Flexible fitting in 3D-EM with incomplete data on superfamily variability

We present a substantial improvement of S-flexfit, our recently proposed method for flexible fitting in three dimensional electron microscopy (3D-EM) at a resolution range of 8-12A, together with a comparison of the method capabilities with Normal Mode Analysis (NMA), application examples and a user's guide. S-flexfit uses the evolutionary information contained in protein domain databases like CATH, by means of the structural alignment of the elements of a protein superfamily. The added development is based on a recent extension of the Singular Value Decomposition (SVD) algorithm specifically designed for situations with missing data: Incremental Singular Value Decomposition (ISVD). ISVD can manage gaps and allows considering more aminoacids in the structural alignment of a superfamily, extending the range of application and producing better models for the fitting step of our methodology. Our previous SVD-based flexible fitting approach can only take into account positions with no gaps in the alignment, being appropriate when the superfamily members are relatively similar and there are few gaps. However, with new data coming from structural proteomics works, the later situation is becoming less likely, making ISVD the technique of choice for further works. We present the results of using ISVD in the process of flexible fitting with both simulated and experimental 3D-EM maps (GroEL and Poliovirus 135S cell entry intermediate).     

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.     

SPI-EM: towards a tool for predicting CATH superfamilies in 3D-EM maps

In this paper the theoretical framework used to build a superfamily probability in electron microscopy (SPI-EM) is presented. SPI-EM is a new tool for determining the homologous superfamily to which a protein domain belongs looking at its three-dimensional electron microscopy map. The homologous superfamily is assigned according to the domain-architecture database CATH. Our method follows a probabilistic approach applied to the results of fitting protein domains into maps of proteins and the computation of local cross-correlation coefficient measures. The method has been tested and its usefulness proven with isolated domains at a resolution of 8 A and 12 A. Results obtained with simulated and experimental data at 10 A suggest that it is also feasible to detect the correct superfamily of the domains when dealing with electron microscopy maps containing multi-domain proteins. The inherent difficulties and limitations that multi-domain proteins impose are discussed. Our procedure is complementary to other techniques existing in the field to detect structural elements in electron microscopy maps like alpha-helices and beta-sheets. Based on the proposed methodology, a database of relevant distributions is being built to serve the community.     

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.     

Biased coarse-grained molecular dynamics simulation approach for flexible fitting of X-ray structure into cryo electron microscopy maps

Several approaches have been introduced to interpret, in terms of high-resolution structure, low-resolution structural data as obtained from cryo-EM. As conformational changes are often observed in biological molecules, these techniques need to take into account the flexibility of proteins. Flexibility has been described in terms of movement between rigid domains and between rigid secondary structure elements, which present some limitations for studying dynamical properties. Normal mode analysis has also been used, but is limited to medium resolution data. All-atom molecular dynamics fitting techniques are more appropriate to fit structures into higher-resolution data as full protein flexibility is considered, but are cumbersome in terms of computational time. Here, we introduce a coarse-grained approach; a Go-model was used to represent biological molecules, combined with biased molecular dynamics to reproduce accurately conformational transitions. Illustrative examples on simulated data are shown. Accurate fittings can be obtained for resolution ranging from 5 to 20 Å. The approach was also tested on experimental data of Elongation Factor G and Escherichia coli RNA polymerase, where its validity is compared to previous models obtained from different techniques. This comparison demonstrates that quantitative flexible techniques, as opposed to manual docking, need to be considered to interpret low-resolution data.     

Determining and visualizing flexibility in protein structures

How to compare the structures of an ensemble of protein conformations is a fundamental problem in structural biology. As has been previously observed, the widely used RMSD measure due to Kabsch, in which a rigid‐body superposition minimizing the least‐squares positional deviations is performed, has its drawbacks when comparing and visualizing a set of flexible protein structures. Here, we develop a method, fleximatch, of protein structure comparison that takes flexibility into account. Based on a distance matrix measure of flexibility, a weighted superposition of distance matrices rather than of atomic coordinates is performed. Subsequently, this allows a consistent determination of (a) a superposition of structures for visualization, (b) a partitioning of the protein structure into rigid molecular components (core atoms), and (c) an atomic mobility measure. The method is suitable for highlighting both particularly flexible and rigid parts of a protein from structures derived from NMR, X‐ray diffraction or molecular simulation. Proteins 2015; 83:820–826. © 2015 Wiley Periodicals, Inc.     

Integrating electron microscopy information into existing Distributed Annotation Systems

The increase of daily released bioinformatic data has generated new ways of organising and disseminating information. Specifically, in the field of sequence data, many efforts have been made not only to store information in databases, but also to annotate it and then share these annotations through a standard XML (eXtensible Markup Language) protocol and appropriate integration clients. This is the context in which the Distributed Annotation System (DAS) has emerged in genomics. Additionally, initiatives in the field of structural data, such as the extension of DAS to atomic resolution data, which generated the SPICE client, have also occurred. This paper presents 3D-EM DAS, a further extension of the DAS protocol that allows sharing annotations about hybrid models. This annotation system has been built on the basis of the EMDB, which stores Three-dimensional Electron Microscopy (3D-EM) volumes, PDB, which houses atomic coordinates, and UniProt (for protein sequences) databases. In this way, annotations for sequences, atomic coordinates, and 3D-EM volumes are collected and displayed through a single graphical visualization client. Thus, users have an integrated view of all the annotations together with the whole macromolecule (3D-EM map coming from EMDB), the atomic resolution structures fitted into it (coordinates coming from PDB) and the sequences corresponding to each of the structures (from UniProt).     

Conformational changes of the flavivirus E glycoprotein

Dengue virus, a member of the Flaviviridae family, has a surface composed of 180 copies each of the envelope (E) glycoprotein and the membrane (M) protein. The crystal structure of an N-terminal fragment of E has been determined and compared with a previously described structure. The primary difference between these structures is a 10 degrees rotation about a hinge relating the fusion domain DII to domains DI and DIII. These two rigid body components were used for independent fitting of E into the cryo-electron microscopy maps of both immature and mature dengue viruses. The fitted E structures in these two particles showed a difference of 27 degrees between the two components. Comparison of the E structure in its postfusion state with that in the immature and mature virions shows a rotation approximately around the same hinge. Flexibility of E is apparently a functional requirement for assembly and infection of flaviviruses.     

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.     

FlexProt: alignment of flexible protein structures without a predefinition of hinge regions.

FlexProt is a novel technique for the alignment of flexible proteins. Unlike all previous algorithms designed to solve the problem of structural comparisons allowing hinge-bending motions, FlexProt does not require an a priori knowledge of the location of the hinge(s). FlexProt carries out the flexible alignment, superimposing the matching rigid subpart pairs, and detects the flexible hinge regions simultaneously. A large number of methods are available to handle rigid structural alignment. However, proteins are flexible molecules, which may appear in different conformations. Hence, protein structural analysis requires algorithms that can deal with molecular flexibility. Here, we present a method addressing specifically a flexible protein alignment task. First, the method efficiently detects maximal congruent rigid fragments in both molecules. Transforming the task into a graph theoretic problem, our method proceeds to calculate the optimal arrangement of previously detected maximal congruent rigid fragments. The fragment arrangement does not violate the protein sequence order. A clustering procedure is performed on fragment-pairs which have the same 3-D rigid transformation regardless of insertions and deletions (such as loops and turns) which separate them. Although the theoretical worst case complexity of the algorithm is O(n(6)), in practice FlexProt is highly efficient. It performs a structural comparison of a pair of proteins 300 amino acids long in about seven seconds on a standard desktop PC (400 MHz Pentium II processor with 256MB internal memory). We have performed extensive experiments with the algorithm. An assortment of these results is presented here. FlexProt can be accessed via WWW at bioinfo3d.cs.tau.ac.il/FlexProt/.     

Structural and functional characterization of α-isopropylmalate synthase and citramalate synthase, members of the LeuA dimer superfamily

The manipulation of modular regulatory domains from allosteric enzymes represents a possible mechanism to engineer allostery into non-allosteric systems. Currently, there is insufficient understanding of the structure/function relationships in modular regulatory domains to rationally implement this methodology. The LeuA dimer regulatory domain represents a well-conserved, novel fold responsible for the regulation of two enzymes involved in branched chain amino acid biosynthesis, α-isopropylmalate synthase and citramalate synthase. The LeuA dimer regulatory domain is responsible for the feedback inhibition of these enzymes by their respective downstream products. Both enzymes display multidomain architecture with a conserved N-terminal TIM barrel catalytic domain and a C-terminal (βββα)2 LeuA dimer domain joined by a flexible linker region. Due to the similarity of three-dimensional structure and catalytic mechanism combined with low sequence similarity, we propose these enzymes can be classified as members of the LeuA dimer superfamily. Despite their similarity, members of the LeuA dimer superfamily display diversity in their allosteric mechanisms. In this review, structural aspects of the LeuA dimer superfamily are discussed followed by three examples highlighting the diversity of allosteric mechanisms in the LeuA dimer superfamily.     

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.     

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.     

Normal mode-based fitting of atomic structure into electron density maps: application to sarcoplasmic reticulum Ca-ATPase

A method for the flexible docking of high-resolution atomic structures into lower resolution densities derived from electron microscopy is presented. The atomic structure is deformed by an iterative process using combinations of normal modes to obtain the best fit of the electron microscopical density. The quality of the computed structures has been evaluated by several techniques borrowed from crystallography. Two atomic structures of the SERCA1 Ca-ATPase corresponding to different conformations were used as a starting point to fit the electron density corresponding to a different conformation. The fitted models have been compared to published models obtained by rigid domain docking, and their relation to the known crystallographic structures are explored by normal mode analysis. We find that only a few number of modes contribute significantly to the transition. The associated motions involve almost exclusively rotation and translation of the cytoplasmic domains as well as displacement of cytoplasmic loops. We suggest that the movements of the cytoplasmic domains are driven by the conformational change that occurs between nonphosphorylated and phosphorylated intermediate, the latter being mimicked by the presence of vanadate at the phosphorylation site in the electron microscopy structure.     

An atomic resolution structure for human fibroblast growth factor 1

A 1.10-A atomic resolution X-ray structure of human fibroblast growth factor 1 (FGF-1), a member of the beta-trefoil superfold, has been determined. The beta-trefoil is one of 10 fundamental protein superfolds and is the only superfold to exhibit 3-fold structural symmetry (comprising 3 "trefoil" units). The quality of the diffraction data permits unambiguous assignment of Asn, Gln, and His rotamers, Pro ring pucker, as well as refinement of atomic anisotropic displacement parameters (ADPs). The FGF-1 structure exhibits numerous core-packing defects, detectable using a 1.0-A probe radius. In addition to contributing to the relatively low thermal stability of FGF-1, these defects may also permit domain motions within the structure. The availability of refined ADPs allows a translation/libration/screw (TLS) analysis of putative rigid body domains. The TLS analysis shows that beta-strands 6-12 together form a rigid body, and there is a clear demarcation in TLS motions between the adjacent carboxyl- and amino-termini. Although separate from beta-strands 6-12, the individual beta-strands 1-5 do not exhibit correlated motions; thus, this region appears to be comparatively flexible. The heparin-binding contacts of FGF-1 are located within beta-strands 6-12; conversely, a significant portion of the receptor-binding contacts are located within beta-strands 1-5. Thus, the observed rigid body motion in FGF-1 appears related to the ligand-binding functionalities.     

The structure of neurexin 1α reveals features promoting a role as synaptic organizer

α-neurexins are essential synaptic adhesion molecules implicated in autism spectrum disorder and schizophrenia. The α-neurexin extracellular domain consists of six LNS domains interspersed by three EGF-like repeats and interacts with many different proteins in the synaptic cleft. To understand how α-neurexins might function as synaptic organizers, we solved the structure of the neurexin 1α extracellular domain (n1α) to 2.65 ?. The L-shaped molecule can be divided into a flexible repeat I (LNS1-EGF-A-LNS2), a rigid horseshoe-shaped repeat II (LNS3-EGF-B-LNS4) with structural similarity to so-called reelin repeats, and an extended repeat III (LNS5-EGF-B-LNS6) with controlled flexibility. A 2.95 ? structure of n1α carrying splice insert SS#3 in LNS4 reveals that SS#3 protrudes as a loop and does not alter the rigid arrangement of repeat II. The global architecture imposed by conserved structural features enables α-neurexins to recruit and organize proteins in distinct and variable ways, influenced by splicing, thereby promoting synaptic function.     

QUAFIT: A Novel Method for the Quaternary Structure Determination from Small-Angle Scattering Data

The new QUAFIT method for determining the quaternary structure of biological macromolecular assemblies by analyzing x-ray or neutron small-angle scattering data is presented. The method is based on the idea that asymmetric monomers, formed by rigid domains of known atomic structure possibly connected by flexible linkers of known sequence, are assembled according to a point-group symmetry combined with a screw axis. Scattering amplitudes of domains and linkers are determined by means of a spherical harmonics expansion and combined to get the form factor of the assembly. To avoid any overlap among domains, the contact distance between two asymmetric domains is determined as a function of their orientation by a new algorithm, based on Stone's Invariants expansion. To account for continuity and compactness of the whole assembly, an anisotropic Lennard-Jones potential among domains, written in terms of the contact distances, is included in the merit function. QUAFIT allows for the simultaneous presence of oligomerization intermediates as well as of monomers distributed over multiple conformations. QUAFIT has been tested by studying the structure of a high molecular weight protein, the hemocyanin from Octopus vulgaris, under solution conditions that stabilize the decameric form or induce dissociation into monomers, respectively. Results are in very good agreement with the structural model derived from electron microscopy observations.