Low-angle X-ray scattering by disordered and partially ordered helical systems

A model has been developed to calculate the diffraction given by a disordered set of thick coils of helical conformation. Double coils placed inside a cylinder of different density are considered. The cylinder accounts for the presence of substances which may interact with the double coil in a random manner. The thickness of each coil, pitch and radius of gyration, outer cylinder diameter and its density are the parameters that influence the diffraction maxima observed. It is demonstrated that when the parameter Z (pitch/radius) increases, the peaks tend to overlap. The relative position (α) of the two coils is also studied. When they are diametrically opposed, only even layer-line peaks are detected. At intermediate positions, other peaks appear, the intensity of which depends strongly on the precise value of α. An interesting result is that the relative position of the peaks for any single coil is constant and does not depend on the dimensions of the coil. The central scattering increases considerably if one of the two-component coils becomes a straight cylinder coaxial with the primitive coil. As a result the lower layer-line peaks do not show. On the other hand, the intensity due to the central equatorial peak diminishes when some packing order is introduced between coils. The model is suitable for interpreting the specific case of nucleohistone patterns.