Algebraic direct methods for few-atoms structure models

Combining solution wide-angle X-ray scattering and crystallography: determination of molecular envelope and heavy-atom sites

Solving the phase problem remains central to crystallographic structure determination. A six-dimensional search method of molecular replacement (FSEARCH) can be used to locate a low-resolution molecular envelope determined from small-angle X-ray scattering (SAXS) within the crystallographic unit cell. This method has now been applied using the higher-resolution envelope provided by combining SAXS and WAXS (wide-angle X-ray scattering) data. The method was tested on horse hemoglobin, using the most probable model selected from a set of a dozen bead models constructed from SAXS/WAXS data using the program GASBOR at 5 A resolution (q(max) = 1.25 A(-1)) to phase a set of single-crystal diffraction data. It was found that inclusion of WAXS data is essential for correctly locating the molecular envelope in the crystal unit cell, as well as for locating heavy-atom sites. An anomalous difference map was calculated using phases out to 8 A resolution from the correctly positioned envelope; four distinct peaks at the 3.2sigma level were identified, which agree well with the four iron sites of the known structure (Protein Data Bank code 1ns9). In contrast, no peaks could be found close to the iron sites if the molecular envelope was constructed using the data from SAXS alone (q(max) = 0.25 A(-1)). The initial phases can be used as a starting point for a variety of phase-extension techniques, successful application of which will result in complete phasing of a crystallographic data set and determination of the internal structure of a macromolecule to atomic resolution. It is anticipated that the combination of FSEARCH and WAXS techniques will facilitate the initial structure determination of proteins and provide a good foundation for further structure refinement.