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.     

Current developments in Coot for macromolecular model building of Electron Cryo‐microscopy and Crystallographic Data

Coot is a tool widely used for model building, refinement, and validation of macromolecular structures. It has been extensively used for crystallography and, more recently, improvements have been introduced to aid in cryo‐EM model building and refinement, as cryo‐EM structures with resolution ranging 2.5–4 A are now routinely available. Model building into these maps can be time‐consuming and requires experience in both biochemistry and building into low‐resolution maps. To simplify and expedite the model building task, and minimize the needed expertise, new tools are being added in Coot. Some examples include morphing, Geman‐McClure restraints, full‐chain refinement, and Fourier‐model based residue‐type‐specific Ramachandran restraints. Here, we present the current state‐of‐the‐art in Coot usage.     

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.     

Refinement of Protein Structures into Low-Resolution Density Maps Using Rosetta

We describe a method based on Rosetta structure refinement for generating high-resolution, all-atom protein models from electron cryomicroscopy density maps. A local measure of the fit of a model to the density is used to directly guide structure refinement and to identify regions incompatible with the density that are then targeted for extensive rebuilding. Over a range of test cases using both simulated and experimentally generated data, the method consistently increases the accuracy of starting models generated either by comparative modeling or by hand-tracing the density. The method can achieve near-atomic resolution starting from density maps at 4-6 Å resolution.     

NMMD: Efficient Cryo-EM Flexible Fitting Based on Simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.     

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.     

On the reliability of peptide nonplanarity seen in ultra‐high resolution crystal structures

Ultra‐high resolution protein crystal structures have been considered as relatively reliable sources for defining details of protein geometry, such as the extent to which the peptide unit deviates from planarity. Chellapa and Rose (Proteins 2015; 83:1687) recently called this into question, reporting that for a dozen representative protein structures determined at ～1 Å resolution, the diffraction data could be equally well fit with models restrained to have highly planar peptides, i.e. having a standard deviation of the ω torsion angles of only ～1° instead of the typically observed value of ～6°. Here, we document both conceptual and practical shortcomings of that study and show that the more tightly restrained models are demonstrably incorrect and do not fit the diffraction data equally well. We emphasize the importance of inspecting electron density maps when investigating the agreement between a model and its experimental data. Overall, this report reinforces that modern standard refinement protocols have been well‐conceived and that ultra‐high resolution protein crystal structures, when evaluated carefully and used with an awareness of their levels of coordinate uncertainty, are powerful sources of information for providing reliable information about the details of protein geometry.     

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.     

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.     

On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

Multiple hydration layers in cubic insulin crystals.

Cubic insulin crystals contain approximately 30-A-diameter channels filled with aqueous solvent, providing a useful system in which to analyze hydration structure at a variety of distances from protein surfaces. Beginning with an atomic model for the protein and ordered water molecules, the density distribution in the solvent volume of the phasing model was iteratively refined to improve the fit of calculated structure factors with x-ray diffraction data. The free R value, which compares calculated structure factors with a subset of observed structure factors deliberately omitted from the refinement, was used to provide an objective confirmation of the effectiveness of the refinement procedure. Electron density maps of the solvent, computed using the solvent-refined phases and complete low-resolution diffraction data, reveal multiple hydration layers around the protein.     

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.     

Integrative structure and function of the yeast exocyst complex

Exocyst is an evolutionarily conserved hetero‐octameric tethering complex that plays a variety of roles in membrane trafficking, including exocytosis, endocytosis, autophagy, cell polarization, cytokinesis, pathogen invasion, and metastasis. Exocyst serves as a platform for interactions between the Rab, Rho, and Ral small GTPases, SNARE proteins, and Sec1/Munc18 regulators that coordinate spatial and temporal fidelity of membrane fusion. However, its mechanism is poorly described at the molecular level. Here, we determine the molecular architecture of the yeast exocyst complex by an integrative approach, based on a 3D density map from negative‐stain electron microscopy (EM) at ~16 Å resolution, 434 disuccinimidyl suberate and 1‐ethyl‐3‐(3‐dimethylaminopropyl)carbodiimide hydrochloride cross‐links from chemical‐crosslinking mass spectrometry, and partial atomic models of the eight subunits. The integrative structure is validated by a previously determined cryo‐EM structure, cross‐links, and distances from in vivo fluorescence microscopy. Our subunit configuration is consistent with the cryo‐EM structure, except for Sec5. While not observed in the cryo‐EM map, the integrative model localizes the N‐terminal half of Sec3 near the Sec6 subunit. Limited proteolysis experiments suggest that the conformation of Exo70 is dynamic, which may have functional implications for SNARE and membrane interactions. This study illustrates how integrative modeling based on varied low‐resolution structural data can inform biologically relevant hypotheses, even in the absence of high‐resolution data.     

Molding atomic structures into intermediate-resolution cryo-EM density maps of ribosomal complexes using real-space refinement

Real-space refinement has been previously introduced as a flexible fitting method to interpret medium-resolution cryo-EM density maps in terms of atomic structures. In this way, conformational changes related to functional processes can be analyzed on the molecular level. In the application of the technique to the ribosome, quasiatomic models have been derived that have advanced our understanding of translocation. In this article, the choice of parameters for the fitting procedure is discussed. The quality of the fitting depends critically on the number of rigid pieces into which the model is divided. Suitable quality indicators are crosscorrelation, R factor, and density residual, all of which can also be locally applied. The example of the ribosome may provide some guidelines for general applications of real-space refinement to flexible fitting problems.     

Scoring functions for cryoEM density fitting

In fitting atomic structures into cryoEM density maps of macromolecular assemblies, the cross-correlation function (CCF) is the most prevalent method of scoring the goodness-of-fit. However, there are still many possible, less studied ways of scoring fits. In this paper, we introduce four scores new to cryoEM fitting and compare their performance to three known scores. Our benchmark consists of (a) 4 protein assemblies with simulated maps at 5-20 ? resolution, including the heptameric ring of GroEL; and (b) 4 experimental maps of GroEL at ～6-23 ? resolution with corresponding fitted atomic models. We perturb each fit 1000 times and assess each new fit with each score. The correlation between a score and the Cα RMSD of each fit from the "correctly" fitted structure shows that the CCF is one of the best scores, but in certain situations could be augmented or even replaced by other scores. For instance, our implementation of a score based on mutual information outperforms or is comparable to the CCF in almost all test cases, and our new "envelope score" works as well as the CCF at sub-nanometer resolution but is an order of magnitude faster to calculate. The results also suggest that the width of the Gaussian function used to blur the atomic structure into a density map can significantly affect the fitting process. Finally, we show that our score-testing method, when combined with the Laplacian CCF or the mutual information scores, can be used as a statistical tool for improving cryoEM density fitting.     

Combining electron microscopic with x-ray crystallographic structures

Analgorithm has been developed for placing three-dimensional atomic structures into appropriately scaled cryoelectron microscopy maps. The first stage in this process is to conduct a three-dimensional angular search in which the center of gravity of an X-ray crystallographically determined structure is placed on a selected position in the cryoelectron microscopy map. The quality of the fit is measured by the sum of the density at each atomic position. The second stage is to refine the three angles and three translational parameters for the best (usually 25 to 100) fits. Useful criteria for this refinement include the sum of densities at atomic sites, the lack of atoms in negative or low density, the absence of atomic clashes between symmetry-related positions of the atomic structure, and the distances between identifiable features in the map and their positions on the fitted atomic structure. These refinements generally lead to a convergence of the originally chosen, top scoring fits to just a few (about 3 to 8) acceptable possibilities. Usually, the best remaining fit is clearly superior to any of the others.     

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 ?.     

The integrative role of cryo electron microscopy in molecular and cellular structural biology

After gradually moving away from preparation methods prone to artefacts such as plastic embedding and negative staining for cell sections and single particles, the field of cryo electron microscopy (cryo‐EM) is now heading off at unprecedented speed towards high‐resolution analysis of biological objects of various sizes. This ‘revolution in resolution’ is happening largely thanks to new developments of new‐generation cameras used for recording the images in the cryo electron microscope which have much increased sensitivity being based on complementary metal oxide semiconductor devices. Combined with advanced image processing and 3D reconstruction, the cryo‐EM analysis of nucleoprotein complexes can provide unprecedented insights at molecular and atomic levels and address regulatory mechanisms in the cell. These advances reinforce the integrative role of cryo‐EM in synergy with other methods such as X‐ray crystallography, fluorescence imaging or focussed‐ion beam milling as exemplified here by some recent studies from our laboratory on ribosomes, viruses, chromatin and nuclear receptors. Such multi‐scale and multi‐resolution approaches allow integrating molecular and cellular levels when applied to purified or in situ macromolecular complexes, thus illustrating the trend of the field towards cellular structural biology.     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

Normal-mode refinement of anisotropic thermal parameters for potassium channel KcsA at 3.2 A crystallographic resolution

We report a normal-mode method for anisotropic refinement of membrane-protein structures, based on a hypothesis that the global near-native-state disordering of membrane proteins in crystals follows low-frequency normal modes. Thus, a small set of modes is sufficient to represent the anisotropic thermal motions in X-ray crystallographic refinement. By applying the method to potassium channel KcsA at 3.2 A, we obtained a structural model with an improved fit with the diffraction data. Moreover, the improved electron density maps allowed for large structural adjustments for 12 residues in each subunit, including the rebuilding of 3 missing side chains. Overall, the anisotropic KcsA structure at 3.2 A was systematically closer to a 2.0 A KcsA structure, especially in the selectivity filter. Furthermore, the anisotropic thermal ellipsoids from the refinement revealed functionally relevant structural flexibility. We expect this method to be a valuable tool for structural refinement of many membrane proteins with moderate-resolution diffraction data.