Recent advances in direct phasing methods for heavy-atom substructure determination.

Macromolecular crystal structure determination has typically been a two-step process. When diffraction data from multiple chemically isomorphous or anomalously scattering crystals are available, the positions of heavy atoms from amplitude differences arising from native-derivative crystal pairs or an anomalously scattering crystal are first located and phasing of the whole protein structure is then completed using the heavy-atom substructure as a bootstrap. Shake-and-Bake, a direct-methods-based dual-space refinement procedure, provides heavy-atom substructure solutions by finding the constrained global minimum of a probabilistically defined minimal function. This minimal function relies on probabilistic estimates of the cosines of the structure invariants. A novel statistically defined minimal function that utilizes the statistical properties of the structure invariants has recently been proposed and tested. Applications of the statistical Shake-and-Bake procedure show that statistical direct methods provide a simple, reliable and efficient method of heavy-atom substructure determination.