Refinement of protein structures by iterative comparative modeling and CryoEM density fitting

We developed a method for structure characterization of assembly components by iterative comparative protein structure modeling and fitting into cryo-electron microscopy (cryoEM) density maps. Specifically, we calculate a comparative model of a given component by considering many alternative alignments between the target sequence and a related template structure while optimizing the fit of a model into the corresponding density map. The method relies on the previously developed Moulder protocol that iterates over alignment, model building, and model assessment. The protocol was benchmarked using 20 varied target-template pairs of known structures with less than 30% sequence identity and corresponding simulated density maps at resolutions from 5A to 25A. Relative to the models based on the best existing sequence profile alignment methods, the percentage of C(alpha) atoms that are within 5A of the corresponding C(alpha) atoms in the superposed native structure increases on average from 52% to 66%, which is half-way between the starting models and the models from the best possible alignments (82%). The test also reveals that despite the improvements in the accuracy of the fitness function, this function is still the bottleneck in reducing the remaining errors. To demonstrate the usefulness of the protocol, we applied it to the upper domain of the P8 capsid protein of rice dwarf virus that has been studied by cryoEM at 6.8A. The C(alpha) root-mean-square deviation of the model based on the remotely related template, bluetongue virus VP7, improved from 8.7A to 6.0A, while the best possible model has a C(alpha) RMSD value of 5.3A. Moreover, the resulting model fits better into the cryoEM density map than the initial template structure. The method is being implemented in our program MODELLER for protein structure modeling by satisfaction of spatial restraints and will be applicable to the rapidly increasing number of cryoEM density maps of macromolecular assemblies.     

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.     

Combined approaches to flexible fitting and assessment in virus capsids undergoing conformational change

Fitting of atomic components into electron cryo-microscopy (cryoEM) density maps is routinely used to understand the structure and function of macromolecular machines. Many fitting methods have been developed, but a standard protocol for successful fitting and assessment of fitted models has yet to be agreed upon among the experts in the field. Here, we created and tested a protocol that highlights important issues related to homology modelling, density map segmentation, rigid and flexible fitting, as well as the assessment of fits. As part of it, we use two different flexible fitting methods (Flex-EM and iMODfit) and demonstrate how combining the analysis of multiple fits and model assessment could result in an improved model. The protocol is applied to the case of the mature and empty capsids of Coxsackievirus A7 (CAV7) by flexibly fitting homology models into the corresponding cryoEM density maps at 8.2 and 6.1 Å resolution. As a result, and due to the improved homology models (derived from recently solved crystal structures of a close homolog – EV71 capsid – in mature and empty forms), the final models present an improvement over previously published models. In close agreement with the capsid expansion observed in the EV71 structures, the new CAV7 models reveal that the expansion is accompanied by ∼5° counterclockwise rotation of the asymmetric unit, predominantly contributed by the capsid protein VP1. The protocol could be applied not only to viral capsids but also to many other complexes characterised by a combination of atomic structure modelling and cryoEM density fitting.     

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.     

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.     

Resolution and Probabilistic Models of Components in CryoEM Maps of Mature P22 Bacteriophage

CryoEM continues to produce density maps of larger and more complex assemblies with multiple protein components of mixed symmetries. Resolution is not always uniform throughout a cryoEM map, and it can be useful to estimate the resolution in specific molecular components of a large assembly. In this study, we present procedures to 1) estimate the resolution in subcomponents by gold-standard Fourier shell correlation (FSC); 2) validate modeling procedures, particularly at medium resolutions, which can include loop modeling and flexible fitting; and 3) build probabilistic models that combine high-accuracy priors (such as crystallographic structures) with medium-resolution cryoEM densities. As an example, we apply these methods to new cryoEM maps of the mature bacteriophage P22, reconstructed without imposing icosahedral symmetry. Resolution estimates based on gold-standard FSC show the highest resolution in the coat region (7.6 Å), whereas other components are at slightly lower resolutions: portal (9.2 Å), hub (8.5 Å), tailspike (10.9 Å), and needle (10.5 Å). These differences are indicative of inherent structural heterogeneity and/or reconstruction accuracy in different subcomponents of the map. Probabilistic models for these subcomponents provide new insights, to our knowledge, and structural information when taking into account uncertainty given the limitations of the observed density.     

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.     

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.     

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.     

UCSF Chimera, MODELLER, and IMP: an integrated modeling system

Structural modeling of macromolecular complexes greatly benefits from interactive visualization capabilities. Here we present the integration of several modeling tools into UCSF Chimera. These include comparative modeling by MODELLER, simultaneous fitting of multiple components into electron microscopy density maps by IMP MultiFit, computing of small-angle X-ray scattering profiles and fitting of the corresponding experimental profile by IMP FoXS, and assessment of amino acid sidechain conformations based on rotamer probabilities and local interactions by Chimera.     

Derivation of rules for comparative protein modeling from a database of protein structure alignments

We describe a database of protein structure alignments as well as methods and tools that use this database to improve comparative protein modeling. The current version of the database contains 105 alignments of similar proteins or protein segments. The database comprises 416 entries, 78,495 residues, 1,233 equivalent entry pairs, and 230,396 pairs of equivalent alignment positions. At present, the main application of the database is to improve comparative modeling by satisfaction of spatial restraints implemented in the program MODELLER (?ali A, Blundell TL, 1993, J Mol Biol 234:779–815). To illustrate the usefulness of the database, the restraints on the conformation of a disulfide bridge provided by an equivalent disulfide bridge in a related structure are derived from the alignments; the prediction success of the disulfide dihedral angle classes is increased to approximately 80%, compared to approximately 55% for modeling that relies on the stereochemistry of disulfide bridges alone. The second example of the use of the database is the derivation of the probability density function for comparative modeling of the cis/trans isomerism of the proline residues; the prediction success is increased from 0% to 82.9% for cis-proline and from 93.3% to 96.2% for trans-proline. The database is available via electronic mail.     

A machine learning approach for the identification of protein secondary structure elements from electron cryo-microscopy density maps

The accuracy of the secondary structure element (SSE) identification from volumetric protein density maps is critical for de-novo backbone structure derivation in electron cryo-microscopy (cryoEM). It is still challenging to detect the SSE automatically and accurately from the density maps at medium resolutions (～5-10 ?). We present a machine learning approach, SSELearner, to automatically identify helices and β-sheets by using the knowledge from existing volumetric maps in the Electron Microscopy Data Bank. We tested our approach using 10 simulated density maps. The averaged specificity and sensitivity for the helix detection are 94.9% and 95.8%, respectively, and those for the β-sheet detection are 86.7% and 96.4%, respectively. We have developed a secondary structure annotator, SSID, to predict the helices and β-strands from the backbone Cα trace. With the help of SSID, we tested our SSELearner using 13 experimentally derived cryo-EM density maps. The machine learning approach shows the specificity and sensitivity of 91.8% and 74.5%, respectively, for the helix detection and 85.2% and 86.5% respectively for the β-sheet detection in cryoEM maps of Electron Microscopy Data Bank. The reduced detection accuracy reveals the challenges in SSE detection when the cryoEM maps are used instead of the simulated maps. Our results suggest that it is effective to use one cryoEM map for learning to detect the SSE in another cryoEM map of similar quality.     

ADP_EM: fast exhaustive multi-resolution docking for high-throughput coverage

MOTIVATION: Efficient fitting tools are needed to take advantage of a fast growth of atomic models of protein domains from crystallography or comparative modeling, and low-resolution density maps of larger molecular assemblies. Here, we report a novel fitting algorithm for the exhaustive and fast overlay of partial high-resolution models into a low-resolution density map. The method incorporates a fast rotational search based on spherical harmonics (SH) combined with a simple translational scanning. RESULTS: This novel combination makes it possible to accurately dock atomic structures into low-resolution electron-density maps in times ranging from seconds to a few minutes. The high-efficiency achieved with simulated and experimental test cases preserves the exhaustiveness needed in these heterogeneous-resolution merging tools. The results demonstrate its efficiency, robustness and high-throughput coverage. AVAILABILITY: http://sbg.cib.csic.es/Software/ADP_EM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

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.     

Hidden Markov models that use predicted secondary structures for fold recognition.

There are many proteins that share the same fold but have no clear sequence similarity. To predict the structure of these proteins, so called "protein fold recognition methods" have been developed. During the last few years, improvements of protein fold recognition methods have been achieved through the use of predicted secondary structures (Rice and Eisenberg, J Mol Biol 1997;267:1026-1038), as well as by using multiple sequence alignments in the form of hidden Markov models (HMM) (Karplus et al., Proteins Suppl 1997;1:134-139). To test the performance of different fold recognition methods, we have developed a rigorous benchmark where representatives for all proteins of known structure are matched against each other. Using this benchmark, we have compared the performance of automatically-created hidden Markov models with standard-sequence-search methods. Further, we combine the use of predicted secondary structures and multiple sequence alignments into a combined method that performs better than methods that do not use this combination of information. Using only single sequences, the correct fold of a protein was detected for 10% of the test cases in our benchmark. Including multiple sequence information increased this number to 16%, and when predicted secondary structure information was included as well, the fold was correctly identified in 20% of the cases. Moreover, if the correct secondary structure was used, 27% of the proteins could be correctly matched to a fold. For comparison, blast2, fasta, and ssearch identifies the fold correctly in 13-17% of the cases. Thus, standard pairwise sequence search methods perform almost as well as hidden Markov models in our benchmark. This is probably because the automatically-created multiple sequence alignments used in this study do not contain enough diversity and because the current generation of hidden Markov models do not perform very well when built from a few sequences.     

Identification of subunit-subunit interactions in bacteriophage P22 procapsids by chemical cross-linking and mass spectrometry

Viral capsids are dynamic structures which self-assemble and undergo a series of structural transformations to form infectious viruses. The dsDNA bacteriophage P22 is used as a model system to study the assembly and maturation of icosahedral dsDNA viruses. The P22 procapsid, which is the viral capsid precursor, is assembled from coat protein with the aid of scaffolding protein. Upon DNA packaging, the capsid lattice expands and becomes a stable virion. Chemical cross-linking analyzed by mass spectrometry was used to identify residue specific inter- and intra-subunit interactions in the P22 procapsids. All the intersubunit cross-links occurred between residues clustered in a loop region (residues 157-207) which was previously identified by mass spectrometry based on hydrogen/deuterium exchange and biochemical experiments. DSP and BS3 which have similar distance constraints (12 angstroms and 11.4 angstroms, respectively) cross-linked the same residues between two subunits in the procapsids (K183-K183), whereas DST, a shorter cross-linker, cross-linked lysine 175 in one subunit to lysine 183 in another subunit. The replacement of threonine with a cysteine at residue 182 immediately adjacent to the K183 cross-linking site resulted in slow spontaneous disulfide bond formation in the procapsids without perturbing capsid integrity, thus suggesting flexibility within the loop region and close proximity between neighboring loop regions. To build a detailed structure model, we have predicted the secondary structure elements of the P22 coat protein, and attempted to thread the prediction onto identified helical elements of cryoEM 3D reconstruction. In this model, the loop regions where chemical cross-linkings occurred correspond to the extra density (ED) regions which protrude upward from the outside of the capsids and face one another around the symmetry axes.     

Automated three-dimensional reconstruction of keyhole limpet hemocyanin type 1

We have reconstructed a three-dimensional map of keyhole limpet hemocyanin isoform 1 (KLH1), using our automated data collection software, Leginon, integrated with particle selection algorithms, and the SPIDER reconstruction package. KLH1, a 7.9 MDa macromolecule, is an extracellular respiratory pigment composed of two asymmetric decamers, and presents an overall D(5) point-group symmetry. The reconstruction is in agreement with previous data published on molluscan hemocyanins. The reconstructed map (11.3A resolution, 3sigma criterion) was used to fit an available X-ray crystallography structure of Octopus dofleini Odg, solved at 2.3A [J. Mol. Biol. 278 (4) (1998) 855], with satisfactory results. The results validate the approach of automating the cryoEM process and demonstrate that the quality of the images acquired and the particles selected is comparable to those obtained using manual methods. Several problems remain to be solved however before these results can be generalized.     

RNA-Protein Interactions in Some Small Plant Viruses

Abstract

The structure of the three quasi-equivalent protein subunits A, B and C of the spherical, T = 3 southern bean mosaic virus (SBMV) have been carefully built in accordance with a refined electron density map of the complete virus. The lower electron density in the RNA portion of the map could not be explicitly interpreted in terms of a preferred RNA structure on which some icosahedral symmetry might have been imposed. However, the extremely basic nature of the interior surface of the coat protein must be associated with the binding and organization of the RNA. Comparison with the small spherical, T = 1 satellite tobacco necrosis virus (STNV; Liljas et al., J. Mol. Biol. 159, 93–108,1982) and the T = 1 aggregate of alfalfa mosaic virus (AMV) protein (Fukuyama et al., J. Mol. Biol. 150, 33–41, 1981) showed similar results.

The pattern of basic residues on the SBMV coat protein surface facing the RNA is able to dock a 9 base pair double-helical A-RNA structure with surprising accuracy. The basic residues are each associated with a different phosphate and the protein can make interactions with five bases in the minor groove. This may be one of a small number of ways in which the RNA interacts with SBMV coat protein.

The self-assembly of SBMV has been studied in relation to the presence of the 63 basic amino-terminal coat protein sequence, pH, Ca²⁺ and Mg²⁺ ions and RNA. These results have led to a two-state model where the “relaxed” dimers initially self-assemble into 10-mer caps which nucleate the assembly of T = 1 or T = 3 capsids depending on the charge state of the carboxyl group clusters in the subunit contact region. The two-state condition of dimers in a viral coat protein extends the range of structures originally envisaged by Caspar and Klug (Cold Spring Harbor Symp. Quant. Biol. 27, 1–24, 1962).     

Flexible fitting of high-resolution x-ray structures into cryoelectron microscopy maps using biased molecular dynamics simulations

A methodology for flexible fitting of all-atom high-resolution structures into low-resolution cryoelectron microscopy (cryo-EM) maps is presented. Flexibility of the modeled structure is simulated by classical molecular dynamics and an additional effective potential is introduced to enhance the fitting process. The additional potential is proportional to the correlation coefficient between the experimental cryo-EM map and a synthetic map generated for an all-atom structure being fitted to the map. The additional forces are calculated as a gradient of the correlation coefficient. During the molecular dynamics simulations under the additional forces, the molecule undergoes a conformational transition that maximizes the correlation coefficient, which results in a high-accuracy fit of all-atom structure into a cryo-EM map. Using five test proteins that exhibit structural rearrangement during their biological activity, we demonstrate performance of our method. We also test our method on the experimental cryo-EM of elongation factor G and show that the model obtained is comparable to previous studies. In addition, we show that overfitting can be avoided by assessing the quality of the fitted model in terms of correlation coefficient and secondary structure preservation.     

Systematic and Comparative Evaluation of Software Programs for Template‐Based Modeling of Protein Structures

Modeling protein structures is critical for understanding protein functions in various biological and biotechnological studies. Among representative protein structure modeling approaches, template‐based modeling (TBM) is by far the most reliable and most widely used approach to model protein structures. However, it still remains as a challenge to select appropriate software programs for pairwise alignments and model building, two major steps of the TBM. In this paper, pairwise alignment methods for TBM are first compared with respect to the quality of structure models built using these methods. This comparative study is conducted using comprehensive datasets, which cover 6185 domain sequences from Structural Classification of Proteins extended for soluble proteins, and 259 Protein Data Bank entries (whole protein sequences) from Orientations of Proteins in Membranes database for membrane proteins. Overall, a profile‐based method, especially PSI‐BLAST, consistently shows high performance across the datasets and model evaluation metrics used. Next, use of two model building programs, MODELLER and SWISS‐MODEL, does not seem to significantly affect the quality of protein structure models built except for the Hard group (a group of relatively less homologous proteins) of membrane proteins. The results presented in this study will be useful for more accurate implementation of TBM.