Mechanical properties of mineralized collagen fibrils as influenced by demineralization

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

In Vitro Fracture Testing of Submicron Diameter Collagen Fibril Specimens

Mechanical testing of collagenous tissues at different length scales will provide improved understanding of the mechanical behavior of structures such as skin, tendon, and bone, and also guide the development of multiscale mechanical models. Using a microelectromechanical-systems (MEMS) platform, stress-strain response curves up to failure of type I collagen fibril specimens isolated from the dermis of sea cucumbers were obtained in vitro. A majority of the fibril specimens showed brittle fracture. Some displayed linear behavior up to failure, while others displayed some nonlinearity. The fibril specimens showed an elastic modulus of 470 ± 410 MPa, a fracture strength of 230 ± 160 MPa, and a fracture strain of 80% ± 44%. The fibril specimens displayed significantly lower elastic modulus in vitro than previously measured in air. Fracture strength/strain obtained in vitro and in air are both significantly larger than those obtained in vacuo, indicating that the difference arises from the lack of intrafibrillar water molecules produced by vacuum drying. Furthermore, fracture strength/strain of fibril specimens were different from those reported for collagenous tissues of higher hierarchical levels, indicating the importance of obtaining these properties at the fibrillar level for multiscale modeling.     

Molecular modeling of the axial and circumferential elastic moduli of tubulin

Microtubules play a number of important mechanical roles in almost all cell types in nearly all major phylogenetic trees. We have used a molecular mechanics approach to perform tensile tests on individual tubulin monomers and determined values for the axial and circumferential moduli for all currently known complete sequences. The axial elastic moduli, in vacuo, were found to be 1.25 GPa and 1.34 GPa for α- and β-bovine tubulin monomers. In the circumferential direction, these moduli were 378 MPa for α- and 460 MPa for β-structures. Using bovine tubulin as a template, 269 homologous tubulin structures were also subjected to simulated tensile loads yielding an average axial elastic modulus of 1.10 ± 0.14 GPa for α-tubulin structures and 1.39 ± 0.68 GPa for β-tubulin. Circumferentially the α- and β-moduli were 936 ± 216 MPa and 658 ± 134 MPa, respectively. Our primary finding is that that the axial elastic modulus of tubulin diminishes as the length of the monomer increases. However, in the circumferential direction, no correlation exists. These predicted anisotropies and scale dependencies may assist in interpreting the macroscale behavior of microtubules during mitosis or cell growth. Additionally, an intergenomic approach to investigating the mechanical properties of proteins may provide a way to elucidate the evolutionary mechanical constraints imposed by nature upon individual subcellular components.     

Mechanical properties of collagen fibrils

The formation of collagen fibers from staggered subfibrils still lacks a universally accepted model. Determining the mechanical properties of single collagen fibrils (diameter 50-200 nm) provides new insights into collagen structure. In this work, the reduced modulus of collagen was measured by nanoindentation using atomic force microscopy. For individual type 1 collagen fibrils from rat tail, the modulus was found to be in the range from 5 GPa to 11.5 GPa (in air and at room temperature). The hypothesis that collagen anisotropy is due to the subfibrils being aligned along the fibril axis is supported by nonuniform surface imprints performed by high load nanoindentation.     

Quantitative Morphological Analysis Reveals Ultrastructural Diversity of Amyloid Fibrils from α-Synuclein Mutants

High resolution atomic force microscopy is a powerful tool to characterize nanoscale morphological features of protein amyloid fibrils. Comparison of fibril morphological properties between studies has been hampered by differences in analysis procedures and measurement error determination used by various authors. We describe a fibril morphology analysis method that allows for quantitative comparison of features of amyloid fibrils of any amyloidogenic protein measured by atomic force microscopy. We have used tapping mode atomic force microscopy in liquid to measure the morphology of fibrillar aggregates of human wild-type α-synuclein and the disease-related mutants A30P, E46K, and A53T. Analysis of the images shows that fibrillar aggregates formed by E46K α-synuclein have a smaller diameter (9.0 ± 0.8 nm) and periodicity (mode at 55 nm) than fibrils of wild-type α-synuclein (height 10.0 ± 1.1 nm; periodicity has a mode at 65 nm). Fibrils of A30P have smaller diameter still (8.1 ± 1.2 nm) and show a variety of periodicities. This quantitative analysis procedure enables comparison of the results with existing models for assembly of amyloid fibrils.     

Nanomechanical Mapping of Hydrated Rat Tail Tendon Collagen I Fibrils

Collagen fibrils play an important role in the human body, providing tensile strength to connective tissues. These fibrils are characterized by a banding pattern with a D-period of 67 nm. The proposed origin of the D-period is the internal staggering of tropocollagen molecules within the fibril, leading to gap and overlap regions and a corresponding periodic density fluctuation. Using an atomic force microscope high-resolution modulus maps of collagen fibril segments, up to 80 μm in length, were acquired at indentation speeds around 10⁵ nm/s. The maps revealed a periodic modulation corresponding to the D-period as well as previously undocumented micrometer scale fluctuations. Further analysis revealed a 4/5, gap/overlap, ratio in the measured modulus providing further support for the quarter-staggered model of collagen fibril axial structure. The modulus values obtained at indentation speeds around 10⁵ nm/s are significantly larger than those previously reported. Probing the effect of indentation speed over four decades reveals two distinct logarithmic regimes of the measured modulus and point to the existence of a characteristic molecular relaxation time around 0.1 ms. Furthermore, collagen fibrils exposed to temperatures between 50 and 62°C and cooled back to room temperature show a sharp decrease in modulus and a sharp increase in fibril diameter. This is also associated with a disappearance of the D-period and the appearance of twisted subfibrils with a pitch in the micrometer range. Based on all these data and a similar behavior observed for cross-linked polymer networks below the glass transition temperature, we propose that collagen I fibrils may be in a glassy state while hydrated.     

Amyloid toxicity in skeletal myoblasts: Implications for inclusion-body myositis

Skeletal muscle disorder, inclusion-body myositis (IBM) has been known for accumulation of amyloid characteristic proteins in muscle. To understand the biophysical basis of IBM, the interaction of amyloid fibrils with skeletal myoblast cells (SMC) has been studied in vitro. Synthetic insulin fibrils and Aβ_25-35 fibrils were used for this investigation. From the saturation binding analysis, the calculated dissociation constant (K_d) for insulin fibril and Aβ_25-35 fibrils were 69.37 ± 11.17 nM and 115.60 ± 12.17 nM, respectively. The fibrillar insulin comparatively has higher affinity binding to SMC than Aβ fibrils. The competitive binding studies with native insulin showed that the amount of bound insulin fibril was significantly decreased due to displacement of native insulin. However, the presence of native insulin is not altered the binding of β-amyloid fibril. The cytotoxicity of insulin amyloid intermediates was measured. The pre-fibrillar intermediates of insulin showed significant toxicity (35%) as compared to matured fibrils. Myoblast treated with β-amyloid fibrils showed more oxidative damage than the insulin fibril. Cell differentiating action of amyloidic insulin was assayed by creatine kinase activity. The insulin fibril treated cells differentiated more slowly compared to native insulin. However, β-amyloid fibrils do not show cell differentiation property. These findings reinforce the hypothesis that accumulation of amyloid related proteins is significant for the pathological events that could lead to muscle degeneration and weakness in IBM.     

Elastic energy storage in human articular cartilage: estimation of the elastic modulus for type II collagen and changes associated with osteoarthritis.

The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.     

Mechanical properties of human patellar tendon at the hierarchical levels of tendon and fibril

Tendons are strong hierarchical structures, but how tensile forces are transmitted between different levels remains incompletely understood. Collagen fibrils are thought to be primary determinants of whole tendon properties, and therefore we hypothesized that the whole human patellar tendon and its distinct collagen fibrils would display similar mechanical properties. Human patellar tendons (n = 5) were mechanically tested in vivo by ultrasonography. Biopsies were obtained from each tendon, and individual collagen fibrils were dissected and tested mechanically by atomic force microscopy. The Young's modulus was 2.0 ± 0.5 GPa, and the toe region reached 3.3 ± 1.9% strain in whole patellar tendons. Based on dry cross-sectional area, the Young's modulus of isolated collagen fibrils was 2.8 ± 0.3 GPa, and the toe region reached 0.86 ± 0.08% strain. The measured fibril modulus was insufficient to account for the modulus of the tendon in vivo when fibril content in the tendon was accounted for. Thus, our original hypothesis was not supported, although the in vitro fibril modulus corresponded well with reported in vitro tendon values. This correspondence together with the fibril modulus not being greater than that of tendon supports that fibrillar rather than interfibrillar properties govern the subfailure tendon response, making the fibrillar level a meaningful target of intervention. The lower modulus found in vitro suggests a possible adverse effect of removing the tissue from its natural environment. In addition to the primary work comparing the two hierarchical levels, we also verified the existence of viscoelastic behavior in isolated human collagen fibrils.     

Micromechanical response of mineral and collagen phases in bone

We report the first simultaneous quantification of Young's modulus in the separate material phases of bone: collagen and carbonated hydroxyapatite. High-energy X-ray scattering and in situ loading revealed macroscopic, mineral, and collagen Young's moduli (90% confidence limit) for a canine fibula equaled 24.7(0.2) GPa, 38.2(0.5) GPa {for 00.4 and 43.6(1.4) GPa for 22.2}, and 18(1.2) GPa, respectively. The mineral contained compressive residual stresses on the order of -60 to -80 MPa before loading and had a stress enhancement (ratio of internal to applied stress) between 2.0 and 2.3. The diffraction peak width increased with increasing applied stress, mainly along the bone's longitudinal direction, and peak widths returned to pre-deformation values when load was removed. In a second fibula section from the same animal, the mineral's internal stress changed from -50 MPa (22.2 reflection) to -75 MPa (00.4) just after removal from formalin to -10 MPa after eight hours immersion in phosphate-buffered saline; the corresponding change in collagen D-spacing DeltaD/D equaled 4.2x10(-3).     

Collagen fibril diameter distribution does not reflect changes in the mechanical properties of in vitro stress-deprived tendons

The purpose of this study was to determine if an association exists between the tensile properties and the collagen fibril diameter distribution in in vitro stress-deprived rat tail tendons. Rat tail tendons were paired into two groups of 21 day stress-deprived and 0 time controls and compared using transmission electron microscopy (n = 6) to measure collagen fibril diameter distribution and density, and mechanical testing (n =6) to determine ultimate stress and tensile modulus. There was a statistically significant decrease in both ultimate tensile strength (control: 17.95+/-3.99 MPa, stress-deprived: 6.79+/-3.91 MPa) and tensile modulus (control: 312.8+/-89.5 MPa, stress-deprived: 176.0+/-52.7 MPa) in the in vitro stress-deprived tendons compared to controls. However, there was no significant difference between control and stress-deprived tendons in the number of fibrils per tendon counted, mean fibril diameter, mean fibril density, or fibril size distribution. The results of this study demonstrate that the decrease in mechanical properties observed in in vitro stress-deprived rat tail tendons is not correlated with the collagen fibril diameter distribution and, therefore, the collagen fibril diameter distribution does not, by itself, dictate the decrease in mechanical properties observed in in vitro stress-deprived rat tail tendons.     

Growth of Collagen Fibril Seeds from Embryonic Tendon: Fractured Fibril Ends Nucleate New Tip Growth

Collagen fibrils are the principal tensile element of vertebrate tissues where they occur in the extracellular matrix as spatially organised arrays. A major challenge is to understand how the mechanisms of nucleation, growth and remodelling yield fibrils of tissue-specific diameter and length. Here we have developed a seeding system whereby collagen fibrils were isolated from avian embryonic tendon and added to purified collagen solution, in order to characterise fibril surface nucleation and growth mechanisms. Fragmentation of tendon in liquid nitrogen followed by Dounce homogenisation generated fibril length fragments. Most (> 94%) of the fractured ends of fibrils, which show an abrupt square profile, were found to act as nucleation sites for further growth by molecular accretion. The mechanism of this nucleation and growth process was investigated by transmission electron microscopy, atomic force microscopy and scanning transmission electron microscopy mass mapping. Typically, a single growth spur occurred on the N-terminal end of seed fibrils whilst twin spurs frequently formed on the C-terminal end before merging into a single tip projection. The surface nucleation and growth process generated a smoothly tapered tip that achieved maximum diameter when the axial extension reached ∼ 13 μm. Lateral growth also occurred along the entire length of all seed fibrils that contained tip projections. The data support a model of collagen fibril growth in which the broken ends of fibrils are nucleation sites for propagation in opposite axial directions. The observed fibril growth behaviour has direct relevance to tendon matrix remodelling and repair processes that might involve rupture of collagen fibrils.     

Conformation and sequence evidence for two-fold symmetry in left-handed beta-helix fold

The glycosaminoglycan (GAG) side-chains of small leucine-rich proteoglycans have been postulated to mechanically cross-link adjacent collagen fibrils and contribute to tendon mechanics. Enzymatic depletion of tendon GAGs (chondroitin and dermatan sulfate) has emerged as a preferred method to experimentally assess this role. However, GAG removal is typically incomplete and the possibility remains that extant GAGs may remain mechanically functional. The current study specifically investigated the potential mechanical effect of the remaining GAGs after partial enzymatic digestion.A three-dimensional finite element model of tendon was created based upon the concept of proteoglycan mediated inter-fibril load sharing. Approximately 250 interacting, discontinuous collagen fibrils were modeled as having a length of 400 μm, being composed of rod elements of length 67 nm and E-modulus 1 GPa connected in series. Spatial distribution and diameters of these idealized fibrils were derived from a representative cross-sectional electron micrograph of tendon. Rod element lengths corresponded to the collagen fibril D-Period, widely accepted to act as a binding site for decorin and biglycan, the most abundant proteoglycans in tendon. Each element node was connected to nodes of any neighboring fibrils within a radius of 100 nm, the slack length of unstretched chondroitin sulfate. These GAG cross-links were the sole mechanism for lateral load sharing among the discontinuous fibrils, and were modeled as bilinear spring elements. Simulation of tensile testing of tendon with complete cross-linking closely reproduced corresponding experiments on rat tail tendons. Random reduction of 80% of GAG cross-links (matched to a conservative estimate of enzymatic depletion efficacy) predicted a drop of 14% in tendon modulus. Corresponding mechanical properties derived from experiments on rat tail tendons treated in buffer with and without chondroitinase ABC were apparently unaffected, regardless of GAG depletion. Further tests for equivalence, conservatively based on effect size limits predicted by the model, confirmed equivalent stiffness between enzymatically depleted tendons and their native controls.Although the model predicts that relatively small quantities of GAGs acting as primary collagen cross-linking elements could provide mechanical integrity to the tendon, partial enzymatic depletion of GAGs should result in mechanical changes that are not reflected in analogous experimental testing. We thus conclude that GAG side chains of small leucine-rich proteoglycans are not a primary determinant of tensile mechanical behavior in mature rat tail tendons.     

Advanced Glycation End-Products Reduce Collagen Molecular Sliding to Affect Collagen Fibril Damage Mechanisms but Not Stiffness

Advanced glycation end-products (AGE) contribute to age-related connective tissue damage and functional deficit. The documented association between AGE formation on collagens and the correlated progressive stiffening of tissues has widely been presumed causative, despite the lack of mechanistic understanding. The present study investigates precisely how AGEs affect mechanical function of the collagen fibril – the supramolecular functional load-bearing unit within most tissues. We employed synchrotron small-angle X-ray scattering (SAXS) and carefully controlled mechanical testing after introducing AGEs in explants of rat-tail tendon using the metabolite methylglyoxal (MGO). Mass spectrometry and collagen fluorescence verified substantial formation of AGEs by the treatment. Associated mechanical changes of the tissue (increased stiffness and failure strength, decreased stress relaxation) were consistent with reports from the literature. SAXS analysis revealed clear changes in molecular deformation within MGO treated fibrils. Underlying the associated increase in tissue strength, we infer from the data that MGO modified collagen fibrils supported higher loads to failure by maintaining an intact quarter-staggered conformation to nearly twice the level of fibril strain in controls. This apparent increase in fibril failure resistance was characterized by reduced side-by-side sliding of collagen molecules within fibrils, reflecting lateral molecular interconnectivity by AGEs. Surprisingly, no change in maximum fibril modulus (2.5 GPa) accompanied the changes in fibril failure behavior, strongly contradicting the widespread assumption that tissue stiffening in ageing and diabetes is directly related to AGE increased fibril stiffness. We conclude that AGEs can alter physiologically relevant failure behavior of collagen fibrils, but that tissue level changes in stiffness likely occur at higher levels of tissue architecture.     

Viscoelastic properties of isolated collagen fibrils

Understanding the viscoelastic behavior of collagenous tissues with complex hierarchical structures requires knowledge of the properties at each structural level. Whole tissues have been studied extensively, but less is known about the mechanical behavior at the submicron, fibrillar level. Using a microelectromechanical systems platform, in vitro coupled creep and stress relaxation tests were performed on collagen fibrils isolated from the sea cucumber dermis. Stress-strain-time data indicate that isolated fibrils exhibit viscoelastic behavior that could be fitted using the Maxwell-Weichert model. The fibrils showed an elastic modulus of 123 ± 46 MPa. The time-dependent behavior was well fit using the two-time-constant Maxwell-Weichert model with a fast time response of 7 ± 2 s and a slow time response of 102 ± 5 s. The fibrillar relaxation time was smaller than literature values for tissue-level relaxation time, suggesting that tissue relaxation is dominated by noncollagenous components (e.g., proteoglycans). Each specimen was tested three times, and the only statistically significant difference found was that the elastic modulus is larger in the first test than in the subsequent two tests, indicating that viscous properties of collagen fibrils are not sensitive to the history of previous tests.     

Pectinase treatments on technical fibres of flax: Effects on water sorption and mechanical properties

This study is focused on enzymatically upgrading the functional properties of flax fibres. Green flax fibres were treated with a polygalacturonase and a pectate lyase (PaL) and their properties were compared with dew-retted fibres. Morphological observations, vapour-sorption analyses and mechanical measurements showed that PaL-treatment was able not only to mime retting in terms of bundle division, but also to improve the mechanical properties of technical fibres. Conversely, these properties were shifted down after the polygalacturonase treatment, mainly due to the presence of contaminating glycanases. At the level of the elementary fibres, nanoindentation data indicated the highest stiffness of the secondary wall for PaL-treated fibres. The tensile properties exhibited equal, but moderate values of the Young's modulus (∼37 ± 14 GPa) and breaking strength (∼650 ± 300 MPa) for retted and PaL-treated fibres; we hypothesize an impact of the growth conditions on the fibre chemical structure with an excess of matrix pectins compared to the amount of glucomannan coating the cellulose microfibrils.     

Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells. Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process. The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution. In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz. We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample. By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase. Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process. These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering.     

Fibrillogenesis in dense collagen solutions: a physicochemical study

Fibrillogenesis, the formation of collagen fibrils, is a key factor in connective tissue morphogenesis. To understand to what extent cells influence this process, we systematically studied the physicochemistry of the self-assembly of type I collagen molecules into fibrils in vitro. We report that fibrillogenesis in solutions of type I collagen, in a high concentration range close to that of living tissues (40-300 mg/ml), yields strong gels over wide pH and ionic strength ranges. Structures of gels were described by combining microscopic observations (transmission electron microscopy) with small- and wide-angle X-ray scattering analysis, and the influence of concentration, pH, and ionic strength on the fibril size and organization was evaluated. The typical cross-striated pattern and the corresponding small-angle X-ray scattering 67-nm diffraction peaks were visible in all conditions in the pH 6 to pH 12 range. In reference conditions (pH 7.4, ionic strength = 150 mM, 20 °C), collagen concentration greatly influences the overall macroscopic structure of the resultant fibrillar gels, as well as the morphology and structure of the fibrils themselves. At a given collagen concentration, increasing the ionic strength from 24 to 261 mM produces larger fibrils until the system becomes biphasic. We also show that fibrils can form in acidic medium (pH ∼ 2.5) at very high collagen concentrations, beyond 150 mg/ml, which suggests a possible cholesteric-to-smectic phase transition. This set of data demonstrates how simple physicochemical parameters determine the molecular organization of collagen. Such an in vitro model allows us to study the intricate process of fibrillogenesis in conditions of molecular packing close to that which occurs in biological tissue morphogenesis.     

Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons--a computational study from molecular to microstructural level

Experimental studies on immature tendons have shown that the collagen fibril net is discontinuous. Manifold evidences, despite not being conclusive, indicate that mature tissue is discontinuous as well. According to composite theory, there is no requirement that the fibrils should extend from one end of the tissue to the other; indeed, an interfibrillar matrix with a low elastic modulus would be sufficient to guarantee the mechanical properties of the tendon. Possible mechanisms for the stress-transfer involve the interfibrillar proteoglycans and can be related to the matrix shear stress and to electrostatic non-covalent forces. Recent studies have shown that the glycosaminoglycans (GAGs) bound to decorin act like bridges between contiguous fibrils connecting adjacent fibril every 64-68 nm; this architecture would suggest their possible role in providing the mechanical integrity of the tendon structure. The present paper investigates the ability of decorin GAGs to transfer forces between adjacent fibrils. In order to test this hypothesis the stiffness of chondroitin-6-sulphate, a typical GAG associated to decorin, has been evaluated through the molecular mechanics approach. The obtained GAG stiffness is piecewise linear with an initial plateau at low strains (<800%) and a high stiffness region (3.1 x 10(-11)N/nm) afterwards. By introducing the calculated GAG stiffness in a multi-fibril model, miming the relative mature tendon architecture, the stress-strain behaviour of the collagen fibre was determined. The fibre incremental elastic modulus obtained ranges between 100 and 475 MPa for strains between 2% and 6%. The elastic modulus value depends directly on the fibril length, diameter and inversely on the interfibrillar distance. In particular, according to the obtained results, the length of the fibril is likely to play the major role in determining stiffness in mature tendons.     

Image correlation spectroscopy of multiphoton images correlates with collagen mechanical properties

Multiphoton microscopy (MPM) holds promise as a noninvasive imaging technique for characterizing collagen structure, and thus mechanical properties, through imaging second harmonic generation (SHG) and two-photon fluorescence in engineered and real connective tissues. Controlling polymerization pH to manipulate collagen gel microstructure, we quantified pore and fiber dimensions using both standard methods and image correlation spectroscopy (ICS) on MPM, scanning electron, and darkfield microscopy images. The latter two techniques are used to confirm microstructural measurements made from MPM images. As polymerization pH increased from 5.5 to 8.5, mean fiber diameter decreased from 3.7 ± 0.7 μm to 1.6 ± 0.3 μm, the average pore size decreased from 81.7 ± 3.7 μm² to 7.8 ± 0.4 μm², and the pore area fraction decreased from 56.8% ± 0.8% to 18.0% ± 1.3% (measured from SHG images), whereas the storage modulus G′ and loss modulus G′, components of the shear modulus, increased ∼33-fold and ∼16-fold, respectively. A characteristic length scale measured using ICS, W_ICS, correlates well with the mean fiber diameter from SHG images (R² = 0.95). Semiflexible network theory predicts a scaling relationship of the collagen gel storage modulus (G′) depending upon mesh size and fiber diameter, which are estimated from SHG images using ICS. We conclude that MPM and ICS are an effective combination to assess bulk mechanical properties of collagen hydrogels in a noninvasive, objective, and systematic fashion and may be useful for specific in vivo applications.