LAUSR

Small-angle x-ray scattering (SAXS) from fibrils embedded in a fixed, thin section of tissue includes contributions from the fibrils; the polymeric matrix surrounding the fibrils; other constituents of the tissue; and cross-terms due to the spatial correlation between fibrils and neighbouring molecules. This complex mixture severely limits the amount of information that can be extracted from scattering studies. However, availability of micro- and nano-beams has made possible measurement of scattering from very small volumes which, in some cases, may be dominated by a single fibrillar constituent. In those cases, information about the predominant species may be accessible. Nevertheless, even in these cases, the correlations between the positions of fibrils and other constituents have significant impact on the observed scattering. Here, we propose strategies to extract partial information about fibril structure and tissue organization on the basis of SAXS from samples of this type. We show that the spatial correlation function of the fibril in the direction perpendicular to the fibril axis can be computed and contains information about the predominant fibril structure and the organization of the surrounding tissue matrix. It has significant advantages over approaches based on techniques developed for x-ray solution scattering. We present examples of the calculation of correlation in different types of samples to demonstrate the kinds of information that can be obtained from these measurements. Synopsis The availability of micro- and nano- x-ray beams is making possible measurement of scattering from very small volumes, opening possibilities for deriving in situ structural information on fibrillar constituents in complex materials and tissues. This work outlines a set of strategies for confronting the formidable technical obstacles to extracting useful structural information from scattering derived from these materials.