Single particle 3D reconstruction for 2D crystal images of membrane proteins

In cases where ultra-flat cryo-preparations of well-ordered two-dimensional (2D) crystals are available, electron crystallography is a powerful method for the determination of the high-resolution structures of membrane and soluble proteins. However, crystal unbending and Fourier-filtering methods in electron crystallography three-dimensional (3D) image processing are generally limited in their performance for 2D crystals that are badly ordered or non-flat. Here we present a single particle image processing approach, which is implemented as an extension of the 2D crystallographic pipeline realized in the 2dx software package, for the determination of high-resolution 3D structures of membrane proteins. The algorithm presented, addresses the low single-to-noise ratio (SNR) of 2D crystal images by exploiting neighborhood correlation between adjacent proteins in the 2D crystal. Compared with conventional single particle processing for randomly oriented particles, the computational costs are greatly reduced due to the crystal-induced limited search space, which allows a much finer search space compared to classical single particle processing. To reduce the considerable computational costs, our software features a hybrid parallelization scheme for multi-CPU clusters and computer with high-end graphic processing units (GPUs). We successfully apply the new refinement method to the structure of the potassium channel MloK1. The calculated 3D reconstruction shows more structural details and contains less noise than the map obtained by conventional Fourier-filtering based processing of the same 2D crystal images.     

A maximum likelihood approach to two-dimensional crystals

Maximum likelihood (ML) processing of transmission electron microscopy images of protein particles can produce reconstructions of superior resolution due to a reduced reference bias. We have investigated a ML processing approach to images centered on the unit cells of two-dimensional (2D) crystal images. The implemented software makes use of the predictive lattice node tracking in the MRC software, which is used to window particle stacks. These are then noise-whitened and subjected to ML processing. Resulting ML maps are translated into amplitudes and phases for further processing within the 2dx software package. Compared with ML processing for randomly oriented single particles, the required computational costs are greatly reduced as the 2D crystals restrict the parameter search space. The software was applied to images of negatively stained or frozen hydrated 2D crystals of different crystal order. We find that the ML algorithm is not free from reference bias, even though its sensitivity to noise correlation is lower than for pure cross-correlation alignment. Compared with crystallographic processing, the newly developed software yields better resolution for 2D crystal images of lower crystal quality, and it performs equally well for well-ordered crystal images.     

Surface topography of the p3 and p6 annexin V crystal forms determined by atomic force microscopy

Annexin V is a member of a family of structurally homologous proteins sharing the ability to bind to negatively charged phospholipid membranes in a Ca(2+)-dependent manner. The structure of the soluble form of annexin V has been solved by X-ray crystallography, while electron crystallography of two-dimensional (2D) crystals has been used to reveal the structure of its membrane-bound form. Two 2D crystal forms of annexin V have been reported to date, with either p6 or p3 symmetry. Atomic force microscopy has previously been used to investigate the growth and the topography of the p6 crystal form on supported phospholipid bilayers (Reviakine et al., 1998). The surface structure of the second crystal form, p3, is presented in this study, along with an improved topographic map of the p6 crystal form. The observed topography is correlated with the structure determined by X-ray crystallography.     

Crystal and molecular structure of cyclo(L-prolyl-glycyl)3. A cyclic hexapeptide with a cis peptide bond

The crystal structure of cyclo(L-Pro-Gly)3 was solved using X-ray crystallographic techniques. The backbone of the peptide is asymmetric and is made up of five trans peptide units and one cis peptide. There is a hydrogen bonded water bridge that links the carbonyl oxygens, O1 and O4. The molecules exist as dimers in the crystal lattice. The two molecules of the dimer are related by crystallographic twofold symmetry and are linked by two N-H ... O hydrogen bonds. The crystals are trigonal, space group P3(2)12 with a = 11.379(3), c = 32.93(1) and z = 6. The structure was solved by multisolution methods and refined by least squares technique to an R of 0.083.     

Preliminary crystallographic study of an L-asparaginase from Vibrio succinogenes

Crystals of an L-asparaginase from Vibrio succinogenes were obtained with the hanging drop method from ammonium sulphate-containing solutions. The crystals belong to the orthorhombic space group P22(1)2(1) with unit cell dimensions of a = 71.3 A, b = 85.8 A, c = 114.0 A, and contain two tetrameric enzyme molecules per unit cell. There are two subunits in the asymmetric unit; a molecular dyad is coincident with the crystallographic dyad. The crystal lattice is similar to that reported for an Escherichia coli asparaginase. Rotation function calculations have revealed that the V. succinogenes enzyme has 222 point group symmetry in the crystal. The second and third molecular dyads differ, however, from the corresponding E. coli asparaginase dyads by approximately 40 degrees. The crystals diffract to at least 2.2 A resolution and are suitable for X-ray crystallographic structure determination.     

Crystal structure analysis and refinement at 2.5 A of hexameric C-phycocyanin from the cyanobacterium Agmenellum quadruplicatum. The molecular model and its implications for light-harvesting

The crystal structure of the light-harvesting protein-pigment complex C-phycocyanin from the cyanobacterium Agmenellum quadruplicatum has been determined by Patterson search techniques on the basis of the molecular model of C-phycocyanin from Mastigocladus laminosus. The crystal unit cell (space group P321) contains three (alpha beta)6 hexamers centred on the crystallographic triads. The hexamer at the origin of the unit cell exhibits crystallographic 32 point symmetry. The other two hexamers (independent of the former) show crystallographic 3-fold and local 2-fold symmetry. The 3-fold redundancy of the asymmetric unit of the crystal cell was used in the refinement process, which proceeded by cyclic averaging, model building and energy-restrained crystallographic refinement. Refinement was terminated with a conventional crystallographic R-value of 0.20 with data to 2.5 A resolution. The two independent hexamers of the unit cell are identical within the limits of error at all levels of aggregation. Two trimers, which closely resemble the M. laminosus C-phycocyanin, are aggregated head-to-head to form the hexamer. Both trimers fit complementarily and are held together by polar and ionic interactions. Conservation of the amino acid residues involved in protein-chromophore and intermonomer interactions suggests common structural features for all biliproteins. Most probably, the hexameric aggregation form present in the crystals is closely related to the discs of native phycobilisome rods. All tetrapyrrole chromophores are extended but with different geometries enforced by different protein surroundings. In particular, interactions of the propionic side-chains with arginine residues and of the pyrrole nitrogen atoms with aspartate residues define configuration and conformation of the chromophores. Relative chromophore distances and orientations have been determined and a preferential pathway for the energy transfer suggested. Accordingly, within a hexamer the absorbed energy is funneled to chromophore B84 and then transduced via B84 chromophores along the phycobilisome rods.     

Electron microscopy of decorated crystals for the determination of crystallographic rotation and translation parameters in large protein complexes.

The lumazine synthase/riboflavin synthase complex of Bacillus subtilis consists of an icosahedral capsid of 60 beta subunits enclosing a core of 3 alpha subunits. The preparation of reconstituted hollow capsids consisting of 60 beta subunits and their crystallization in a hexagonal (space group P6(3)22) and in a monoclinic (space group C2) modification have been described. The rotational and translational parameters of the protein molecules in both crystal forms were studied by electron microscopy of freeze-etch replicas and by Patterson correlation techniques. Decoration with silver and image processing provided images with the positions of the 3-fold and 5-fold molecular axes being labelled by metal clusters. This allowed the unequivocal determination of the orientation and translational position of the protein molecules with respect to the crystallographic axes in the hexagonal modification. From inspection of the decoration images it was immediately obvious that the hexagonal crystal forms of alpha 3 beta 60 and of beta 60 are isomorphous. In the monoclinic crystals, a local icosahedral 2-fold coincides with the crystallographic 2-fold axis. The exact solution of the particle orientation was determined by interpretation of Patterson self-rotation functions for the icosahedral symmetry axes. Rotational and translational parameters for the monoclinic modification are given. A rational procedure for the efficient application of freeze-etching techniques in order to elucidate the packing in crystals of large proteins is described.     

Structure of D-glyceraldehyde-3-phosphate dehydrogenase from Palinurus versicolor in a tetragonal crystal form

D-glyceraldehyde-3-phosphate dehydrogenase (holo-GAPDH) from Palinurus versicolor was crystallized in a novel crystal form by the method of sitting-drop vapor diffusion.The crystals have space group P4212,cell parameters a=15.49 nm,c=8.03 nm and two subunits per asymmetric unit.The crystal structure at 0.34 nm was determined by the molecular replacement method.The final model has crystallographic Rfree and R factors of 0.274 and 0.262,and r.m.s.deviations of 0.002 nm for bond lengths and 2.33°for bond angles.The two subunits in asymmetric unit are similar to each other not only in the three-dimensional structure,but also in average temperature factors.This result demonstrates that the obvious difference in average temperature factors for the different subunits in C2 crystal form reported previously may be attributed to the different crystallographic environments of the subunits.This further supports that holo-GAPDH has a good 222 molecular symmetry.     

Analysis of solvent content and oligomeric states in protein crystals—does symmetry matter?

A nonredundant set of 9081 protein crystal structures in the Protein Data Bank was used to examine the solvent content, the number of polypeptide chains, and the oligomeric states of proteins in crystals as a function of crystal symmetry (as classified by crystal systems and space groups). It was found that there is a correlation between solvent content and crystal symmetry. Surprisingly, proteins crystallizing in lower symmetry systems have lower solvent content compared to those crystallizing in higher symmetry systems. Nevertheless, there is no universal correlation between solvent content and preferences of macromolecules to crystallize in certain space groups. Crystal symmetry as a function of oligomeric state was examined, where trimers, tetramers, and hexamers were found to prefer to crystallize in systems where the oligomer symmetry could be incorporated in the crystal symmetry. Our analysis also shows that the frequency distribution within the enantiomorphous pairs of space groups does not differ significantly, in contrast to previous reports.     

Conformational switching by the scaffolding protein D directs the assembly of bacteriophage phiX174

The three-dimensional structure of bacteriophage phiX174 external scaffolding protein D, prior to its interaction with other structural proteins, has been determined to 3.3 angstroms by X-ray crystallography. The crystals belong to space group P4(1)2(1)2 with a dimer in the asymmetric unit that closely resembles asymmetric dimers observed in the phiX174 procapsid structure. Furthermore, application of the crystallographic 4(1) symmetry operation to one of these dimers generates a tetramer similar to the tetramer in the icosahedral asymmetric unit of the procapsid. These data suggest that both dimers and tetramers of the D protein are true morphogenetic intermediates and can form independently of other proteins involved in procapsid morphogenesis. The crystal structure of the D scaffolding protein thus represents the state of the polypeptide prior to procapsid assembly. Hence, comparison with the procapsid structure provides a rare opportunity to follow the conformational switching events necessary for the construction of complex macromolecular assemblies.     

Crystal structure of the cyclomaltohexaose (alpha-cyclodextrin) complex with isosorbide dinitrate. Guest-modulated channel-type structure

The crystal structure of the 2:1 complex of cyclomaltohexaose (alpha-cyclodextrin, alpha-CD) with isosorbide dinitrate was determined by single-crystal X-ray analysis. In the crystal with the space group C2, two cyclomaltohexaose molecules form a head-to-head dimer with the secondary hydroxy-group sides facing each other. The dimer unit is stacked along the crystallographic c-axis to form a channel-type structure. The isosorbide dinitrate molecule is encapsulated in the cylindrical cavity of the cyclomaltohexaose dimer. The dimeric structure exhibits pseudo twofold symmetry, and the guest molecule is disordered on the local symmetry axis. The isosorbide moiety is located at the center of the dimer cavity, and the nitrate groups penetrate into the cyclomaltohexaose rings. The guest molecule modulates the dimer structure to attain the most stable accommodation into the cavity. The cyclomaltohexaose molecules are laterally shifted away from each other to create the cavity fitted to the shape of the guest molecule. As the result, the intermolecular hydrogen bonds between secondary hydroxy-groups are not fully formed, but the dimeric structure is stabilized by the interaction with the guest molecule.     

Isolation and structural elucidation of two new labdane diterpenoids from the aerial part of Roylea cinerea

Two new labdane diterpenoids, cinereanoid A (1) and cinereanoid B (2), along with five known compounds, calyone (3), pilloin (4), 1-methylindole-3-carboxaldehyde (5), β-sitosterol (6) and stigmasterol (7) were isolated from the aerial parts of Roylea cinerea (Lamiaceae). The new structures were determined by using IR, MS, 1D, 2D NMR spectroscopy. The structure of both new compounds was further confirmed by single crystal X-ray crystallographic analysis. In this study we have also reported single crystal X-ray structure of compound 3 which unambiguously confirmed the relative stereochemistry of tertiary hydroxyl and methyl groups, as it was not established by earlier report. Compounds 4 and 5 were isolated for the first time from this plant. In view of very few reports about this species, this report has increased the phytochemical knowledge about R. cinerea.     

Preliminary crystallographic study of a ribulose-1,5-bisphosphate carboxylase-oxygenase from Chromatium vinosum

Crystals of a ribulose-1,5-bisphosphate carboxylase-oxygenase from Chromatium vinosum were obtained with the hanging-drop vapor diffusion technique, using polyethylene glycol 4000 as precipitant. The crystal belongs to the cubic system, space group I432, with unit cell dimension a = 245.9 A. An asymmetric unit includes one-quarter (L2S2, L: large subunit, S: small subunit) of a hexadecameric molecule (L8S8, 544,000 Mr), which is located on the crystallographic point symmetry 222 or 4. The crystal diffracts to at least 3.0 A resolution.     

Molecular symmetry of fructose-1,6-diphosphatase by X-ray diffraction analysis.

Large single crystals of rabbit liver fructose-1,6-diphosphatase suitable for a high resolution structure analysis have been grown from polyethylene glycol. The space group of these crystals is I222 with a = 75 A, b = 81 A, and c = 132 A and there are 2 tetrameric molecules in the unit cell. These crystals have one protein subunit as the crystallographic asymmetric unit and establish point group symmetry 222 as the molecular symmetry.     

Use of Relibase for retrieving complex three-dimensional interaction patterns including crystallographic packing effects

Relibase is a database system that has been specially designed to handle protein-ligand data. Included within Relibase is a tool that can be used to systematically analyse protein-ligand interaction patterns specified by three-dimensional (3D) constraints, revealing favorable combinations of interacting functional groups and their preferred interaction geometries. This paper describes the Relibase 3D query tools, including novel extensions (Relibase+) for handling crystallographic packing effects. Examples illustrating the broad range of functionality for defining 3D interaction patterns and the application of such queries in drug design comprise carbonyl-carbonyl interactions, zinc binding site environments, and ligand-ligand interactions in the crystal packing.     

On the validation of crystallographic symmetry and the quality of structures

In 2008, Zwart and colleagues observed that the fraction of the structures deposited in the PDB alleged to have “pseudosymmetry” or “special noncrystallographic symmetry” (NCS) was about 6%, and that this percentage was rising annually. A few years later, Poon and colleagues found that 2% of all the crystal structures in the PDB belonged to higher symmetry space groups than those assigned to them. Here, I report an analysis of the X-ray diffraction data deposited for this class of structures, which shows that most of the “pseudosymmetry” and “special NCS” that has been reported is in fact true crystallographic symmetry (CS). This distinction is important because the credibility of crystal structures depends heavily on quality control statistics such as R_free that are unreliable when they are computed incorrectly, which they often are when CS is misidentified as “special NCS” or “pseudosymmetry”. When mistakes of this kind are made, artificially low values of R_free can give unjustified confidence in the accuracy of the reported structures.     

Two-Dimensional Crystallization of Brush Border Myosin I

Brush border myosin-I (BBMI) is a single-headed unconventional myosin found in the microvilli of intestinal epithelial cells, where it links the core bundle of actin filaments to the plasma membrane. An association of BBMI with anionic phospholipids has been shown to be mediated by a carboxy-terminal domain which is rich in basic amino acids. We have exploited this natural affinity of BBMI for negatively charged lipids to form two-dimensional (2D) crystals of this protein which are suitable for structural analysis by electron crystallographic techniques. The 2D crystals which we have obtained belong to one of two space groups, p22₁2₁or p2. We present here projection maps calculated from images of negatively stained crystals for each of these crystal types to a resolution of 20 Å and show that the asymmetric unit is the same in both crystal types.     

Heavy riboflavin synthase from Bacillus subtilis. Particle dimensions, crystal packing and molecular symmetry

Heavy riboflavin synthase from Bacillus subtilis is an enzyme complex consisting of approximately three alpha-subunits (Mr 23.5 X 10(3)) and 60 beta-subunits (Mr 16 X 10(3)). The enzyme has been crystallized from phosphate buffer in a hexagonal crystal modification that belongs to space group P6(3)22. The asymmetric unit of the crystal cell contains ten beta-subunits. The structure of this unusual 10(6) Mr protein has been studied by small-angle X-ray scattering, electron microscopy of three-dimensional crystals, and crystallographic methods. The scattering curves can be interpreted in terms of a hollow sphere model with a ratio of inner and outer radius of 0.3:1. A diameter of 168 A was estimated from the scattering curves, in close agreement with electron microscopic studies. An aggregate with the stoichiometry beta 60, which was obtained by ligand-driven reaggregation of isolated beta-subunits, showed similar shape and dimensions, but a larger value for the ratio Ri/Ra. Electron micrographs of freeze-etched enzyme crystals showed approximately spherical molecules, which were arranged in hexagonal layers. The lattice constants found from the micrographs are in good agreement with the values derived from X-ray diffraction data. Rotation function calculations in Patterson space showed a set of peaks for 2-fold, 3-fold and 5-fold local rotation axes, accurately consistent with icosahedral symmetry and with the particle orientation A shown in the Appendix. The crystal packing can be described as follows: enzyme particles with icosahedral symmetry (point group 532) are located at points 32 of the hexagonal cell, corresponding to positions (0, 0, 0) and (0, 0, 1/2) on the 6-fold screw axes. From the data reported, it may be concluded that the enzyme structure can be described as an icosahedral capsid of 60 beta-subunits with the triangulation number T = 1. The alpha-subunits are located in the central core space of the capsid, but their spatial orientation is incompletely understood.     

2dx_merge: data management and merging for 2D crystal images

Electron crystallography of membrane proteins determines the structure of membrane-reconstituted and two-dimensionally (2D) crystallized membrane proteins by low-dose imaging with the transmission electron microscope, and computer image processing. We have previously presented the software system 2dx, for user-friendly image processing of 2D crystal images. Its central component 2dx_image is based on the MRC program suite, and allows the optionally fully automatic processing of one 2D crystal image. We present here the program 2dx_merge, which assists the user in the management of a 2D crystal image processing project, and facilitates the merging of the data from multiple images. The merged dataset can be used as a reference to re-process all images, which usually improves the resolution of the final reconstruction. Image processing and merging can be applied iteratively, until convergence is reached. 2dx is available under the GNU General Public License at http://2dx.org.     

A new crystal form for the dodecamer C-G-C-G-A-A-T-T-C-G-C-G: symmetry effects on sequence-dependent DNA structure

The dodecanucleotide d(CGCGAATTCGCG) has been crystallised in the space group P3(2)12, representing a new crystal form for this sequence. The structure has been solved by molecular replacement and refined at 1.8 A resolution. The present structure contrasts with previous ones for this sequence since it is situated on a crystallographic 2-fold axis, and the crystal symmetry reflects the palindromic nature of this sequence. Some features accord with previous observations, notably that the minor groove is hydrated with a continuous spine of solvent. There is no evidence of alkali metal ions within this spine. The minor groove retains its narrow width, although it is now symmetric and extends over the A/T tract. Various base and base-pair morphological parameters have been examined. Their values do not show significant correlations with earlier reports, suggesting that crystal packing effects on them are more dominant than has been hitherto realised.