Simulation of small-angle x-ray scattering from collagen fibrils and comparison with experimental patterns

Simulation of small-angle x-ray scattering from collagen in healthy and cancerous breast tissue may reveal detailed information on the structural changes in collagen. Collagen fibril is modelled as a cylinder with axially periodic step-function electron density, and packing is approximated by placing the cylinders in small hexagonal bundles. The intensity from a bundle is calculated by summing analytical scattering amplitudes from the cylinders, and intensities from several bundles with varying lattice constants are averaged. Comparisons with more complex models are made to estimate the robustness of the model. The oscillations in the equatorial direction are not significantly affected by added complexity. The relative intensities of the Bragg peaks in the meridional direction can be tuned by modifying the axial electron density distribution. Tests with different fibril radius distributions show that the average radius can be determined with an accuracy of +/-0.5 nm but that the shape of the radius distribution cannot be accurately determined from the scattering patterns. The effect of multiple scattering and the detector point-spread function (PSF) is considered, and the PSF may make a significant contribution to the final slope of the scattering pattern. Comparisons with observed scattering indicate that the model is basically correct at the supra-molecular level.