Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM

A new method for the flexible fitting of high-resolution structures into low-resolution maps of macromolecular complexes from electron microscopy has been recently described in applications to simulated electron density maps. This method uses a linear combination of low-frequency normal modes in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. Gradient-following techniques in the coordinate space of collective normal modes are used to optimize the overall correlation coefficient between computed and measured electron densities. With this approach, multi-scale flexible fitting can be performed using all-atoms or Calpha atoms. In this paper, illustrative studies of normal mode based flexible fitting to experimental cryo-EM maps are presented for three different systems. Large, functionally relevant conformational changes for elongation factor G bound to the ribosome, Escherichia coli RNA polymerase and cowpea chlorotic mottle virus are elucidated as the result of the application of NMFF from high-resolution structures to cryo-electron microscopy maps.     

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.     

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.     

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.     

Consensus among flexible fitting approaches improves the interpretation of cryo-EM data

Cryo-elecron microscopy (cryo-EM) can provide important structural information of large macromolecular assemblies in different conformational states. Recent years have seen an increase in structures deposited in the Protein Data Bank (PDB) by fitting a high-resolution structure into its low-resolution cryo-EM map. A commonly used protocol for accommodating the conformational changes between the X-ray structure and the cryo-EM map is rigid body fitting of individual domains. With the emergence of different flexible fitting approaches, there is a need to compare and revise these different protocols for the fitting. We have applied three diverse automated flexible fitting approaches on a protein dataset for which rigid domain fitting (RDF) models have been deposited in the PDB. In general, a consensus is observed in the conformations, which indicates a convergence from these theoretically different approaches to the most probable solution corresponding to the cryo-EM map. However, the result shows that the convergence might not be observed for proteins with complex conformational changes or with missing densities in cryo-EM map. In contrast, RDF structures deposited in the PDB can represent conformations that not only differ from the consensus obtained by flexible fitting but also from X-ray crystallography. Thus, this study emphasizes that a "consensus" achieved by the use of several automated flexible fitting approaches can provide a higher level of confidence in the modeled configurations. Following this protocol not only increases the confidence level of fitting, but also highlights protein regions with uncertain fitting. Hence, this protocol can lead to better interpretation of cryo-EM data.     

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.     

INFOS: spectrum fitting software for NMR analysis

Software for fitting of NMR spectra in MATLAB is presented. Spectra are fitted in the frequency domain, using Fourier transformed lineshapes, which are derived using the experimental acquisition and processing parameters. This yields more accurate fits compared to common fitting methods that use Lorentzian or Gaussian functions. Furthermore, a very time-efficient algorithm for calculating and fitting spectra has been developed. The software also performs initial peak picking, followed by subsequent fitting and refinement of the peak list, by iteratively adding and removing peaks to improve the overall fit. Estimation of error on fitting parameters is performed using a Monte-Carlo approach. Many fitting options allow the software to be flexible enough for a wide array of applications, while still being straightforward to set up with minimal user input.     

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/.     

Mechanisms of SecM-Mediated Stalling in the Ribosome

Nascent-peptide modulation of translation is a common regulatory mechanism of gene expression. In this mechanism, while the nascent peptide is still in the exit tunnel of the ribosome, it induces translational pausing, thereby controlling the expression of downstream genes. One example is SecM, which inhibits peptide-bond formation in the ribosome's peptidyl transferase center (PTC) during its own translation, upregulating the expression of the protein translocase SecA. Although biochemical experiments and cryo-electron microscopy data have led to the identification of some residues involved in SecM recognition, the full pathway of interacting residues that connect SecM to the PTC through the ribosome has not yet been conclusively established. Here, using the cryo-electron microscopy data, we derived the first (to our knowledge) atomic model of the SecM-stalled ribosome via molecular-dynamics flexible fitting, complete with P- and A-site tRNAs. Subsequently, we carried out simulations of native and mutated SecM-stalled ribosomes to investigate possible interaction pathways between a critical SecM residue, R163, and the PTC. In particular, the simulations reveal the role of SecM in altering the position of the tRNAs in the ribosome, and thus demonstrate how the presence of SecM in the exit tunnel induces stalling. Finally, steered molecular-dynamics simulations in which SecM was pulled toward the tunnel exit suggest how SecA interacting with SecM from outside the ribosome relieves stalling.     

Domain motions of EF-G bound to the 70S ribosome: insights from a hand-shaking between multi-resolution structures

Molecular modeling and information processing techniques were combined to refine the structure of translocase (EF-G) in the ribosome-bound form against data from cryoelectron microscopy (cryo-EM). We devised a novel multi-scale refinement method based on vector quantization and force-field methods that gives excellent agreement between the flexibly docked structure of GDP. EF-G and the cryo-EM density map at 17 A resolution. The refinement reveals a dramatic "induced fit" conformational change on the 70S ribosome, mainly involving EF-G's domains III, IV, and V. The rearrangement of EF-G's structurally preserved regions, mediated and guided by flexible linkers, defines the site of interaction with the GTPase-associated center of the ribosome.     

Highly constrained multiple-copy refinement of protein crystal structures

In the course of refining atomic protein structures, one often encounters difficulty with molecules that are unusually flexible or otherwise disordered. We approach the problem by combining two relatively recent developments: simultaneous refinement of multiple protein conformations and highly constrained refinement. A constrained Langevin dynamics refinement is tested on two proteins: neurotrophin-3 and glutamine synthetase. The method produces closer agreement between the calculated and observed scattering amplitudes than standard, single-copy, Gaussian atomic displacement parameter refinement. This is accomplished without significantly increasing the number of fitting parameters in the model. These results suggest that loop motion in proteins within a crystal lattice can be extensive and that it is poorly modeled by isotropic Gaussian distributions for each atom. Proteins 29:426–432, 1997. © 1997 Wiley-Liss, Inc.     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

Symmetry-restrained flexible fitting for symmetric EM maps

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.     

Computational prediction of atomic structures of helical membrane proteins aided by EM maps

Integral membrane proteins pose a major challenge for protein-structure prediction because only approximately 100 high-resolution structures are available currently, thereby impeding the development of rules or empirical potentials to predict the packing of transmembrane alpha-helices. However, when an intermediate-resolution electron microscopy (EM) map is available, it can be used to provide restraints which, in combination with a suitable computational protocol, make structure prediction feasible. In this work we present such a protocol, which proceeds in three stages: 1), generation of an ensemble of alpha-helices by flexible fitting into each of the density rods in the low-resolution EM map, spanning a range of rotational angles around the main helical axes and translational shifts along the density rods; 2), fast optimization of side chains and scoring of the resulting conformations; and 3), refinement of the lowest-scoring conformations with internal coordinate mechanics, by optimizing the van der Waals, electrostatics, hydrogen bonding, torsional, and solvation energy contributions. In addition, our method implements a penalty term through a so-called tethering map, derived from the EM map, which restrains the positions of the alpha-helices. The protocol was validated on three test cases: GpA, KcsA, and MscL.     

Conformation and dynamics of ribosomal stalk protein L12 in solution and on the ribosome

During translation, the ribosome and several of its constituent proteins undergo structural transitions between different functional states. Protein L12, present in four copies in prokaryotic ribosomes, forms a flexible "stalk" with key functions in factor-dependent GTP hydrolysis during translocation. Here we have used heteronuclear NMR spectroscopy to characterize L12 conformation and dynamics in solution and on the ribosome. Isolated L12 forms a symmetric dimer mediated by the N-terminal domains (NTDs), to which each C-terminal domain (CTD) is connected via an unstructured hinge segment. The overall structure can be described as three ellipsoids joined by flexible linkers. No persistent contacts are seen between the two CTDs, or between the NTD and CTD in the L12 dimer in solution. In the (1)H-(15)N HSQC spectrum of the Escherichia coli 70S ribosome, a single set of cross-peaks are observed for residues 40-120 of L12, the intensities of which correspond to only two of four protein copies. The structure of the CTDs observed on the ribosome is indistinguishable from that of isolated L12. These results indicate that two CTDs with identical average structures are mobile and extend away from the ribosome, while the other two copies most likely interact tightly with the ribosome even in the absence of translational factors.     

PaFlexPepDock: Parallel Ab-Initio Docking of Peptides onto Their Receptors with Full Flexibility Based on Rosetta

Structural information related to protein–peptide complexes can be very useful for novel drug discovery and design. The computational docking of protein and peptide can supplement the structural information available on protein–peptide interactions explored by experimental ways. Protein–peptide docking of this paper can be described as three processes that occur in parallel: ab-initio peptide folding, peptide docking with its receptor, and refinement of some flexible areas of the receptor as the peptide is approaching. Several existing methods have been used to sample the degrees of freedom in the three processes, which are usually triggered in an organized sequential scheme. In this paper, we proposed a parallel approach that combines all the three processes during the docking of a folding peptide with a flexible receptor. This approach mimics the actual protein–peptide docking process in parallel way, and is expected to deliver better performance than sequential approaches. We used 22 unbound protein–peptide docking examples to evaluate our method. Our analysis of the results showed that the explicit refinement of the flexible areas of the receptor facilitated more accurate modeling of the interfaces of the complexes, while combining all of the moves in parallel helped the constructing of energy funnels for predictions.     

Flexible fitting to cryo-electron microscopy maps with coarse-grained elastic network models

Cryo-electron microscopy has become an important tool for protein structure determination in recent decades. Since proteins may exist in multiple conformational states, combining high resolution X-ray or NMR structures with cryo-electron microscopy maps is a useful approach to obtain proteins in different functional states. Flexible fitting methods used in cryo-electron microscopy aim to obtain an unknown protein conformation from a high resolution structure and a cryo-electron microscopy map. Since all-atom flexible fitting is computationally expensive, many efficient flexible fitting algorithms that utilize coarse-grained elastic network models have been proposed. In this study, we investigated performance of three coarse-grained elastic network model-based flexible fitting methods (EMFF, iModFit, NMFF) using 25 protein pairs at four resolutions. This study shows that the application of coarse-grained elastic network models to flexible fitting of cryo-electron microscopy maps can provide fast and fruitful models of various conformational states of proteins.