Low-resolution Diffraction Data Research Articles

Direct phasing algorithm for protein crystals with high solvent content using low-resolution diffraction data.

Over the past decade, iterative projection algorithms, an effective approach to recovering phases from a single intensity measurement, have found application in protein crystallography to directly surmount the `phase problem'. However, previous studies have always assumed that some prior knowledge constraints (i.e. a low-resolution envelope about the protein structure in the crystal cell or histogram matching requiring a similar density distribution to the target crystal) must be known for successful phase retrieval, thus hindering its widespread application. In this study, a novel phase-retrieval workflow is proposed that eliminates the need for a reference density distribution by utilizing low-resolution diffraction data in phasing algorithms. The approach involves randomly assigning one out of 12 possible phases at 30° intervals (or two for centric reflections) to produce an initial envelope, which is then refined through density modification after each run of phase retrieval. To evaluate the success of the phase-retrieval procedure, information entropy is introduced as a new metric. This approach was validated using ten protein structures with high solvent content, demonstrating its effectiveness and robustness.

Homology-based loop modeling yields more complete crystallographic protein structures.

Inherent protein flexibility, poor or low-resolution diffraction data or poorly defined electron-density maps often inhibit the building of complete structural models during X-ray structure determination. However, recent advances in crystallographic refinement and model building often allow completion of previously missing parts. This paper presents algorithms that identify regions missing in a certain model but present in homologous structures in the Protein Data Bank (PDB), and 'graft' these regions of interest. These new regions are refined and validated in a fully automated procedure. Including these developments in the PDB-REDO pipeline has enabled the building of 24 962 missing loops in the PDB. The models and the automated procedures are publicly available through the PDB-REDO databank and webserver. More complete protein structure models enable a higher quality public archive but also a better understanding of protein function, better comparison between homologous structures and more complete data mining in structural bioinformatics projects.

Towards in cellulo virus crystallography

Viruses are a significant threat to both human health and the economy, and there is an urgent need for novel anti-viral drugs and vaccines. High-resolution viral structures inform our understanding of the virosphere, and inspire novel therapies. Here we present a method of obtaining such structural information that avoids potentially disruptive handling, by collecting diffraction data from intact infected cells. We identify a suitable combination of cell type and virus to accumulate particles in the cells, establish a suitable time point where most cells contain virus condensates and use electron microscopy to demonstrate that these are ordered crystalline arrays of empty capsids. We then use an X-ray free electron laser to provide extremely bright illumination of sub-micron intracellular condensates of bacteriophage phiX174 inside living Escherichia coli at room temperature. We have been able to collect low resolution diffraction data. Despite the limited resolution and completeness of these initial data, due to a far from optimal experimental setup, we have used novel methodology to determine a putative space group, unit cell dimensions, particle packing and likely maturation state of the particles.

Structure determination from X-ray powder diffraction data at low resolution

Knowledge of the structural arrangement of atoms in solids is necessary to facilitate the study of their properties. The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimeter 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 micro-crystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern. Direct Methods routinely solve crystal structures when single-crystal diffraction data are available at atomic resolution (1.0-1.2Å), but fail to determine micro-crystal structures due to reflections overlapping and low-resolution powder diffraction data. By artificially and intelligently extending the measured data to atomic resolution, we have successfully solved structures having low-resolution diffraction data that were hard to solve by other direct-method based computation procedures. The newly developed method, Powder Shake-and-Bake, is implemented in a computer program PowSnB. PowSnB can be incorporated into the state-of-the-art software package EXPO that includes powder data reduction, structure determination and structure refinement. The new combination could have potential to solve structures that have never been solved before by direct-methods approach.

Issues in solving complex molecular crystal structures from lab PXRD data

Developments (both software and methodological) in crystal structure determination from powder X-ray diffraction data have resulted in increasingly complex molecular structures now being solved from relatively low-resolution diffraction data. This can lead to the publication of structures that clearly do not meet the rigorous chemical and crystallographic standards that one normally associates with published crystal structures. As such, considerable attention should be paid to the quality of the final refined crystal structure, with chemical sense playing as important a role as the fit of the structure to the data. This presentation will focus upon some issues that impact upon the final quality of the published structure as derived from lab PXRD data, and suggest strategies for maximising the chances of a successful structure solution and refinement. These include the preparation of structural models for use in global optimisation, the use of rigid-body-type refinements, the critical assessment of output crystal structures and the use of DFT-D to validate such crystal structures. The presentation will be illustrated with examples drawn mostly from the world of pharmaceutical research and will include an introduction that puts the role of structure determination from powder diffraction data into context in terms of accessible structural complexity.

Polarizable atomic multipole X-ray refinement: weighting schemes for macromolecular diffraction

In the past, weighting between the sum of chemical and data-based targets in macromolecular crystallographic refinement was based on comparing the gradients or Hessian diagonal terms of the two potential functions. Here, limitations of this scheme are demonstrated, especially in the context of a maximum-likelihood target that is inherently weighted by the model and data errors. In fact, the congruence between the maximum-likelihood target and a chemical potential based on polarizable atomic multipole electrostatics evaluated with Ewald summation has opened the door to a transferable static weight. An optimal static weight is derived from first principles and is demonstrated to be transferable across a broad range of data resolutions in the context of a recent implementation of X-ray crystallographic refinement using the polarizable AMOEBA force field and it is shown that the resulting models are balanced with respect to optimizing both R(free) and MolProbity scores. Conversely, the classical automatic weighting scheme is shown to lead to underfitting or overfitting of the data and poor model geometry. The benefits of this approach for low-resolution diffraction data, where the need for prior chemical information is of particular importance, are also highlighted. It is demonstrated that this method is transferable between low- and high-resolution maximum-likelihood-based crystallographic refinement, which proves for the first time that resolution-dependent parameterization of either the weight or the chemical potential is unnecessary.

Crystal structure of a novel non-Pfam protein PF2046 solved using low resolution B-factor sharpening and multi-crystal averaging methods

Sometimes crystals cannot diffract X-rays beyond 3.0 Å resolution due to the intrinsic flexibility associated with the protein. Low resolution diffraction data not only pose a challenge to structure determination, but also hamper interpretation of mechanistic details. Crystals of a 25.6 kDa non-Pfam, hypothetical protein, PF2046, diffracted X-rays to 3.38 Å resolution. A combination of Se-Met derived heavy atom positions with multiple cycles of B-factor sharpening, multi-crystal averaging, restrained refinement followed by manual inspection of electron density and model building resulted in a final model with a R value of 23.5 (R(free)= 24.7). The asymmetric unit was large and consisted of six molecules arranged as a homodimer of trimers. Analysis of the structure revealed the presence of a RNA binding domain suggesting a role for PF2046 in the processing of nucleic acids.

Super-resolution biomolecular crystallography with low-resolution data.

X-ray diffraction plays a pivotal role in understanding of biological systems by revealing atomic structures of proteins, nucleic acids, and their complexes, with much recent interest in very large assemblies like the ribosome. Since crystals of such large assemblies often diffract weakly (resolution worse than 4 Å), we need methods that work at such low resolution. In macromolecular assemblies, some of the components may be known at high resolution, while others are unknown: current refinement methods fail as they require a high-resolution starting structure for the entire complex1. Determining such complexes, which are often of key biological importance, should be possible in principle as the number of independent diffraction intensities at a resolution below 5 Å generally exceed the number of degrees of freedom. Here we introduce a new method that adds specific information from known homologous structures but allows global and local deformations of these homology models. Our approach uses the observation that local protein structure tends to be conserved as sequence and function evolve. Cross-validation with Rfree determines the optimum deformation and influence of the homology model. For test cases at 3.5 – 5 Å resolution with known structures at high resolution, our method gives significant improvements over conventional refinement in the model coordinate accuracy, the definition of secondary structure, and the quality of electron density maps. For re-refinements of a representative set of 19 low-resolution crystal structures from the PDB, we find similar improvements. Thus, a structure derived from low-resolution diffraction data can have quality similar to a high-resolution structure. Our method is applicable to studying weakly diffracting crystals using X-ray micro-diffraction2 as well as data from new X-ray light sources3. Use of homology information is not restricted to X-ray crystallography and cryo-electron microscopy: as optical imaging advances to sub-nanometer resolution4,5, it can use similar tools.

Interpreting a Low Resolution Map of Human U1 snRNP Using Anomalous Scatterers

SummaryWe recently determined the crystal structure of the functional core of human U1 snRNP, consisting of nine proteins and one RNA, based on a 5.5 Å resolution electron density map. At 5–7 Å resolution, α helices and β sheets appear as rods and slabs, respectively, hence it is not possible to determine protein fold de novo. Using inverse beam geometry, accurate anomalous signals were obtained from weakly diffracting and radiation sensitive P1 crystals. We were able to locate anomalous scatterers with positional errors below 2 Å. This enabled us not only to place protein domains of known structure accurately into the map but also to trace an extended polypeptide chain, of previously undetermined structure, using selenomethionine derivatives of single methionine mutants spaced along the sequence. This method of Se-Met scanning, in combination with structure prediction, is a powerful tool for building a protein of unknown fold into a low resolution electron density map.

Dimeric Quaternary Structure of the Prototypical Dual Specificity Phosphatase VH1

The Vaccinia virus H1 gene product, VH1, is a dual specificity phosphatase that down-regulates the cellular antiviral response by dephosphorylating STAT1. The crystal structure of VH1, determined at 1.32 A resolution, reveals a novel dimeric quaternary structure, which exposes two active sites spaced approximately 39 A away from each other. VH1 forms a stable dimer via an extensive domain swap of the N-terminal helix (residues 1-20). In vitro, VH1 can dephosphorylate activated STAT1, in a reaction that is competed by the nuclear transport adapter importin alpha5. Interestingly, VH1 is inactive with respect to STAT1 bound to DNA, suggesting that the viral phosphatase acts predominantly on the cytoplasmic pool of activated STAT1. We propose that the dimeric quaternary structure of VH1 is essential for specific recognition of activated STAT1, which prevents its nuclear translocation, thus blocking interferon-gamma signal transduction and antiviral response.

The Fourier transforms of curves and filaments and their application to low-resolution protein crystallography

A numerical method for computing the Fourier transform of an arbitrary space curve is described. The method is applicable to all sufficiently smooth curves and relies on the local geometric parameters describing a curve. The numerical results for a helical curve are compared with the exact analytical theory for the transform of a helix. It is shown that the transform of a filamentary density distribution radially symmetric around a curve is equivalent to the transform of that curve scaled by an appropriately defined weight function. These filamentary density distributions in conjunction with the numerical transform evaluation method can be used for simulating low-resolution diffraction data for protein crystals. Crystallographic structure factors obtained from a filament model representing a simple three-helix-bundle protein are compared with those calculated from conventional coordinate models. At low resolution, the filamentary representation provides an excellent approximation of the structure factors obtained from the standard coordinate model, but requires far fewer independent parameters.

X-ray structure determination at low resolution

As an example of structure determination in the 3.5-4.5 A resolution range, crystal structures of the ATPase p97/VCP, consisting of an N-terminal domain followed by a tandem pair of ATPase domains (D1 and D2), are discussed. The structures were originally solved by molecular replacement with the high-resolution structure of the N-D1 fragment of p97/VCP, whereas the D2 domain was manually built using its homology to the D1 domain as a guide. The structure of the D2 domain alone was subsequently solved at 3 A resolution. The refined model of D2 and the high-resolution structure of the N-D1 fragment were then used as starting models for re-refinement against the low-resolution diffraction data for full-length p97. The re-refined full-length models showed significant improvement in both secondary structure and R values. The free R values dropped by as much as 5% compared with the original structure refinements, indicating that refinement is meaningful at low resolution and that there is information in the diffraction data even at approximately 4 A resolution that objectively assesses the quality of the model. It is concluded that de novo model building is problematic at low resolution and refinement should start from high-resolution crystal structures whenever possible.

Improved Structures of Full-Length p97, an AAA ATPase: Implications for Mechanisms of Nucleotide-Dependent Conformational Change

The ATPases associated with various cellular activities (AAA) protein p97 has been implicated in a variety of cellular processes, including endoplasmic reticulum-associated degradation and homotypic membrane fusion. p97 belongs to a subgroup of AAA proteins that contains two nucleotide binding domains, D1 and D2. We determined the crystal structure of D2 at 3.0 A resolution. This model enabled rerefinement of full-length p97 in different nucleotide states against previously reported low-resolution diffraction data to significantly improved R values and Ramachandran statistics. Although the overall fold remained similar, there are significant improvements, especially around the D2 nucleotide binding site. The rerefinement illustrates the importance of knowledge of high-resolution structures of fragments covering most of the whole molecule. The structures suggest that nucleotide hydrolysis is transformed into larger conformational changes by pushing of one D2 domain by its neighbor in the hexamer, and transmission of nucleotide-state information through the D1-D2 linker to displace the N-terminal, effector binding domain.

Ultralow-resolutionab initiophasing of filamentous proteins: crystals from a six-Ig fragment of titin as a case study

Low-resolution diffraction data (resolution below 12 angstroms) from crystals of a filamentous six-Ig fragment of titin, I65-I70, were used in ab initio phasing with the aim of calculating its lattice packing and molecular envelope. Filamentous molecules, characterized by marked anisometry and idiosyncratic crystal lattices, have not been addressed before using this methodology. In this study, low-resolution phasing (19-122 angstroms) successfully identified the region of the unit cell occupied by the molecule. Phase extension to a higher resolution (12 angstroms) yielded regions of high density that corresponded either to the positions of individual Ig domains or to zones of dense intermolecular contacts, hindering the identification of individual domains and the interpretation of electron-density maps in terms of a molecular model. This problem resulted from the acutely uneven packing of the molecules in the crystal and it was further accentuated by the presence of partially disordered regions in the molecule. Addition of low-resolution reflections with phases computed ab initio to those obtained experimentally using MIRAS improved the initial electron-density maps of the atomic model, demonstrating the generic utility of low-resolution phases for the structure-elucidation process, even when individual molecules cannot be resolved in the lattice.

On 'globbicity' of low-resolution protein structures.

Using Harker's [Harker (1953). Acta Cryst. 6, 731-736] idea of spherically averaged polyatomic groups or 'globs' as the units of structure suitable for analyzing low-resolution diffraction data from protein crystals, 'globbic' scattering factors have been calculated for main-chain peptide units and amino-acid side-chain groups to 3 A resolution via Debye's [Debye (1915). Ann. Phys. (Leipzig), 46, 809-823] scattering formula. It is shown that the scattering factors are insensitive to intra-globbic conformational variation and can be approximated fairly well by a single-Gaussian formula, i.e. fg(s) = Zg exp(-1.7Zgs2), where s = (sin theta)/lambda and Zg is the total electron count for the atoms of the glob. Phase errors due to the globbic approximation and their effect on electron-density maps at 3.5 A resolution have been assessed via calculations for the crambin structure; this analysis indicates that the globbic scattering factors will be useful in efforts to develop procedures for direct-methods phasing of diffraction data to approximately 3.5 A resolution from protein crystals.

Multiple hydration layers in cubic insulin crystals

Cubic insulin crystals contain approximately 30-A-diameter channels filled with aqueous solvent, providing a useful system in which to analyze hydration structure at a variety of distances from protein surfaces. Beginning with an atomic model for the protein and ordered water molecules, the density distribution in the solvent volume of the phasing model was iteratively refined to improve the fit of calculated structure factors with x-ray diffraction data. The free R value, which compares calculated structure factors with a subset of observed structure factors deliberately omitted from the refinement, was used to provide an objective confirmation of the effectiveness of the refinement procedure. Electron density maps of the solvent, computed using the solvent-refined phases and complete low-resolution diffraction data, reveal multiple hydration layers around the protein.

Inside polyomavirus at 25-A resolution.

Empty capsids and complete virions of polyomavirus crystallize isomorphously. Here we use difference Fourier analysis of X-ray diffraction data at 25-A resolution from these crystals to obtain an electron-density map of the inside of the virion. The polyomavirus capsid is built from 72 pentamers of VP1 that form three different types of connections in the T = 7d icosahedral surface lattice. Self-assembly of purified recombinant VP1 into capsid-like aggregates has shown that switching of the bonding specificity to form the unanticipated non-equivalent connections is an inherent property of the VP1 pentamers. Our map of the inside of the virion displays 72 prongs of electron density extending from the core into the axial cavities of the VP1 pentamers. We identify these prongs with the VP2 and VP3 molecules, which may function to guide the assembly of the highly ordered capsid on the nucleohistone core. The atomic structure of the closely related simian virus-40 capsid has been determined from the high-resolution diffraction data. Our polyomavirus map, calculated using all the low-resolution diffraction data, shows no indication of regular order inside the spherical core.

A restrained-parameter thermal-factor refinement procedure

Retention of known geometry, with regard to mean atomic positions, has proved useful in the refinement of macromolecules. In structures with a paucity of diffraction data and large displacements of the atoms from their mean positions, it is also of value to restrain the thermal factors to be consistent with known stereochemistry. This paper presents a technique for accomplishing this by restraining the variances of the interatomic distributions (which are functions of the mean atomic positions and the thermal parameters) to suitably small values. This procedure allows meaningful anisotropic refinement of macromolecules to be carried out with low-resolution diffraction data. Anisotropic thermal parameters obtained in this way should prove useful in understanding the dynamics of the biological functions of macromolecules.