Implementation of cluster analysis for ab initio phasing using the molecular envelope from solution X-ray scattering

Solution of the phase problem is central to crystallographic structure determination. The conventional methods of isomorphous replacement (MIR or SIR) and molecular replacement are ineffective in the absence of a suitable isomorphous heavy-atom derivative or knowledge of the structure of a homologous protein. A recent method utilizing the low-resolution molecular shape determined from solution X-ray scattering data has shown to be successful in locating the molecular shape within the crystallographic unit cell in the case of the trimer nitrite reductase (NiR, 105 kDa) [Hao et al. (1999), Acta Cryst. D55, 243–246]. This was achieved by performing a direct real-space search for orientation and translation using knowledge of the orientation of the polar angles of the non-crystallographic axis obtained by performing a self-rotation on crystallographic data. This effectively reduces the potential six-dimensional search to a four-dimensional one (Eulerian angle γ and three translational parameters). In the case of NiR, the direct four-dimensional search produced a clear solution that was in good agreement with the known structure. The program FSEARCH incorporating this method has been generalized to handle molecules from all space groups and in particular those in possession of non-crystallographic symmetry. However, the method employed was initially unsuccessful when applied to the small dimeric molecule superoxide dismutase (SOD, 32 kDa) owing to the absence of strong reflections at low resolution caused by saturation at the detector. The determined solution deviated greatly from that of the known structure [Hough & Hasnain (1999), J. Mol. Biol. 287, 579–592]. It was found that once these absent reflections were replaced by a series of randomly generated intensity values and cluster analysis was performed on the output, the signal-to-noise ratio was improved and a most probable solution was found. The electron-density map of the stochastically determined solution agrees well with the known structure; the phase error calculated from this map was 67° within 14 Å resolution.