Advances in thefree lunchmethod

A new density-modification procedure extending the application of the recent |ρ|-based phasing algorithm to larger crystal structures

The incorporation of the new peakness-enhancing fast Fourier transform compatible ipp procedure (ipp = inner-pixel preservation) into the recently published S_M algorithm based on |ρ| [Rius (2020). Acta Cryst A76, 489-493] improves its phasing efficiency for larger crystal structures with atomic resolution data. Its effectiveness is clearly demonstrated via a collection of test crystal structures (taken from the Protein Data Bank) either starting from random phase values or by using the randomly shifted modulus function (a Patterson-type synthesis) as initial ρ estimate. It has been found that in the presence of medium scatterers (e.g. S or Cl atoms) crystal structures with 1500 × c atoms in the unit cell (c = number of centerings) can be routinely solved. In the presence of strong scatterers like Fe, Cu or Zn atoms this number increases to around 5000 × c atoms. The implementation of this strengthened S_M algorithm is simple, since it only includes a few easy-to-adjust parameters.

Resolution Dependence of an Ab Initio Phasing Method in Protein X-ray Crystallography

For direct phasing of protein crystals, a method based on the hybrid-input-output (HIO) algorithm has been proposed and tested on a variety of structures. So far, however, the diffraction data have been limited to high-resolution ones, i.e., higher than 2 Å. In principle, the methodology can be applied to data of lower resolutions, which might be particularly useful for phasing membrane protein crystals. For resolutions higher than 3.5 Å, it seems the atomic structure is solvable. For data of lower resolutions, information of the secondary structures and the protein boundary can still be obtained. Examples are given to support the conclusions. Real experimental data are used. Two aspects of the observed data have been discussed: removal of the measured low-resolution reflections and involvement of the unmeasured high-resolution reflections. The ab initio phasing employs histogram matching for density modification. A question arises whether the reference histogram used should match the resolution of the diffraction data or not. It seems that there is an optimal histogram which is good to use for data at various resolutions.

Solving proteins at non-atomic resolution by direct methods: update

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 structure factor amplitude. The subsequent phase expansion and refinement required for full structure solution are difficult. Here a new phase refinement procedure is described, which combines (1–2) difference Fourier synthesis with electron density modification techniques and thevive la differenceand Free Lunch algorithms. This procedure is able to solve data resistant to other direct space refinement procedures.

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 usenphantom derivatives, withn≥ 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.

Experimental Phasing: Substructure Solution and Density Modification as Implemented in SHELX

This chapter describes experimental phasing methods as implemented in SHELX. After introducing fundamental concepts underlying all experimental phasing approaches, the methods used by SHELXC/D/E are described in greater detail, such as dual-space direct methods, Patterson seeding and density modification with the sphere of influence algorithm. Intensity differences from data for experimental phasing can also be used for the generation and usage of difference maps with ANODE for validation and phasing purposes. A short section describes how molecular replacement can be combined with experimental phasing methods. The second half covers practical challenges, such as prerequisites for successful experimental phasing, evaluation of potential solutions, and what to do if substructure search or density modification fails. It is also shown how auto-tracing in SHELXE can improve automation and how it ties in with automatic model building after phasing.

Constraint-induced direct phasing method

The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimetre in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented microcrystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern. Although single-crystal diffraction data consist of discrete spots or X-ray reflections, the diffraction of microcrystals in a powder forms rings so that the reflections overlap. Thus, the analysis is more challenging due to unavoidable errors in the structure-factor amplitudes and the low-resolution data available for structure determination. This paper introduces a constraint-induced phasing method that (i) improves structure solutions measured by success rate, quality of solutions and various figures of merit, and (ii) extends low-resolution powder diffraction data to atomic resolution by adding unmeasured reflections. Application results have shown clearly that the constraint-induced phasing method is an effective way to produce initial structure models that are suitable for further structural refinement and completion.

Direct-methods structure determination of a trypanosome RNA-editing substrate fragment with translational pseudosymmetry

Using direct methods starting from random phases, the crystal structure of a 32-base-pair RNA (675 non-H RNA atoms in the asymmetric unit) was determined using only the native diffraction data (resolution limit 1.05 Å) and the computer program SIR2014. The almost three helical turns of the RNA in the asymmetric unit introduced partial or imperfect translational pseudosymmetry (TPS) that modulated the intensities when averaged by the l Miller indices but still escaped automated detection. Almost six times as many random phase sets had to be tested on average to reach a correct structure compared with a similar-sized RNA hairpin (27 nucleotides, 580 non-H RNA atoms) without TPS. More sensitive methods are needed for the automated detection of partial TPS.

Phase improvementviathePhantom Derivativetechnique: 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 byab initioapproaches. Here, a novel method to expand density modification is presented, termed thePhantom derivativetechnique, which is based on non-existent structure factors and is of particular interest in molecular replacement. ThePhantom derivativeapproach 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 forab initiophasing 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: theREVANpipeline

TheREVANpipeline aiming at the solution of protein structuresviamolecular replacement (MR) has been assembled. It is the successor toREVA, a pipeline that is particularly efficient when the sequence identity (SI) between the target and the model is greater than 0.30. TheREVANandREVAprocedures coincide when the SI is >0.30, but differ substantially in worse conditions. To treat these cases,REVANcombines a variety of programs and algorithms (REMO09,REFMAC,DM,DSR,VLD,free lunch,Coot,Buccaneerandphenix.autobuild). The MR model, suitably rotated and positioned, is first refined by a standardREFMACrefinement procedure, and the corresponding electron density is then submitted to cycles ofDM–VLD–REFMAC. The nextREFMACapplications exploit the better electron densities obtained at the end of theVLD–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 whichCootplays a basic role, and it is then cyclically resubmitted toREFMAC–EDM–VLDcycles. The phases thus obtained are submitted tofree lunchand allow most of the test structures studied by DiMaioet al.[(2011),Nature (London),473, 540–543] to be solved without using energy-guided programs.

Refining a model electron-density mapviathePhantom Derivativemethod

ThePhantom Derivative(PhD) method [Giacovazzo (2015),Acta Cryst.A71, 483–512] has recently been described forab initioand non-ab initiophasing. 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 initiovariant 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 ofPhDis able to extend and refine phases in a way that is competitive with other electron-density modification techniques.

Analysis of rapidly synthesized guest-filled porous complexes with synchrotron radiation: practical guidelines for the crystalline sponge method

A detailed set of synthetic and crystallographic guidelines for the crystalline sponge method based upon the analysis of expediently synthesized crystal sponges using third-generation synchrotron radiation are reported. The procedure for the synthesis of the zinc-based metal-organic framework used in initial crystal sponge reports has been modified to yield competent crystals in 3 days instead of 2 weeks. These crystal sponges were tested on some small molecules, with two being unexpectedly difficult cases for analysis with in-house diffractometers in regard to data quality and proper space-group determination. These issues were easily resolved by the use of synchrotron radiation using data-collection times of less than an hour. One of these guests induced a single-crystal-to-single-crystal transformation to create a larger unit cell with over 500 non-H atoms in the asymmetric unit. This led to a non-trivial refinement scenario that afforded the best Flack x absolute stereochemical determination parameter to date for these systems. The structures did not require the use of PLATON/SQUEEZE or other solvent-masking programs, and are the highest-quality crystalline sponge systems reported to date where the results are strongly supported by the data. A set of guidelines for the entire crystallographic process were developed through these studies. In particular, the refinement guidelines include strategies to refine the host framework, locate guests and determine occupancies, discussion of the proper use of geometric and anisotropic displacement parameter restraints and constraints, and whether to perform solvent squeezing/masking. The single-crystal-to-single-crystal transformation process for the crystal sponges is also discussed. The presented general guidelines will be invaluable for researchers interested in using the crystalline sponge method at in-house diffraction or synchrotron facilities, will facilitate the collection and analysis of reliable high-quality data, and will allow construction of chemically and physically sensible models for guest structural determination.

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 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.