Hybrid approaches: applying computational methods in cryo-electron microscopy

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.

EvoSeg: Automated Electron Microscopy Segmentation through Random Forests and Evolutionary Optimization

Electron Microscopy Maps are key in the study of bio-molecular structures, ranging from borderline atomic level to the sub-cellular range. These maps describe the envelopes that cover possibly a very large number of proteins that form molecular machines within the cell. Within those envelopes, we are interested to find what regions correspond to specific proteins so that we can understand how they function, and design drugs that can enhance or suppress a process that they are involved in, along with other experimental purposes. A classic approach by which we can begin the exploration of map regions is to apply a segmentation algorithm. This yields a mask where each voxel in 3D space is assigned an identifier that maps it to a segment; an ideal segmentation would map each segment to one protein unit, which is rarely the case. In this work, we present a method that uses bio-inspired optimization, through an Evolutionary-Optimized Segmentation algorithm, to iteratively improve upon baseline segments obtained from a classical approach, called watershed segmentation. The cost function used by the evolutionary optimization is based on an ideal segmentation classifier trained as part of this development, which uses basic structural information available to scientists, such as the number of expected units, volume and topology. We show that a basic initial segmentation with the additional information allows our evolutionary method to find better segmentation results, compared to the baseline generated by the watershed.

[Progress in filters for denoising cryo-electron microscopy images]

Cryo-electron microscopy (cryo-EM) imaging has the unique potential to bridge the gap between cellular and molecular biology. Therefore, cryo-EM three-dimensional (3D) reconstruction has been rapidly developed in recent several years and applied widely in life science research to reveal the structures of large macromolecular assemblies and cellular complexes, which is critical to understanding their functions at all scales. Although the technical breakthrough in recent years, for example, the introduction of the direct detection device (DDD) camera and the development of cryo-EM software tools, made the three cryo-EM pioneers share the 2017 Nobel Prize, several bottleneck problems still exist that hamper the further increase of the resolution of single-particle reconstruction and hold back the application of in situ subnanometer structure determination by cryo-tomography. Radiation damage is still the key limiting factor in cryo-EM. In order to minimize the radiation damage and preserve as much resolution as possible, the imaging conditions of a low dose and weak contrast make cryo-EM images extremely noisy with very low signal-to-noise ratios (SNR), generally about 0.1. The high noise will obscure the fine details in cryo-EM images or reconstructed maps. Thus, a method to reduce the level of noise and improve the resolution has become an important issue. In this paper, we systematically reviewed and compared some robust filters in the cryo-EM field of two aspects, single-particle analysis (SPA) and cryo-electron tomography (cryo-ET), and especially studied their applications, such as, 3D reconstruction, visualization, structural analysis, and interpretation. Conventional approaches to noise reduction in cryo-EM imaging include the use of Gaussian, median, and bilateral filters, among other means. A Gaussian filter selects an appropriate filter kernel to conduct spatial convolution with a noisy image. Although noise with larger standard deviations in cryo-EM images can be suppressed and satisfactory performance is achieved in certain cases, this filter also blurs the images and over-smooths small-scale image features. This is especially detrimental when precise quantitative information needs to be extracted. Unlike a Gaussian filter, a median filter is based on the order statistics of the image and selects the median intensity in a window of the adjacent pixels to denoise the image. Although this filter is robust to outliers, it suffers from aliasing problems that possibly result in incorrect information for cryo-EM structure interpretation. A bilateral filter is a nonlinear filter that performs spatial weighted averaging and is more selective in the pixels allowing to contribute to the weighted sum, excluding the high frequency noise from the smoothing process. Thus, this filter can be used to smooth out noise while maintaining the edge details, which is similar to an anisotropic diffusion filter, and distinct from a Gaussian filter but its utility will be limited when the SNR of a cryo-EM image is very low. Generally, spatial filtering methods have the disadvantage of losing image resolution when reducing noise. A wavelet transform can exploit the wavelet's natural ability to separate a signal from noise at multiple image scales to allow for joint resolution in both the spatial and frequency domains, and thus has the potential to outperform existing methods. The modified wavelet shrinkage filter we developed can offer a remarkable improvement in image quality with a good compromise between detail preservation and noise smoothing. We expect that our review study on different filters can provide benefits to cryo-EM applications and the interpretation of biological structures.

Using NMR Chemical Shifts and Cryo-EM Density Restraints in Iterative Rosetta-MD Protein Structure Refinement

Cryo-EM has become one of the prime methods for protein structure elucidation, frequently yielding density maps with near-atomic or medium resolution. If protein structures cannot be deduced unambiguously from the density maps, computational structure refinement tools are needed to generate protein structural models. We have previously developed an iterative Rosetta-MDFF protocol that used cryo-EM densities to refine protein structures. Here we show that, in addition to cryo-EM densities, incorporation of other experimental restraints into the Rosetta-MDFF protocol further improved refined structures. We used NMR chemical shift (CS) data integrated with cryo-EM densities in our hybrid protocol in both the Rosetta step and the molecular dynamics (MD) simulations step. In 15 out of 18 cases for all MD rounds, the refinement results obtained when density maps and NMR chemical shift data were used in combination outperformed those of density map-only refinement. Notably, the improvement in refinement was highest when medium and low-resolution density maps were used. With our hybrid method, the RMSDs of final models obtained were always better than the RMSDs obtained by our previous protocol with just density refinement for both medium (6.9 Å) and low (9 Å) resolution maps. For all the six test proteins with medium resolution density maps (6.9 Å), the final refined structure RMSDs were lower for the hybrid method than for the cryo-EM only refinement. The final refined RMSDs were less than 1.5 Å when our hybrid protocol was used with 4 Å density maps. For four out of the six proteins the final RMSDs were even less than 1 Å. This study demonstrates that by using a combination of cryo-EM and NMR restraints, it is possible to refine structures to atomic resolution, outperforming single restraint refinement. This hybrid protocol will be a valuable tool when only low-resolution cryo-EM density data and NMR chemical shift data are available to refine structures.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

Structural and mechanistic insights into human splicing factor SF3b complex derived using an integrated approach guided by the cryo-EM density maps

Pre-mRNA splicing in eukaryotes is performed by the spliceosome, a highly complex macromolecular machine. SF3b is a multi-protein complex which recognizes the branch point adenosine of pre-mRNA as part of a larger U2 snRNP or U11/U12 di-snRNP in the dynamic spliceosome machinery. Although a cryo-EM map is available for human SF3b complex, the structure and relative spatial arrangement of all components in the complex are not yet known. We have recognized folds of domains in various proteins in the assembly and generated comparative models. Using an integrative approach involving structural and other experimental data, guided by the available cryo-EM density map, we deciphered a pseudo-atomic model of the closed form of SF3b which is found to be a "fuzzy complex" with highly flexible components and multiplicity of folds. Further, the model provides structural information for 5 proteins (SF3b10, SF3b155, SF3b145, SF3b130 and SF3b14b) and localization information for 4 proteins (SF3b10, SF3b145, SF3b130 and SF3b14b) in the assembly for the first time. Integration of this model with the available U11/U12 di-snRNP cryo-EM map enabled elucidation of an open form. This now provides new insights on the mechanistic features involved in the transition between closed and open forms pivoted by a hinge region in the SF3b155 protein that also harbors cancer causing mutations. Moreover, the open form guided model of the 5' end of U12 snRNA, which includes the branch point duplex, shows that the architecture of SF3b acts as a scaffold for U12 snRNA: pre-mRNA branch point duplex formation with potential implications for branch point adenosine recognition fidelity.

Improved cryoEM-Guided Iterative Molecular Dynamics--Rosetta Protein Structure Refinement Protocol for High Precision Protein Structure Prediction

Many excellent methods exist that incorporate cryo-electron microscopy (cryoEM) data to constrain computational protein structure prediction and refinement. Previously, it was shown that iteration of two such orthogonal sampling and scoring methods – Rosetta and molecular dynamics (MD) simulations – facilitated exploration of conformational space in principle. Here, we go beyond a proof-of-concept study and address significant remaining limitations of the iterative MD–Rosetta protein structure refinement protocol. Specifically, all parts of the iterative refinement protocol are now guided by medium-resolution cryoEM density maps, and previous knowledge about the native structure of the protein is no longer necessary. Models are identified solely based on score or simulation time. All four benchmark proteins showed substantial improvement through three rounds of the iterative refinement protocol. The best-scoring final models of two proteins had sub-Ångstrom RMSD to the native structure over residues in secondary structure elements. Molecular dynamics was most efficient in refining secondary structure elements and was thus highly complementary to the Rosetta refinement which is most powerful in refining side chains and loop regions.

Case study on the evolution of hetero-oligomer interfaces based on the differences in paralogous proteins

We addressed the evolutionary trace of hetero-oligomer interfaces by comparing the structures of paralogous proteins; one of them is a monomer or homo-oligomer and the other is a hetero-oligomer. We found different trends in amino acid conservation pattern and hydrophobicity between homo-oligomer and hetero-oligomer. The degree of amino acid conservation in the interface of homo-oligomer has no obvious difference from that in the surface, whereas the degree of conservation is much higher in the interface of hetero-oligomer. The interface of homo-oligomer has a few very conserved residue positions, whereas the residue conservation in the interface of hetero-oligomer tends to be higher. In addition, the interface of hetero-oligomer has a tendency of being more hydrophobic compared with the one in homo-oligomer. We conjecture that these differences are related to the inherent symmetry in homo-oligomers that cannot exist in hetero-oligomers. Paucity of the structural data precludes statistical tests of these tendencies, yet the trend can be applied to the prediction of the interface of hetero-oligomer. We obtained putative interfaces of the subunits in CPSF (cleavage and polyadenylation specificity factor), one of the human pre-mRNA 3′-processing complexes. The locations of predicted interface residues were consistent with the known experimental data.

Protein structure prediction guided by crosslinking restraints--A systematic evaluation of the impact of the crosslinking spacer length

Recent development of high-resolution mass spectrometry (MS) instruments enables chemical crosslinking (XL) to become a high-throughput method for obtaining structural information about proteins. Restraints derived from XL-MS experiments have been used successfully for structure refinement and protein-protein docking. However, one formidable question is under which circumstances XL-MS data might be sufficient to determine a protein's tertiary structure de novo? Answering this question will not only include understanding the impact of XL-MS data on sampling and scoring within a de novo protein structure prediction algorithm, it must also determine an optimal crosslinker type and length for protein structure determination. While a longer crosslinker will yield more restraints, the value of each restraint for protein structure prediction decreases as the restraint is consistent with a larger conformational space. In this study, the number of crosslinks and their discriminative power was systematically analyzed in silico on a set of 2055 non-redundant protein folds considering Lys-Lys, Lys-Asp, Lys-Glu, Cys-Cys, and Arg-Arg reactive crosslinkers between 1 and 60Å. Depending on the protein size a heuristic was developed that determines the optimal crosslinker length. Next, simulated restraints of variable length were used to de novo predict the tertiary structure of fifteen proteins using the BCL::Fold algorithm. The results demonstrate that a distinct crosslinker length exists for which information content for de novo protein structure prediction is maximized. The sampling accuracy improves on average by 1.0 Å and up to 2.2 Å in the most prominent example. XL-MS restraints enable consistently an improved selection of native-like models with an average enrichment of 2.1.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Modeling protein assemblies in the proteome

Most (if not all) proteins function when associated in multimolecular assemblies. Attaining the structures of protein assemblies at the atomic scale is an important aim of structural biology. Experimentally, structures are increasingly available, and computations can help bridge the resolution gap between high- and low-resolution scales. Existing computational methods have made substantial progress toward this aim; however, current approaches are still limited. Some involve manual adjustment of experimental data; some are automated docking methods, which are computationally expensive and not applicable to large-scale proteome studies; and still others exploit the symmetry of the complexes and thus are not applicable to nonsymmetrical complexes. Our study aims to take steps toward overcoming these limitations. We have developed a strategy for the construction of protein assemblies computationally based on binary interactions predicted by a motif-based protein interaction prediction tool, PRISM (Protein Interactions by Structural Matching). Previously, we have shown its power in predicting pairwise interactions. Here we take a step toward multimolecular assemblies, reflecting the more prevalent cellular scenarios. With this method we are able to construct homo-/hetero-complexes and symmetric/asymmetric complexes without a limitation on the number of components. The method considers conformational changes and is applicable to large-scale studies. We also exploit electron microscopy density maps to select a solution from among the predictions. Here we present the method, illustrate its results, and highlight its current limitations.

Iterative Molecular Dynamics-Rosetta Protein Structure Refinement Protocol to Improve Model Quality

Rosetta is one of the prime tools for high resolution protein structure refinement. While its scoring function can distinguish native-like from non-native-like conformations in many cases, the method is limited by conformational sampling for larger proteins, that is, leaving a local energy minimum in which the search algorithm may get stuck. Here, we test the hypothesis that iteration of Rosetta with an orthogonal sampling and scoring strategy might facilitate exploration of conformational space. Specifically, we run short molecular dynamics (MD) simulations on models created by de novo folding of large proteins into cryoEM density maps to enable sampling of conformational space not directly accessible to Rosetta and thus provide an escape route from the conformational traps. We present a combined MD-Rosetta protein structure refinement protocol that can overcome some of these sampling limitations. Two of four benchmark proteins showed incremental improvement through all three rounds of the iterative refinement protocol. Molecular dynamics is most efficient in applying subtle but important rearrangements within secondary structure elements and is thus highly complementary to the Rosetta refinement, which focuses on side chains and loop regions.

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.

BCL::Score--knowledge based energy potentials for ranking protein models represented by idealized secondary structure elements

The topology of most experimentally determined protein domains is defined by the relative arrangement of secondary structure elements, i.e. α-helices and β-strands, which make up 50–70% of the sequence. Pairing of β-strands defines the topology of β-sheets. The packing of side chains between α-helices and β-sheets defines the majority of the protein core. Often, limited experimental datasets restrain the position of secondary structure elements while lacking detail with respect to loop or side chain conformation. At the same time the regular structure and reduced flexibility of secondary structure elements make these interactions more predictable when compared to flexible loops and side chains. To determine the topology of the protein in such settings, we introduce a tailored knowledge-based energy function that evaluates arrangement of secondary structure elements only. Based on the amino acid C_β atom coordinates within secondary structure elements, potentials for amino acid pair distance, amino acid environment, secondary structure element packing, β-strand pairing, loop length, radius of gyration, contact order and secondary structure prediction agreement are defined. Separate penalty functions exclude conformations with clashes between amino acids or secondary structure elements and loops that cannot be closed. Each individual term discriminates for native-like protein structures. The composite potential significantly enriches for native-like models in three different databases of 10,000–12,000 protein models in 80–94% of the cases. The corresponding application, “BCL::ScoreProtein,” is available at www.meilerlab.org.

Fitting multimeric protein complexes into electron microscopy maps using 3D Zernike descriptors

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root-mean-square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.

Conventions and workflows for using Situs

Situs is a modular program package for the multi-scale modeling of atomic resolution structures and low-resolution biophysical data from electron microscopy, tomography or small-angle X-ray scattering. This article provides an overview of recent developments in the Situs package, with an emphasis on workflows and conventions that are important for practical applications. The modular design of the programs facilitates scripting in the bash shell that allows specific programs to be combined in creative ways that go beyond the original intent of the developers. Several scripting-enabled functionalities, such as flexible transformations of data type, the use of symmetry constraints or the creation of two-dimensional projection images, are described. The processing of low-resolution biophysical maps in such workflows follows not only first principles but often relies on implicit conventions. Situs conventions related to map formats, resolution, correlation functions and feature detection are reviewed and summarized. The compatibility of the Situs workflow with CCP4 conventions and programs is discussed.

Optimal number of coarse-grained sites in different components of large biomolecular complexes

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

Ab initio protein modeling into CryoEM density maps using EM-Fold

EM-Fold was used to build models for nine proteins in the maps of GroEL (7.7 Å resolution) and ribosome (6.4 Å resolution) in the ab initio modeling category of the 2010 cryo-electron microscopy modeling challenge. EM-Fold assembles predicted secondary structure elements (SSEs) into regions of the density map that were identified to correspond to either α-helices or β-strands. The assembly uses a Monte Carlo algorithm where loop closure, density-SSE length agreement, and strength of connecting density between SSEs are evaluated. Top-scoring models are refined by translating, rotating, and bending SSEs to yield better agreement with the density map. EM-Fold produces models that contain backbone atoms within SSEs only. The RMSD values of the models with respect to native range from 2.4 to 3.5 Å for six of the nine proteins. EM-Fold failed to predict the correct topology in three cases. Subsequently, Rosetta was used to build loops and side chains for the very best scoring models after EM-Fold refinement. The refinement within Rosetta's force field is driven by a density agreement score that calculates a cross-correlation between a density map simulated from the model and the experimental density map. All-atom RMSDs as low as 3.4 Å are achieved in favorable cases. Values above 10.0 Å are observed for two proteins with low overall content of secondary structure and hence particularly complex loop modeling problems. RMSDs over residues in secondary structure elements range from 2.5 to 4.8 Å.

MultiFit: a web server for fitting multiple protein structures into their electron microscopy density map

Advances in electron microscopy (EM) allow for structure determination of large biological assemblies at increasingly higher resolutions. A key step in this process is fitting multiple component structures into an EM-derived density map of their assembly. Here, we describe a web server for this task. The server takes as input a set of protein structures in the PDB format and an EM density map in the MRC format. The output is an ensemble of models ranked by their quality of fit to the density map. The models can be viewed online or downloaded from the website. The service is available at; http://salilab.org/multifit/ and http://bioinfo3d.cs.tau.ac.il/.

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.

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.

A fast mathematical programming procedure for simultaneous fitting of assembly components into cryoEM density maps

MOTIVATION

Single-particle cryo electron microscopy (cryoEM) typically produces density maps of macromolecular assemblies at intermediate to low resolution (approximately 5-30 A). By fitting high-resolution structures of assembly components into these maps, pseudo-atomic models can be obtained. Optimizing the quality-of-fit of all components simultaneously is challenging due to the large search space that makes the exhaustive search over all possible component configurations computationally unfeasible.

RESULTS

We developed an efficient mathematical programming algorithm that simultaneously fits all component structures into an assembly density map. The fitting is formulated as a point set matching problem involving several point sets that represent component and assembly densities at a reduced complexity level. In contrast to other point matching algorithms, our algorithm is able to match multiple point sets simultaneously and not only based on their geometrical equivalence, but also based on the similarity of the density in the immediate point neighborhood. In addition, we present an efficient refinement method based on the Iterative Closest Point registration algorithm. The integer quadratic programming method generates an assembly configuration in a few seconds. This efficiency allows the generation of an ensemble of candidate solutions that can be assessed by an independent scoring function. We benchmarked the method using simulated density maps of 11 protein assemblies at 20 A, and an experimental cryoEM map at 23.5 A resolution. Our method was able to generate assembly structures with root-mean-square errors <6.5 A, which have been further reduced to <1.8 A by the local refinement procedure.

AVAILABILITY

The program is available upon request as a Matlab code package.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Online.

Integrative structure modeling of macromolecular assemblies from proteomics data

Proteomics techniques have been used to generate comprehensive lists of protein interactions in a number of species. However, relatively little is known about how these interactions result in functional multiprotein complexes. This gap can be bridged by combining data from proteomics experiments with data from established structure determination techniques. Correspondingly, integrative computational methods are being developed to provide descriptions of protein complexes at varying levels of accuracy and resolution, ranging from complex compositions to detailed atomic structures.

Practically useful: what the Rosetta protein modeling suite can do for you

The objective of this review is to enable researchers to use the software package Rosetta for biochemical and biomedicinal studies. We provide a brief review of the six most frequent research problems tackled with Rosetta. For each of these six tasks, we provide a tutorial that illustrates a basic Rosetta protocol. The Rosetta method was originally developed for de novo protein structure prediction and is regularly one of the best performers in the community-wide biennial Critical Assessment of Structure Prediction. Predictions for protein domains with fewer than 125 amino acids regularly have a backbone root-mean-square deviation of better than 5.0 Å. More impressively, there are several cases in which Rosetta has been used to predict structures with atomic level accuracy better than 2.5 Å. In addition to de novo structure prediction, Rosetta also has methods for molecular docking, homology modeling, determining protein structures from sparse experimental NMR or EPR data, and protein design. Rosetta has been used to accurately design a novel protein structure, predict the structure of protein−protein complexes, design altered specificity protein−protein and protein−DNA interactions, and stabilize proteins and protein complexes. Most recently, Rosetta has been used to solve the X-ray crystallographic phase problem.

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.

Single-particle reconstruction of biological macromolecules in electron microscopy--30 years

This essay gives the autho's personal account on the development of concepts underlying single-particle reconstruction, a technique in electron microscopy of macromolecular assemblies with a remarkable record of achievements as of late. The ribosome proved to be an ideal testing ground for the development of specimen preparation methods, cryo-EM techniques, and algorithms, with discoveries along the way as a rich reward. Increasingly, cryo-EM and single-particle reconstruction, in combination with classification techniques, is revealing dynamic information on functional molecular machines uninhibited by molecular contacts.