Non-equilibrium growth and twist of cross-linked collagen fibrils

Torsion and bistability of double-twist elastomers

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting-like effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain - at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions, due to residual torques.

Modeling collagen fibril self-assembly from extracellular medium in embryonic tendon

Collagen is a key structural component of multicellular organisms and is arranged in a highly organized manner. In structural tissues such as tendons, collagen forms bundles of parallel fibers between cells, which appear within a 24-h window between embryonic day 13.5 (E13.5) and E14.5 during mouse embryonic development. Current models assume that the organized structure of collagen requires direct cellular control, whereby cells actively lay down collagen fibrils from cell surfaces. However, such models appear incompatible with the time and length scales of fibril formation. We propose a phase-transition model to account for the rapid development of ordered fibrils in embryonic tendon, reducing reliance on active cellular processes. We develop phase-field crystal simulations of collagen fibrillogenesis in domains derived from electron micrographs of inter-cellular spaces in embryonic tendon and compare results qualitatively and quantitatively to observed patterns of fibril formation. To test the prediction of this phase-transition model that free protomeric collagen should exist in the inter-cellular spaces before the formation of observable fibrils, we use laser-capture microdissection, coupled with mass spectrometry, which demonstrates steadily increasing free collagen in inter-cellular spaces up to E13.5, followed by a rapid reduction of free collagen that coincides with the appearance of less-soluble collagen fibrils. The model and measurements together provide evidence for extracellular self-assembly of collagen fibrils in embryonic mouse tendon, supporting an additional mechanism for rapid collagen fibril formation during embryonic development.

Mineralized Collagen Fibrils: An Essential Component in Determining the Mechanical Behavior of Cortical Bone

Bone comprises mechanically different materials in a specific hierarchical structure. Mineralized collagen fibrils (MCFs), represented by tropocollagen molecules and hydroxyapatite nanocrystals, are the fundamental unit of bone. The mechanical characterization of MCFs provides the unique adaptive mechanical competence to bone to withstand mechanical load. The structural and mechanical role of MCFs is critical in the deformation mechanisms of bone and the marvelous strength and toughness possessed by bone. However, the role of MCFs in the mechanical behavior of bone across multiple length scales is not fully understood. In the present study, we shed light upon the latest progress regarding bone deformation at multiple hierarchical levels and emphasize the role of MCFs during bone deformation. We propose the concept of hierarchical deformation of bone to describe the interconnected deformation process across multiple length scales of bone under mechanical loading. Furthermore, how the deterioration of bone caused by aging and diseases impairs the hierarchical deformation process of the cortical bone is discussed. The present work expects to provide insights on the characterization of MCFs in the mechanical properties of bone and lays the framework for the understanding of the multiscale deformation mechanics of bone.

Temporal application of lysyl oxidase during hierarchical collagen fiber formation differentially effects tissue mechanics

The primary source of strength in menisci, tendons, and ligaments are hierarchical collagen fibers; however, these fibers are not regenerated after injury nor in engineered replacements, resulting in limited repair options. Collagen strength is reliant on fiber alignment, density, diameter, and crosslinking. Recently, we developed a culture system which guides cells in high-density collagen gels to develop native-like hierarchically organized collagen fibers, which match native fiber alignment and diameters by 6 weeks. However, tensile moduli plateau at 1MPa, suggesting crosslinking may be lacking. Collagen crosslinking is regulated by lysyl oxidase (LOX) which forms immature crosslinks that condense into mature trivalent crosslinks. Trivalent crosslinks are thought to be the primarily source of strength in fibers, but it's not well understood how they form. The objective of this study was to evaluate the effect of exogenous LOX in our culture system at different stages of hierarchical fiber formation to produce stronger replacements and to better understand factors affecting crosslink maturation. We found treatment with LOX isoform LOXL2 did not restrict hierarchical fiber formation, with constructs still forming aligned collagen fibrils by 2 weeks, larger fibers by 4 weeks, and early fascicles by 6 weeks. However, LOXL2 treatment did significantly increase mature pyridinium (PYD) crosslink accumulation and tissue mechanics, with timing of LOXL2 supplementation during fiber formation having a significant effect. Overall, we found one week of LOXL2 supplementation at 4 weeks produced constructs with native-like fiber organization, increased PYD accumulation, and increased mechanics, ultimately matching the tensile modulus of immature bovine menisci. STATEMENT OF SIGNIFICANCE: Collagen fibers are the primary source of strength and function in connective tissues throughout the body, however it remains a challenge to develop these fibers in engineered replacements, greatly reducing treatment options. Here we demonstrate lysyl oxidase like 2 (LOXL2) can be used to significantly improve the mechanics of tissue engineered constructs, but timing of application is important and will most likely depend on degree of collagen organization or maturation. Currently there is limited understanding of how collagen crosslinking is regulated, and this system is a promising platform to further investigate cellular regulation of LOX crosslinking. Understanding the mechanism that regulates LOX production and activity is needed to ultimately regenerate functional repair or replacements for connective tissues throughout the body.

Collagen fibril assembly: New approaches to unanswered questions

Collagen fibrils are essential for metazoan life. They are the largest, most abundant, and most versatile protein polymers in animals, where they occur in the extracellular matrix to form the structural basis of tissues and organs. Collagen fibrils were first observed at the turn of the 20th century. During the last 40 years, the genes that encode the family of collagens have been identified, the structure of the collagen triple helix has been solved, the many enzymes involved in the post-translational modifications of collagens have been identified, mutations in the genes encoding collagen and collagen-associated proteins have been linked to heritable disorders, and changes in collagen levels have been associated with a wide range of diseases, including cancer. Yet despite extensive research, a full understanding of how cells assemble collagen fibrils remains elusive. Here, we review current models of collagen fibril self-assembly, and how cells might exert control over the self-assembly process to define the number, length and organisation of fibrils in tissues.

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils - such as fibrils from skin or corneal tissue.

Chiral phase-coexistence in compressed double-twist elastomers

We adapt the theory of anisotropic rubber elasticity to model cross-linked double-twist liquid crystal cylinders such as exhibited in biological systems. In mechanical extension we recover strain-straightening, but with an exact expression in the small twist-angle limit. In compression, we observe coexistence between high and low twist phases. Coexistence begins at small compressive strains and is robustly observed for any anisotropic cross-links and for general double-twist functions - but disappears at large twist angles. Within the coexistence region, significant compression of double-twist cylinders is allowed at constant stress. Our results are qualitatively consistent with previous observations of swollen or compressed collagen fibrils, indicating that this phenomenon may be readily accessible experimentally.