Crystallographic Electron-density Maps Research Articles

High-Resolution Cryo-EM Maps and Models: A Crystallographer's Perspective

The appearance of ten high-resolution cryoelectron microscopy (cryo-EM) maps of proteins, ribosomes, and viruses was compared with the experimentally phased crystallographic electron density maps of four proteins. We found that maps calculated at a similar resolution by the two techniques are quite comparable in their appearance, although cryo-EM maps, even when sharpened, seem to be a little less detailed. An analysis of models fitted to the cryo-EM maps indicated the presence of significant problems in almost all of them, including incorrect geometry, clashes between atoms, and discrepancies between the map density and the fitted models. In particular, the treatment of the atomic displacement (B) factors was meaningless in almost all analyzed cryo-EM models. Stricter cryo-EM structure deposition standards and their better enforcement are needed.

A log-likelihood-gain intensity target for crystallographic phasing that accounts for experimental error.

The crystallographic diffraction experiment measures Bragg intensities; crystallographic electron-density maps and other crystallographic calculations in phasing require structure-factor amplitudes. If data were measured with no errors, the structure-factor amplitudes would be trivially proportional to the square roots of the intensities. When the experimental errors are large, and especially when random errors yield negative net intensities, the conversion of intensities and their error estimates into amplitudes and associated error estimates becomes nontrivial. Although this problem has been addressed intermittently in the history of crystallographic phasing, current approaches to accounting for experimental errors in macromolecular crystallography have numerous significant defects. These have been addressed with the formulation of LLGI, a log-likelihood-gain function in terms of the Bragg intensities and their associated experimental error estimates. LLGI has the correct asymptotic behaviour for data with large experimental error, appropriately downweighting these reflections without introducing bias. LLGI abrogates the need for the conversion of intensity data to amplitudes, which is usually performed with the French and Wilson method [French & Wilson (1978), Acta Cryst. A35, 517-525], wherever likelihood target functions are required. It has general applicability for a wide variety of algorithms in macromolecular crystallography, including scaling, characterizing anisotropy and translational noncrystallographic symmetry, detecting outliers, experimental phasing, molecular replacement and refinement. Because it is impossible to reliably recover the original intensity data from amplitudes, it is suggested that crystallographers should always deposit the intensity data in the Protein Data Bank.

Automated identification of crystallographic ligands using sparse-density representations.

A novel procedure for the automatic identification of ligands in macromolecular crystallographic electron-density maps is introduced. It is based on the sparse parameterization of density clusters and the matching of the pseudo-atomic grids thus created to conformationally variant ligands using mathematical descriptors of molecular shape, size and topology. In large-scale tests on experimental data derived from the Protein Data Bank, the procedure could quickly identify the deposited ligand within the top-ranked compounds from a database of candidates. This indicates the suitability of the method for the identification of binding entities in fragment-based drug screening and in model completion in macromolecular structure determination.

Location of the dsRNA-dependent polymerase, VP1, in rotavirus particles.

Double-stranded RNA (dsRNA) viruses transcribe and replicate RNA within an assembled, inner capsid particle; only plus-sense mRNA emerges into the intracellular milieu. During infectious entry of a rotavirus particle, the outer layer of its three-layer structure dissociates, delivering the inner double-layered particle (DLP) into the cytosol. DLP structures determined by X-ray crystallography and electron cryomicroscopy (cryoEM) show that the RNA coils uniformly into the particle interior, avoiding a "fivefold hub" of more structured density projecting inward from the VP2 shell of the DLP along each of the twelve 5-fold axes. Analysis of the X-ray crystallographic electron density map suggested that principal contributors to the hub are the N-terminal arms of VP2, but reexamination of the cryoEM map has shown that many features come from a molecule of VP1, randomly occupying five equivalent and partly overlapping positions. We confirm here that the electron density in the X-ray map leads to the same conclusion, and we describe the functional implications of the orientation and position of the polymerase. The exit channel for the nascent transcript directs the nascent transcript toward an opening along the 5-fold axis. The template strand enters from within the particle, and the dsRNA product of the initial replication step exits in a direction tangential to the inner surface of the VP2 shell, allowing it to coil optimally within the DLP. The polymerases of reoviruses appear to have similar positions and functional orientations.

Automatic rebuilding and optimization of crystallographic structures in the Protein Data Bank

Motivation: Macromolecular crystal structures in the Protein Data Bank (PDB) are a key source of structural insight into biological processes. These structures, some >30 years old, were constructed with methods of their era. With PDB_REDO, we aim to automatically optimize these structures to better fit their corresponding experimental data, passing the benefits of new methods in crystallography on to a wide base of non-crystallographer structure users.Results: We developed new algorithms to allow automatic rebuilding and remodeling of main chain peptide bonds and side chains in crystallographic electron density maps, and incorporated these and further enhancements in the PDB_REDO procedure. Applying the updated PDB_REDO to the oldest, but also to some of the newest models in the PDB, corrects existing modeling errors and brings these models to a higher quality, as judged by standard validation methods.Availability and Implementation: The PDB_REDO database and links to all software are available at http://www.cmbi.ru.nl/pdb_redo.Contact: r.joosten@nki.nl; a.perrakis@nki.nlSupplementary Information: Supplementary data are available at Bioinformatics online.

Geometric properties of nucleic acids with potential for autobuilding

Medium- to high-resolution X-ray structures of DNA and RNA molecules were investigated to find geometric properties useful for automated model building in crystallographic electron-density maps. We describe a simple method, starting from a list of electron-density 'blobs', for identifying backbone phosphates and nucleic acid bases based on properties of the local electron-density distribution. This knowledge should be useful for the automated building of nucleic acid models into electron-density maps. We show that the distances and angles involving C1' and the P atoms, using the pseudo-torsion angles \eta' and \theta\,' that describe the ...P-C1'-P-C1'... chain, provide a promising basis for building the nucleic acid polymer. These quantities show reasonably narrow distributions with asymmetry that should allow the direction of the phosphate backbone to be established.

A moment invariant for evaluating the chirality of three-dimensional objects

Chirality is an important feature of three-dimensional objects and a key concept in chemistry, biology and many other disciplines. However, it has been difficult to quantify, largely owing to computational complications. Here we present a general chirality measure, called the chiral invariant (CI), which is applicable to any three-dimensional object containing a large amount of data. The CI distinguishes the hand of the object and quantifies the degree of its handedness. It is invariant to the translation, rotation and scale of the object, and tolerant to a modest amount of noise in the experimental data. The invariant is expressed in terms of moments and can be computed in almost no time. Because of its universality and computational efficiency, the CI is suitable for a wide range of pattern-recognition problems. We demonstrate its applicability to molecular atomic models and their electron density maps. We show that the occurrence of the conformations of the macromolecular polypeptide backbone is related to the value of the CI of the constituting peptide fragments. We also illustrate how the CI can be used to assess the quality of a crystallographic electron density map.

Pattern-recognition-based detection of planar objects in three-dimensional electron-density maps

A pattern-recognition-based method for the detection of planar objects in protein or DNA/RNA crystal structure determination is described. The procedure derives a set of rotation-invariant numeric features from local regions in the asymmetric unit of a crystallographic electron-density map. These features, primarily moments of various orders, capture different aspects of the local shape of objects in the electron density. Feature classification is achieved using a linear discriminant that is trained to optimize the contrast between planar and nonplanar objects. In five selected test cases with X-ray data spanning 2.0-3.0 A resolution, the procedure identified the correct location and orientation for almost all of the double-ring and a majority of the single-ring planar groups. The accuracy of the location of the plane centres is of the order of 0.5 A, even in moderately noisy density maps.

Phase perturbation as a means of electron density map quality evaluation

This paper describes a new means for evaluating the quality of crystallographic electron density maps. It has been found that a better data set possesses greater robustness against perturbations applied to the phases. Thus it allows recognition of a more precise phase set and provides a way to select the best or reject the worst from several noisy data sets derived from the same crystal structure. The results indicate that calculation of the correlations by the procedure described here can be useful in ranking electron density maps in this aspect of quality. The method suggested has potential use for selecting a better molecular replacement solution, as well as for evaluating trial phase sets inab initiophasing procedures.

Recognition of secondary structural elements in low-resolution crystallographic electron density maps

Recognition of secondary structural elements in low-resolution crystallographic electron density maps

Architecture of a Fungal Fatty Acid Synthase at 5 Å Resolution

All steps of fatty acid synthesis in fungi are catalyzed by the fatty acid synthase, which forms a 2.6-megadalton alpha6beta6 complex. We have determined the molecular architecture of this multienzyme by fitting the structures of homologous enzymes that catalyze the individual steps of the reaction pathway into a 5 angstrom x-ray crystallographic electron density map. The huge assembly contains two separated reaction chambers, each equipped with three sets of active sites separated by distances up to approximately 130 angstroms, across which acyl carrier protein shuttles substrates during the reaction cycle. Regions of the electron density arising from well-defined structural features outside the catalytic domains separate the two reaction chambers and serve as a matrix in which domains carrying the various active sites are embedded. The structure rationalizes the compartmentalization of fatty acid synthesis, and the spatial arrangement of the active sites has specific implications for our understanding of the reaction cycle mechanism and of the architecture of multienzymes in general.

Architecture of initiation-competent 12-subunit RNA polymerase II.

RNA polymerase (Pol) II consists of a 10-polypeptide catalytic core and the two-subunit Rpb4/7 complex that is required for transcription initiation. Previous structures of the Pol II core revealed a "clamp," which binds the DNA template strand via three "switch regions," and a flexible "linker" to the C-terminal repeat domain (CTD). Here we derived a model of the complete Pol II by fitting structures of the core and Rpb4/7 to a 4.2-A crystallographic electron density map. Rpb4/7 protrudes from the polymerase "upstream face," on which initiation factors assemble for promoter DNA loading. Rpb7 forms a wedge between the clamp and the linker, restricting the clamp to a closed position. The wedge allosterically prevents entry of the promoter DNA duplex into the active center cleft and induces in two switch regions a conformation poised for template-strand binding. Interaction of Rpb4/7 with the linker explains Rpb4-mediated recruitment of the CTD phosphatase to the CTD during Pol II recycling. The core-Rpb7 interaction and some functions of Rpb4/7 are apparently conserved in all eukaryotic and archaeal RNA polymerases but not in the bacterial enzyme.

High-resolution crystallographic map interpretation.

This article describes a method for rapid interpretation of high-resolution crystallographic electron-density maps. The implemented algorithm searches for fragments of structure found in proteins and links these together to identify uniquely the atomic structure and sequence order of the atoms within a protein. The algorithm uses a two-dimensional sub-graph isomorphism method with a subsequent post-processing step to screen the results to find correct three-dimensional solutions to each search fragment. The final screening of ambiguous solutions found is performed using incomplete difference distance matrices. The algorithm has an intrinsic error-correction technique that is necessary for analysis of experimental data and should be applicable to a number of fields of bioinfomatics.

Pattern-recognition methods to identify secondary structure within X-ray crystallographic electron-density maps.

The interpretation of macromolecular crystallographic electron-density maps is a difficult and traditionally a manual step in the determination of a protein structure. The visualization of information within an electron-density map can be extremely arduous owing to the amount and complexity of information present. The ability to see the overall fold and structure of the molecule is usually lost among all the detail, particularly with larger structures. This paper describes a novel method of analysis of electron density in real space that can determine the secondary structure of a protein within minutes without any user intervention. The method is able to work with poor data as well as good data at resolutions down to 3.5A and is integral to the functionality of QUANTA. This article describes the methodology of the pattern recognition and its use with a number of sets of experimental data.

A new software routine that automates the fitting of protein X-ray crystallographic electron-density maps.

The classical approach to building the amino-acid residues into the initial electron-density map requires days to weeks of a skilled investigator's time. Automating this procedure should not only save time, but has the potential to provide a more accurate starting model for input to refinement programs. The new software routine MAID builds the protein structure into the electron-density map in a series of sequential steps. The first step is the fitting of the secondary alpha-helix and beta-sheet structures. These 'fits' are then used to determine the local amino-acid sequence assignment. These assigned fits are then extended through the loop regions and fused with the neighboring sheet or helix. The program was tested on the unaveraged 2.5 A selenomethionine multiple-wavelength anomalous dispersion (SMAD) electron-density map that was originally used to solve the structure of the 291-residue protein human heart short-chain L-3-hydroxyacyl-CoA dehydrogenase (SHAD). Inputting just the map density and the amino-acid sequence, MAID fitted 80% of the residues with an r.m.s.d. error of 0.43 A for the main-chain atoms and 1.0 A for all atoms without any user intervention. When tested on a higher quality 1.9 A SMAD map, MAID correctly fitted 100% (418) of the residues. A major advantage of the MAID fitting procedure is that it maintains ideal bond lengths and angles and constrains phi/psi angles to the appropriate Ramachandran regions. Recycling the output of this new routine through a partial structure-refinement program may have the potential to completely automate the fitting of electron-density maps.

A 9 Å Resolution X-Ray Crystallographic Map of the Large Ribosomal Subunit

The 50S subunit of the ribosome catalyzes the peptidyl-transferase reaction of protein synthesis. We have generated X-ray crystallographic electron density maps of the large ribosomal subunit from Haloarcula marismortui at various resolutions up to 9 Å using data from crystals that diffract to 3 Å. Positioning a 20 Å resolution EM image of these particles in the crystal lattice produced phases accurate enough to locate the bound heavy atoms in three derivatives using difference Fourier maps, thus demonstrating the correctness of the EM model and its placement in the unit cell. At 20 Å resolution, the X-ray map is similar to the EM map; however, at 9 Å it reveals long, continuous, but branched features whose shape, diameter, and right-handed twist are consistent with segments of double-helical RNA that crisscross the subunit.

Structural comparisons of the native and reactive-centre-cleaved forms of α1-antitrypsin by neutron- and X-ray-scattering in solution

alpha 1-Antitrypsin is the best-characterized member of the serpin (serine-proteinase inhibitor) superfamily. Its solution structure was studied by high-flux neutron-scattering and synchrotron X-ray-scattering. Neutron data show that its absorption coefficient A1% 280,1cm is 5.4. The neutron radius of gyration RG at infinite contrast for native alpha 1-antitrypsin is 2.61 nm, characteristic of a moderately elongated structure, and its cross-sectional RG is 1.34 nm. The internal inhomogeneity of scattering densities within alpha 1-antitrypsin is high at 29 x 10(-5). The X-ray RG is 2.91 nm, in good agreement with the neutron RG of 2.82 nm in 1H2O. This RG is unchanged in reactive-centre-cleaved alpha 1-antitrypsin. These parameters are also unchanged at pH 8 in sodium/potassium phosphate buffers up to 0.6 M. The neutron and X-ray curves for native alpha 1-antitrypsin were compared with Debye simulation based on the crystal structure of reactive-centre-cleaved (papain) alpha 1-antitrypsin. After allowance for residues not visible in the crystallographic electron-density map, and rejoining the proteolysed site between Met-358 and Ser-359 by means of a relatively minor conformational re-arrangement, good agreement to a structural resolution of 4 nm is obtained with the neutron data in two contrasts and with the X-ray data. The structures of the native and cleaved forms of alpha 1-antitrypsin are thus similar within the resolution of solution scattering. This places an upper limit on the magnitude of the presumed conformational changes that occur in alpha 1-antitrypsin on reactive-centre cleavage, as indicated in earlier spectroscopic investigations of the Met-358-Ser-359 peptide-bond cleavage. Methods for scattering-curve simulations from crystal structures are critically assessed. The RG data lead to dimensions of 7.8 nm x 4.9 nm x 2.2 nm for native alpha 1-antitrypsin. The high internal inhomogeneity and the asymmetric shorter semi-axes of 4.9 nm and 2.2 nm suggest that the three oligosaccharide chains of alpha 1-antitrypsin are essentially freely extended into solvent in physiological conditions. This conclusion is also supported by the Debye simulations, and by modelling based on hydrodynamic parameters.