EMatch: an efficient method for aligning atomic resolution subunits into intermediate-resolution cryo-EM maps of large macromolecular assemblies

Variability of Protein Structure Models from Electron Microscopy

An increasing number of biomolecular structures are solved by electron microscopy (EM). However, the quality of structure models determined from EM maps vary substantially. To understand to what extent structure models are supported by information embedded in EM maps, we used two computational structure refinement methods to examine how much structures can be refined using a dataset of 49 maps with accompanying structure models. The extent of structure modification as well as the disagreement between refinement models produced by the two computational methods scaled inversely with the global and the local map resolutions. A general quantitative estimation of deviations of structures for particular map resolutions are provided. Our results indicate that the observed discrepancy between the deposited map and the refined models is due to the lack of structural information present in EM maps and thus these annotations must be used with caution for further applications.

Cryo-EM Data Are Superior to Contact and Interface Information in Integrative Modeling

Protein-protein interactions carry out a large variety of essential cellular processes. Cryo-electron microscopy (cryo-EM) is a powerful technique for the modeling of protein-protein interactions at a wide range of resolutions, and recent developments have caused a revolution in the field. At low resolution, cryo-EM maps can drive integrative modeling of the interaction, assembling existing structures into the map. Other experimental techniques can provide information on the interface or on the contacts between the monomers in the complex. This inevitably raises the question regarding which type of data is best suited to drive integrative modeling approaches. Systematic comparison of the prediction accuracy and specificity of the different integrative modeling paradigms is unavailable to date. Here, we compare EM-driven, interface-driven, and contact-driven integrative modeling paradigms. Models were generated for the protein docking benchmark using the ATTRACT docking engine and evaluated using the CAPRI two-star criterion. At 20 Å resolution, EM-driven modeling achieved a success rate of 100%, outperforming the other paradigms even with perfect interface and contact information. Therefore, even very low resolution cryo-EM data is superior in predicting heterodimeric and heterotrimeric protein assemblies. Our study demonstrates that a force field is not necessary, cryo-EM data alone is sufficient to accurately guide the monomers into place. The resulting rigid models successfully identify regions of conformational change, opening up perspectives for targeted flexible remodeling.

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.

Cross-validation in cryo-EM-based structural modeling

Single-particle cryo-EM is a powerful approach to determine the structure of large macromolecules and assemblies thereof in many cases at subnanometer resolution. It has become popular to refine or flexibly fit atomic models into density maps derived from cryo-EM experiments. These density maps are typically significantly lower in resolution than electron density maps obtained from X-ray diffraction experiments, such that the number of parameters that need to be determined is much larger than the number of experimental observables. Overfitting and misinterpretation of the density, thus, become a serious problem. For diffraction data, a cross-validation approach was introduced almost 20 y ago; however, no such approach has been described yet for structure refinement against cryo-EM density maps, although the overfitting problem is, because of the lower resolution, significantly larger. We present a cross-validation approach for real-space refinement against cryo-EM density maps in analogy to cross-validation typically used in crystallography. Our approach is able to detect overfitting and allows for optimizing the choice of restraints used in the refinement. The approach is shown on three protein structures with simulated data and experimental data of the rotavirus double-layer particle. Because cross-validation requires splitting the dataset into at least two independent sets, we further present an approach to quantify correlations between the structure factor sets. This analysis is also helpful for other cross-validation applications, such as refinements against diffraction data or 3D reconstructions of cryo-EM density maps.

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.

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.

Interpretation of very low resolution X-ray electron-density maps using core objects

A novel approach to obtaining structural information from macromolecular X-ray data extending to resolutions as low as 20 A is presented. Following a simple map-segmentation procedure, the approximate shapes of the domains forming the structure are identified. A pattern-recognition comparative analysis of these shapes and those derived from the structures of domains from the PDB results in candidate structural models that can be used for a fit into the density map. It is shown that the placed candidate models can be employed for subsequent phase extension to higher resolution.

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.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Recognition of interaction interface residues in low-resolution structures of protein assemblies solely from the positions of C(alpha) atoms

BACKGROUND

The number of available structures of large multi-protein assemblies is quite small. Such structures provide phenomenal insights on the organization, mechanism of formation and functional properties of the assembly. Hence detailed analysis of such structures is highly rewarding. However, the common problem in such analyses is the low resolution of these structures. In the recent times a number of attempts that combine low resolution cryo-EM data with higher resolution structures determined using X-ray analysis or NMR or generated using comparative modeling have been reported. Even in such attempts the best result one arrives at is the very course idea about the assembly structure in terms of trace of the C(alpha) atoms which are modeled with modest accuracy.

METHODOLOGY/PRINCIPAL FINDINGS

In this paper first we present an objective approach to identify potentially solvent exposed and buried residues solely from the position of C(alpha) atoms and amino acid sequence using residue type-dependent thresholds for accessible surface areas of C(alpha). We extend the method further to recognize potential protein-protein interface residues. CONCLUSION/ SIGNIFICANCE: Our approach to identify buried and exposed residues solely from the positions of C(alpha) atoms resulted in an accuracy of 84%, sensitivity of 83-89% and specificity of 67-94% while recognition of interfacial residues corresponded to an accuracy of 94%, sensitivity of 70-96% and specificity of 58-94%. Interestingly, detailed analysis of cases of mismatch between recognition of interface residues from C(alpha) positions and all-atom models suggested that, recognition of interfacial residues using C(alpha) atoms only correspond better with intuitive notion of what is an interfacial residue. Our method should be useful in the objective analysis of structures of protein assemblies when positions of only (alpha) positions are available as, for example, in the cases of integration of cryo-EM data and high resolution structures of the components of the assembly.

X-ray crystallography in drug discovery

Macromolecular X-ray crystallography is an important and powerful technique in drug discovery, used by pharmaceutical companies in the discovery process of new medicines. The detailed analysis of crystal structures of protein-ligand complexes allows the study of the specific interactions of a particular drug with its protein target at the atomic level. It is used to design and improve drugs. The starting point of these studies is the preparation of suitable crystals of complexes with potential ligands, which can be achieved by using different strategies described in this chapter. In addition, an introduction to X-ray crystallography is given, highlighting the fundamental steps necessary to determine the three-dimensional structure of protein-ligand complexes, as well as some of the tools and criteria to validate crystal structures available in databases.

Combining efficient conformational sampling with a deformable elastic network model facilitates structure refinement at low resolution

Structural studies of large proteins and protein assemblies are a difficult and pressing challenge in molecular biology. Experiments often yield only low-resolution or sparse data that are not sufficient to fully determine atomistic structures. We have developed a general geometry-based algorithm that efficiently samples conformational space under constraints imposed by low-resolution density maps obtained from electron microscopy or X-ray crystallography experiments. A deformable elastic network (DEN) is used to restrain the sampling to prior knowledge of an approximate structure. The DEN restraints dramatically reduce over-fitting, especially at low resolution. Cross-validation is used to optimally weight the structural information and experimental data. Our algorithm is robust even for noise-added density maps and has a large radius of convergence for our test case. The DEN restraints can also be used to enhance reciprocal space simulated annealing refinement.

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

Cryo-EM has become an increasingly powerful technique for elucidating the structure, dynamics, and function of large flexible macromolecule assemblies that cannot be determined at atomic resolution. However, due to the relatively low resolution of cryo-EM data, a major challenge is to identify components of complexes appearing in cryo-EM maps. Here, we describe EMatch, a novel integrated approach for recognizing structural homologues of protein domains present in a 6-10 A resolution cryo-EM map and constructing a quasi-atomic structural model of their assembly. The method is highly efficient and has been successfully validated on various simulated data. The strength of the method is demonstrated by a domain assembly of an experimental cryo-EM map of native GroEL at 6 A resolution.

ADP_EM: fast exhaustive multi-resolution docking for high-throughput coverage

MOTIVATION

Efficient fitting tools are needed to take advantage of a fast growth of atomic models of protein domains from crystallography or comparative modeling, and low-resolution density maps of larger molecular assemblies. Here, we report a novel fitting algorithm for the exhaustive and fast overlay of partial high-resolution models into a low-resolution density map. The method incorporates a fast rotational search based on spherical harmonics (SH) combined with a simple translational scanning.

RESULTS

This novel combination makes it possible to accurately dock atomic structures into low-resolution electron-density maps in times ranging from seconds to a few minutes. The high-efficiency achieved with simulated and experimental test cases preserves the exhaustiveness needed in these heterogeneous-resolution merging tools. The results demonstrate its efficiency, robustness and high-throughput coverage.

AVAILABILITY

http://sbg.cib.csic.es/Software/ADP_EM.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.