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.     

Conformational heterogeneity and probability distributions from single-particle cryo-electron microscopy

Single-particle cryo-electron microscopy (cryo-EM) is a technique that takes projection images of biomolecules frozen at cryogenic temperatures. A major advantage of this technique is its ability to image single biomolecules in heterogeneous conformations. While this poses a challenge for data analysis, recent algorithmic advances have enabled the recovery of heterogeneous conformations from the noisy imaging data. Here, we review methods for the reconstruction and heterogeneity analysis of cryo-EM images, ranging from linear-transformation-based methods to nonlinear deep generative models. We overview the dimensionality-reduction techniques used in heterogeneous 3D reconstruction methods and specify what information each method can infer from the data. Then, we review the methods that use cryo-EM images to estimate probability distributions over conformations in reduced subspaces or predefined by atomistic simulations. We conclude with the ongoing challenges for the cryo-EM community.     

A method of focused classification, based on the bootstrap 3D variance analysis, and its application to EF-G-dependent translocation

The bootstrap-based method for calculation of the 3D variance in cryo-EM maps reconstructed from sets of their projections was applied to a dataset of functional ribosomal complexes containing the Escherichia coli 70S ribosome, tRNAs, and elongation factor G (EF-G). The variance map revealed regions of high variability in the intersubunit space of the ribosome: in the locations of tRNAs, in the putative location of EF-G, and in the vicinity of the L1 protein. This result indicated heterogeneity of the dataset. A method of focused classification was put forward in order to sort out the projection data into approximately homogenous subsets. The method is based on the identification and localization of a region of high variance that a subsequent classification step can be focused on by the use of a 3D spherical mask. After initial classification, template volumes are created and are subsequently refined using a multireference 3D projection alignment procedure. In the application to the ribosome dataset, the two resulting structures were interpreted as resulting from ribosomal complexes with bound EF-G and an empty A site, or, alternatively, from complexes that had no EF-G bound but had both A and P sites occupied by tRNA. The proposed method of focused classification proved to be a successful tool in the analysis of the heterogeneous cryo-EM dataset. The associated calculation of the correlations within the density map confirmed the conformational variability of the complex, which could be interpreted in terms of the ribosomal elongation cycle.     

Cross-correlation of common lines: a novel approach for single-particle reconstruction of a structure containing a flexible domain

We describe a novel approach to sorting class averages of a structure in multiple conformational states in order to generate 3D reconstructions that account for conformational variability present in the sample. The method assumes that the relative Euler angles between class averages are known, then uses a common lines approach to match any given class against a set of distinct conformations from a selected view of the structure. We show the effectiveness of the method both on model data and on an experimental dataset for which the conformational variability is limited to a defined region within the structure. During our studies of hepatitis C virus (HCV) internal ribosome entry site (IRES) interaction with the human translation initiation factor eIF3, we observed that the IRES RNA included a flexible region holding multiple conformations. While current classification methods were used to produce two-dimensional averages of the complex showing these different conformations, no method existed for relating these averages in three dimensions. Our approach overcame these limitations, giving us structural insight that was previously not possible.     

Docking multiple conformations of a flexible ligand into a protein binding site using NMR restraints

A method is described for docking a large, flexible ligand using intra-ligand conformational restraints from exchange-transferred NOE (etNOE) data. Numerous conformations of the ligand are generated in isolation, and a subset of representative conformations is selected. A crude model of the protein-ligand complex is used as a template for overlaying the selected ligand structures, and each complex is conformationally relaxed by molecular mechanics to optimize the interaction. Finally, the complexes were assessed for structural quality. Alternative approaches are described for the three steps of the method: generation of the initial docking template; selection of a subset of ligand conformations; and conformational sampling of the complex. The template is generated either by manual docking using interactive graphics or by a computational grid-based search of the binding site. A subset of conformations from the total number of peptides calculated in isolation is selected based on either low energy and satisfaction of the etNOE restraints, or a cluster analysis of the full set. To optimize the interactions in the complex, either a restrained Monte Carlo-energy minimization (MCM) protocol or a restrained simulated annealing (SA) protocol were used. This work produced 53 initial complexes of which 8 were assessed in detail. With the etNOE conformational restraints, all of the approaches provide reasonable models. The grid-based approach to generate an initial docking template allows a large volume to be sampled, and as a result, two distinct binding modes were identified for a fifteen-residue peptide binding to an enzyme active site.     

A local-optimization refinement algorithm in single particle analysis for macromolecular complex with multiple rigid modules

Single particle analysis, which can be regarded as an average of signals from thousands or even millions of particle projections, is an efficient method to study the three-dimensional structures of biological macromolecules. An intrinsic assumption in single particle analysis is that all the analyzed particles must have identical composition and conformation. Thus specimen heterogeneity in either composition or conformation has raised great challenges for high-resolution analysis. For particles with multiple conformations, inaccurate alignments and orientation parameters will yield an averaged map with diminished resolution and smeared density. Besides extensive classification approaches, here based on the assumption that the macromolecular complex is made up of multiple rigid modules whose relative orientations and positions are in slight fluctuation around equilibriums, we propose a new method called as local optimization refinement to address this conformational heterogeneity for an improved resolution. The key idea is to optimize the orientation and shift parameters of each rigid module and then reconstruct their three-dimensional structures individually. Using simulated data of 80S/70S ribosomes with relative fluctuations between the large (60S/50S) and the small (40S/30S) subunits, we tested this algorithm and found that the resolutions of both subunits are significantly improved. Our method provides a proof-of-principle solution for high-resolution single particle analysis of macromolecular complexes with dynamic conformations.     

Calculation of conformational ensembles from potentials of mean force. An approach to the knowledge-based prediction of local structures in globular proteins

We present a prototype of a new approach to the folding problem of polypeptide chains. This approach is based on the analysis of known protein structures. It derives the energy potentials for the atomic interactions of all amino acid residue pairs as a function of the distance between the involved atoms. These potentials are then used to calculate the energies of all conformations that exist in the data base with respect to a given sequence. Then, by using only the most stable conformations, clusters of the most probable conformations for the given sequence are obtained. To discuss the results properly we introduce a new classification of segments based on their conformational stability. Special care is taken to allow for sparse data sets. The use of the method is demonstrated in the discussion of the identical oligopeptide sequences found in different conformations in unrelated proteins. VNTFV, for example, adopts a beta-strand in ribonuclease but it is found in an alpha-helical conformation in erythrocruorin. In the case of VNTFV the ensemble obtained consists of a single cluster of beta-strand conformations, indicating that this may be the preferred conformation for the pentapeptide. When the flanking residues are included in the calculation the hepapeptide P-VNTFV-H (ribonuclease) again yields an ensemble of beta-strands. However, in the ensemble of D-VNTFV-A (erythrocruorin) the major cluster is of alpha-helical type. In the present study we concentrate on the local aspects of protein conformations. However, the theory presented is quite general and not restricted to oligopeptides. We indicate extensions of the approach to the calculation of global conformations of proteins as well as conceivable applications to a number of molecular systems.     

Effect of charge on protein preferred orientation at the air–water interface in cryo-electron microscopy

The air–water interface (AWI) tends to adsorb proteins and frequently causes preferred orientation problems in cryo-electron microscopy (cryo-EM). Here, we examined cryo-EM data from protein samples frozen with different detergents and found that both anionic and cationic detergents promoted binding of proteins to the AWI. By contrast, some of the nonionic and zwitterionic detergents tended to prevent proteins from attaching to the AWI. The protein orientation distributions with different anionic detergents were similar and resembled that obtained without detergent. By contrast, cationic detergents gave distinct orientation distributions. Our results indicate that proteins adsorb to charged interface and the negative charge of the AWI plays an important role in adsorbing proteins in the conventional cryo-EM sample preparation. According to these findings, a new method was developed by adding anionic detergent at a concentration between 0.002% and 0.005%. Using this method, the protein particles exhibited a more evenly distributed orientations and still adsorbed to the AWI enabling them embedding in a thin layer of ice with high concentration, which will benefit the cryo-EM structural determination.     

Constructing ensembles of flexible fragments in native proteins by iterative stochastic elimination is relevant to protein-protein interfaces

We investigate the extent to which ensembles of flexible fragments (FF), generated by our loop conformational search method, include conformations that are near experimental and reflect conformational changes that these FFs undergo when binary protein-protein complexes are formed. Twenty-eight FFs, which are located in protein-protein interfaces and have different conformations in the bound structure (BS) and unbound structure (UbS) were extracted. The conformational space of these fragments in the BS and UbS was explored with our method which is based on the iterative stochastic elimination (ISE) algorithm. Conformational search of BSs generated bound ensembles and conformational search of UbSs produced unbound ensembles. ISE samples conformations near experimental (less than 1.05 A root mean square deviation, RMSD) for 51 out of the 56 examined fragments in the bound and unbound ensembles. In 14 out of the 28 unbound fragments, it also samples conformations within 1.05 A from the BS in the unbound ensemble. Sampling the bound conformation in the unbound ensemble demonstrates the potential biological relevance of the predicted ensemble. The 10 lowest energy conformations are the best choice for docking experiments, compared with any other 10 conformations of the ensembles. We conclude that generating conformational ensembles for FFs with ISE is relevant to FF conformations in the UbS and BS. Forming ensembles of the isolated proteins with our method prior to docking represents more comprehensively their inherent flexibility and is expected to improve docking experiments compared with results obtained by docking only UbSs.     

Flexible fitting of high-resolution x-ray structures into cryoelectron microscopy maps using biased molecular dynamics simulations

A methodology for flexible fitting of all-atom high-resolution structures into low-resolution cryoelectron microscopy (cryo-EM) maps is presented. Flexibility of the modeled structure is simulated by classical molecular dynamics and an additional effective potential is introduced to enhance the fitting process. The additional potential is proportional to the correlation coefficient between the experimental cryo-EM map and a synthetic map generated for an all-atom structure being fitted to the map. The additional forces are calculated as a gradient of the correlation coefficient. During the molecular dynamics simulations under the additional forces, the molecule undergoes a conformational transition that maximizes the correlation coefficient, which results in a high-accuracy fit of all-atom structure into a cryo-EM map. Using five test proteins that exhibit structural rearrangement during their biological activity, we demonstrate performance of our method. We also test our method on the experimental cryo-EM of elongation factor G and show that the model obtained is comparable to previous studies. In addition, we show that overfitting can be avoided by assessing the quality of the fitted model in terms of correlation coefficient and secondary structure preservation.     

GalaxyDomDock: An Ab Initio Domain–domain Docking Web Server for Multi-domain Protein Structure Prediction

A significant proportion of proteins comprise multiple domains. Domain–domain docking is a tool that predicts multi-domain protein structures when individual domain structures can be accurately predicted but when domain orientations cannot be predicted accurately. GalaxyDomDock predicts an ensemble of domain orientations from given domain structures by docking. Such information would also be beneficial in elucidating the functions of proteins that have multiple states with different domain orientations. GalaxyDomDock is an ab initio domain–domain docking method based on GalaxyTongDock, a previously developed protein–protein docking method. Infeasible domain orientations for the given linker are effectively screened out from the docked conformations by a geometric filter, using the Dijkstra algorithm. In addition, domain linker conformations are predicted by adopting a loop sampling method FALC. The proposed GalaxyDomDock outperformed existing ab initio domain–domain docking methods, such as AIDA and Rosetta, in performance tests on the Rosetta benchmark set of two-domain proteins. GalaxyDomDock also performed better than or comparable to AIDA on the AIDA benchmark set of two-domain proteins and two-domain proteins containing discontinuous domains, including the benchmark set in which each domain of the set was modeled by the recent version of AlphaFold. The GalaxyDomDock web server is freely available as a part of GalaxyWEB at http://galaxy.seoklab.org/domdock.     

A new clustering of antibody CDR loop conformations

Previous analyses of the complementarity-determining regions (CDRs) of antibodies have focused on a small number of “canonical” conformations for each loop. This is primarily the result of the work of Chothia and coworkers, most recently in 1997. Because of the widespread utility of antibodies, we have revisited the clustering of conformations of the six CDR loops with the much larger amount of structural information currently available. In this work, we were careful to use a high-quality data set by eliminating low-resolution structures and CDRs with high B-factors or high conformational energies. We used a distance function based on directional statistics and an effective clustering algorithm with affinity propagation. With this data set of over 300 nonredundant antibody structures, we were able to cover 28 CDR-length combinations (e.g., L1 length 11, or “L1-11” in our CDR-length nomenclature) for L1, L2, L3, H1, and H2. The Chothia analysis covered only 20 CDR-lengths. Only four of these had more than one conformational cluster, of which two could easily be distinguished by gene source (mouse/human; κ/λ) and one could easily be distinguished purely by the presence and the positions of Pro residues (L3-9). Thus, using the Chothia analysis does not require the complicated set of “structure-determining residues” that is often assumed. Of our 28 CDR-lengths, 15 have multiple conformational clusters, including 10 for which the Chothia analysis had only one canonical class. We have a total of 72 clusters for non-H3 CDRs; approximately 85% of the non-H3 sequences can be assigned to a conformational cluster based on gene source and/or sequence. We found that earlier predictions of “bulged” versus “nonbulged” conformations based on the presence or the absence of anchor residues Arg/Lys94 and Asp101 of H3 have not held up, since all four combinations lead to a majority of conformations that are bulged. Thus, the earlier analyses have been significantly enhanced by the increased data. We believe that the new classification will lead to improved methods for antibody structure prediction and design.     

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.     

Dynamics of EF-G interaction with the ribosome explored by classification of a heterogeneous cryo-EM dataset

A method of supervised classification using two available structure templates was applied to investigate the possible heterogeneity existing in a large cryo-EM dataset of an Escherichia coli 70S ribosome-EF-G complex. Two subpopulations showing the ribosome in distinct conformational states, related by a ratchet-like rotation of the 30S subunit with respect to the 50S subunit, were extracted from the original dataset. The possible presence of additional intermediate states is discussed.     

Symmetry-restrained flexible fitting for symmetric EM maps

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.     

Computational separation of conformational heterogeneity using cryo-electron tomography and 3D sub-volume averaging

We have previously used cryo-electron tomography combined with sub-volume averaging and classification to obtain 3D structures of macromolecular assemblies in cases where a single dominant species was present, and applied these methods to the analysis of a variety of trimeric HIV-1 and SIV envelope glycoproteins (Env). Here, we extend these studies by demonstrating automated, iterative, missing wedge-corrected 3D image alignment and classification methods to distinguish multiple conformations that are present simultaneously. We present a method for measuring the spatial distribution of the vector elements representing distinct conformational states of Env. We identify data processing strategies that allow clear separation of the previously characterized closed and open conformations, as well as unliganded and antibody-liganded states of Env when they are present in mixtures. We show that identifying and removing spikes with the lowest signal-to-noise ratios improves the overall accuracy of alignment between individual Env sub-volumes, and that alignment accuracy, in turn, determines the success of image classification in assessing conformational heterogeneity in heterogeneous mixtures. We validate these procedures for computational separation by successfully separating and reconstructing distinct 3D structures for unliganded and antibody-liganded as well as open and closed conformations of Env present simultaneously in mixtures.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images

We present the codimensional principal component analysis (PCA), a novel and straightforward method for resolving sample heterogeneity within a set of cryo-EM 2D projection images of macromolecular assemblies. The method employs PCA of resampled 3D structures computed using subsets of 2D data obtained with a novel hypergeometric sampling scheme. PCA provides us with a small subset of dominating "eigenvolumes" of the system, whose reprojections are compared with experimental projection data to yield their factorial coordinates constructed in a common framework of the 3D space of the macromolecule. Codimensional PCA is unique in the dramatic reduction of dimensionality of the problem, which facilitates rapid determination of both the plausible number of conformers in the sample and their 3D structures. We applied the codimensional PCA to a complex data set of Thermus thermophilus 70S ribosome, and we identified four major conformational states and visualized high mobility of the stalk base region.     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.