Deformation micromechanisms of collagen fibrils under uniaxial tension

Interfibrillar shear stress is the loading mechanism of collagen fibrils in tendon

Despite the critical role tendons play in transmitting loads throughout the musculoskeletal system, little is known about the microstructural mechanisms underlying their mechanical function. Of particular interest is whether collagen fibrils in tendon fascicles bear load independently or if load is transferred between fibrils through interfibrillar shear forces. We conducted multiscale experimental testing and developed a microstructural shear lag model to explicitly test whether interfibrillar shear load transfer is indeed the fibrillar loading mechanism in tendon. Experimental correlations between fascicle macroscale mechanics and microscale interfibrillar sliding suggest that fibrils are discontinuous and share load. Moreover, for the first time, we demonstrate that a shear lag model can replicate the fascicle macroscale mechanics as well as predict the microscale fibrillar deformations. Since interfibrillar shear stress is the fundamental loading mechanism assumed in the model, this result provides strong evidence that load is transferred between fibrils in tendon and possibly other aligned collagenous tissues. Conclusively establishing this fibrillar loading mechanism and identifying the involved structural components should help develop repair strategies for tissue degeneration and guide the design of tissue engineered replacements.

Modelling the mechanics of partially mineralized collagen fibrils, fibres and tissue

Progressive stiffening of collagen tissue by bioapatite mineral is important physiologically, but the details of this stiffening are uncertain. Unresolved questions about the details of the accommodation of bioapatite within and upon collagen's hierarchical structure have posed a central hurdle, but recent microscopy data resolve several major questions. These data suggest how collagen accommodates bioapatite at the lowest relevant hierarchical level (collagen fibrils), and suggest several possibilities for the progressive accommodation of bioapatite at higher hierarchical length scales (fibres and tissue). We developed approximations for the stiffening of collagen across spatial hierarchies based upon these data, and connected models across hierarchies levels to estimate mineralization-dependent tissue-level mechanics. In the five possible sequences of mineralization studied, percolation of the bioapatite phase proved to be an important determinant of the degree of stiffening by bioapatite. The models were applied to study one important instance of partially mineralized tissue, which occurs at the attachment of tendon to bone. All sequences of mineralization considered reproduced experimental observations of a region of tissue between tendon and bone that is more compliant than either tendon or bone, but the size and nature of this region depended strongly upon the sequence of mineralization. These models and observations have implications for engineered tissue scaffolds at the attachment of tendon to bone, bone development and graded biomimetic attachment of dissimilar hierarchical materials in general.

Glycation cross-linking induced mechanical-enzymatic cleavage of microscale tendon fibers

Recent molecular modeling data using collagen peptides predicted that mechanical force transmitted through intermolecular cross-links resulted in collagen triple helix unwinding. These simulations further predicted that this unwinding, referred to as triple helical microunfolding, occurred at forces well below canonical collagen damage mechanisms. Based in large part on these data, we hypothesized that mechanical loading of glycation cross-linked tendon microfibers would result in accelerated collagenolytic enzyme damage. This hypothesis is in stark contrast to reports in literature that indicated that individually mechanical loading or cross-linking each retards enzymatic degradation of collagen substrates. Using our Collagen Enzyme Mechano-Kinetic Automated Testing (CEMKAT) System we mechanically loaded collagen-rich tendon microfibers that had been chemically cross-linked with sugar and tested for degrading enzyme susceptibility. Our results indicated that cross-linked fibers were >5 times more resistant to enzymatic degradation while unloaded but became highly susceptible to enzyme cleavage when they were stretched by an applied mechanical deformation.

Revisiting the Fundamentals in the Design and Control of Nanoparticulate Colloids in the Frame of Soft Chemistry

This review presents thoughts on some of the fundamental features of conceptual models applied in the design of fine particles in the frames of colloid and soft chemistry. A special emphasis is placed on the limitations of these models, an acknowledgment of which is vital in improving their intricacy and effectiveness in predicting the outcomes of the corresponding experimental settings. Thermodynamics of self-assembly phenomena illustrated on the examples of protein assembly and micellization is analyzed in relation to the previously elaborated thesis that each self-assembly in reality presents a co-assembly, since it implies a mutual reorganization of the assembling system and its immediate environment. Parameters used in the design of fine particles by precipitation are discussed while referring to solubility product, various measures of supersaturation levels, induction time, nucleation and crystal growth rates, interfacial energies, and the Ostwald-Lussac law of phases. Again, the main drawbacks and inadequacies of using the aforementioned parameters in tailoring the materials properties in a soft and colloidal chemical setting were particularly emphasized. The basic and practical limitations of zeta-potential analyses, routinely used to stabilize colloidal dispersions and initiate specific interactions between soft chemical entities, were also outlined. The final section of the paper reiterates the unavoidable presence of practical qualitative models in the design and control of nanoparticulate colloids, which is supported by the overwhelming complexity of quantitative relationships that govern the processes of their formation and assembly.

A new multiscale model for the mechanical behavior of vein walls

The purpose of the present work is to propose a new multiscale model for the prediction of the mechanical behavior of vein walls. This model is based on one of our previous works which considered scale transitions applied to undulated collagen fibers. In the present work, the scale below was added to take the anisotropy of collagen fibrils into account. One scale above was also added, modeling the global reorientation of collagen fibers inside the vessel wall. The model was verified on experimental data from the literature, leading to a satisfactory agreement. The proposed multiscale approach also allows the extraction of local stresses and strains at each scale. This approach is presented here in the case of vein walls, but can easily be extended to other tissues which contain similar constituents.

In situ cell-matrix mechanics in tendon fascicles and seeded collagen gels: implications for the multiscale design of biomaterials

Designing biomaterials to mimic and function within the complex mechanobiological conditions of connective tissues requires a detailed understanding of the micromechanical environment of the cell. The objective of our study was to measure the in situ cell-matrix strains from applied tension in both tendon fascicles and cell-seeded type I collagen scaffolds using laser scanning confocal microscopy techniques. Tendon fascicles and collagen gels were fluorescently labelled to simultaneously visualise the extracellular matrix and cell nuclei under applied tensile strains of 5%. There were significant differences observed in the micromechanics at the cell-matrix scale suggesting that the type I collagen scaffold did not replicate the pattern of native tendon strains. In particular, although the overall in situ tensile strains in the matrix were quite similar (∼2.5%) between the tendon fascicles and the collagen scaffolds, there were significant differences at the cell-matrix boundary with visible shear across cell nuclei of >1 μm measured in native tendon which was not observed at all in the collagen scaffolds. Similarly, there was significant non-uniformity of intercellular strains with relative sliding observed between cell rows in tendon which again was not observed in the collagen scaffolds where the strain environment was much more uniform. If the native micromechanical environment is not replicated in biomaterial scaffolds, then the cells may receive incorrect or mixed mechanical signals which could affect their biosynthetic response to mechanical load in tissue engineering applications. This study highlights the importance of considering the microscale mechanics in the design of biomaterial scaffolds and the need to incorporate such features in computational models of connective tissues.

Fibrillar structure and elasticity of hydrating collagen: a quantitative multiscale approach

It is well known that hydration of collagenous tissues leads to their swelling, as well as to softening of their elastic behavior. However, it is much less clear which microstructural and micromechanical "rules" are involved in this process. Here, we develop a theoretical approach cast in analytical mathematical formulations, which is experimentally validated by a wealth of independent tests on collagenous tissues, such as X-ray diffraction, vacuum drying, mass measurements, and Brillouin light scattering. The overall emerging picture is the following: air-drying leaves water only in the gap zones between the triple-helical collagen molecules; upon re-hydration, the extrafibrillar space is established at volumes directly proportional to the hydration-induced swelling of the (micro) fibrils, until the maximum equatorial distance between the long collagen molecules is reached. Thereafter, the volume of the fibrils stays constant, and only the extrafibrillar volume continues to grow. At all these hydration stages, the elastic behavior is governed by the same, hydration-invariant mechanical interaction pattern of only two, interpenetrating mechanical phases: transversely isotropic molecular collagen and isotropic water (or empty pores in the vacuum-dried case).

A review of combined experimental and computational procedures for assessing biopolymer structure-process-property relationships

Tailored biomaterials with tunable functional properties are desirable for many applications ranging from drug delivery to regenerative medicine. To improve the predictability of biopolymer materials functionality, multiple design parameters need to be considered, along with appropriate models. In this article we review the state of the art of synthesis and processing related to the design of biopolymers, with an emphasis on the integration of bottom-up computational modeling in the design process. We consider three prominent examples of well-studied biopolymer materials - elastin, silk, and collagen - and assess their hierarchical structure, intriguing functional properties and categorize existing approaches to study these materials. We find that an integrated design approach in which both experiments and computational modeling are used has rarely been applied for these materials due to difficulties in relating insights gained on different length- and time-scales. In this context, multiscale engineering offers a powerful means to accelerate the biomaterials design process for the development of tailored materials that suit the needs posed by the various applications. The combined use of experimental and computational tools has a very broad applicability not only in the field of biopolymers, but can be exploited to tailor the properties of other polymers and composite materials in general.

Bimodal collagen fibril diameter distributions direct age-related variations in tendon resilience and resistance to rupture

Scaling relationships have been formulated to investigate the influence of collagen fibril diameter (D) on age-related variations in the strain energy density of tendon. Transmission electron microscopy was used to quantify D in tail tendon from 1.7- to 35.3-mo-old (C57BL/6) male mice. Frequency histograms of D for all age groups were modeled as two normally distributed subpopulations with smaller (D(D1)) and larger (D(D2)) mean Ds, respectively. Both D(D1) and D(D2) increase from 1.6 to 4.0 mo but decrease thereafter. From tensile tests to rupture, two strain energy densities were calculated: 1) u(E) [from initial loading until the yield stress (σ(Y))], which contributes primarily to tendon resilience, and 2) u(F) [from σ(Y) through the maximum stress (σ(U)) until rupture], which relates primarily to resistance of the tendons to rupture. As measured by the normalized strain energy densities u(E)/σ(Y) and u(F)/σ(U), both the resilience and resistance to rupture increase with increasing age and peak at 23.0 and 4.0 mo, respectively, before decreasing thereafter. Multiple regression analysis reveals that increases in u(E)/σ(Y) (resilience energy) are associated with decreases in D(D1) and increases in D(D2), whereas u(F)/σ(U) (rupture energy) is associated with increases in D(D1) alone. These findings support a model where age-related variations in tendon resilience and resistance to rupture can be directed by subtle changes in the bimodal distribution of Ds.

Experiments in Nanomechanical Properties of Live Osteoblast Cells and Cell–Biomaterial Interface

Characterizing the mechanical characteristics of living cells and cell–biomaterial composite is an important area of research in bone tissue engineering. In this work, an in situ displacement-controlled nanoindentation technique (using Hysitron Triboscope) is developed to perform nanomechanical characterization of living cells (human osteoblasts) and cell–substrate constructs under physiological conditions (cell culture medium; 37 °C). In situ elastic moduli (E) of adsorbed proteins on tissue culture polystyrene (TCPS) under cell culture media were found to be ∼4 GPa as revealed by modulus mapping experiments. The TCPS substrates soaked in cell culture medium showed significant difference in surface nanomechanical properties (up to depths of ∼12 nm) as compared to properties obtained from deeper indentations. Atomic force microscopy (AFM) revealed the cytoskeleton structures such as actin stress fiber networks on flat cells which are believed to impart the structural integrity to cell structure. Load-deformation response of cell was found to be purely elastic in nature, i.e., cell recovers its shape on unloading as indicated by linear loading and unloading curves obtained at 1000 nm indentation depth. The elastic response of cells is obtained during initial cell adhesion (ECell, 1 h, 1000 nm = 4.4–12.4 MPa), cell division (ECell, 2 days, 1000 nm = 1.3–3.0 MPa), and cell spreading (ECell, 2 days, 1000 nm = 6.9–11.6 MPa). Composite nanomechanical responses of cell–TCPS constructs were obtained by indentation at depths of 2000 nm and 3000 nm on cell-seeded TCPS. Elastic properties of cell–substrate composites were mostly dominated by stiff TCPS (EBulk = 5 GPa) lying underneath the cell.

Structural and mechanical differences between collagen homo- and heterotrimers: relevance for the molecular origin of brittle bone disease

Collagen constitutes one-third of the human proteome, providing mechanical stability, elasticity, and strength to organisms. Normal type I collagen is a heterotrimer triple-helical molecule consisting of two α-1 chains and one α-2 chain. The homotrimeric isoform of type I collagen, which consists of three α-1 chains, is only found in fetal tissues, fibrosis, and cancer in humans. A mouse model of the genetic brittle bone disease, osteogenesis imperfect, oim, is characterized by a replacement of the α-2 chain by an α-1 chain, resulting also in a homotrimer collagen molecule. Experimental studies of oim mice tendon and bone have shown reduced mechanical strength compared to normal mice. The relationship between the molecular content and the decrease in strength is, however, still unknown. Here, fully atomistic simulations of a section of mouse type I heterotrimer and homotrimer collagen molecules are developed to explore the effect of the substitution of the α-2 chain. We calculate the persistence length and carry out a detailed analysis of the structure to determine differences in structural and mechanical behavior between hetero- and homotrimers. The results show that homotrimer persistence length is half of that of the heterotrimer (96 Å vs. 215 Å), indicating it is more flexible and confirmed by direct mechanical testing. Our structural analyses reveal that in contrast to the heterotrimer, the homotrimer easily forms kinks and freely rotates with angles much larger than heterotrimer. These local kinks may explain the larger lateral distance between collagen molecules seen in the fibrils of oim mice tendon and could have implications for reducing the intermolecular cross-linking, which is known to reduce the mechanical strength.

Molecular simulations predict novel collagen conformations during cross-link loading

Collagen cross-linking mechanically strengthens tissues during development and aging, but there is limited data describing how force transmitted across cross-links affects molecular conformation. We used Steered Molecular Dynamics (SMD) to model perpendicular force through a side chain. Results predicted that collagen peptides have negligible bending resistance and that mechanical force causes helix disruption below covalent bond failure strength, suggesting alternative molecular conformations precede cross-link rupture and macroscopic damage during mechanical loading.

Statistical model with two order parameters for ductile and soft fiber bundles in nanoscience and biomaterials

Traditional fiber bundles models (FBMs) have been an effective tool to understand brittle heterogeneous systems. However, fiber bundles in modern nano- and bioapplications demand a new generation of FBM capturing more complex deformation processes in addition to damage. In the context of loose bundle systems and with reference to time-independent plasticity and soft biomaterials, we formulate a generalized statistical model for ductile fracture and nonlinear elastic problems capable of handling more simultaneous deformation mechanisms by means of two order parameters (as opposed to one). As the first rational FBM for coupled damage problems, it may be the cornerstone for advanced statistical models of heterogeneous systems in nanoscience and materials design, especially to explore hierarchical and bio-inspired concepts in the arena of nanobiotechnology. Applicative examples are provided for illustrative purposes at last, discussing issues in inverse analysis (i.e., nonlinear elastic polymer fiber and ductile Cu submicron bars arrays) and direct design (i.e., strength prediction).

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.