Wolfgang Kabsch

Automatic processing of rotation diffraction data from crystals of initially unknown symmetry and cell constants

An algorithm has been developed for the automatic interpretation of a given set of observed reciprocal-lattice points. It extracts a reduced cell and assigns indices to each reflection by a graph-theoretical implementation of the local indexing method. All possible symmetries of the observed lattice compatible with the metric of the reduced cell are recognized and reported, together with the unit-cell constants and the linear index transformation relating the conventional to the reduced cell. This algorithm has been incorporated into the program XDS [Kabsch (1988). J. Appl. Cryst. 21, 916–924], which is now able to process single-crystal area-detector data without prior knowledge of the symmetry and the unit-cell constants.

A solution for the best rotation to relate two sets of vectors

A simple procedure is derived which determines a best rotation of a given vector set into a second vector set by minimizing the weighted sum of squared deviations. The method is generalized for any given metric constraint on the transformation.

Evaluation of Single-Crystal X-ray Diffraction Data from a Position-Sensitive Detector

A Fortran program has been developed for the reduction of single-crystal diffraction data from a sequence of adjacent rotation pictures recorded at a fixed X-ray wavelength by an electronic area detector. The electronic pictures (data frames) covering the first 5° of crystal rotation are used to locate strong diffraction spots and to estimate the background. The orientation of the crystal is derived automatically from the list of observed spots and all parameters describing the diffraction pattern are refined. The only input required from the user is the specification of the space group, approximate cell dimensions and detector setting. When the initialization step is finished the program goes back to the first picture and evaluates all data frames in the order they arrive from the measurement. Each element of an electronic picture (pixel) is labelled by the indices of the nearest reflection using the current refined parameters describing the diffraction geometry. If the pixels close to its nearest reflection the counts contribute to the three-dimensional profile; otherwise the counts are used to update the background. Each profile is represented as if the reflection had followed the shortest path through the Ewald sphere and had been recorded on the surface of the sphere. Reflections close to the Ewald sphere are kept in a hash table to allow rapid access for updating the profiles. Reflections which have completely passed through the Ewald sphere are removed from the table and saved for further processing. Intensities are estimated by fitting their profiles to an average shape learned from strong neighbouring reflections. Smoothly varying scaling factors are applied to the Lp-corrected intensities which minimize discrepancies between symmetry-related reflections and fit to a reference data set if available.

Integration, scaling, space‐group assignment and post refinement

The working principles of important steps in processing rotation data are described as employed by the program XDS.

Refined crystal structure of the triphosphate conformation of H−ras p21 at 1.35 A resolution: implications for the mechanism of GTP hydrolysis

The crystal structure of the H‐ras oncogene protein p21 complexed to the slowly hydrolysing GTP analogue GppNp has been determined at 1.35 A resolution. 211 water molecules have been built into the electron density. The structure has been refined to a final R‐factor of 19.8% for all data between 6 A and 1.35 A. The binding sites of the nucleotide and the magnesium ion are revealed in high detail. For the stretch of amino acid residues 61‐65, the temperature factors of backbone atoms are four times the average value of 16.1 A2 due to the multiple conformations. In one of these conformations, the side chain of Gln61 makes contact with a water molecule, which is perfectly placed to be the nucleophile attacking the gamma‐phosphate of GTP. Based on this observation, we propose a mechanism for GTP hydrolysis involving mainly Gln61 and Glu63 as activating species for in‐line attack of water. Nucleophilic displacement is facilitated by hydrogen bonds from residues Thr35, Gly60 and Lys16. A mechanism for rate enhancement by GAP is also proposed.

A discussion of the solution for the best rotation to relate two sets of vectors

A method is discussed for obtaining the best proper rotation to relate two sets of vectors.

Automatic indexing of rotation diffraction patterns

A method is described which assigns indices to a set of single-crystal reflections recorded by the rotation-oscillation technique using a fixed X-ray wavelength. It is assumed that the space group and approximate unit-cell parameters are known. The unknown crystal orientation is determined directly from the observed diffraction pattern of one or several oscillation data records. A local indexing procedure is described which tolerates large initial errors in the parameters controlling the diffraction pattern. These parameters are refined subsequently, thereby satisfying the constraints imposed by the space-group symmetry.

How good are predictions of protein secondary structure

The three most widely used methods for the prediction of protein secondary structure from the amino acid sequence are tested on 62 proteins of known structure using a program package and data collection not previously available. None of these methods predicts better than 56% of the residues correctly, for a three state model (helix, sheet and loop). The algorithms of Robson [J. Mol. Biol. (1978) 120, 97–120] and Lim [J. Mol. Biol. (1974) 88, 873–894] are the best of those tested. New methods, now under development, can be tested against this benchmark.

Three-dimensional structures of H-ras p21 mutants: Molecular basis for their inability to function as signal switch molecules

The X-ray structures of the guanine nucleotide binding domains (amino acids 1-166) of five mutants of the H-ras oncogene product p21 were determined. The mutations described are Gly-12----Arg, Gly-12----Val, Gln-61----His, Gln-61----Leu, which are all oncogenic, and the effector region mutant Asp-38----Glu. The resolutions of the crystal structures range from 2.0 to 2.6 A. Cellular and mutant p21 proteins are almost identical, and the only significant differences are seen in loop L4 and in the vicinity of the gamma-phosphate. For the Gly-12 mutants the larger side chains interfere with GTP binding and/or hydrolysis. Gln-61 in cellular p21 adopts a conformation where it is able to catalyze GTP hydrolysis. This conformation has not been found for the mutants of Gln-61. Furthermore, Leu-61 cannot activate the nucleophilic water because of the chemical nature of its side chain. The D38E mutation preserves its ability to bind GAP.

The actin fold.

X‐ray structure analysis of actin and of the NH2‐terminal domain of the heat‐shock cognate protein Hsc70 has revealed an unexpected extensive structural similarity between these two molecules. Despite the absence of significant similarity of their amino acid sequences, both proteins share the same core architecture and a common nucleotide binding site resembling the structure of hexokinase. All three are ATPases or kinases and bind ATP in association with Mg2+ or Ca2+. The common fold consists of two α/β domains, which are connected by a putative hinge with an ATP‐binding site situated between the domains. Each domain contains a five‐stranded β‐sheet of identical topology, which suggests that the molecules may have evolved by gene duplication. From a comparison of the three aligned structures, a fingerprint sequence of the adenine nucleotide binding pocket was derived, which predicted that members of the glycerol kinase family should also have a similar fold of their nucleotide binding domain. This was later confirmed when the X‐ray structure was published. Data base search with a refined consensus sequence has retrieved other sugar kinases, as well as the prokaryotic cell cycle proteins FtsA, MreB, and StbA, and two Escherichia coli phosphatases. These proteins are predicted to possess a structure similar to actin in the common core region. As exemplified for actin, Hsc70, and glycerol kinase, the diversity of biological function is provided by the polymorphism of the loops joining the β‐strands and helices in the core region and by inserted domains that show high variability.—Kabsch, W., Holmes, K. C. The actin fold. FASEB J. 9, 167–174 (1995)