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.

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.

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.

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.

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.

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.

EDM-DEDM and protein crystal structure solution.

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 combined EDM with DEDM (difference electron-density modification); the method was applied to the refinement of phases obtained by molecular replacement, ab initio or SAD phasing [Caliandro, Carrozzini, Cascarano, Giacovazzo, Mazzone & Siliqi (2009), Acta Cryst. D65, 249-256] and was more effective in improving phases than EDM alone. In this paper, a novel fully automated protocol for protein structure refinement based on the iterative application of automated model-building programs combined with the additional power derived from the EDM-DEDM algorithm is presented. The cyclic procedure was successfully tested on challenging cases for which all other approaches had failed.

Advances in the EDM-DEDM procedure.

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, is expected to provide a representation of the full structure that is more accurate than that obtained by the observed Fourier synthesis. In the same paper, the DEDM algorithm was combined with the EDM (electron-density modification) approach to give the EDM-DEDM procedure which, when applied to practical molecular-replacement cases, was able to improve the model structures. In this paper, it is shown that EDM-DEDM suffers from some critical points that did not allow cyclical application of the procedure. These points are identified and modifications are made to allow iteration of the procedure. The applications indicate that EDM-DEDM may become a fundamental tool in protein crystallography.

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.

Minimally resolution biased electron-density maps.

Electron-density maps are calculated by Fourier syntheses with coefficients based on structure factors. Diffraction experiments provide intensities up to a limited resolution; as a consequence, the Fourier syntheses always show series-termination errors. The worse the resolution, the less accurate is the Fourier representation of the electron density. In general, each atomic peak is shifted from the correct position, shows a deformed (with respect to the true distribution of the electrons in the atomic domain) profile, and is surrounded by a series of negative and positive ripples of gradually decreasing amplitude. An algorithm is described which is able to reduce the resolution bias by relocating the peaks in more correct positions and by modifying the peak profile to better fit the real atomic electron densities. Some experimental tests are performed showing the usefulness of the procedure.

The (Fo-Fc) Fourier synthesis: a probabilistic study.

(F(o)-F(c)) and (2F(o)-F(c)) 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 (F(o)-F(c)). This has allowed a better understanding of the features of the difference Fourier synthesis; in particular, a subset of well phased reflections has been separated from the subset of reflections best phased by the standard F(o) Fourier synthesis. An iterative procedure, based on the electron-density modification of the difference Fourier map, has been devised which aims to improve phase and modulus estimates of the reflections with higher variance value, by using as lever arm the set of reflections with lower variance value. The new procedure (DEDM) has been implemented and verified on a wide set of test structures, the partial models of which were obtained by molecular replacement or by automatic model-building routines applied to experimental electron-density maps. Phase and modulus estimates of the difference Fourier syntheses improve in all the test cases; as a consequence, the quality of the difference Fourier maps also improves in the region where the target structure deviates from the partial model. A new procedure is suggested, combining DEDM with standard electron-density modification techniques, which leads to significant reduction of the phase errors. The procedure may be considered a starting point for further developments.

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.

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.

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.

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.

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.