Neutron diffraction studies of collagen in fully mineralized bone

Neutron diffraction measurements have been made of the equatorial and meridional spacings of collagen in fully mineralized mature bovine bone and demineralized bone collagen, in both wet and dry conditions. The collagen equatorial spacing in wet mineralized bovine bone is 1.24 nm, substantially lower than the 1.53 nm value observed in wet demineralized bovine bone collagen. Corresponding spacings for dry bone and demineralized bone collagen are 1.16 nm and 1.12 nm, respectively. The collagen meridional long spacing in mineralized bovine bone is 63.6 nm wet and 63.4 nm dry. These data indicate that collagen in fully mineralized bovine bone is considerably more closely packed than had been assumed previously, with a packing density similar to that of the relatively crystalline collagens such as wet rat tail tendon. The data also suggest that less space is available for mineral within the collagen fibrils in bovine bone than had previously been assumed, and that the major portion of the mineral in this bone must be located outside the fibrils.     

A new molecular model for collagen elasticity based on synchrotron X-ray scattering evidence.

Collagen is the most abundant structural protein in vertebrates. The specific shape of its stress-strain curve is crucial for the function of a number of organs. Although the macroscopic mechanical behavior of collagen is well known, there is still no explanation of the elastic process at the supramolecular level. We have performed in situ synchrotron x-ray scattering experiments, which show that the amount of lateral molecular order increases upon stretching of collagen fibers. In strain cycling experiments the relation between strain and diffuse equatorial scattering was found to be linear in the "heel" region of the stress-strain curve. A new molecular model for collagen elasticity is proposed, which, based on the existence of thermally activated molecular kinks, reproduces this linearity and gives a simple explanation for the form of the stress-strain curve of collagen.     

A generalized packing model for type I collagen

Only tail tendon (TT) collagen has a sharp X-ray diffraction pattern, so that packing models for the equatorial arrangement of molecules in collagen fibrils have been developed primarily for TT collagen. A more general structure is developed applicable to all type I collagen tissues. Comparison of water content-equatorial diffraction spacing plots of several collagens shows all have essentially the same dry state diffraction spacing but differ as water content increases. TT collagen has the least spacing and the sharpest pattern. The interplanar spacing of the Hulmes-Miller quasi-hexagonal model for TT collagen was used to calculate the intermolecular spacing, which matched the observed diffraction spacing for bone matrix collagen. It is inferred that wet bone matrix collagen packs in a rectangular pattern because of the interaction between the many intermolecular crosslinks and the water absorbed on the collagen molecules. This argument also indicates that TT collagen packs into a quasi-hexagonal scheme because there are fewer intermolecular crosslinks than in bone matrix collagen.     

A study of dense mineralized tissue by neutron diffraction

Neutron diffraction studies of mineralized tissue show a close relationship between the wet state equatorial diffraction spacing and wet tissue density expressable as a second-order polynomial. The molecular fractional shrinkage when the tissue is dried shows a straight line dependence on wet tissue density with a correlation of 0.98. Since the dry state equatorial diffraction spacing is much less than for the corresponding wet state, even in fully mineralized bone, the collagen molecules must be displaced through a mineral-free volume while drying. The mineral can only be located within the available volume of the dried tissue whether intra- or extrafibrillar. The dimension of the dry state equatorial spacing for each of the tissues examined is close to that of dried tendon collagen. It appears unlikely that hydroxyapatite crystallites can be accommodated radially between collagen molecules in bone if the packing is like that of dried tail tendon collagen. The only mineral within the fibrils must be in the intermolecular gaps. It is estimated on the basis of the volume of the axial intermolecular gaps and the minimum extrafibrillar volume that the intrafibrillar mineral can be no more than 20% of the total mineral and may be less than 10%.     

Structure of corneal scar tissue: an X-ray diffraction study.

Full-thickness corneal wounds (2 mm diameter) were produced in rabbits at the Schepens Eye Research Institute, Boston. These wounds were allowed to heal for periods ranging from 3 weeks to 21 months. The scar tissue was examined using low- and wide-angle x-ray diffraction from which average values were calculated for 1) the center-to-center collagen fibril spacing, 2) the fibril diameter, 3) the collagen axial periodicity D, and 4) the intermolecular spacing within the collagen fibrils. Selected samples were processed for transmission electron microscopy. The results showed that the average spacing between collagen fibrils within the healing tissue remained slightly elevated after 21 months and there was a small increase in the fibril diameter. The collagen D-periodicity was unchanged. There was a significant drop in the intermolecular spacing in the scar tissues up to 6 weeks, but thereafter the spacing returned to normal. The first-order equatorial reflection in the low-angle pattern was visible after 3 weeks and became sharper and more intense with time, suggesting that, as healing progressed, the number of nearest neighbor fibrils increased and the distribution of nearest neighbor spacings reduced. This corresponded to the fibrils becoming more ordered although, even after 21 months, normal packing was not achieved. Ultrastructural changes in collagen fibril density measured from electron micrographs were consistent with the increased order of fibril packing measured by x-ray diffraction. The results suggest that collagen molecules have a normal axial and lateral arrangement within the fibrils of scar tissue. The gradual reduction in the spread of interfibrillar spacings may be related to the progressive decrease in the light scattered from the tissue as the wound heals.     

Mineralization of type I collagen

It was previously found that the lateral spacing of the collagen molecules in wet mineralized tissues is exactly proportional to the inverse wet density. Several properties were investigated and the same type of relationship was observed each time. A possible explanation is offered. It is hypothesized that mineral is deposited initially in the extrafibrillar space so as to isolate the fibrils. Further deposition reduces the net free fibril volume thereby decreasing the spacing between collagen molecules. The linear relationship is derived from density considerations together with limitations on the collagen packing structure described as the generalized packing model. Three experimental situations were studied: lateral spacing wet tissue versus density; lateral spacing dry tissue versus density; and lateral spacing versus water content. The observed variations of the spacing can be attributed to a structure where the mass of the tissue remains constant but the volume decreases linearly with increasing mineral content.     

Dynamic light scattering from collagen solutions. II. Photon correlation study of the depolarized light.

The depolarized forward-scattered light from solutions of rat tail collagen has been studied by photon correlation spectroscopy. The measured autocorrelation function is seen to decay on two widely different time scales. The decay time for the fast component is consistent with the rotational diffusion of rodlike collagen monomers. The slowly decaying autocorrelation component is attributed to large nonspecific aggregates of collagen. A substantial fraction of the collagen is in this aggregated form. Extrapolation of the faster decay times to zero concentration yields a value of θ = 1082 ± 30 sec^?1 for the rotational diffusion coefficient of the collagen monomer.     

Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Background

Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel.

Results

We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible.

Conclusions

It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance.     

Ageing of the human corneal stroma: structural and biochemical changes.

High and low angle X-ray diffraction patterns from the corneal stroma give information about the mean intermolecular spacing of the collagen molecules and the mean interfibrillar spacing of the collagen fibrils, respectively. X-ray data were collected, using a high intensity synchrotron source, from human corneas and sclera at approximately physiological hydration. The spacings were measured as a function of tissue age. Between birth and 90 years there is an increase in the cross-sectional area associated with each molecule in corneal collagen from approx. 3.04 nm2 to 3.46 nm2, and an increase in scleral collagen from approx. 2.65 nm2 to 3.19 nm2. These changes may be due to an increase in the extent of non-enzymic cross-linking between collagen molecules over the age range. We have investigated this possibility by measuring collagen glycation using the thiobarbituric acid assay and the subsequent advanced glycation end-products (AGEs) using fluorescence emission. The results obtained have shown an age-related increase in glycation and AGEs in both tissues. We have also demonstrated a decrease in the interfibrillar spacing of corneal collagen with increasing age which may be related to changes in the proteoglycan composition of the interfibrillar matrix.     

A resonance model gives the response to membrane potential for an ion channel: II. Simplification of the calculation, and prediction of stochastic resonance

In a previous communication (Green, 1998), the initial step in ion channel gating for voltage-gated channels was attributed to the tunneling of a proton between groups with similar p K values, under the influence of an electric field. This is in contrast to the standard thermally activated model, which leads to a "Boltzmann equation" for the gating current. In the paper that introduced the present model, the current-voltage curve was determined from a resonance effect, in which gating began when the local voltage crossed a threshold, causing a proton to tunnel to a new location. We have therefore investigated further the consequences of tunneling as the first step in gating; we find a method of improving the previous calculation. We also calculate a consequence of our model that has yet to be experimentally looked for, stochastic resonance. With gating a threshold process, one expects that such an effect should exist. Only a small effect is predicted by our calculation, but it may be detectable. If it is it would make possible the determination of important characteristics of the initiation of gating. For this reason it is worth determining the nature of the stochastic resonance to be expected. In addition, we have investigated further the possible ways of understanding our resonance model itself. The model assumes that not all channels have the same threshold, as local perturbations in the potential interfere. We therefore assume a Gaussian distribution of the thresholds, which is simpler than in the previous paper, in which a Gaussian gave inadequate results with the method used there. In this paper, we have reduced the number of parameters to two, and obtained the current-voltage curve, gating current, the response to a large sine wave (in the previous paper, the model was more complex), and stochastic resonance.     

Analysis of equatorial x-ray diffraction patterns from muscle fibers: factors that affect the intensities.

Previously we have shown that cross-bridge attachment to actin and the radial position of the myosin heads surrounding the thick filament backbone affect the equatorial x-ray diffraction intensities in different ways (Yu, 1989). In the present study, other factors frequently encountered experimentally are analyzed by a simple model of the filament lattice. It is shown that the ordering/disordering of filaments, lattice spacing changes, the azimuthal redistributions of cross-bridges, and variations in the ordered/disordered population of cross-bridges surrounding the thick filaments can distinctly affect the equatorial intensities. Consideration of Fourier transforms of individual components of the unit cell can provide qualitative explanations for the equatorial intensity changes. Criteria are suggested that can be used to distinguish the influence of some factors from others.     

A synchrotron radiation X-ray diffraction study of the crystallinity of tendon fibres

The equatorial diffraction pattern of tendon collagen fibres was measured during short successive exposures at different lengths using a double focusing X-ray synchrotron radiation camera with film and with an area detector. Similarly, patterns from thin fibres from premature rats were recorded. The patterns unambiguously illustrate the relationship between fibre crystallinity and the age of the animal. Further, the results indicate that in the initial part of the linear region of the stiffness-versus-length curve, the collagen fibres are characterized by a quasihexagonal arrangement of collagen molecules, whereas at the end of this region, the molecular arrangement becomes hexagonal.     

Radial packing, order, and disorder in collagen fibrils.

Collagen fibrils resemble smectic, liquid crystals in being highly ordered axially but relatively disordered laterally. In some connective tissues, x-ray diffraction reveals three-dimensional crystallinity in the molecular packing within fibrils, although the continued presence of diffuse scatter indicates significant underlying disorder. In addition, several observations from electron microscopy suggest that the molecular packing is organized concentrically about the fibril core. In the present work, theoretical equatorial x-ray diffraction patterns for a number of models for collagen molecular packing are calculated and compared with the experimental data from tendon fibrils. None of the models suggested previously can account for both the crystalline Bragg peaks and the underlying diffuse scatter. In addition, models in which any of the nearest-neighbor, intermolecular vectors are perpendicular to the radial direction are inconsistent with the observed radial orientation of the principal approximately 4 nm Bragg spacing. Both multiple-start spiral and concentric ring models are devised in which one of the nearest-neighbor vectors is along the radial direction. These models are consistent with the radial orientation of the approximately 4 nm spacing, and energy minimization results in radially oriented crystalline domains separated by disordered grain boundaries. Theoretical x-ray diffraction patterns show a combination of sharp Bragg peaks and underlying diffuse scatter. Close agreement with the observed equatorial diffraction pattern is obtained. The concentric ring model is consistent with the observation that the diameters of collagen fibrils are restricted to discrete values.     

Ageing of the human corneal stroma: structural and biochemical changes

High and low angle X-ray diffraction patterns from the corneal stroma give information about the mean intermolecular spacing of the collagen molecules and the mean interfibrillar spacing of the collagen fibrils, respectively. X-ray data were collected, using a high intensity synchrotron source, from human corneas and sclera at approximately physiological hydration. The spacings were measured as a function of tissue age. Between birth and 90 years there is an increase in the cross-sectional area associated with each molecule in corneal collagen from approx. 3.04 nm² to 3.46 nm², and an increase in scleral collagen from approx. 2.65 nm² to 3.19 nm². These changes may be due to an increase in the extent of non-enzymatic cross-linking between collagen molecules over the age range. We have investigated this possibility by measuring collagen glycation using the thiobarbituric acid assay and the subsequent advanced glycation end-products (AGEs) using fluorescence emission. The results obtained have shown an age-related increase in glycation and AGEs in both tissues. We have also demonstrated a decrease in the interfibrillar spacing of corneal collagen with increasing age which may be related to changes in the proteoglycan composition of the interfibrillar matrix.     

X-ray diffraction study into the effects of liming on the structure of collagen

The manufacture of parchment from animal skin involves processes that remove hair, fats, and other macromolecules. Although it is well understood that the collagen fibers "open up" during processing, this study uses small and wide-angle X-ray diffraction to measure quantitatively the changes induced at the nanoscopic and microscopic levels. The axial rise per residue distance within the collagen molecules is unaffected by salt and lime treatments. Salting of the hides appears to remove noncollagenous materials. The intermolecular lateral packing distance between the hydrated collagen molecules (1.4 nm) increases after salting ( approximately 1.5 nm) and liming ( approximately 1.55 nm); drying is responsible for a reduction to approximately 1.2 nm in all samples. The axial staggered array (d spacing) is reduced by 1 nm after liming and is unaffected by drying. The average fibril diameter increases from 103.2 to 114.5 nm following liming, and the fibril-to-fibril distance increases from 122.6 to 136.1 nm.     

X-ray diffraction studies of the corneal stroma.

A low-angle diffraction pattern has been obtained from corneal stroma. This pattern arises both from the arrangement of the collagen fibrils and from the packing of the tropocollagen molecules along the axes of the fibrils. The spacing arising from the packing of the fibrils increases homogeneously on swelling although the tissue as a whole swells only radially referred to the intact eye. The necessary rearrangement of the fibrils for this type of swelling to occur might result in the formation of regions devoid of collagen fibrils and the water not in the lattice of collagen fibrils could be synonymous with the lakes postulated by Benedek (1971) to explain the loss of transparency on swelling.The spacings due to the packing of the tropocollagen molecules are unusual in that, although they index as the third and fifth orders of the well-known 66 nm repeat, the first order of this spacing is absent. Calculation of the Patterson function for corneal collagen leads to peaks in electron density separated by distances of 0.38 and 0.24 of the repeat distance.     

Modeling the effect of collagen fibril alignment on ligament mechanical behavior

Ligament mechanical behavior is primarily regulated by fibrous networks of type I collagen. Although these fibrous networks are typically highly aligned, healthy and injured ligament can also exhibit disorganized collagen architecture. The objective of this study was to determine whether variations in the collagen fibril network between neighboring ligaments can predict observed differences in mechanical behavior. Ligament specimens from two regions of bovine fetlock joints, which either exhibited highly aligned or disorganized collagen fibril networks, were mechanically tested in uniaxial tension. Confocal microscopy and FiberFit software were used to quantify the collagen fibril dispersion and mean fibril orientation in the mechanically tested specimens. These two structural parameters served as inputs into an established hyperelastic constitutive model that accounts for a continuous distribution of planar fibril orientations. The ability of the model to predict differences in the mechanical behavior between neighboring ligaments was tested by (1) curve fitting the model parameters to the stress response of the ligament with highly aligned fibrils and then (2) using this model to predict the stress response of the ligament with disorganized fibrils by only changing the parameter values for fibril dispersion and mean fibril orientation. This study found that when using parameter values for fibril dispersion and mean fibril orientation based on confocal imaging data, the model strongly predicted the average stress response of ligaments with disorganized fibrils (\(R^{2}=0.97\)); however, the model only successfully predicted the individual stress response of ligaments with disorganized fibrils in half the specimens tested. Model predictions became worse when parameters for fibril dispersion and mean fibril orientation were not based on confocal imaging data. These findings emphasize the importance of collagen fibril alignment in ligament mechanics and help advance a mechanistic understanding of fibrillar networks in healthy and injured ligament.     

Neutron studies of collagen in lathyritic bone

Lathyrism is induced because BAPN inhibits lysyl oxidase mediated crosslinking in collagen. Various degrees of lathyrism were induced in weanling NZ white rabbits by controlling the daily dose level in six groups: 0, 0.05, 0.1, 0.2, 0.4 and 1.0 g/kg/day for 12 weeks. Three properties, equatorial diffraction spacing in bone collagen, the fraction of bone matrix soluble in 0.5 m acetic acid and bone density were related to BAPN dosage. Equatorial diffraction spacing increased from 1.235 to 1.275 nm, the soluble bone matrix fraction increased from 0.087 to 0.275 and the minimum bone density decreased from 1.98 to 1.74 g/cm³. There seems to be no minimum critical dose for BAPN. The fastest change in bone properties occurs at the lowest dosages. There is a dose dependent relationship between BAPN and lysyl oxidase mediated crosslinking density as measured by the acid soluble bone matrix fraction. It is not clear that other bone properties are directly or indirectly controlled by the bone collagen lysyl oxidase mediated crosslinking.     

Quantification of Collagen Ultrastructure after Penetrating Keratoplasty – Implications for Corneal Biomechanics

Purpose

To quantify long-term changes in stromal collagen ultrastructure following penetrating keratoplasty (PK), and evaluate their possible implications for corneal biomechanics.

Methods

A pair of 16 mm post-mortem corneo-scleral buttons was obtained from a patient receiving bilateral penetrating keratoplasty 12 (left)/28 (right) years previously. Small-angle x-ray scattering quantified collagen fibril spacing, diameter and spatial order at 0.5 mm or 0.25 mm intervals along linear scans across the graft margin. Corresponding control data was collected from two corneo-scleral buttons with no history of refractive surgery. Wide-angle x-ray scattering quantified collagen fibril orientation at 0.25 mm (horizontal)×0.25 mm (vertical) intervals across both PK specimens. Quantification of orientation changes in the graft margin were verified by equivalent analysis of data from a 13 year post-operative right PK specimen obtained from a second patient in a previous study, and comparison made with new and published data from normal corneas.

Results

Marked changes to normal fibril alignment, in favour of tangentially oriented collagen, were observed around the entire graft margin in all PK specimens. The total number of meridional fibrils in the wound margin was observed to decrease by up to 40%, with the number of tangentially oriented fibrils increasing by up to 46%. As a result, in some locations the number of fibrils aligned parallel to the wound outnumbered those spanning it by up to five times. Localised increases in fibril spacing and diameter, with an accompanying reduction in matrix order, were also evident.

Conclusions

Abnormal collagen fibril size and spatial order within the PK graft margin are indicative of incomplete stromal wound remodelling and the long term persistence of fibrotic scar tissue. Lasting changes in collagen fibril orientation in and around PK wounds may alter corneal biomechanics and compromise the integrity of the graft-host interface in the long term.