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.     

Photosystem I, an improved model of the stromal subunits PsaC, PsaD, and PsaE

An improved electron density map of photosystem I (PSI) calculated at 4-A resolution yields a more detailed structural model of the stromal subunits PsaC, PsaD, and PsaE than previously reported. The NMR structure of the subunit PsaE of PSI from Synechococcus sp. PCC7002 (Falzone, C. J., Kao, Y.-H., Zhao, J., Bryant, D. A., and Lecomte, J. T. J. (1994) Biochemistry 33, 6052-6062) has been used as a model to interpret the region of the electron density map corresponding to this subunit. The spatial orientation with respect to other subunits is described as well as the possible interactions between the stromal subunits. A first model of PsaD consisting of a four-stranded beta-sheet and an alpha-helix is suggested, indicating that this subunit partly shields PsaC from the stromal side. In addition to the improvements on the stromal subunits, the structural model of the membrane-integral region of PSI is also extended. The current electron density map allows the identification of the N and C termini of the subunits PsaA and PsaB. The 11-transmembrane alpha-helices of these subunits can now be assigned uniquely to the hydrophobic segments identified by hydrophobicity analyses.     

A probabilistic approach to protein backbone tracing in electron density maps

One particularly time-consuming step in protein crystallography is interpreting the electron density map; that is, fitting a complete molecular model of the protein into a 3D image of the protein produced by the crystallographic process. In poor-quality electron density maps, the interpretation may require a significant amount of a crystallographer's time. Our work investigates automating the time-consuming initial backbone trace in poor-quality density maps. We describe ACMI (Automatic Crystallographic Map Interpreter), which uses a probabilistic model known as a Markov field to represent the protein. Residues of the protein are modeled as nodes in a graph, while edges model pairwise structural interactions. Modeling the protein in this manner allows the model to be flexible, considering an almost infinite number of possible conformations, while rejecting any that are physically impossible. Using an efficient algorithm for approximate inference--belief propagation--allows the most probable trace of the protein's backbone through the density map to be determined. We test ACMI on a set of ten protein density maps (at 2.5 to 4.0 A resolution), and compare our results to alternative approaches. At these resolutions, ACMI offers a more accurate backbone trace than current approaches.     

X-Ray Diffraction of Myelin Membrane: II. Determination of the Phase Angles of the Frog Sciatic Nerve by Heavy Atom Labeling and Calculation of the Electron Density Distribution of the Membrane

The phase signs of the five main X-ray reflections from normal frog sciatic nerve have been determined as all positive using a technique of labeling with very small amounts of heavy metal. The changes in intensity of the individual reflections were studied as a function of uptake of metal label by the membrane. The possible localization of the metal label was decided from computer-analogue studies and from Patterson calculations. These phases are different from those determined by previous workers using techniques of trial of the best set of phases, or a step model, to give the best fit of the combined intensity data of normal and swollen myelin membranes. The electron density map has been calculated using eight reflections and their experimentally determined phases. The map shows an inner low electron density region which is different from that shown by earlier calculations. The center of the low electron density region shows a small region of increased electron density. However, without fixing absolute electron density levels in the map, it is not yet possible to allocate regions of low electron density to pure lipid or lipoprotein. The map shows the two sides of the membranes to be different in molecular structure without significant water spaces between the membranes.     

Improvement of the 2.5 Å resolution model of cytochrome b562 by redetermining the primary structure and using molecular graphics

The amino acid sequence of cytochrome b₅₆₂ has been redetermined and fitted to a 2.5 Å electron density map. A combination of cyanogen bromide fragmentation, proteolytic cleavages and manual and automatic sequencing was used. The model was built on an MMS-X molecular graphics system by interactively fitting the model to the electron density.The results indicate that the protein is 106 rather than 110 residues in length. The largest change required has been the rearrangement and modification of a continuous stretch of 11 residues of the original sequence. The electron density map confirms most of these changes, some of which were proposed before the revised sequence became available.     

Low-resolution structure refinement in electron microscopy

A real-space structure refinement method, originally developed for macromolecular X-ray crystallography, has been applied to protein structure analysis by electron microscopy (EM). This method simultaneously optimizes the fit of an atomic model to a density map and the stereo-chemical properties of the model by minimizing an energy function. The performance of this method is characterized at different resolution and signal-to-noise ratio conditions typical for EM electron density maps. A multi-resolution scheme is devised to improve the convergence of the refinement on the global energy minimum. Applications of the method to various model systems are demonstrated here. The first case is the arrangement of FlgE molecules in the helical filament of flagellar hook, in which refinement with segmented rigid bodies improves the density correlation and reduces severe van der Waals contacts among the symmetry-related subunits. The second case is a conformational analysis of the NSF AAA ATPase in which a multi-conformer model is used in the refinement to investigate the arrangement of the two ATPase domains in the molecule. The third case is a docking simulation in which the crystal structure of actin and the NOE data from NMR experiments on the dematin headpiece are combined with a low-resolution EM density map to generate an atomic model of the F-actin-dematin headpiece structure.     

Visualization of beta-sheets and side-chain clusters in two-dimensional periodic arrays of streptavidin on phospholipid monolayers by electron crystallography.

The biotin-binding protein streptavidin was crystallized as two-dimensional periodic arrays on biotinylated phospholipid monolayers. Electron diffraction patterns and images of the arrays embedded in vitreous ice were recorded to near-atomic resolution. Amplitudes and phases of structure factors were computed and combined to produce a 3 A projection density map. The reliability of the map was verified by comparing it to the available x-ray atomic model of the molecule. Projection densities from beta-strands and some amino acid side chains were identified from the electron cryomicroscopy map. These results demonstrate the first near-atomic image of this type of protein periodic array by electron crystallography, which has a great potential to aid in the structural characterization of molecular arrays engineered on a monolayer for various basic or biotechnological applications.     

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.     

Building the atomic model for the bacterial flagellar filament by electron cryomicroscopy and image analysis

The bacterial flagellar filament is a helical propeller for bacterial locomotion. It is a well-ordered helical assembly of a single protein, flagellin, and its tubular structure is formed by 11 protofilaments, each in either of the two distinct conformations, L- and R-type, for supercoiling. We have been studying the three-dimensional structures of the flagellar filaments by electron cryomicroscopy and recently obtained a density map of the R-type filament up to 4 angstroms resolution from an image data set containing only about 41,000 molecular images. The density map showed the features of the alpha-helical backbone and some large side chains, which allowed us to build the complete atomic model as one of the first atomic models of macromolecules obtained solely by electron microscopy image analysis (Yonekura et al., 2003a). We briefly review the structure and the structure analysis, and point out essential techniques that have made this analysis possible.     

Atomic co-ordinates for yeast phenylalanine tRNA

Atomic coordinates are presented for yeast tRNA^Phe derived from a wire skeletal model fitted to an electron density map at 2.5 Å resolution obtained by isomorphous replacement.     

Using cryoEM Reconstruction and Phase Extension to Determine Crystal Structure of Bacteriophage ϕ6 Major Capsid Protein

Bacteriophage ?6 is a double-stranded RNA virus that has been extensively studied as a model organism. Here we describe structure determination of ?6 major capsid protein P1. The protein crystallized in base centered orthorhombic space group C222₁. Matthews’s coefficient indicated that the crystals contain from four to seven P1 subunits in the crystallographic asymmetric unit. The self-rotation function had shown presence of fivefold axes of non-crystallographic symmetry in the crystals. Thus, electron density map corresponding to a P1 pentamer was excised from a previously determined cryoEM reconstruction of the ?6 procapsid at 7 Å resolution and used as a model for molecular replacement. The phases for reflections at higher than 7 Å resolution were obtained by phase extension employing the fivefold non-crystallographic symmetry present in the crystal. The averaged 3.6 Å-resolution electron density map was of sufficient quality to allow model building.     

Automated protein model building combined with iterative structure refinement.

In protein crystallography, much time and effort are often required to trace an initial model from an interpretable electron density map and to refine it until it best agrees with the crystallographic data. Here, we present a method to build and refine a protein model automatically and without user intervention, starting from diffraction data extending to resolution higher than 2.3 A and reasonable estimates of crystallographic phases. The method is based on an iterative procedure that describes the electron density map as a set of unconnected atoms and then searches for protein-like patterns. Automatic pattern recognition (model building) combined with refinement, allows a structural model to be obtained reliably within a few CPU hours. We demonstrate the power of the method with examples of a few recently solved structures.     

Crystal structure of the trigonal form of bovine beta-lactoglobulin and of its complex with retinol at 2.5 A resolution

The structure of the trigonal crystal form of bovine beta-lactoglobulin has been determined by X-ray diffraction methods. An electron density map, calculated with phases obtained by the multiple isomorphous replacement method, served as a starting point for alternate cycles of model building and restrained least-squares refinement. The model of the molecule fitted to the initial Fourier map was the one built for the orthorhombic crystal form of beta-lactoglobulin, solved at 2.8 A resolution (1 A = 0.1 nm). The final R factor for 1456 atoms (1276 non-hydrogen protein atoms and 180 solvent atoms) is 0.22, including 5245 reflections from 6.0 to 2.5 A. The molecule shows significant differences in the two crystal forms mentioned, mainly due to different packing. In the trigonal form, the species crystallized does not appear to be dimeric, but a linear polymer with tight intermolecular contacts. A difference electron density map between the complex of beta-lactoglobulin with retinol and the native protein shows no significant peaks in the cavity which, in the similar retinol-binding protein, binds the chromophore. Instead, differences are found at a surface pocket, which is limited almost completely by hydrophobic residues.     

X-ray structure of lipoamide dehydrogenase from Azotobacter vinelandii determined by a combination of molecular and isomorphous replacement techniques

The crystal structure of lipoamide dehydrogenase from Azotobacter vinelandii has been determined by a combination of molecular replacement and isomorphous replacement techniques yielding eventually a good-quality 2.8 A electron density map. Initially, the structure determination was attempted by molecular replacement procedures alone using a model of human glutathione reductase, which has 26% sequence identity with this bacterial dehydrogenase. The rotation function yielded the correct orientation of the model structure both when the glutathione reductase dimer and monomer were used as starting model. The translation function could not be solved, however. Consequently, data for two heavy-atom derivatives were collected using the Hamburg synchotron facilities. The derivatives had several sites in common, which was presumably a major reason why the electron density map obtained by isomorphous information alone was of poor quality. Application of solvent flattening procedures cleaned up the map considerably, however, showing clearly the outline of the lipoamide dehydrogenase dimer, which has a molecular weight of 100,000. Application of the "phased translation function", which combines the phase information of both isomorphous and molecular replacement, led to an unambiguous determination of the position of the model structure in the lipoamide dehydrogenase unit cell. The non-crystallographic 2-fold axis of the dimer was optimized by several cycles of constrained-restrained least-squares refinement and subsequently used for phase improvement by 2-fold density averaging. After ten cycles at 3.5 A, the resolution was gradually extended to 2.8 A in another 140 cycles. The 2.8 A electron density distribution obtained in this manner was of much improved quality and allowed building of an atomic model of A. vinelandii lipoamide dehydrogenase. It appears that in the orthorhombic crystals used each dimer is involved in contacts with eight surrounding dimers, leaving unexplained why the crystals are rather fragile. Contacts between subunits within one dimer, which are quite extensive, can be divided into two regions separated by a cavity. In one of the contact regions, the level of sequence identity with glutathione reductase is very low but it is quite high in the other. The folding of the polypeptide chain in each subunit is quite similar to that of glutathione reductase, as is the extended conformation of the co-enzyme FAD.(ABSTRACT TRUNCATED AT 400 WORDS)     

Fibrinogen structure in projection at 18 A resolution. Electron density by co-ordinated cryo-electron microscopy and X-ray crystallography

Electron microscope images of frozen-hydrated crystals of a proteolytically modified fibrinogen show excellent preservation of the structure. An electron density map of the key centric projection of the crystal at 18 A resolution has been obtained by combining the phases derived from cryo-electron microscopy with X-ray amplitudes. Simulation methods developed in earlier studies have been used to interpret the map. In contrast to the earlier images, the map allows us to visualize the coiled-coil region of the molecule and possible substructure in the beta domains. The map also shows that there is a marked difference in density in the two regions corresponding to the molecular ends where the gamma domains interact. A possible interpretation of this finding is provided by assuming substructure in the gamma domains and the breaking of molecular symmetry where these domains interact. Some additional constraints useful for the determination of the three-dimensional structure were obtained from cryo-electron micrographs of a perpendicular view at 25 A resolution. Implications of this working model for the molecular length and contacts in the filaments in both the crystal and fibrin are described. The data used here will be valuable as a starting point for obtaining the three-dimensional structure.     

Structure of porcine heart cytoplasmic malate dehydrogenase: combining X-ray diffraction and chemical sequence data in structural studies

The amino acid sequence of cytoplasmic malate dehydrogenase (sMDH) has been determined by a combination of X-ray crystallographic and chemical sequencing methods. The initial molecular model incorporated an "X-ray amino acid sequence" that was derived primarily from an evaluation of a multiple isomorphous replacement phased electron density map calculated at 2.5-A resolution. Following restrained least-squares crystallographic refinement, difference electron density maps were calculated from model phases, and attempts were made to upgrade the X-ray amino acid sequence. The method used to find the positions of peptides in the X-ray structure was similar to those used for studying protein homology and was shown to be successful for large fragments. For sMDH, X-ray methods by themselves were insufficient to derive a complete amino acid sequence, even with partial chemical sequence data. However, for this relatively large molecule at medium resolution, the electron density maps were of considerable help in determining the linear position of peptide fragments. The N-acetylated polypeptide chain of sMDH has 331 amino acids and has been crystallographically refined to an R factor of 19% for 2.5-A resolution diffraction data.     

Structure determination of clathrin coats to subnanometer resolution by single particle cryo-electron microscopy

Clathrin triskelions can assemble into lattices of different shapes, sizes and symmetries. For many years, the structures of clathrin lattices have been studied by single particle cryo-electron microscopy, which probed the architecture of the D6 hexagonal barrel clathrin coat at the molecular level. By introducing additional image processing steps we have recently produced a density map for the D6 barrel clathrin coat at subnanometer resolution, enabling us to generate an atomic model for this lattice [Fotin, A., Cheng, Y., Sliz, P., Grigorieff, N., Harrison, S.C., Kirchhausen, T., Walz, T., 2004. Molecular model for a complete clathrin lattice from electron cryomicroscopy. Nature 432, 573-579]. We describe in detail here the image processing steps that we have added to produce a density map at this high resolution. These procedures should be generally applicable and may thus help determine the structures of other large protein assemblies to higher resolution by single particle cryo-electron microscopy.     

Cryo‐EM map interpretation and protein model‐building using iterative map segmentation

A procedure for building protein chains into maps produced by single‐particle electron cryo‐microscopy (cryo‐EM) is described. The procedure is similar to the way an experienced structural biologist might analyze a map, focusing first on secondary structure elements such as helices and sheets, then varying the contour level to identify connections between these elements. Since the high density in a map typically follows the main‐chain of the protein, the main‐chain connection between secondary structure elements can often be identified as the unbranched path between them with the highest minimum value along the path. This chain‐tracing procedure is then combined with finding side‐chain positions based on the presence of density extending away from the main path of the chain, allowing generation of a C_α model. The C_α model is converted to an all‐atom model and is refined against the map. We show that this procedure is as effective as other existing methods for interpretation of cryo‐EM maps and that it is considerably faster and produces models with fewer chain breaks than our previous methods that were based on approaches developed for crystallographic maps.     

Structure of polymerizable lipid bilayers. I--1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine, a tubule-forming phosphatidylcholine

This report presents the first X-ray diffraction data on diacetylenic phospholipids. The tubule-forming polymerizable lipid, 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DC8,9PC), was studied by low angle X-ray diffraction from partially dehydrated oriented multibilayers in both polymerized and unpolymerized form. Bilayers of this material were found to be highly ordered, yielding as many as 16 orders of lamellar diffraction, in both the polymerized and unpolymerized states. The unit cell dimension was very small for a lipid of this size. In addition to the features usually observed in the electron density profile structure of phospholipid bilayers, the electron-dense diacetylenic portions of the fatty acyl chain produced electron density maxima at two well-defined levels on each side of the bilayer approximately 15 A and 9 A from the bilayer midplane. A model molecular conformation deduced from the one-dimensional electron density map features all-trans acyl chains tilted at approximately 28 degrees from the bilayer normal that are interdigitated with chains of the opposing monolayer by approximately two carbons at the bilayer center. The linear diacetylene moieties on beta- and gamma-chains appear at different positions along the bilayer normal axis and are roughly parallel to the bilayer surface. This model is discussed in terms of a polymerization mechanism.     

Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.