Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253 ± 21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

A coarse-grained molecular dynamics investigation of the role of mineral arrangement on the mechanical properties of mineralized collagen fibrils

Mineralized collagen fibrils (MCFs) comprise collagen molecules and hydroxyapatite (HAp) crystals and are considered universal building blocks of bone tissue, across different bone types and species. In this study, we developed a coarse-grained molecular dynamics (CGMD) framework to investigate the role of mineral arrangement on the load-deformation behaviour of MCFs. Despite the common belief that the collagen molecules are responsible for flexibility and HAp minerals are responsible for stiffness, our results showed that the mineral phase was responsible for limiting collagen sliding in the large deformation regime, which helped the collagen molecules themselves undergo high tensile loading, providing a substantial contribution to the ultimate tensile strength of MCFs. This study also highlights different roles for the mineralized and non-mineralized protofibrils within the MCF, with the mineralized groups being primarily responsible for load carrying due to the presence of the mineral phase, while the non-mineralized groups are responsible for crack deflection. These results provide novel insight into the load-deformation behaviour of MCFs and highlight the intricate role that both collagen and mineral components have in dictating higher scale bone biomechanics.

Exploring the Mechanical Properties and Performance of Type-I Collagen at Various Length Scales: A Progress Report

Collagen is the basic protein of animal tissues and has a complex hierarchical structure. It plays a crucial role in maintaining the mechanical and structural stability of biological tissues. Over the years, it has become a material of interest in the biomedical industries thanks to its excellent biocompatibility and biodegradability and low antigenicity. Despite its significance, the mechanical properties and performance of pure collagen have been never reviewed. In this work, the emphasis is on the mechanics of collagen at different hierarchical levels and its long-term mechanical performance. In addition, the effect of hydration, important for various applications, was considered throughout the study because of its dramatic influence on the mechanics of collagen. Furthermore, the discrepancies in reports of the mechanical properties of collagenous tissues (basically composed of 20-30% collagen fibres) and those of pure collagen are discussed.

Strain rate induced toughening of individual collagen fibrils

The nonlinear mechanical behavior of individual nanoscale collagen fibrils is governed by molecular stretching and sliding that result in a viscous response, which is still not fully understood. Toward this goal, the in vitro mechanical behavior of individual reconstituted mammalian collagen fibrils was quantified in a broad range of strain-rates, spanning roughly six orders of magnitude, from 10^-4 to 35 s^-1. It is shown that the nonlinear mechanical response is strain rate sensitive with the tangent modulus in the linear deformation regime increasing monotonically from 214 ± 8 to 358 ± 11 MPa. More pronounced is the effect of the strain rate on the ultimate tensile strength that is found to increase monotonically by a factor of four, from 42 ± 6 to 160 ± 14 MPa. Importantly, fibril strengthening takes place without a reduction in ductility, which results in equivalently large increase in toughness with the increasing strain rate. This experimental strain rate dependent mechanical response is captured well by a structural constitutive model that incorporates the salient features of the collagen microstructure via a process of gradual recruitment of kinked tropocollagen molecules, thus giving rise to the initial "toe-heel" mechanical behavior, followed by molecular stretching and sustained intermolecular slip that is initiated at a strain rate dependent stress threshold. The model shows that the fraction of tropocollagen molecules undergoing straightening increases continuously during loading, whereas molecular sliding is initiated after a small fibril strain (1%-2%) and progressively increases with applied strain.

Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals

Self-similar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractional-order derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractional-order temporal responses. We further expanded the fractal hyper-cell (FHC) viscoelasticity theory to investigate this spatio-temporal correlation. The FHC element was first compared with other material elements and spring–dashpot viscoelastic models, thereby highlighting its discrete and fractal nature. To demonstrate the utility of an FHC, tree-like, ladder-like and triangle-like FHCs were abstracted from human cartilage, tendons and muscle cross-sections, respectively. The duality and symmetry of the FHC element were further discussed, where operating the duality transformation generated new types of FHC elements, and the symmetry breaking of an FHC altered its fractional-order viscoelastic responses. Thus, the correlations between the staggering patterns of FHCs and their rheological power-law orders were established, and the viscoelastic behaviour of the multi-level FHC elements fitted well in stress relaxation experiments at both the macro- and nano-levels of the tendon hierarchy. The FHC element provides a theoretical basis for understanding the connections between structural degeneration of bio-tissues during ageing or disease and their functional changes.

Frequency dependent inelastic response of collagen architecture of pig dermis under cyclic tensile loading: An experimental study

The evaluation of collagen architecture of the dermis in response to mechanical stimulation is important as it affects the macroscopic mechanical properties of the dermis. A detailed understanding of the processes involved in the alteration of the collagen structure is required to correlate the mechanical stimulation with tissue remodeling. This study investigated the effect of cyclic frequencies i.e. low (0.1 Hz), medium (2.0 Hz), and high (5.0 Hz) (physiological range) in the alteration of pig dermis collagen structure and its correlation with the macroscopic mechanical response of the dermis. The assessment of the collagen structure of virgin and mechanical tested specimens at tropocollagen, collagen fibril, and fiber level was performed using Fourier-transform infrared-attenuated total reflection (FTIR-ATR), atomic force microscopy (AFM), and scanning electron microscopy (SEM) respectively. After 10³ cycles, a significantly higher alteration in collagen structure with discrete plastic-type damage was found for low frequency. This frequency dependent alteration of the collagen structure was found in correlation with the dermis macroscopic response. The value of inelastic strain, stress softening, damage parameter (reduction in elastic modulus), and reduction in energy dissipation were observed significantly large for slow frequency. A power-law based empirical relations, as a function of frequency and number of cycles, were proposed to predict the value of inelastic strain and damage parameter. This study also suggests that hierarchical structural response against the mechanical stimulation is time-dependent rather than cycle-dependent, may affect the tissue remodeling.

Mechanics of Mineralized Collagen Fibrils upon Transient Loads

Collagen is a key structural protein in the human body, which undergoes mineralization during the formation of hard tissues. Earlier studies have described the mechanical behavior of bone at different scales, highlighting material features across hierarchical structures. Here we present a study that aims to understand the mechanical properties of mineralized collagen fibrils upon tensile/compressive transient loads, investigating how the kinetic energy propagates and it is dissipated at the molecular scale, thus filling a gap of knowledge in this area. These specific features are the mechanisms that nature has developed to passively dissipate stress and prevent structural failures. In addition to the mechanical properties of the mineralized fibrils, we observe distinct nanomechanical behaviors for the two regions (i.e., overlap and gap) of the D-period to highlight the effect of the mineralization. We notice decreasing trends for both wave speeds and Young's moduli over input velocity with a marked strengthening effect in the gap region due to the accumulation of the hydroxyapatite. In contrast, the dissipative behavior is not affected by either loading conditions or the mineral percentage, showing a stronger damping effect upon faster inputs compatible to the bone behavior at the macroscale. Our results offer insights into the dissipative behavior of mineralized collagen composites to design and characterize bioinspired composites for replacement devices (e.g., prostheses for sound transmission or conduction) or optimized structures able to bear transient loads, for example, impact, fatigue, in structural applications.

Wave Propagation and Energy Dissipation in Collagen Molecules

Collagen is the key protein of connective tissue (i.e., skin, tendons and ligaments, and cartilage, among others), accounting for 25-35% of the whole-body protein content and conferring mechanical stability. This protein is also a fundamental building block of bone because of its excellent mechanical properties together with carbonated hydroxyapatite minerals. Although the mechanical resilience and viscoelasticity have been studied both in vitro and in vivo from the molecular to tissue level, wave propagation properties and energy dissipation have not yet been deeply explored, in spite of being crucial to understanding the vibration dynamics of collagenous structures (e.g., eardrum, cochlear membranes) upon impulsive loads. By using a bottom-up atomistic modeling approach, here we study a collagen peptide under two distinct impulsive displacement loads, including longitudinal and transversal inputs. Using a one-dimensional string model as a model system, we investigate the roles of hydration and load direction on wave propagation along the collagen peptide and the related energy dissipation. We find that wave transmission and energy-dissipation strongly depend on the loading direction. Also, the hydrated collagen peptide can dissipate five times more energy than dehydrated one. Our work suggests a distinct role of collagen in term of wave transmission of different tissues such as tendon and eardrum. This study can step toward understanding the mechanical behavior of collagen upon transient loads, impact loading and fatigue, and designing biomimetic and bioinspired materials to replace specific native tissues such as the tympanic membrane.

Viscoelasticity in natural tissues and engineered scaffolds for tissue reconstruction

Viscoelasticity of living tissues plays a critical role in tissue homeostasis and regeneration, and its implication in disease development and progression is being recognized recently. In this review, we first explored the state of knowledge regarding the potential application of tissue viscoelasticity in disease diagnosis. In order to better characterize viscoelasticity with local resolution and non-invasiveness, emerging characterization methods have been developed with the potential to be supplemented to existing facilities. To understand cellular responses to matrix viscoelastic behaviors in vitro, hydrogels made of natural polymers have been developed and the relationships between their molecular structure and viscoelastic behaviors, are elucidated. Moreover, how cells perceive the viscoelastic microenvironment and cellular responses including cell attachment, spreading, proliferation, differentiation and matrix production, have been discussed. Finally, some future perspective on an integrated mechanobiological comprehension of the viscoelastic behaviors involved in tissue homeostasis, cellular responses and biomaterial design are highlighted. STATEMENT OF SIGNIFICANCE: Tissue- or organ-scale viscoelastic behavior is critical for homeostasis, and the molecular basis and cellular responses of viscoelastic materials at micro- or nano-scale are being recognized recently. We summarized the potential applications of viscoelasticity in disease diagnosis enabled by emerging non-invasive characterization technologies, and discussed the underlying mechanism of viscoelasticity of hydrogels and current understandings of cell regulatory functions of them. With a growing understanding of the molecular basis of hydrogel viscoelasticity and recognition of its regulatory functions on cell behaviors, it is important to bring the clinical insights on how these characterization technologies and engineered materials may contribute to disease diagnosis and treatment. This review explains the basics in characterizing viscoelasticity with our hope to bridge the gap between basic research and clinical applications.

Multiscale mechanical effects of native collagen cross-linking in tendon

The hierarchical structure of tendon allows for attenuation of mechanical strain down decreasing length scales. While reorganization of collagen fibers accounts for microscale strain attenuation, cross-linking between collagen molecules contributes to deformation mechanisms at the fibrillar and molecular scales. Divalent and trivalent enzymatic cross-links form during the development of collagen fibrils through the enzymatic activity of lysyl oxidase (LOX). By establishing connections between telopeptidyl and triple-helical domains of adjacent molecules within collagen fibrils, these cross-links stiffen the fibrils by resisting intermolecular sliding. Ultimately, greater enzymatic cross-linking leads to less compliant and stronger tendon as a result of stiffer fibrils. In contrast, nonenzymatic cross-links such as glucosepane and pentosidine are not produced during development but slowly accumulate through glycation of collagen. Therefore, these cross-links are only expected to be present in significant quantities in advanced age, where there has been sufficient time for glycation to occur, and in diabetes, where the presence of more free sugar in the extracellular matrix increases the rate of glycation. Unlike enzymatic cross-links, current evidence suggests that nonenzymatic cross-links are at least partially isolated to the surface of collagen fibers. As a result, glycation has been proposed to primarily impact tendon mechanics by altering molecular interactions at the fiber interface, thereby diminishing sliding between fibers. Thus, increased nonenzymatic cross-linking decreases microscale strain attenuation and the viscous response of tendon. In conclusion, enzymatic and nonenzymatic collagen cross-links have demonstrable and distinct effects on the mechanical properties of tendon across different length scales.

Appropriate Tensile Mode and Timing of Applying Tension to Promote Tendon Gel Regeneration

"Tendon gel" secreted from a parent tendon is regenerated for tendon repair by applying tension. However, the details of the tensile stimulus have not been clarified. This study aimed to evaluate an appropriate tensile stimulus mode and the optimal timing of applying tension to promote tendon gel regeneration. Tendon gel was prepared using a film model method in mice and was preserved in vivo for 3, 5, and 10 days. Unlike tendon gel on day 3 or day 5, a fibrous structure developed in the tendon gel on day 10 when tension was applied. Infrared spectroscopy revealed that characteristic peaks appearing for the tendon gel on days 3 and 5 disappeared on day 10. Disappearance of the peaks indicated maturity of the tendon gel, and it showed the optimal timing for tension application to the tendon gel. The effect of tensile load on tendon gel preserved for 10 days was investigated using a tensile test, a creep test, or a cycle test. In the tensile test, tendon gel was elongated into a thin cord of collagen fibers with an increase in stress, and the maximum diameter of the collagen fiber was approximately 50 times larger than that in the normal Achilles tendon of mice. The results suggest that the diameter of the oriented collagen fiber is controllable by adjusting the applied load and the time in mature tendon gel.