Fragment-based phase extension for three-dimensional structure determination of membrane proteins by electron crystallography

In electron crystallography, membrane protein structure is determined from two-dimensional crystals where the protein is embedded in a membrane. Once large and well-ordered 2D crystals are grown, one of the bottlenecks in electron crystallography is the collection of image data to directly provide experimental phases to high resolution. Here, we describe an approach to bypass this bottleneck, eliminating the need for high-resolution imaging. We use the strengths of electron crystallography in rapidly obtaining accurate experimental phase information from low-resolution images and accurate high-resolution amplitude information from electron diffraction. The low-resolution experimental phases were used for the placement of α helix fragments and extended to high resolution using phases from the fragments. Phases were further improved by density modifications followed by fragment expansion and structure refinement against the high-resolution diffraction data. Using this approach, structures of three membrane proteins were determined rapidly and accurately to atomic resolution without high-resolution image data.     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.     

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.     

Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques.

There is a growing body of low-resolution structural data that can be utilized to devise structural models for large RNAs and ribonucleoproteins. These models are routinely built manually. We introduce an automated refinement protocol to utilize such data for building low-resolution three-dimensional models using the tools of molecular mechanics. In addition to specifying the positions of each nucleotide, the protocol provides quantitative estimates of the uncertainties in those positions, i.e., the resolution of the model. In typical applications, the resolution of the models is about 10-20 A. Our method uses reduced representations and allows us to refine three-dimensional structures of systems as big as the 16S and 23S ribosomal RNAs, which are about one to two orders of magnitude larger than nucleic acids that can be examined by traditional all-atom modeling methods. Nonatomic resolution structural data--secondary structure, chemical cross-links, chemical and enzymatic footprinting patterns, protein positions, solvent accessibility, and so on--are combined with known motifs in RNA structure to predict low-resolution models of large RNAs. These structural constraints are imposed on the RNA chain using molecular mechanics-type potential functions with parameters based on the quality of experimental data. Surface potential functions are used to incorporate shape and positional data from electron microscopy image reconstruction experiments into our models. The structures are optimized using techniques of energy refinement to get RNA folding patterns. In addition to providing a consensus model, the method finds the range of models consistent with the data, which allows quantitative evaluation of the resolution of the model. The method also identifies conflicts in the experimental data. Although our protocol is aimed at much larger RNAs, we illustrate these techniques using the tRNA structure as an example and test-bed.     

Determining RNA three-dimensional structures using low-resolution data

Knowing the 3-D structure of an RNA is fundamental to understand its biological function. Nowadays X-ray crystallography and NMR spectroscopy are systematically applied to newly discovered RNAs. However, the application of these high-resolution techniques is not always possible, and thus scientists must turn to lower resolution alternatives. Here, we introduce a pipeline to systematically generate atomic resolution 3-D structures that are consistent with low-resolution data sets. We compare and evaluate the discriminative power of a number of low-resolution experimental techniques to reproduce the structure of the Escherichia coli tRNA(VAL) and P4-P6 domain of the Tetrahymena thermophila group I intron. We test single and combinations of the most accessible low-resolution techniques, i.e. hydroxyl radical footprinting (OH), methidiumpropyl-EDTA (MPE), multiplexed hydroxyl radical cleavage (MOHCA), and small-angle X-ray scattering (SAXS). We show that OH-derived constraints are accurate to discriminate structures at the atomic level, whereas EDTA-based constraints apply to global shape determination. We provide a guide for choosing which experimental techniques or combination of thereof is best in which context. The pipeline represents an important step towards high-throughput low-resolution RNA structure determination.     

Solution structural studies and low-resolution model of the Schizosaccharomyces pombe sap1 protein

Sap1 is a DNA-binding protein involved in controlling the mating type switch in fission yeast Schizosaccharomyces pombe. In the absence of any significant sequence similarity with any structurally known protein, a variety of biophysical techniques has been used to probe the solution low-resolution structure of the sap1 protein. First, sap1 is demonstrated to be an unusually elongated dimer in solution by measuring the translational diffusion coefficient with two independent techniques: dynamic light-scattering and ultracentrifugation. Second, sequence analysis revealed the existence of a long coiled-coil region, which is responsible for dimerization. The length of the predicted coiled-coil matches estimates drawn from the hydrodynamic experimental behaviour of the molecule. In addition, the same measurements done on a shorter construct with a coiled-coil region shortened by roughly one-half confirmed the localization of the long coiled-coil region. A crude T-shape model incorporating all these information was built. Third, small-angle X-ray scattering (SAXS) of the free molecule provided additional evidence for the model. In particular, the P(r) curve strikingly demonstrates the existence of long intramolecular distances. Using a novel 3D reconstruction algorithm, a low resolution 3D model of the protein has been independently constructed that matches the SAXS experimental data. It also fits the translation diffusion coefficients measurements and agrees with the first T-shaped model. This low-resolution model has clearly biologically relevant new functional implications, suggesting that sap1 is a bifunctional protein, with the two active sites being separated by as much as 120 A; a tetrapeptide repeated four times at the C terminus of the molecule is postulated to be of utmost functional importance.     

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

BackgroundAtomic 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.MethodWe 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.ResultsThe 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.ConclusionsThe proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.General significanceHigh-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.     

Functional Dynamics of Hexameric Helicase Probed by Hydrogen Exchange and Simulation

The biological function of large macromolecular assemblies depends on their structure and their dynamics over a broad range of timescales; for this reason, it is a significant challenge to investigate these assemblies using conventional experimental techniques. One of the most promising experimental techniques is hydrogen-deuterium exchange detected by mass spectrometry. Here, we describe to our knowledge a new computational method for quantitative interpretation of deuterium exchange kinetics and apply it to a hexameric viral helicase P4 that unwinds and translocates RNA into a virus capsid at the expense of ATP hydrolysis. Room-temperature dynamics probed by a hundred nanoseconds of all-atom molecular dynamics simulations is sufficient to predict the exchange kinetics of most sequence fragments and provide a residue-level interpretation of the low-resolution experimental results. The strategy presented here is also a valuable tool to validate experimental data, e.g., assignments, and to probe mechanisms that cannot be observed by x-ray crystallography, or that occur over timescales longer than those that can be realistically simulated, such as the opening of the hexameric ring.     

Functional Dynamics of Hexameric Helicase Probed by Hydrogen Exchange and Simulation

The biological function of large macromolecular assemblies depends on their structure and their dynamics over a broad range of timescales; for this reason, it is a significant challenge to investigate these assemblies using conventional experimental techniques. One of the most promising experimental techniques is hydrogen-deuterium exchange detected by mass spectrometry. Here, we describe to our knowledge a new computational method for quantitative interpretation of deuterium exchange kinetics and apply it to a hexameric viral helicase P4 that unwinds and translocates RNA into a virus capsid at the expense of ATP hydrolysis. Room-temperature dynamics probed by a hundred nanoseconds of all-atom molecular dynamics simulations is sufficient to predict the exchange kinetics of most sequence fragments and provide a residue-level interpretation of the low-resolution experimental results. The strategy presented here is also a valuable tool to validate experimental data, e.g., assignments, and to probe mechanisms that cannot be observed by x-ray crystallography, or that occur over timescales longer than those that can be realistically simulated, such as the opening of the hexameric ring.     

A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data

The application of powder diffraction methods to problems in structural biology is generally regarded as intractable because of the large number of unresolved, overlapping X‐ray reflections. Here, we use information about unit cell lattice parameters, space group transformations, and chemical composition as a priori information in a bootstrap process that resolves the ambiguities associated with overlapping reflections. The measured ratios of reflections that can be resolved experimentally are used to refine the position, the shape, and the orientation of low‐resolution molecular structures within the unit cell, in leading to the resolution of the overlapping reflections. The molecular model is then made progressively more sophisticated as additional diffraction information is included in the analysis. We apply our method to the recovery of the structure of the bacteriorhodopsin molecule (bR) to a resolution of 7 Å using experimental data obtained from two‐dimensional purple membrane crystals. The approach can be used to determine the structure factors directly or to provide reliable low‐resolution phase information that can be refined further by the conventional methods of protein crystallography.     

Biased coarse-grained molecular dynamics simulation approach for flexible fitting of X-ray structure into cryo electron microscopy maps

Several approaches have been introduced to interpret, in terms of high-resolution structure, low-resolution structural data as obtained from cryo-EM. As conformational changes are often observed in biological molecules, these techniques need to take into account the flexibility of proteins. Flexibility has been described in terms of movement between rigid domains and between rigid secondary structure elements, which present some limitations for studying dynamical properties. Normal mode analysis has also been used, but is limited to medium resolution data. All-atom molecular dynamics fitting techniques are more appropriate to fit structures into higher-resolution data as full protein flexibility is considered, but are cumbersome in terms of computational time. Here, we introduce a coarse-grained approach; a Go-model was used to represent biological molecules, combined with biased molecular dynamics to reproduce accurately conformational transitions. Illustrative examples on simulated data are shown. Accurate fittings can be obtained for resolution ranging from 5 to 20 Å. The approach was also tested on experimental data of Elongation Factor G and Escherichia coli RNA polymerase, where its validity is compared to previous models obtained from different techniques. This comparison demonstrates that quantitative flexible techniques, as opposed to manual docking, need to be considered to interpret low-resolution data.     

Use of structure comparison methods for the refinement of protein structure predictions. I. Identifying the structural family of a protein from low-resolution models.

Predicting the three-dimensional structure of proteins is still one of the most challenging problems in molecular biology. Despite its difficulty, several investigators have started to produce consistently low-resolution predictions for small proteins. However, in most of these cases, the prediction accuracy is still too low to make them useful. In the present article, we address the problem of obtaining better-quality predictions, starting from low-resolution models. To this end, we have devised a new procedure that uses these models, together with structure comparison methods, to identify the structural family of the target protein. This would allow, in a second step not described in the present work, to refine the predictions using conserved features of the identified family. In our approach, the structure database is investigated using predictions, at different accuracy levels, for a given protein. As query structures, we used both low-resolution versions of the native structures, as well as different sets of low accuracy predictions. In general, we found that for predictions with a resolution of > or =5-7 A, structure comparison methods were able to identify the fold of a protein in the top positions.     

Structural properties of prion protein protofibrils and fibrils: an experimental assessment of atomic models

Decades after the prion protein was implicated in transmissible spongiform encephalopathies, the structure of its toxic isoform and its mechanism of toxicity remain unknown. By gathering available experimental data, albeit low resolution, a few pieces of the prion puzzle can be put in place. Currently, there are two fundamentally different models of a prion protofibril. One has its building blocks derived from a molecular dynamics simulation of the prion protein under amyloidogenic conditions, termed the spiral model. The other model was constructed by threading a portion of the prion sequence through a beta-helical structure from the Protein Data Bank. Here we compare and contrast these models with respect to all of the available experimental information, including electron micrographs, symmetries, secondary structure, oligomerization interfaces, enzymatic digestion, epitope exposure, and disaggregation profiles. Much of this information was not available when the two models were introduced. Overall, we find that the spiral model is consistent with all of the experimental results. In contrast, it is difficult to reconcile several of the experimental observables with the beta-helix model. While the experimental constraints are of low resolution, in bringing together the previously disconnected experiments, we have developed a clearer picture of prion aggregates. Both the improved characterization of prion aggregates and the existing atomic models can be used to devise further experiments to better elucidate the misfolding pathway and the structure of prion protofibrils.     

Sharpening high resolution information in single particle electron cryomicroscopy

Advances in single particle electron cryomicroscopy have made possible to elucidate routinely the structure of biological specimens at subnanometer resolution. At this resolution, secondary structure elements are discernable by their signature. However, identification and interpretation of high resolution structural features are hindered by the contrast loss caused by experimental and computational factors. This contrast loss is traditionally modeled by a Gaussian decay of structure factors with a temperature factor, or B-factor. Standard restoration procedures usually sharpen the experimental maps either by applying a Gaussian function with an inverse ad hoc B-factor, or according to the amplitude decay of a reference structure. EM-BFACTOR is a program that has been designed to widely facilitate the use of the novel method for objective B-factor determination and contrast restoration introduced by Rosenthal and Henderson [Rosenthal, P.B., Henderson, R., 2003. Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. J. Mol. Biol. 333, 721-745]. The program has been developed to interact with the most common packages for single particle electron cryomicroscopy. This sharpening method has been further investigated via EM-BFACTOR, concluding that it helps to unravel the high resolution molecular features concealed in experimental density maps, thereby making them better suited for interpretation. Therefore, the method may facilitate the analysis of experimental data in high resolution single particle electron cryomicroscopy.     

Applying an empirical hydropathic forcefield in refinement may improve low-resolution protein X-ray crystal structures

Background

The quality of X-ray crystallographic models for biomacromolecules refined from data obtained at high-resolution is assured by the data itself. However, at low-resolution, >3.0 Å, additional information is supplied by a forcefield coupled with an associated refinement protocol. These resulting structures are often of lower quality and thus unsuitable for downstream activities like structure-based drug discovery.

Methodology

An X-ray crystallography refinement protocol that enhances standard methodology by incorporating energy terms from the HINT (Hydropathic INTeractions) empirical forcefield is described. This protocol was tested by refining synthetic low-resolution structural data derived from 25 diverse high-resolution structures, and referencing the resulting models to these structures. The models were also evaluated with global structural quality metrics, e.g., Ramachandran score and MolProbity clashscore. Three additional structures, for which only low-resolution data are available, were also re-refined with this methodology.

Results

The enhanced refinement protocol is most beneficial for reflection data at resolutions of 3.0 Å or worse. At the low-resolution limit, ≥4.0 Å, the new protocol generated models with Cα positions that have RMSDs that are 0.18 Å more similar to the reference high-resolution structure, Ramachandran scores improved by 13%, and clashscores improved by 51%, all in comparison to models generated with the standard refinement protocol. The hydropathic forcefield terms are at least as effective as Coulombic electrostatic terms in maintaining polar interaction networks, and significantly more effective in maintaining hydrophobic networks, as synthetic resolution is decremented. Even at resolutions ≥4.0 Å, these latter networks are generally native-like, as measured with a hydropathic interactions scoring tool.     

X-ray analysis of the disk of tobacco mosaic virus protein. 3. A low resolution electron density map

The structure of the disk of tobacco mosaic virus protein at low resolution has been determined by X-ray crystal analysis. Signs for the three principal projections were found by isomorphous replacement, using a mercury derivative. The heavy-atom positions were located by interpretation of difference Patterson maps on the basis of the non-crystallographic 17-fold rotational symmetry of the disk, and of the packing of the disks determined in the preceding paper (Finch et al., 1974).The electron density in the corresponding three projections was computed to a resolution of 6 Å. From the projections in the [100] and [010] directions, which are at right-angles to the 17-fold rotation axis, a three-dimensional electron density map has been calculated making use of the non-crystallographic symmetry. The procedure is similar to the three-dimensional image reconstruction technique used in electron microscopy.The map indicates that the subunits in the two rings face the same way and, hence, that the disk is polar. There are differences between the subunits in the two rings at high radius, which are presumably a consequence of the pairing interaction responsible for stabilizing the two-layer polar structure. The map has been compared with a low-resolution map of the intact virus, and certain common features can be identified, notably the site of the nucleic acid.     

Lumbricus terrestris hemoglobin: A comparison of small-angle X-ray scattering and cryoelectron microscopy data

The quaternary structure of Lumbricus terrestris hemoglobin was investigated by small-angle x-ray scattering (SAXS). Based on the SAXS data from several independent experiments, a three-dimensional (3D) consensus model was established to simulate the solution structure of this complex protein at low resolution (about 3 nm) and to yield the particle dimensions. The model is built up from a large number of small spheres of different weights, a result of the two-step procedure used to calculate the SAXS model. It accounts for the arrangement of 12 subunits in a hexagonal bilayer structure and for an additional central unit of cylinder-like shape. This model provides an excellent fit of the experimental scattering curve of the protein up to h = 1 nm⁻¹ and a nearly perfect fit of the experimental distance distribution function p(r) in the whole range. Scattering curves and p(r) functions were also calculated for low-resolution models based on 3D reconstructions obtained by cryoelectron microscopy (EM). The calculated functions of these models also provide a very good fit of the experimental scattering curve (even at h > 1 nm⁻¹) and p(r) function, if hydration is taken into account and the original model coordinates are slightly rescaled. The comparison of models reveals that both the SAXS-based and the EM-based model lead to a similar simulation of the protein structure and to similar particle dimensions. The essential differences between the models concern the hexagonal bilayer arrangement (eclipsed in the SAXS model, one layer slightly rotated in the EM model), and the mass distribution, mainly on the surface and in the central part of the protein complex. © John Wiley & Sons, Inc. Biopoly 45: 289–298, 1998     

Simulated tempering yields insight into the low-resolution Rosetta scoring functions

Rosetta is a structure prediction package that has been employed successfully in numerous protein design and other applications.1 Previous reports have attributed the current limitations of the Rosetta de novo structure prediction algorithm to inadequate sampling, particularly during the low-resolution phase.2-5 Here, we implement the Simulated Tempering (ST) sampling algorithm67 in Rosetta to address this issue. ST is intended to yield canonical sampling by inducing a random walk in temperatures space such that broad sampling is achieved at high temperatures and detailed exploration of local free energy minima is achieved at low temperatures. ST should therefore visit basins in accordance with their free energies rather than their energies and achieve more global sampling than the localized scheme currently implemented in Rosetta. However, we find that ST does not improve structure prediction with Rosetta. To understand why, we carried out a detailed analysis of the low-resolution scoring functions and find that they do not provide a strong bias towards the native state. In addition, we find that both ST and standard Rosetta runs started from the native state are biased away from the native state. Although the low-resolution scoring functions could be improved, we propose that working entirely at full-atom resolution is now possible and may be a better option due to superior native-state discrimination at full-atom resolution. Such an approach will require more attention to the kinetics of convergence, however, as functions capable of native state discrimination are not necessarily capable of rapidly guiding non-native conformations to the native state.     

Bayesian Inference of Initial Models in Cryo-Electron Microscopy Using Pseudo-atoms

Single-particle cryo-electron microscopy is widely used to study the structure of macromolecular assemblies. Tens of thousands of noisy two-dimensional images of the macromolecular assembly viewed from different directions are used to infer its three-dimensional structure. The first step is to estimate a low-resolution initial model and initial image orientations. This is a challenging global optimization problem with many unknowns, including an unknown orientation for each two-dimensional image. Obtaining a good initial model is crucial for the success of the subsequent refinement step. We introduce a probabilistic algorithm for estimating an initial model. The algorithm is fast, has very few algorithmic parameters, and yields information about the precision of estimated model parameters in addition to the parameters themselves. Our algorithm uses a pseudo-atomic model to represent the low-resolution three-dimensional structure, with isotropic Gaussian components as moveable pseudo-atoms. This leads to a significant reduction in the number of parameters needed to represent the three-dimensional structure, and a simplified way of computing two-dimensional projections. It also contributes to the speed of the algorithm. We combine the estimation of the unknown three-dimensional structure and image orientations in a Bayesian framework. This ensures that there are very few parameters to set, and specifies how to combine different types of prior information about the structure with the given data in a systematic way. To estimate the model parameters we use Markov chain Monte Carlo sampling. The advantage is that instead of just obtaining point estimates of model parameters, we obtain an ensemble of models revealing the precision of the estimated parameters. We demonstrate the algorithm on both simulated and real data.