Structure determination using high-order spatial correlations in single-particle X-ray scattering.

Single-particle imaging using X-ray free-electron lasers (XFELs) is a promising technique for observing nanoscale biological samples under near-physiological conditions. However, as the sample's orientation in each diffraction pattern is unknown, advanced algorithms are required to reconstruct the 3D diffraction intensity volume and subsequently the sample's density model. While most approaches perform 3D reconstruction via determining the orientation of each diffraction pattern, a correlation-based approach utilizes the averaged spatial correlations of diffraction intensities over all patterns, making it well suited for processing experimental data with a poor signal-to-noise ratio of individual patterns. Here, a method is proposed to determine the 3D structure of a sample by analyzing the double, triple and quadruple spatial correlations in diffraction patterns. This ab initio method can reconstruct the basic shape of an irregular unsymmetric 3D sample without requiring any prior knowledge of the sample. The impact of background and noise on correlations is investigated and corrected to ensure the success of reconstruction under simulated experimental conditions. Additionally, the feasibility of using the correlation-based approach to process incomplete partial diffraction patterns is demonstrated. The proposed method is a variable addition to existing algorithms for 3D reconstruction and will further promote the development and adoption of XFEL single-particle imaging techniques.

Advancing cryo-electron microscopy data analysis through accelerated simulation-based flexible fitting approaches.

Flexible fitting based on molecular dynamics simulation is a technique for structure modeling from cryo-EM data. It has been utilized for nearly two decades, and while cryo-EM resolution has improved significantly, it remains a powerful approach that can provide structural and dynamical insights that are not directly accessible from experimental data alone. Molecular dynamics simulations provide a means to extract atomistic details of conformational changes that are encoded in cryo-EM data and can also assist in improving the quality of structural models. Additionally, molecular dynamics simulations enable the characterization of conformational heterogeneity in cryo-EM data. We will summarize the advancements made in these techniques and highlight recent developments in this field.

Molecular size dependence on achievable resolution from XFEL single-particle 3D reconstruction.

Single-particle analysis using x-ray free-electron lasers (XFELs) is a novel method for obtaining structural information of samples in a state close to nature. In particular, it is suitable for observing the inner structure of large biomolecules by taking advantage of the high transmittance of x-rays. However, systematic studies on the resolution achievable for large molecules are lacking. In this study, the molecular size dependence of the resolution of a three-dimensional (3D) structure resulting from XFEL single-particle reconstruction is evaluated using synthetic data. Evidently, 3D structures of larger molecules can be restored with higher detail (defined relative to the molecular sizes) than smaller ones; however, reconstruction with high absolute resolution (defined in nm-1) is challenging. Our results provide useful information for the experimental design of 3D structure reconstruction using coherent x-ray diffraction patterns of single-particles.

MDSPACE: Extracting Continuous Conformational Landscapes from Cryo-EM Single Particle Datasets Using 3D-to-2D Flexible Fitting based on Molecular Dynamics Simulation.

This article presents an original approach for extracting atomic-resolution landscapes of continuous conformational variability of biomolecular complexes from cryo electron microscopy (cryo-EM) single particle images. This approach is based on a new 3D-to-2D flexible fitting method, which uses molecular dynamics (MD) simulation and is embedded in an iterative conformational-landscape refinement scheme. This new approach is referred to as MDSPACE, which stands for Molecular Dynamics simulation for Single Particle Analysis of Continuous Conformational hEterogeneity. The article describes the MDSPACE approach and shows its performance using synthetic and experimental datasets.

High-resolution structure of phosphoketolase from Bifidobacterium longum determined by cryo-EM single-particle analysis.

In bifidobacteria, phosphoketolase (PKT) plays a key role in the central hexose fermentation pathway called "bifid shunt." The three-dimensional structure of PKT from Bifidobacterium longum with co-enzyme thiamine diphosphate (ThDpp) was determined at 2.1 Å resolution by cryo-EM single-particle analysis using 196,147 particles to build up the structural model of a PKT octamer related by D4 symmetry. Although the cryo-EM structure of PKT was almost identical to the X-ray crystal structure previously determined at 2.2 Å resolution, several interesting structural features were observed in the cryo-EM structure. Because this structure was solved at relatively high resolution, it was observed that several amino acid residues adopt multiple conformations. Among them, Q546-D547-H548-N549 (the QN-loop) demonstrate the largest structural change, which seems to be related to the enzymatic function of PKT. The QN-loop is at the entrance to the substrate binding pocket. The minor conformer of the QN-loop is similar to the conformation of the QN-loop in the crystal structure. The major conformer is located further from ThDpp than the minor conformer. Interestingly, the major conformer in the cryo-EM structure of PKT resembles the corresponding loop structure of substrate-bound Escherichia coli transketolase. That is, the minor and major conformers may correspond to "closed" and "open" states for substrate access, respectively. Moreover, because of the high-resolution analysis, many water molecules were observed in the cryo-EM structure of PKT. Structural features of the water molecules in the cryo-EM structure are discussed and compared with water molecules observed in the crystal structure.

NMMD: Efficient Cryo-EM Flexible Fitting Based on Simultaneous Normal Mode and Molecular Dynamics atomic displacements.

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.

A hybrid approach to study large conformational transitions of biomolecules from single particle XFEL diffraction data.

X-ray free-electron laser (XFEL) is the latest generation of the X-ray source that could become an invaluable technique in structural biology. XFEL has ultrashort pulse duration, extreme peak brilliance, and high spatial coherence, which could enable the observation of the biological molecules in near nature state at room temperature without crystallization. However, for biological systems, due to their low diffraction power and complexity of sample delivery, experiments and data analysis are not straightforward, making it extremely challenging to reconstruct three-dimensional (3D) structures from single particle XFEL data. Given the current limitations to the amount and resolution of the data from such XFEL experiments, we propose a new hybrid approach for characterizing biomolecular conformational transitions by using a single 2D low-resolution XFEL diffraction pattern in combination with another known conformation. In our method, we represent the molecular structure with a coarse-grained model, the Gaussian mixture model, to describe large conformational transitions from low-resolution XFEL data. We obtain plausible 3D structural models that are consistent with the XFEL diffraction pattern by deforming an initial structural model to maximize the similarity between the target pattern and the simulated diffraction patterns from the candidate models. We tested the proposed algorithm on two biomolecules of different sizes with different complexities of conformational transitions, adenylate kinase, and elongation factor 2, using synthetic XFEL data. The results show that, with the proposed algorithm, we can successfully describe the conformational transitions by flexibly fitting the coarse-grained model of one conformation to become consistent with an XFEL diffraction pattern simulated from another conformation. In addition, we showed that the incident beam orientation has some effect on the accuracy of the 3D structure modeling and discussed the reasons for the inaccuracies for certain orientations. The proposed method could serve as an alternative approach for retrieving information on 3D conformational transitions from the XFEL diffraction patterns to interpret experimental data. Since the molecules are represented by Gaussian kernels and no atomic structure is needed in principle, such a method could also be used as a tool to seek initial models for 3D reconstruction algorithms.

Reconstruction of Three-Dimensional Conformations of Bacterial ClpB from High-Speed Atomic-Force-Microscopy Images.

ClpB belongs to the cellular disaggretase machinery involved in rescuing misfolded or aggregated proteins during heat or other cellular shocks. The function of this protein relies on the interconversion between different conformations in its native condition. A recent high-speed-atomic-force-microscopy (HS-AFM) experiment on ClpB from Thermus thermophilus shows four predominant conformational classes, namely, open, closed, spiral, and half-spiral. Analyses of AFM images provide only partial structural information regarding the molecular surface, and thus computational modeling of three-dimensional (3D) structures of these conformations should help interpret dynamical events related to ClpB functions. In this study, we reconstruct 3D models of ClpB from HS-AFM images in different conformational classes. We have applied our recently developed computational method based on a low-resolution representation of 3D structure using a Gaussian mixture model, combined with a Monte-Carlo sampling algorithm to optimize the agreement with target AFM images. After conformational sampling, we obtained models that reflect conformational variety embedded within the AFM images. From these reconstructed 3D models, we described, in terms of relative domain arrangement, the different types of ClpB oligomeric conformations observed by HS-AFM experiments. In particular, we highlighted the slippage of the monomeric components around the seam. This study demonstrates that such details of information, necessary for annotating the different conformational states involved in the ClpB function, can be obtained by combining HS-AFM images, even with limited resolution, and computational modeling.

Protocol for Retrieving Three-Dimensional Biological Shapes for a Few XFEL Single-Particle Diffraction Patterns.

X-ray free-electron laser (XFEL) scattering promises to probe single biomolecular complexes without crystallization, enabling the study of biomolecular structures under near-physiological conditions at room temperature. However, such structural determination of biomolecules is extremely challenging thus far. In addition to the large numbers of diffraction patterns required, the orientation of each diffraction pattern needs to be accurately estimated and the missing phase information needs to be recovered for three-dimensional (3D) structure reconstruction. Given the current limitations to the amount and resolution of the data available from single-particle XFEL scattering experiments, we propose an alternative approach to find plausible 3D biological shapes from a limited number of diffraction patterns to serve as a starting point for further analyses. In our proposed strategy, small sets of input (e.g., five) XFEL diffraction patterns were matched against a library of diffraction patterns simulated from 1628 electron microscopy (EM) models to find potential matching 3D models that are consistent with the input diffraction patterns. This approach was tested for three example cases: EMD-3457 (Thermoplasma acidophilum 20S proteasome), EMD-5141 (Escherichia coli 70S ribosome complex), and EMD-5152 (budding yeast Nup84 complex). We observed that choosing the best strategy to define matching regions on the diffraction patterns is critical for identifying correctly matching diffraction patterns. While increasing the number of input diffraction patterns improved the matches in some cases, we found that the resulting matches are more dependent on the uniqueness or complexity of the shape as captured in the individual input diffraction patterns and the availability of a similar 3D biological shape in the search library. The protocol could be useful for finding candidate models for a limited amount of low-resolution data, even when insufficient for reconstruction, performing a quick exploration of new data upon collection, and the analysis of the conformational heterogeneity of the particle of interest as captured within the diffraction patterns.

Computational Protocol for Assessing the Optimal Pixel Size to Improve the Accuracy of Single-particle Cryo-electron Microscopy Maps.

Cryo-electron microscopy (cryo-EM) single-particle analysis has come a long way in achieving atomic-level resolution when imaging biomolecules. To obtain the best possible three-dimensional (3D) structure in cryo-EM, many parameters have to be carefully considered. Here we address the often-overlooked parameter of the pixel size, which describes the magnification of the image produced by the experiment. While efforts are made to refine and validate this parameter in the analysis of cryo-EM experimental data, there is no systematic protocol in place. Since the pixel size parameter can have an impact on the resolution and accuracy of a cryo-EM map, and the atomic resolution 3D structure models derived from it, we propose a computational protocol to estimate the appropriate pixel size parameter. In our protocol, we fit and refine atomic structures against cryo-EM maps at multiple pixel sizes. The resulting fitted and refined structures are evaluated using the GOAP (generalized orientation-dependent, all-atom statistical potential) score, which we found to perform better than other commonly used functions, such as Molprobity and the correlation coefficient from refinement. Finally, we describe the efficacy of this protocol in retrieving appropriate pixel sizes for several examples; simulated data based on yeast elongation factor 2 and experimental data from Gro-EL chaperone, beta-galactosidase, and the TRPV1 ion channel.

Integrative/Hybrid Modeling Approaches for Studying Biomolecules.

The structural and dynamical characterization of biomolecules holds central importance in the endeavor to understand the molecular mechanisms regulating living systems. However, owing to the inherent heterogeneity of biomolecular interactions within cells, it is often difficult to understand the overall structure and dynamics of biomolecules using any experimental method in isolation. In this regard, hybrid methods that combine data from multiple experiments to generate a comprehensive model of biomolecular complexes have gained prominence in the last few years. In this article, we discuss the advancements in hybrid methods, with a particular focus on the role of computation in their development and application. We further outline the future directions that hybrid methods are likely to take, regarding the advancements in techniques such as X-ray free-electron laser single- particle imaging, and electron cryo-tomography. Finally, we conclude the review by highlighting the future goals of broader consensus and collaboration within the integrative/hybrid structural biology community and for disseminating the data generated by hybrid modeling efforts.

Crystal contact-free conformation of an intrinsically flexible loop in protein crystal: Tim21 as the case study.

BACKGROUND: In protein crystals, flexible loops are frequently deformed by crystal contacts, whereas in solution, the large motions result in the poor convergence of such flexible loops in NMR structure determinations. We need an experimental technique to characterize the structural and dynamic properties of intrinsically flexible loops of protein molecules. METHODS: We designed an intended crystal contact-free space (CCFS) in protein crystals, and arranged the flexible loop of interest in the CCFS. The yeast Tim 21 protein was chosen as the model protein, because one of the loops (loop 2) is distorted by crystal contacts in the conventional crystal. RESULTS: Yeast Tim21 was fused to the MBP protein by a rigid α-helical linker. The space created between the two proteins was used as the CCFS. The linker length provides adjustable freedom to arrange loop 2 in the CCFS. We re-determined the NMR structure of yeast Tim21, and conducted MD simulations for comparison. Multidimensional scaling was used to visualize the conformational similarity of loop 2. We found that the crystal contact-free conformation of loop 2 is located close to the center of the ensembles of the loop 2 conformations in the NMR and MD structures. CONCLUSIONS: Loop 2 of yeast Tim21 in the CCFS adopts a representative, dominant conformation in solution. GENERAL SIGNIFICANCE: No single powerful technique is available for the characterization of flexible structures in protein molecules. NMR analyses and MD simulations provide useful, but incomplete information. CCFS crystallography offers a third route to this goal.

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images.

BACKGROUND: Atomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial. METHOD: We aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image. RESULTS: The algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations. CONCLUSIONS: The proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail. GENERAL SIGNIFICANCE: High-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.

Conformational ensemble of an intrinsically flexible loop in mitochondrial import protein Tim21 studied by modeling and molecular dynamics simulations.

BACKGROUND: Tim21, a subunit of a highly dynamic translocase of the inner mitochondrial membrane (TIM23) complex, translocates proteins by interacting with subunits in the translocase of the outer membrane (TOM) complex and Tim23 channel in the TIM23 complex. A loop segment in Tim21, which is in close proximity of the binding site of Tim23, has different conformations in X-ray, NMR and new crystal contact-free space (CCFS) structures. MD simulations can provide information on the structure and dynamics of the loop in solution. METHODS: The conformational ensemble of the loop was characterized using loop modeling and molecular dynamics (MD) simulations. RESULTS: MD simulations confirmed mobility of the loop. Multidimensional scaling and clustering were used to characterize the dynamic conformational ensemble of the loop. Free energy landscape showed that the CCFS crystal structure occupied a low energy region as compared to the conventional X-ray crystal structure. Analysis of crystal packing indicates that the CCFS provides larger conformational space for the motions of the loop. CONCLUSIONS: Our work reported the conformational ensemble of the loop in solution, which is in agreement with the structure obtained from CCFS approach. The combination of the experimental techniques and computational methods is beneficial for studying highly flexible regions of proteins. GENERAL SIGNIFICANCE: Computational methods, such as loop modeling and MD simulations, have proved to be useful for studying conformational flexibility of proteins. These methods in integration with experimental techniques such as CCFS has the potential to transform the studies on flexible regions of proteins.

Cryo-Cooling Effect on DHFR Crystal Studied by Replica-Exchange Molecular Dynamics Simulations.

Cryo-cooling is routinely performed before x-ray diffraction image collection to reduce the damage to crystals due to ionizing radiation. It has been suggested that although backbone structures are usually very similar between room temperature and cryo-temperature, cryo-cooling may hamper biologically relevant dynamics. In this study, the crystal of Escherichia coli dihydrofolate reductase is studied with replica-exchange molecular dynamics simulation, and the results are compared with the crystal structure determined at cryo-temperature and room temperature with the time-averaged ensemble method. Although temperature dependence of unit cell compaction and root mean-square fluctuation of Cα is found in accord with experiment, it is found that the protein structure at low temperature can be more heterogeneous than the ensemble of structures reported by using the time-averaged ensemble method, encouraging further development of the time-averaged ensemble method and indicating that data should be examined carefully to avoid overinterpretation of one average structure.

Acceleration of cryo-EM Flexible Fitting for Large Biomolecular Systems by Efficient Space Partitioning.

Flexible fitting is a powerful technique to build the 3D structures of biomolecules from cryoelectron microscopy (cryo-EM) density maps. One popular method is a cross-correlation coefficient-based approach, where the molecular dynamics (MD) simulation is carried out with the biasing potential that includes the cross-correlation coefficient between the experimental and simulated density maps. Here, we propose efficient parallelization schemes for the calculation of the cross-correlation coefficient to accelerate flexible fitting. Our schemes are tested for small, medium, and large biomolecules using CPU and hybrid CPU + GPU architectures. The scheme for the atomic decomposition MD is suitable for small proteins such as Ca2+-ATPase with the all-atom Go model, while that for the domain decomposition MD is better for larger systems such as ribosome with the all-atom Go or the all-atom explicit solvent models. Our methods allow flexible fitting for various biomolecules with reasonable computational cost. This approach also connects high-resolution structure refinements with investigation of protein structure-function relationship.

Computational investigation of the conformational dynamics in Tom20-mitochondrial presequence tethered complexes.

The translocase of the outer membrane (TOM) mediates the membrane permeation of mitochondrial matrix proteins. Tom20 is a subunit of the TOM complex and binds to the N-terminal region (ie, presequence) in mitochondrial matrix precursor proteins. Previous experimental studies indicated that the presequence recognition by Tom20 was achieved in a dynamic-equilibrium among multiple bound states of the α-helical presequence. Accordingly, the co-crystallization of Tom20 and a presequence peptide required a disulfide-bond cross-linking. A 3-residue spacer sequence (XAG) was inserted between the presequence and the anchoring Cys residue at the C-terminus to not disturb the movement of the presequence peptide in the binding site of Tom20. Two crystalline forms were obtained according to Ala or Tyr at the X position of the spacer sequence, which may reflect the dynamic-equilibrium of the presequence. Here, we have performed replica-exchange molecular dynamics (REMD) simulations to study the effect of disulfide-bond linker and single amino acid difference in the spacer region of the linker on the conformational dynamics of Tom20-presequence complex. Free energy and network analyses of the REMD simulations were compared against previous simulations of non-tethered system. We concluded that the disulfide-bond tethering did not strongly affect the conformational ensemble of the presequence peptide in the complex. Further investigation showed that the choice of Ala or Tyr at the X position did not affect the most distributions of the conformational ensemble of the presequence. The present study provides a rational basis for the disulfide-bond tethering to study the dynamics of weakly binding complexes.

Parameter optimization for 3D-reconstruction from XFEL diffraction patterns based on Fourier slice matching.

Single-particle analysis (SPA) by X-ray free electron laser (XFEL) is a novel method that can observe biomolecules and living tissue that are difficult to crystallize in a state close to nature. To reconstruct three-dimensional (3D) molecular structure from two-dimensional (2D) XFEL diffraction patterns, we have to estimate the incident beam angle to the molecule for each pattern to assemble the 3D-diffraction intensity distribution using interpolation, and retrieve the phase information. In this study, we investigated the optimal parameter sets to assemble the 3D-diffraction intensity distribution from simulated 2D-diffraction patterns of ribosome. In particular, we examined how the parameters need to be adjusted for diffraction patterns with different binning sizes and beam intensities to obtain the highest resolution of molecular structure phase retrieved from the 3D-diffraction intensity. We found that resolution of restored molecular structure is sensitive to the interpolation parameters. Using the optimal parameter set, a linear oversampling ratio of around four is found to be sufficient for correct angle estimation and phase retrieval from the diffraction patterns of SPA by XFEL.

Gaussian mixture model for coarse-grained modeling from XFEL.

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.