EMatch: discovery of high resolution structural homologues of protein domains in intermediate resolution cryo-EM maps

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.

Fitting Low-Resolution Protein Structures into Cryo-EM Density Maps by Multiobjective Optimization of Global and Local Correlations

The rigid-body fitting of predicted structural models into cryo-electron microscopy (cryo-EM) density maps is a necessary procedure for density map-guided protein structure determination and prediction. We proposed a novel multiobjective optimization protocol, MOFIT, which performs a rigid-body density-map fitting based on particle swarm optimization (PSO). MOFIT was tested on a large set of 292 nonhomologous single-domain proteins. Starting from structural models predicted by I-TASSER, MOFIT achieved an average coordinate root-mean-square deviation of 2.46 Å, which was 1.57, 2.79, and 3.95 Å lower than three leading single-objective function-based methods, where the differences were statistically significant with p-values of 1.65 × 10^-6, 6.36 × 10^-8, and 6.44 × 10^-11 calculated using two-tail Student's t tests. Detailed analyses showed that the major advantages of MOFIT lie in the multiobjective protocol and the extensive PSO search simulations guided by the composite objective functions, which integrates complementary correlation coefficients from the global structure, local fragments, and individual residues with the cryo-EM density maps.

Advances in Structure Modeling Methods for Cryo-Electron Microscopy Maps

Cryo-electron microscopy (cryo-EM) has now become a widely used technique for structure determination of macromolecular complexes. For modeling molecular structures from density maps of different resolutions, many algorithms have been developed. These algorithms can be categorized into rigid fitting, flexible fitting, and de novo modeling methods. It is also observed that machine learning (ML) techniques have been increasingly applied following the rapid progress of the ML field. Here, we review these different categories of macromolecule structure modeling methods and discuss their advances over time.

Analytical Approaches to Improve Accuracy in Solving the Protein Topology Problem

To take advantage of recent advances in genomics and proteomics it is critical that the three-dimensional physical structure of biological macromolecules be determined. Cryo-Electron Microscopy (cryo-EM) is a promising and improving method for obtaining this data, however resolution is often not sufficient to directly determine the atomic scale structure. Despite this, information for secondary structure locations is detectable. De novo modeling is a computational approach to modeling these macromolecular structures based on cryo-EM derived data. During de novo modeling a mapping between detected secondary structures and the underlying amino acid sequence must be identified. DP-TOSS (Dynamic Programming for determining the Topology Of Secondary Structures) is one tool that attempts to automate the creation of this mapping. By treating the correspondence between the detected structures and the structures predicted from sequence data as a constraint graph problem DP-TOSS achieved good accuracy in its original iteration. In this paper, we propose modifications to the scoring methodology of DP-TOSS to improve its accuracy. Three scoring schemes were applied to DP-TOSS and tested: (i) a skeleton-based scoring function; (ii) a geometry-based analytical function; and (iii) a multi-well potential energy-based function. A test of 25 proteins shows that a combination of these schemes can improve the performance of DP-TOSS to solve the topology determination problem for macromolecule proteins.

Flexible Fitting of Atomic Models into Cryo-EM Density Maps Guided by Helix Correspondences

Although electron cryo-microscopy (cryo-EM) has recently achieved resolutions of better than 3 Å, at which point molecular modeling can be done directly from the density map, analysis and annotation of a cryo-EM density map still primarily rely on fitting atomic or homology models to the density map. In this article, we present, to our knowledge, a new method for flexible fitting of known or modeled protein structures into cryo-EM density maps. Unlike existing methods that are guided by local density gradients, our method is guided by correspondences between the α-helices in the density map and model, and does not require an initial rigid-body fitting step. Compared with current methods on both simulated and experimental density maps, our method not only achieves greater accuracy for proteins with large deformations but also runs as fast or faster than many of the other flexible fitting routines.

Multidirectional Image Sensing for Microscopy Based on a Rotatable Robot

Image sensing at a small scale is essentially important in many fields, including microsample observation, defect inspection, material characterization and so on. However, nowadays, multi-directional micro object imaging is still very challenging due to the limited field of view (FOV) of microscopes. This paper reports a novel approach for multi-directional image sensing in microscopes by developing a rotatable robot. First, a robot with endless rotation ability is designed and integrated with the microscope. Then, the micro object is aligned to the rotation axis of the robot automatically based on the proposed forward-backward alignment strategy. After that, multi-directional images of the sample can be obtained by rotating the robot within one revolution under the microscope. To demonstrate the versatility of this approach, we view various types of micro samples from multiple directions in both optical microscopy and scanning electron microscopy, and panoramic images of the samples are processed as well. The proposed method paves a new way for the microscopy image sensing, and we believe it could have significant impact in many fields, especially for sample detection, manipulation and characterization at a small scale.

gEMfitter: a highly parallel FFT-based 3D density fitting tool with GPU texture memory acceleration

Fitting high resolution protein structures into low resolution cryo-electron microscopy (cryo-EM) density maps is an important technique for modeling the atomic structures of very large macromolecular assemblies. This article presents "gEMfitter", a highly parallel fast Fourier transform (FFT) EM density fitting program which can exploit the special hardware properties of modern graphics processor units (GPUs) to accelerate both the translational and rotational parts of the correlation search. In particular, by using the GPU's special texture memory hardware to rotate 3D voxel grids, the cost of rotating large 3D density maps is almost completely eliminated. Compared to performing 3D correlations on one core of a contemporary central processor unit (CPU), running gEMfitter on a modern GPU gives up to 26-fold speed-up. Furthermore, using our parallel processing framework, this speed-up increases linearly with the number of CPUs or GPUs used. Thus, it is now possible to use routinely more robust but more expensive 3D correlation techniques. When tested on low resolution experimental cryo-EM data for the GroEL-GroES complex, we demonstrate the satisfactory fitting results that may be achieved by using a locally normalised cross-correlation with a Laplacian pre-filter, while still being up to three orders of magnitude faster than the well-known COLORES program.

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.

FOLD-EM: automated fold recognition in medium- and low-resolution (4-15 Å) electron density maps

MOTIVATION

Owing to the size and complexity of large multi-component biological assemblies, the most tractable approach to determining their atomic structure is often to fit high-resolution radiographic or nuclear magnetic resonance structures of isolated components into lower resolution electron density maps of the larger assembly obtained using cryo-electron microscopy (cryo-EM). This hybrid approach to structure determination requires that an atomic resolution structure of each component, or a suitable homolog, is available. If neither is available, then the amount of structural information regarding that component is limited by the resolution of the cryo-EM map. However, even if a suitable homolog cannot be identified using sequence analysis, a search for structural homologs should still be performed because structural homology often persists throughout evolution even when sequence homology is undetectable, As macromolecules can often be described as a collection of independently folded domains, one way of searching for structural homologs would be to systematically fit representative domain structures from a protein domain database into the medium/low resolution cryo-EM map and return the best fits. Taken together, the best fitting non-overlapping structures would constitute a 'mosaic' backbone model of the assembly that could aid map interpretation and illuminate biological function.

RESULT

Using the computational principles of the Scale-Invariant Feature Transform (SIFT), we have developed FOLD-EM-a computational tool that can identify folded macromolecular domains in medium to low resolution (4-15 Å) electron density maps and return a model of the constituent polypeptides in a fully automated fashion. As a by-product, FOLD-EM can also do flexible multi-domain fitting that may provide insight into conformational changes that occur in macromolecular assemblies.

RENNSH: a novel α-helix identification approach for intermediate resolution electron density maps

Accurate identification of protein secondary structures is beneficial to understand three-dimensional structures of biological macromolecules. In this paper, a novel refined classification framework is proposed, which treats alpha-helix identification as a machine learning problem by representing each voxel in the density map with its Spherical Harmonic Descriptors (SHD). An energy function is defined to provide statistical analysis of its identification performance, which can be applied to all the α-helix identification approaches. Comparing with other existing α-helix identification methods for intermediate resolution electron density maps, the experimental results demonstrate that our approach gives the best identification accuracy and is more robust to the noise.

Macromolecular assembly structures by comparative modeling and electron microscopy

Advances in electron microscopy allow for structure determination of large biological machines at increasingly higher resolutions. A key step in this process is fitting component structures into the electron microscopy-derived density map of their assembly. Comparative modeling can contribute by providing atomic models of the components, via fold assignment, sequence-structure alignment, model building, and model assessment. All four stages of comparative modeling can also benefit from consideration of the density map. In this chapter, we describe numerous types of modeling problems restrained by a density map and available protocols for finding solutions. In particular, we provide detailed instructions for density map-guided modeling using the Integrative Modeling Platform (IMP), MODELLER, and UCSF Chimera.

Protein surface characterization using an invariant descriptor

Aim. To develop a new invariant descriptor for the characterization of protein surfaces, suitable for various analysis tasks, such as protein functional classification, and search and retrieval of protein surfaces over a large database. Methods. We start with a local descriptor of selected circular patches on the protein surface. The descriptor records the distance distribution between the central residue and the residues within the patch, keeping track of the number of particular pairwise residue cooccurrences in the patch. A global descriptor for the entire protein surface is then constructed by combining information from the local descriptors. Our method is novel in its focus on residue-specific distance distributions, and the use of residue-distance co-occurrences as the basis for the proposed protein surface descriptors. Results. Results are presented for protein classification and for retrieval for three protein families. For the three families, we obtained an area under the curve for precision and recall ranging from 0.6494 (without residue co-occurrences) to 0.6683 (with residue co-occurrences). Large-scale screening using two other protein families placed related family members at the top of the rank, with a number of uncharacterized proteins also retrieved. Comparative results with other proposed methods are included.

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/.

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.

Using Sculptor and Situs for simultaneous assembly of atomic components into low-resolution shapes

We describe an integrated software system called Sculptor that combines visualization capabilities with molecular modeling algorithms for the analysis of multi-scale data sets. Sculptor features extensive special purpose visualization techniques that are based on modern GPU programming and are capable of representing complex molecular assemblies in real-time. The integration of graphics and modeling offers several advantages. The user interface not only eases the usually steep learning curve of pure algorithmic techniques, but it also permits instant analysis and post-processing of results, as well as the integration of results from external software. Here, we implemented an interactive peak-selection strategy that enables the user to explore a preliminary score landscape generated by the colors tool of Situs. The interactive placement of components, one at a time, is advantageous for low-resolution or ambiguously shaped maps, which are sometimes difficult to interpret by the fully automatic peak selection of colors. For the subsequent refinement of the preliminary models resulting from both interactive and automatic peak selection, we have implemented a novel simultaneous multi-body docking in Sculptor and Situs that softly enforces shape complementarities between components using the normalization of the cross-correlation coefficient. The proposed techniques are freely available in Situs version 2.6 and Sculptor version 2.0.

MOTIF-EM: an automated computational tool for identifying conserved regions in CryoEM structures

We present a new, first-of-its-kind, fully automated computational tool MOTIF-EM for identifying regions or domains or motifs in cryoEM maps of large macromolecular assemblies (such as chaperonins, viruses, etc.) that remain conformationally conserved. As a by-product, regions in structures that are not conserved are revealed: this can indicate local molecular flexibility related to biological activity. MOTIF-EM takes cryoEM volumetric maps as inputs. The technique used by MOTIF-EM to detect conserved sub-structures is inspired by a recent breakthrough in 2D object recognition. The technique works by constructing rotationally invariant, low-dimensional representations of local regions in the input cryoEM maps. Correspondences are established between the reduced representations (by comparing them using a simple metric) across the input maps. The correspondences are clustered using hash tables and graph theory is used to retrieve conserved structural domains or motifs. MOTIF-EM has been used to extract conserved domains occurring in large macromolecular assembly maps, including as those of viruses P22 and epsilon 15, Ribosome 70S, GroEL, that remain structurally conserved in different functional states. Our method can also been used to build atomic models for some maps. We also used MOTIF-EM to identify the conserved folds shared among dsDNA bacteriophages HK97, Epsilon 15, and ô29, though they have low-sequence similarity.

Contact:mitul@cs.stanford.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Using diffusion distances for flexible molecular shape comparison

Background

Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.

Results

In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.

Conclusions

We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.

IDSS: deformation invariant signatures for molecular shape comparison

Background

Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison (MSC) treat them as rigid bodies, which may lead to incorrect measure of the shape similarity of flexible molecules.

Results

To address the issue we introduce a new shape descriptor, called Inner Distance Shape Signature (IDSS), for describing the 3D shapes of flexible molecules. The inner distance is defined as the length of the shortest path between landmark points within the molecular shape, and it reflects well the molecular structure and deformation without explicit decomposition. Our IDSS is stored as a histogram which is a probability distribution of inner distances between all sample point pairs on the molecular surface. We show that IDSS is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. Our approach reduces the 3D shape comparison problem of flexible molecules to the comparison of IDSS histograms.

Conclusion

The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. We demonstrate the effectiveness of IDSS within a molecular search engine application for a benchmark containing abundant conformational changes of molecules. Such comparisons in several thousands per second can be carried out. The presented IDSS method can be considered as an alternative and complementary tool for the existing methods for rigid MSC. The binary executable program for Windows platform and database are available from .

Hybrid approaches: applying computational methods in cryo-electron microscopy

Recent advances in cryo-electron microscopy have led to an increasing number of high (3-5A) to medium (5-10A) resolution cryoEM density maps. These density maps contain valuable information about the protein structure but frequently require computational algorithms to aid their structural interpretation. It is these hybrid approaches between cryoEM and computational protein structure prediction algorithms that will shape protein structure elucidation from density maps.

Inferential optimization for simultaneous fitting of multiple components into a CryoEM map of their assembly

Models of macromolecular assemblies are essential for a mechanistic description of cellular processes. Such models are increasingly obtained by fitting atomic-resolution structures of components into a density map of the whole assembly. Yet, current density-fitting techniques are frequently insufficient for an unambiguous determination of the positions and orientations of all components. Here, we describe MultiFit, a method used for simultaneously fitting atomic structures of components into their assembly density map at resolutions as low as 25 A. The component positions and orientations are optimized with respect to a scoring function that includes the quality-of-fit of components in the map, the protrusion of components from the map envelope, and the shape complementarity between pairs of components. The scoring function is optimized by our exact inference optimizer DOMINO (Discrete Optimization of Multiple INteracting Objects) that efficiently finds the global minimum in a discrete sampling space. MultiFit was benchmarked on seven assemblies of known structure, consisting of up to seven proteins each. The input atomic structures of the components were obtained from the Protein Data Bank, as well as by comparative modeling based on a 16-99% sequence identity to a template structure. A near-native configuration was usually found as the top-scoring model. Therefore, MultiFit can provide initial configurations for further refinement of many multicomponent assembly structures described by electron microscopy.

Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.

YUP.SCX: coaxing atomic models into medium resolution electron density maps

The structures of large macromolecular complexes in different functional states can be determined by cryo-electron microscopy, which yields electron density maps of low to intermediate resolutions. The maps can be combined with high-resolution atomic structures of components of the complex, to produce a model for the complex that is more accurate than the formal resolution of the map. To this end, methods have been developed to dock atomic models into density maps rigidly or flexibly, and to refine a docked model so as to optimize the fit of the atomic model into the map. We have developed a new refinement method called YUP.SCX. The electron density map is converted into a component of the potential energy function to which terms for stereochemical restraints and volume exclusion are added. The potential energy function is then minimized (using simulated annealing) to yield a stereochemically-restrained atomic structure that fits into the electron density map optimally. We used this procedure to construct an atomic model of the 70S ribosome in the pre-accommodation state. Although some atoms are displaced by as much as 33A, they divide themselves into nearly rigid fragments along natural boundaries with smooth transitions between the fragments.