A fast and robust method for determining the parameters for a flat (mask‐based) bulk‐solvent model and overall scaling in macromolecular crystallographic structure refinement and other related ...calculations is described. This method uses analytical expressions for the determination of optimal values for various scale factors. The new approach was tested using nearly all entries in the PDB for which experimental structure factors are available. In general, the resulting R factors are improved compared with previously implemented approaches. In addition, the new procedure is two orders of magnitude faster, which has a significant impact on the overall runtime of refinement and other applications. An alternative function is also proposed for scaling the bulk‐solvent model and it is shown that it outperforms the conventional exponential function. Similarly, alternative methods are presented for anisotropic scaling and their performance is analyzed. All methods are implemented in the Computational Crystallography Toolbox (cctbx) and are used in PHENIX programs.
This paper accompanies a lecture given at the 2003 CCP4 Study Weekend on experimental phasing. The first part is an overview of the fundamentals of Patterson methods and direct methods with the ...audience of the CCP4 Study Weekend in mind. In the second part, a new hybrid substructure search is outlined.
A number of conventions for the parameterization of atomic anisotropic displacements are used in the literature and in crystallographic programs. Here we summarize the commonly used conventions, with ...a special emphasis on their application in macromolecular crystallography. We then describe a new software toolbox for the handling of the various parameterizations of atomic anisotropic displacements and their interconversion. All algorithms are integrated into the freely available Computational Crystallography Toolbox.
The FOCUS method, in which both crystal chemical information and powder diffraction data are included in the structure determination process, is presented. FOCUS combines automatic Fourier recycling ...with a specialized topology search specific to zeolites, which can be described as having three‐dimensional four‐connected framework structures. The capabilities of FOCUS have been tested with seven examples of medium to high complexity. The method was then applied to three novel zeolite structures and a promising model could be obtained in each case. Experience shows that the approach of using chemical and geometric knowledge can compensate for some of the information that is lost as a result of the overlap problem. At the same time, there is an intrinsic disadvantage: any method based on assumptions of certain structural properties is also limited to materials which conform to these assumptions. Examples which show the consequences of relaxing the structural assumptions are also given.
A new software suite, called Crystallography & NMR System (CNS), has been developed for macromolecular structure determination by X‐ray crystallography or solution nuclear magnetic resonance (NMR) ...spectroscopy. In contrast to existing structure‐determination programs the architecture of CNS is highly flexible, allowing for extension to other structure‐determination methods, such as electron microscopy and solid‐state NMR spectroscopy. CNS has a hierarchical structure: a high‐level hypertext markup language (HTML) user interface, task‐oriented user input files, module files, a symbolic structure‐determination language (CNS language), and low‐level source code. Each layer is accessible to the user. The novice user may just use the HTML interface, while the more advanced user may use any of the other layers. The source code will be distributed, thus source‐code modification is possible. The CNS language is sufficiently powerful and flexible that many new algorithms can be easily implemented in the CNS language without changes to the source code. The CNS language allows the user to perform operations on data structures, such as structure factors, electron‐density maps, and atomic properties. The power of the CNS language has been demonstrated by the implementation of a comprehensive set of crystallographic procedures for phasing, density modification and refinement. User‐friendly task‐oriented input files are available for nearly all aspects of macromolecular structure determination by X‐ray crystallography and solution NMR.
The computation of reduced unit cells is an important building block for a number of crystallographic applications, but unfortunately it is very easy to demonstrate that the conventional ...implementation of cell reduction algorithms is not numerically stable. A numerically stable implementation of the Niggli‐reduction algorithm of Křivý & Gruber Acta Cryst. (1976), A32, 297–298 is presented. The stability is achieved by consistently using a tolerance in all floating‐point comparisons. The tolerance must be greater than the accumulated rounding errors. A second stable algorithm is also presented, the minimumreduction, that does not require using a tolerance. It produces a cell with minimum lengths and all angles acute or obtuse. The algorithm is a simplified and modified version of the Buerger‐reduction algorithm of Gruber Acta Cryst. (1973), A29, 433–440. Both algorithms have been enhanced to generate a change‐of‐basis matrix along with the parameters of the reduced cell.
The FOCUS approach to zeolite structure determination from powder diffraction data has been applied to data from four different zeolitic materials. The solutions of the structures of two ...aluminophosphate molecular sieves, YUL‐89 (AWO topology) and YUL‐90 (ZON topology), are used to demonstrate routine applications of the procedure. The high‐silica zeolite ZSM‐5 (MFI topology), which has 12 Si atoms (38 framework atoms) in the asymmetric unit, and the gallophosphate cloverite (‐CLO topology), the framework of which is not fully fourfold connected, provide examples of extreme cases, which challenge the limits of the FOCUS algorithm. Taken together, the four examples give an overview of the practical aspects of the FOCUS method and illustrate its potential and its limitations.
Algorithms are presented for three‐dimensional crystallographic space groups, handling tasks such as the generation of symmetry operations, the characterization of symmetry operations (determination ...of rotation‐part type, axis direction, sense of rotation, screw or glide part and location part), the determination of space‐group type identified by the space‐group number of the International Tables for Crystallography (Dordrecht: Kluwer Academic Publishers) and the generation of structure‐seminvariant vectors and moduli. The latter are an algebraic description of allowed origin shifts, which are important in crystal structure determination methods or for comparing crystal structures. The space‐group type determination produces a change‐of‐basis matrix which transforms a given space‐group representation to the standard one according to the International Tables for Crystallography. The algorithms were implemented and tested using the SgInfo library. The source code is free for non‐commercial applications.
Equations in Sections 2.3 and 2.4 of the article by Afonine et al. Acta Cryst. (2013). D69, 625–634 are corrected.
The article by Afonine et al. Acta Cryst. (2013). D69, 625–634 is corrected.
Algorithms for the treatment of special positions in three‐dimensional crystallographic space groups are presented. These include an algorithm for the determination of the site‐symmetry group given ...the coordinates of a point, an algorithm for the determination of the exact location of the nearest special position, an algorithm for the assignment of a Wyckoff letter given the site‐symmetry group, and an alternative algorithm for the assignment of a Wyckoff letter given the coordinates of a point directly. All algorithms are implemented in ISO C++ and are integrated into the Computational Crystallography Toolbox. The source code is freely available.
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