Annamaria Mazzone

SIR2011: a new package for crystal structure determination and refinement

SIR2011, the successor of SIR2004, is the latest program of the SIR suite. It can solve ab initio crystal structures of small- and medium-size molecules, as well as protein structures, using X-ray or electron diffraction data. With respect to the predecessor the program has several new abilities: e.g. a new phasing method (VLD) has been implemented, it is able to exploit prior knowledge of the molecular geometry via simulated annealing techniques, it can use molecular replacement methods for solving proteins, it includes new tools like free lunch and new approaches for electron diffraction data, and it visualizes three-dimensional electron density maps. The graphical interface has been further improved and allows the straightforward use of the program even in difficult cases.

Crystal structure determination and refinement via SIR2014

SIR2014 is the latest program of the SIR suite for crystal structure solution of small, medium and large structures. A variety of phasing algorithms have been implemented, both ab initio (standard or modern direct methods, Patterson techniques, Vive la Difference) and non-ab initio (simulated annealing, molecular replacement). The program contains tools for crystal structure refinement and for the study of three-dimensional electron-density maps via suitable viewers.

Ab initio phasing of proteins with heavy atoms at non-atomic resolution: pushing the size limit of solvable structures up to 7890 non-H atoms in the asymmetric unit

The success of the ab initio phasing process mainly depends on two parameters: data resolution and structural complexity. In agreement with the Sheldrick rule, the presence of heavy atoms can also play a nonnegligible role in the success of direct methods. The increased efficiency of the Patterson methods and the advent of new phasing techniques based on extrapolated reflections have changed the state of the art. In particular, it is not clear how much the resolution limit and the structural complexity may be pushed in the presence of heavy atoms. In this paper, it is shown that the limits fixed by the Sheldrick rule may be relaxed if the structure contains heavy atoms and that ab initio techniques can succeed even when the data resolution is about 2 A, a limit unthinkable a few years ago. The method is successful in solving a structure with 7890 non-H atoms in the asymmetric unit at a resolution of 1.65 A, a considerable advance on the previous record of 6319 atoms at atomic resolution.

Molecular replacement: the probabilistic approach of the program REMO09 and its applications

The method of joint probability distribution functions has been applied to molecular replacement techniques. The rotational search is performed by rotating the reciprocal lattice of the protein with respect to the calculated transform of the model structure; the translation search is performed by fast Fourier transform. Several cases of prior information are studied, both for the rotation and for the translation step: e.g. the conditional probability density for the rotation or the translation of a monomer is found both for ab initio and when the rotation and/or the translation values of other monomers are given. The new approach has been implemented in the program REMO09, which is part of the package for global phasing IL MILIONE [Burla, Caliandro, Camalli, Cascarano, De Caro, Giacovazzo, Polidori, Siliqi & Spagna (2007). J. Appl. Cryst. 40, 609-613]. A large set of test structures has been used for checking the efficiency of the new algorithms, which proved to be significantly robust in finding the correct solutions and in discriminating them from noise. An important design concept is the high degree of automatism: REMO09 is often capable of providing a reliable model of the target structure without any user intervention.

Crystal structure solution of small-to-medium-sized molecules at non-atomic resolution

Data resolution limits the information carried by diffraction data and is therefore the most critical limit for the success of ab initio crystal structure solution. To overcome this limit, two methods have recently been proposed, namely the correction of resolution bias in electron-density maps and extrapolation of the structure factors beyond the data resolution limit. The first method has successfully been applied to powder data and the second to protein data. Neither of them has been applied to single-crystal data from small or medium-sized molecules. A third technique, the active use of the PSI-0 triplets in a tangent procedure, was applied to small molecules in the early days of crystallography, but it soon became obsolete because of the great success of methods combining reciprocal and direct space techniques. This paper explores the role of data resolution for small-to-medium-sized molecules and studies the usefulness of three auxiliary techniques, i.e. active use of the PSI-0 triplets, resolution bias correction and extrapolation of the structure factors.

SUNBIM: a package for X-ray imaging of nano- and biomaterials using SAXS, WAXS, GISAXS and GIWAXS techniques

SUNBIM (supramolecular and submolecular nano- and biomaterials X-ray imaging) is a suite of integrated programs which, through a user-friendly graphical user interface, are optimized to perform the following: (i) q-scale calibration and two-dimensional → one-dimensional folding on small- and wide-angle X-ray scattering (SAXS/WAXS) and grazing-incidence SAXS/WAXS (GISAXS/GIWAXS) data, also including possible eccentricity corrections for WAXS/GIWAXS data; (ii) background evaluation and subtraction, denoising, and deconvolution of the primary beam angular divergence on SAXS/GISAXS profiles; (iii) indexing of two-dimensional GISAXS frames and extraction of one-dimensional GISAXS profiles along specific cuts; (iv) scanning microscopy in absorption and SAXS contrast. The latter includes collection of transmission and SAXS data, respectively, in a mesh across a mm2 area, organization of the as-collected data into a single composite image of transmission values or two-dimensional SAXS frames, analysis of the composed data to derive the absorption map and/or the spatial distribution, and orientation of nanoscale structures over the scanned area.

The use of VLD (vive la difference) in the molecular-replacement approach: a pipeline

VLD (vive la difference) is a novel ab initio phasing approach that is able to drive random phases to the correct values. It has been applied to small, medium and protein structures provided that the data resolution was atomic. It has never been used for non-ab initio cases in which some phase information is available but the data resolution is usually very far from 1 Å. In this paper, the potential of VLD is tested for the first time for a classical non-ab initio problem: molecular replacement. Good preliminary experimental results encouraged the construction of a pipeline for leading partial molecular-replacement models with errors to refined solutions in a fully automated way. The pipeline moduli and their interaction are described, together with applications to a wide set of test cases.

Variance of electron-density maps in space group P1

The expected mean-square error of electron-density maps (observed and difference) is traditionally estimated as a function of the variance of the observed amplitudes. The usual purpose is to evaluate the reliability of the structural parameters suggested by the final electron-density maps. Accordingly, such calculations are performed after the refinement stage, when the phases are considered perfectly determined. In this paper a mathematical expression for the variance (observed, difference and hybrid) is obtained for each point of an electron-density map for the space group P1 under a different hypothesis: the current phases are distributed on the trigonometric circle about the correct values, according to von Mises distributions. The variance calculation may then be performed at any stage of the phasing process, starting from a random up to a highly correlated model. It has been shown that the variance does not change dramatically from point to point of the map; therefore emphasis has been given to the concept of map variance, which allows an easier study of its properties. When the model is highly correlated with the target structure the conclusive formulas reduce to those previously described in the literature. The properties of the variance are discussed: it is shown that they are the basis for the most successful phasing procedures.

Protein phasing at non-atomic resolution by combining Patterson and VLD techniques

Phasing proteins at non-atomic resolution is still a challenge for any ab initio method. A variety of algorithms [Patterson deconvolution, superposition techniques, a cross-correlation function (C map), the VLD (vive la difference) approach, the FF function, a nonlinear iterative peak-clipping algorithm (SNIP) for defining the background of a map and the free lunch extrapolation method] have been combined to overcome the lack of experimental information at non-atomic resolution. The method has been applied to a large number of protein diffraction data sets with resolutions varying from atomic to 2.1 Å, with the condition that S or heavier atoms are present in the protein structure. The applications include the use of ARP/wARP to check the quality of the final electron-density maps in an objective way. The results show that resolution is still the maximum obstacle to protein phasing, but also suggest that the solution of protein structures at 2.1 Å resolution is a feasible, even if still an exceptional, task for the combined set of algorithms implemented in the phasing program. The approach described here is more efficient than the previously described procedures: e.g. the combined use of the algorithms mentioned above is frequently able to provide phases of sufficiently high quality to allow automatic model building. The method is implemented in the current version of SIR2014.

Estimates of triplet invariants given a model structure

The triplet structure invariant is estimated via the method of joint probability distribution functions when a model structure is available. The six-variate probability distribution function P(Eh, Ek, E−h−k, Eph, Epk, Ep,−h−k) is studied under the condition that imperfect isomorphism between the target and model structures exist. The results are compared with those available in the literature, which were obtained under the condition of perfect isomorphism. It is shown that the new formalism is more suitable for real cases, where perfect isomorphism is very rare.