The effect of matrix tension-compression nonlinearity and fixed negative charges on chondrocyte responses in cartilage

Thorough analyses of the mechano-electrochemical interaction between articular cartilage matrix and the chondrocytes are crucial to understanding of the signal transduction mechanisms that modulate the cell metabolic activities and biosynthesis. Attempts have been made to model the chondrocytes embedded in the collagen-proteoglycan extracellular matrix to determine the distribution of local stress-strain field, fluid pressure and the time-dependent deformation of the cell. To date, these models still have not taken into account a remarkable characteristic of the cartilage extracellular matrix given rise from organization of the collagen fiber architecture, now known as the tension-compression nonlinearity (TCN) of the tissue, as well as the effect of negative charges attached to the proteoglycan molecules, and the cell cytoskeleton that interacts with mobile ions in the interstitial fluid to create osmotic and electro-kinetic events in and around the cells. In this study, we proposed a triphasic, multi-scale, finite element model incorporating the Conewise Linear Elasticity that can describe the various known coupled mechanical, electrical and chemical events, while at the same time representing the TCN of the extracellular matrix. The model was employed to perform a detailed analysis of the chondrocytes' deformational and volume responses, and to quantitatively describe the mechano-electrochemical environment of these cells. Such a model describes contributions of the known detailed micro-structural and composition of articular cartilage. Expectedly, results from model simulations showed substantial effects of the matrix TCN on the cell deformational and volume change response. A low compressive Poisson's ratio of the cartilage matrix exhibiting TCN resulted in dramatic recoiling behavior of the tissue under unconfined compression and induced significant volume change in the cell. The fixed charge density of the chondrocyte and the pericellular matrix were also found to play an important role in both the time-dependent and equilibrium deformation of the cell. The pericellular matrix tended to create a uniform osmolarity around the cell and overall amplified the cell volume change. It is concluded that the proposed model can be a useful tool that allows detailed analysis of the mechano-electrochemical interactions between the chondrocytes and its surrounding extracellular matrix, which leads to more quantitative insights in the cell mechano-transduction.     

Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation

The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.     

A Conewise Linear Elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage

A biphasic mixture model is developed that can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37, 1-38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H-A = 0.64 +/- 0.22 MPa, k2 = 3.62 +/- 0.97 x 10(-16) m4/N.s, r2 = 0.95 +/- 0.03), the tensile modulus, compressive Poisson ratio, and radial permeability were obtained from unconfined compression (E+Y = 12.75 +/- 1.56 MPa, v- = 0.03 +/- 0.01, kr = 6.06 +/- 2.10 x 10(-16) m4/N.s, r2 = 0.99 +/- 0.00), and the shear modulus was obtained from torsional shear (mu = 0.17 +/- 0.06 MPa). The model was also employed to predict the interstitial fluid pressure successfully at the center of the cartilage plug in unconfined compression (r2 = 0.98 +/- 0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.     

The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension-compression stress-strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73-84] to incorporate tension-compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576-586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1-38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123-130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension-compression nonlinearity.     

Osteoarthritic changes in the biphasic mechanical properties of the chondrocyte pericellular matrix in articular cartilage

The pericellular matrix (PCM) is a narrow region of cartilaginous tissue that surrounds chondrocytes in articular cartilage. Previous modeling studies indicate that the mechanical properties of the PCM relative to those of the extracellular matrix (ECM) can significantly affect the stress-strain, fluid flow, and physicochemical environments of the chondrocyte, suggesting that the PCM plays a biomechanical role in articular cartilage. The goals of this study were to measure the mechanical properties of the PCM using micropipette aspiration coupled with a linear biphasic finite element model, and to determine the alterations in the mechanical properties of the PCM with osteoarthritis (OA). Using a recently developed isolation technique, chondrons (the chondrocyte and its PCM) were mechanically extracted from non-degenerate and osteoarthritic human cartilage. The transient mechanical behavior of the PCM was well-described by a biphasic model, suggesting that the viscoelastic response of the PCM is attributable to flow-dependent effects, similar to that of the ECM. With OA, the mean Young's modulus of the PCM was significantly decreased (38.7+/-16.2 kPa vs. 23.5+/-12.9 kPa, p < 0.001), and the permeability was significantly elevated (4.19+/-3.78 x10(-17) m(4)/Ns vs. 10.2+/-9.38 x 10(-17) m(4)/Ns, p < 0.01). The Poisson's ratio was similar for both non-degenerate and OA PCM (0.044+/-0.063 vs. 0.030+/-0.068, p > 0.6). These findings suggest that the PCM may undergo degenerative processes with OA, similar to those occurring in the ECM. In combination with previous theoretical models of cell-matrix interactions in cartilage, our findings suggest that changes in the properties of the PCM with OA may have an important influence on the biomechanical environment of the chondrocyte.     

The apparent viscoelastic behavior of articular cartilage--the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows

Articular cartilage was modeled rheologically as a biphasic poroviscoelastic material. A specific integral-type linear viscoelastic model was used to describe the constitutive relation of the collagen-proteoglycan matrix in shear. For bulk deformation, the matrix was assumed either to be linearly elastic, or viscoelastic with an identical reduced relaxation spectrum as in shear. The interstitial fluid was considered to be incompressible and inviscid. The creep and the rate-controlled stress-relaxation experiments on articular cartilage under confined compression were analyzed using this model. Using the material data available in the literature, it was concluded that both the interstitial fluid flow and the intrinsic matrix viscoelasticity contribute significantly to the apparent viscoelastic behavior of this tissue under confined compression.     

A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage.

The indentation problem of a thin layer of hydrated soft tissue such as cartilage or meniscus by a circular plane-ended indenter is investigated. The tissue is represented by a biphasic continuum model consisting of a solid phase (collagen and proteoglycan) and a fluid phase (interstitial water). A finite element formulation of the linear biphasic continuum equations is used to solve an axisymmetric approximation of the indentation problem. We consider stress-relaxation problems for which analytic solution is intractable; where the indenter is impermeable (solid) and/or when the interface between the indenter and tissue is perfectly adhesive. Thicknesses corresponding to a thin and thick specimen are considered to examine the effects of tissue thickness. The different flow, pressure, stress and strain fields which are predicted within the tissue, over time periods typically used in the mechanical testing of soft tissues, will be presented. Results are compared with the case of a porous free-draining indenter with a perfectly lubricated tissue-indenter interface, for which an analytic solution is available, to show the effects of friction at the tissue-indenter interface, and the effects of an impermeable indenter. While these effects are present for both thin and thick tissues, they are shown to be more significant for the thin tissue. We also examine the effects of the stiffness of the subchondral bone on the response of the soft tissue and demonstrate that the subchondral bone substrate can be modeled as a rigid, impermeable boundary. The effects of a curved tissue-subchondral bone interface, and the early time response are also studied. For physiologically reasonable levels of curvature, we will show that the curved tissue-subchrondal bone interface has negligible influence on the tissue response away from the interface. In addition, the short-time stress-relaxation responses of the tissue (e.g., at times less than 1s) demonstrate the essential role of the fluid phase in supporting the load applied to the tissue, and by extrapolation to shorter times characteristics of normal joint motion, suggest the essential role of a biphasic model in representing soft tissue behavior in joint response.     

New resource for the computation of cartilage biphasic material properties with the interpolant response surface method

Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48–1.58 MPa), Poisson's ratio (0.00–0.05) and permeability (1.7 × 10^? 15–5.4 × 10^? 15 m⁴/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish.     

Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63-72, Lai et al., 1991, J. Biomech. Eng., 113, pp. 245-258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576-586; Curnier et al., 1995, J. Elasticity, 37, pp. 1-38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.     

The roles of annexins and types II and X collagen in matrix vesicle-mediated mineralization of growth plate cartilage

Annexins II, V, and VI are major components of matrix vesicles (MV), i.e. particles that have the critical role of initiating the mineralization process in skeletal tissues. Furthermore, types II and X collagen are associated with MV, and these interactions mediated by annexin V stimulate Ca(2+) uptake and mineralization of MV. However, the exact roles of annexin II, V, and VI and the interaction between annexin V and types II and X collagen in MV function and initiation of mineralization are not well understood. In this study, we demonstrate that annexin II, V, or VI mediate Ca(2+) influx into phosphatidylserine (PS)-enriched liposomes, liposomes containing lipids extracted from authentic MV, and intact authentic MV. The annexin Ca(2+) channel blocker, K-201, not only inhibited Ca(2+) influx into fura-2-loaded PS-enriched liposomes mediated by annexin II, V, or VI, but also inhibited Ca(2+) uptake by authentic MV. Types II and X collagen only bound to liposomes in the presence of annexin V but not in the presence of annexin II or VI. Binding of these collagens to annexin V stimulated its Ca(2+) channel activities, leading to an increased Ca(2+) influx into the liposomes. These findings indicate that the formation of annexin II, V, and VI Ca(2+) channels in MV together with stimulation of annexin V channel activity by collagen (types II and X) binding can explain how MV are able to rapidly take up Ca(2+) and initiate the formation of the first crystal phase.     

The roles of intrinsic disorder in orchestrating the Wnt-pathway

The canonical Wnt-pathway plays a number of crucial roles in the development of organism. Malfunctions of this pathway lead to various diseases including cancer. In the inactivated state, this pathway involves five proteins, Axin, CKI-α, GSK-3β, APC, and β-catenin. We analyzed these proteins by a number of computational tools, such as PONDR(r)VLXT, PONDR(r)VSL2, MoRF-II predictor and Hydrophobic Cluster Analysis (HCA) to show that each of the Wnt-pathway proteins contains several intrinsically disordered regions. Based on a comprehensive analysis of published data we conclude that these disordered regions facilitate protein-protein interactions, post-translational modifications, and signaling. The scaffold protein Axin and another large protein, APC, act as flexible concentrators in gathering together all other proteins involved in the Wnt-pathway, emphasizing the role of intrinsically disordered regions in orchestrating the complex protein-protein interactions. We further explore the intricate roles of highly disordered APC in regulation of β-catenin function. Intrinsically disordered APC helps the collection of β-catenin from cytoplasm, facilitates the b-catenin delivery to the binding sites on Axin, and controls the final detachment of β-catenin from Axin.     

Experimental verification of the crucial roles of Glu73 in the catalytic activity and structural stability of goose type lysozyme

The roles of Glu(73), which has been proposed to be a catalytic residue of goose type (G-type) lysozyme based on X-ray structural studies, were investigated by means of its replacement with Gln, Asp, and Ala using ostrich egg-white lysozyme (OEL) as a model. No remarkable differences in secondary structure or substrate binding ability were observed between the wild type and Glu(73)-mutated proteins, as evaluated by circular dichroism (CD) spectroscopy and chitin-coated celite chromatography. Substitution of Glu(73) with Gln or Ala abolished the enzymatic activity toward both the bacterial cell substrate and N-acetylglucosamine pentamer, (GlcNAc)(5), while substitution with Asp did not abolish but drastically reduced the activity of OEL. These results demonstrate that the carboxyl group of Glu(73) is directly involved in the catalytic action of G-type lysozyme. Furthermore, the stabilities of all three mutants, which were determined from the thermal and guanidine hydrochloride (GdnHCl) unfolding curves, respectively, were significantly decreased relative to those of the wild type. The results obtained clearly indicate the crucially important roles of Glu(73) in the structural stability as well as in the catalytic activity of G-type lysozyme.     

β1-Integrins in the cartilage matrix

Integrins are cell-surface receptors that mediate cell attachment to extracellular matrix components. The pericellular matrix in cartilage not only is a mechanical framework, but is also important for chondrocyte differentiation and stabilization of the phenotype. The interaction between chondrocytes and pericellular matrix is mediated, in part, by integrin receptors. We have previously demonstrated the presence of beta1-integrins in the cartilage matrix of organoid culture of limb buds from 12-day-old mouse embryos by immunohistological methods. In order to corroborate these findings, we have further investigated the distribution of integrins in the cartilage matrix by immunoelectron microscopy and by immunoprecipitation methods. Cartilage tissue of limb buds of 17-day-old mouse embryos was treated with collagenase and the cell-free and cellular protein-free supernatant was removed and used for immunoprecipitation experiments. Immunoprecipitation with antibodies against beta1-, alpha1-, alpha3-, and alpha5beta1-integrins and collagen type II, followed by immunoblotting with the same antibodies, demonstrated the presence of these integrins and collagen type II in the supernatant. The integrins found in the cartilage matrix could have been either secreted or shed by the cells. The question as to whether they have a function in the cartilage matrix, such as interlinking, in the matrix organization or in the stabilization of matrix components remains to be elucidated.     

Polymer dynamics as a mechanistic model for the flow-independent viscoelasticity of cartilage

The initial, rapid, flow independent, apparent stress relaxation of articular cartilage disks deformed by unconfined compressive displacement is shown to be consistent with the theory of polymer dynamics. A relaxation function for polymers based upon a mechanistic model of molecular interaction (reptation) appropriately approximated early, flow independent relaxation of stress. It is argued that the theory of polymer dynamics, with its reliance on mechanistic models of molecular interaction, is an appropriate technique for application to and the understanding of rapid, flow independent, stress relaxation in cartilage.     

Immunological analysis of chick notochord and cartilage matrix development with antisera to cartilage matrix macromolecules

Transverse frozen sections from the postcephalic region of stage 9-16 chick embryos and from the wing bud region of stage 17-31 embryos were stained with antibodies to the major extracellular matrix components of cartilage. These probes included unfractionated A1 and A2 antisera to the major cartilage proteoglycan, affinity-purified purified antibodies to the proteoglycan core protein and to Type II collagen, and a monoclonal antibody to keratan sulfate. In embryos as early as stage 10, notochord stained specifically with the keratan sulfate monoclonal antibody. At this stage the notochord, as well as surrounding tissues, were negative to cartilage proteoglycan and collagen antibodies. Positive staining with the latter probes was coordinately acquired by notochord cells and their accompanying sheath around stage 15, while surrounding tissues remained negative. At this stage, the ventral region of the perispinal cord sheath exhibited light staining with the proteoglycan and keratan sulfate antibodies though failing to react to Type II collagen antibodies. Positive staining of notochord and ventral spinal cord persisted through later developmental stages. As revealed by immunofluorescence, definitive vertebral chondroblasts first emerged at approximately stage 23 and definitive limb chondroblasts at stage 25. The results are discussed in terms of the possible multiple roles of notochord in early embryogenesis.     

Association between proteoglycans and matrix vesicles in the extracellular matrix of growth plate cartilage

Matrix vesicles (MV) are microstructures localized to the extracellular matrix of developing hard tissues that induce mineral formation. MV proteins are not well characterized, and little is known of how they interact with the surrounding matrix. However, recent electron microscopic studies indicate that MV interact with matrix proteins in growth plate cartilage. In the studies now reported, procedures developed for dissecting various components from isolated MV led to the discovery that two major vesicle proteins (38 and 46 kDa) are readily released from MV by low ionic strength solutions. These low ionic strength-soluble proteins (LISSP) were shown to be major fragments of the link protein (LP) and hyaluronic acid-binding region (HABR) of matrix proteoglycans: they react immunologically with highly specific monoclonal antibodies to LP and HABR, and the NH2-terminal sequence of the 38-kDa LISSP is essentially identical to residues 40-78 of chicken cartilage LP and that the 46-kDa LISSP represents HABR. Release of both LISSP is enhanced by hyaluronidase treatment, indicating anchorage by a hyaluronate-mediated mechanism. Both LP and HABR are firmly attached to MV in either isotonic or hypertonic solutions. In contrast, our other studies show that dissociation of type II collagen from MV occurs only with hypertonic salts which do not release the LISSP. Thus, strong interactions occur under physiological conditions between MV and both the proteoglycans and collagens, but these take place by different mechanisms.     

Articular cartilage and changes in Arthritis: Noncollagenous proteins and proteoglycans in the extracellular matrix of cartilage

Cartilage contains numerous noncollagenous proteins in its extracellular matrix, including proteoglycans. At least 40 such molecules have been identified, differing greatly in structure, distribution, and function. Some are present in only selected cartilages or cartilage zones, some vary in their presence with a person's development and age, and others are more universal in their expression. Some may not even be made by the chondrocytes, but may arise by absorption from the synovial fluid. In many cases, the molecules' function is unclear, but the importance of others is illustrated by their involvement in genetic disorders. This review provides a selective survey of these molecules and discusses their structure, function, and involvement in inherited and arthritic disorders.     

The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation

The relative importance of fluid-dependent and fluid-independent transient mechanical behavior in articular cartilage was examined for tensile and unconfined compression testing using a fibril reinforced model. The collagen matrix of articular cartilage was modeled as viscoelastic using a quasi-linear viscoelastic formulation with strain-dependent elastic modulus, while the proteoglycan matrix was considered as linearly elastic. The collagen viscoelastic properties were obtained by fitting experimental data from a tensile test. These properties were used to investigate unconfined compression testing, and the sensitivity of the properties was also explored. It was predicted that the stress relaxation observed in tensile tests was not caused by fluid pressurization at the macroscopic level. A multi-step tensile stress relaxation test could be approximated using a hereditary integral in which the elastic fibrillar modulus was taken to be a linear function of the fibrillar strain. Applying the same formulation to the radial fibers in unconfined compression, stress relaxation could not be simulated if fluid pressurization were absent. Collagen viscoelasticity was found to slightly weaken fluid pressurization in unconfined compression, and this effect was relatively more significant at moderate strain rates. Therefore, collagen viscoelasticity appears to play an import role in articular cartilage in tensile testing, while fluid pressurization dominates the transient mechanical behavior in compression. Collagen viscoelasticity plays a minor role in the mechanical response of cartilage in unconfined compression if significant fluid flow is present.