Phasing diffuse scattering. Application of the SIR2002 algorithm to the non-crystallographic phase problem

A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV energy. The reconstructed image fits well with a scanning-electron-microscope (SEM) image of the same sample. The algorithm, which uses only the density modification portion of the SIR2002 program, is compared with the results obtained via the Gerchberg-Saxton-Fienup HiO algorithm. The new algorithm requires no knowledge of the object's boundary and proceeds from low to high resolution. In this way, the relationship between density modification in crystallography and the HiO algorithm used in signal and image processing is elucidated.

Solving non-periodic structures using direct methods: phasing diffuse scattering

The problem of reconstructing the charge density of a non-periodic sample from its diffuse X-ray scattering is considered. For a sample known to be isolated, an artificial superlattice may be assumed and the numerical direct methods of crystallography applied to the continuous distribution of diffuse scattering in order to solve the phase problem. This method is applied to simulated soft-X-ray transmission speckle patterns from a two-dimensional array of gold balls of 50 nm diameter. The results are relevant to efforts to phase the scattering from many individual macromolecules that cannot be crystallized, and to the scattering from individual inorganic nanoparticles.

Phase extension to weaker reflections of proteins via a partial structure based tangent formula

When some molecular fragment is well located, the so called partial structure based tangent formula may be used to recovery the complete crystal structure. The formula has been extensively applied to small molecules and initial applications to proteins have also been performed. We will show in this paper that the formula may be successfully applied to macromolecules, to refine phase values and to extend the phase information to weaker reflections, even in absence of prior information (at atomic level) on part of the crystal structure. Experimental tests have been performed via a modified form of the program SIR2000.

SIR2000, a program for the automatic ab initio crystal structure solution of proteins

A new phasing procedure is described working both in direct and in reciprocal space. The procedure has been implemented into the program SIR2000, the heir to SIR99, and it is able routinely to solve ab initio crystal structures of proteins without any use of prior information and any user intervention. The moduli and the flow diagram of SIR2000 are also described and its efficiency tested on several protein diffraction data sets. Success has been attained for crystal structures with up to almost 2000 non-hydrogen atoms in the asymmetric unit and resolution higher than 1.2 A. The phasing process is analysed to provide a better insight into the role of the various steps of the procedure.

Structures of nanometre-size crystals determined from selected-area electron diffraction data

The structure of a new modification of Ti2Se, the beta-phase, and several related inorganic crystal structures containing elements with atomic numbers between 16 and 40 have been solved by quasi-automatic direct methods from single-crystal electron diffraction patterns of nanometre-size crystals, using the kinematical approximation. The crystals were several thousand times smaller than the minimum size required for single-crystal X-ray diffraction. Atomic coordinates were found with an average accuracy of 0.2 A or better. Experimental data were obtained by standardized techniques for recording and quantifying electron diffraction patterns. The SIR97 program for solving crystal structures from three-dimensional X-ray diffraction data by direct methods was modified to work also with two-dimensional electron diffraction data.