Combining electron microscopy and comparative protein structure modeling

LPTD: a novel linear programming-based topology determination method for cryo-EM maps

SUMMARY

Topology determination is one of the most important intermediate steps toward building the atomic structure of proteins from their medium-resolution cryo-electron microscopy (cryo-EM) map. The main goal in the topology determination is to identify correct matches (i.e. assignment and direction) between secondary structure elements (SSEs) (α-helices and β-sheets) detected in a protein sequence and cryo-EM density map. Despite many recent advances in molecular biology technologies, the problem remains a challenging issue. To overcome the problem, this article proposes a linear programming-based topology determination (LPTD) method to solve the secondary structure topology problem in three-dimensional geometrical space. Through modeling of the protein's sequence with the aid of extracting highly reliable features and a distance-based scoring function, the secondary structure matching problem is transformed into a complete weighted bipartite graph matching problem. Subsequently, an algorithm based on linear programming is developed as a decision-making strategy to extract the true topology (native topology) between all possible topologies. The proposed automatic framework is verified using 12 experimental and 15 simulated α-β proteins. Results demonstrate that LPTD is highly efficient and extremely fast in such a way that for 77% of cases in the dataset, the native topology has been detected in the first rank topology in <2 s. Besides, this method is able to successfully handle large complex proteins with as many as 65 SSEs. Such a large number of SSEs have never been solved with current tools/methods.

AVAILABILITY AND IMPLEMENTATION

The LPTD package (source code and data) is publicly available at https://github.com/B-Behkamal/LPTD. Moreover, two test samples as well as the instruction of utilizing the graphical user interface have been provided in the shared readme file.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Molecular activities and ligand-binding specificities of StAR-related lipid transfer domains: exploring integrated in silico methods and ensemble-docking approaches

In this study, cholesterol biotransformation gene-set of human steroidogenic acute regulatory protein-related lipid transfer (START) domains were evaluated from high-throughput gene screening approaches. It was shown that STARD1, STARD3 and STARD4 proteins are better effective transporters of cholesterol than STARD5 and STARD6 domains. Docking studies show a strong agreement with gene ontology enrichment data. According to both complementary strategies, it was found that only STARD1, STARD3 and STARD4 are potentially involved in cholesterol biotransformation in mitochondria through Ω1-loop of C-terminal α4-helical domain. Ensemble docking assessment for a set of selected chemicals of protein-chemical networks has shown possible binding probabilities with START domains. Among those, reproductive toxicity evoked drugs (mifepristone), insecticides (rotenone), tobacco pulmonary carcinogens (benzo(a)pyrene) and endocrine disruptor chemicals (EDCs) including perfluorooctanesulfonic acid (PFOS) and aflatoxin B₁ (AFB₁) potentially bound with novel hotspot residues of the α4-helical domain. Compound representation space and clustering approaches reveal that the START proteins show more sensitivity with these lead scaffolds, so they could provide probable barrier assets in cholesterol and steroidogenic acute regulatory (StAR) binding and leads adverse consequences in steroidogenesis. These findings indicate potential START domains and their binding levels with toxic chemicals; sorted viewpoints could be useful as a promising way to identify chemicals with related steroidogenisis impacts on human health.

Improved metrics for comparing structures of macromolecular assemblies determined by 3D electron-microscopy

Recent developments in 3-dimensional electron microcopy (3D-EM) techniques and a concomitant drive to look at complex molecular structures, have led to a rapid increase in the amount of volume data available for biomolecules. This creates a demand for better methods to analyse the data, including improved scores for comparison, classification and integration of data at different resolutions. To this end, we developed and evaluated a set of scoring functions that compare 3D-EM volumes. To test our scores we used a benchmark set of volume alignments derived from the Electron Microscopy Data Bank. We find that the performance of different scores vary with the map-type, resolution and the extent of overlap between volumes. Importantly, adding the overlap information to the local scoring functions can significantly improve their precision and accuracy in a range of resolutions. A combined score involving the local mutual information and overlap (LMI_OV) performs best overall, irrespective of the map category, resolution or the extent of overlap, and we recommend this score for general use. The local mutual information score itself is found to be more discriminatory than cross-correlation coefficient for intermediate-to-low resolution maps or when the map size and density distribution differ significantly. For comparing map surfaces, we implemented two filters to detect the surface points, including one based on the 'extent of surface exposure'. We show that scores that compare surfaces are useful at low resolutions and for maps with evident surface features. All the scores discussed are implemented in TEMPy (http://tempy.ismb.lon.ac.uk/).

A guide to the 3D structure of the ryanodine receptor type 1 by cryoEM

Signal transduction by the ryanodine receptor (RyR) is essential in many excitable cells including all striated contractile cells and some types of neurons. While its transmembrane domain is a classic tetrameric, six-transmembrane cation channel, the cytoplasmic domain is uniquely large and complex, hosting a multiplicity of specialized domains. The overall outline and substructure readily recognizable by electron microscopy make RyR a geometrically well-behaved specimen. Hence, for the last two decades, the 3D structural study of the RyR has tracked closely the technological advances in electron microscopy, cryo-electron microscopy (cryoEM), and computerized 3D reconstruction. This review summarizes the progress in the structural determination of RyR by cryoEM and, bearing in mind the leap in resolution provided by the recent implementation of direct electron detection, analyzes the first near-atomic structures of RyR. These reveal a complex orchestration of domains controlling the channel's function, and help to understand how this could break down as a consequence of disease-causing mutations.

The Importance of Non-accessible Crosslinks and Solvent Accessible Surface Distance in Modeling Proteins with Restraints From Crosslinking Mass Spectrometry

Crosslinking mass spectrometry (XL-MS) is becoming an increasingly popular technique for modeling protein monomers and complexes. The distance restraints garnered from these experiments can be used alone or as part of an integrative modeling approach, incorporating data from many sources. However, modeling practices are varied and the difference in their usefulness is not clear. Here, we develop a new scoring procedure for models based on crosslink data—Matched and Nonaccessible Crosslink score (MNXL). We compare its performance with that of other commonly-used scoring functions (Number of Violations and Sum of Violation Distances) on a benchmark of 14 protein domains, each with 300 corresponding models (at various levels of quality) and associated, previously published, experimental crosslinks (XLdb). The distances between crosslinked lysines are calculated either as Euclidean distances or Solvent Accessible Surface Distances (SASD) using a newly-developed method (Jwalk). MNXL takes into account whether a crosslink is nonaccessible, i.e. an experimentally observed crosslink has no corresponding SASD in a model due to buried lysines. This metric alone is shown to have a significant impact on modeling performance and is a concept that is not considered at present if only Euclidean distances are used. Additionally, a comparison between modeling with SASD or Euclidean distance shows that SASD is superior, even when factoring out the effect of the nonaccessible crosslinks. Our benchmarking also shows that MNXL outperforms the other tested scoring functions in terms of precision and correlation to Cα-RMSD from the crystal structure. We finally test the MNXL at different levels of crosslink recovery (i.e. the percentage of crosslinks experimentally observed out of all theoretical ones) and set a target recovery of ∼20% after which the performance plateaus.

Improving the Accuracy of Fitted Atomic Models in Cryo-EM Density Maps of Protein Assemblies Using Evolutionary Information from Aligned Homologous Proteins

Cryo-Electron Microscopy (cryo-EM) has become an important technique to obtain structural insights into large macromolecular assemblies. However the resolution of the density maps do not allow for its interpretation at atomic level. Hence they are combined with high resolution structures along with information from other experimental or bioinformatics techniques to obtain pseudo-atomic models. Here, we describe the use of evolutionary conservation of residues as obtained from protein structures and alignments of homologous proteins to detect errors in the fitting of atomic structures as well as improve accuracy of the protein-protein interfacial regions in the cryo-EM density maps.

Mass spectrometry coupled experiments and protein structure modeling methods

With the accumulation of next generation sequencing data, there is increasing interest in the study of intra-species difference in molecular biology, especially in relation to disease analysis. Furthermore, the dynamics of the protein is being identified as a critical factor in its function. Although accuracy of protein structure prediction methods is high, provided there are structural templates, most methods are still insensitive to amino-acid differences at critical points that may change the overall structure. Also, predicted structures are inherently static and do not provide information about structural change over time. It is challenging to address the sensitivity and the dynamics by computational structure predictions alone. However, with the fast development of diverse mass spectrometry coupled experiments, low-resolution but fast and sensitive structural information can be obtained. This information can then be integrated into the structure prediction process to further improve the sensitivity and address the dynamics of the protein structures. For this purpose, this article focuses on reviewing two aspects: the types of mass spectrometry coupled experiments and structural data that are obtainable through those experiments; and the structure prediction methods that can utilize these data as constraints. Also, short review of current efforts in integrating experimental data in the structural modeling is provided.

iMODFIT: efficient and robust flexible fitting based on vibrational analysis in internal coordinates

Here, we employed the collective motions extracted from Normal Mode Analysis (NMA) in internal coordinates (torsional space) for the flexible fitting of atomic-resolution structures into electron microscopy (EM) density maps. The proposed methodology was validated using a benchmark of simulated cases, highlighting its robustness over the full range of EM resolutions and even over coarse-grained representations. A systematic comparison with other methods further showcased the advantages of this proposed methodology, especially at medium to lower resolutions. Using this method, computational costs and potential overfitting problems are naturally reduced by constraining the search in low-frequency NMA space, where covalent geometry is implicitly maintained. This method also effectively captures the macromolecular changes of a representative set of experimental test cases. We believe that this novel approach will extend the currently available EM hybrid methods to the atomic-level interpretation of large conformational changes and their functional implications.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

Consensus among multiple approaches as a reliability measure for flexible fitting into cryo-EM data

Cryo-electron microscopy (cryo-EM) can provide low-resolution density maps of large macromolecular assemblies. As the number of structures deposited in the Protein Data Bank by fitting a high-resolution structure into a low-resolution cryo-EM map is increasing, there is a need to revise the protocols and improve the measures for fitting. A recent study suggested using a combination of multiple automated flexible fitting approaches to improve the interpretation of cryo-EM data. The current work further explores the use of multiple approaches by validating this "consensus" fitting approach and deriving a local reliability measure. Here four different flexible fitting approaches are applied for fitting an initial structure into a simulated density map of known target structure from a dataset of proteins. It is found that the models produced from different approaches often have a consensus in conformation and are also near to the target structure, whereas cases not showing consensus are away from the target. A high correlation is also observed between the RMSF profiles calculated with respect to the average and the target structures, which indicates that the relation between consensus and accuracy can also be extended to a per-residue level. Therefore, the RMSF among the fitted models is proposed as a local reliability measure, which can be used to assess the reliability of the fit at specific regions. Hence, we encourage the community to use consensus flexible fitting with different methods to report on local reliability of the resulting models and improve the interpretation of cryo-EM data.

Combined approaches to study virus structures

A virus particle must work as a safe box for protecting its genome, but at the same time it has to undergo dramatic conformational changes in order to preserve itself by propagating in a cell infection. Thus, viruses are miniaturized wonders whose structural complexity requires them to be investigated by a combination of different techniques that can tackle both static and dynamic processes. In this chapter we will illustrate how major structural techniques such as X-ray crystallography and electron microscopy have been and can be combined with other techniques to determine the structure of complex viruses. The power of these hybrid method approaches are revealed through the various examples provided.

Conventional electron microscopy, cryo-electron microscopy and cryo-electron tomography of viruses

Electron microscopy (EM) techniques have been crucial for understanding the structure of biological specimens such as cells, tissues and macromolecular assemblies. Viruses and related viral assemblies are ideal targets for structural studies that help to define essential biological functions. Whereas conventional EM methods use chemical fixation, dehydration, and staining of the specimens, cryo-electron microscopy (cryo-EM) preserves the native hydrated state. Combined with image processing and three-dimensional reconstruction techniques, cryo-EM provides 3D maps of these macromolecular complexes from projection images, at subnanometer to near-atomic resolutions. Cryo-EM is also a major technique in structural biology for dynamic studies of functional complexes, which are often unstable, flexible, scarce or transient in their native environments. As a tool, cryo-EM complements high-resolution techniques such as X-ray diffraction and NMR spectroscopy; these synergistic hybrid approaches provide important new information. Three-dimensional cryo-electron tomography goes further, and allows the study of viruses not only in their physiological state, but also in their natural environment in the cell, thereby bridging structural studies at the molecular and cellular levels.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

Reconstructing virus structures from nanometer to near-atomic resolutions with cryo-electron microscopy and tomography

The past few decades have seen tremendous advances in single-particle electron -cryo-microscopy (cryo-EM). The field has matured to the point that near-atomic resolution density maps can be generated for icosahedral viruses without the need for crystallization. In parallel, substantial progress has been made in determining the structures of nonicosahedrally arranged proteins in viruses by employing either single-particle cryo-EM or cryo-electron tomography (cryo-ET). Implicit in this course have been the availability of a new generation of electron cryo-microscopes and the development of the computational tools that are essential for generating these maps and models. This methodology has enabled structural biologists to analyze structures in increasing detail for virus particles that are in different morphogenetic states. Furthermore, electron imaging of frozen, hydrated cells, in the process of being infected by viruses, has also opened up a new avenue for studying virus structures "in situ". Here we present the common techniques used to acquire and process cryo-EM and cryo-ET data and discuss their implications for structural virology both now and in the future.

DERIVING TOPOLOGY AND SEQUENCE ALIGNMENT FOR THE HELIX SKELETON IN LOW-RESOLUTION PROTEIN DENSITY MAPS

Cryoelectron microscopy (cryoEM) is an experimental technique to determine the three-dimensional (3D) structure of large protein complexes. Currently, this technique is able to generate protein density maps at 6–9 Å resolution, at which the skeleton of the structure (which is composed of α-helices and β-sheets) can be visualized. As a step towards predicting the entire backbone of the protein from the protein density map, we developed a method to predict the topology and sequence alignment for the skeleton helices. Our method combines the geometrical information of the skeleton helices with the Rosetta ab initio structure prediction method to derive a consensus topology and sequence alignment for the skeleton helices. We tested the method with 60 proteins. For 45 proteins, the majority of the skeleton helices were assigned a correct topology from one of our top ten predictions. The offsets of the alignment for most of the assigned helices were within ±2 amino acids in the sequence. We also analyzed the use of the skeleton helices as a clustering tool for the decoy structures generated by Rosetta. Our comparison suggests that the topology clustering is a better method than a general overlap clustering method to enrich the ranking of decoys, particularly when the decoy pool is small.

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.

From isotropic to anisotropic side chain representations: comparison of three models for residue contact estimation

The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the -to- atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the Protein Data Bank. The results indicate that the ADC model is the most accurate and ISS is the worst. The AES model eliminates about 95% of the incorrectly counted contact-pairs in the ISS model. Algorithm analysis shows that AES model is the most computational intensive while ADC model has moderate computational cost. We derived a dataset of the mis-estimated contact pairs by AES model. The most misjudged pairs are Arg-Glu, Arg-Asp and Arg-Tyr. Such a dataset can be useful for developing the improved AES model by incorporating the pair-specific information for the cutoff distance.

Exploring the spatial and temporal organization of a cell's proteome

To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.

Determining macromolecular assembly structures by molecular docking and fitting into an electron density map

Structural models of macromolecular assemblies are instrumental for gaining a mechanistic understanding of cellular processes. Determining these structures is a major challenge for experimental techniques, such as X-ray crystallography, NMR spectroscopy and electron microscopy (EM). Thus, computational modeling techniques, including molecular docking, are required. The development of most molecular docking methods has so far been focused on modeling of binary complexes. We have recently introduced the MultiFit method for modeling the structure of a multisubunit complex by simultaneously optimizing the fit of the model into an EM density map of the entire complex and the shape complementarity between interacting subunits. Here, we report algorithmic advances of the MultiFit method that result in an efficient and accurate assembly of the input subunits into their density map. The successful predictions and the increasing number of complexes being characterized by EM suggests that the CAPRI challenge could be extended to include docking-based modeling of macromolecular assemblies guided by EM.

Fingerprint-based structure retrieval using electron density

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy.

Automated protein structure modeling with SWISS-MODEL Workspace and the Protein Model Portal

Comparative protein structure modeling is a computational approach to build three-dimensional structural models for proteins using experimental structures of related protein family members as templates. Regular blind assessments of modeling accuracy have demonstrated that comparative protein structure modeling is currently the most reliable technique to model protein structures. Homology models are often sufficiently accurate to substitute for experimental structures in a wide variety of applications. Since the usefulness of a model for specific application is determined by its accuracy, model quality estimation is an essential component of protein structure prediction. Comparative protein modeling has become a routine approach in many areas of life science research since fully automated modeling systems allow also nonexperts to build reliable models. In this chapter, we describe practical approaches for automated protein structure modeling with SWISS-MODEL Workspace and the Protein Model Portal.

Normal Mode Flexible Fitting of High-Resolution Structures of Biological Molecules Toward SAXS Data

We present a method to reconstruct a three-dimensional protein structure from an atomic pair distribution function derived from the scattering intensity profile from SAXS data by flexibly fitting known x-ray structures. This method uses a linear combination of low-frequency normal modes from an elastic network description of the molecule in an iterative manner to deform the structure to conform optimally to the target pair distribution function derived from SAXS data. For computational efficiency, the protein and water molecules included in the protein first hydration shell are coarse-grained. In this paper, we demonstrate the validity of our coarse-graining approach to study SAXS data. Illustrative results of our flexible fitting studies on simulated SAXS data from five different proteins are presented.

CHOYCE: a web server for constrained homology modelling with cryoEM maps

SUMMARY

CHOYCE is a web server for homology modelling of protein components and the fitting of those components into cryo electron microscopy (cryoEM) maps of their assemblies. It provides an interactive approach to improving the selection of models based on the quality of their fit into the EM map.

AVAILABILITY

http://choyce.ismb.lon.ac.uk/

CONTACT

m.topf@cryst.bbk.ac.uk; reda.rawi@uni-due.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Building and refining protein models within cryo-electron microscopy density maps based on homology modeling and multiscale structure refinement

Automatic modeling methods using cryoelectron microscopy (cryoEM) density maps as constraints are promising approaches to building atomic models of individual proteins or protein domains. However, their application to large macromolecular assemblies has not been possible largely due to computational limitations inherent to such unsupervised methods. Here we describe a new method, EM-IMO (electron microscopy-iterative modular optimization), for building, modifying and refining local structures of protein models using cryoEM maps as a constraint. As a supervised refinement method, EM-IMO allows users to specify parameters derived from inspections so as to guide, and as a consequence, significantly speed up the refinement. An EM-IMO-based refinement protocol is first benchmarked on a data set of 50 homology models using simulated density maps. A multiscale refinement strategy that combines EM-IMO-based and molecular dynamics-based refinement is then applied to build backbone models for the seven conformers of the five capsid proteins in our near-atomic-resolution cryoEM map of the grass carp reovirus virion, a member of the Aquareovirus genus of the Reoviridae family. The refined models allow us to reconstruct a backbone model of the entire grass carp reovirus capsid and provide valuable functional insights that are described in the accompanying publication [Cheng, L., Zhu, J., Hui, W. H., Zhang, X., Honig, B., Fang, Q. & Zhou, Z. H. (2010). Backbone model of an aquareovirus virion by cryo-electron microscopy and bioinformatics. J. Mol. Biol. (this issue). doi:10.1016/j.jmb.2009.12.027.]. Our study demonstrates that the integrated use of homology modeling and a multiscale refinement protocol that combines supervised and automated structure refinement offers a practical strategy for building atomic models based on medium- to high-resolution cryoEM density maps.

Structure prediction for the helical skeletons detected from the low resolution protein density map

Background

The current advances in electron cryo-microscopy technique have made it possible to obtain protein density maps at about 6-10 Å resolution. Although it is hard to derive the protein chain directly from such a low resolution map, the location of the secondary structures such as helices and strands can be computationally detected. It has been demonstrated that such low-resolution map can be used during the protein structure prediction process to enhance the structure prediction.

Results

We have developed an approach to predict the 3-dimensional structure for the helical skeletons that can be detected from the low resolution protein density map. This approach does not require the construction of the entire chain and distinguishes the structures based on the conformation of the helices. A test with 35 low resolution density maps shows that the highest ranked structure with the correct topology can be found within the top 1% of the list ranked by the effective energy formed by the helices.

Conclusion

The results in this paper suggest that it is possible to eliminate the great majority of the bad conformations of the helices even without the construction of the entire chain of the protein. For many proteins, the effective contact energy formed by the secondary structures alone can distinguish a small set of likely structures from the pool.

EM-fold: De novo folding of alpha-helical proteins guided by intermediate-resolution electron microscopy density maps

In medium-resolution (7-10 A) cryo-electron microscopy (cryo-EM) density maps, alpha helices can be identified as density rods whereas beta-strand or loop regions are not as easily discerned. We are proposing a computational protein structure prediction algorithm "EM-Fold" that resolves the density rod connectivity ambiguity by placing predicted alpha helices into the density rods and adding missing backbone coordinates in loop regions. In a benchmark of 11 mainly alpha-helical proteins of known structure a native-like model is identified in eight cases (rmsd 3.9-7.9 A). The three failures can be attributed to inaccuracies in the secondary structure prediction step that precedes EM-Fold. EM-Fold has been applied to the approximately 6 A resolution cryo-EM density map of protein IIIa from human adenovirus. We report the first topological model for the alpha-helical 400 residue N-terminal region of protein IIIa. EM-Fold also has the potential to interpret medium-resolution density maps in X-ray crystallography.

Biomolecular pleiomorphism probed by spatial interpolation of coarse models

In low resolution structures of biological assemblies one can often observe conformational deviations that require a flexible rearrangement of structural domains fitted at the atomic level. We are evaluating interpolation methods for the flexible alignment of atomic models based on coarse models. Spatial interpolation is well established in image-processing and visualization to describe the overall deformation or warping of an object or an image. Combined with a coarse representation of the biological system by feature vectors, such methods can provide a flexible approximation of the molecular structure. We have compared three well-known interpolation techniques and evaluated the results by comparing them with constrained molecular dynamics. One method, inverse distance weighting interpolation, consistently produced models that were nearly indistinguishable on the alpha carbon level from the molecular dynamics results. The method is simple to apply and enables flexing of structures by non-expert modelers. This is useful for the basic interpretation of volumetric data in biological applications such as electron microscopy. The method can be used as a general interpretation tool for sparsely sampled motions derived from coarse models.

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.

Molecular electron microscopy: state of the art and current challenges

The objective of molecular electron microscopy (EM) is to use electron microscopes to visualize the structure of biological molecules. This Review provides a brief overview of the methods used in molecular EM, their respective strengths and successes, and current developments that promise an even more exciting future for molecular EM in the structural investigation of proteins and macromolecular complexes, studied in isolation or in the context of cells and tissues.

An efficient conformational sampling method for homology modeling

The structural refinement of protein models is a challenging problem in protein structure prediction (Moult et al., Proteins 2003;53(Suppl 6):334-339). Most attempts to refine comparative models lead to degradation rather than improvement in model quality, so most current comparative modeling procedures omit the refinement step. However, it has been shown that even in the absence of alignment errors and using optimal templates, methods based on a single template have intrinsic limitations, and that refinement is needed to improve model accuracy. It is thought that failure of current methods originates on one hand from the inaccuracy of the effective free energy functions adopted, which do not represent properly the energetic balance in the native state, and on the other hand from the difficulty to sample the high dimensional and rugged free energy landscape of protein folding, in the search for the global minimum. Here, we address this second issue. We define the evolutionary and vibrational armonics subspace (EVA), a reduced sampling subspace that consists of a combination of evolutionarily favored directions, defined by the principal components of the structural variation within a homologous family, plus topologically favored directions, derived from the low frequency normal modes of the vibrational dynamics, up to 50 dimensions. This subspace is accurate enough so that the cores of most proteins can be represented within 1 A accuracy, and reduced enough so that Replica Exchange Monte Carlo (Hukushima and Nemoto, J Phys Soc Jpn 1996;65:1604-1608; Hukushima et al., Int J Mod Phys C: Phys Comput 1996;7:337-344; Mitsutake et al., J Chem Phys 2003;118:6664-6675; Mitsutake et al., J Chem Phys 2003;118:6676-6688) (REMC) can be applied. REMC is one of the best sampling methods currently available, but its applicability is restricted to spaces of small dimensionality. We show that the combination of the EVA subspace and REMC can essentially solve the optimization problem for backbone atoms in the reduced sampling subspace, even for rather rugged free energy landscapes. Applications and limitations of this methodology are finally discussed.

Protein structure fitting and refinement guided by cryo-EM density

For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.

Normal-mode flexible fitting of high-resolution structure of biological molecules toward one-dimensional low-resolution data

We present a method for reconstructing a 3D structure from a pair distribution function by flexibly fitting known x-ray structures toward a conformation that agrees with the low-resolution data. This method uses a linear combination of low-frequency normal modes from elastic-network description of the molecule in an iterative manner to deform the structure optimally to conform to the target pair distribution function. A simple function, pair distance distribution function between atoms, is chosen as a test model to establish computational algorithms-optimization algorithm and scoring function-that can utilize low-resolution 1D data. To select a correct structural model based on less information, we developed a scoring function that takes into account a characteristic of pair distribution functions. In addition, we employ a new optimization algorithm, the trusted region method, that relies on both first and second derivatives of the scoring function. Illustrative results of our studies on simulated 1D data from five different proteins, for which large conformational changes are known to occur, are presented.

Optimization of electrostatic interactions in protein-protein complexes

In this article, we present a statistical analysis of the electrostatic properties of 298 protein-protein complexes and 356 domain-domain structures extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom). For each structure in the dataset we calculated the total electrostatic energy of the binding and its two components, Coulombic and reaction field energy. It was found that in a vast majority of the cases (>90%), the total electrostatic component of the binding energy was unfavorable. At the same time, the Coulombic component of the binding energy was found to favor the complex formation while the reaction field component of the binding energy opposed the binding. It was also demonstrated that the components in a wild-type (WT) structure are optimized/anti-optimized with respect to the corresponding distributions, arising from random shuffling of the charged side chains. The degree of this optimization was assessed through the Z-score of WT energy in respect to the random distribution. It was found that the Z-scores of Coulombic interactions peak at a considerably negative value for all 654 cases considered while the Z-score of the reaction field energy varied among different types of complexes. All these findings indicate that the Coulombic interactions within WT protein-protein complexes are optimized to favor the complex formation while the total electrostatic energy predominantly opposes the binding. This observation was used to discriminate WT structures among sets of structural decoys and showed that the electrostatic component of the binding energy is not a good discriminator of the WT; while, Coulombic or reaction field energies perform better depending upon the decoy set used.

Bridging from molecular simulation to biochemical networks

How can we make the connection between the three-dimensional structures of individual proteins and understanding how complex biological systems involving many proteins work? The modelling and simulation of protein structures can help to answer this question for systems ranging from multimacromolecular complexes to organelles and cells. On one hand, multiscale modelling and simulation techniques are advancing to permit the spatial and temporal properties of large systems to be simulated using atomic-detail structures. On the other hand, the estimation of kinetic parameters for the mathematical modelling of biochemical pathways using protein structure information provides a basis for iterative manipulation of biochemical pathways guided by protein structure. Recent advances include the structural modelling of protein complexes on the genomic level, novel coarse-graining strategies to increase the size of the system and the time span that can be simulated, and comparative molecular field analyses to estimate enzyme kinetic parameters.

Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.

Density-based score for selecting near-native atomic models of unknown structures

We present a low-resolution density-based scoring scheme for selecting high-quality models from a large pool of lesser quality models. We use pre-configured decoy data sets that contain large numbers of models with different degrees of correctness to evaluate the performance of the strategy. We find that the scoring scheme consistently identifies one of the highest quality models for a wide variety of target structures, resolution ranges, and noise models. Tests with experimental data yield similar results.

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.

PROTCOM: searchable database of protein complexes enhanced with domain-domain structures

The database of protein complexes (PROTCOM) is a compilation of known 3D structures of protein–protein complexes enriched with artificially created domain–domain structures using the available entries in the Protein Data Bank. The domain–domain structures are generated by parsing single chain structures into loosely connected domains and are important features of the database. The database () could be used for benchmarking purposes of the docking and other algorithms for predicting 3D structures of protein–protein complexes. The database can be utilized as a template database in the homology or threading methods for modeling the 3D structures of unknown protein–protein complexes. PROTCOM provides the scientific community with an integrated set of tools for browsing, searching, visualizing and downloading a pool of protein complexes. The user is given the option to select a subset of entries using a combination of up to 10 different criteria. As on July 2006 the database contains 1770 entries, each of which consists of the known 3D structures and additional relevant information that can be displayed either in text-only or in visual mode.

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).

Structural model of human endoglin, a transmembrane receptor responsible for hereditary hemorrhagic telangiectasia

Endoglin is a type I membrane protein expressed as a disulphide-linked homodimer on human vascular endothelial cells whose haploinsufficiency is responsible for the dominant vascular dysplasia known as hereditary hemorrhagic telangiectasia (HHT). Structurally, endoglin belongs to the zona pellucida (ZP) family of proteins that share a ZP domain of approximately 260 amino acid residues at their extracellular region. Endoglin is a component of the TGF-beta receptor complex, interacts with the TGF-beta signalling receptors types I and II, and modulates cellular responses to TGF-beta. Here, we have determined for the first time the three-dimensional structure of the approximately 140 kDa extracellular domain of endoglin at 25 A resolution, using single-particle electron microscopy (EM). This reconstruction provides the general architecture of endoglin, which arranges as a dome made of antiparallel oriented monomers enclosing a cavity at one end. A high-resolution structure of endoglin has also been modelled de novo and found to be consistent with the experimental reconstruction. Each subunit comprises three well-defined domains, two of them corresponding to ZP regions, organised into an open U-shaped monomer. This domain arrangement was found to closely resemble the overall structure derived experimentally and the three modelled de novo domains were tentatively assigned to the domains observed in the EM reconstruction. This molecular model was further tested by tagging endoglin's C terminus with an IgG Fc fragment visible after 3D reconstruction of the labelled protein. Combined, these data provide the structural framework to interpret endoglin's functional domains and mutations found in HHT patients.

Flexible Fitting in 3D-EM Guided by the Structural Variability of Protein Superfamilies

A method for flexible fitting of molecular models into three-dimensional electron microscopy (3D-EM) reconstructions at a resolution range of 8-12 A is proposed. The approach uses the evolutionarily related structural variability existing among the protein domains of a given superfamily, according to structural databases such as CATH. A structural alignment of domains belonging to the superfamily, followed by a principal components analysis, is performed, and the first three principal components of the decomposition are explored. Using rigid body transformations for the secondary structure elements (SSEs) plus the cyclic coordinate descent algorithm to close the loops, stereochemically correct models are built for the structure to fit. All of the models are fitted into the 3D-EM map, and the best one is selected based on crosscorrelation measures. This work applies the method to both simulated and experimental data and shows that the flexible fitting was able to produce better results than rigid body fitting.

Electrostatic properties of protein-protein complexes

Statistical electrostatic analysis of 37 protein-protein complexes extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom) is presented. It is shown that small interfaces have a higher content of charged and polar groups compared to large interfaces. In a vast majority of the cases the average pKa shifts for acidic residues induced by the complex formation are negative, indicating that complex formation stabilizes their ionizable states, whereas the histidines are predicted to destabilize the complex. The individual pKa shifts show the same tendency since 80% of the interfacial acidic groups were found to lower their pKas, whereas only 25% of histidines raise their pKa upon the complex formation. The interfacial groups have been divided into three sets according to the mechanism of their pKa shift, and statistical analysis of each set was performed. It was shown that the optimum pH values (pH of maximal stability) of the complex tend to be the same as the optimum pH values of the complex components. This finding can be used in the homology-based prediction of the 3D structures of protein complexes, especially when one needs to evaluate and rank putative models. It is more likely for a model to be correct if both components of the model complex and the entire complex have the same or at least similar values of the optimum pH.

Protein complex compositions predicted by structural similarity

Proteins function through interactions with other molecules. Thus, the network of physical interactions among proteins is of great interest to both experimental and computational biologists. Here we present structure-based predictions of 3387 binary and 1234 higher order protein complexes in Saccharomyces cerevisiae involving 924 and 195 proteins, respectively. To generate candidate complexes, comparative models of individual proteins were built and combined together using complexes of known structure as templates. These candidate complexes were then assessed using a statistical potential, derived from binary domain interfaces in PIBASE (). The statistical potential discriminated a benchmark set of 100 interface structures from a set of sequence-randomized negative examples with a false positive rate of 3% and a true positive rate of 97%. Moreover, the predicted complexes were also filtered using functional annotation and sub-cellular localization data. The ability of the method to select the correct binding mode among alternates is demonstrated for three camelid VHH domain—porcine α–amylase interactions. We also highlight the prediction of co-complexed domain superfamilies that are not present in template complexes. Through integration with MODBASE, the application of the method to proteomes that are less well characterized than that of S.cerevisiae will contribute to expansion of the structural and functional coverage of protein interaction space. The predicted complexes are deposited in MODBASE ().

Conformer generation under restraints

Conformational sampling by direct optimization of an all-atom energy function is ineffective and inefficient because of the ruggedness of the energy landscape. Discrete sampling schemes represent an attractive alternative for generating ensembles of conformers consistent with spatial restraints derived from empirical data. Conformational sampling is becoming increasingly important for structure prediction as the bottleneck in accurate prediction shifts from energy functions to the methods used to find low-energy conformers. Experimental structure determination remains a perennial challenge as investigators tackle larger macromolecular systems, and begin to incorporate more complete descriptions of uncertainty, heterogeneity and dynamics into their models. Computational approaches that combine dense, discrete sampling with all-atom energy evaluation and refinement may help to overcome the remaining barriers to solving these problems.