Elastic properties of collagen in bone determined by measuring the Debye-Waller factor

Determining paracrystallinity in mixed-tacticity polyhydroxybutyrates

A method to robustly determine paracrystalline contents from Rietveld-refined powder X-ray data is presented and discussed for the example of mixed-tacticity polyhydroxybutyrates.

Recently, the authors reported on the development of crystallinity in mixed-tacticity polyhydroxybutyrates. Comparable values reported in the literature vary depending on the manner of determination, the discrepancies being partially attributable to scattering from paracrystalline portions of the material. These portions can be qualified by peak profile fitting or quantified by allocation of scattered X-ray intensities. However, the latter requires a good quality of the former, which in turn must additionally account for peak broadening inherent in the measurement setup, and due to limited crystallite sizes and the possible presence of microstrain. Since broadening due to microstrain and paracrystalline order both scale with scattering vector, they are easily confounded. In this work, a method to directionally discern these two influences on the peak shape in a Rietveld refinement is presented. Allocating intensities to amorphous, bulk and paracrystalline portions with changing tactic disturbance provided internal validations of the obtained directional numbers. In addition, the correlation between obtained thermal factors and Young’s moduli, determined in earlier work, is discussed.

Determination of the elastic modulus of β-lactoglobulin amyloid fibrils by measuring the Debye-Waller factor

Although amyloid fibrils are associated with amyloidoses, they are now being considered as novel biomaterials for industrial use due to their structural stability in the matured state. Therefore, the physical characteristics of these materials need to be clarified prior to their industrial application. In the present study, the mechanical properties of amyloid fibrils precursored by β-lactoglobulin were investigated. Previous studies have examined the stiffness or modulus values of these fibrils using atomic force microscopy. However, the modulus values reported, even for amyloid fibrils from the same precursor proteins, range over three orders of magnitude, from a few MPa to GPa, depending on the experimental methods employed under specific loading conditions. We determined the elastic modulus of amyloid fibrils by measuring spontaneous thermal fluctuations in the material, the Debye-Waller factor. This method does not require any contact between the probe and material or any loading. The vibrational modes of a fibril were considered in order to estimate mechanical parameters. The modulus value determined along the fibril axis for single amyloid fibrils was slightly smaller than those reported in the literature. The smaller modulus value suggests the existence of less ordered proto-fibrils in our specimen, which was confirmed by the AFM images.