Gorgon and pathwalking: macromolecular modeling tools for subnanometer resolution density maps

The complex interplay of proteins and other molecules, often in the form of large transitory assemblies, are critical to cellular function. Today, X-ray crystallography and electron cryo-microscopy (cryo-EM) are routinely used to image these macromolecular complexes, though often at limited resolutions. Despite the rapidly growing number of macromolecular structures, few tools exist for modeling and annotating structures in the range of 3-10 ? resolution. To address this need, we have developed a number of utilities specifically targeting subnanometer resolution density maps. As part of the 2010 Cryo-EM Modeling Challenge, we demonstrated two of our latest de novo modeling tools, Pathwalking and Gorgon, as well as a tool for secondary structure identification (SSEHunter) and a new rigid-body/flexible fitting tool in Gorgon. In total, we submitted 30 structural models from ten different subnanometer resolution data sets in four of the six challenge categories. Each of our utlities produced accurate structural models and annotations across the various density maps. In the end, the utilities that we present here offer users a robust toolkit for analyzing and modeling protein structure in macromolecular assemblies at non-atomic resolutions.     

A core-weighted fitting method for docking atomic structures into low-resolution maps: application to cryo-electron microscopy

Cryo-electron microscopy of "single particles" is a powerful method to analyze structures of large macromolecular assemblies that are not amenable to investigation by traditional X-ray crystallographic methods. A key step in these studies is to obtain atomic interpretations of multiprotein complexes by fitting atomic structures of individual components into maps obtained from electron microscopic data. Here, we report the use of a "core-weighting" method, combined with a grid-threading Monte Carlo (GTMC) approach for this purpose. The "core" of an individual structure is defined to represent the part where the density distribution is least likely to be altered by other components that comprise the macromolecular assembly of interest. The performance of the method has been evaluated by its ability to determine the correct fit of (i) the alpha-chain of the T-cell receptor variable domain into a simulated map of the alphabeta complex at resolutions between 5 and 40 A, and (ii) the E2 catalytic domain of the pyruvate dehydrogenase into an experimentally determined map, at 14 A resolution, of the icosahedral complex formed by 60 copies of this enzyme. Using the X-ray structures of the two test cases as references, we demonstrate that, in contrast to more traditional methods, the combination of the core-weighting method and the grid-threading Monte Carlo approach can identify the correct fit reliably and rapidly from the low-resolution maps that are typical of structures determined with the use of single-particle electron microscopy.     

Automated segmentation of molecular subunits in electron cryomicroscopy density maps

Electron cryomicroscopy (cryoEM) is capable of imaging large macromolecular machines composed of multiple components. However, it is currently only possible to achieve moderate resolution at which it may be possible to computationally extract the individual components in the machine. In this work, we present application details of an automated method for detecting and segmenting the components of a large machine in an experimentally determined density map. This method is applicable to object with and without symmetry and takes advantage of global and local symmetry axes if present. We have applied this segmentation algorithm to several cryoEM data sets already deposited in EMDB with various complexities, symmetries and resolutions and validated the results using manually segmented density and available structures of the components in the PDB. As such, automated segmentation could become a useful tool for the analysis of the ever-increasing number of structures of macromolecular machines derived from cryoEM.     

Atomic resolution structures of oxidized [4Fe-4S] ferredoxin from Bacillus thermoproteolyticus in two crystal forms: systematic distortion of [4Fe-4S] cluster in the protein

Diffraction data of two crystal forms (forms I and II) of [4Fe-4S] ferredoxin from Bacillus thermoproteolyticus have been collected to 0.92 A and 1.00 A resolutions, respectively, at 100 K using synchrotron radiation. Anisotropic temperature factors were introduced for all non-hydrogen atoms in the refinement with SHELX-97, in which stereochemical restraints were applied to the protein chain but not to the [4Fe-4S] cluster. The final crystallographic R-factors are 9.8 % for 7.0-0.92 A resolution data of the form I and 11.2 % for the 13.3-1.0 A resolution data of the form II. Many hydrogen atoms as well as multiple conformations for several side-chains have been identified. The present refinement has revised the conformations of several peptide bonds and side-chains assigned previously at 2.3 A resolution; the largest correction was that the main-chain of Pro1 and the side-chain of Lys2 were changed by rotating the C(alpha)-C bond of Lys2. Although the overall structures in the two crystal forms are very similar, conformational differences are observed in the two residues at the middle (Glu29 and Asp30) and the C-terminal residues, which have large temperature factors. The [4Fe-4S] cluster is a distorted cube with non-planar rhombic faces. Slight but significant compression of the four Fe-S bonds along one direction is observed in both crystal forms, and results in the D(2d) symmetry of the cluster. The compressed direction of the cluster relative to the protein is conserved in the two crystal forms and consistent with that in one of the clusters in Clostridium acidurici ferredoxin.     

Studying cellular architecture in three dimensions with improved resolution: Ta replicas revisited

Metal replicas have been used for surface analysis of biological structures with a variety of spatial resolutions. Platinum (Pt) has been the metal of choice because it provides very stable replicas and images of high contrast. Some other metals, such as tantalum (Ta) have been reported to provide better resolution on isolated macromolecular complexes and cellular structures. Our goal is to study the gain in detail with Ta and to evaluate if it provides enough detail and resolution to assist in the study of complex volumes of intact cellular structures obtained by methods that reach molecular resolution. To this purpose Pt and Ta replicas of cellular structures and viruses have been studied by transmission electron microscopy (TEM). Replicas of Ta show new details on the surface of two types of isolated viral particles such as 100 nm bunyaviruses and large, > 300 nm, vaccinia virus (VV). Inside cells, the structural pieces that build VV immature particles are visualized only in Ta replicas. Looking for smaller intracellular complexes, new details are also seen in nuclear pores from Ta replicas. Additional masses, most likely representing the cargo during transport, are distinguished in some of the pores. Visualization of proteins in plasma membranes strongly suggests that detail and resolution of Ta replicas are similar to those estimated for 3D maps currently obtained by electron tomography of viruses and cells.     

Sub-Angstrom resolution enzyme X-ray structures: is seeing believing?

Recent technical advances in crystallographic analysis, particularly highly focused and high brilliance synchrotron beam lines, have significantly improved the resolutions that are attainable for many macromolecular crystal structures. The Protein Data Bank (http://www.rcsb.org/pdb/) contains an increasing number of atomic resolution structures, which are providing a wealth of structural information that was not previously visible in lower resolution electron density maps. Here, we review the importance of visualizing hydrogen atoms and multiple sidechain conformations or anisotropy, as well as substrate strain, at sub-Angstrom resolution. The additional structural features that are visible in the electron density maps as a result of atomic resolution data provide a better understanding of the catalytic mechanisms of cholesterol oxidase, ribonuclease A, beta-lactamase, serine proteases, triosephosphate isomerase and endoglucanase.     

Multi-resolution contour-based fitting of macromolecular structures

A novel contour-based matching criterion is presented for the quantitative docking of high-resolution structures of components into low-resolution maps of macromolecular complexes. The proposed Laplacian filter is combined with a six-dimensional search using fast Fourier transforms to rapidly scan the rigid-body degrees of freedom of a probe molecule relative to a fixed target density map. A comparison of the docking performance with the standard cross-correlation criterion demonstrates that contour matching with the Laplacian filter significantly extends the viable resolution range of correlation-based fitting to resolutions as low as 30 A. The gain in docking precision at medium to low resolution (15-30 A) is critical for image reconstructions from electron microscopy (EM). The new algorithm enables for the first time the reliable docking of smaller molecular components into EM densities of large biomolecular assemblies at such low resolutions. As an example of the practical effectiveness of contour-based fitting, a new pseudo-atomic model of a microtubule was constructed from a 20 A resolution EM map and from atomic structures of alpha and beta tubulin subunits.     

Constructing and validating initial Cα models from subnanometer resolution density maps with pathwalking

A significant number of macromolecular structures solved by electron cryo-microscopy and X-ray crystallography obtain resolutions of 3.5-6?, at which direct atomistic interpretation is difficult. To address this, we developed pathwalking, a semi-automated protocol to enumerate reasonable Cα models from near-atomic resolution density maps without a structural template or sequence-structure correspondence. Pathwalking uses an approach derived from the Traveling Salesman Problem to rapidly generate an ensemble of initial models for individual proteins, which can later be optimized to produce full atomic models. Pathwalking can also be used to validate and identify potential structural ambiguities in models generated from near-atomic resolution density maps. In this work, examples from the EMDB and PDB are used to assess the broad applicability and accuracy of our method. With the growing number of near-atomic resolution density maps from cryo-EM and X-ray crystallography, pathwalking can become an important tool in modeling protein structures.     

Bridging the information gap: computational tools for intermediate resolution structure interpretation

Due to large sizes and complex nature, few large macromolecular complexes have been solved to atomic resolution. This has lead to an under-representation of these structures, which are composed of novel and/or homologous folds, in the library of known structures and folds. While it is often difficult to achieve a high-resolution model for these structures, X-ray crystallography and electron cryomicroscopy are capable of determining structures of large assemblies at low to intermediate resolutions. To aid in the interpretation and analysis of such structures, we have developed two programs: helixhunter and foldhunter. Helixhunter is capable of reliably identifying helix position, orientation and length using a five-dimensional cross-correlation search of a three-dimensional density map followed by feature extraction. Helixhunter's results can in turn be used to probe a library of secondary structure elements derived from the structures in the Protein Data Bank (PDB). From this analysis, it is then possible to identify potential homologous folds or suggest novel folds based on the arrangement of alpha helix elements, resulting in a structure-based recognition of folds containing alpha helices. Foldhunter uses a six-dimensional cross-correlation search allowing a probe structure to be fitted within a region or component of a target structure. The structural fitting therefore provides a quantitative means to further examine the architecture and organization of large, complex assemblies. These two methods have been successfully tested with simulated structures modeled from the PDB at resolutions between 6 and 12 A. With the integration of helixhunter and foldhunter into sequence and structural informatics techniques, we have the potential to deduce or confirm known or novel folds in domains or components within large complexes.     

Crystal structures of Escherichia coli RecA in a compressed helical filament

The X-ray crystal structure of uncomplexed Escherichia coli RecA protein has been determined in three new crystal forms at resolutions of 1.9 A, 2.0 A, and 2.6 A. The RecA protein used for this study contains the extra residues Gly-Ser-His-Met at the N terminus, but retains normal ssDNA-dependent ATPase and coprotease activities. In all three crystals, RecA is packed in a right-handed helical filament with a pitch of approximately 74 A. These RecA filaments are compressed relative to the original crystal structure of RecA, which has a helical pitch of 82.7 A. In the structures of the compressed RecA filament, the monomer-monomer interface and the core domain are essentially the same as in the RecA structure with the 83 A pitch. The change in helical pitch is accommodated by a small movement of the N-terminal domain, which is reoriented to preserve the contacts it makes at the monomer-monomer interface. The new crystal structures show significant variation in the orientation and conformation of the C-terminal domain, as well as in the inter-filament packing interactions. In crystal form 2, a calcium ion is bound closely to a beta-hairpin of the C-terminal domain and to Asp38 of a neighboring filament, and residues 329-331 of the C-terminal tail become ordered to contact a neighboring filament. In crystal forms 3 and 4, a sulfate ion or a phosphate anion is bound to the same site on RecA as the beta-phosphate group of ADP, causing an opening of the P-loop. Altogether, the structures show the conformational variability of RecA protein in the crystalline state, providing insight into many aspects of RecA function.     

Succinct data structures for assembling large genomes

MOTIVATION: Second-generation sequencing technology makes it feasible for many researches to obtain enough sequence reads to attempt the de novo assembly of higher eukaryotes (including mammals). De novo assembly not only provides a tool for understanding wide scale biological variation, but within human biomedicine, it offers a direct way of observing both large-scale structural variation and fine-scale sequence variation. Unfortunately, improvements in the computational feasibility for de novo assembly have not matched the improvements in the gathering of sequence data. This is for two reasons: the inherent computational complexity of the problem and the in-practice memory requirements of tools. RESULTS: In this article, we use entropy compressed or succinct data structures to create a practical representation of the de Bruijn assembly graph, which requires at least a factor of 10 less storage than the kinds of structures used by deployed methods. Moreover, because our representation is entropy compressed, in the presence of sequencing errors it has better scaling behaviour asymptotically than conventional approaches. We present results of a proof-of-concept assembly of a human genome performed on a modest commodity server.     

A local-optimization refinement algorithm in single particle analysis for macromolecular complex with multiple rigid modules

Single particle analysis, which can be regarded as an average of signals from thousands or even millions of particle projections, is an efficient method to study the three-dimensional structures of biological macromolecules. An intrinsic assumption in single particle analysis is that all the analyzed particles must have identical composition and conformation. Thus specimen heterogeneity in either composition or conformation has raised great challenges for high-resolution analysis. For particles with multiple conformations, inaccurate alignments and orientation parameters will yield an averaged map with diminished resolution and smeared density. Besides extensive classification approaches, here based on the assumption that the macromolecular complex is made up of multiple rigid modules whose relative orientations and positions are in slight fluctuation around equilibriums, we propose a new method called as local optimization refinement to address this conformational heterogeneity for an improved resolution. The key idea is to optimize the orientation and shift parameters of each rigid module and then reconstruct their three-dimensional structures individually. Using simulated data of 80S/70S ribosomes with relative fluctuations between the large (60S/50S) and the small (40S/30S) subunits, we tested this algorithm and found that the resolutions of both subunits are significantly improved. Our method provides a proof-of-principle solution for high-resolution single particle analysis of macromolecular complexes with dynamic conformations.     

Ensemble refinement of protein crystal structures: validation and application

X-ray crystallography typically uses a single set of coordinates and B factors to describe macromolecular conformations. Refinement of multiple copies of the entire structure has been previously used in specific cases as an alternative means of representing structural flexibility. Here, we systematically validate this method by using simulated diffraction data, and we find that ensemble refinement produces better representations of the distributions of atomic positions in the simulated structures than single-conformer refinements. Comparison of principal components calculated from the refined ensembles and simulations shows that concerted motions are captured locally, but that correlations dissipate over long distances. Ensemble refinement is also used on 50 experimental structures of varying resolution and leads to decreases in R(free) values, implying that improvements in the representation of flexibility observed for the simulated structures may apply to real structures. These gains are essentially independent of resolution or data-to-parameter ratio, suggesting that even structures at moderate resolution can benefit from ensemble refinement.     

Teaching electron diffraction and imaging of macromolecules.

Electron microscopic analysis can be used to determine the three-dimensional structures of macromolecules at resolutions ranging between 3 and 30 A. It differs from nuclear magnetic resonance spectroscopy or x-ray crystallography in that it allows an object's Coulomb potential functions to be determined directly from images and can be used to study relatively complex macromolecular assemblies in a crystalline or noncrystalline state. Electron imaging already has provided valuable structural information about various biological systems, including membrane proteins, protein-nucleic acid complexes, contractile and motile protein assemblies, viruses, and transport complexes for ions or macromolecules. This article, organized as a series of lectures, presents the biophysical principles of three-dimensional analysis of objects possessing different symmetries.     

Ab initio modeling of the herpesvirus VP26 core domain assessed by CryoEM density

Efforts in structural biology have targeted the systematic determination of all protein structures through experimental determination or modeling. In recent years, 3-D electron cryomicroscopy (cryoEM) has assumed an increasingly important role in determining the structures of these large macromolecular assemblies to intermediate resolutions (6–10 Å). While these structures provide a snapshot of the assembly and its components in well-defined functional states, the resolution limits the ability to build accurate structural models. In contrast, sequence-based modeling techniques are capable of producing relatively robust structural models for isolated proteins or domains. In this work, we developed and applied a hybrid modeling approach, utilizing cryoEM density and ab initio modeling to produce a structural model for the core domain of a herpesvirus structural protein, VP26. Specifically, this method, first tested on simulated data, utilizes the cryoEM density map as a geometrical constraint in identifying the most native-like models from a gallery of models generated by ab initio modeling. The resulting model for the core domain of VP26, based on the 8.5-Å resolution herpes simplex virus type 1 (HSV-1) capsid cryoEM structure and mutational data, exhibited a novel fold. Additionally, the core domain of VP26 appeared to have a complementary interface to the known upper-domain structure of VP5, its cognate binding partner. While this new model provides for a better understanding of the assembly and interactions of VP26 in HSV-1, the approach itself may have broader applications in modeling the components of large macromolecular assemblies.     

Exploring vitreous cryo-section-induced compression at the macromolecular level using electron cryo-tomography; 80S yeast ribosomes appear unaffected

Vitreous cryo-section-induced compression influences the interpretation and the reliability of electron microscopy images and tomographic reconstructions. Previous studies of this deformation have been focused at the cellular level where considerable compression occurs, yet the degree of possible intracellular macromolecular deformation has remained unclear. Here, electron cryo-tomographic reconstructions of vitreous cryo-sections show that 80S ribosomes, both intracellular and in an isolated state, appear able to resist section-induced compression. Our observations indicate that vitreous section-induced compression is non-uniform between whole cells that have been sectioned and their intracellular macromolecular complexes. We conclude that electron cryo-tomography of vitreous cryo-sections, in spite of section-induced compression, is a suitable technique for charting the structural organization of cellular nanomachines, such as ribosomes, in a cellular environment.     

Precision requirements and data compression in CryoEM/CryoET

With larger, higher speed detectors and improved automation, individual CryoEM instruments are capable of producing a prodigious amount of data each day, which must then be stored, processed and archived. While it has become routine to use lossless compression on raw counting-mode movies, the averages which result after correcting these movies no longer compress well. These averages could be considered sufficient for long term archival, yet they are conventionally stored with 32 bits of precision, despite high noise levels. Derived images are similarly stored with excess precision, providing an opportunity to decrease project sizes and improve processing speed. We present a simple argument based on propagation of uncertainty for safe bit truncation of flat-fielded images combined with lossless compression. The same method can be used for most derived images throughout the processing pipeline. We test the proposed strategy on two standard, data-limited CryoEM data sets, demonstrating that these limits are safe for real-world use. We find that 5 bits of precision is sufficient for virtually any raw CryoEM data and that 8–12 bits is sufficient for intermediate averages or final 3-D structures. Additionally, we detail and recommend specific rules for discretization of data as well as a practical compressed data representation that is tuned to the specific needs of CryoEM.     

FitEM2EM--tools for low resolution study of macromolecular assembly and dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top.     

YUP.SCX: coaxing atomic models into medium resolution electron density maps

The structures of large macromolecular complexes in different functional states can be determined by cryo-electron microscopy, which yields electron density maps of low to intermediate resolutions. The maps can be combined with high-resolution atomic structures of components of the complex, to produce a model for the complex that is more accurate than the formal resolution of the map. To this end, methods have been developed to dock atomic models into density maps rigidly or flexibly, and to refine a docked model so as to optimize the fit of the atomic model into the map. We have developed a new refinement method called YUP.SCX. The electron density map is converted into a component of the potential energy function to which terms for stereochemical restraints and volume exclusion are added. The potential energy function is then minimized (using simulated annealing) to yield a stereochemically-restrained atomic structure that fits into the electron density map optimally. We used this procedure to construct an atomic model of the 70S ribosome in the pre-accommodation state. Although some atoms are displaced by as much as 33 Å, they divide themselves into nearly rigid fragments along natural boundaries with smooth transitions between the fragments.     

Video on the Internet: An introduction to the digital encoding, compression, and transmission of moving image data

In this paper, we seek to provide an introduction to the fast-moving field of digital video on the Internet, from the viewpoint of the biological microscopist who might wish to store or access videos, for instance in image databases such as the BioImage Database (http://www.bioimage.org). We describe and evaluate the principal methods used for encoding and compressing moving image data for digital storage and transmission over the Internet, which involve compromises between compression efficiency and retention of image fidelity, and describe the existing alternate software technologies for downloading or streaming compressed digitized videos using a Web browser. We report the results of experiments on video microscopy recordings and three-dimensional confocal animations of biological specimens to evaluate the compression efficiencies of the principal video compression-decompression algorithms (codecs) and to document the artefacts associated with each of them. Because MPEG-1 gives very high compression while yet retaining reasonable image quality, these studies lead us to recommend that video databases should store both a high-resolution original version of each video, ideally either uncompressed or losslessly compressed, and a separate edited and highly compressed MPEG-1 preview version that can be rapidly downloaded for interactive viewing by the database user.