Collagen fibrils are the ultrastructural base of biological tissues and exhibit nonlinear rate-dependent tensile behaviour. In this study, we constitute a visco-hypoelastic model to describe the stress-rate-strain-rate responses in accord with the atomic force microscopy (AFM) uniaxial tensile tests on individual collagen fibrils. The model is decoupled into elastic and dissipative (viscous) components: the elastic component is governed by the rate-dependent neo-Hookean model; the dissipative component is postulated as a function of stress and strain rate. We adopt a two-step minimization process to determine the material parameters of the elastic and viscous responses separately. The predicted stress and stretch are computed with an explicit time-integration scheme to the visco-hypoelastic model. Based on the modelling results, we obtain the elastic properties of individual collagen fibrils with 120.9 MPa in shear modulus and approximately 753.2 MPa in tensile modulus under small deformation (2% strain). The dissipation decays quadratically with the increase of the stress level. This study presents a novel visco-hypoelastic model that successfully predicts the nonlinear rate-dependent tensile responses of individual collagen fibrils in both stress-stretch and stress-rate-strain-rate spaces. We additionally characterize the dissipative behaviour of collagen fibrils owing to viscosity and other rate-dependent effects. Additional experiments and data are needed to validate the potential of this model for large deformations.

The collagen fibrillar network in cartilage, skin and bone is a crucial ultrastructural component of the extracellular matrix (ECM). As a principal stiff element in the ECM, collagen fibrils enables a range of tissue-specific biomechanical functions, including shear, multidirectional elasticity, and stiffness. These properties are believed to be achieved by a synergistic action of individual fibril mechanics, interaction with extrafibrillar matrix molecules and inbuilt spatial organisation, interconnection and gradients. However, the nature of these diverse fibrillar-level mechanisms are not fully clear. Here we show how microfocus synchrotron small-angle X-ray scattering combined with in situ mechanical loading can help elucidate these mechanisms across two different tissue types. First, in diarthrodial joints, co-deformation of Type-II collagen fibrils at the bone(hard)-cartilage(soft) interface is crucial to understanding the biomechanical initiation of degenerative changes like osteoarthritis. Using microcompression on cores from metacarpophalangeal bovine joints, we find that loading induces reductions in fibril pre-strain gradients, increases in angular dispersion, and strain variability in the articular collagen. Changes in osmotic stress both in the extrafibrillar and intrafibrillar space are proposed as primary mechanisms for this behavior. Further and notably, the fibril pre-strain reduces in the calcified cartilage, an unexpected result given the presence of a reinforcing mineral phase. Secondly, in cutaneous (skin) wound healing in a mouse model, early-stage collagen fibrils, in the low-stress wound site, exhibit microscale loci of lowered pre-strain and alignment, with clear spatial structure around the wound bed. As natural in vivo stresses return with healing, the inherent tensile pre-strain returns, coupled with increase in matrix mechanics. Our results show the need to understand fibrillar deformation mechanisms both at individual fibril-level and via mechanisms such as reorientation, molecular ordering, and lateral contraction to capture the full functional variability and adaptability of collagen fibrillar mechanics.

Fibrillar collagen may be viewed as a composite material made of protein, macromolecules (such as glycosaminoglycans and proteoglycans) and water. Yet, the properties of water and the fine interactions of water with the protein constituent of these nanocomposites have only received limited attention. Here, we propose to investigate in-depth water structure and dynamics confined within the microfibril crystal structure of collagen type I to establish its impact on the properties of collagen. We perform large-scale molecular dynamics simulations of a microfibril of collagen [1] at varying degrees of hydration. We found that the properties of water vary strongly with the level of hydration of the microfibril, and spatially along the long axis of the crystal, namely moving from the so-called gap region to the so-called overlap region. In short, at low hydration, water acts as a glue between protein chains; while at high hydration, water acts as a lubricant. Beyond self-assembly and properties of fibrillar collagen, such het- erogeneous structure and anisotropic dynamics may control its biomineralization and the properties of biological tissues such as bone.

[1] Orgel, J.P.; Irving, T.C.; Miller, A.; Wess, T. J.; Proc. Nat. Acad. Sci. 2006, 103, 24.