Showing papers by "George M. Sheldrick published in 2012"

Enhanced rigid-bond restraints

Abstract: The rigid-bond model [Hirshfeld (1976). Acta Cryst. A32, 239–244] states that the mean-square displacements of two atoms are equal in the direction of the bond joining them. This criterion is widely used for verification (as intended by Hirshfeld) and also as a restraint in structure refinement as suggested by Rollett [Crystallographic Computing (1970), edited by F. R. Ahmed et al., pp. 167–181. Copenhagen: Munksgaard]. By reformulating this condition, so that the relative motion of the two atoms is required to be perpendicular to the bond, the number of restraints that can be applied per anisotropic atom is increased from about one to about three. Application of this condition to 1,3-distances in addition to the 1,2-distances means that on average just over six restraints can be applied to the six anisotropic displacement parameters of each atom. This concept is tested against very high resolution data of a small peptide and employed as a restraint for protein refinement at more modest resolution (e.g. 1.7 A).

Practical structure solution with ARCIMBOLDO

Abstract: Since its release in September 2009, the structure-solution program ARCIMBOLDO, based on the combination of locating small model fragments such as polyalanine α-helices with density modification with the program SHELXE in a multisolution frame, has evolved to incorporate other sources of stereochemical or experimental information. Fragments that are more sophisticated than the ubiquitous main-chain α-­helix can be proposed by modelling side chains onto the main chain or extracted from low-homology models, as locally their structure may be similar enough to the unknown one even if the conventional molecular-replacement approach has been unsuccessful. In such cases, the program may test a set of alternative models in parallel against a specified figure of merit and proceed with the selected one(s). Experimental information can be incorporated in three ways: searching within ARCIMBOLDO for an anomalous fragment against anomalous differences or MAD data or finding model fragments when an anomalous substructure has been determined with another program such as SHELXD or is subsequently located in the anomalous Fourier map calculated from the partial fragment phases. Both sources of information may be combined in the expansion process. In all these cases the key is to control the workflow to maximize the chances of success whilst avoiding the creation of an intractable number of parallel processes. A GUI has been implemented to aid the setup of suitable strategies within the various typical scenarios. In the present work, the practical application of ARCIMBOLDO within each of these scenarios is described through the distributed test cases.

Ab initio phasing

Abstract: The background and use of dual-space direct methods for the ab initio phasing of small macromolecules as well as the phasing of heavy-atom substructures of larger biological structures are described. Basic concepts include normalized structure factors, multisolution procedures, random trial structures, phase-refinement formulas, peak-picking techniques, density modification including charge flipping, and recognizing solutions. Other topics discussed are the use of Patterson information to get better starting phases, avoiding false minima, the effects of data resolution, data quality and completeness, special features of space group P1, refinement strategies, and future possibilities. Several independent computer programs that implement these concepts are then briefly described.

Unexpected tautomeric equilibria of the carbanion-enamine intermediate in pyruvate oxidase highlight unrecognized chemical versatility of thiamin

Abstract: Thiamin diphosphate, the vitamin B1 coenzyme, plays critical roles in fundamental metabolic pathways that require acyl carbanion equivalents. Studies on chemical models and enzymes had suggested that these carbanions are resonance-stabilized as enamines. A crystal structure of this intermediate in pyruvate oxidase at 1.1 A resolution now challenges this paradigm by revealing that the enamine does not accumulate. Instead, the intermediate samples between the ketone and the carbanion both interlocked in a tautomeric equilibrium. Formation of the keto tautomer is associated with a loss of aromaticity of the cofactor. The alternate confinement of electrons to neighboring atoms rather than π-conjugation seems to be of importance for the enzyme-catalyzed, redox-coupled acyl transfer to phosphate, which requires a dramatic inversion of polarity of the reacting substrate carbon in two subsequent catalytic steps. The ability to oscillate between a nucleophilic (carbanion) and an electrophilic (ketone) substrate center highlights a hitherto unrecognized versatility of the thiamin cofactor. It remains to be studied whether formation of the keto tautomer is a general feature of all thiamin enzymes, as it could provide for stable storage of the carbanion state, or whether this feature represents a specific trait of thiamin oxidases. In addition, the protonation state of the two-electron reduced flavin cofactor can be fully assigned, demonstrating the power of high-resolution cryocrystallography for elucidation of enzymatic mechanisms.

Continuous β-turn fold of an alternating alanyl/homoalanyl peptide nucleic acid.

Abstract: The crystal structure of the PNA (peptide nucleic acid) oligomer H–Lys–HalG–AlaG–HalC–AlaG–HalC–AlaC–Lys–NH2 (PNA1, amino acids with d-configuration are underlined, Ala = alanyl, Hal = homoalanyl) has been determined by ab initio direct methods and refined against 1.0 A data. The asymmetric unit consists of a tetrameric cage with almost ideal Watson–Crick C–G base pairing of all the guanine and cytosine side-chain substituents. Each PNA strand has a 90° β-turn every second residue, stabilized by three hydrogen bonds between the backbone amides. The first, second, fifth and sixth bases stack on one side of the monomer and pair with the corresponding complementary bases of a second monomer to form a dimer. The two remaining bases on each side of the resulting dimer form Watson–Crick pairs with the complementary bases of a second dimer, leading to a unique cage structure. The extra methylene groups in the homoalanyl residues enable stacking of the bases with an optimal distance between base-planes but also with an appreciable lateral displacement (slide).

Macromolecular applications of SHELX

Abstract: The SHELX system for small-molecule crystallography dates back to the early 1970s. The current refinement program, SHELXL97, is also useful for high-resolution macromolecular refinement. SHELXC, D and E are more recent additions for experimental phasing using single-wavelength anomalous dispersion (SAD), single isomorphous replacement (SIR), combined SAD and SIR (SIRAS), multi-wavelength anomalous dispersion (MAD) and radiation-damage-induced phasing (RIP) data. They are fast and simple to use, and in favourable cases produce high-quality maps despite very weak initial phase information. Keywords: SHELX; SHELXC; SHELXD; SHELXE; SHELXL; refinement; experimental phasing; substructure solution; density modification; autotracing