Solution of the effects of twinning in femtosecond X-ray protein nanocrystallography

With the development of the XFEL (X-ray free electron laser), high quality diffraction patterns from nanocrystals have been achieved. The nanocrystals with different sizes and random orientations are injected to the XFEL beams and the diffraction patterns can be obtained by the so-called diffraction-and-destruction mode. The recovery of orientations is one of the most critical steps in reconstructing the 3D structure of nanocrystals. There is already an approach to solve the orientation problem by using the automated indexing software in crystallography. However, this method cannot distinguish the twin orientations in the cases of the symmetries of Bravais lattices higher than the point groups. Here we propose a new method to solve this problem. The shape transforms of nanocrystals can be determined from all of the intensities around the diffraction spots, and then Fourier transformation of a single crystal cell is obtained. The actual orientations of the patterns can be solved by comparing the values of the Fourier transformations of the crystal cell on the intersections of all patterns. This so-called multiple-common-line method can distinguish the twin orientations in the XFEL diffraction patterns successfully.