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.     

Molecular assessment of the elastic properties of collagen-like homotrimer sequences

Knowledge of the mechanical behavior of collagen molecules is critical for understanding the mechanical properties of collagen fibrils that constitute the main architectural building block of a number of connective tissues. In this study, the elastic properties of four different type I collagen 30-residue long molecular sequences, were studied by performing stretching simulations using the molecular mechanics approach. The energy–molecular length relationship was achieved by means of the geometry optimization procedure for collagen molecule strains up to 10%. The energy was interpolated by a second order function, and the second order of the derivative with respect to the mean length corresponded to the molecule stiffness. According to the hypothesis of linear elastic behavior, except for one sequence, the elastic modulus was around 2.40 GPa. These values are larger than fibril values, and they confirm the hypothesis that tendon mechanical properties are deeply related to tendon hierarchical structure. A possible explanation of the lowest values obtained for one sequence (1.33–1.53 GPa) is provided and discussed.     

Molecular and Mesoscale Mechanisms of Osteogenesis Imperfecta Disease in Collagen Fibrils

Osteogenesis imperfecta (OI) is a genetic disorder in collagen characterized by mechanically weakened tendon, fragile bones, skeletal deformities, and in severe cases, prenatal death. Although many studies have attempted to associate specific mutation types with phenotypic severity, the molecular and mesoscale mechanisms by which a single point mutation influences the mechanical behavior of tissues at multiple length scales remain unknown. We show by a hierarchy of full atomistic and mesoscale simulation that OI mutations severely compromise the mechanical properties of collagenous tissues at multiple scales, from single molecules to collagen fibrils. Mutations that lead to the most severe OI phenotype correlate with the strongest effects, leading to weakened intermolecular adhesion, increased intermolecular spacing, reduced stiffness, as well as a reduced failure strength of collagen fibrils. We find that these molecular-level changes lead to an alteration of the stress distribution in mutated collagen fibrils, causing the formation of stress concentrations that induce material failure via intermolecular slip. We believe that our findings provide insight into the microscopic mechanisms of this disease and lead to explanations of characteristic OI tissue features such as reduced mechanical strength and a lower cross-link density. Our study explains how single point mutations can control the breakdown of tissue at much larger length scales, a question of great relevance for a broad class of genetic diseases.     

Viscoelastic properties of living embryonic tissues: a quantitative study.

A number of properties of certain living embryonic tissues can be explained by considering them as liquids. Tissue fragments left in a shaker bath round up to form spherical aggregates, as do liquid drops. When cells comprising two distinct embryonic tissues are mixed, typically a nucleation-like process takes place, and one tissue sorts out from the other. The equilibrium configurations at the end of such sorting out phenomena have been interpreted in terms of tissue surface tensions arising from the adhesive interactions between individual cells. In the present study we go beyond these equilibrium properties and study the viscoelastic behavior of a number of living embryonic tissues. Using a specifically designed apparatus, spherical cell aggregates are mechanically compressed and their viscoelastic response is followed. A generalized Kelvin model of viscoelasticity accurately describes the measured relaxation curves for each of the four tissues studied. Quantitative results are obtained for the characteristic relaxation times and elastic and viscous parameters. Our analysis demonstrates that the cell aggregates studied here, when subjected to mechanical deformations, relax as elastic materials on short time scales and as viscous liquids on long time scales.     

The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow et al., 2006, Ann Biomed Eng., 34(2), pp. 315-325; Grashow et al., 2006, Ann Biomed. Eng., 34(10), pp. 1509-1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain (epsilonD) and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of 90 N/m. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, epsilonD increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using epsilonD, the tangent modulus of collagen fibrils was estimated to be 95.5+/-25.5 MPa, which was approximately 27 times higher than the tissue tensile tangent modulus of 3.58+/-1.83 MPa. In creep tests performed at 90 N/m equibiaxial tension for 60 min, both tissue strain and epsilonD remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for 90 min epsilonD was found to rapidly decrease in the first 10 min followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was 8.3 min, which was smaller than the tissue-level stress relaxation time constants of 22.0 and 16.9 min in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a "load-locking" behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.     

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 fluid description of bacterial biofilm material properties

A mathematical model describing the constitutive properties of biofilms is required for predicting biofilm deformation, failure, and detachment in response to mechanical forces. Laboratory observations indicate that biofilms are viscoelastic materials. Likewise, current knowledge of biofilm internal structure suggests modeling biofilms as associated polymer viscoelastic systems. Supporting experimental results and a system of viscoelastic fluid equations with a linear Jeffreys viscoelastic stress-strain law are presented here. This system of equations is based on elements of associated polymer physics and is also consistent with presented and previous experimental results. A number of predictions can be made. One particularly interesting result is the prediction of an elastic relaxation time on the order of a few minutes-biofilm disturbances on shorter time scales produce an elastic response, biofilm disturbances on longer time scales result in viscous flow, i.e., nonreversible biofilm deformation. Although not previously recognized, evidence of this phenomenon is in fact present in recent experimental results.     

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.     

Designed to fail: a novel mode of collagen fibril disruption and its relevance to tissue toughness

Collagen fibrils are nanostructured biological cables essential to the structural integrity of many of our tissues. Consequently, understanding the structural basis of their robust mechanical properties is of great interest. Here we present what to our knowledge is a novel mode of collagen fibril disruption that provides new insights into both the structure and mechanics of native collagen fibrils. Using enzyme probes for denatured collagen and scanning electron microscopy, we show that mechanically overloading collagen fibrils from bovine tail tendons causes them to undergo a sequential, two-stage, selective molecular failure process. Denatured collagen molecules-meaning molecules with a reduced degree of time-averaged helicity compared to those packed in undamaged fibrils-were first created within kinks that developed at discrete, repeating locations along the length of fibrils. There, collagen denaturation within the kinks was concentrated within certain subfibrils. Additional denatured molecules were then created along the surface of some disrupted fibrils. The heterogeneity of the disruption within fibrils suggests that either mechanical load is not carried equally by a fibril's subcomponents or that the subcomponents do not possess homogenous mechanical properties. Meanwhile, the creation of denatured collagen molecules, which necessarily involves the energy intensive breaking of intramolecular hydrogen bonds, provides a physical basis for the toughness of collagen fibrils.     

A visco-hyperelastic constitutive approach for modeling polyvinyl alcohol sponge

This study proposes the quasi-linear viscoelastic (QLV) model to characterize the time dependent mechanical behavior of poly(vinyl alcohol) (PVA) sponges. The PVA sponges have implications in many viscoelastic soft tissues, including cartilage, liver, and kidney as an implant. However, a critical barrier to the use of the PVA sponge as tissue replacement material is a lack of sufficient study on its viscoelastic mechanical properties. In this study, the nonlinear mechanical behavior of a fabricated PVA sponge is investigated experimentally and computationally using relaxation and stress failure tests as well as finite element (FE) modeling. Hyperelastic strain energy density functions, such as Yeoh and Neo-Hookean, are used to capture the mechanical behavior of PVA sponge at ramp part, and viscoelastic model is used to describe the viscose behavior at hold part. Hyperelastic material constants are obtained and their general prediction ability is verified using FE simulations of PVA tensile experiments. The results of relaxation and stress failure tests revealed that Yeoh material model can define the mechanical behavior of PVA sponge properly compared with Neo-Hookean one. FE modeling results are also affirmed the appropriateness of Yeoh model to characterize the mechanical behavior of PVA sponge. Thus, the Yeoh model can be used in future biomechanical simulations of the spongy biomaterials. These results can be utilized to understand the viscoelastic behavior of PVA sponges and has implications for tissue engineering as scaffold.     

Viscoelastic properties of collagen: synchrotron radiation investigations and structural model

Collagen type I is the most abundant structural protein in tendon, skin and bone, and largely determines the mechanical behaviour of these connective tissues. To obtain a better understanding of the relationship between structure and mechanical properties, tensile tests and synchrotron X-ray scattering have been carried out simultaneously, correlating the mechanical behaviour with changes in the microstructure. Because intermolecular cross-links are thought to have a great influence on the mechanical behaviour of collagen, we also carried out experiments using cross-link-deficient tail-tendon collagen from rats fed with beta-APN, in addition to normal controls. The load-elongation curve of tendon collagen has a characteristic shape with, initially, an increasing slope, corresponding to an increasing stiffness, followed by yielding and then fracture. Cross-link-deficient collagen produces a quite different curve with a marked plateau appearing in some cases, where the length of the tendon increases at constant stress. With the use of in situ X-ray diffraction, it was possible to measure simultaneously the elongation of the collagen fibrils inside the tendon and of the tendon as a whole. The overall strain of the tendon was always larger than the strain in the individual fibrils, which demonstrates that some deformation is taking place in the matrix between fibrils. Moreover, the ratio of fibril strain to tendon strain was dependent on the applied strain rate. When the speed of deformation was increased, this ratio increased in normal collagen but generally decreased in cross-link-deficient collagen, correlating to the appearance of a plateau in the force-elongation curve indicating creep. We proposed a simple structural model, which describes the tendon at a hierarchical level, where fibrils and interfibrillar matrix act as coupled viscoelastic systems. All qualitative features of the strain-rate dependence of both normal and cross-link-deficient collagen can be reproduced within this model. This complements earlier models that considered the next smallest level of hierarchy, describing the deformation of collagen fibrils in terms of changes in their molecular packing.     

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.     

The in situ supermolecular structure of type I collagen.

BACKGROUND: The proteins belonging to the collagen family are ubiquitous throughout the animal kingdom. The most abundant collagen, type I, readily forms fibrils that convey the principal mechanical support and structural organization in the extracellular matrix of connective tissues such as bone, skin, tendon, and vasculature. An understanding of the molecular arrangement of collagen in fibrils is essential since it relates molecular interactions to the mechanical strength of fibrous tissues and may reveal the underlying molecular pathology of numerous connective tissue diseases. RESULTS: Using synchrotron radiation, we have conducted a study of the native fibril structure at anisotropic resolution (5.4 A axial and 10 A lateral). The intensities of the tendon X-ray diffraction pattern that arise from the lateral packing (three-dimensional arrangement) of collagen molecules were measured by using a method analogous to Rietveld methods in powder crystallography and to the separation of closely spaced peaks in Laue diffraction patterns. These were then used to determine the packing structure of collagen by MIR. CONCLUSIONS: Our electron density map is the first obtained from a natural fiber using these techniques (more commonly applied to single crystal crystallography). It reveals the three-dimensional molecular packing arrangement of type I collagen and conclusively proves that the molecules are arranged on a quasihexagonal lattice. The molecular segments that contain the telopeptides (central to the function of collagen fibrils in health and disease) have been identified, revealing that they form a corrugated arrangement of crosslinked molecules that strengthen and stabilize the native fibril.     

Influence of temperature on the rheological behavior of a new fucose-containing bacterial exopolysaccharide

The effect of temperature on the rheology of a new fucose-containing extracellular polysaccharide (EPS) was evaluated. The steady state data revealed a shear-thinning behavior, with the viscosity being immediately recovered when the shear rate was decreased. The mechanical spectra indicated viscous solutions with entangled polymer molecules in the range of temperatures studied (from 15 °C to 65 °C). In addition, the Time-Temperature Superposition principle was successfully applied and the Cox-Merz rule was valid, reinforcing the idea of a thermorheologically simple behavior for the EPS in aqueous solution. Furthermore, the viscous and viscoelastic properties at 25 °C were maintained after consecutive heating and cooling cycles, indicating a good thermal stability under temperature fluctuations.     

Towards a fibrous composite with dynamically controlled stiffness: lessons from echinoderms

Sea urchins and sea cucumbers, like other echinoderms, control the tensile properties of their connective tissues by regulating stress transfer between collagen fibrils. The collagen fibrils are spindle-shaped and up to 1 mm long with a constant aspect ratio of approx. 2000. They are organized into a tissue by an elastomeric network of fibrillin microfibrils. Interactions between the fibrils are regulated by soluble macromolecules that are secreted by local, neurally controlled, effector cells. We are characterizing the non-linear viscoelastic properties of sea cucumber dermis under different conditions, as well as the structures, molecules and molecular interactions that determine its properties. In addition, we are developing reagents that will bind covalently to fibril surfaces and reversibly form cross-links with other reagents, resulting in a chemically controlled stress-transfer capacity. The information being developed will lead to the design and construction of a synthetic analogue composed of fibres in an elastomeric matrix that contains photo- or electro-sensitive reagents that reversibly form interfibrillar cross-links.     

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

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

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.     

Fracture Mechanics of Collagen Fibrils: Influence of Natural Cross-Links

Tendons are important load-bearing structures, which are frequently injured in both sports and work. Type I collagen fibrils are the primary components of tendons and carry most of the mechanical loads experienced by the tissue, however, knowledge of how load is transmitted between and within fibrils is limited. The presence of covalent enzymatic cross-links between collagen molecules is an important factor that has been shown to influence mechanical behavior of the tendons. To improve our understanding of how molecular bonds translate into tendon mechanics, we used an atomic force microscopy technique to measure the mechanical behavior of individual collagen fibrils loaded to failure. Fibrils from human patellar tendons, rat-tail tendons (RTTs), NaBH₄ reduced RTTs, and tail tendons of Zucker diabetic fat rats were tested. We found a characteristic three-phase stress-strain behavior in the human collagen fibrils. There was an initial rise in modulus followed by a plateau with reduced modulus, which was finally followed by an even greater increase in stress and modulus before failure. The RTTs also displayed the initial increase and plateau phase, but the third region was virtually absent and the plateau continued until failure. The importance of cross-link lability was investigated by NaBH₄ reduction of the rat-tail fibrils, which did not alter their behavior. These findings shed light on the function of cross-links at the fibril level, but further studies will be required to establish the underlying mechanisms.     

Mechanical properties of plant cell walls probed by relaxation spectra

Transformants and mutants with altered cell wall composition are expected to display a biomechanical phenotype due to the structural role of the cell wall. It is often quite difficult, however, to distinguish the mechanical behavior of a mutant's or transformant's cell walls from that of the wild type. This may be due to the plant's ability to compensate for the wall modification or because the biophysical method that is often employed, determination of simple elastic modulus and breakstrength, lacks the resolving power necessary for detecting subtle mechanical phenotypes. Here, we apply a method, determination of relaxation spectra, which probes, and can separate, the viscoelastic properties of different cell wall components (i.e. those properties that depend on the elastic behavior of load-bearing wall polymers combined with viscous interactions between them). A computer program, BayesRelax, that deduces relaxation spectra from appropriate rheological measurements is presented and made accessible through a Web interface. BayesRelax models the cell wall as a continuum of relaxing elements, and the ability of the method to resolve small differences in cell wall mechanical properties is demonstrated using tuber tissue from wild-type and transgenic potatoes (Solanum tuberosum) that differ in rhamnogalacturonan I side chain structure.