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. Although REMO22 can be configured with different protocols according to user directives, it has been developed primarily as an automated tool for determining the crystal structures of macromolecules. To evaluate REMO22's utility in the current crystallographic environment, its experimental results must be compared favorably with those of the most widely used Molecular Replacement (MR) programs. To accomplish this, we chose two leading tools in the field, PHASER and MOLREP. REMO22, along with MOLREP and PHASER, were included in pipelines that contain two additional steps: phase refinement (SYNERGY) and automated model building (CAB). To evaluate the effectiveness of REMO22, SYNERGY and CAB, we conducted experimental tests on numerous macromolecular structures. The results indicate that REMO22, along with its pipeline REMO22 + SYNERGY + CAB, presents a viable alternative to currently used phasing tools.

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. Furthermore, alternative approaches are used depending on whether the ligands belong to the target or to the model chain used in the molecular-replacement step. Robust criteria are then applied to decide whether the AMB model is acceptable or whether it must be modified to fit prior information on the target structure. In the latter case, the model chains are rearranged to fit prior information on the target chains. Here, the performance of the new AMB program CAB applied to various nucleic acid structures is discussed. Other well documented programs such as Nautilus, ARP/wARP and phenix.autobuild were also applied and the experimental results are described.

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. The conditional distributions take into account various types of prior information: in the rotation step the prior information may concern a non-oriented model molecule alone or together with one or more located model molecules. The formulae thus obtained are used to derive figures of merit for recognizing the correct orientation in the rotation step and the correct location in the translation step. The phases obtained by this new version of REMO09 are used as a starting point for a pipeline which in its first step extends and refines the molecular-replacement phases, and in its second step creates the final electron-density map which is automatically interpreted by CAB, an automatic model-building program for proteins and DNA/RNA structures.

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. A good feature of direct methods is that they may work in the absence of any prior information: that is also their weakness. Different types of prior information have been taken into consideration: interatomic distances, interatomic vectors, Patterson peaks, structural model. The method of directly deriving the conditional distributions has been applied to those cases. Some new formulas have been obtained estimating two-, three- and four-phase invariants. Special attention has been dedicated to the practical aspects of the new formulas, in order to simplify their possible use in direct phasing procedures.

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. CAB has been tested on 81 protein structures that were solved via molecular-replacement, anomalous dispersion and ab initio methods. The corresponding phases were submitted to a phase-refinement process that synergically combines current phase-refinement techniques and out-of-mainstream refinement methods [Burla et al. (2017), Acta Cryst. D73, 877-888]. The phases thus obtained were used as input for CAB. The experimental results were compared with those obtained by the sole use of Buccaneer: it is shown that CAB improves the Buccaneer results, both in completeness and in accuracy.

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.g. no electron-density map is calculated as a support for the least-squares procedure.

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. 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.

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 - Fp, mF - Fp and mF - DFp syntheses, are studied. In addition, a fourth new difference synthesis, here denoted as {\overline F_q} synthesis, is proposed. It comes from the study of the same joint probability distribution function from which the VLD approach arose. The properties of the {\overline F_q} syntheses are studied and compared with those of the other three syntheses. The results suggest that the {\overline F_q} difference may be a useful tool for making modern phase refinement procedures more efficient.

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. 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 ϕ (the target phase) were performed; the favourable results confirm the correctness of the theoretical calculations and of the corresponding analysis.

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. Thus, phase improvement or deterioration may be monitored and useless models may be discarded to save computing time. It is also shown that MPF may be applied in different phasing approaches, no matter if ab initio or non ab initio.

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. 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.

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. 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.

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. 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.

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. No observed diffraction amplitudes are available for them: in order to emphasize their unreal nature, the term phantom is added. The paper describes the theoretical basis by which the phantom derivative method may be used to phase the target structure. It may be guessed that 100-300 ancil structures may be sufficient for phasing a target structure, so that the phasing technique may be denoted as the multiple phantom derivative method. Ancil phases and amplitudes may be initially combined with observed target magnitudes to estimate amplitudes and phases of the corresponding phantom derivative. From them suitable algorithms allow one to obtain poor target phase estimates, which are often improved by combining the indications arising from each derivative. Probabilistic criteria are described to recognize the most reliable target phase estimates. The method is cyclic: the target phase estimates just obtained are used to improve amplitudes and phases of each derivative, which, in their turn, are employed to provide better target phase estimates. The method is a fully ab initio method, because it needs only the experimental data of the target structure. The term derivative is maintained with reference to SIR-MIR (single isomorphous replacement-multiple isomorphous replacement) techniques, even if its meaning is different: therefore the reader should think of the phantom derivative method more as a new method than as a variant of SIR-MIR techniques. The differences are much greater than the analogies. The paper also describes how phantom derivatives may be used for improving structure models obtained via other ab initio or non-ab initio techniques. The method is expected to be insensitive to the structural complexity of the target and to the target experimental data resolution, provided it is better than 4-6 Å.

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. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available.

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 Šresolution 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.

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. 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 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.

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. It may be computed at any stage of the phasing process and shows properties that are very useful for the crystal structure determination process. It has been combined with the implication transformation method and with vector-superposition techniques for performing the Patterson deconvolution and obtaining an initial model for dual-space recycling. While Patterson methods are traditionally considered to be more efficient for structures containing heavy atoms, the C map extends their potential to light-atom structures (i.e. containing atoms not heavier than O).

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. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.