Mechanical model for a collagen fibril pair in extracellular matrix

In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled by Hooke’s law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic glycosaminoglycan.     

Stress transfer in collagen fibrils reinforcing connective tissues: effects of collagen fibril slenderness and relative stiffness

Unlike engineering fibre composite materials which comprise of fibres that are uniform cylindrical in shape, collagen fibrils reinforcing the proteoglycan-rich (PG) gel in the extra-cellular matrices (ECMs) of connective tissues are taper-ended (paraboloidal in shape). In an earlier paper we have discussed how taper of a fibril leads to an axial stress up-take which differs from that of a uniform cylindrical fibre and implications for fibril fracture. The present paper focuses on the influence of fibre aspect ratio, q (slenderness), and Young's modulus (stiffness), relative to that of the gel phase, E(R), on the magnitude of the axial tensile stresses generated within a fibril and wider implications on failure at tissue level. Fibre composite models were evaluated using finite element (FE) and mathematical analyses. When the applied force is low, there is elastic stress transfer between the PG gel and a fibril. FE modelling shows that the stress in a fibril increases with E(R) and q. At higher applied forces, there is plastic stress transfer. Mathematical modelling predicts that the stress in a fibril increases linearly with q. For small q values, fibrils may be regarded as fillers with little ability to provide tensile reinforcement. Large q values lead to high stress in a fibril. Such high stresses are beneficial provided they do not exceed the fracture stress of collagen. Modulus difference regulates the strain energy release density, u, for interfacial rupture; large E(R) not only leads to high stress in a fibril but also insures against interfacial rupture by raising the value of u.     

Closest packing of two-stranded coiled-coils as a model for the collagen fibril.

We propose that in the collagen fibril, the triple-helical molecules form two-stranded coiled-coils of period 5 × 670A?. Coiled-coils are packed on a tetragonal lattice and are axially staggered with ten in the unit cell (observed side 55A?) so that it carries the 670A?periodicity of the fibril. When nearest neighbours have opposing supercoil hands, the observed tetragonal lattice represents closest packing of two-stranded coiled-coils. This proposal is consistent with the row line spacings measured from the low angle X-ray diffraction pattern of tendon and explains the systematic absences and the two undisputed equatorial reflections. Unlike explanations for the diffraction pattern which invoke a five-stranded microfibril, our interpretation is consistent with its equatorial intensity distribution.     

High-resolution analysis of the modified quarter-stagger model of the collagen fibril

The location of transverse bands within the major repeating period of positively stained collagen fibrils was determined from electron micrographs by an optical averaging procedure. From these data and the published location of bands in SLS crystallites, we have prepared a two-dimensional representation, accurate to about 25 Å, of the modified quarter-stagger arrangement of molecules in the collagen fibril. With this information it is possible to demonstrate the relationship of loci on individual collagen molecules within the fibril. For example, the site where the collagen molecule is cleaved by tadpole collagenase, the site where a disaccharide unit is covalently bound to the α1-CB5 peptide, and the site of carboxyl-terminal intermolecular cross-linking all occur in the fibril near the amino-terminal edge of the “hole zone;” and the site of amino-terminal cross-linking occurs near the carboxyl-terminal edge of the “hole zone.”     

The mechanism of enhanced insulin amyloid fibril formation by NaCl is better explained by a conformational change model

The high propensity of insulin to fibrillate causes severe biomedical and biotechnological complications. Insulin fibrillation studies attain significant importance considering the prevalence of diabetes and the requirement of functional insulin in each dose. Although studied since the early years of the 20(th) century, elucidation of the mechanism of insulin fibrillation has not been understood completely. We have previously, through several studies, shown that insulin hexamer dissociates into monomer that undergoes partial unfolding before converting into mature fibrils. In this study we have established that NaCl enhances insulin fibrillation mainly due to subtle structural changes and is not a mere salt effect. We have carried out studies both in the presence and absence of urea and Gdn.HCl and compared the relationship between conformation of insulin induced by urea and Gdn.HCl with respect to NaCl at both pH 7.4 (hexamer) and pH 2 (monomer). Fibril formation was followed with a Thioflavin T assay and structural changes were monitored by circular dichroism and size-exclusion chromatography. The results show salt-insulin interactions are difficult to classify as commonly accepted Debye-Hückel or Hofmeister series interactions but instead a strong correlation between the association states and conformational states of insulin and their propensity to fibrillate is evident.     

A new model to simulate the elastic properties of mineralized collagen fibril

Bone, because of its hierarchical composite structure, exhibits an excellent combination of stiffness and toughness, which is due substantially to the structural order and deformation at the smaller length scales. Here, we focus on the mineralized collagen fibril, consisting of hydroxyapatite plates with nanometric dimensions aligned within a protein matrix, and emphasize the relationship between the structure and elastic properties of a mineralized collagen fibril. We create two- and three-dimensional representative volume elements to represent the structure of the fibril and evaluate the importance of the parameters defining its structure and properties of the constituent mineral and collagen phase. Elastic stiffnesses are calculated by the finite element method and compared with experimental data obtained by synchrotron X-ray diffraction. The computational results match the experimental data well, and provide insight into the role of the phases and morphology on the elastic deformation characteristics. Also, the effects of water, imperfections in the mineral phase and mineral content outside the mineralized collagen fibril upon its elastic properties are discussed.     

Relative orientation of collagen molecules within a fibril: a homology model for homo sapiens type I collagen

Type I collagen is an essential extracellular protein that plays an important structural role in tissues that require high tensile strength. However, owing to the molecule’s size, to date no experimental structural data are available for the Homo sapiens species. Therefore, there is a real need to develop a reliable homology model and a method to study the packing of the collagen molecules within the fibril. Through the use of the homology model and implementation of a novel simulation technique, we have ascertained the orientations of the collagen molecules within a fibril, which is currently below the resolution limit of experimental techniques. The longitudinal orientation of collagen molecules within a fibril has a significant effect on the mechanical and biological properties of the fibril, owing to the different amino acid side chains available at the interface between the molecules.     

Type V collagen controls the initiation of collagen fibril assembly

Vertebrate collagen fibrils are heterotypically composed of a quantitatively major and minor fibril collagen. In non-cartilaginous tissues, type I collagen accounts for the majority of the collagen mass, and collagen type V, the functions of which are poorly understood, is a minor component. Type V collagen has been implicated in the regulation of fibril diameter, and we reported recently preliminary evidence that type V collagen is required for collagen fibril nucleation (Wenstrup, R. J., Florer, J. B., Cole, W. G., Willing, M. C., and Birk, D. E. (2004) J. Cell. Biochem. 92, 113-124). The purpose of this study was to define the roles of type V collagen in the regulation of collagen fibrillogenesis and matrix assembly. Mouse embryos completely deficient in pro-alpha1(V) chains were created by homologous recombination. The col5a1-/- animals die in early embryogenesis, at approximately embryonic day 10. The type V collagen-deficient mice demonstrate a virtual lack of collagen fibril formation. In contrast, the col5a1+/- animals are viable. The reduced type V collagen content is associated with a 50% reduction in fibril number and dermal collagen content. In addition, relatively normal, cylindrical fibrils are assembled with a second population of large, structurally abnormal collagen fibrils. The structural properties of the abnormal matrix are decreased relative to the wild type control animals. These data indicate a central role for the evolutionary, ancient type V collagen in the regulation of fibrillogenesis. The complete dependence of fibril formation on type V collagen is indicative of the critical role of the latter in early fibril initiation. In addition, this fibril collagen is important in the determination of fibril structure and matrix organization.     

Proteolysis of the collagen fibril in osteoarthritis

The development of cartilage pathology in osteoarthritis involves excessive damage to the collagen fibrillar network, which appears to be mediated primarily by the chondrocyte-generated cytokines interleukin-1 and tumour necrosis factor alpha and the collagenases matrix metalloproteinase-1 (MMP-1) and MMP-13. The damage to matrix caused by these and other MMPs can result in the production of sufficient degradation products that can themselves elicit further degradation, leading to chondrocyte differentiation and eventually matrix mineralization and cell death. Knowledge of these MMPs, cellular receptors and cytokine pathways, and the ability to selectively antagonize them by selective blockade of function, may provide valuable therapeutic opportunities in the treatment of osteoarthritis and other joint diseases involving cartilage resorption, such as rheumatoid arthritis. The ability to detect the products of these degradative events released into body fluids of patients may enable us to monitor disease activity, predict disease progression and determine more rapidly the efficacy of new therapeutic agents.     

Collagen fibril structure is affected by collagen concentration and decorin

Collagen fibrils were obtained in vitro by aggregation from acid-soluble type I collagen at different initial concentrations and with the addition of decorin core or intact decorin. All specimens were observed by scanning electron microscopy and atomic force microscopy. In line with the findings of other authors, lacking decorin, collagen fibrils undergo an extensive lateral association leading to the formation of a continuous three-dimensional network. The addition of intact decorin or decorin core was equally effective in preventing lateral fusion and restoring the normal fibril appearance. In addition, the fibril diameter was clearly dependent on the initial collagen concentration but not on the presence/absence of proteoglycans. An unusual fibril structure was observed as a result of a very low initial collagen concentration, leading to the formation of huge, irregular superfibrils apparently formed by the lateral coalescence of lesser fibrils, and with a distinctive coil-structured surface. Spots of incomplete fibrillogenesis were occasionally found, where all fibrils appeared made of individual, interwined subfibrils, confirming the presence of a hierarchical association mechanism.     

The role of hydrophobic bonding in collagen fibril formation: a quantitative model

A model has been developed for approximating the free energy of collagen fibril formation (ΔF_f) and the equilibrium solubility of collagen under physiological conditions. The model utilizes an expression of Flory for rodlike polymers, with the modification that the “pure” anisotropic phase is defined as a collagen fibril containing about 0.3 g water/g collagen. The model also assumes that χ₁, the polymer–solvent interaction term, is entirely due to hydrophobic effects. χ₁ is estimated from hydrophobic bond energies of amino acid side chains, using the results of Némethy and Scheraga. The temperature dependence of χ₁ is utilized to calculate equilibrium solubilities and ΔF_f as a function of temperature.     

A mechanical model for collagen fibril load sharing in peripheral nerve of diabetic and nondiabetic rats

Peripheral neuropathy affects approximately 50% of the 15 million Americans with diabetes. It has been suggested that mechanical effects related to collagen glycation are related to the permanence of neuropathy. In the present paper, we develop a model for load transfer in a whole nerve, using a simple pressure vessel approximation, in order to assess the significant of stiffening of the collagenous nerve sheath on endoneurial fluid pressure. We also develop a fibril-scale mechanics model for the nerve, to model the straightening of wavy fibrils, producing the toe region observed in nerve tissue, and also to interrogate the effects of interfibrillar crosslinks on the overall properties of the tissue. Such collagen crosslinking has been implicated in complications in diabetic tissues. Our fibril-scale model uses a two-parameter Weibull model for fibril strength, in combination with statistical parameters describing fibril modulus, angle, wave-amplitude, and volume fraction to capture both toe region and failure region behavior of whole rat sciatic nerve. The extrema of equal and local load-sharing assumptions are used to map potential differences in diabetic and nondiabetic tissues. This work may ultimately be useful in differentiating between the responses of normal and heavily crosslinked tissue.     

Unit fibril models derived from the molecular topography of collagen

The geometrical properties of collagen molecules place certain restrictions on possible three-dimensional packing models. With certain reasonable assumptions involving the macromolecular structure of collagen, a model for the surface topography of the monomeric unit is developed and two possible models for molecular packing, one hexagonal and the other non-hexagonal, are inferred. The non-hexagonal packing model is identical to the pentagonal unit fibril first postulated by J. W. Smith on different grounds, while the hexagonal model is one of three previously suggested by us on more general assumptions. The two models are compared to available data on collagen packing, and the bulk of the evidence would seem to favor the pentagonal model.     

The mechanism of nucleation for in vitro collagen fibril formation.

The formation of collagen fibrils from soluble monomers and aggregates by thermal gelation at neutral pH can be divided into two distinct stages: a nucleation phase and a growth phase. Turbidity studies of the kinetics of the precipitation reaction show that the lag-phase time or nucleation reaction time, t′_l, is markedly temperature dependent while the growth reaction time is temperature independent. The activation energy of the nucleation reaction is essentially constant over the temperature range studied. In monitoring the nucleation-phase reaction by various physicochemical techniques, including viscosity, sedimentation equilibrium, and light scattering, no evidence for the formation of aggregates was observed. Enrichment of the initial collagen solution with aggregates accelerates nucleation, but de novo nuclei formation is still required even in highly aggregated collagen preparations. Removal of pepsin and pronase susceptible peptides lengthens the nucleation reaction time and increases the sensitivity of the rate of nuclei formation to changes in ionic strength. Electron microscope studies show the fibrils formed from the protease-treated collagen to be less well organized. With pepsin-treated collagen, subfibrils and obliquely striated fibrils are seen, showing that while microfibrils are formed interactions between them are modulated by the enzyme susceptible peptides in the same way that these regions modulate nuclei assembly. It appears that pepsin and pronase susceptible peptide regions of collagen play a more prominent role in the in vitro assembly of collagen molecules to form D-stagger nuclei and fibrils than do ionic interactions between helical molecular regions. A mechanism of nucleation of collagen fibrillogenesis is discussed.     

Actin filaments are required for fibripositor-mediated collagen fibril alignment in tendon

Cells in tendon deposit parallel arrays of collagen fibrils to form a functional tissue, but how this is achieved is unknown. The cellular mechanism is thought to involve the formation of intracellular collagen fibrils within Golgi to plasma membrane carriers. This is facilitated by the intracellular processing of procollagen to collagen by members of the tolloid and ADAMTS families of enzymes. The carriers subsequently connect to the extracellular matrix via finger-like projections of the plasma membrane, known as fibripositors. In this study we have shown, using three-dimensional electron microscopy, the alignment of fibripositors with intracellular fibrils as well as an orientated cable of actin filaments lining the cytosolic face of a fibripositor. To demonstrate a specific role for the cytoskeleton in coordinating extracellular matrix assembly, cytochalasin was used to disassemble actin filaments and nocodazole or colchicine were used to disrupt microtubules. Microtubule disruption delayed procollagen transport through the secretory pathway, but fibripositor numbers were unaffected. Actin filament disassembly resulted in rapid loss of fibripositors and a subsequent disappearance of intracellular fibrils. Procollagen secretion or processing was not affected by cytochalasin treatment, but the parallelism of extracellular collagen fibrils was altered. In this case a significant proportion of collagen fibrils were found to no longer be orientated with the long axis of the tendon. The results suggest an important role for the actin cytoskeleton in the alignment and organization of the collagenous extracellular matrix in embryonic tendon.     

Estimation of the binding force of the collagen molecule-decorin core protein complex in collagen fibril

Decorin belongs to the small leucine proteoglycans family and is considered to play an important role in extracellular matrix organization. Experimental studies suggest that decorin is required for the assembly of collagen fibrils, as well as for the development of proper tissue mechanical properties. In tendons, decorins tie adjoining collagen fibrils together and probably guarantee the mechanical coupling of fibrils. The decorin molecule consists of one core protein and one glycosaminoglycan chain covalently linked to a serine residue of the core protein. Several studies have indicated that each core protein binds to the surface of collagen fibrils every 67 nm, by interacting non-covalently to one collagen molecule of the fibril surface, while the decorin glycosaminoglycans extend from the core protein to connect to another decorin core protein laying on adjacent fibril surface. The present paper investigates the complex composed of one decorin core protein and one collagen molecule in order to obtain their binding force. For this purpose, molecular models of collagen molecules type I and decorin core protein were developed and their interaction energies were evaluated by means of the molecular mechanics approach. Results show that the complex is characterized by a maximum binding force of about 12.4 x 10(3) nN and a binding stiffness of 8.33 x 10(-8) N/nm; the attained binding force is greater than the glycosaminoglycan chain's ultimate strength, thus indicating that overloads are likely to damage the collagen fibre's mechanical integrity by disrupting the glycosaminoglycan chains rather than by causing decorin core protein detachment from the collagen fibril.