The highly resolved excess electron distance distribution of biopolymers in solution: calculation from intermediate-angle X-ray scattering and interpretation

X-ray and neutron scattering provide valuable and specific information about the internal structure of macromolecules in solution. The excess electron distance distribution function of a macromolecule p(r), derived from the scattering by a Fourier transformation, is more directly structurally interpretable than the scattering curve itself. This is especially the case when a set of atomic coordinates is available as a `starting structure' and when the p(r) function is highly resolved. A procedure is proposed for calculation of the high-resolution p(r) function at distances greater than 0.4 nm. To reduce termination errors in the distance distribution function, the difference between the scattered intensity of the molecule, calculated using atomic coordinates, and the scattered intensity of the `independent' atoms of the macromolecule is modified by a Hamming window and then Fourier transformed. A more direct structural interpretation of changes in the highly resolved p(r) function is possible by the correlation of known structural elements in proteins and nucleic acids with main features of the electron distance distribution function via the so-called distance plot.