A new model for packing of type-I collagen molecules in the native fibril

A specific fibril model is presented consisting of bundles of five-stranded microfibrils, which are usually disordered (except axially) but under lateral compression become ordered. The features are as follows (whereD = 234 residues or 67 nm): (1)D-staggered collagen molecules 4.5D long in the helical microfibril have a left-handed supercoil with a pitch of 400–700 residues, but microfibrils need not have helical symmetry. (2) Straight-tilted 0.5-D overlap regions on a near-hexagonal lattice contribute the discrete x-ray diffraction reflections arising from lateral order, while the gap regions remain disordered. (3) The overlap regions are equivalent, but are crystallographically distinguished by systematic displacements from the near-hexagonal lattice. (4) The unit cell is the same as in a recently proposed three-dimensional crystal model, and calculated intensities in the equatorial region of the x-ray diffraction pattern agree with observed values.     

On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment

The key parameters influencing the elastic properties of the mineralized turkey leg tendon (MTLT) were investigated. Two structurally different tissue types appearing in the MTLT were considered: circumferential and interstitial tissue. These differ in their amount of micropores and their average diameter of the mineralized collagen fibril bundles. A multiscale model representing the apparent elastic stiffness tensor of MTLT tissue was developed using the Mori–Tanaka and the self-consistent homogenization schemes. The volume fraction of mineral (hydroxyapatite) in the fibril bundle, \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) , and the tissue microporosity are the variables of the model. The MTLT model was analyzed performing a global sensitivity analysis (Elementary Effects method) and a parametric study. The stiffnesses parallel (axial) and perpendicular (transverse) to the MTLT long axis were the only significantly sensitive components of the apparent stiffness tensor of MTLT tissue. The most important parameters influencing these apparent stiffnesses are \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) , tissue microporosity, as well as shape and distribution of the minerals in the fibril bundle (intra- vs. interfibrillar). The predicted apparent stiffness was converted to acoustic impedance for model validation. From measurements on embedded MTLT samples, including 50- and 200-MHz scanning acoustic microscopy as well as synchrotron radiation micro-computed tomography, we obtained site-matched acoustic impedance and \(\hbox {vf}_{{\text {ha}}}^{{\text {MCFB}}}\) data of circumferential and interstitial tissue. The experimental and the model data compare very well for both tissue types (relative error 6–8 %).     

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.”     

ColBuilder: A server to build collagen fibril models

Type I collagen is the main structural component of many tissues in the human body. It provides excellent mechanical properties to connective tissue and acts as a protein interaction hub. There is thus a wide interest in understanding the properties and diverse functions of type I collagen at the molecular level. A precondition is an atomistic collagen I structure as it occurs in native tissue. To this end, we built full-atom models of cross-linked collagen fibrils by integrating the low-resolution structure of collagen fibril available from x-ray fiber diffraction with high-resolution structures of short collagen-like peptides from x-ray crystallography and mass spectrometry data. We created a Web resource of collagen models for 20 different species with a large variety of cross-link types and localization within the fibril to facilitate structure-based analyses and simulations of type I collagen in health and disease. To easily enable simulations, we provide parameters of the modeled cross-links for an Amber force field. The repository of collagen models is available at https://colbuilder.h-its.org.     

Mechanical properties of mineralized collagen fibrils as influenced by demineralization

Dentin and bone derive their mechanical properties from a complex arrangement of collagen type-I fibrils reinforced with nanocrystalline apatite mineral in extra- and intrafibrillar compartments. While mechanical properties have been determined for the bulk of the mineralized tissue, information on the mechanics of the individual fibril is limited. Here, atomic force microscopy was used on individual collagen fibrils to study structural and mechanical changes during acid etching. The characteristic 67 nm periodicity of gap zones was not observed on the mineralized fibril, but became apparent and increasingly pronounced with continuous demineralization. AFM-nanoindentation showed a decrease in modulus from 1.5 GPa to 50 MPa during acid etching of individual collagen fibrils and revealed that the modulus profile followed the axial periodicity. The nanomechanical data, Raman spectroscopy and SAXS support the hypothesis that intrafibrillar mineral etches at a substantially slower rate than the extrafibrillar mineral. These findings are relevant for understanding the biomechanics and design principles of calcified tissues derived from collagen matrices.     

A new mathematical model to simulate AVA cold-induced vasodilation reaction to local cooling

The purpose of this work was to integrate a new mathematical model with a bioheat model, based on physiology and first principles, to predict thermoregulatory arterio-venous anastomoses (AVA) and cold-induced vasodilation (CIVD) reaction to local cooling. The transient energy balance equations of body segments constrained by thermoregulatory controls were solved numerically to predict segmental core and skin temperatures, and arterial blood flow for given metabolic rate and environmental conditions. Two similar AVA–CIVD mechanisms were incorporated. The first was activated during drop in local skin temperature (<32 °C). The second mechanism was activated at a minimum finger skin temperature, T _{CIVD, min}, where the AVA flow is dilated and constricted once the skin temperature reached a maximum value. The value of T _CIVD,min was determined empirically from values reported in literature for hand immersions in cold fluid. When compared with published data, the model predicted accurately the onset time of CIVD at 25 min and T _CIVD,min at 10 °C for hand exposure to still air at 0 °C. Good agreement was also obtained between predicted finger skin temperature and experimentally published values for repeated immersion in cold water at environmental conditions of 30, 25, and 20 °C. The CIVD thermal response was found related to core body temperature, finger skin temperature, and initial finger sensible heat loss rate upon exposure to cold fluid. The model captured central and local stimulations of the CIVD and accommodated observed variability reported in literature of onset time of CIVD reaction and T _CIVD,min.     

Bone stiffness explained by the liquid crystal model for the collagen fibril

A liquid crystal model for the structure of the collagen fibril explains how calcium phosphate crystals are capable of stiffening collagen fibrils in bone. Collagen fibrils consist of an oriented array of parallel rod-shaped collagen molecules. According to the liquid crystal model fibrils respond to tensile stress, applied in the axial direction, by some of the molecules tilting and changing their side-to-side arrangement. In bone the presence of crystals packed between the collagen molecules hinders the side-to-side rearrangement so that the response of the fibrils to stress is inhibited. Therefore the fibrils are stiffer in bone than in uncalcified tissue.     

A novel model-gel-tissue assay analysis for comparing tumor elastic properties to collagen content

In previous work, a new assay was realized for determining soft-tissue mechanical properties. The method, named the model-gel-tissue (MGT) assay, couples material testing with a finite element model built from a micro-CT image acquisition of a gel-embedded tissue specimen to determine its mechanical properties. Given recent reports demonstrating that increased stromal collagen promotes mammary tumor initiation and proliferation, in this paper, the MGT assay is used to evaluate the modulus of murine mammary tumors and is subsequently correlated quantitatively to type I collagen content. In addition, preliminary testing of the assay sensitivity with respect to gel-volume to tissue-mass ratio is reported here. The results demonstrate a strong linear correlation between tumor mechanical properties and collagen content (R ² = 0.9462). This result is important because mechanical stiffness as provided by the MGT assay is very similar to parameters under clinical investigation using elastographic imaging techniques. The sensitivity tests indicated that an approximate gel-volume to tissue-mass ratio threshold of 16.5 ml g⁻¹ is needed for successful analysis. This is an important result in that it presents guideline constraints for conducting this analysis.     

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.     

A new technique to study the mechanical properties of collagen lattices.

A new technique to study the mechanical properties of collagen lattices or dermal equivalents is described. With the help of the load-extension curve obtained with a uniaxial traction apparatus, a stiffness modulus varying from 0.06 to 1 MPa is calculated from the studied parameters (duration of culture, collagen and fibroblast concentration). The technique is presented as a new tool for testing the effect of pharmacological agents on the mechanical properties of the skin.     

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.     

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.     

Assembly of type I collagen: fusion of fibril subunits and the influence of fibril diameter on mechanical properties.

Structural stability of the extracellular matrix is primarily a consequence of fibrillar collagen and the extent of cross-linking. The relationship between collagen self-assembly, consequent fibrillar shape and mechanical properties remains unclear. Our laboratory developed a model system for the preparation of self-assembled type I collagen fibers with fibrillar substructure mimicking the hierarchical structures of tendon. The present study evaluates the effects of pH and temperature during self-assembly on fibrillar structure, and relates the structural effects of these treatments on the uniaxial tensile mechanical properties of self-assembled collagen fibers. Results of the analysis of fibril diameter distributions and mechanical properties of the fibers formed under the different incubation conditions indicate that fibril diameters grow via the lateral fusion of discrete approximately 4 nm subunits, and that fibril diameter correlates positively with the low strain modulus. Fibril diameter did not correlate with either the ultimate tensile strength or the high strain elastic modulus, which suggests that lateral aggregation and consequently fibril diameter influences mechanical properties during small strain mechanical deformation. We hypothesize that self-assembly is mediated by the formation of fibrillar subunits that laterally and linearly fuse resulting in fibrillar growth. Lateral fusion appears important in generating resistance to deformation at low strain, while linear fusion leading to longer fibrils appears important in the ultimate mechanical properties at high strain.     

Simultaneous processing of fibril formation and cross-linking improves mechanical properties of collagen

In vitro "simultaneous processing" was investigated in which fibril formation of collagen and cross-linking occur simultaneously in the presence of 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC) as a cross-linking reagent. Fibril formation in simultaneous processing was monitored using turbidity. The EDC in simultaneous processing increased T(1/2) (time required for half of the plateau value in turbidity) and decreased the degree of the fibril formation dose dependently. The reduced fibril formation rate (T(1/2) > 60 s) suggests the introduction of intrafibrillar cross-linking during fibril formation. The collagen gels prepared using simultaneous processing had a compressive modulus that was 6-fold higher than that using sequential processing, which is an advantage of simultaneous processing. Atomic force microscopy images acquired under water on the wet gels demonstrated that the simultaneous processing provided a unique double-network structure: intrafibrillarly cross-linked collagen fibrils among which nonfibrous collagens act as interfibrillar cross-linkages.     

A new ecological-wind erosion model to simulate the impacts of aeolian transport on dryland vegetation patterns

Drylands cover more than 40% of the land surface of the Earth and are characterized by patchy vegetation and that permits erosion of the surface. Vegetation-aeolian transport is an important feedback in drylands, particularly those undergoing shrub encroachment. Although one side of the feedback, the influence of vegetation loss on aeolian transport, has been well studied, the other, the influence of aeolian transport on existing vegetation, has been never studied in detail. In this study, a new ecological-wind erosion model (ECO-WEMO) that contains an aeolian transport component was created to simulate how aeolian transport impacts vegetation pattern and causes the state change. Two modeling scenarios were investigated: 1) stable grass and shrub communities without/with aeolian transport and 2) unstable shrub and grass communities without/with aeolian transport disturbed by different drought conditions. The first scenario focuses on the simulation of the influence of aeolian transport on vegetation communities and the second scenario focuses on the simulation of the state change of vegetation communities. The results from the first scenario show that: First, the mean biomasses of grass and shrub become consistent in the case of no wind in both shrub-dominated and grass-dominated communities. Second, the mean biomass of shrub becomes higher than the grass in the case of wind in shrub-dominated communities and the mean biomass of grass becomes higher than the shrub in the case of wind in grass-dominated communities. Third, the dust flux of shrub-dominated communities is higher than the grass-dominated communities. Fourth, the net change in surface height in shrub-dominated communities has a considerably higher range than in grass-dominated communities. Fifth, the spatial pattern of shrub-dominated communities is sparser than the spatial pattern of grass in the vegetation communities in the case of wind. The results from the second scenario show that: First, the state change only took place from grass-dominated communities to shrub-dominated communities in the condition of drought. Second, the state change only took place in the case of wind. Third, the state change didn't take place after the slight and moderate droughts but only took place after the drought. Fourth, large vegetation biomass reduction only took place in the case of wind after the severe drought. Our results confirm, in a modeling context, the important role that aeolian transport can play in vegetation dynamics and state change in deserts.     

Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking

Experimental evidence demonstrates that collagen cross-linking in bone tissue significantly influences its deformation and failure behavior yet difficulties exist in determining the independent biomechanical effects of collagen cross-linking using in vitro and in vivo experiments. The aim of this study is to use a nano-scale composite material model of mineral and collagen to determine the independent roles of enzymatic and non-enzymatic cross-linking on the mechanical behavior of a mineralized collagen fibril. Stress–strain curves were obtained under tensile loading conditions without any collagen cross-links, with only enzymatic cross-links (modeled by cross-linking the end terminal position of each collagen domain), or with only non-enzymatic cross-links (modeled by random placement of cross-links within the collagen–collagen interfaces). Our results show enzymatic collagen cross-links have minimal effect on the predicted stress–strain curve and produce a ductile material that fails through debonding of the mineral–collagen interface. Conversely, non-enzymatic cross-links significantly alter the predicted stress–strain response by inhibiting collagen sliding. This inhibition leads to greater load transfer to the mineral, which minimally affects the predicted stress, increases modulus and decreases post-yield strain and toughness. As a consequence the toughness of bone that has more non-enzymatically mediated collagen cross-links will be drastically reduced.     

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.     

Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model

Mineralized collagen fibrils are the basic building blocks of bone tissue at the supramolecular level. Several disease states, manipulation of the expression of specific proteins involved in biomineralization, and treatment with different agents alter the extent of mineralization as well as the morphology of mineral crystals which in turn affect the mechanical function of bone tissue. An experimental assessment of mineralized fibers' mechanical properties is challenged by their small size, leaving analytical and computational models as a viable alternative for investigation of the fibril-level mechanical properties. In the current study the variation of the elastic stiffness tensor of mineralized collagen fibrils with changing mineral volume fraction and mineral aspect ratios was predicted via a micromechanical model. The partitioning of applied stresses between mineral and collagen phases is also predicted for normal and shear loading of fibrils. Model predictions resulted in transversely isotropic collagen fibrils in which the modulus along the longer axis of the fibril was the greatest. All the elastic moduli increased with increasing mineral volume fraction whereas Poisson's ratios decreased with the exception of v12 (=v21). The partitioning of applied stresses were such that the stresses acting on mineral crystals were about 1.5, 15, and 3 times greater than collagen stresses when fibrils were loaded transversely, longitudinally, and in shear, respectively. In the overall the predictions were such that: (a) greatest modulus along longer axis; (b) the greatest mineral/collagen stress ratio along the longer axis of collagen fibers (i.e., greatest relief of stresses acting on collagen); and (c) minimal lateral contraction when fibers are loaded along the longer axis. Overall, the pattern of mineralization as put forth in this model predicts a superior mechanical function along the longer axis of collagen fibers, the direction which is more likely to experience greater stresses.