Cryo-EM Data Are Superior to Contact and Interface Information in Integrative Modeling

Protein-protein interactions carry out a large variety of essential cellular processes. Cryo-electron microscopy (cryo-EM) is a powerful technique for the modeling of protein-protein interactions at a wide range of resolutions, and recent developments have caused a revolution in the field. At low resolution, cryo-EM maps can drive integrative modeling of the interaction, assembling existing structures into the map. Other experimental techniques can provide information on the interface or on the contacts between the monomers in the complex. This inevitably raises the question regarding which type of data is best suited to drive integrative modeling approaches. Systematic comparison of the prediction accuracy and specificity of the different integrative modeling paradigms is unavailable to date. Here, we compare EM-driven, interface-driven, and contact-driven integrative modeling paradigms. Models were generated for the protein docking benchmark using the ATTRACT docking engine and evaluated using the CAPRI two-star criterion. At 20 Å resolution, EM-driven modeling achieved a success rate of 100%, outperforming the other paradigms even with perfect interface and contact information. Therefore, even very low resolution cryo-EM data is superior in predicting heterodimeric and heterotrimeric protein assemblies. Our study demonstrates that a force field is not necessary, cryo-EM data alone is sufficient to accurately guide the monomers into place. The resulting rigid models successfully identify regions of conformational change, opening up perspectives for targeted flexible remodeling.     

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.     

Chasing funnels on protein-protein energy landscapes at different resolutions

Studies of intermolecular energy landscapes are important for understanding protein association and adequate modeling of protein interactions. Landscape representation at different resolutions can be used for the refinement of docking predictions and detection of macro characteristics, like the binding funnel. A representative set of protein-protein complexes was used to systematically map the intermolecular landscape by grid-based docking. The change of the resolution was achieved by varying the range of the potential, according to the variable resolution GRAMM methodology. A formalism was developed to consistently parameterize the potential and describe essential characteristics of the landscape. The results of gradual landscape smoothing, from high to low resolution, indicate that i), the number of energy basins, the landscape ruggedness, and the slope decrease accordingly; ii), the number of near-native matches, defined as those inside the funnel, increases until the trend breaks down at critical resolution; the rate of the increase and the critical resolution are specific to the type of a complex (enzyme inhibitor, antigen-antibody, and other), reflect known underlying recognition factors, and correlate with earlier determined estimates of the funnel size; iii), the native/nonnative energy gap, a major characteristic of the energy minima hierarchy, remains constant; and iv), the putative funnel (defined as the deepest basin) has the largest average depth-related ruggedness and slope, at all resolutions. The results facilitate better understanding of the binding landscapes and suggest directions for implementation in practical docking protocols.     

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

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

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.     

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

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

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

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

Structural studies of the translational apparatus.

Significant progress is occurring at an accelerated rate in structural studies of ribosomes. A 3D cryoelectron microscopy map of the 70S ribosome from Escherichia coli is available at 15 A resolution and a combination of cryoelectron microscopy with X-ray crystallography has yielded a 9 A resolution map of the 50S subunit from Haloarcula marismortui, an archaebacterium. For eukaryotes, 3D cryomaps of the 80S ribosomes from yeast and from mammals have now been produced at resolutions in the range 20 to 30 A. The most ground-breaking results have been obtained from the 3D mapping of ligands in functional studies of prokaryotic ribosomes. These studies, which directly visualize the protein synthesis machine in action, have brought new excitement to a field that was relatively dormant during the past decade.     

Voltage-gated K+ channel from mammalian brain: 3D structure at 18A of the complete (alpha)4(beta)4 complex

Voltage-sensitive K(+) channels (Kv) serve numerous important roles, e.g. in the control of neuron excitability and the patterns of synaptic activity. Here, we use electron microscopy (EM) and single particle analysis to obtain the first, complete structure of Kv1 channels, purified from rat brain, which contain four transmembrane channel-forming alpha-subunits and four cytoplasmically-associated beta-subunits. The 18A resolution structure reveals an asymmetric, dumb-bell-shaped complex with 4-fold symmetry, a length of 140A and variable width. By fitting published X-ray data for recombinant components to our EM map, the modulatory (beta)(4) was assigned to the innermost 105A end, the N-terminal (T1)(4) domain of the alpha-subunit to the central 50A moiety and the pore-containing portion to the 125A membrane part. At this resolution, the selectivity filter could not be localised. Direct contact of the membrane component with the central (T1)(4) domain occurs only via peripheral connectors, permitting communication between the channel and beta-subunits for coupling of responses to changes in excitability and metabolic status of neurons.     

Automated segmentation of molecular subunits in electron cryomicroscopy density maps

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

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.     

Improving integrative 3D modeling into low‐ to medium‐resolution electron microscopy structures with evolutionary couplings

Electron microscopy (EM) continues to provide near‐atomic resolution structures for well‐behaved proteins and protein complexes. Unfortunately, structures of some complexes are limited to low‐ to medium‐resolution due to biochemical or conformational heterogeneity. Thus, the application of unbiased systematic methods for fitting individual structures into EM maps is important. A method that employs co‐evolutionary information obtained solely from sequence data could prove invaluable for quick, confident localization of subunits within these structures. Here, we incorporate the co‐evolution of intermolecular amino acids as a new type of distance restraint in the integrative modeling platform in order to build three‐dimensional models of atomic structures into EM maps ranging from 10–14 Å in resolution. We validate this method using four complexes of known structure, where we highlight the conservation of intermolecular couplings despite dynamic conformational changes using the BAM complex. Finally, we use this method to assemble the subunits of the bacterial holo‐translocon into a model that agrees with previous biochemical data. The use of evolutionary couplings in integrative modeling improves systematic, unbiased fitting of atomic models into medium‐ to low‐resolution EM maps, providing additional information to integrative models lacking in spatial data.     

Detection of secondary and supersecondary structures of proteins from cryo-electron microscopy

Recent advances in three-dimensional electron microscopy (3D EM) have enabled the quantitative visualization of the structural building blocks of proteins at improved resolutions. We provide algorithms to detect the secondary structures (α-helices and β-sheets) from proteins for which the volumetric maps are reconstructed at 6–10 Å resolution. Additionally, we show that when the resolution is coarser than 10 Å, some of the supersecondary structures can be detected from 3D EM maps. For both these algorithms, we employ tools from computational geometry and differential topology, specifically the computation of stable/unstable manifolds of certain critical points of the distance function induced by the molecular surface. Our results connect mathematically well-defined constructions with bio-chemically induced structures observed in proteins.     

HingeProt: automated prediction of hinges in protein structures

Proteins are highly flexible molecules. Prediction of molecular flexibility aids in the comprehension and prediction of protein function and in providing details of functional mechanisms. The ability to predict the locations, directions, and extent of molecular movements can assist in fitting atomic resolution structures to low-resolution EM density maps and in predicting the complex structures of interacting molecules (docking). There are several types of molecular movements. In this work, we focus on the prediction of hinge movements. Given a single protein structure, the method automatically divides it into the rigid parts and the hinge regions connecting them. The method employs the Elastic Network Model, which is very efficient and was validated against a large data set of proteins. The output can be used in applications such as flexible protein-protein and protein-ligand docking, flexible docking of protein structures into cryo-EM maps, and refinement of low-resolution EM structures. The web server of HingeProt provides convenient visualization of the results and is available with two mirror sites at http://www.prc.boun.edu.tr/appserv/prc/HingeProt3 and http://bioinfo3d.cs.tau.ac.il/HingeProt/.     

Damped-dynamics flexible fitting

In fitting atomic structures into EM maps, it often happens that the map corresponds to a different conformation of the structure. We have developed a new methodology to handle these situations that preserves the covalent geometry of the structure and allows the modeling of large deformations. The first goal is achieved by working in generalized coordinates (positional and internal coordinates), and the second by avoiding harmonic potentials. Instead, we use dampers (shock absorbers) between every pair of atoms, combined with a force field that attracts the atomic structure toward incompletely occupied regions of the EM map. The trajectory obtained by integrating the resulting equations of motion converges to a conformation that, in our validation cases, was very close to the target atomic structure. Compared to current methods, our approach is more efficient and robust against wrong solutions and to overfitting, and does not require user intervention or subjective decisions. Applications to the computation of transition pathways between known conformers, homology and loop modeling, as well as protein docking, are also discussed.     

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.     

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.     

Using situs for flexible and rigid-body fitting of multiresolution single-molecule data

We describe here a set of multiresolution visualization and docking procedures that we refer to as the Situs package. The package was developed to provide an efficient and robust method for the fitting of atomic structures into low-resolution data. The current release was optimized specifically for the visualization and docking of single molecules. A novel 3D graphics viewer, volslice3d, was developed for the package to provide an immersive virtual reality environment for measuring and rendering volumetric data sets. The precision of single-molecule, rigid-body docking was tested on simulated (noise-free) low-resolution density maps. For spatial resolutions near 20 A typically arising in electron microscopy image reconstructions, a docking precision on the order of 1 A can be achieved. The shape-matching score captured the correct solutions in all 10 trial cases and was sufficiently stringent to yield unique matches in 8 systems. Novel routines were developed for the flexible docking of atomic structures whose shape deviates from the corresponding low-resolution shape. Test calculations on isoforms of actin and lactoferrin demonstrate that the flexible docking faithfully reproduces conformational differences with a precision < 2 A if atomic structures are locally conserved.