A new study of the  sigmaA parameter has been undertaken to understand itsbehaviour when the diffraction amplitude distributions are far from the standardWilson distributions. The study has led to the formulation of a new statisticalinterpretation of  sigmaA, expressed in terms of a correlation factor. The newformulas allow a more accurate use of  sigmaA in electron-density modification procedures.

The difference electron density has recently been revisited via the method ofjoint probability distribution functions [Burla et al. (2010). Acta Cryst. A66, 347-361]. New Fourier coefficients were devised which were the basis of a new abinitio method for the solution of the phase problem (i.e. VLD, vive la difference).In this paper we study the joint probability distribution functions P(F, Fp, Fq),where Fq is the structure factor corresponding to the ideal hybrid Fouriersynthesis rhoq =  trho -wrhop and t and w are any pair of real numbers. New Fouriercoefficients for the calculations of any hybrid synthesis are obtained, and theproperties of the corresponding electron-density maps are discussed. The firstapplications show the correctness of our theoretical approach and suggestpossible applications in phasing procedures.

New methods have been recently developed to improve the structure solution of macromolecules by ab initio (Patterson or Direct Methods) and non ab initio (Molecular Replacement) approaches. Phasing proteins at non-atomic resolution is still a challenge for any ab initio method. The combined use of different algorithms [Patterson deconvolution and superposition techniques, cross-correlation function (C-Map), the VLD (Vive la Difference) approach included in the Direct Space Refinement (DSR) procedure, a new probabilistic formula estimating triplet invariants and capable of exploiting a model electron density maps, the FREE LUCH extrapolation method, a new FOM to identify the correct solution] allow to overcome the lack of experimental information. The new methods have been applied to a large number of protein diffraction data with resolution up to 2.1Å, under the condition that Ca or heavier atoms are in the structure. Results show that solving proteins at limited resolution is a feasible task, achievable even by new Direct Methods algorithms, against the traditional common believe that atomic resolution is a necessary condition for the success of a direct ab initio phasing process.A new procedure (REVAN) , aiming at solving protein structures via Molecular Replacement and density guided optimization algorithms, has been assembled. It combines a variety of programs (REMO09, REFMAC, COOT) and algorithms (Cowtan-EDM, DSR, VLD, FREE LUNCH), and can successfully lead to the structure solution also when the sequence identity between target and model structures is smaller than 0.30 and data resolution up to ~ 3Å. The application to a wide set of test structures (including difficult cases proposed by DiMaio et al. (2011), solved by using MR procedures together with energy guided programs) suggests that REVAN is quite effective even far from atomic resolution and, in combination with EDM techniques and sequence mutation algorithms, it is able to efficiently extend and refine the set of phases, reducing its average error.The final step of the automatic solving process (ab initio or MR approaches) is the application of an Automated Model Building program (i.e. Buccaneer, Nautilus, ARP-wARP or Phenix-Autobuild) in order to recover the correct structure. Results suggest that the quality of the phases at the end of the phasing process is good enough to lead the AMB program to success.These new efficient procedures are implemented in the current version of the software package SIR2014.

The REVAN pipeline aiming at the solution of protein structures via molecular replacement (MR) has been assembled. It is the successor to REVA, a pipeline that is particularly efficient when the sequence identity (SI) between the target and the model is greater than 0.30. The REVAN and REVA procedures coincide when the SI is >0.30, but differ substantially in worse conditions. To treat these cases, REVAN combines a variety of programs and algorithms (REMO09, REFMAC, DM, DSR, VLD, free lunch, Coot, Buccaneer and phenix. autobuild). The MR model, suitably rotated and positioned, is first refined by a standard REFMAC refinement procedure, and the corresponding electron density is then submitted to cycles of DM-VLD-REFMAC. The next REFMAC applications exploit the better electron densities obtained at the end of the VLD-EDM sections (a procedure called vector refinement). In order to make the model more similar to the target, the model is submitted to mutations, in which Coot plays a basic role, and it is then cyclically resubmitted to REFMAC-EDM-VLD cycles. The phases thus obtained are submitted to free lunch and allow most of the test structures studied by DiMaio et al. [(2011), Nature (London), 473, 540-543] to be solved without using energy-guided programs.

The VLD algorithm relies on the properties of the difference Fourier synthesisand is designed for solving crystal structures in the correct space group, startingfrom random models. The standard approach has been modified by integrating itwith the RELAX procedure, for translating to the correct position misplacedbut correctly oriented models. A better control of the parameters and additionalphase refinement cycles were able to improve the quality of the solutions and tomake superfluous, for macromolecules and medium-sized molecules, the least-squares refinement cycles that, in the standard VLD approach, follow thephasing step. As a result, the efficiency of the new VLD algorithm is stronglyincreased; it has been checked using a wide variety of practical cases andcompared with the effectiveness of direct methods.

The identification of the extinction symbol is routine for single-crystal X-raydata. Because of peak overlap and possible preferred orientation the task ismore difficult for powder diffraction data, but recent computer programs basedon probabilistic approaches have made it more automatic. This paper describesa new algorithm for the automatic identification of the Laue group and of theextinction symbol from electron diffraction intensities. The algorithm has astatistical basis and tries to deal with the severe problems arising from the oftennonkinematical nature of the diffraction intensities and from the limitedaccuracy of the lattice parameters determined via electron diffraction. Theapproach has been checked using a wide set of test structures.

alpha-Helices are peculiar atomic arrangements characterizing protein structures. Their occurrence can be used within crystallographic methods as minimal a priori information to drive the phasing process towards solution. Recently, brute-force methods have been developed which search for all possible positions of alpha-helices in the crystal cell by molecular replacement and explore all of them systematically. Knowing the alpha-helix orientations in advance would be a great advantage for this kind of approach. For this purpose, a fully automatic procedure to find alpha-helix orientations within the Patterson map has been developed. The method is based on Fourier techniques specifically addressed to the identification of helical shapes and operating on Patterson maps described in spherical coordinates. It supplies a list of candidate orientations, which are then refined by using a figure of merit based on a rotation function calculated for a template polyalanine helix oriented along the current direction. The orientation search algorithm has been optimized to work at 3 A resolution, while the candidates are refined against all measured reflections. The procedure has been applied to a large number of protein test structures, showing an overall efficiency of 77% in finding alpha-helix orientations, which decreases to 48% on limiting the number of candidate solutions (to 13 on average). The information obtained may be used in many aspects in the framework of molecular-replacement phasing, as well as to constrain the generation of models in computational modelling programs. The procedure will be accessible through the next release of IL MILIONE and could be decisive in the solution of new unknown structures.

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 Différence) 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.

The statistical features of the amplitudes obtained via precession electron diffraction have been studied,with particular concern with their effects on direct phasing procedures. A new algorithm, denoted by BEA,is described: according to it, the average amplitude of the symmetry equivalent reflections is used in the Direct Methods step. Once an even imperfect structural model is available, the best amplitude among theequivalent reflections is used to improve the model. It is shown that BEA is able to provide more complete structural models, to make the phasing process more straightforward and to end with crystallographicresidual much better than those usually obtained by electron diffraction.

The crystal structure of U6Fe5Al8Si9 was re-determined by electron crystallography, using selected area electron diffraction (SAED) and high resolution (HRTEM) images, taken along the [0 0 1] direction. The obtained results are very similar to those found previously by X-ray powder diffraction. The differences between the atomic positions found by SAED and HRTEM images and those found by X-ray powder diffraction were 0.11 and 0.08 angstrom, respectively. (C) 2013 Elsevier Ltd. All rights reserved.

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.

The crystal structure solution of small-medium size molecules via single crystal X-ray data is almost a routineprocess. When single crystals of sufficient dimensions are not available, electron diffraction is a usefulalternative: the structure solution however may still be a challenge. We have modified the standard version ofSir2008 to include several new tools, which are expected to make the phasing process more straightforward.Additional work is in progress: in Sir2011, the heir of Sir2008, particular emphasis will be given to a newprocedure for the determination of the space groups, to a new approach (BEA) aiming at reducing in thepractice the disturbing effects of the dynamical scattering and to the simulated annealing algorithm, as aphasing tool particularly useful in case of organic structures, when scarce or poor experimental data areavailable.

The efficient multipurpose figure of merit MPF has been defined andcharacterized. It may be very helpful in phasing procedures. Indeed, it mightbe used for establishing the centric or acentric nature of an unknown structure,for identifying the presence of some pseudotranslational symmetry, forrecognizing the correct solution in multisolution approaches and for estimatingthe quality of structure models as they become available during the phasingprocess. Thus, phase improvement or deterioration may be monitored anduseless models may be discarded to save computing time. It is also shown thatMPF may be applied in different phasing approaches, no matter if ab initio ornon ab initio.

Two new computational methods dedicated to neutron crystallography, called n-FreeLunch and DNDM-NDM, have been developed and successfully tested. The aim in developing these methods is to determine hydrogen and deuterium positions in macromolecular structures by using information from neutron density maps. Of particular interest is resolving cases in which the geometrically predicted hydrogen or deuterium positions are ambiguous. The methods are an evolution of approaches that are already applied in X-ray crystallography: extrapolation beyond the observed resolution (known as the FreeLunch procedure) and a difference electron-density modification (DEDM) technique combined with the electron-density modification (EDM) tool (known as DEDM-EDM). It is shown that the two methods are complementary to each other and are effective in finding the positions of H and D atoms in neutron density maps.

Density modification is a general standard technique which may be used to improve electron density derived from experimental phasing and also to refine densities obtained by ab initio approaches. Here, a novel method to expand density modification is presented, termed the Phantom derivative technique, which is based on non-existent structure factors and is of particular interest in molecular replacement. The Phantom derivative approach uses randomly generated ancil structures with the same unit cell as the target structure to create non-existent derivatives of the target structure, called phantom derivatives, which may be used for ab initio phasing or for refining the available target structure model. In this paper, it is supposed that a model electron density is available: it is shown that ancil structures related to the target obtained by shifting the target by origin-permissible translations may be employed to refine model phases. The method enlarges the concept of the ancil, is as efficient as the canonical approach using random ancils and significantly reduces the CPU refinement time. The results from many real test cases show that the proposed methods can substantially improve the quality of electron-density maps from molecular-replacement-based phases.

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. © 2014 International Union of Crystallography.

The Phantom Derivative (PhD) method [Giacovazzo (2015), Acta Cryst. A71, 483-512] has recently been described for ab initio and non-ab initio phasing. It is based on the random generation of structures with the same unit cell and the same space group as the target structure (called ancil structures), which are used to create derivatives devoid of experimental diffraction amplitudes. In this paper, the non-ab initio variant of the method was checked using phase sets obtained by molecular-replacement techniques as a starting point for phase extension and refinement. It has been shown that application of PhD is able to extend and refine phases in a way that is competitive with other electron-density modification techniques.

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.

Ab initio and non-ab initio phasing methods are often unable to provide phases of sufficient quality to allow the molecular interpretation of the resulting electron-density maps. Phase extension and refinement is therefore a necessary step: its success or failure can make the difference between solution and nonsolution of the crystal structure. Today phase refinement is trusted to electron-density modification (EDM) techniques, and in practice to dual-space methods which try, via suitable constraints in direct and in reciprocal space, to generate higher quality electron-density maps. The most popular EDM approaches, denoted here as mainstream methods, are usually part of packages which assist crystallographers in all of the structure-solution steps from initial phasing to the point where the molecular model perfectly fits the known features of protein chemistry. Other phase-refinement approaches that are based on different sources of information, denoted here as out-of-mainstream methods, are not frequently employed. This paper aims to show that mainstream and out-of-mainstream methods may be combined and may lead to dramatic advances in the present state of the art. The statement is confirmed by experimental tests using molecular-replacement, SAD-MAD and ab initio techniques.The synergy between current phase-refinement techniques and out-of-mainstream refinement methods leads to a dramatic advance in the state of the art.

When a model structure, and more generally a model electron density rho(M)(r), is available, its cross-correlation function C(u) with the unknown true structure rho(r) cannot be exactly calculated. A useful approximation of C(u) is obtained by replacing exp[i(phi(h) - phi(Mh))] by its expected value. In this case C'(u), a potentially useful approximation of the function C(u), is obtained. In this paper the main crystallographic properties of the functions C(u) and C'(u) are established. It is also shown that such functions may be useful for the success of the phasing process.

This study clarifies why, in the phantom derivative (PhD) approach, randomly created structures can help in refining phases obtained by other methods. For this purpose the joint probability distribution of target, model, ancil and phantom derivative structure factors and its conditional distributions have been studied. Since PhD may use n phantom derivatives, with n >= 1, a more general distribution taking into account all the ancil and derivative structure factors has been considered, from which the conditional distribution of the target phase has been derived. The corresponding conclusive formula contains two components. The first is the classical Srinivasan & Ramachandran term, relating the phases of the target structure with the model phases. The second arises from the combination of two correlations: that between model and derivative (the first is a component of the second) and that between derivative and target. The second component mathematically codifies the information on the target phase arising from model and derivative electron-density maps. The result is new, and explains why a random structure, uncorrelated with the target structure, adds useful information on the target phases, provided a model structure is known. Some experimental tests aimed at checking if the second component really provides information on phi (the target phase) were performed; the favourable results confirm the correctness of the theoretical calculations and of the corresponding analysis.

VLD (vive la difference) is a novel ab initio phasing approachthat is able to drive random phases to the correct values. Ithas been applied to small, medium and protein structuresprovided that the data resolution was atomic. It has neverbeen used for non-ab initio cases in which some phaseinformation is available but the data resolution is usually very ?far from 1 A. In this paper, the potential of VLD is tested forthe first time for a classical non-ab initio problem: molecularreplacement. Good preliminary experimental results encour-aged the construction of a pipeline for leading partialmolecular-replacement models with errors to refined solutionsin a fully automated way. The pipeline moduli and theirinteraction are described, together with applications to a wideset of test cases.

A fully ordered structure is reported for the polymorph of triphenylsilanol-4,4 0 -bipyridyl (4/1), 4C 18 H 16 OSiÁC 10 H 8 N 2 , having Z 0 = 4. The asymmetric unit contains four similar but distinct five-molecule aggregates, in which the central bipyridyl unit is linked to two molecules of triphenylsilanol via O--H...N hydrogen bonds, with a further pair of triphenylsilanol molecules linked to the first pair via O-- H...O hydrogen bonds. An extensive series of C-- HÁ Á Á(arene) hydrogen bonds links these aggregates into complex sheets. This structure is compared with a previously reported structure [Bowes, Ferguson, Lough & Glidewell (2003). Acta Cryst. B59, 277-286], which was based on an erroneous disordered structural model arising from a false direct-methods solution with reference to a strong pseudo- inversion centre.

The VLD (vive la difference) phasing algorithm combines the model electrondensity with the difference electron density via reciprocal space relationships toobtain new phase values and drive them to the correct values. The process isiterative and has been applied to small and medium-size structures and toproteins. Hybrid Fourier syntheses show properties that are intermediatebetween those of the observed synthesis (whose peaks should correspond to themost probable atomic positions) and those of the difference synthesis (whosepositive and negative peaks should correspond to missed atomic positions and tofalse atoms of the model, respectively). Thanks to these properties some hybridsyntheses can be used in the phase extension and refinement step, to reduce themodel bias and more rapidly move to the target structure. They have beenrecently revisited via the method of joint probability distribution functions[Burla, Carrozzini, Cascarano, Giacovazzo & Polidori (2011). Acta. Cryst. A67,447-455]. The results suggested that VLD could be usefully combined, for abinitio phasing, with the hybrid rather than with the difference Fourier synthesis.This paper explores the feasibility of such a combination and shows that theoriginal VLD algorithm is only one of several variants, all with relevant phasingcapacity. The study explores the role of several parameters in order to design astandard procedure with optimized phasing power.