An ionised/non-ionised dual porosity model of intervertebral disc tissue

The volume of the intrafibrillar water space – i.e. the water contained inside the collagen fibres – is a key parameter that is relevant to concepts of connective tissue structure and function. Confined compression and swelling experiments on annulus fibrosus samples are interpreted in terms of a dual porosity model that distinguishes between a non-ionised intrafibrillar porosity and an ionised extrafibrillar porosity. Both porosities intercommunicate and are saturated with a monovalent ionic solution, i.c. NaCl. The extrafibrillar fixed charge density of the samples is assessed using radiotracer techniques and the collagen content is evaluated by measurement of hydroxyproline concentration. The interpretation of the experimental data yields values for the intrafibrillar water content, the average activity coefficient of the ions, the Donnan osmotic coefficient, the fraction of intrafibrillar water, the stress-free deformation state, and an effective stress–strain relationship as a function of the radial position in the disc. A linear fit between the second Piola–Kirchhoff effective stress and Green–Lagrange strain yielded an effective stiffness: H_e=1.087 ± 0.657 MPa. The average fraction of intrafibrillar water was 1.16 g/g collagen. The results were sensitive to changes in the activity and osmotic coefficients and the fraction of intrafibrillar water. The fixed charge density increased with distance from the outer edge of the annulus, whereas the hydroxyproline decreased.The authors wish to thank Dr. Jill Urban for her advice concerning fixed charge density measurements, and Ing. Paul Willems for his assistance with the experiments. The research of Dr. J. M. Huyghe has been made possible through a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

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.     

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     

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.     

Influence of solvent composition on the mechanical properties of arterial elastin

We have investigated the effects of changes in solution composition on the mechanical properties of rings of arterial elastin. The time course of force equilibration at constant strain following a change in the composition of the bathing solution was measured. Both the force developed during slow extension and force relaxation following rapid straining were also measured in each of the test solutions. The results are difficult to summarize because all of the primitive quantities measured--sample dimension, slope of the force-extension curve, force overshoot and time of relaxation--as well as the derived quantities such as elastic modulus changed in different and apparently uncorrelated ways. Changes in pH and ionic composition of the bathing solution had small effects consistent with the low fixed charge density of elastin. Solutions of glucose, sucrose, and ethylene glycol had larger effects consistent with changes in hydrophobic interactions. The viscosity of the solution that penetrated the intrafibrillar space of the elastin appeared to be a major determinant of the dynamic response.     

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%.     

The effects of solutes on the freezing properties of and hydration forces in lipid lamellar phases.

Quantitative deuterium nuclear magnetic resonance is used to study the freezing behavior of the water in phosphatidylcholine lamellar phases, and the effect upon it of dimethylsulfoxide (DMSO), sorbitol, sucrose, and trehalose. When sufficient solute is present, an isotropic phase of concentrated aqueous solution may coexist with the lamellar phase at freezing temperatures. We determine the composition of both unfrozen phases as a function of temperature by using the intensity of the calibrated free induction decay signal (FID). The presence of DMSO or sorbitol increases the hydration of the lamellar phase at all freezing temperatures studied, and the size of the increase in hydration is comparable to that expected from their purely osmotic effect. Sucrose and trehalose increase the hydration of the lamellar phase, but, at concentrations of several molal, the increase is less than that which their purely osmotic effect would be expected to produce. A possible explanation is that very high volume fractions of sucrose and trehalose disrupt the water structure and thus reduce the repulsive hydration interaction between membranes. Because of their osmotic effect, all of the solutes studied reduced the intramembrane mechanical stresses produced in lamellar phases by freezing. Sucrose and trehalose at high concentrations produce a greater reduction than do the other solutes.     

The effects of hydration on the dynamic mechanical properties of elastin

The dynamic mechanical properties of elastin have been quantified over a temperature and hydration range appropriate for a biological polymer. Composite curves of the tensile properties at constant water contents between 28.1 and 44.6% (g water/100 g protein) were typical of an amorphous polymer going through its glass transition. Water content had no effect on the shape of the curves, but shifted them a distance aC along the frequency axis. The combined effects of hydration and temperature are given in a series of isoshift curves where elastin's properties are constant along any one curve. A 1% change in hydration has the same effect as a 1 degrees-2 degrees change in temperature, depending on the initial water content and temperature. Theoretical isoshift curves that matched the experimental data were predicted using the WLF equation and coefficients determined from the data. These data form a basis to predict the role of elastin in arterial disease based on changes in its chemical and physical environment.     

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).     

Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach

Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling.     

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.     

Effects of lipids on elastin's viscoelastic properties

Sodium dodecyl sulfate (SDS) was used as a model lipid to identify the molecular basis of possible lipid-induced changes in the viscoelastic behavior of arterial elastin. The chemical composition of the elastin network and the interfibrillar space was calculated from the chemical content of the elastin sample and its swelling behavior. Viscoelastic behavior was measured in aqueous SDS and in SDS plus 1 M sucrose, a deswelling agent. Viscoelastic behavior was also measured in sucrose and potassium thiocyanate solutions to identify the effects of swelling and of changes in network composition exclusive of any direct SDS effects. The hydration of the elastin network decreased at low SDS levels and increased at higher SDS levels. The elastin was stiffer in the dehydrated network and less stiff in the hydrated network. However, once the degree of hydration exceeded that of elastin in pure water, no further decrease in stiffness was obtained despite continued increase in swelling. The stiffness of the network could be accounted for entirely by changes in network hydration. There was no evidence that SDS had any effect on elastin's conformation. We predict that arterial lipids will interact with elastin in a similar way and will have only small effects on elastin's viscoelastic behavior.     

The density and free water of cholinergic synaptic vesicles as a function of osmotic pressure

Synaptic vesicles from the cholinergic electromotor nerve terminals of Torpedo marmorata are among the most uniform subcellular organelles known and are osmotically sensitive. Changes in density accompanying osmotic perturbation have enabled changes in water content to be calculated; when referred to a standard state of known volume and water content, fractional and absolute water contents could be calculated for the perturbed states and compared with the fractional free water content as measured by the glycerol space. Under hyperosmotic conditions, discrepancies were found between these two estimates, the glycerol space falling more rapidly than the water space predicted from the density change. This is attributed to a failure of glycerol to displace water imbibed by the membrane as it collapses round an aqueous core of decreasing volume. 'Reserve' vesicles obeyed a relationship between density, osmotic load and osmolality derived for a perfect osmometer, and independent estimates of fractional free water content under standard conditions and osmotic load were made. The former of these agreed well with the glycerol space under standard conditions and the latter agreed with previous estimates of the osmotic load using morphological and analytical data and an assumed activity coefficient of 0.65. Finally, it was possible to model the interconversion of reserve and recycling vesicles more accurately than in previous work.     

Critical Role of Silicon in Directing the Bio-inspired Mineralization of Gelatin in the Presence of Hydroxyapatite

Significant progress has been made on understanding the critical role of organic components in directing the collagen mineralization.We hypothesize that the inorganic trace elements might also play important role in the mineralization of collagenous matrix.To this aim,we systematically compared the in-vitro biomineralization behaviors of gelatin,gelatin-HA and gelatin-SiHA electrospun membranes.The results indicated that the presence of Si ions played a striking influence on the nucleation behaviors and mineralized structures.The gelatin-SiHA samples demonstrated more homogeneous nucleation within the gelatin fiber and growth along the fiber direction,in comparison with the heterogeneous nucleation and growth of spherulitic clusters on top of the nanofiber surface,i.e.extrafibrillar mineralization.The likely shift of the nucleation mode to the intrafibrillar mineralization in the presence of Si ions led to good alignment of apatite c-axis with the long axis of the nanofiber,resulting in a mineralization process and microstructure that were closer to those in natural bone.Cellular response analysis indicated that Si incorporation improved the MSC attachment and cytoskeleton organization.Such findings might have important implication in both understanding the complex mechanisms involved in collagen mineralization and optimal designing of advanced bio-inspired materials with potential superior mechanical and biological properties.     

Dynamic mechanical properties of elastin.

The dynamic mechanical properties of water-swollen elastin under physiological conditions have been investigated. When elastin is tested as a colsed, fixed-volume system, mechanical data could be temperature shifted to produce master curves. Master curves for elastin hydrated at 36°C (water content, 0.46 g water/g protein) and 55°C (water content, 0.41 g/g) were constructed, and in both cases elastin goes through a glass transition, with the glass transition temperatures of -46 and -21°C, respectively. Temperature shift data used to construct the master curves follow the WLF equation, and the glass transition appears to be characteristic of an amorphous, random-polymer network. For elastin tested as an open, variable-volume system free to change its swollen volume as temperature is changed, dynamic mechanical properties appear to be virtually independent of temperature. No glass transition is observed because elastin swelling increases with decreased temperature, and the increase in water content shifts elastin away from its glass transition. It is suggested that the hydrophobic character of elastin, which gives rise to the unusual swelling properties of elastin, evolved to provide a temperature-independent elastomer for the cold-blooded, lower vertebrates.     

The increase in denaturation temperature following cross-linking of collagen is caused by dehydration of the fibres

Differential scanning calorimetry (DSC) was used to study the thermal stability of native and synthetically cross-linked rat-tail tendon at different levels of hydration, and the results compared with native rat-tail tendon. Three cross-linking agents of different length between functional groups were used: malondialdehyde (MDA), glutaraldehyde and hexamethylene diisocyanate (HMDC). Each yielded the same linear relation between the reciprocal of the denaturation temperature in Kelvin, T(max), and the water volume fraction, epsilon (1/T(max)=0.000731epsilon+0.002451) up to a critical hydration level, the volume fraction of water in the fully hydrated fibre. Thereafter, water was in excess, T(max) was constant and the fibre remained unchanged, no matter how much excess water was added. This T(max) value and the corresponding intrafibrillar volume fraction of water were as follows: 84.1 degrees C and 0.48 for glutaraldehyde treated fibres, 74.1 degrees C and 0.59 for HMDC treated fibres, 69.3 degrees C and 0.64 for MDA treated fibres, and 65.1 degrees C and 0.69 for untreated native fibres. Borohydride reduction of the native enzymic aldimines did not increase the denaturation temperature of the fibres. As all samples yielded the same temperature at the same hydration, the temperature could not be affected by the nature of the cross-link other than through its effect on hydration. Cross-linking therefore caused dehydration of the fibres by drawing the collagen molecules closer together and it was the reduced hydration that caused the increased temperature stability. The cross-linking studied here only reduced the quantity of water between the molecules and did not affect the water in intimate contact with, or bound to, the molecule itself. The enthalpy of denaturation was therefore unaffected by cross-linking. Thus, the "polymer-in-a-box" mechanism of stabilization, previously proposed to explain the effect of dehydration on the thermal properties of native tendon, explained the new data also. In this mechanism, the configurational entropy of the unfolding molecule is reduced by its confinement in the fibre lattice, which shrinks on cross-linking.     

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.     

Elastin dehydration through the liquid and the vapor phase: A comparison of osmotic stress models

The swelling and viscoelastic behaviors of samples of purified arterial elastin were investigated to develop a model for studying the viscoelastic behavior of elastin. Two osmotic stress models were used: the vapor phase model (VPM), in which the stress on the elastin sample was applied through the vapor phase by equilibrating the sample over a saline solution, and the liquid phase model (LPM), in which the stress was applied through the liquid phase by equilibrating the sample in aqueous solutions of large molecular weight polymers. The elastin in the VPM showed a highly varied viscoelastic response, and was slightly stiffer and had a slightly higher damping coefficient than the elastin in the LPM at equivalent nominal relative humidities. We believe the difference in behavior of the elastin in the two models was due to geometric distortions of the elastin that occur during dehydration in the VPM. In the LPM, the spaces between the elastin fibrils are filled with water, and in the VPM these spaces collapse when the water is removed. Removal of only the interfibrillar water deswelled the tissue and increased its stiffness and damping coefficient. Viscoelastic spectra obtained at different levels of osmotic stress in the LPM were reducible to one master curve, indicating that the dominant effect of dehydration is a nonspecific reduction of molecular mobility. We conclude that the LPM is a better model than the VPM for studying the effects of dehydration on the mechanical behavior of elastin. © 1996 John Wiley & Sons, Inc.     

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.