Giovanni Luca Cascarano

• PhD Crystallography
• Italian National Research Council

Patterson superposition techniques are a historical method for solving the structures of small molecules ab initio, provided they contain heavy atoms in the unit cell. In the 1990s, they were combined with effective EDM procedures and succeeded in the crystal structure solution of macromolecular structures with resolution data up to 1.6–1.9 Å. In t...

A description of REMO22, a new molecular replacement program for proteins and nucleic acids, is provided. This program, as with REMO09, can use various types of prior information through appropriate conditional distribution functions. Its efficacy in model searching has been validated through several test cases involving proteins and nucleic acids....

CAB, a recently described automated model-building (AMB) program, has been modified to work effectively with nucleic acids. To this end, several new algorithms have been introduced and the libraries have been updated. To reduce the input average phase error, ligand heavy atoms are now located before starting the CAB interpretation of the electron-d...

In this study, the properties of observed, difference, and hybrid syntheses (hybrid indicates a combination of observed and difference syntheses) are investigated from two points of view. The first has a statistical nature and aims to estimate the amplitudes of peaks corresponding to the model atoms, belonging or not belonging to the target structu...

Obtaining high-quality models for nucleic acid structures by automated model building programs (AMB) is still a challenge. The main reasons are the rather low resolution of the diffraction data and the large number of rotatable bonds in the main chains. The application of the most popular and documented AMB programs (e.g., PHENIX.AUTOBUILD, NAUTILU...

Although the success of molecular-replacement techniques requires the solution of a six-dimensional problem, this is often subdivided into two three-dimensional problems. REMO09 is one of the programs which have adopted this approach. It has been revisited in the light of a new probabilistic approach which is able to directly derive conditional dis...

The program Buccaneer, a well known fast and efficient automatic model-building program, is also a tool for phase refinement: indeed, input phases are used to calculate electron-density maps that are interpreted in terms of a molecular model, from which new phase estimates may be obtained. This specific property is shared by all other automatic mod...

The method of the joint probability distribution function was applied in order to estimate the normal structure factor amplitudes of the anomalous scatterer substructure in a FEL experiment. The two-wavelength case was examined. In this, the prior knowledge of the moduli (formula Presented) was used to predict the value of |F0a|, which is the struc...

Crystallographic least-squares techniques, the main tool for crystal structure refinement of small and medium-size molecules, are for the first time used for ab initio phasing. It is shown that the chief obstacle to such use, the least-squares severe convergence limits, may be overcome by a multi-solution procedure able to progressively recognize a...

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. To...

Difference electron densities do not play a central role in modern phase refinement approaches, essentially because of the explosive success of the EDM (electron-density modification) techniques, mainly based on observed electron-density syntheses. Difference densities however have been recently rediscovered in connection with the VLD (Vive la Diff...

Direct methods can be used to solve proteins of great structural complexity even when diffraction data are at non-atomic resolution. However, one of the main obstacles to the wider application of direct methods is that they reliably phase only a small fraction of the observed reflections, those with a sufficiently large value of the normalized stru...

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 d...

The efficient multipurpose figure of merit MPF has been defined and characterized. It may be very helpful in phasing procedures. Indeed, it might be used for establishing the centric or acentric nature of an unknown structure, for identifying the presence of some pseudotranslational symmetry, for recognizing the correct solution in multisolution ap...

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 factor...

A new probabilistic formula estimating triplet invariants and capable of exploiting a model electron-density map gradually created during the ab initio phasing process has been tested on a set of protein structures with data at non-atomic resolution. All the structures contain heavy atoms larger than Ca, and show a structural complexity which may a...

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 e...

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 subst...

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...

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 a...

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...

A fully ordered structure is reported for the polymorph of tri­phenyl­silanol–4,4′-bipyridyl (4/1), 4C18H16OSi·C10H8N2, having Z′ = 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 o...

A new study of the σA parameter has been undertaken to understand its behaviour when the diffraction amplitude distributions are far from the standard Wilson distributions. The study has led to the formulation of a new statistical interpretation of σA, expressed in terms of a correlation factor. The new formulas allow a more accurate use of σA in e...

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 usu...

The VLD algorithm relies on the properties of the difference Fourier synthesis and is designed for solving crystal structures in the correct space group, starting from random models. The standard approach has been modified by integrating it with the RELAX procedure, for translating to the correct position misplaced but correctly oriented models. A...

The cross-correlation function between the target and a model electron density, denoted as the C map, has been crystallographically characterized. In particular, a study of its interatomic vectors and of their relation with the Patterson vectors has been undertaken. Since the C map is not available during the phasing process, the C′ map, its centri...

The structure determination of porous materials is always a challenging problem, especially when big high quality crystals are not available. Electron crystallography is a unique technique to tackle this problem since it can provide structural information from tiny crystals. 1 High resolution transmission electron microscope (HRTEM) images can be e...

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 co...

The identification of the extinction symbol is routine for single-crystal X-ray data. Because of peak overlap and possible preferred orientation the task is more difficult for powder diffraction data, but recent computer programs based on probabilistic approaches have made it more automatic. This paper describes a new algorithm for the automatic id...

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 implemente...

α-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 α-helices in the crystal cell by molecu...

The VLD algorithm relies on the properties of the difference Fourier synthesis and is designed for solving crystal structures in the correct space group, starting from random models. The standard approach has been modified by integrating it with the RELAX procedure, for translating to the correct position misplaced but correctly oriented models. A...

The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst. A66, 347–361]. New Fourier coefficients were devised which were the basis of a new ab initio method for the solution of the phase problem (i.e. VLD, vive la difference). In this paper we study the...

The crystal structure solution of small-medium size molecules via single crystal X-ray data is almost a routine process. When single crystals of sufficient dimensions are not available, electron diffraction is a useful alternative: the structure solution however may still be a challenge. We have modified the standard version of Sir2008 to include s...

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...

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 e...

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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 approxi...

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 infor...

Electron-density modification (EDM) procedures are the classical tool for driving model phases closer to those of the target structure. They are often combined with automated model-building programs to provide a correct protein model. The task is not always performed, mostly because of the large initial phase error. A recently proposed procedure co...

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...

The DEDM (difference electron-density modification) algorithm has been described in a recent paper [Caliandro et al. (2008), Acta Cryst. A64, 519–528]: it breaks down the collinearity between model structure phases and difference structure phase estimates. The new difference electron-density pro­duced by DEDM, summed to the calculated Fourier maps,...

(Fo − Fc) and (2Fo − Fc) Fourier syntheses are considered the most powerful tools for recovering the remainder of a structure and for correcting crystal structure models. A probabilistic approach has been applied to derive the formula for the variance for the expected value of the coefficient (Fo − Fc). This has allowed a better understanding of th...

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 ba...

New algorithms have been devised and implemented in the program SIR2007 for the deconvolution of Patterson maps via the use of implication transformations and of the minimum superposition function. The new algorithms concern several practical aspects, such as the use of weighted Patterson syntheses to simplify the recognition of useful pivot peaks,...

In the present paper, the third and last of a series ( the first two papers were dedicated to the crystal structure solution of proteins), the Patterson superposition method, based on the use of the symmetry minimum function, has been applied to powder diffraction patterns. The method has been modified to take into account the special challenges of...

The most critical limit of macromolecular crystallography, the experimental data resolution, is partially `tricked' by the `free lunch method' ( non-measured reflection extrapolation). The best electron density map available when only observed data are used may be employed to extrapolate moduli and phases of unobserved reflections behind and beyond...

IL MILIONE(1) is a suite of computer programs devoted to protein crystal structure determination by X-ray crystallography. It may be used in the following key activities. ( a) Ab initio phasing, via Patterson or direct methods. The program may succeed even with structures with up to 6000 non-H atoms in the asymmetric unit, provided that atomic reso...

The Patterson techniques, recently developed by the same authors for the ab initio crystal structure solution of proteins, have been applied to single and multiple anomalous diffraction (SAD and MAD) data to find the substructure of the anomalous scatterers. An automatic procedure has been applied to a large set of test structures, some of which we...

The Patterson superposition methods described by Burla et al. [ J. Appl. Cryst. (2006), 39 , 527–535], based on the use of the `multiple implication functions', have been enriched by supplementary filtering techniques based on some general (resolution-dependent) features of both the Patterson and the electron density maps. The method has been imple...

Direct methods combined with direct-space refinement procedures are the standard tools for ab initio crystal structure solution of macromolecules via diffraction data collected up to atomic or quasi-atomic resolution. An entirely direct-space approach is described here: it includes an automated Patterson deconvolution method, based on the minimum s...

A new program for molecular replacement, REMO, has been written. In the rotation step, the orientation of the model molecule is found by rotating the weighted reciprocal lattice of the protein with respect to the calculated transform of the model structure: the fitting is searched in the reciprocal space. The space group of the model structure is a...

Owing to the limited experimental resolution of data in macromolecular crystallography, ab initio phasing is successful only when atomic or quasi-atomic resolution data are available. It is shown that extrapolating the moduli and phases of non-measured reflections beyond and behind the experimental resolution limit makes the ab initio phasing proce...

The case of imperfect partial structures has been revisited via the method of joint probability distribution functions.

The method of the joint probability distribution functions has been applied to the case in which observed (with errors) and calculated structure factors are available, the latter referred to a part of the structure with finite errors in the coordinates, the thermal parameters and the scattering factors. Results obtained by other authors are confirm...

Limited experimental resolution is a unavoidable feature in macromolecular crystallography: it may hinder or make difficult the determination of the crystal structure. A novel procedure is presented which from an approximate electron-density map extrapolates the moduli and phases of non-measured reflections beyond and behind the experimental resolu...

SIR2004 is the evolution of the SIR2002 program [Burla, Camalli, Carrozzini, Cascarano, Giacovazzo, Polidori & Spagna ( 2003). J. Appl. Cryst. 36, 1103]. It is devoted to the solution of crystal structures by direct and Patterson methods. Several new features implemented in SIR2004 make this program efficient: it is able to solve ab initio both sma...

All ab initio techniques for solving protein crystal structures use multisolution approaches. Several figures of merit that are found in the literature are efficient in the last steps of the phasing process, when some trials converge to the correct solution with a relatively small average phase error. Early figures of merit are much more critical;...

Two algorithms are described for limiting data resolution and for predicting the most informative wavelength combinations in MAD techniques. Both have been successfully tested using experimental data from a large set of test structures.

A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV en...

A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV en...

Up close and flexible: An X-ray diffraction analysis of a Bpa-containing analogue of the lipopeptaibol trichogin GA IV strongly points to the conclusion that caution should be exercised in utilizing this highly flexible, benzophenone-based photoprobe acritically in biochemical and biophysical studies. As a result of the different side-chain conform...

An automated Patterson deconvolution technique, based on the minimum superposition function, has been implemented into the SIR2002 package, a program for the ab initio determination of small and large molecules. The procedure, combined with the direct-space phase refinement routines present in the SIR2002 program, has been designed to solve protein...

The conformations of two [2]rotaxanes, each comprising alpha-cyclodextrin as the rotor, a stilbene as the axle and 2,4,6-trinitrophenyl substituents as the capping groups, have been examined in solution and in the solid state, using (1)H NMR spectroscopy and X-ray crystallography, respectively. In solution, introducing substituents onto the stilben...

New algorithms for solving ab initio protein crystal structures have been identified and implemented in a modified version of the program SIR2002. They succeed in solving numerous protein structures diffracting at atomic resolution; the solution was also attained when data were cut at 1.4 Å resolution. The direct-space refinement procedure of SIR20...

A new direct-methods program, SIR2002, which has been designed to solve both small and large crystal structures, is described.

All the techniques today available for the ab initio crystal structure solution of proteins require that the atomicity condition is satisfied. Accordingly, diffraction data at resolution equal or better than 1.2 Å are necessary. This condition reduces the role of the ab initio techniques in macromolecular crystallography. The computer program SIR20...

The problem of reconstructing the charge density of a non-periodic sample from its diffuse X-ray scattering is considered. For a sample known to be isolated, an artificial superlattice may be assumed and the numerical direct methods of crystallography applied to the continuous distribution of diffuse scattering in order to solve the phase problem....

The method of joint probability distribution functions is applied in order to estimate the structure-factor moduli of the anomalous scatterer substructure both in the SAD (single-wavelength anomalous dispersion) and in the MAD (multi-wavelength anomalous dispersion) cases. The experimental data ||, ||, …, ||, || measured at n wavelengths are used s...

The program SIR2002, the heir of SIR2000-N, shows two important new features: a) a figure of merit which is able to recognize the trials potentially able to provide the correct solution; b) a procedure capable of exploiting electron density distributions misplaced with respect to the correct origin. The two features dramatically increase the power...