The Automatic Solution of Macromolecular Crystal Structures via Molecular Replacement Techniques: REMO22 and Its Pipeline.

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.

Towards the automatic crystal structure solution of nucleic acids: automated model building using the new CAB program.

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-density maps.

How far are we from automatic crystal structure solution via molecular-replacement techniques?

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 distribution functions without passing through a previous calculation of the joint probability distributions.

Updating direct methods.

The standard method of joint probability distribution functions, so crucial for the development of direct methods, has been revisited and updated. It consists of three steps: identification of the reflections which may contribute to the estimation of a given structure invariant or seminvariant, calculation of the corresponding joint probability distribution, and derivation of the conditional distribution of the invariant or seminvariant phase given the values of some diffracted amplitudes. In this article the conditional distributions are derived directly without passing through the second step.

CAB: a cyclic automatic model-building procedure.

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 model-building programs and allows their cyclic use, as is usually performed in other phase-refinement methods (for example electron-density modification techniques). Buccaneer has been included in a cyclic procedure, called CAB, aimed at increasing the rate of success of Buccaneer and the quality of the molecular models provided.

Phasing via pure crystallographic least squares: an unexpected feature.

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 and discard model atoms in false positions and to include in the current model new atoms sufficiently close to correct positions. The applications show that the least-squares procedure is able to solve many small structures without the use of important ancillary tools: e.

Synergy among phase-refinement techniques in macromolecular crystallography.

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.

About difference electron densities and their properties.

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 Difference) approach, because they are a strong support for strengthening EDM approaches and for ab initio crystal structure solution. In this paper the properties of the most documented difference electron densities, here denoted as F - F, mF - F and mF - DF syntheses, are studied.

The phantom derivative method when a structure model is available: about its theoretical basis.

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.

MPF, a multipurpose figure of merit for phasing procedures.

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 approaches and for estimating the quality of structure models as they become available during the phasing process.

Phase improvement via the Phantom Derivative technique: ancils that are related to the target structure.

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.

Refining a model electron-density map via the Phantom Derivative method.

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.

Advances in molecular-replacement procedures: the REVAN pipeline.

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.

Solution of the phase problem at non-atomic resolution by the phantom derivative method.

For a given unknown crystal structure (the target), n random structures, arbitrarily designed without any care for their chemical consistency and usually uncorrelated with the target, are sheltered in the same unit cell as the target structure and submitted to the same space-group symmetry. (These are called ancil structures.) The composite structures, whose electron densities are the sum of the target and of the ancil electron densities, are denoted derivatives.

From direct-space discrepancy functions to crystallographic least squares.

Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency.

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.

Triphenylsilanol-4,4'-bipyridyl (4/1): the Z' = 4 polymorph revisited.

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 of triphenylsilanol molecules linked to the first pair via O-H···O hydrogen bonds. An extensive series of C-H···π(arene) hydrogen bonds links these aggregates into complex sheets.

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.

On the use of the C map in Patterson deconvolution procedures.

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 centric modification, is considered.

Covariance and correlation estimation in electron-density maps.

Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al.

About the hybrid Fourier syntheses: a probabilistic approach.

The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst.

Estimation of the variance in any point of an electron-density map for any space group.

In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218] a mathematical expression of the variance at any point of the unit cell has been described.

About the σA estimate.

The resolution parameter σ(A) is currently used for evaluating the degree of similarity between a model and the target structure. Here, quasi-Wilson distributions are used to represent the local statistics of the normalized amplitudes both for the target and for the model structure. The study uses the joint probability distribution approach to provide (i) a description of the statistical properties of the σ(A) parameter; (ii) a deeper insight into the role, for the σ(A) estimate, of the high-order moments of the target and of the model structure-factor distributions; and (iii) new statistical formulas for estimating σ(A).

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.