A machine learning approach for the identification of protein secondary structure elements from electron cryo-microscopy density maps

The accuracy of the secondary structure element (SSE) identification from volumetric protein density maps is critical for de-novo backbone structure derivation in electron cryo-microscopy (cryoEM). It is still challenging to detect the SSE automatically and accurately from the density maps at medium resolutions (～5-10 ?). We present a machine learning approach, SSELearner, to automatically identify helices and β-sheets by using the knowledge from existing volumetric maps in the Electron Microscopy Data Bank. We tested our approach using 10 simulated density maps. The averaged specificity and sensitivity for the helix detection are 94.9% and 95.8%, respectively, and those for the β-sheet detection are 86.7% and 96.4%, respectively. We have developed a secondary structure annotator, SSID, to predict the helices and β-strands from the backbone Cα trace. With the help of SSID, we tested our SSELearner using 13 experimentally derived cryo-EM density maps. The machine learning approach shows the specificity and sensitivity of 91.8% and 74.5%, respectively, for the helix detection and 85.2% and 86.5% respectively for the β-sheet detection in cryoEM maps of Electron Microscopy Data Bank. The reduced detection accuracy reveals the challenges in SSE detection when the cryoEM maps are used instead of the simulated maps. Our results suggest that it is effective to use one cryoEM map for learning to detect the SSE in another cryoEM map of similar quality.     

Re-examining the spectra of macromolecules. Current practice of spectral quasi B-factor flattening

The analysis of structure factors in 3D cryo-EM Coulomb potential maps and their “enhancement” at the end of the reconstruction process is a well-established practice, normally referred to as sharpening. The aim is to increase contrast and, in this way, to help tracing the atomic model. The most common way to accomplish this enhancement is by means of the so-called B-factor correction, which applies a global filter to boost high frequencies with some dampening considerations related to noise amplification. The results are maps with a better visual aspect and a quasiflat spectrum at medium and high frequencies. This practice is so widespread that most map depositions in the Electron Microscopy Data Base (EMDB) only contain sharpened maps. Here, the use in cryoEM of global B-factor corrections is theoretically and experimentally analyzed. Results clearly illustrate that protein spectra present a falloff. Thus, spectral quasi-flattening may produce protein spectra with distortions when compared with experimental ones, this fact, combined with the practice of reporting only sharpened maps, generates a sub-optimal situation in terms of data preservation, reuse and reproducibility. Now that the field is more advanced, we put forward two suggestions: (1) to use methods which keep more faithfully the original experimental signal properties of macromolecules when “enhancing” the map, and (2) to further stress the need to deposit the original experimental maps without any postprocessing or sharpening, not only the enhanced maps. In the absence of access to these original maps data is lost, preventing their future analysis with new methods.     

Three-Dimensional Reconstruction with Contrast Transfer Function Correction from Energy-Filtered Cryoelectron Micrographs: Procedure and Application to the 70SEscherichia coliRibosome

Cryoelectron microscopy provides the means of studying macromolecules in their native state. However, the contrast transfer function (CTF) makes the images and the three-dimensional (3D) maps derived from them difficult to interpret. We developed methods to determine the CTF from experimental data and to obtain a CTF-corrected 3D reconstruction. The CTF correction and 3D reconstruction accomplished in one step make it easy to combine different defocus data sets and decrease the error accumulation in the computation. These methods were applied to energy-filtered images of the 70SEscherichia coliribosome, resulting in a distortion-free 3D map of the ribosome at 1/24.5 Å⁻¹resolution, as determined by the differential phase residual resolution criterion.     

Low-Resolution Density Maps from Atomic Models: How Stepping “Back” Can Be a Step “Forward”

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15–40 Å), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

Inference of Euler angles for single-particle analysis by means of evolutionary algorithms

Single-particle analysis is one of the methods for structural studies of protein and macromolecules; it requires advanced image analysis of electron micrographics. Reconstructing three-dimensional (3D) structure from microscope images is not an easy analysis because of the low image resolution of images and lack of the directional information of images in 3D structure. To improve the resolution, different projections are aligned, classified, and averaged. Inferring the orientations of these images is so difficult that the task of reconstructing 3D structures depends upon the experience of researchers. But recently, a method to reconstruct 3D structures was automatically devised. In this paper, we propose a new method for determining Euler angles of projections by applying genetic algorithms. We empirically show that the proposed approach has improved the previous one in terms of computational time and acquired precision.     

Low-resolution density maps from atomic models: how stepping "back" can be a step "forward"

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15-40 A), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

Automated cryoEM data acquisition and analysis of 284742 particles of GroEL

One of the goals in developing our automated electron microscopy data acquisition system, Leginon, was to improve both the ease of use and the throughput of the process of acquiring low dose images of macromolecular specimens embedded in vitreous ice. In this article, we demonstrate the potential of the Leginon system for high-throughput data acquisition by describing an experiment in which we acquired images of more than 280,000 particles of GroEL in a single 25 h session at the microscope. We also demonstrate the potential for an automated pipeline for molecular microscopy by showing that these particles can be subjected to completely automated procedures to reconstruct a three-dimensional (3D) density map to a resolution better than 8 A. In generating the 3D maps, we used a variety of metadata associated with the data acquisition and processing steps to sort and select the particles. These metadata provide a number of insights into factors that affect the quality of the acquired images and the resulting reconstructions. In particular, we show that the resolution of the reconstructed 3D density maps improves with decreasing ice thickness. These data provide a basis for assessing the capabilities of high-throughput macromolecular microscopy.     

Computational approaches for automatic structural analysis of large biomolecular complexes

We present computational solutions to two problemsof macromolecular structure interpretation from reconstructedthree-dimensional electron microscopy (3D-EM) maps of largebio-molecular complexes at intermediate resolution (5A-15A). Thetwo problems addressed are: (a) 3D structural alignment (matching)between identified and segmented 3D maps of structure units(e.g. trimeric configuration of proteins), and (b) the secondarystructure identification of a segmented protein 3D map (i.e.locations of a-helices, b -sheets). For problem (a), we presentan efficient algorithm to correlate spatially (and structurally)two 3D maps of structure units. Besides providing a similarityscore between structure units, the algorithm yields an effectivetechnique for resolution refinement of repeated structure units,by 3D alignment and averaging. For problem (b), we present anefficient algorithm to compute eigenvalues and link eigenvectorsof a Gaussian convoluted structure tensor derived from theprotein 3D Map, thereby identifying and locating secondarystructural motifs of proteins. The efficiency and performanceof our approach is demonstrated on several experimentallyreconstructed 3D maps of virus capsid shells from single-particlecryo-EM, as well as computationally simulated protein structuredensity 3D maps generated from protein model entries in theProtein Data Bank.     

Estimating loop length from CryoEM images at medium resolutions

Background

De novo protein modeling approaches utilize 3-dimensional (3D) images derived from electron cryomicroscopy (CryoEM) experiments. The skeleton connecting two secondary structures such as α-helices represent the loop in the 3D image. The accuracy of the skeleton and of the detected secondary structures are critical in De novo modeling. It is important to measure the length along the skeleton accurately since the length can be used as a constraint in modeling the protein.

Results

We have developed a novel computational geometric approach to derive a simplified curve in order to estimate the loop length along the skeleton. The method was tested using fifty simulated density images of helix-loop-helix segments of atomic structures and eighteen experimentally derived density data from Electron Microscopy Data Bank (EMDB). The test using simulated density maps shows that it is possible to estimate within 0.5Å of the expected length for 48 of the 50 cases. The experiments, involving eighteen experimentally derived CryoEM images, show that twelve cases have error within 2Å.

Conclusions

The tests using both simulated and experimentally derived images show that it is possible for our proposed method to estimate the loop length along the skeleton if the secondary structure elements, such as α-helices, can be detected accurately, and there is a continuous skeleton linking the α-helices.

     

A near atomic resolution structure of a Melanocarpus albomyces laccase

It is becoming routine for cryoEM single particle reconstructions to result in 3D electron density maps with resolutions of 10 Å, but maps with resolutions of 5 Å or better are still celebrated events. The electron microscope has a resolving power to better than 2 Å, and thus should not be a limiting factor; instead the practical limitations in resolution most likely arise from a combination of specimen preparation methods, data collection parameters, and data analysis procedures. With the aid of a highly automated system for acquiring images, coupled to a relational database to keep track of all processing parameters, we have taken a systematic approach to optimizing parameters affecting the resolution of single particle reconstructions. Using GroEL as a test-bed, we performed a series of 3D reconstructions where we systematically varied the number of particles used in computing the map, the accelerating voltage of the microscope, and the electron dose used to acquire the images. We also investigated methods for excluding unacceptable or “bad” particles from contributing to the final 3D map. Using relatively standard instrumentation (Tecnai F20, 4K × 4K CCD, side entry cold stage) and a completely automated approach, these approaches resulted in a map with a nominal resolution of 5.4 Å (FSC_0.5) in which secondary structure is clearly discernable and the handedness of some of the α-helices in the GroEL structure can be determined.     

Initial evaluation of a direct detection device detector for single particle cryo-electron microscopy

We report on initial results of using a new direct detection device (DDD) for single particle reconstruction of vitreous ice embedded specimens. Images were acquired on a Tecnai F20 at 200 keV and a nominal magnification of 29,000×. This camera has a significantly improved signal to noise ratio and modulation transfer function (MTF) at 200 keV compared to a standard CCD camera installed on the same microscope. Control of the DDD has been integrated into Leginon, an automated data collection system. Using GroEL as a test specimen, we obtained images of ∼30 K particles with the CCD and the DDD from the same specimen sample using essentially identical imaging conditions. Comparison of the maps reconstructed from the CCD images and the DDD images demonstrates the improved performance of the DDD. We also obtained a 3D reconstruction from ∼70 K GroEL particles acquired using the DDD; the quality of the density map demonstrates the potential of this new recording device for cryoEM data acquisition.     

Development of a Three-Dimensional Hand Model Using Three-Dimensional Stereophotogrammetry: Assessment of Image Reproducibility

Purpose

Using three-dimensional (3D) stereophotogrammetry precise images and reconstructions of the human body can be produced. Over the last few years, this technique is mainly being developed in the field of maxillofacial reconstructive surgery, creating fusion images with computed tomography (CT) data for precise planning and prediction of treatment outcome. Though, in hand surgery 3D stereophotogrammetry is not yet being used in clinical settings.

Methods

A total of 34 three-dimensional hand photographs were analyzed to investigate the reproducibility. For every individual, 3D photographs were captured at two different time points (baseline T0 and one week later T1). Using two different registration methods, the reproducibility of the methods was analyzed. Furthermore, the differences between 3D photos of men and women were compared in a distance map as a first clinical pilot testing our registration method.

Results

The absolute mean registration error for the complete hand was 1.46 mm. This reduced to an error of 0.56 mm isolating the region to the palm of the hand. When comparing hands of both sexes, it was seen that the male hand was larger (broader base and longer fingers) than the female hand.

Conclusions

This study shows that 3D stereophotogrammetry can produce reproducible images of the hand without harmful side effects for the patient, so proving to be a reliable method for soft tissue analysis. Its potential use in everyday practice of hand surgery needs to be further explored.     

Towards the saturation of the pepper linkage map by alignment of three intraspecific maps including known-function genes.

Three populations composed of a total of 215 doubled haploid lines and 151 F2 individuals were used to design an intraspecific consensus map of pepper (Capsicum annuum L.). The individual maps varied from 685 to 1668 cM with 16 to 20 linkage groups (LGs). The alignment of the three individual maps permitted the arrangement of 12 consensus major linkage groups corresponding to the basic chromosome number of pepper and displaying a complex correspondence with the tomato map. The consensus map contained 100 known-function gene markers and 5 loci of agronomic interest (the disease-resistance loci L, pvr2, and Pvr4; the C locus, which determines capsaicin content; and the up locus, controlling the erect habit of the fruits). The locations of three other disease-resistance loci (Tsw, Me3, and Bs3) and the y locus, which determines the yellow fruit colour, were also found on this consensus map thanks to linked markers. Here we report on the first functional detailed map in pepper. The use of candidate gene sequences as genetic markers allowed us to localize four clusters of disease-resistance gene analogues and to establish syntenic relationships with other species.     

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.     

Combined method of whole mount and block-face imaging: Acquisition of 3D data of gene expression pattern from conventional in situ hybridization

Visualization of spatiotemporal expression of a gene of interest is a fundamental technique for analyzing the involvements of genes in organ development. In situ hybridization (ISH) is one of the most popular methods for visualizing gene expression. When conventional ISH is performed on sections or whole-mount specimens, the gene expression pattern is represented in 2-dimensional (2D) microscopic images or in the surface view of the specimen. To obtain 3-dimensional (3D) data of gene expression from conventional ISH, the “serial section method” has traditionally been employed. However, this method requires an extensive amount of time and labor because it requires researchers to collect a tremendous number of sections, label all sections by ISH, and image them before 3D reconstruction. Here, we proposed a rapid and low-cost 3D imaging method that can create 3D gene expression patterns from conventional ISH-labeled specimens. Our method consists of a combination of whole-mount ISH and Correlative Microscopy and Blockface imaging (CoMBI). The whole-mount ISH-labeled specimens were sliced using a microtome or cryostat, and all block-faces were imaged and used to reconstruct 3D images by CoMBI. The 3D data acquired using our method showed sufficient quality to analyze the morphology and gene expression patterns in the developing mouse heart. In addition, 2D microscopic images of the sections can be obtained when needed. Correlating 2D microscopic images and 3D data can help annotate gene expression patterns and understand the anatomy of developing organs. These results indicated that our method can be useful in the field of developmental biology.     

Protein structure fitting and refinement guided by cryo-EM density

For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.     

Reconstruction of 3D structures from protein contact maps

The prediction of the protein tertiary structure from solely its residue sequence (the so called Protein Folding Problem) is one of the most challenging problems in Structural Bioinformatics. We focus on the protein residue contact map. When this map is assigned it is possible to reconstruct the 3D structure of the protein backbone. The general problem of recovering a set of 3D coordinates consistent with some given contact map is known as a unit-disk-graph realization problem and it has been recently proven to be NP-Hard. In this paper we describe a heuristic method (COMAR) that is able to reconstruct with an unprecedented rate (3-15 seconds) a 3D model that exactly matches the target contact map of a protein. Working with a non-redundant set of 1760 proteins, we find that the scoring efficiency of finding a 3D model very close to the protein native structure depends on the threshold value adopted to compute the protein residue contact map. Contact maps whose threshold values range from 10 to 18 Ångstroms allow reconstructing 3D models that are very similar to the proteins native structure.     

Structural asymmetry in a trimeric Na+/betaine symporter, BetP, from Corynebacterium glutamicum

The Na⁺-coupled symporter BetP catalyzes the uptake of the compatible solute betaine in the soil bacterium Corynebacterium glutamicum. BetP also senses hyperosmotic stress and regulates its own activity in response to stress level. We determined a three-dimensional (3D) map (at 8 Å in-plane resolution) of a constitutively active mutant of BetP in a C. glutamicum membrane environment by electron cryomicroscopy of two-dimensional crystals. The map shows that the constitutively active mutant, which lacks the C-terminal domain involved in osmosensing, is trimeric like wild-type BetP. Recently, we reported the X-ray crystal structure of BetP at 3.35 Å, in which all three protomers displayed a substrate-occluded state. Rigid-body fitting of this trimeric structure to the 3D map identified the periplasmic and cytoplasmic sides of the membrane. Fitting of an X-ray monomer to the individual protomer maps allowed assignment of transmembrane helices and of the substrate pathway, and revealed differences in trimer architecture from the X-ray structure in the tilt angle of each protomer with respect to the membrane. The three protomer maps showed pronounced differences around the substrate pathway, suggesting three different conformations within the same trimer. Two of those protomer maps closely match those of the atomic structures of the outward-facing and inward-facing states of the hydantoin transporter Mhp1, suggesting that the BetP protomer conformations reflect key states of the transport cycle. Thus, the asymmetry in the two-dimensional maps may reflect cooperativity of conformational changes within the BetP trimer, which potentially increases the rate of glycine betaine uptake.     

Cryo-Electron Microscopy: The field of 1,000+ methods

Cryo-Electron Microscopy (CryoEM) is currently a well-established method to elucidate a biological macromolecule’s three-dimensional (3D) structure. Its success is due to technological and methodological advances in several fronts: sample preparation, electron optics and detection, image acquisition, image processing, and map interpretation. The first methods started in the late 1960s and, since then, new methods on all fronts have continuously been published, maturating the field as we know it now.In terms of publications, we can distinguish several periods, witnessing a substantial acceleration of methodological publications in recent years, pointing out to an increased interest in the domain. On the other hand, this accelerated increase of methods development may confuse practitioners about which method they should be using (and how) and highlight the importance of paying attention to establishing best practices for methods reporting and usage.In this paper, we analyze the trends identified in over 1,000 methodological papers. Our focus is primarily on computational image processing methods. However, our list also covers some aspects of sample preparation and image acquisition.Several interesting ideas stem out from this study: (1) Single Particle Analysis (SPA) has largely accelerated in the last decade and sample preparation methods in the last five years; (2) Electron Tomography is not yet in a rapidly growing phase, but it is foreseeable that it will soon be; (3) the work horses of SPA are 3D classification, 3D reconstruction, and 3D alignment, and there have been many papers on these topics, which are not considered to be solved yet, but ever improving; and (4) since the resolution revolution, atomic modelling has also caught on as a hot topic.