Stretching single molecules of connective tissue glycans to characterize their shape-maintaining elasticity

A discrete-to-continuum model for the human cornea with application to keratoconus

We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue. We demonstrate that, for physiological values of the IOP, the predictions of the discrete model converge to those of the continuum model. We use the continuum model to simulate the progression of the degenerative disease known as keratoconus, characterized by a localized bulging of the corneal shell. We assign a spatial distribution of damage (i.e. reduction of the stiffness) to the mechanical properties of the structural elements and predict the resulting macroscopic shape of the cornea, showing that a large reduction in the element stiffness results in substantial corneal thinning and a significant increase in the curvature of both the anterior and posterior surfaces.

Structure and Strength of Bovine and Equine Amniotic Membrane

Simple Summary

Thin, strong scaffold materials are needed for surgical applications. There is a limited selection of available materials and new materials are required. Amnionic membrane from cattle and horses were investigated for this purpose. The structure of these materials was characterized with synchrotron techniques and the strength was measured. A possible relationship between the structure and strength was identified. These amnion materials from animal sources are strong, thin, and elastic materials, although weaker than some other collagen tissues. They may be suitable for use in surgery as an alternative to material from human donors.

Abstract

Thin, strong scaffold materials are needed for surgical applications. New materials are required, particularly those readily available, such as from non-human sources. Bovine amniotic membrane (antepartum) and equine amniotic membrane (postpartum) were characterized with tear and tensile tests. The structural arrangement of the collagen fibrils was determined by small-angle X-ray scattering, scanning electron microscopy, and ultrasonic imaging. Bovine amnion had a thickness-normalized tear strength of 12.6 (3.8) N/mm, while equine amnion was 14.8 (5.3) N/mm. SAXS analysis of the collagen fibril arrangement yielded an orientation index of 0.587 (0.06) and 0.681 (0.05) for bovine and equine, respectively. This may indicate a relationship between more highly aligned collagen fibrils and greater strength, as seen in other materials. Amnion from bovine or equine sources are strong, thin, elastic materials, although weaker than other collagen tissue materials commonly used, that may find application in surgery as an alternative to material from human donors.

An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load

An insight into changes of soft biological tissue ultrastructures under loading conditions is essential to understand their response to mechanical stimuli. Therefore, this study offers an approach to investigate the arrangement of collagen fibrils and proteoglycans (PGs), which are located within the mechanically loaded aortic wall. The human aortic samples were either fixed directly with glutaraldehyde in the load-free state or subjected to a planar biaxial extension test prior to fixation. The aortic ultrastructure was recorded using electron tomography. Collagen fibrils and PGs were segmented using convolutional neural networks, particularly the ESPNet model. The 3D ultrastructural reconstructions revealed a complex organization of collagen fibrils and PGs. In particular, we observed that not all PGs are attached to the collagen fibrils, but some fill the spaces between the fibrils with a clear distance to the collagen. The complex organization cannot be fully captured or can be severely misinterpreted in 2D. The approach developed opens up practical possibilities, including the quantification of the spatial relationship between collagen fibrils and PGs as a function of the mechanical load. Such quantification can also be used to compare tissues under different conditions, e.g., healthy and diseased, to improve or develop new material models. STATEMENT OF SIGNIFICANCE: The developed approach enables the 3D reconstruction of collagen fibrils and proteoglycans as they are embedded in the loaded human aortic wall. This methodological pipeline comprises the knowledge of arterial mechanics, imaging with transmission electron microscopy and electron tomography, segmentation of 3D image data sets with convolutional neural networks and finally offers a unique insight into the ultrastructural changes in the aortic tissue caused by mechanical stimuli.

Proteoglycans in the periodontium: A review with emphasis on specific distributions, functions, and potential applications

Proteoglycans (PGs) are largely glycosylated proteins, consisting of a linkage sugar, core proteins, and glycosaminoglycans (GAGs). To date, more than 40 kinds of PGs have been identified, and they can be classified as intracellular, cell surface, pericellular, and extracellular PGs according to cellular locations. To illustrate, extracellular PGs are known for regulating the homeostasis of the extracellular matrix; cell-surface PGs play a role in mediating cell adhesion and binding various growth factors. In the field of periodontology, PGs are implicated in cellular proliferation, migration, adhesion, contractility, and anoikis, thereby exerting a profound influence on periodontal tissue development, wound repair, the immune response, biomechanics, and pathological process. Additionally, the expression patterns of some PGs are dynamic and cell-specific. Therefore, determining the roles and spatial-temporal expression patterns of PGs in the periodontium could shed light on treatments for wound healing, tissue regeneration, periodontitis, and gingival overgrowth. In this review, close attention is paid to the distributions, functions, and potential applications of periodontal PGs. Related genetically modified animal experiments and involved signal transduction cascades are summarized for improved understanding of periodontal PGs. To date, however, there is a large amount of speculation on this topic that requires rigorous experiments for validation.

Bovine Meniscus Middle Zone Tissue: Measurement of Collagen Fibril Behavior During Compression

BACKGROUND

Type I collagen is the major component of the extracellular matrix of the knee's meniscus and plays a central role in that joint's biomechanical properties. Repair and reconstruction of tissue damage often requires a scaffold to assist the body to rebuild. The middle zone of bovine meniscus is a material that may be useful for the preparation of extracellular matrix scaffolds.

METHODS

Here, synchrotron-based small-angle X-ray scattering (SAXS) patterns of bovine meniscus were collected during unconfined compression. Collagen fibril orientation, D-spacing, compression distance and force were measured.

RESULTS

The collagen fibrils in middle zone meniscal fibrocartilage become more highly oriented perpendicular to the direction of compression. The D-spacing also increases, from 65.0 to 66.3 nm with compression up to 0.43 MPa, representing a 1.8% elongation of collagen fibrils perpendicular to the compression.

CONCLUSION

The elasticity of the collagen fibrils under tension along their length when the meniscus is compressed, therefore, contributes to the overall elastic response of the meniscus only under loads that exceed those likely to be experienced physiologically.

A damage model for collagen fibres with an application to collagenous soft tissues

We propose a mechanical model to account for progressive damage in collagen fibres within fibrous soft tissues. The model has a similar basis to the pseudoelastic model that describes the Mullins effect in rubber but it also accounts for the effect of cross-links between collagen fibres. We show that the model is able to capture experimental data obtained from rat tail tendon fibres, and the combined effect of damage and collagen cross-links is illustrated for a simple shear test. The proposed three-dimensional framework allows a straightforward implementation in finite-element codes, which are needed to analyse more complex boundary-value problems for soft tissues under supra-physiological loading or tissues weakened by disease.

Role of proteoglycans on the biochemical and biomechanical properties of dentin organic matrix

OBJECTIVE

Proteoglycans (PGs) are multifunctional biomacromolecules of the extracellular matrix of collagen-based tissues. In teeth, besides a pivotal regulatory role on dentin biomineralization, PGs provide mechanical support to the mineralized tissue and compressive strength to the biosystem. This study assessed enzymatic protocols for selective PGs removal from demineralized dentin to determine the roles of these biomacromolecules in the bulk mechanical properties and biostability of type I collagen.

METHODS

Selective removal of glycosaminoglycans chains (GAGs) and PGs from demineralized dentin was carried out by enzymatic digestion protocols using chondroitinase ABC (c-ABC) and trypsin (Try). A comprehensive study design included assessment of dentin matrix mass loss, biodegradability of the PGs/GAGs-depleted dentin matrix, ultimate tensile strength (UTS) and energy to fracture tests. Quantitative data was statistically analyzed by two-way and one-way ANOVA followed by the appropriate post hoc tests (α=0.05).

RESULTS

Transmission electron microscopy images show effective GAGs removal by c-ABC and Try and both enzymatic methods released statistically similar amounts of GAGs from the demineralized dentin. Try digestion resulted in about 25% dentin matrix mass loss and increased susceptibility to collagenolytic digestion when compared to c-ABC (p=0.0224) and control (p=0.0901). Moreover, PGs digestion by Try decreased the tensile strengths of dentin. Statistically lower energy to fracture was observed in c-ABC-treated dentin matrix.

CONCLUSIONS

GAGs plays a pivotal role on tissue mechanics and anisotropy, while the core protein of PGs have a protective role on matrix biostability.

Dentin on the nanoscale: Hierarchical organization, mechanical behavior and bioinspired engineering

OBJECTIVE

Knowledge of the structural organization and mechanical properties of dentin has expanded considerably during the past two decades, especially on a nanometer scale. In this paper, we review the recent literature on the nanostructural and nanomechanical properties of dentin, with special emphasis in its hierarchical organization.

METHODS

We give particular attention to the recent literature concerning the structural and mechanical influence of collagen intrafibrillar and extrafibrillar mineral in healthy and remineralized tissues. The multilevel hierarchical structure of collagen, and the participation of non-collagenous proteins and proteoglycans in healthy and diseased dentin are also discussed. Furthermore, we provide a forward-looking perspective of emerging topics in biomaterials sciences, such as bioinspired materials design and fabrication, 3D bioprinting and microfabrication, and briefly discuss recent developments on the emerging field of organs-on-a-chip.

RESULTS

The existing literature suggests that both the inorganic and organic nanostructural components of the dentin matrix play a critical role in various mechanisms that influence tissue properties.

SIGNIFICANCE

An in-depth understanding of such nanostructural and nanomechanical mechanisms can have a direct impact in our ability to evaluate and predict the efficacy of dental materials. This knowledge will pave the way for the development of improved dental materials and treatment strategies.

CONCLUSIONS

Development of future dental materials should take into consideration the intricate hierarchical organization of dentin, and pay particular attention to their complex interaction with the dentin matrix on a nanometer scale.

Structural Characterization of Sodium Alginate and Calcium Alginate

Alginate readily aggregates and forms a physical gel in the presence of cations. The association of the chains, and ultimately gel structure and mechanics, depends not only on ion type, but also on the sequence and composition of the alginate chain that ultimately determines its stiffness. Chain flexibility is generally believed to decrease with guluronic residue content, but it is also known that both polymannuronate and polyguluronate blocks are stiffer than heteropolymeric blocks. In this work, we use atomistic molecular dynamics simulation to primarily explore the association and aggregate structure of different alginate chains under various Ca(2+) concentrations and for different alginate chain composition. We show that Ca(2+) ions in general facilitate chain aggregation and gelation. However, aggregation is predominantly affected by alginate monomer composition, which is found to correlate with chain stiffness under certain solution conditions. In general, greater fractions of mannuronic monomers are found to increase chain flexibility of heteropolymer chains. Furthermore, differences in chain guluronic acid content are shown to lead to different interchain association mechanisms, such as lateral association, zipper mechanism, and entanglement, where the mannuronic residues are shown to operate as an elasticity moderator and therefore promote chain association.

Collagen cross linking and fibril alignment in pericardium

Cross linking was found to be a factor in collagen fibril alignment in pericardium tissue.

Collagen fibril strain, recruitment and orientation for pericardium under tension and the effect of cross links

The response to stress of collagen fibrils in bovine pericardium depends on the nature of the cross links.

Collagen fibril diameter and leather strength

The main structural component of leather and skin is type I collagen in the form of strong fibrils. Strength is an important property of leather, and the way in which collagen contributes to the strength is not fully understood. Synchrotron-based small angle X-ray scattering (SAXS) is used to measure the collagen fibril diameter of leather from a range of animals, including sheep and cattle, that had a range of tear strengths. SAXS data were fit to a cylinder model. The collagen fibril diameter and tear strength were found to be correlated in bovine leather (r(2) = 0.59; P = 0.009), with stronger leather having thicker fibrils. There was no correlation between orientation index, i.e., fibril alignment, and fibril diameter for this data set. Ovine leather showed no correlation between tear strength and fibril diameter, nor was there a correlation across a selection of other animal leathers. The findings presented here suggest that there may be a different structural motif in skin compared with tendon, particularly ovine skin or leather, in which the diameter of the individual fibrils contributes less to strength than fibril alignment does.

Facilitating high-force single-polysaccharide stretching using covalent attachment of one end of the chain

Single polysaccharide force spectroscopy has yielded particularly interesting data, the interpretation of which requires the marriage of statistical-mechanical theories of polymer physics to the complexities afforded by possible force-induced conformational transitions of the constituent sugar rings. However, the difficulty of designing handles for the specific attachment of the different ends of polysaccharide chains to substrates, such as piezoelectric scanners, cantilevers or microbeads has meant that the majority of studies to date have been carried out with the polymer physisorbed to the substrates between which it is stretched, or at best chemically attached via bonds formed at uncontrolled locations along the length of the molecule. This means that the lengths of obtained polysaccharide stretches, as well as the forces that can be placed on the molecule without generating detachment, are generally smaller than those obtainable for polymers that offer the ability to be covalently attached to substrates specifically at their ends. As a consequence it is troublesome and tedious to record a statistically significant number of force curves that extend chains to high enough forces to investigate certain conformational transitions, such as the boat-to-inverted chair, exhibited by polysaccharides such as pectin. Herein, single molecule force-extension curves have been measured for the several pectin samples using AFM. The results are compared when either (1) the polymers have been physisorbed between the cantilever and the surface of the piezo-electric scanner, under several different solvent conditions of pH and ionic strength, or (2) the polymer molecule has been chemically attached at one end to the piezo surface using a recently reported coupling procedure. In fact, using such a chemical attachment to tether the end of the polysaccharide, reduced the frequency of successful stretching events obtained in a particular location, confirming the role of surface diffusion in the physisorbed experiments. Nevertheless, when polymer stretches were successfully recorded, the force that could be applied before detachment was significantly increased, indicating that this methodology has great potential for improving the acquisition of data reporting on force-induced conformational transitions of the sugar ring that require the application of significant stresses.

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.

An irreversible constitutive model for fibrous soft biological tissue: a 3-D microfiber approach with demonstrative application to abdominal aortic aneurysms

Understanding the failure and damage mechanisms of soft biological tissue is critical to a sensitive and specific characterization of tissue injury tolerance and its relation to biological responses. Despite increasing experimental and analytical efforts, failure-related irreversible effects of soft biological tissue are still poorly understood. There is still no clear definition of what "damage" of a soft biological material is, and conventional macroscopic indicators, as known from damage of engineering materials for example, may not identify the tissue's tolerance to injury appropriately. To account for the complex three-dimensional arrangement of collagen, a microfiber model approach is applied, where constitutive relations for collagen fibers are integrated over the unit sphere, which in turn defines the tissue's macroscopic properties. A collagen fiber is represented by a bundle of proteoglycan cross-linked collagen fibrils that undergoes irreversible deformations when exceeding its elastic tensile limit. The proposed constitutive model is able to predict strain stiffening at physiological strain levels and does not exhibit a clear macroscopic elastic limit, two typical features known from soft biological tissue testing. An elastic-predictor/plastic-corrector implementation of the model is followed and constitutive parameters are estimated from in vitro test data from a particular abdominal aortic aneurysm (AAA). Damage-based structural instabilities of the AAA under different inflation conditions are investigated, where the collagen orientation density has been estimated from its in vivo stress state.

Insights into the potential functionality of single-chain force-induced conformational transitions in polymer networks: implications for polysaccharide signaling in the plant cell wall

The behavior of biopolymer networks comprised of clickable polysaccharide chains that can undergo force-induced conformational transitions was investigated during straining using a simulation technique. The simulation was carried out both using an affine deformation field and alternatively using Lees-Edwards boundary conditions as an example of a nonaffine case. In the affine situation the simulated stress-strain curves were found to be consistent with results obtained by evaluating the molecular force-extension curve at a single average extension and calculating the bulk modulus as an average over all possible orientations with respect to the deformation. While in all cases examined the macroscopic mechanical responses of networks of randomly oriented chains, consisting either of simple extensible wormlike chains or their clickable analogs, were found to be indistinguishable, the simulation additionally allowed the number of chains containing sugar rings in different conformational states to be monitored, and this was found to change significantly during straining. This supports the hypothesis that in networks of randomly oriented clickable polysaccharide chains, such conformational transitions could have biological significance as stress switches in signaling processes but that they are unlikely to affect the bulk rheological properties of tissue.

Force-extension formula for the worm-like chain model from a variational principle

Stiff polymers, such as single-stranded DNA, unstructured RNA and cellulose, are all basically extremely long rods with relatively short repeating monomers. The simplest model for describing such stiff polymers is called the freely jointed chain model, which treats a molecule as a chain of perfectly rigid subunits of orientationally independent statistical segments, joined together by perfectly flexible hinges. A more realistic model that incorporates the entropic elasticity of a molecule, called the worm-like chain model, has been proposed by assuming that each monomer resists the bending force. Some force-extension formulae for the worm-like chain model have been previously found in terms of interpolation and numerical solutions resulting from statistical mechanics. In this paper, however, we adopt a variational principle to seek the minimum energy configuration of a stretched molecule by incorporating all the possible orientations of each monomer under thermal equilibrium, i.e., constant temperature. We determine a force-extension formula for the worm-like chain model analytically. We find that our formula suggests new terms such as the free energy and the cut-off force of a molecule, which define a clear transition from the entropic regime to the enthalpic regime and the fracture of the molecule, respectively. In addition, we predict two possible phase changes for a stretched molecule, i.e., from a super-helix to a soliton and then from a soliton to a vertical twisted line. We show theoretically that a molecule must undergo at least one phase change before it is fully stretched into its total contour length. This new formula is used to fit recent experimental data and shows a good agreement with some current literature that uses a statistical approach. Finally, an instability analysis is adopted to investigate the sensitivity of the new formula subject to small changes in temperature.

Decorin core protein (decoron) shape complements collagen fibril surface structure and mediates its binding

Decorin is the archetypal small leucine rich repeat proteoglycan of the vertebrate extracellular matrix (ECM). With its glycosaminoglycuronan chain, it is responsible for stabilizing inter-fibrillar organization. Type I collagen is the predominant member of the fibrillar collagen family, fulfilling both organizational and structural roles in animal ECMs. In this study, interactions between decoron (the decorin core protein) and binding sites in the d and e₁ bands of the type I collagen fibril were investigated through molecular modeling of their respective X-ray diffraction structures. Previously, it was proposed that a model-based, highly curved concave decoron interacts with a single collagen molecule, which would form extensive van der Waals contacts and give rise to strong non-specific binding. However, the large well-ordered aggregate that is the collagen fibril places significant restraints on modes of ligand binding and necessitates multi-collagen molecular contacts. We present here a relatively high-resolution model of the decoron-fibril collagen complex. We find that the respective crystal structures complement each other well, although it is the monomeric form of decoron that shows the most appropriate shape complementarity with the fibril surface and favorable calculated energies of interaction. One molecule of decoron interacts with four to six collagen molecules, and the binding specificity relies on a large number of hydrogen bonds and electrostatic interactions, primarily with the collagen motifs KXGDRGE and AKGDRGE (d and e₁ bands). This work helps us to understand collagen-decorin interactions and the molecular architecture of the fibrillar ECM in health and disease.

Interrogation of Single Synthetic Polymer Chains and Polysaccharides by AFM-Based Force Spectroscopy

This contribution reviews selected mechanical experiments on individual flexible macromolecules using single-molecule force spectroscopy (SMFS) based on atomic force microscopy. Focus is placed on the analysis of elasticity and conformational changes in single polymer chains upon variation of the external environment, as well as on conformational changes induced by the mechanical stress applied to individual macromolecular chains. Various experimental strategies regarding single-molecule manipulation and SMFS testing are discussed, as is theoretical analysis through single-chain elasticity models derived from statistical mechanics. Moreover, a complete record, reported to date, of the parameters obtained when applying the models to fit experimental results on synthetic polymers and polysaccharides is presented.

Investigation of the effects of fine structure on the nanomechanical properties of pectin

Pectin is an important structural polysaccharide found in the cell walls of all land plants. While in detail its composition and its organization in muro are complex, it is predominantly a copolymer of galacturonic acid and its methylesterified counterpart. Previous single-molecule stretching studies carried out on a sparsely methylesterified pectin sample indicated the importance of force-induced conformational transitions of the pyranose ring during extension, and the possible biological role of such transitions was discussed. More heavily methylesterified samples are better biomimetic models of the polymeric components as found in the plant cell wall, in particular being less restricted by the shackles of the significant intermolecular interactions expected to constrain the behavior of bare galacturonic acid sequences. Density functional theory calculations revealed that upon extending galacturonic acid monomers, whether methylesterified or not, the initial ((4)C1) chair structure is transformed to a ((3)S5) skew boat and that subsequently upon further elongation, via an intermediate inverted skew boat ((5)S3), the inverted chair ((1)C4) is reached. Experimentally, the force-extension curve of highly methylesterified pectin was found to be solvent dependent in the same manner as the un-esterified sample, indicating that minimal changes in the strength of interring hydrogen bonding result from such a substitution, and finally, as only subtle changes in the force-extension behavior of pectin resulted from changes in the degree of methylesterification, previous speculations about the role of force-induced transformations in vivo are supported.

Zonular fibers, multimolecular composition as related to function (elasticity) and pathology

Zonular fibers (ZF) play an important role in accommodation. With the rapid increase over the last decade of the oldest part of the population in industrialized countries, age-dependent loss of accommodation became an increasingly important problem. It appeared therefore interesting to review old and recent literature on ZF, their composition, structure and pathological alterations. By comparing former and recent reports it appeared to us, that several previous reports were not sufficiently taken in consideration for the understanding of the rheological properties of ZF. Elastin and proteoglycans-glycosaminoglycans were reported previously as constituents of ZF. Their presence besides fibrillin, the major constituent, helps to explain the rheological properties of these fibers, and especially their elasticity and its age- and pathology-dependent decline. Our review points also to some of the major problems, which remain to be addressed by future experiments.

Model for stretching elastic biopolymers which exhibit conformational transformations

We derive an expression that represents the physical behavior of a polysaccharide molecule as it is stretched from the entropic region, through one or more ring conformational transformations, into the Hookean regime. The model adapts existing models in order to accommodate one or more force-induced conformational transformations of the glycan rings and is based on the concept of equilibrium between the clicked (longer conformers) and unclicked states. This equilibrium is determined by the Gibbs energy difference between these two states which is perturbed in favor of the clicked states by the force applied to the molecule. The derived expression is used to generate force-extension curves for model polymers and can illustrate the effect of the Gibbs energy for each transformation on the shape of these curves. It is also used to fit the force-extension curves of polysaccharides to obtain the Gibbs energy differences between the conformers. Good agreement was found between this model and experimental data on carboxymethylamylose, dextran, alginate, and pectin.

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.

Cartilage elasticity resides in shape module decoran and aggrecan sumps of damping fluid: implications in osteoarthrosis

Cartilage ultrastructure is based on collagen fibrils tied together by proteoglycans (PGs). Interfibrillar orthogonal PG bridges ('shape modules') were located by electron histochemistry using Cupromeronic blue methodology. Their frequency and size, similar to those in tendon, cornea, etc., were compatible with biochemical estimates of tissue decoran (formerly decorin), the PG component of shape module bridges. Digestion by hyaluronanase and chondroitinase AC helped to identify aggrecan and decoran and exemplified the destruction of shape modular organization by glycan-splitting agents. The anionic glycosaminoglycan (AGAG) of decoran, dermochondan sulphate (DS, formerly dermatan sulphate), contains L-iduronate, an elastic sugar unit. Chondroitan, keratan (present in aggrecan) and hyaluronan are not similarly elastic but can participate in sliding-filament reversible deformability. Mechanical properties predicted for the interfibrillar bridges accord with anisotropic stress/strain responses of articular cartilage to compressive or tensile stresses. We propose that fluid from pericellular aggrecan-rich domains moves under pressure into the interterritorial fibrillar arrays against the elastic resistance of the shape modules, which return the fluid, post-compression, to its original position. Cartilage is tendon-like, with the addition of expansile aggrecan-rich reservoirs of aqueous shock absorber fluid. Rupture or loss of interfibrillar ties would allow expansile PG to force the collagenous matrix apart, imbibing water, increasing swelling and fissuring--characteristic manifestations of osteoarthrosis (OA), a joint disease of major economic importance. Decoran may be a primary target of the OA disease process.