Deriving folds of macromolecular complexes through electron cryomicroscopy and bioinformatics approaches

Constrained cyclic coordinate descent for cryo-EM images at medium resolutions: beyond the protein loop closure problem

The cyclic coordinate descent (CCD) method is a popular loop closure method in protein structure modeling. It is a robotics algorithm originally developed for inverse kinematic applications. We demonstrate an effective method of building the backbone of protein structure models using the principle of CCD and a guiding trace. For medium-resolution 3-dimensional (3D) images derived using cryo-electron microscopy (cryo-EM), it is possible to obtain guiding traces of secondary structures and their skeleton connections. Our new method, constrained cyclic coordinate descent (CCCD), builds α-helices, β-strands, and loops quickly and fairly accurately along predefined traces. We show that it is possible to build the entire backbone of a protein fairly accurately when the guiding traces are accurate. In a test of 10 proteins, the models constructed using CCCD show an average of 3.91 Å of backbone root mean square deviation (RMSD). When the CCCD method is incorporated in a simulated annealing framework to sample possible shift, translation, and rotation freedom, the models built with the true topology were ranked high on the list, with an average backbone RMSD100 of 3.76 Å. CCCD is an effective method for modeling atomic structures after secondary structure traces and skeletons are extracted from 3D cryo-EM images.

The neuronal porosome complex in health and disease

Cup-shaped secretory portals at the cell plasma membrane called porosomes mediate the precision release of intravesicular material from cells. Membrane-bound secretory vesicles transiently dock and fuse at the base of porosomes facing the cytosol to expel pressurized intravesicular contents from the cell during secretion. The structure, isolation, composition, and functional reconstitution of the neuronal porosome complex have greatly progressed, providing a molecular understanding of its function in health and disease. Neuronal porosomes are 15 nm cup-shaped lipoprotein structures composed of nearly 40 proteins, compared to the 120 nm nuclear pore complex composed of >500 protein molecules. Membrane proteins compose the porosome complex, making it practically impossible to solve its atomic structure. However, atomic force microscopy and small-angle X-ray solution scattering studies have provided three-dimensional structural details of the native neuronal porosome at sub-nanometer resolution, providing insights into the molecular mechanism of its function. The participation of several porosome proteins previously implicated in neurotransmission and neurological disorders, further attest to the crosstalk between porosome proteins and their coordinated involvement in release of neurotransmitter at the synapse.

Neuronal Porosome-The Secretory Portal at the Nerve Terminal: It's Structure-Function, Composition, and Reconstitution

Cup-shaped secretory portals at the cell plasma membrane called porosomes mediate secretion from cells. Membrane bound secretory vesicles transiently dock and fuse at the cytosolic compartment of the porosome base to expel intravesicular contents to the outside during cell secretion. In the past decade, the structure, isolation, composition, and functional reconstitution of the neuronal porosome complex has been accomplished providing a molecular understanding of its structure-function. Neuronal porosomes are 15 nm cup-shaped lipoprotein structures composed of nearly 40 proteins. Being a membrane-associated supramolecular complex has precluded determination of the atomic structure of the porosome. However recent studies using small-angle X-ray solution scattering (SAXS), provide at sub-nanometer resolution, the native 3D structure of the neuronal porosome complex associated with docked synaptic vesicle at the nerve terminal. Additionally, results from the SAXS study and earlier studies using atomic force microscopy, provide the possible molecular mechanism involved in porosome-mediated neurotransmitter release at the nerve terminal.

Porosome in Cystic Fibrosis

Macromolecular structures embedded in the cell plasma membrane called ‘porosomes’, are involved in the regulated fractional release of intravesicular contents from cells during secretion. Porosomes range in size from 15 nm in neurons and astrocytes to 100-180 nm in the exocrine pancreas and neuroendocrine cells. Porosomes have been isolated from a number of cells, and their morphology, composition, and functional reconstitution well documented. The 3D contour map of the assembly of proteins within the porosome complex, and its native X-ray solution structure at sub-nm resolution has also advanced. This understanding now provides a platform to address diseases that may result from secretory defects. Water and ion binding to mucin impart hydration, critical for regulating viscosity of the mucus in the airways epithelia. Appropriate viscosity is required for the movement of mucus by the underlying cilia. Hence secretion of more viscous mucus prevents its proper transport, resulting in chronic and fatal airways disease such as cystic fibrosis (CF). CF is caused by the malfunction of CF transmembrane conductance regulator (CFTR), a chloride channel transporter, resulting in viscous mucus in the airways. Studies in mice lacking functional CFTR secrete highly viscous mucous that adhered to the epithelium. Since CFTR is known to interact with the t-SNARE protein syntaxin-1A, and with the chloride channel CLC-3, which are also components of the porosome complex, the interactions between CFTR and the porosome complex in the mucin-secreting human airway epithelial cell line Calu-3 was hypothesized and tested. Results from the study demonstrate the presence of approximately 100 nm in size porosome complex composed of 34 proteins at the cell plasma membrane in Calu-3 cells, and the association of CFTR with the complex. In comparison, the nuclear pore complex measures 120 nm and is comprised of over 500 protein molecules. The involvement of CFTR in porosome-mediated mucin secretion is hypothesized, and is currently being tested.

Solving the Secondary Structure Matching Problem in Cryo-EM De Novo Modeling Using a Constrained K-Shortest Path Graph Algorithm

Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.

Intensity-based skeletonization of CryoEM gray-scale images using a true segmentation-free algorithm

Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the image can be captured using a single segmentation. In this paper, we present a segmentation-free approach to extract the gray-scale curve-like skeletons. The approach relies on a novel representation of the 3D image, where the image is modeled as a graph and a set of volume trees. A test containing 36 synthesized maps and one authentic map shows that our approach can improve the performance of the two tested tools used in de novo modeling. The improvements were 62 and 13 percent for Gorgon and DP-TOSS, respectively.

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.

RANKING VALID TOPOLOGIES OF THE SECONDARY STRUCTURE ELEMENTS USING A CONSTRAINT GRAPH

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6–10 Å resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N2 2N) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.

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.

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.

Reduction of the secondary structure topological space through direct estimation of the contact energy formed by the secondary structures

Background

Electron cryomicroscopy is a fast developing technique aiming at the determination of the 3-dimensional structures of large protein complexes. Using this technique, protein density maps can be generated with 6 to 10 Å resolution. At such resolutions, the secondary structure elements such as helices and β-strands appear to be skeletons and can be computationally detected. However, it is not known which segment of the protein sequence corresponds to which of the skeletons. The topology in this paper refers to the linear order and the directionality of the secondary structures. For a protein with N helices and M strands, there are (N!2^N)(M!2^M) different topologies, each of which maps N helix segments and M strand segments on the protein sequence to N helix and M strand skeletons. Since the backbone position is not available in the skeleton, each topology of the skeletons corresponds to additional freedom to position the atoms in the skeletons.

Results

We have developed a method to construct the possible atomic structures for the helix skeletons by sampling the solution space of all the possible topologies of the skeletons. Our method also ranks the possible structures based on the contact energy formed by the secondary structures, rather than the entire chain. If we assume that the backbone atomic positions are known for the skeletons, then the native topology of the secondary structures can be found in the top 30% of the ranked list of all possible topologies for all the 30 proteins tested, and within the top 5% for most of the 30 proteins. Without assuming the backbone location of the skeletons, the possible atomic structures of the skeletons can be constructed using the axis of the skeleton and the sequence segments. The best constructed structure for the skeletons has RMSD to native between 4 and 5 Å for the four tested α-proteins. These best constructed structures were ranked the 17^th, 31^st, 16^th and 5^th respectively for the four proteins out of 32066, 391833, 98755 and 192935 possible assignments in the pool.

Conclusion

Our work suggested that the direct estimation of the contact energy formed by the secondary structures is quite effective in reducing the topological space to a small subset that includes a near native structure for the skeletons.

Model-building strategies for low-resolution X-ray crystallographic data

Interpretation of low-resolution X-ray crystallographic data can prove to be a difficult task. The challenges faced in electron-density interpretation, the strategies that have been employed to overcome them and developments to automate the process are reviewed.

The interpretation of low-resolution X-ray crystallographic data proves to be challenging even for the most experienced crystallographer. Ambiguity in the electron-density map makes main-chain tracing and side-chain assignment difficult. However, the number of structures solved at resolutions poorer than 3.5 Å is growing rapidly and the structures are often of high biological interest and importance. Here, the challenges faced in electron-density interpretation, the strategies that have been employed to overcome them and developments to automate the process are reviewed. The methods employed in model generation from electron microscopy, which share many of the same challenges in providing high-confidence models of macromolecular structures and assemblies, are also considered.

Electron microscopy of integrins

Integrins are a family of heterodimeric, cell-surface receptors that mediate interactions between the cytoskeleton and the extracellular matrix. We have used electron microscopy and single-particle image analysis combined with molecular modeling to investigate the structures of the full-length integrin alpha(IIb)beta(3) and the ectodomain of alpha(V)beta(3) in a complex with fibronectin. The full-length integrin alpha(IIb)beta(3) is purified from human platelets by ion exchange and gel filtration chromatography in buffers containing the detergent octyl-beta-D-glucopyranoside, whereas the recombinant ectodomain of alpha(V)beta(3) is soluble in aqueous buffer. Transmission electron microscopy is performed either in negative stain, where the protein is embedded in a heavy metal such as uranyl acetate, or in the frozen-hydrated state, where the sample is flash-frozen such that the buffer is vitrified and native conditions are preserved. Individual integrin particles are selected from low-dose micrographs, either by manual identification or an automated method using a cross-correlation search of the micrograph against a set of reference images. Due to the small size of integrin heterodimers (approximately 250 kDa) and the low electron dose required to minimize beam damage, the signal-to-noise level of individual particles is quite low, both by negative-stain electron microscopy and electron cryomicroscopy. Consequently, it is necessary to average many particle images with equivalent views. The particle images are subjected to reference-free alignment and classification, in which the particles are aligned to a common view and further grouped by statistical methods into classes with common orientations. Assessment of the structure from a set of two-dimensional averaged projections is often difficult, and a further three-dimensional (3D) reconstruction analysis is performed to classify each particle as belonging to a specific projection from a single 3D model. The 3D reconstruction algorithm is an iterative projection-matching routine in which the classified particles are used to construct a new, 3D map for the next iteration. Docking of known high-resolution structures of individual subdomains within the molecular envelope of the 3D EM map is used to derive a pseudoatomic model of the integrin complex. This approach of 3D EM image analysis and pseudoatomic modeling is a powerful strategy for exploring the structural biology of transmembrane signaling by integrins because it is likely that multiple conformational states will be difficult to crystallize, whereas the different states should be amenable to electron cryomicroscopy.

Computing a family of skeletons of volumetric models for shape description

Skeletons are important shape descriptors in object representation and recognition. Typically, skeletons of volumetric models are computed using iterative thinning. However, traditional thinning methods often generate skeletons with complex structures that are unsuitable for shape description, and appropriate pruning methods are lacking. In this paper, we present a new method for computing skeletons of volumetric models by alternating thinning and a novel skeleton pruning routine. Our method creates a family of skeletons parameterized by two user-specified numbers that determine respectively the size of curve and surface features on the skeleton. As demonstrated on both real-world models and protein images in bio-medical research, our method generates skeletons with simple and meaningful structures that are particularly suitable for describing cylindrical and plate-like shapes.

Cryoelectron microscopy of icosahedral virus particles

With the rapid progresses in both instrumentation and computing, it is increasingly straightforward and routine to determine the structures of icosahedral viruses to subnanometer resolutions (6-10 A) by cryoelectron microscopy and image reconstruction. In this resolution range, secondary structure elements of protein subunits can be clearly discerned. Combining the three-dimensional density map and bioinformatics of the protein components, the folds of the virus capsid shell proteins can be derived. This chapter will describe the experimental and computational procedures that lead to subnanometer resolution structural determinations of icosahedral virus particles. In addition, we will describe how to extract useful structural information from the three-dimensional maps.

Combining electron microscopy and comparative protein structure modeling

Recently, advances have been made in methods and applications that integrate electron microscopy density maps and comparative modeling to produce atomic structures of macromolecular assemblies. Electron microscopy can benefit from comparative modeling through the fitting of comparative models into electron microscopy density maps. Also, comparative modeling can benefit from electron microscopy through the use of intermediate-resolution density maps in fold recognition, template selection and sequence-structure alignment.

Predicting oligomeric assemblies: N-mers a primer

Multi-protein complexes play key roles in many biological processes. However, since the structures of these assemblies are hard to resolve experimentally, the detailed mechanism of how they work cooperatively in the cell has remained elusive. Similarly, recent advances on in silico prediction of protein-protein interactions have so far avoided this difficult problem. In this paper, we present a general algorithm to predict molecular assemblies of homo-oligomers. Given the number of N-mers and the 3D structure of one monomer, the method samples all the possible symmetries that N-mers can be assembled. Based on a scoring function that clusters the low free energy structures at each binding interface, the algorithm predicts the complex structure as well as the symmetry of the protein assembly. The method is quite general and does not involve any free parameters. The algorithm has been implemented as a public server and integrated to the protein-protein complex prediction server ClusPro. Using this application, we validated predictions for trimers, tetramers (discriminating between dimer of dimers and 4-fold symmetry structures), pentamers and hexamers (discriminating between trimer of dimers, dimer of trimers, and 6-fold symmetry structures), for a total of 107 assemblies. For 85% of the multimers, the server predicts the complex structure within an average rms deviation of 2A from the full crystal. For complexes that involve more than one binding interface, the cluster size at each surface provides a strong indication as to which interface forms first. With improving scoring functions and computer power, our multimer docking approach could be used as a framework to address the more general problem of multi-protein assemblies.

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.

A structural perspective on protein-protein interactions

Structures of macromolecular complexes are necessary for a mechanistic description of biochemical and cellular processes. They can be solved by experimental methods, such as X-ray crystallography, NMR spectroscopy and electron microscopy, as well as by computational protein structure prediction, docking and bioinformatics. Recent advances and applications of these methods emphasize the need for hybrid approaches that combine a variety of data to achieve better efficiency, accuracy, resolution and completeness.

A 9 angstroms single particle reconstruction from CCD captured images on a 200 kV electron cryomicroscope

Sub-nanometer resolution structure determination is becoming a common practice in electron cryomicroscopy of macromolecular assemblies. The data for these studies have until now been collected on photographic film. Using cytoplasmic polyhedrosis virus (CPV), a previously determined structure, as a test specimen, we show the feasibility of obtaining a 9 angstroms structure from images acquired from a 4 k x 4 k Gatan CCD on a 200 kV electron cryomicroscope. The match of the alpha-helices in the protein components of the CPV with the previous structure of the same virus validates the suitability of this type of camera as the recording media targeted for single particle reconstructions at sub-nanometer resolution.

Using surface envelopes for discrimination of molecular models

Shape information about macromolecules is increasingly available but is difficult to use in modeling efforts. We demonstrate that shape information alone can often distinguish structural models of biological macromolecules. By using a data structure called a surface envelope (SE) to represent the shape of the molecule, we propose a method that generates a fitness score for the shape of a particular molecular model. This score correlates well with root mean squared deviation (RMSD) of the model to the known test structures and can be used to filter models in decoy sets. The scoring method requires both alignment of the model to the SE in three-dimensional space and assessment of the degree to which atoms in the model fill the SE. Alignment combines a hybrid algorithm using principal components and a previously published iterated closest point algorithm. We test our method against models generated from random atom perturbation from crystal structures, published decoy sets used in structure prediction, and models created from the trajectories of atoms in molecular modeling runs. We also test our alignment algorithm against experimental electron microscopic data from rice dwarf virus. The alignment performance is reliable, and we show a high correlation between model RMSD and score function. This correlation is stronger for molecular models with greater oblong character (as measured by the ratio of largest to smallest principal component).

Multiple structural alignment by secondary structures: algorithm and applications

We present MASS (Multiple Alignment by Secondary Structures), a novel highly efficient method for structural alignment of multiple protein molecules and detection of common structural motifs. MASS is based on a two-level alignment, using both secondary structure and atomic representation. Utilizing secondary structure information aids in filtering out noisy solutions and achieves efficiency and robustness. Currently, only a few methods are available for addressing the multiple structural alignment task. In addition to using secondary structure information, the advantage of MASS as compared to these methods is that it is a combination of several important characteristics: (1) While most existing methods are based on series of pairwise comparisons, and thus might miss optimal global solutions, MASS is truly multiple, considering all the molecules simultaneously; (2) MASS is sequence order-independent and thus capable of detecting nontopological structural motifs; (3) MASS is able to detect not only structural motifs, shared by all input molecules, but also motifs shared only by subsets of the molecules. Here, we show the application of MASS to various protein ensembles. We demonstrate its ability to handle a large number (order of tens) of molecules, to detect nontopological motifs and to find biologically meaningful alignments within nonpredefined subsets of the input. In particular, we show how by using conserved structural motifs, one can guide protein-protein docking, which is a notoriously difficult problem. MASS is freely available at http://bioinfo3d.cs.tau.ac.il/MASS/.

Applications of a bilateral denoising filter in biological electron microscopy

Due to the sensitivity of biological sample to the radiation damage, the low dose imaging conditions used for electron microscopy result in extremely noisy images. The processes of digitization, image alignment, and 3D reconstruction also introduce additional sources of noise in the final 3D structure. In this paper, we investigate the effectiveness of a bilateral denoising filter in various biological electron microscopy applications. In contrast to the conventional low pass filters, which inevitably smooth out both noise and structural features simultaneously, we found that bilateral filter holds a distinct advantage in being capable of effectively suppressing noise without blurring the high resolution details. In as much, we have applied this technique to individual micrographs, entire 3D reconstructions, segmented proteins, and tomographic reconstructions.