Application of Known X-ray Phases in the Crystallographic Study of a Small Protein

Three-beam convergent-beam electron diffraction for measuring crystallographic phases

Under almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic method exists. In this work, a set of simple analytical expressions is derived for the intensity distribution in convergent-beam electron diffraction (CBED) patterns recorded under three-beam conditions. It is shown that these expressions can be used to identify features in three-beam CBED patterns from which three-phase invariants can be extracted directly, without any iterative refinement processes. The octant, in which the three-phase invariant lies, can be determined simply by inspection of the indexed CBED patterns (i.e. the uncertainty of the phase measurement is ±22.5°). This approach is demonstrated with the experimental measurement of three-phase invariants in two simple test cases: centrosymmetric Si and non-centrosymmetric GaAs. This method may complement existing structure determination methods by providing direct measurements of three-phase invariants to replace 'guessed' invariants in ab initio phasing methods and hence provide more stringent constraints to the structure solution.

Phasing methods for protein crystallography

The phase problem has been formulated as one of constrained global minimization and it leads to the minimal principle, which is the theoretical basis of 'Shake-and-Bake'--an algorithm for the automatic solution of the phase problem, ab initio. A related approach (termed 'Half-Baked') that, as in Shake-and-Bake, alternates phase refinement in reciprocal space with density modification in real space, has recently been formulated. The traditional techniques of direct methods have been integrated with isomorphous replacement and anomalous scattering and the first applications have been made. The accurate measurement of a limited number of structure invariants by means of multiple beam X-ray diffraction has become a reality. A feasibility study shows that, in combination with the direct method, the ability to measure the values of the structure invariants experimentally will strengthen existing techniques.