Real-space refinement with DireX: from global fitting to side-chain improvements

Single-particle cryo-electron microscopy (cryo-EM) has become an important tool to determine the structure of large biomolecules and assemblies thereof. However, the achievable resolution varies considerably over a wide range of about 3.5-20 ?. The interpretation of these intermediate- to low-resolution density maps in terms of atomic models is a big challenge and an area of active research. Here, we present our real-space structure refinement program DireX, which was developed primarily for cryo-EM-derived density maps. The basic principle and its main features are described. DireX employs Deformable Elastic Network (DEN) restraints to reduce overfitting by decreasing the effective number of degrees of freedom used in the refinement. Missing or reduced density due to flexible parts of the protein can lead to artifacts in the structure refinement, which is addressed through the concept of restrained grouped occupancy refinement. Furthermore, we describe the performance of DireX in the 2010 Cryo-EM Modeling Challenge, where we chose six density maps of four different proteins provided by the Modeling Challenge exemplifying typical refinement results at a large resolution range from 3 to 23 ?.     

Cryo‐EM model validation using independent map reconstructions

An increasing number of cryo‐electron microscopy (cryo‐EM) density maps are being generated with suitable resolution to trace the protein backbone and guide sidechain placement. Generating and evaluating atomic models based on such maps would be greatly facilitated by independent validation metrics for assessing the fit of the models to the data. We describe such a metric based on the fit of atomic models with independent test maps from single particle reconstructions not used in model refinement. The metric provides a means to determine the proper balance between the fit to the density and model energy and stereochemistry during refinement, and is likely to be useful in determining values of model building and refinement metaparameters quite generally.     

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.     

Fitting low-resolution cryo-EM maps of proteins using constrained geometric simulations

Recent experimental advances in producing density maps from cryo-electron microscopy (cryo-EM) have challenged theorists to develop improved techniques to provide structural models that are consistent with the data and that preserve all the local stereochemistry associated with the biomolecule. We develop a new technique that maintains the local geometry and chemistry at each stage of the fitting procedure. A geometric simulation is used to drive the structure from some appropriate starting point (a nearby experimental structure or a modeled structure) toward the experimental density, via a set of small incremental motions. Structural motifs such as α-helices can be held rigid during the fitting procedure as the starting structure is brought into alignment with the experimental density. After validating this procedure on simulated data for adenylate kinase and lactoferrin, we show how cryo-EM data for two different GroEL structures can be fit using a starting x-ray crystal structure. We show that by incorporating the correct local stereochemistry in the modeling, structures can be obtained with effective resolution that is significantly higher than might be expected from the nominal cryo-EM resolution.     

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.     

ATTRACT-EM: A New Method for the Computational Assembly of Large Molecular Machines Using Cryo-EM Maps

Many of the most important functions in the cell are carried out by proteins organized in large molecular machines. Cryo-electron microscopy (cryo-EM) is increasingly being used to obtain low resolution density maps of these large assemblies. A new method, ATTRACT-EM, for the computational assembly of molecular assemblies from their components has been developed. Based on concepts from the protein-protein docking field, it utilizes cryo-EM density maps to assemble molecular subunits at near atomic detail, starting from millions of initial subunit configurations. The search efficiency was further enhanced by recombining partial solutions, the inclusion of symmetry information, and refinement using a molecular force field. The approach was tested on the GroES-GroEL system, using an experimental cryo-EM map at 23.5 Å resolution, and on several smaller complexes. Inclusion of experimental information on the symmetry of the systems and the application of a new gradient vector matching algorithm allowed the efficient identification of docked assemblies in close agreement with experiment. Application to the GroES-GroEL complex resulted in a top ranked model with a deviation of 4.6 Å (and a 2.8 Å model within the top 10) from the GroES-GroEL crystal structure, a significant improvement over existing methods.     

Cryo-electron microscopy targets in CASP13: Overview and evaluation of results

Structures of seven CASP13 targets were determined using cryo-electron microscopy (cryo-EM) technique with resolution between 3.0 and 4.0 Å. We provide an overview of the experimentally derived structures and describe results of the numerical evaluation of the submitted models. The evaluation is carried out by comparing coordinates of models to those of reference structures (CASP-style evaluation), as well as checking goodness-of-fit of modeled structures to the cryo-EM density maps. The performance of contributing research groups in the CASP-style evaluation is measured in terms of backbone accuracy, all-atom local geometry and similarity of inter-subunit interfaces. The results on the cryo-EM targets are compared with those on the whole set of eighty CASP13 targets. A posteriori refinement of the best models in their corresponding cryo-EM density maps resulted in structures that are very close to the reference structure, including some regions with better fit to the density.     

Ab initio protein modeling into CryoEM density maps using EM-Fold

EM-Fold was used to build models for nine proteins in the maps of GroEL (7.7 ? resolution) and ribosome (6.4 ? resolution) in the ab initio modeling category of the 2010 cryo-electron microscopy modeling challenge. EM-Fold assembles predicted secondary structure elements (SSEs) into regions of the density map that were identified to correspond to either α-helices or β-strands. The assembly uses a Monte Carlo algorithm where loop closure, density-SSE length agreement, and strength of connecting density between SSEs are evaluated. Top-scoring models are refined by translating, rotating, and bending SSEs to yield better agreement with the density map. EM-Fold produces models that contain backbone atoms within SSEs only. The RMSD values of the models with respect to native range from 2.4 to 3.5 ? for six of the nine proteins. EM-Fold failed to predict the correct topology in three cases. Subsequently, Rosetta was used to build loops and side chains for the very best scoring models after EM-Fold refinement. The refinement within Rosetta's force field is driven by a density agreement score that calculates a cross-correlation between a density map simulated from the model and the experimental density map. All-atom RMSDs as low as 3.4 ? are achieved in favorable cases. Values above 10.0 ? are observed for two proteins with low overall content of secondary structure and hence particularly complex loop modeling problems. RMSDs over residues in secondary structure elements range from 2.5 to 4.8 ?.     

Finding rigid bodies in protein structures: Application to flexible fitting into cryoEM maps

We present RIBFIND, a method for detecting flexibility in protein structures via the clustering of secondary structural elements (SSEs) into rigid bodies. To test the usefulness of the method in refining atomic structures within cryoEM density we incorporated it into our flexible fitting protocol (Flex-EM). Our benchmark includes 13 pairs of protein structures in two conformations each, one of which is represented by a corresponding cryoEM map. Refining the structures in simulated and experimental maps at the 5–15 Å resolution range using rigid bodies identified by RIBFIND shows a significant improvement over using individual SSEs as rigid bodies. For the 15 Å resolution simulated maps, using RIBFIND-based rigid bodies improves the initial fits by 40.64% on average, as compared to 26.52% when using individual SSEs. Furthermore, for some test cases we show that at the sub-nanometer resolution range the fits can be further improved by applying a two-stage refinement protocol (using RIBFIND-based refinement followed by an SSE-based refinement). The method is stand-alone and could serve as a general interactive tool for guiding flexible fitting into EM maps.     

Structure of the complex formed by bovine trypsin and bovine pancreatic trypsin inhibitor. II. Crystallographic refinement at 1.9 A resolution

The crystal structure of the complex formed by bovine trypsin and bovine pancreatic trypsin inhibitor has been refined with data to 1.9 Å resolution, using a procedure described by Deisenhofer &; Steigemann (1974) in their refinement of the crystal structure of the free inhibitor. This procedure involves cycles consisting of phase calculation using the current atomic model, Fourier synthesis using these phases and the observed structure factor amplitudes and Diamond's real-space refinement (Diamond, 1971,1974). At various stages, difference Fourier syntheses are calculated to detect and correct gross errors in the model and to localize solvent molecules.The refinement progressed smoothly, starting with the model obtained from the isomorphous Fourier map at 2.6 Å resolution. The R-factor is 0.23 for 20,500 significantly measured reflections to 1.9 Å resolution, using an over-all temperature factor of 20 Ų. The estimated standard deviation of atomic positions is 0.09 Å.An objective assessment of the upper limit of the error in the atomic coordinates of the final model is possible by comparing the inhibitor component in the model of the complex with the refined structure of the free inhibitor (Deisenhofer &; Steigemann, 1974). The mean deviation of main-chain atoms of the two molecular models in internal segments is 0.25 Å, of main-chain dihedral angles 5.1 ° and side-chain dihedral angles 6.5 °.A comparison of the trypsin component with α-chymotrypsin (Birktoft &; Blow, 1972) showed a mean deviation of main-chain atoms of 0.75 Å. The structures are closely similar and the various deletions and insertions cause local structural differences only.     

BCL::EM-Fit: rigid body fitting of atomic structures into density maps using geometric hashing and real space refinement

Cryo-electron microscopy (cryoEM) can visualize large macromolecular assemblies at resolutions often below 10? and recently as good as 3.8-4.5 ?. These density maps provide important insights into the biological functioning of molecular machineries such as viruses or the ribosome, in particular if atomic-resolution crystal structures or models of individual components of the assembly can be placed into the density map. The present work introduces a novel algorithm termed BCL::EM-Fit that accurately fits atomic-detail structural models into medium resolution density maps. In an initial step, a "geometric hashing" algorithm provides a short list of likely placements. In a follow up Monte Carlo/Metropolis refinement step, the initial placements are optimized by their cross correlation coefficient. The resolution of density maps for a reliable fit was determined to be 10 ? or better using tests with simulated density maps. The algorithm was applied to fitting of capsid proteins into an experimental cryoEM density map of human adenovirus at a resolution of 6.8 and 9.0 ?, and fitting of the GroEL protein at 5.4 ?. In the process, the handedness of the cryoEM density map was unambiguously identified. The BCL::EM-Fit algorithm offers an alternative to the established Fourier/Real space fitting programs. BCL::EM-Fit is free for academic use and available from a web server or as downloadable binary file at http://www.meilerlab.org.     

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.     

Influence of the Cytoplasmic Domains of Aquaporin-4 on Water Conduction and Array Formation

Phosphorylation of Ser180 in cytoplasmic loop D has been shown to reduce the water permeability of aquaporin (AQP) 4, the predominant water channel in the brain. However, when the structure of the S180D mutant (AQP4M23S180D), which was generated to mimic phosphorylated Ser180, was determined to 2.8 Å resolution using electron diffraction patterns, it showed no significant differences from the structure of the wild-type channel. High-resolution density maps usually do not resolve protein regions that are only partially ordered, but these can sometimes be seen in lower-resolution density maps calculated from electron micrographs. We therefore used images of two-dimensional crystals and determined the structure of AQP4M23S180D at 10 Å resolution. The features of the 10-Å density map are consistent with those of the previously determined atomic model; in particular, there were no indications of any obstruction near the cytoplasmic pore entrance. In addition, water conductance measurements, both in vitro and in vivo, show the same water permeability for wild-type and mutant AQP4M23, suggesting that the S180D mutation neither reduces water conduction through a conformational change nor reduces water conduction by interacting with a protein that would obstruct the cytoplasmic channel entrance. Finally, the 10-Å map shows a cytoplasmic density in between four adjacent tetramers that most likely represents the association of four N termini. This finding supports the critical role of the N terminus of AQP4 in the stabilization of orthogonal arrays, as well as their interference through lipid modification of cysteine residues in the longer N-terminal isoform.     

Crystal structure of human immunoglobulin fragment Fab New refined at 2.0 A resolution.

The three-dimensional structure of the human immunoglobulin fragment Fab New (IgG1, lambda) has been refined to a crystallographic R-factor of 16.9% to 2 A resolution. Rms deviations of the final model from ideal geometry are 0.014 A for bond distances and 3.03 degrees for bond angles. Refinement was based on a new X-ray data set including 28,301 reflections with F > 2.5 sigma(F) from 6.0 to 2.0 A resolution. The starting model for the refinement procedure reported here is from the Brookhaven Protein Data Bank entry 3FAB (rev. 1981). Differences between the initial and final models include modified polypeptide-chain folding in the third complementarity-determining region (CDR3) and the third framework region (FR3) of VH and in some exposed loops of CL and CH1. Amino acid sequence changes were determined at a number of positions by inspection of difference electron density maps. The incorporation of amino acid sequence changes results in an improved VH framework model for the "humanization" of monoclonal antibodies.     

Molecular modeling studies on the ribosome

In the absence of a high resolution crystal structure for the ribosome, numerous research groups are carrying out low resolution structural studies using neutron diffraction, electron microscopy, fluorescence energy transfer, chemical crosslinking, chemical footprinting studies, and other methods. We have developed a computer-based refinement method for incorporating these data into low resolution three-dimensional models. The method is based on a molecular mechanics approach, with proteins represented by spherical particles of suitable diameter and the ribosomal RNA represented by a string of spherical pseudoatoms, one for each nucleotide. Experimental data are used to derive constraints that are introduced through a special force field (potential function). Models are refined by simulated annealing. Since every term in the force field is quadratic, any model that satisfies all of the input data has an energy of zero; higher energies indicate residual unsatisfied constraints. The residual energy provides a quantitative statement of model quality and can be used to identify conflicts in the experimental data. The method has been applied to the refinement of a low resolution model for the 30S subunit (the small subunit) of theE. coli ribosome. Since this is a very underdetermined system, the range of acceptable models has also been explored. This provides an estimate of the resolution of the structure, which is about 15 Å overall, with the uncertainty in position of individual nucleotides ranging from about 5 Å to 50 Å.     

Real space refinement of acto-myosin structures from sectioned muscle

We have adapted a real space refinement protocol originally developed for high-resolution crystallographic analysis for use in fitting atomic models of actin filaments and myosin subfragment 1 (S1) to 3-D images of thin-sectioned, plastic-embedded whole muscle. The rationale for this effort is to obtain a refinement protocol that will optimize the fit of the model to the density obtained by electron microscopy and correct for poor geometry introduced during the manual fitting of a high-resolution atomic model into a lower resolution 3-D image. The starting atomic model consisted of a rigor acto-S1 model obtained by X-ray crystallography and helical reconstruction of electron micrographs. This model was rebuilt to fit 3-D images of rigor insect flight muscle at a resolution of 7 nm obtained by electron tomography and image averaging. Our highly constrained real space refinement resulted in modest improvements in the agreement of model and reconstruction but reduced the number of conflicting atomic contacts by 70% without loss of fit to the 3-D density. The methodology seems to be well suited to the derivation of stereochemically reasonable atomic models that are consistent with experimentally determined 3-D reconstructions computed from electron micrographs.     

Neutron and X-ray crystallographic analysis of the human α-thrombin–bivalirudin complex at pD 5.0: Protonation states and hydration structure of the enzyme–product complex

The protonation states and hydration structures of the α-thrombin–bivalirudin complex were studied by joint XN refinement of the single crystal X-ray and neutron diffraction data at resolutions of 1.6 and 2.8 Å, respectively. The atomic distances were estimated by carrying out X-ray crystallographic analysis at 1.25 Å resolution. The complex represents a model of the enzyme-product (EP) complex of α-thrombin. The neutron scattering length maps around the active site suggest that the side chain of H57/H was deuterated. The joint XN refinement showed that occupancies for Dδ1 and Dε2 of H57/H were 1.0 and 0.7, respectively. However, no significant neutron scattering length density was observed around the hydroxyl oxygen Oγ of S195/H, which was close to the carboxylic carbon atom of dFPR-COOH. These observations suggest that the Oγ atom of S195/H is deprotonated and maintains its nucleophilicity in the EP complex. In addition to the active site, the hydration structures of the S1 subsite and the Exosite I, which are involved in the recognition of bivalirudin, are presented.     

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.     

Sequencing a protein by x-ray crystallography. II. Refinement of yeast hexokinase B co-ordinates and sequence at 2.1 A resolution.

Although the amino acid sequence of yeast hexokinase B has not been determined by chemical means, crystallographic refinement of the hexokinase monomer was carried out at 2.1 Å resolution to improve both the atomic co-ordinates and the amino acid sequence, which had been obtained from a 2.5 Å electron density map. The atomic co-ordinates were adjusted by real-space refinement into a multiple isomorphous replacement map, followed by automated difference Fourier refinement, and restrained parameter structure factor least-squares refinement. The amino acid sequence was altered periodically after visual inspection of (F_o ? F_c) difference electron density maps. Evidence of the improvement in the amino acid sequence was provided by the better agreement between the X-ray and chemically derived amino acid compositions, and most importantly by the ability to locate two short peptides which had been chemically sequenced. While only 6 out of the 18 residues in these two peptides agree with the sequence of the original model, 12 residues agree with the sequence of the refined model and the others differ by only an atom or two. The refined model contains 3293 of of the 3596 non-hydrogen atoms expected from the amino acid composition and 152 bound water molecules. The crystallographic R factor at 2.1 Å is 0.25.We show that there are several advantages to refining the structure of even a protein of unknown sequence. (1) Improved phases can be obtained to the resolution limit of the diffraction pattern starting with a model derived from a 2.5 Å map. (2) The accuracy of the amino acid sequence derived by X-ray methods alone can be substantially improved. (3) Functionally important residues can be identified before chemical sequence information is available. (4) The improved X-ray sequence should greatly reduce the effort required to obtain a chemical sequence; since peptides as short as eight or nine residues can be located in the refined X-ray sequence, peptides do not need to be overlapped by chemical means.