Coherent x-ray imaging of collagen fibril distributions within intact tendons

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

The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the assembly of collagen fibrils in vivo is too large to diffuse within assembled fibrils, and so is incompatible with a fully equilibrium mechanism for fibril formation. We propose that enzymatic cross-links are formed at the fibril surface during the growth of collagen fibrils; as a consequence no significant reorientation of previously cross-linked collagen molecules occurs inside collagen fibrils during fibril growth in vivo. By imposing local equilibrium only at the fibril surface, we develop a coarse-grained quantitative model of in vivo fibril structure that incorporates a double-twist orientation of collagen molecules and a periodic D-band density modulation along the fibril axis. Radial growth is controlled by the concentration of available collagen molecules outside the fibril. In contrast with earlier equilibrium models of fibril structure, we find that all fibrils can exhibit a core-shell structure that is controlled only by the fibril radius. At small radii a core is developed with a linear double-twist structure as a function of radius. Within the core the double-twist structure is largely independent of the D-band. Within the shell at larger radii, the structure approaches a constant twist configuration that is strongly coupled with the D-band. We suggest a stable radius control mechanism that corneal fibrils can exploit near the edge of the linear core regime; while larger tendon fibrils use a cruder version of growth control that does not select a preferred radius.

Probing multi-scale mechanical damage in connective tissues using X-ray diffraction

The accumulation of microstructural collagen damage following repetitive loading is linked to painful and debilitating tendon injuries. As a hierarchical, semi-crystalline material, collagen mechanics can be studied using X-ray diffraction. The aim of the study was to describe multi-structural changes in tendon collagen following controlled plastic damage (5% permanent strain). We used small angle X-ray scattering (SAXS) to interrogate the spacing of collagen molecules within a fibril, and wide angle X-ray scattering (WAXS) to measure molecular strains under macroscopic loading. Simultaneous recordings of SAXS and WAXS patterns, together with whole-tissue strain in physiologically hydrated rat-tail tendons were made during increments of in situ tensile loading. Results showed that while tissue level modulus was unchanged, fibril modulus decreased significantly, and molecular modulus significantly increased. Further, analysis of higher order SAXS peaks suggested structural changes in the gap and overlap regions, possibly localising the damage to molecular cross-links. Our results provide new insight into the fundamental damage processes at work in collagenous tissues and point to new directions for their mitigation and repair.

STATEMENT OF SIGNIFICANCE

This article reports the first in situ loading synchrotron studies on mechanical damage in collagenous tissues. We provide new insight into the nano- and micro-structural mechanisms of damage processes. Pre-damaged tendons showed differential alteration of moduli at macro, micro and nano-scales as measured using X-ray scattering techniques. Detailed analysis of higher order diffraction peaks suggested damage is localised to molecular cross-links. The results are consistent with previous X-ray scattering studies of tendons and also with recent thermal stability studies on damaged material. Detailed understanding of damage mechanisms is essential in the development of new therapies promoting tissue repair.

Tomography of a Cryo-immobilized Yeast Cell Using Ptychographic Coherent X-Ray Diffractive Imaging

The structural investigation of noncrystalline, soft biological matter using x-rays is of rapidly increasing interest. Large-scale x-ray sources, such as synchrotrons and x-ray free electron lasers, are becoming ever brighter and make the study of such weakly scattering materials more feasible. Variants of coherent diffractive imaging (CDI) are particularly attractive, as the absence of an objective lens between sample and detector ensures that no x-ray photons scattered by a sample are lost in a limited-efficiency imaging system. Furthermore, the reconstructed complex image contains quantitative density information, most directly accessible through its phase, which is proportional to the projected electron density of the sample. If applied in three dimensions, CDI can thus recover the sample's electron density distribution. As the extension to three dimensions is accompanied by a considerable dose applied to the sample, cryogenic cooling is necessary to optimize the structural preservation of a unique sample in the beam. This, however, imposes considerable technical challenges on the experimental realization. Here, we show a route toward the solution of these challenges using ptychographic CDI (PCDI), a scanning variant of coherent imaging. We present an experimental demonstration of the combination of three-dimensional structure determination through PCDI with a cryogenically cooled biological sample—a budding yeast cell (Saccharomyces cerevisiae)—using hard (7.9 keV) synchrotron x-rays. This proof-of-principle demonstration in particular illustrates the potential of PCDI for highly sensitive, quantitative three-dimensional density determination of cryogenically cooled, hydrated, and unstained biological matter and paves the way to future studies of unique, nonreproducible biological cells at higher resolution.

Micromechanical poroelastic finite element and shear-lag models of tendon predict large strain dependent Poisson's ratios and fluid expulsion under tensile loading

As tendons are loaded, they reduce in volume and exude fluid to the surrounding medium. Experimental studies have shown that tendon stretching results in a Poisson's ratio greater than 0.5, with a maximum value at small strains followed by a nonlinear decay. Here we present a computational model that attributes this macroscopic observation to the microscopic mechanism of the load transfer between fibrils under stretch. We develop a finite element model based on the mechanical role of the interfibrillar-linking elements, such as thin fibrils that bridge the aligned fibrils or macromolecules such as glycosaminoglycans (GAGs) in the interfibrillar sliding and verify it with a theoretical shear-lag model. We showed the existence of a previously unappreciated structure-function mechanism whereby the Poisson's ratio in tendon is affected by the strain applied and interfibrillar-linker properties, and together these features predict tendon volume shrinkage under tensile loading. During loading, the interfibrillar-linkers pulled fibrils toward each other and squeezed the matrix, leading to the Poisson's ratio larger than 0.5 and fluid expulsion. In addition, the rotation of the interfibrillar-linkers with respect to the fibrils at large strains caused a reduction in the volume shrinkage and eventual nonlinear decay in Poisson's ratio at large strains. Our model also predicts a fluid flow that has a radial pattern toward the surrounding medium, with the larger fluid velocities in proportion to the interfibrillar sliding.

High-dynamic-range coherent diffractive imaging: ptychography using the mixed-mode pixel array detector

Coherent (X-ray) diffractive imaging (CDI) is an increasingly popular form of X-ray microscopy, mainly due to its potential to produce high-resolution images and the lack of an objective lens between the sample and its corresponding imaging detector. One challenge, however, is that very high dynamic range diffraction data must be collected to produce both quantitative and high-resolution images. In this work, hard X-ray ptychographic coherent diffractive imaging has been performed at the P10 beamline of the PETRA III synchrotron to demonstrate the potential of a very wide dynamic range imaging X-ray detector (the Mixed-Mode Pixel Array Detector, or MM-PAD). The detector is capable of single photon detection, detecting fluxes exceeding 1 × 10(8) 8-keV photons pixel(-1) s(-1), and framing at 1 kHz. A ptychographic reconstruction was performed using a peak focal intensity on the order of 1 × 10(10) photons µm(-2) s(-1) within an area of approximately 325 nm × 603 nm. This was done without need of a beam stop and with a very modest attenuation, while `still' images of the empty beam far-field intensity were recorded without any attenuation. The treatment of the detector frames and CDI methodology for reconstruction of non-sensitive detector regions, partially also extending the active detector area, are described.