straight line dependence on wet tissue density with a correlation of 0.98. Since the dry state equatorial diffraction spacing is much less than for the corresponding wet state, even in fully mineralized bone, the collagen molecules must be displaced through a mineral-free volume while drying. The mineral can only be located within the available volume of the dried tissue whether intra- or extrafibrillar. The dimension of the dry state equatorial spacing for each of the tissues examined is close to that of dried tendon collagen. It appears unlikely that hydroxyapatite crystallites can be accommodated radially between collagen molecules in bone if the packing is like that of dried tail tendon collagen. The only mineral within the fibrils must be in the intermolecular gaps. It is estimated on the basis of the volume of the axial intermolecular gaps and the minimum extrafibrillar volume that the intrafibrillar mineral can be no more than 20% of the total mineral and may be less than 10%.     

MV-mimicking micelles loaded with PEG-serine-ACP nanoparticles to achieve biomimetic intra/extra fibrillar mineralization of collagen in vitro

Since their discovery, matrix vesicles (MVs) containing minerals have received considerable attention for their role in the mineralization of bone, dentin and calcified cartilage. Additionally, MVs' association with collagen fibrils, which serve as the scaffold for calcification in the organic matrix, has been repeatedly highlighted. The primary purpose of the present study was to establish a MVs–mimicking model (PEG-S-ACP/micelle) in vitro for studying the exact mechanism of MVs-mediated extra/intra fibrillar mineralization of collagen in vivo. In this study, high-concentration serine was used to stabilize the amorphous calcium phosphate (S-ACP), which was subsequently mixed with polyethylene glycol (PEG) to form PEG-S-ACP nanoparticles. The nanoparticles were loaded in the polysorbate 80 micelle through a micelle self-assembly process in an aqueous environment. This MVs–mimicking model is referred to as the PEG-S-ACP/micelle model. By adjusting the pH and surface tension of the PEG-S-ACP/micelle, two forms of minerals (crystalline mineral nodules and ACP nanoparticles) were released to achieve the extrafibrillar and intrafibrillar mineralization, respectively. This in vitro mineralization process reproduced the mineral nodules mediating in vivo extrafibrillar mineralization and provided key insights into a possible mechanism of biomineralization by which in vivo intrafibrillar mineralization could be induced by ACP nanoparticles released from MVs. Also, the PEG-S-ACP/micelle model provides a promising methodology to prepare mineralized collagen scaffolds for repairing bone defects in bone tissue engineering.     

Mechanical effects of ionic replacements in articular cartilage. Part I: The constitutive model

A three-phase multi-species electro–chemo-mechanical model of articular cartilage is developed that accounts for the effect of two water compartments, namely intrafibrillar water stored in between collagen fibrils and extrafibrillar water covering proteoglycans. The collagen fibers constitute the solid phase while intrafibrillar water and dissolved NaCl and CaCl₂ on one hand and extrafibrillar water, ions Na⁺, Ca²⁺ and Cl^? and proteoglycans on the other hand, form the two fluid phases. The complete picture that includes time-dependent mass transfers between the two fluid phases, diffusion of water and ions and electrical flow emerges from the Clausius–Duhem inequality but it is deferred to further study. The analysis is restricted to equilibrium states. The present work complements the mechanical model developed in Loret and Simões (Mech Material 36(5-6): 515-541, 2004a) where the presence of the sole NaCl was considered. In its current version, the model can handle mechanical and chemical loadings and unloadings involving the two salts, NaCl and CaCl₂. In order to reproduce experimental data, the shielding effects are made cation-dependent. Strong orientation of collagen fibers parallel to the joint surface implies anisotropic mechanical properties. Electro–chemo-mechanical couplings result in a chemistry-dependent apparent tensile Poisson’s ratio, that increases to large values as the solution gets fresher. The model captures these aspects as well. The features of the model are first exposed in an infinitesimal strain context. Subsequently, large strains that typically occur in uniaxial traction under deionized water are accounted for, and a nonlinear anisotropic hyperelastic behavior is developed. Parametric identification and simulations of actual loading processes are described in a companion paper, Loret and Simões (Biomech Model Mechanobiol, in press, DOI 10.1007/s10237-004-0063-6).     

The osmotic pressure of chondroitin sulphate solutions: experimental measurements and theoretical analysis

We used equilibrium dialysis to measure the osmotic pressure of chondroitin sulphate (CS) solutions as a function of their concentration and fixed charge density (FCD) and the ionic strength and composition of the solution. Osmotic pressure varied nonlinearly with the concentration of chondroitin sulphate and in 0.15 M NaCl at FCDs typical of uncompressed cartilage (approximately 0.4 mmol/g extrafibrillar H2O) was approximately 3 atmospheres. Osmotic pressure fell by 60% as solution ionic strength increased up to about 1 M, but remained relatively constant at higher ionic strengths. The ratio of Ca2+ to Na+ in the medium was a minor determinant of osmotic pressure. The data are compared with a theoretical model of the electrostatic contribution to osmotic pressure calculated from the Poisson-Boltzmann equation using a rod-in-cell model for CS. The effective radius of the polyelectrolyte rod is taken as a free parameter. The model qualitatively reproduces the non-linear concentration dependence, but underestimates the osmotic pressure by an amount that is independent of ionic strength. This difference, presumably arising from oncotic and entropic effects, is approximately 1/3 of the total osmotic pressure at physiological polymer concentrations and ionic strength.     

Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization

We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils’ shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.     

Accumulation of anthocyanins enhanced by a high osmotic potential in grape (Vitis vinifera L.) cell suspensions

A cell suspension of grape, Vitis vinifera L. cv Gamay Fréaux, was grown under different conditions of water stress (high external osmotic potential) induced by an increase of sucrose concentration or by the addition of mannitol to the culture medium. Best growth (cell density) was achieved in the low osmotic potential medium. Increasing the osmotic potential of the medium from –0.5 MPa to –0.9 MPa medium resulted in a significant increase in accumulation of anthocyanins in pigmented cells. Regulation of the osmotic potential of culture medium may be useful in controlling anthocyanin production.     

A quantitative analysis of elastic,entropic, electrostatic,and osmotic forces within relaxed skinned muscle fibers

The elastic behavior of mechanically skinned skeletal muscle fibers in relaxing solution is modelled using equations developed by Flory (1953) for the elasticity of non-biological polymers. Mechanically, the relaxed skinned fiber is considered to be a semi-crystalline network of inextensible polymer chains, which are periodically cross-linked and which are bathed in an aqueous medium. We consider (1) configurational elastic forces in the network, (2) entropic forces due to mixing of polymer and water, (3) electrostatic forces due to fixed charges on the muscle proteins and mobile charges in the bathing solution, and (4) compressive forces due to large colloids in the bathing solution. Van der Waals forces are not considered since calculations show that they are probably negligible under our conditions. We derive an expression which relates known quantities (ionic strength, osmotic compressive pressure, and fiber width), experimentally estimated quantities (fixed charge density and volume fraction of muscle proteins), and derived quantities (concentration of cross-links and a parameter reflecting the interaction energy between protein and water).The model was tested by comparison with observed changes in skinned fiber width under a variety of experimental conditions which included changes in osmotic compressive pressure, pH, sarcomere length, and ionic strength. Over a wide range of compressive pressure (0–36 atm) the theory predicted the nonlinear relation between fiber width and logarithm of pressure. The direction and magnitude of the decrease in width when pH was decreased to 4 could be modelled asssuming the fixed charge density on the protein network was 0.34 moles of electrons per liter protein, a value in accordance with the estimates of others. The relation between width and sarcomere length over the complete range of compressive pressures could be modelled with the assumption that the number of cross-links increases somewhat with sarcomere length. Changes of width with ionic strength were modelled assuming that increasing salt concentration both increased the electrostatic shielding of fixed charges and decreased the number of cross-links. The decrease of fiber width in 1% glutaraldehyde was modelled by assuming that the concentration of crosslinks increased by some 10%. The theory predicted the order of magnitude but not the detailed shape of the passive tension-length relation which may indicate that, as with non-biological polymers, the theory does not adequately describe the behavior of semi-crystalline networks at high degrees of deformation.In summary, the theory provides a semiquantitative approach to an understanding of the nature and relative magnitudes of the forces underlying the mechanical behavior of relaxed skinned fibers. It indicates, for instance, that when fibers are returned to near their in vivo size with 3% PVP, the forces in order of their importance are: ¦ elastic forces ¦ ¦ entropic forces > ¦ electrostatic forces ¦ ¦ osmotic compressive forces ¦.     

Physicochemical properties of arterial elastin and its associated glycoproteins

Microfibrillar glycoproteins are a significant component of vascular elastic tissue, but little is known about their contribution to vascular physiology and pathology. We have investigated some physicochemical properties of the glycoproteins that may be pertinent to these roles. Because of the difficulty in isolating intact glycoproteins in a form and quantity suitable for physicochemical examination, we based our analysis on a comparison of the properties of porcine thoracic aorta and pulmonary artery extracted with GuHCl and collagenase (preparation GC) and after further treatment with dithioerythritol to remove glycoproteins (preparation GC/DTE). Amino acid analysis showed that GC/DTE had the amino acid composition of pure elastin while GC contained a higher proportion of polar amino acids, particularly in the aortic preparation. GC stained with alcian blue, particularly in the intimal region, but GC/DTE did not. GC had a higher water content and a slower viscoelastic response and the circumferential elastic modulus was approximately 50% lower (whether expressed in terms of sample weight or elastin content). Clearly, therefore, the microfibrils do not stiffen the network and may prevent the alignment of elastin fibers in the circumferential direction. Their effect on hydration may arise either because they impose mechanical constraints on the geometry of the network or because they modify the inter‐ and intramolecular hydrophobic or electrostatic interactions that influence the tissue organization and hydration. Molecular probe measurements of the intrafibrillar pore structure using radiolabeled and fluorescent probes showed that removal of the microfibrils caused a slight decrease in the extrafibrillar water space and a larger decrease in the intrafibrillar water space. Sucrose, a small probe molecule, was able to penetrate most of the intrafibrillar water space when microfibrils were present but was virtually excluded when they were not. Potentiometric titration and radiotracer assays of ion binding both showed that the microfibrils contribute a considerable negative charge (−9 μmoles/g wet tissue in the aortic preparation and −16 μmoles/g wet weight in the pulmonary artery) and increase calcium binding by approximately 30%. © 1999 John Wiley & Sons, Inc. Biopoly 49: 255–265, 1999     

X-ray diffraction studies on the structure of hydrated collagen

The temperature dependence of the humidity-sensitive spacing, d, related to the lateral packing of collagen molecules was measured for fully hydrated collagen. In the vicinity of 0°C, a sudden change in d was observed, which was reversible with temperature. In the diffraction profile, below 0°C, a set of diffraction peaks identified with the hexagonal crystalline form of ice was observed. With the reduction in water content, the intensity of the set of diffraction peaks decreased and was found to be zero at a water content of 0.38 g/g collagen. These results were considered to be caused by the frozen water in collagen fibril below 0°C. According to the water content dependence of d, it was considered that up to a certain water content water absorbed would be stowed in the intermolecular space of collagen and above that water content water molecules would aggregate to make pools, i. e., extrafibrillar spaces. The unfreezable bound water was considered to be located in the intermolecular space of collagen. Size of the extrafibrillar space, determined from the intensity analysis of a smallangle x-ray scattering pattern, corroborates the speculation that the water showed in the extrafibrillar space is freezable and free. The formation of the hexagonal crystalline form of ice in the extrafibrillar space was considered to cause the sudden change in d at 0°C.     

Novel technique for online characterization of cartilaginous tissue properties

The goal of tissue engineering is to use substitutes to repair and restore organ function. Bioreactors are an indispensable tool for monitoring and controlling the unique environment for engineered constructs to grow. However, in order to determine the biochemical properties of engineered constructs, samples need to be destroyed. In this study, we developed a novel technique to nondestructively online-characterize the water content and fixed charge density of cartilaginous tissues. A new technique was developed to determine the tissue mechano-electrochemical properties nondestructively. Bovine knee articular cartilage and lumbar annulus fibrosus were used in this study to demonstrate that this technique could be used on different types of tissue. The results show that our newly developed method is capable of precisely predicting the water volume fraction (less than 3% disparity) and fixed charge density (less than 16.7% disparity) within cartilaginous tissues. This novel technique will help to design a new generation of bioreactors which are able to actively determine the essential properties of the engineered constructs, as well as regulate the local environment to achieve the optimal conditions for cultivating constructs.     

Preparative electrophoresis: on the estimation of maximum temperature

The quantity of proteins processed by an electrophoretic technique is proportional to the cross-sectional area of the gel. For preparative purifications, an increase in the cross-sectional area is desired, but the Joule heating phenomenon restricts such an increase. The governing heat equation is analyzed and simplified with reference to Counteracting Chromatographic Electrophoresis. The application of the method of weighted residuals yields a compact and accurate solution for the maximum temperature rise in the column which is suitable for design calculations. Similar estimations indicate the efficiency of heat dissipation in annular configuration.List of Symbols C _p specific heat capacity, J g^–1 K^–1 - h heat transfer coefficient at the wall, W cm^–2K^–1 - i current density, A cm^–2 - k effective thermal conductivity of the packing, W cm^–1 K^–1 - k _b electrical conductivity of the buffer, mho cm^–1 - k _e effective electrical conductivity of the packing, mho cm^–1 - k _g electrical conductivity of the gel, mho cm^–1 - L length of the packing, cm - N _Pr Prandtl number - N _Re Reynolds number - r radial coordinate, cm - r _i inner radius of annulus, cm - r _o outer radius of annulus, cm - S heat source term, defined by eqn. (6) - T temperature, K - T _c cooling fluid temperature, K - T _i initial temperature, K - T _max highest temperature in the column, K - u superficial buffer velocity, cm s^–1 - V voltage gradient, V cm^–1 - porosity of the packing, dimensionless - buffer density, g cm^–3 - temperature, dimensionless Material presented in this paper has been adapted from the author's dissertation [15] which was accepted (supervisor: Dr. Jean B. Hunter) by the Cornell University Graduate Faculty in partial requirement of a graduate degree. Thoughtful discussions with Professors J. Robert Cooke and Michael L. Shuler regarding the annulus problem and the financial support provided by the Department of Agricultural and Biological Engineering, Cornell University, Ithaca, USA are gratefully appreciated.     

Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma.

Ultrastructural data from x-ray diffraction studies of the cornea were used to estimate the refractive indices of the collagen fibrils and extrafibrillar material of human, ox, trout, and rabbit corneas. X-ray diffraction measurements of the size and spacing of the collagen fibrils and the separation between the constituent molecules of the fibrils were taken from a previous species study. The tissue volume fractions occupied by the stromal components were estimated and their refractive indices were calculated using the Gladstone-Dale law of mixtures. For the fibrils and extrafibrillar material, the refractive indices in the human cornea were 1.411 and 1.365; for the ox 1.413 and 1.357; for the rabbit 1.416 and 1.357; and for the trout 1.418 and 1.364, respectively. An alternative estimate based on the physical properties and chemical composition of bovine cornea, accounting for interfibrillar type VI collagen and cellular water, produced similar estimates of 1.416 and 1.356 for the fibrils and extrafibrillar material, respectively.     

Water relations and mucopolysaccharide increases for a winter hardy cactus during acclimation to subzero temperatures

Summary Thickness, relative water content (RWC), osmotic pressure, water potential isotherms, and mucopolysaccharide content were measured for the photosynthetic chlorenchyma and the water-storage parenchyma of the winter hardy cactus, Opuntia humifusa, after shifting from day/night air temperatures of 25° C/15° C to 5° C/–5° C. After 14 d at 5° C/–5° C, the average fraction of water contained in the symplast decreased from 0.92 to 0.78, the water potential of saturated (fully hydrated) tissue was essentially unchanged, but the osmotic pressure of saturated tissue decreased (by 0.15 MPa for the chlorenchyma and 0.12 MPa for the water-storage parenchyma). After 7 weeks at 5° C/–5° C, tissue thickness was reduced by 61% for the chlorenchyma and 65% for the water-storage parenchyma, and the RWC decreased by 42% and 68%, respectively; these changes contributed to an osmotic pressure increase of 0.55 MPa for the chlorenchyma and 0.34 MPa for the water-storage parenchyma. During the 7 week acclimation to low temperature, mucopolysaccharide increased by 114% for the chlorenchyma and by 89% for the water-storage parenchyma. The water potential of the extracted mucopolysaccharide was relatively constant for an RWC between 1.00 and 0.30, decreasing abruptly below 0.30. Changes in water relations parameters and in mucopolysaccharide content during low-temperature acclimation may reduce water efflux from the cells, and thus reduce damage due to rapid dehydration during extracellular freezing.     

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.     

Tectorial membrane material properties in Tecta(Y)(1870C/+) heterozygous mice

The solid component of the tectorial membrane (TM) is a porous matrix made up of the radial collagen fibers and the striated sheet matrix. The striated sheet matrix is believed to contribute to shear impedance in both the radial and longitudinal directions, but the molecular mechanisms involved have not been determined. A missense mutation in Tecta, a gene that encodes for the α-tectorin protein in the striated sheet matrix, causes a 60-dB threshold shift in mice with relatively little reduction in outer hair cell amplification. Here, we show that this threshold shift is coupled to changes in shear impedance, response to osmotic pressure, and concentration of fixed charge of the TM. In Tecta^Y1870C/+ mice, the tectorin content of the TM was reduced, as was the content of glycoconjugates reacting with the lectin wheat germ agglutinin. Charge measurements showed a decrease in fixed charge concentration from −6.4±1.4 mmol/L in wild-types to −2.1±0.7 mmol/L in Tecta^Y1870C/+ TMs. TMs from Tecta^Y1870C/+ mice showed little volume change in response to osmotic pressure compared to those of wild-type mice. The magnitude of both radial and longitudinal TM shear impedance was reduced by 10±1.6 dB in Tecta^Y1870C/+ mice. However, the phase of shear impedance was unchanged. These changes are consistent with an increase in the porosity of the TM and a corresponding decrease of the solid fraction. Mechanisms by which these changes can affect the coupling between outer and inner hair cells are discussed.     

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.