On the application of phase relationships to complex structures. XXVI. Developments of the Sayre-equation tangent formula

New strategies for Direct Methods

The combination of the random approach with the representations method proved of large usefulness. Very difficult structures can be routinary solved via the package SIR92 which integrates the two strategies. A new method is proposed which actively uses the information contained in the psi-zero triplets in order to drive phases towards the correct values.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

The direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c6, a heme-containing redox protein with 89 amino acids, a Fe atom and 151 solvent water molecules in the asymmetric unit and data to 1.1 Å resolution. The crystal system is rhombohedral with space group R3, cell parameters a = b = c = 40.43(10) Å, α = β = γ = 80.25(5)°. Starting with initially random phases, useful phase sets could be obtained from multiple trials of direct methods based on reciprocal space. The E-map corresponding to the phase set with the lowest mean phase error, 45.4°, showed a distorted octahedral coordination around the Fe site. The phase estimates from the metal atom and a few neighbouring atoms in the initial E-map have been improved by density modification procedure (PERP) operating in direct space. The resulting electron density map can be interpreted readily by an automated procedure to build up the protein structure.

Phase retrieval by iterated projections

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map when a particular choice is made for two of the parameters. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby the form of stagnation encountered by alternating projection schemes is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved.

Structure of the UmuD' protein and its regulation in response to DNA damage

For life to be sustained, mistakes in DNA repair must be tolerated when damage obscures the genetic information. In bacteria such as Escherichia coli, DNA damage elicits the well regulated 'SOS response'. For the extreme case of damage that cannot be repaired by conventional enzymes, there are proteins that allow the replication of DNA through such lesions, but with a reduction in the fidelity of replication. Essential proteins in this mutagenic process are RecA, DNA polymerase III, UmuD, UmuD' and UmuC (umu: UV mutagenesis). Regulation of this response involves a RecA-mediated self-cleavage of UmuD to produce UmuD'. To understand this system in more detail, we have determined the crystal structure of the E. coli UmuD' mutagenesis protein at 2.5 A resolution. Globular heads folded in an unusual Beta-structure associate to form molecular dimers, and extended amino-terminal tails associate to produce crystallized filaments. The structure provides insight into the mechanism of the self-cleavage reaction that UmuD-like proteins undergo as part of the global SOS response.

The crystal and molecular structure of the trisaccharide erlose trihydrate

Erlose [beta-D-fructofuranosyl O-alpha-D-glucopyranosyl-(1-->4)-D-glucopyranoside] trihydrate, C18H32 O16.3H2O, M(r) = 558.48, is orthorhombic, P2(1)2(1)2(1) with a = 31.164(7), b = 13.111(5), c = 11.636(5) A, and Z = 8. The structure was solved by direct methods, and refined to R = 0.035 for 3926 observed reflections. The unit cell contains two independent molecules having a similar conformation. The conformation of the alpha-(1-->2) glycosidic linkage is similar to that observed in erlose monohydrate, whereas the conformation of the alpha-(1-->4) glycosidic linkage differs significantly. The molecule has no intramolecular hydrogen-bonds except for the minor components of three-center bonds, but indirect intramolecular hydrogen-bonds through the water molecules are formed. The hydrogen-bond system in the crystal structure consists of infinite and finite chains crosslinked by water molecules.