Analysis of diffracted intensities from finite protein crystals with incomplete unit cells

Developments in experimental techniques in micro electron diffraction and serial X-ray crystallography provide the opportunity to collect diffraction data from protein nanocrystals. Incomplete unit cells on the surfaces of protein crystals can affect the distribution of diffracted intensities for crystals with very high surface-to-volume ratios. The extraction of structure factors from diffraction data for such finite protein crystals sizes is considered here. A theoretical model for the continuous diffracted intensity distribution for data merged from finite crystals with two symmetry-related sub-units of the conventional unit cell is presented. This is used to extend a whole-pattern fitting technique to account for incomplete unit cells in the extraction of structure factor amplitudes. The accuracy of structure factor amplitudes found from this whole-pattern fitting technique and from an integration approach are evaluated.