Robert H. Blessing

An empirical correction for absorption anisotropy

A least-squares procedure is described for modeling an empirical transmission surface as sampled by multiple symmetry-equivalent and/or azimuth rotation-equivalent intensity measurements. The fitting functions are sums of real spherical harmonic functions of even order, ylm(-u0) + ylm(u1), 2 < or = l = 2n < or = 8. The arguments of the functions are the components of unit direction vectors, -u0 for the reverse incident beam and u1 for the scattered beam, referred to crystal-fixed Cartesian axes. The procedure has been checked by calculations against standard absorption test data.

Outlier Treatment in Data Merging

Experience with a variety of diffraction data-reduction problems has led to several strategies for dealing with mismeasured outliers in multiply measured data sets. Key features of the schemes employed currently include outlier identification based on the values ymedian = median(|Fi|2), σmedian = median[σ(|Fi|2)], and |Δ|median = median(|Δi|) = median[||Fi|2-median (|Fi|2)|] in samples with i = 1, 2 ..... n and n ≥ 2 measurements; and robust/resistant averaging weights based on values of |zi| = |Δi|/max{σmedian, |Δ|median[n/(n−1)]1/2}. For outlier discrimination or down-weighting, sample median values have the advantage of being much less outlier-based than sample mean values would be.

Data Reduction and Error Analysis for Accurate Single Crystal Diffraction Intensities

Abstract Principles and procedures of diffraction data processing are described. Reflection integration limits are obtained from a least squares analysis of peak profile widths, based on the principles of convolution synthesis of peak profiles. An approximate, empirical thermal diffuse scattering correction is obtained from a least squares analysis of thermal diffuse scattering (TDS) intensity estimates, based on fitting intersecting straight lines to the background profile near the peak limits. Time-dependent scaling according to standard reference reflection intensities is based on least squares fitted scaling polynomials and may be weighted by anisotropic, intensity-dependent or scattering-angle-dependent factors. Inter-set scaling of data subsets and averaging of replicate and equivalent measurements, which includes several criteria for detecting and rejecting outlier measurements, provide a basis for a bivariate analysis of variance on F2 0 and (sin θ)/λ. Error analysis at each stage of the data proc...

The structure of T6 human insulin at 1.0 A resolution.

The structure of T(6) human insulin has been determined at 120 K at a resolution of 1.0 A and refined to a residual of 0.183. As a result of cryofreezing, the first four residues of the B chain in one of the two crystallographically independent AB monomers in the hexameric [Zn(1/3)(AB)(2)Zn(1/3)](3) complex undergo a conformational shift that displaces the C(alpha) atom of PheB1 by 7.86 A relative to the room-temperature structure. A least-squares superposition of all backbone atoms of the room-temperature and low-temperature structures yielded a mean displacement of 0.422 A. Omitting the first four residues of the B chain reduced the mean displacement to 0.272 A. At 120 K, nine residues were found to exhibit two discrete side-chain conformations, but only two of these residues are in common with the seven residues found to have disordered side chains in the room-temperature structure. As a result of freezing, the disorder observed at room temperature in both ArgB22 side chains is eliminated. The close contact between pairs of O( epsilon 2) atoms in GluB13 observed at room temperature is maintained at cryotemperature and suggests that a carboxylate-carboxylic acid centered hydrogen bond exists [-C(=O)-O.H.O-C(=O)-] such that the H atom is equally shared between the two partially charged O atoms.

Difference structure-factor normalization for heavy-atom or anomalous-scattering substructure determinations

Procedures are described for normalizing structure-factor difference magnitudes, |Δ|F||SIR = ||FDer| − |FNat|| ≤ |FHeavy| or |Δ|F||SAS = ||F+h| − |F−h|| ≤ 2|F′′|, to prepare data for probabilistic direct methods phasing to determine heavy-atom or anomalous-scattering substructures in SIR (single-derivative isomorphous replacement) or SAS (single-wavelength anomalous scattering) cases. Applications of the procedures in several recent determinations of multi-selenium substructures in selenomethionyl proteins via SnB direct-methods phasing are briefly summarized.

Towards automated protein structure determination: BnP, the SnB-PHASES interface

Abstract The direct-methods program SnB provides an efficient means for solving protein substructures containing many heavy-atom sites (current record: 160). In order to meet the high-throughput requirements of structural genomics projects, substructure determination needs to be tightly integrated with other aspects of the protein-phasing process. This has been accomplished through the design of a common Java interface, BnP, for SnB and components of PHASES, a popular and proven program suite that provides all the tools necessary to proceed from substructure refinement to the computation of an unambiguous protein electron-density map. Therefore, BnP will facilitate a high degree of automation and enable rapid structure determination by both experienced and novice crystallographers.

Topological analysis of experimental electron densities

Practical computing algorithms are described for analysing the topology of experimental electron density distributions represented as either three-dimensional grid densities or multipolar pseudoatom superpositions. The algorithms are implemented in the program NEWPROP, results from which are illustrated with applications to two N-acetyl, C-methylamide blocked amino acid crystal structures.

The first protein crystal structure determined from high-resolution X-ray powder diffraction data: a variant of T3R3 human insulin-zinc complex produced by grinding.

X-ray diffraction analysis of protein structure is often limited by the availability of suitable crystals. However, the absence of single crystals need not present an insurmountable obstacle in protein crystallography any more than it does in materials science, where powder diffraction techniques have developed to the point where complex oxide, zeolite and small organic molecular structures can often be solved from powder data alone. Here, that fact is demonstrated with the structure solution and refinement of a new variant of the T(3)R(3) Zn-human insulin complex produced by mechanical grinding of a polycrystalline sample. High-resolution synchrotron X-ray powder diffraction data were used to solve this crystal structure by molecular replacement adapted for Rietveld refinement. A complete Rietveld refinement of the 1630-atom protein was achieved by combining 7981 stereochemical restraints with a 4800-step (d(min) = 3.24 A) powder diffraction pattern and yielded the residuals R(wp) = 3.73%, R(p) = 2.84%, R(F)(2) = 8.25%. It was determined that the grinding-induced phase change is accompanied by 9.5 and 17.2 degrees rotations of the two T(3)R(3) complexes that comprise the crystal structure. The material reverts over 2-3 d to recover the original T(3)R(3) crystal structure. A Rietveld refinement of this 815-atom protein by combining 3886 stereochemical restraints with a 6000-step (d(min) = 3.06 A) powder diffraction pattern yielded the residuals R(wp) = 3.46%, R(p) = 2.64%, R(F)(2) = 7.10%. The demonstrated ability to solve and refine a protein crystal structure from powder diffraction data suggests that this approach can be employed, for example, to examine structural changes in a series of protein derivatives in which the structure of one member is known from a single-crystal study.

R6 hexameric insulin complexed with m-cresol or resorcinol.

The structures of three R(6) human insulin hexamers have been determined. Crystals of monoclinic m-cresol-insulin, monoclinic resorcinol-insulin and rhombohedral m-cresol-insulin diffracted to 1. 9, 1.9 and 1.78 A, respectively, and have been refined to residuals of 0.195, 0.179 and 0.200, respectively. In all three structures, a phenolic derivative is found to occupy the phenolic binding site, where it forms hydrogen bonds to the carbonyl O atom of CysA6 and the N atom of CysA11. Two additional phenolic derivative binding sites were identified within or between hexamers. The structures of all three hexamers are nearly identical, although a large displacement of the N-terminus of one B chain in both monoclinic structures results from coordination to a sodium ion which is located between symmetry-related hexamers. Other minor differences in structure arise from differences in packing in the monoclinic cell compared with the rhombohedral cell. Based upon the differences in conformation of the GluB13 side chains in T(6), T(3)R(f)(3) and R(6) hexamers, the deprotonation of these side chains appears to be associated with the T-->R conformational transition.

The structure of T6 bovine insulin.

Porcine insulin differs in sequence from bovine insulin at residues A8 (Thr in porcine-->Ala in bovine) and A10 (Ile in porcine-->Val in bovine). The structure of T6 hexameric bovine insulin has been determined to 2.25 A resolution at room temperature and refined to a residual of 0.162. The structure of the independent dimer is nearly identical to the T6 porcine insulin dimer: the mean displacement of all backbone atoms is 0.16 A, with the largest displacements occurring at AlaB30. Each of two independent zinc ions is octahedrally coordinated by three HisB10 side chains and three water molecules. As has been observed in both human and porcine insulin, the GluB13 side chains are directed towards the center of the hexamer, where a short contact of 2.57 A occurs between two independent carboxyl O atoms, again suggesting the presence of a centered hydrogen bond. No significant displacements of backbone atoms or changes in conformation are observed at A8 or A10. Since there are no interhexamer hydrogen-bonded contacts involving A8 in either porcine or bovine insulin, the change in the identity of this residue appears to have little or no effect upon the packing of the hexamers in the unit cell. In contrast, the side chains of the three A10 residues in one trimer make van der Waals contacts with the A10 side chains in a translationally related hexamer. As a consequence of the loss of the C(delta1) atom from the isoleucine residue in porcine insulin to produce valine in bovine insulin, there is a 0.36 A decrease in the distance between independent pairs of C(beta) atoms and a 0.24 A decrease in the c dimension of the unit cell. Thus, the net effect of the change in sequence at A10 is to strengthen the stabilizing hydrophobic interactions between hexamers.