Effect of Electrostatic Interactions between Glycosaminoglycans on the Shear Stiffness of Cartilage: A Molecular Model and Experiments

Structural origins of cartilage shear mechanics

Articular cartilage is a remarkable material able to sustain millions of loading cycles over decades of use outperforming any synthetic substitute. Crucially, how extracellular matrix constituents alter mechanical performance, particularly in shear, remains poorly understood. Here, we present experiments and theory in support of a rigidity percolation framework that quantitatively describes the structural origins of cartilage's shear properties and how they arise from the mechanical interdependence of the collagen and aggrecan networks making up its extracellular matrix. This framework explains that near the cartilage surface, where the collagen network is sparse and close to the rigidity threshold, slight changes in either collagen or aggrecan concentrations, common in early stages of cartilage disease, create a marked weakening in modulus that can lead to tissue collapse. More broadly, this framework provides a map for understanding how changes in composition throughout the tissue alter its shear properties and ultimate in vivo function.

Spatiotemporal changes in mechanical matrisome components of the human ovary from prepuberty to menopause

STUDY QUESTION

How do elastic matrisome components change during the lifetime of the human ovary?

SUMMARY ANSWER

The deposition and remodeling of mechanical matrisome components (collagen, elastin, elastin microfibril interface-located protein 1 (EMILIN-1), fibrillin-1 and glycosaminoglycans (GAGs)) that play key roles in signaling pathways related to follicle activation and development evolve in an age- and follicle stage-related manner.

WHAT IS KNOWN ALREADY

The mechanobiology of the human ovary and dynamic reciprocity that exists between ovarian cells and their microenvironment is of high importance. Indeed, while the localization of primordial follicles in the collagen-rich ovarian cortex offers a rigid physical environment that supports follicle architecture and probably plays a role in their survival, ovarian extracellular matrix (ECM) stiffness limits follicle expansion and hence oocyte maturation, maintaining follicles in their quiescent state. As growing follicles migrate to the medulla of the ovary, they encounter a softer, more pliant ECM, allowing expansion and development. Thus, changes in the rigidity of the ovarian ECM have a direct effect on follicle behavior. Evidence supporting a role for the physical environment in follicle activation was provided in clinical practice by ovarian tissue fragmentation, which promoted actin polymerization and disrupted ovarian Hippo signaling, leading to increased expression of downstream growth factors, promotion of follicle growth and generation of mature oocytes.

STUDY DESIGN, SIZE, DURATION

We investigated quantitative spatiotemporal changes in collagen, elastin, EMILIN-1, fibrillin-1 and GAGs from prepuberty to menopause, before conducting a closer analysis of the ECM surrounding follicles, from primordial to secondary stages, in both prepubertal and tissue from women of reproductive age. The study included ovarian tissue (cortex) from 68 patients of different ages: prepubertal (n = 16; mean age [±SD]=8 ± 2 years); reproductive (n = 21; mean age [±SD]=27 ± 4 years); menopausal with estrogen-based HRT (n = 7; mean age [±SD]=58 ± 4 years); and menopausal without HRT (n = 24; mean age [±SD]=61 ± 5 years).

PARTICIPANTS/MATERIALS, SETTING, METHODS

Quantitative investigations of collagen and GAG deposition in ovarian tissue throughout a woman's lifetime were conducted by analyzing brightfield images. Characteristic features of collagen fiber content were based on polarized light microscopy, since polarized light changes with fiber thickness. To evaluate the deposition and distribution of elastin, fibrillin-1 and EMILIN-1, multiplex immunofluorescence was used on at least three sections from each patient. Image processing and tailored bioinformatic analysis were applied to enable spatiotemporal quantitative evaluation of elastic system component deposition in the human ovary over its lifetime.

MAIN RESULTS AND THE ROLE OF CHANCE

While collagen levels increased with age, fibrillin-1 and EMILIN-1 declined. Interestingly, collagen and elastin reached their peak in reproductive-age women compared to prepubertal (P < 0.01; P = 0.262) and menopausal subjects with (P = 0.706; P < 0.01) and without (P = 0.987; P = 0.610) HRT, indicating a positive impact of secreted estrogen and hormone treatment on collagen and elastin preservation. Interestingly, HRT appears to affect elastin presence in ovarian tissue, since a significantly higher (P < 0.05) proportion of elastin was detected in biopsies from menopausal women taking HRT compared to those not. Higher GAG levels were found in adult ovaries compared to prepubertal ovaries (P < 0.05), suggesting changes in tissue ultrastructure and elasticity with age. In this context, elevated GAG values are suspected to participate in hampering formation of the fibrillin-1 network (r = -0.2475; P = 0.04687), which explains its decline over time. This decline partially accounts for the decrease in EMILIN-1 (r = 0.4149; P = 0.00059). Closer examination of the ECM surrounding follicles from the primordial to the secondary stage, both before and after puberty, points to high levels of mechanical stress placed on prepubertal follicles compared to the more compliant ECM around reproductive-age follicles, as suggested by the higher collagen levels and lower elastin content detected mainly around primordial (P < 0.0001; P < 0.0001, respectively) and primary (P < 0.0001; P < 0.001, respectively) follicles. Such a stiff niche is nonpermissive to prepubertal follicle activation and growth, and is more inclined to quiescence.

LARGE SCALE DATA

Not applicable.

LIMITATIONS, REASONS FOR CAUTION

The duration and form of administered HRT were not considered when studying the menopausal patient group undergoing treatment. Moreover, we cannot exclude interference from other nongynecological medications taken by the study patients on ovarian ECM properties since there is no information in the literature describing the impact of each medication on the ECM. Finally, since the ECM is by definition a very heterogeneous meshwork of proteins, the use of two-dimensional histology could be a limitation. Single time points on fixed tissues could also present limitations, since following ovary dynamics from prepuberty to menopause in the same patient is not feasible.

WIDER IMPLICATIONS OF THE FINDINGS

From a biomechanical perspective, our study revealed important changes to ECM properties dictating the mechanical features of ovarian tissue, in line with the existing literature. Our findings pave the way for possible therapeutic targets at the ECM level in the context of female fertility and ovarian rejuvenation, such as mechanical stimulation, antifibrotic treatments, and prevention or reversion of elastic ECM degradation. Our study also sheds light on the follicle-specific ECM composition that is dependent on follicle stage and age. These data will prove very useful in designing biomimetic scaffolds and tissue-engineered models like the artificial ovary. Indeed, they emphasize the importance of encapsulating each type of isolated follicle in an appropriate biomaterial that must replicate the corresponding functional perifollicular ECM and respect ovarian tissue heterogeneity in order to guarantee its biomimicry.

STUDY FUNDING/COMPETING INTEREST(S)

This study was supported by grants from the Fonds National de la Recherche Scientifique de Belgique (FNRS) (C.A.A. is an FRS-FNRS research associate; grant 5/4/150/5 awarded to M.M.D.) and the Université Catholique de Louvain (PhD grant 'Coopération au développement' awarded to E.O.). None of the authors have any competing interests to declare.

The Contribution of Glycosaminoglycans/Proteoglycans to Aortic Mechanics in Health and Disease: A Critical Review

While elastin and collagen have received a lot of attention as major contributors to aortic biomechanics, glycosaminoglycans (GAGs) and proteoglycans (PGs) recently emerged as additional key players whose roles must be better elucidated if one hopes to predict aortic ruptures caused by aneurysms and dissections more reliably. GAGs are highly negatively charged polysaccharide molecules that exist in the extracellular matrix (ECM) of the arterial wall. In this critical review, we summarize the current understanding of the contributions of GAGs/PGs to the biomechanics of the normal aortic wall, as well as in the case of aortic diseases such as aneurysms and dissections. Specifically, we describe the fundamental swelling behavior of GAGs/PGs and discuss their contributions to residual stresses and aortic stiffness, thereby highlighting the importance of taking these polyanionic molecules into account in mathematical and numerical models of the aorta. We suggest specific lines of investigation to further the acquisition of experimental data to complement simulations and solidify our current understanding. We underscore different potential roles of GAGs/PGs in thoracic aortic aneurysm (TAAD) and abdominal aortic aneurysm (AAA). Namely, we report findings according to which the accumulation of GAGs/PGs in TAAD causes stress concentrations which may be sufficient to initiate and propagate delamination. On the other hand, there seems to be no clear indication of a relationship between the marked reduction in GAG/PG content and the stiffening and weakening of the aortic wall in AAA.

Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson-Boltzmann electrostatic interactions within cartilage.

The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity

The strain-generated potential (SGP) is a well-established mechanism in cartilaginous tissues whereby mechanical forces generate electrical potentials. In articular cartilage (AC) and the intervertebral disc (IVD), studies on the SGP have focused on fluid- and ionic-driven effects, namely Donnan, diffusion and streaming potentials. However, recent evidence has indicated a direct coupling between strain and electrical potential. Piezoelectricity is one such mechanism whereby deformation of most biological structures, like collagen, can directly generate an electrical potential. In this review, the SGP in AC and the IVD will be revisited in light of piezoelectricity and mechanotransduction. While the evidence base for physiologically significant piezoelectric responses in tissue is lacking, difficulties in quantifying the physiological response and imperfect measurement techniques may have underestimated the property. Hindering our understanding of the SGP further, numerical models to-date have negated ferroelectric effects in the SGP and have utilised classic Donnan theory that, as evidence argues, may be oversimplified. Moreover, changes in the SGP with degeneration due to an altered extracellular matrix (ECM) indicate that the significance of ionic-driven mechanisms may diminish relative to the piezoelectric response. The SGP, and these mechanisms behind it, are finally discussed in relation to the cell response.

Modeling In Vivo Interstitial Hydration-Pressure Relationships in Skin and Skeletal Muscle

A theoretical understanding of hydrostatic pressure-fluid volume relationships, or equations of state, of interstitial fluid in skin and skeletal muscle through mathematical/physical modeling is lacking. Here, we investigate at the microscopic level forces that seem to underlie and determine the movements of fluid and solid tissue elements on the microscopic as well as on the macroscopic level. Effects that occur during variation of hydration due to interaction between expanding glycosaminoglycans (GAGs) and the collagen interstitial matrix of tissue seem to be of major importance. We focus on these interactions that let effects from spherical GAGs expand and contract relative to collagen on the microscopic level as hydration changes and thereby generate a hydration-dependent electrostatic pressure on the extracellular matrix on the microscopic level. This pressure spreads to macroscopic levels and become a key factor for setting up equations of state for skin and skeletal muscle interstitia. The modeling for a combined skeletal muscle and skin tissue is one dimensional, i.e., a flat box that may mimic central transverse parts of tissue with more complex geometry. Incorporating values of GAG and collagen densities and fluid contents of skin and muscle tissues that are of an order of magnitude found in literature into the model gives interstitial hydrostatic pressure- fluid volume relationships for these tissues that agree well with experimental results.

The structure and mechanical properties of articular cartilage are highly resilient towards transient dehydration

Articular cartilage is a mechanically highly challenged material with very limited regenerative ability. In contrast to elastic cartilage, articular cartilage is exposed to recurring partial dehydration owing to ongoing compression but maintains its functionality over decades. To extend our current understanding of the material properties of articular cartilage, specifically the interaction between the fluid and solid phase, we here analyze the reversibility of tissue dehydration. We perform an artificial dehydration that extends beyond naturally occurring levels and quantify material recovery as a function of the ionic strength of the rehydration buffer. Mechanical (indentation, compression, shear, and friction) measurements are used to evaluate the influence of de- and rehydration on the viscoelastic properties of cartilage. The structure and composition of native and de/rehydrated cartilage are analyzed using histology, scanning electron microscopy, and atomic force microscopy along with a 1,9-dimethylmethylene blue (DMMB) assay. A broad range of mechanical and structural properties of cartilage can be restored after de- and rehydration provided that a physiological salt solution is used for rehydration. We detect only minor alterations in the microarchitecture of rehydrated cartilage in the superficial zone and find that these alterations do not interfere with the viscoelastic and tribological properties of the tissue.

STATEMENT OF SIGNIFICANCE

We here demonstrate the sturdiness of articular cartilage towards changes in fluid content and show that articular cartilage recovers a broad range of its material properties after dehydration. We analyze the reversibility of tissue dehydration to extend our current understanding of how the material properties of cartilage are established, focusing on the interaction between the fluid and solid phase. Our findings suggest that the high resilience of the tissue minimizes the risk of irreversible material failure and thus compensates, at least in part, its poor regenerative abilities. Tissue engineering approaches should thus not only reproduce the correct tissue mechanics but also its pronounced sturdiness to guarantee a similar longevity.

Osteoarthritis year in review 2015: mechanics

Motivated by the conceptual framework of multi-scale biomechanics, this narrative review highlights recent major advances with a focus on gait and joint kinematics, then tissue-level mechanics, cell mechanics and mechanotransduction, matrix mechanics, and finally the nanoscale mechanics of matrix macromolecules. A literature review was conducted from January 2014 to April 2015 using PubMed to identify major developments in mechanics related to osteoarthritis (OA). Studies of knee adduction, flexion, rotation, and contact mechanics have extended our understanding of medial compartment loading. In turn, advances in measurement methodologies have shown how injuries to both the meniscus and ligaments, together, can alter joint kinematics. At the tissue scale, novel findings have emerged regarding the mechanics of the meniscus as well as cartilage superficial zone. Moving to the cell level, poroelastic and poro-viscoelastic mechanisms underlying chondrocyte deformation have been reported, along with the response to osmotic stress. Further developments have emerged on the role of calcium signaling in chondrocyte mechanobiology, including exciting findings on the function of mechanically activated cation channels newly found to be expressed in chondrocytes. Finally, AFM-based nano-rheology systems have enabled studies of thin murine tissues and brush layers of matrix molecules over a wide range of loading rates including high rates corresponding to impact injury. With OA acknowledged to be a disease of the joint as an organ, understanding mechanical behavior at each length scale helps to elucidate the connections between cell biology, matrix biochemistry and tissue structure/function that may play a role in the pathomechanics of OA.

Evolution of osmotic pressure in solid tumors

The mechanical microenvironment of solid tumors includes both fluid and solid stresses. These stresses play a crucial role in cancer progression and treatment and have been analyzed rigorously both mathematically and experimentally. The magnitude and spatial distribution of osmotic pressures in tumors, however, cannot be measured experimentally and to our knowledge there is no mathematical model to calculate osmotic pressures in the tumor interstitial space. In this study, we developed a triphasic biomechanical model of tumor growth taking into account not only the solid and fluid phase of a tumor, but also the transport of cations and anions, as well as the fixed charges at the surface of the glycosaminoglycan chains. Our model predicts that the osmotic pressure is negligible compared to the interstitial fluid pressure for values of glycosaminoglycans (GAGs) taken from the literature for sarcomas, melanomas and adenocarcinomas. Furthermore, our results suggest that an increase in the hydraulic conductivity of the tumor, increases considerably the intratumoral concentration of free ions and thus, the osmotic pressure but it does not reach the levels of the interstitial fluid pressure.

Adapting a commercial shear rheometer for applications in cartilage research

Cartilage research typically requires a broad range of experimental characterization techniques and thus various testing setups. Here, we describe how several of those tests can be performed with a single experimental platform, i.e. a commercial shear rheometer. Although primarily designed for shear experiments, such a rheometer can be equipped with different adapters to perform indentation and creep measurements, quantify alterations in the sample thickness, and conduct friction measurements in addition to shear rheology. Beyond combining four distinct experimental methods into one setup, the modified rheometer allows for performing material characterizations over a broad range of time scales, frequencies, and normal loads.

Incorporation of aggrecan in interpenetrating network hydrogels to improve cellular performance for cartilage tissue engineering

Interpenetrating network (IPN) hydrogels were recently introduced to the cartilage tissue engineering literature, with the approach of encapsulating cells in thermally gelling agarose that is then soaked in a poly(ethylene glycol) diacrylate (PEGDA) solution, which is then photopolymerized. These IPNs possess significantly enhanced mechanical performance desirable for cartilage regeneration, potentially allowing patients to return to weight-bearing activities quickly after surgical implantation. In an effort to improve cell viability and performance, inspiration was drawn from previous studies that have elicited positive chondrogenic responses to aggrecan, the proteoglycan largely responsible for the compressive stiffness of cartilage. Aggrecan was incorporated into the IPNs in conservative concentrations (40 μg/mL), and its effect was contrasted with the incorporation of chondroitin sulfate (CS), the primary glycosaminoglycan associated with aggrecan. Aggrecan was incorporated by physical entrapment within agarose and methacrylated CS was incorporated by copolymerization with PEGDA. The IPNs incorporating aggrecan or CS exhibited over 50% viability with encapsulated chondrocytes after 6 weeks. Both aggrecan and CS improved cell viability by 15.6% and 20%, respectively, relative to pure IPNs at 6 weeks culture time. In summary, we have introduced the novel approach of including a raw material from cartilage, namely aggrecan, to serve as a bioactive signal to cells encapsulated in IPN hydrogels for cartilage tissue engineering, which led to improved performance of encapsulated chondrocytes.

Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF-β1 and IGF-1 regulation of articular cartilage fiber modulus

A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ([Formula: see text] were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, [Formula: see text] was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted [Formula: see text] values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF-[Formula: see text]1 treatment was predicted to increase and decrease [Formula: see text] values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease [Formula: see text] values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF-[Formula: see text]1 and IGF-1 treatments, with modulated values strongly dependent on treatment.

Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments despite the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.

Comparison of osmotic swelling influences on meniscal fibrocartilage and articular cartilage tissue mechanics in compression and shear

Although the contribution of the circumferential collagen bundles to the anisotropic tensile stiffness of meniscal tissue has been well described, the implications of interactions between tissue components for other mechanical properties have not been as widely examined. This study compared the effects of the proteoglycan-associated osmotic swelling stress on meniscal fibrocartilage and articular cartilage (AC) mechanics by manipulating the osmotic environment and tissue compressive offset. Cylindrical samples were obtained from the menisci and AC of bovine stifles, equilibrated in phosphate-buffered saline solutions ranging from 0.1× to 10×, and tested in oscillatory torsional shear and unconfined compression. Biochemical analysis indicated that treatments and testing did not substantially alter tissue composition. Mechanical testing revealed tissue-specific responses to both increasing compressive offset and decreasing bath salinity. Most notably, reduced salinity dramatically increased the shear modulus of both axially and circumferentially oriented meniscal tissue explants to a much greater extent than for cartilage samples. Combined with previous studies, these findings suggest that meniscal proteoglycans have a distinct structural role, stabilizing, and stiffening the matrix surrounding the primary circumferential collagen bundles.

The Effect of Ionic Strength on the Mechanical, Structural and Transport Properties of Peptide Hydrogels

It is found that the elastic modulus of a peptide hydrogel increases linearly with the logarithm of its ionic strength. This result indicates that the elastic modulus of this class of hydrogels can be tuned by the ionic strength in a highly predictable manner. Small-angle X-ray scattering studies reveal that higher ionic strength leads to thinner but more rigid peptide fibers that are packed more densely. The self-diffusion coefficient of small molecules inside the hydrogel decrease linearly with its ionic strength, but this decrease is mainly a salt effect rather than diffusion barriers imposed by the hydrogel matrix.

Time-dependent nanomechanics of cartilage

In this study, atomic force microscopy-based dynamic oscillatory and force-relaxation indentation was employed to quantify the time-dependent nanomechanics of native (untreated) and proteoglycan (PG)-depleted cartilage disks, including indentation modulus E(ind), force-relaxation time constant τ, magnitude of dynamic complex modulus |E(∗)|, phase angle δ between force and indentation depth, storage modulus E', and loss modulus E″. At ∼2 nm dynamic deformation amplitude, |E(∗)| increased significantly with frequency from 0.22 ± 0.02 MPa (1 Hz) to 0.77 ± 0.10 MPa (316 Hz), accompanied by an increase in δ (energy dissipation). At this length scale, the energy dissipation mechanisms were deconvoluted: the dynamic frequency dependence was primarily governed by the fluid-flow-induced poroelasticity, whereas the long-time force relaxation reflected flow-independent viscoelasticity. After PG depletion, the change in the frequency response of |E(∗)| and δ was consistent with an increase in cartilage local hydraulic permeability. Although untreated disks showed only slight dynamic amplitude-dependent behavior, PG-depleted disks showed great amplitude-enhanced energy dissipation, possibly due to additional viscoelastic mechanisms. Hence, in addition to functioning as a primary determinant of cartilage compressive stiffness and hydraulic permeability, the presence of aggrecan minimized the amplitude dependence of |E(∗)| at nanometer-scale deformation.

Nanomechanics of the Cartilage Extracellular Matrix

Cartilage is a hydrated biomacromolecular fiber composite located at the ends of long bones that enables proper joint lubrication, articulation, loading, and energy dissipation. Degradation of extracellular matrix molecular components and changes in their nanoscale structure greatly influence the macroscale behavior of the tissue and result in dysfunction with age, injury, and diseases such as osteoarthritis. Here, the application of the field of nanomechanics to cartilage is reviewed. Nanomechanics involves the measurement and prediction of nanoscale forces and displacements, intra- and intermolecular interactions, spatially varying mechanical properties, and other mechanical phenomena existing at small length scales. Experimental nanomechanics and theoretical nanomechanics have been applied to cartilage at varying levels of material complexity, e.g., nanoscale properties of intact tissue, the matrix associated with single cells, biomimetic molecular assemblies, and individual extracellular matrix biomolecules (such as aggrecan, collagen, and hyaluronan). These studies have contributed to establishing a fundamental mechanism-based understanding of native and engineered cartilage tissue function, quality, and pathology.

On Mechanics of Connective Tissue: Assessing the Electrostatic Contribution to Corneal Stroma Elasticity

The extracellular matrix plays a crucial role in defining the mechanical properties of connective tissues like cornea, heart, tendon, bone and cartilage among many others. The unique properties of these collagenous tissues arise because of both the hierarchal structure of collagens and the presence of negatively charged proteoglycans (PGs) which hold collagen fibers together. Here, in an effort to understand the mechanics of these structures, using the nonlinear Poison-Boltzmann (PB) equation, we study the electrostatic contribution to the elasticity of corneal stroma due to the presence of negatively charged PG glycosminoglycans (GAGs). Since collagens and GAGs have a regular hexagonal arrangement inside the corneal stroma, a triangular unit cell is chosen. The finite element method is used to solve the PB equation inside this domain and to obtain the electric potential and ionic distributions. Having the ion and potential distributions throughout the unit cell, the electrostatic free energy is computed and the tissue elasticity is calculated using the energy method. It is shown that as the ionic bath concentration increases; the electrostatic contribution to tissue elasticity is reduced.

Cytoskeletal forces produced by extremely low-frequency electric fields acting on extracellular glycoproteins

The physical mechanism by which cells transduce an applied electric field is not well understood. This article establishes for the first time a direct, quantitative model that links the field to cytoskeletal forces. In a previous article, applied electric fields of physiological strength were shown to produce significant mechanical torques at the cellular level. In this article, the corresponding forces exerted on the cytoskeleton are computed and found to be comparable in magnitude to mechanical forces known to produce physiological effects. In addition to the electrical force, the viscous drag force exerted by the surrounding medium and the restoring force exerted by the neighboring structures are considered in the analysis. For an applied electric field of 10 V/m, the force transmitted to the CD44 receptor of a hyaluronan chain in cartilage is about 1 pN at 10 Hz and 7 pN at 1 Hz. For an applied electric field of 100 V/m, the force transmitted to the cytoskeleton at one focus of the glycocalyx is about 0.5 pN at 10 Hz and 1.3 pN at 1 Hz. Mechanical forces of similar magnitude have been observed to produce physiological effects. Hence, this electromechanical transduction process is a plausible mechanism for the production of physiological effects by such electric fields.

Polyelectrolyte-coated gold nanorods and their interactions with type I collagen

Gold nanorods (AuNRs) have unique optical properties for numerous biomedical applications, but the interactions between AuNRs and proteins, particularly those of the extracellular matrix (ECM), are poorly understood. Here the effects of AuNRs on the self-assembly, mechanics, and remodeling of type I collagen gels were examined in vitro. AuNRs were modified with polyelectrolyte multilayers (PEMs) to minimize cytotoxicity, and AuNRs with different terminal polymer chemistries were examined for their interactions with collagen by turbidity assays, rheological tests, and microscopy. Gel contraction assays were used to examine the effects of the PEM-coated AuNRs on cell-mediated collagen remodeling. Polyanion-terminated AuNRs significantly reduced the lag (nucleation) phase of collagen self-assembly and significantly increased the dynamic shear modulus of the polymerized gels, whereas polycation-terminated AuNRs had no effect on the mechanical properties of the collagen. Both polyanion- and polycation-terminated AuNRs significantly inhibited collagen gel contraction by cardiac fibroblasts, and the nanoparticles were localized in intra-, peri-, and extracellular compartments, suggesting that PEM-coated AuNRs influence cell behavior via multiple mechanisms. These results demonstrate the significance of nanoparticle-ECM interactions in determining the bioactivity of nanoparticles.

On the thermodynamical admissibility of the triphasic theory of charged hydrated tissues

The triphasic theory on soft charged hydrated tissues (Lai, W. M., Hou, J. S., and Mow, V. C., 1991, "A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage," ASME J. Biomech. Eng., 113, pp. 245-258) attributes the swelling propensity of articular cartilage to three different mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion stress. The aim of this study is to evaluate the thermodynamic plausibility of the triphasic theory. The free energy of a sample of articular cartilage subjected to a closed cycle of mechanical and chemical loading is calculated using the triphasic theory. It is shown that the chemical expansion stress term induces an unphysiological generation of free energy during each closed cycle of loading and unloading. As the cycle of loading and unloading can be repeated an indefinite number of times, any amount of free energy can be drawn from a sample of articular cartilage, if the triphasic theory were true. The formulation for the chemical expansion stress as used in the triphasic theory conflicts with the second law of thermodynamics.

The viscoelasticity of self-assembled proteoglycan combs

Particle tracking microrheology with a fast digital camera allowed the slow and intermediate time regimes (10(-4)-10(1) s) of the linear viscoelasticity of giant aggrecan proteoglycans to be mapped. Combined with diffusing wave spectroscopy experiments this enabled us to probe the linear viscoelasticity of aggrecan over seven orders of magnitude in time (10(-6)-10(1) s) [Palmer et al., Biophys. J., 1999, 76, 1063; Papagiannopoulos et al., Biomacromolecules, 2007, 7, 2162]. When the comb side-groups self-assemble on the hyaluronic acid backbones they cause a dramatic increase in the relaxation time of the solutions and consequently the viscosity of the sample, but leave the elasticity of the solutions relatively unchanged. The experiments illustrate the modular nature of aggrecan's viscosity and clearly demonstrate the role of this molecule in vivo in cartilaginous composites, where it dissipates energy. Both one- and two-particle tracking microrheology were used to investigate the length-scale dependent viscoelasticity of the comb superstructures [Lui et al., Phys. Rev. Lett., 2006, 96, 118104] and the errors inherent in the two techniques were quantified [Savin and Doyle, Biophys. J., 2005, 88, 623; Waigh, Rep. Prog. Phys., 2005, 68, 685]. The behaviour of the viscoelasticity is compared with the predictions of dynamic scaling theory, indicating a significant contribution of the side-chain dynamics to the reptative motion of both the aggrecan aggregate and the monomers. The results have important implications for a molecular understanding of tissue function and pathology in osteoarthritis.

Structure and interactions of aggrecans: statistical thermodynamic approach

Weak polyelectrolytes tethered to cylindrical surfaces are investigated using a molecular theory. These polymers form a model system to describe the properties of aggrecan molecules, which is one of the main components of cartilage. We have studied the structural and thermodynamical properties of two interacting aggrecans with a molecular density functional theory that incorporates the acid-base equilibrium as well as the molecular properties: including conformations, size, shape, and charge distribution of all molecular species. The effect of acidity and salt concentration on the behavior is explored in detail. The repulsive interactions between two cylindrical-shaped aggrecans are strongly influenced by both the salt concentration and the pH. With increasing acidity, the polyelectrolytes of the aggrecan acquire charge and with decreasing salt concentration those charges become less screened. Consequently the interactions increase in size and range with increasing acidity and decreasing salt concentration. The size and range of the forces offers a possible explanation to the aggregation behavior of aggrecans and for their ability to resist compressive forces in cartilage. Likewise, the interdigitation of two aggrecan molecules is strongly affected by the salt concentration as well as the pH. With increasing pH, the number of charges increases, causing the repulsions between the polymers to increase, leading to a lower interdigitation of the two cylindrical polymer layers of the aggrecan molecules. The low interdigitation in charged polyelectrolytes layers provides an explanation for the good lubrication properties of polyelectrolyte layers in general and cartilage in particular.

The mechanical transduction of physiological strength electric fields

In this article it is proposed that electric fields of physiological strength (approximately 100 V/m) are transduced by the mechanical torque they exert on glycoproteins. The resulting mechanical signal is then transmitted to the cytoskeleton and propagated throughout the cell interior. This mechanical coupling is analyzed for transmembrane glycoproteins, such as integrins and the glycocalyx, and for glycoproteins in the extracellular matrix of cartilage. The applied torque is opposed by viscous fluid drag and restoring forces exerted by adjacent molecules in the membrane or cartilage. The resulting system represents a damped, driven harmonic oscillator. The amplitude of oscillation is constant at low frequencies, but falls off rapidly in the range 1-1000 Hz. The transition frequency depends on parameters such as the viscosity of the surrounding fluid and the restoring force exerted by the surrounding structure. The amplitude increases as the fourth power of the length of the transmembrane glycoproteins and as the square of the applied field. This process may operate in concert with other transduction mechanisms, such as the opening of voltage-gated channels and electrodiffusion/osmosis for DC fields.

Normal and frictional forces between surfaces bearing polyelectrolyte brushes

Normal and shear forces were measured as a function of surface separation, D, between hydrophobized mica surfaces bearing layers of a hydrophobic-polyelectrolytic diblock copolymer, poly(methyl methacrylate)- block-poly(sodium sulfonated glycidyl methacrylate) copolymer (PMMA- b-PSGMA). The copolymers were attached to each hydrophobized surface by their hydrophobic PMMA moieties with the nonadsorbing polyelectrolytic PSGMA tails extending into the aqueous medium to form a polyelectrolyte brush. Following overnight incubation in 10 (-4) w/v aqueous solution of the copolymer, the strong hydrophobic attraction between the hydrophobized mica surfaces across water was replaced by strongly repulsive normal forces between them. These were attributed to the osmotic repulsion arising from the confined counterions at long-range, together with steric repulsion between the compressed brush layers at shorter range. The corresponding shear forces on sliding the surfaces were extremely low and below our detection limit (+/-20-30 nN), even when compressed down to a volume fraction close to unity. On further compression, very weak shear forces (130 +/- 30 nN) were measured due to the increase in the effective viscous drag experienced by the compressed, sliding layers. At separations corresponding to pressures of a few atmospheres, the shearing motion led to abrupt removal of most of the chains out of the gap, and the surfaces jumped into adhesive contact. The extremely low frictional forces between the charged brushes (prior to their removal) is attributed to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments.

Cartilage aggrecan can undergo self-adhesion

Here it is reported that aggrecan, the highly negatively charged macromolecule in the cartilage extracellular matrix, undergoes Ca(2+)-mediated self-adhesion after static compression even in the presence of strong electrostatic repulsion in physiological-like solution conditions. Aggrecan was chemically end-attached onto gold-coated planar silicon substrates and gold-coated microspherical atomic force microscope probe tips (end radius R approximately 2.5 mum) at a density ( approximately 40 mg/mL) that simulates physiological conditions in the tissue ( approximately 20-80 mg/mL). Colloidal force spectroscopy was employed to measure the adhesion between opposing aggrecan monolayers in NaCl (0.001-1.0 M) and NaCl + CaCl(2) ([Cl(-)] = 0.15 M, [Ca(2+)] = 0 - 75 mM) aqueous electrolyte solutions. Aggrecan self-adhesion was found to increase with increasing surface equilibration time upon compression (0-30 s). Hydrogen bonding and physical entanglements between the chondroitin sulfate-glycosaminoglycan side chains are proposed as important factors contributing to aggrecan self-adhesion. Self-adhesion was found to significantly increase with decreasing bath ionic strength (and hence, electrostatic double-layer repulsion), as well as increasing Ca(2+) concentration due to the additional ion-bridging effects. It is hypothesized that aggrecan self-adhesion, and the macromolecular energy dissipation that results from this self-adhesion, could be important factors contributing to the self-assembled architecture and integrity of the cartilage extracellular matrix in vivo.

Lateral nanomechanics of cartilage aggrecan macromolecules

To explore the role of the brush-like proteoglycan, aggrecan, in the shear behavior of cartilage tissue, we measured the lateral resistance to deformation of a monolayer of chemically end-attached cartilage aggrecan on a microcontact printed surface in aqueous NaCl solutions via lateral force microscopy. The effects of bath ionic strength (IS, 0.001-1.0 M) and lateral displacement rate (approximately 1-100 microm/s) were studied using probe tips functionalized with neutral hydroxyl-terminated self-assembled alkanethiol monolayers. Probe tips having two different end-radii (R approximately 50 nm and 2.5 microm) enabled access to different length-scales of interactions (nano and micro). The measured lateral force was observed to depend linearly on the applied normal force, and the lateral force to normal force proportionality constant, mu, was calculated. The value mu increased (from 0.03 +/- 0.01 to 0.11 +/- 0.01) with increasing bath IS (0.001-1.0 M) for experiments using the microsized tip due to the larger compressive strain of aggrecan that resulted from increased IS at constant compressive force. With the nanosized tip, mu also increased with IS but by a smaller amount due to the fewer number of aggrecan involved in shear deformation. The variations in lateral force as a function of applied compressive strain epsilon(n) and changes in bath IS suggested that both electrostatic and nonelectrostatic interactions contributed significantly to the shear deformational behavior of the aggrecan layers. While lateral force did not vary with lateral displacement rate at low IS, where elastic-like electrostatic interactions between aggrecan dominated, lateral force increased significantly with displacement rate at physiological and higher IS, suggestive of additional viscoelastic and/or poroelastic interactions within the aggrecan layer. These data provide insights into molecular-level deformation of aggrecan macromolecules that are important to the understanding of cartilage behavior.

Selective and non-selective metalloproteinase inhibitors reduce IL-1-induced cartilage degradation and loss of mechanical properties

Articular cartilage undergoes matrix degradation and loss of mechanical properties when stimulated with proinflammatory cytokines such as interleukin-1 (IL-1). Aggrecanases and matrix metalloproteinases (MMPs) are thought to be principal downstream effectors of cytokine-induced matrix catabolism, and aggrecanase- or MMP-selective inhibitors reduce or block matrix destruction in several model systems. The objective of this study was to use metalloproteinase inhibitors to perturb IL-1-induced matrix catabolism in bovine cartilage explants and examine their effects on changes in tissue compression and shear properties. Explanted tissue was stimulated with IL-1 for up to 24 days in the absence or presence of inhibitors that were aggrecanase-selective, MMP-selective, or non-selective. Analysis of conditioned media and explant digests revealed that aggrecanase-mediated aggrecanolysis was delayed to varying extents with all inhibitor treatments, but that aggrecan release persisted. Collagen degradation was abrogated by MMP- and non-selective inhibitors and reduced by the aggrecanase inhibitor. The inhibitors delayed but did not reduce loss of the equilibrium compression modulus, whereas the losses of dynamic compression and shear moduli were delayed and reduced. The data suggest that non-metalloproteinase mechanisms participate in IL-1-induced matrix degradation and loss of tissue material properties.

Microstructural Modeling of Collagen Network Mechanics and Interactions with the Proteoglycan Gel in Articular Cartilage

Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.

A method for testing compressive properties of single proteoglycan aggregates

This study presents a method for direct measurement of the compressive properties of single molecules of proteoglycan aggregate using a state-of-the-art laser tweezers/interferometer system previously developed to test the tensile properties of single molecules. A typical molecule of proteoglycan aggregate showed a highly non-linear resistance to compression after being compressed to about 25% of its original molecule length.