CryoRes: Local Resolution Estimation of Cryo-EM Density Maps by Deep Learning

Recent progress in cryo-EM research has ignited a revolution in biological macromolecule structure determination. Resolution is an essential parameter for quality assessment of a cryo-EM density map, and it is known that resolution varies in different regions of a map. Currently available methods for local resolution estimation require manual adjustment of parameters and in some cases necessitate acquisition or de novo generation of so-called “half maps”. Here, we developed CryoRes, a deep-learning algorithm to estimate local resolution directly from a single final cryo-EM density map, specifically by learning resolution-aware patterns of density map voxels through supervised training on a large dataset comprising 1,174 experimental cryo-EM density maps. CryoRes significantly outperforms all of the state-of-the-art competing resolution estimation methods, achieving an average RMSE of 2.26 Å for local resolution estimation relative to the currently most reliable FSC-based method blocres, yet requiring only the single final map as input. Further, CryoRes is able to generate a molecular mask for each map, with accuracy 12.12% higher than the masks generated by ResMap. CryoRes is ultra-fast, fully automatic, parameter-free, applicable to cryo-EM subtomogram data, and freely available at https://cryores.zhanglab.net.     

Constructing and validating initial Cα models from subnanometer resolution density maps with pathwalking

A significant number of macromolecular structures solved by electron cryo-microscopy and X-ray crystallography obtain resolutions of 3.5-6?, at which direct atomistic interpretation is difficult. To address this, we developed pathwalking, a semi-automated protocol to enumerate reasonable Cα models from near-atomic resolution density maps without a structural template or sequence-structure correspondence. Pathwalking uses an approach derived from the Traveling Salesman Problem to rapidly generate an ensemble of initial models for individual proteins, which can later be optimized to produce full atomic models. Pathwalking can also be used to validate and identify potential structural ambiguities in models generated from near-atomic resolution density maps. In this work, examples from the EMDB and PDB are used to assess the broad applicability and accuracy of our method. With the growing number of near-atomic resolution density maps from cryo-EM and X-ray crystallography, pathwalking can become an important tool in modeling protein structures.     

Refinement of Protein Structures into Low-Resolution Density Maps Using Rosetta

We describe a method based on Rosetta structure refinement for generating high-resolution, all-atom protein models from electron cryomicroscopy density maps. A local measure of the fit of a model to the density is used to directly guide structure refinement and to identify regions incompatible with the density that are then targeted for extensive rebuilding. Over a range of test cases using both simulated and experimentally generated data, the method consistently increases the accuracy of starting models generated either by comparative modeling or by hand-tracing the density. The method can achieve near-atomic resolution starting from density maps at 4-6 Å resolution.     

Low-resolution structure refinement in electron microscopy

A real-space structure refinement method, originally developed for macromolecular X-ray crystallography, has been applied to protein structure analysis by electron microscopy (EM). This method simultaneously optimizes the fit of an atomic model to a density map and the stereo-chemical properties of the model by minimizing an energy function. The performance of this method is characterized at different resolution and signal-to-noise ratio conditions typical for EM electron density maps. A multi-resolution scheme is devised to improve the convergence of the refinement on the global energy minimum. Applications of the method to various model systems are demonstrated here. The first case is the arrangement of FlgE molecules in the helical filament of flagellar hook, in which refinement with segmented rigid bodies improves the density correlation and reduces severe van der Waals contacts among the symmetry-related subunits. The second case is a conformational analysis of the NSF AAA ATPase in which a multi-conformer model is used in the refinement to investigate the arrangement of the two ATPase domains in the molecule. The third case is a docking simulation in which the crystal structure of actin and the NOE data from NMR experiments on the dematin headpiece are combined with a low-resolution EM density map to generate an atomic model of the F-actin-dematin headpiece structure.     

A novel three-dimensional variant of the watershed transform for segmentation of electron density maps

Electron density maps at moderate resolution are often difficult to interpret due to the lack of recognizable features. This is especially true for electron tomograms that suffer in addition to the resolution limitation from low signal-to-noise ratios. Reliable segmentation of such maps into smaller, manageable units can greatly facilitate interpretation. Here, we present a segmentation approach targeting three-dimensional electron density maps derived by electron microscopy. The approach consists of a novel three-dimensional variant of the immersion-based watershed algorithm. We tested the algorithm on calculated data and applied it to a wide variety of electron density maps ranging from reconstructions of single macromolecules to tomograms of subcellular structures. The results indicate that the algorithm is reliable, efficient, accurate, and applicable to a wide variety of biological problems.     

The atomic resolution crystal structure of atratoxin determined by single wavelength anomalous diffraction phasing

By using single wavelength anomalous diffraction phasing based on the anomalous signal from copper atoms, the crystal structure of atratoxin was determined at the resolution of 1.5 A and was refined to an ultrahigh resolution of 0.87 A. The ultrahigh resolution electron density maps allowed the modeling of 38 amino acid residues in alternate conformations and the location of 322 of 870 possible hydrogen atoms. To get accurate information at the atomic level, atratoxin-b (an analog of atratoxin with reduced toxicity) was also refined to an atomic resolution of 0.92 A. By the sequence and structural comparison of these two atratoxins, Arg(33) and Arg(36) were identified to be critical to their varied toxicity. The effect of copper ions on the distribution of hydrogen atoms in atratoxin was discussed, and the interactions between copper ions and protein residues were analyzed based on a statistical method, revealing a novel pentahedral copper-binding motif.     

Structure of porcine heart cytoplasmic malate dehydrogenase: combining X-ray diffraction and chemical sequence data in structural studies

The amino acid sequence of cytoplasmic malate dehydrogenase (sMDH) has been determined by a combination of X-ray crystallographic and chemical sequencing methods. The initial molecular model incorporated an "X-ray amino acid sequence" that was derived primarily from an evaluation of a multiple isomorphous replacement phased electron density map calculated at 2.5-A resolution. Following restrained least-squares crystallographic refinement, difference electron density maps were calculated from model phases, and attempts were made to upgrade the X-ray amino acid sequence. The method used to find the positions of peptides in the X-ray structure was similar to those used for studying protein homology and was shown to be successful for large fragments. For sMDH, X-ray methods by themselves were insufficient to derive a complete amino acid sequence, even with partial chemical sequence data. However, for this relatively large molecule at medium resolution, the electron density maps were of considerable help in determining the linear position of peptide fragments. The N-acetylated polypeptide chain of sMDH has 331 amino acids and has been crystallographically refined to an R factor of 19% for 2.5-A resolution diffraction data.     

Cryo-electron microscopy modeling by the molecular dynamics flexible fitting method

The increasing power and popularity of cryo-electron microscopy (cryo-EM) in structural biology brought about the development of so-called hybrid methods, which permit the interpretation of cryo-EM density maps beyond their nominal resolution in terms of atomic models. The Cryo-EM Modeling Challenge 2010 is the first community effort to bring together developers of hybrid methods as well as cryo-EM experimentalists. Participating in the challenge, the molecular dynamics flexible fitting (MDFF) method was applied to a number of cryo-EM density maps. The results are described here with special emphasis on the use of symmetry-based restraints to improve the quality of atomic models derived from density maps of symmetric complexes; on a comparison of the stereochemical quality of atomic models resulting from different hybrid methods; and on application of MDFF to electron crystallography data.     

Experimental charge density from electron microscopic maps

The charge density (CD) distribution of an atom is the difference per unit volume between the positive charge of its nucleus and the distribution of the negative charges carried by the electrons that are associated with it. The CDs of the atoms in macromolecules are responsible for their electrostatic potential (ESP) distributions, which can now be visualized using cryo‐electron microscopy at high resolution. CD maps can be recovered from experimental ESP density maps using the negative Laplacian operation. CD maps are easier to interpret than ESP maps because they are less sensitive to long‐range electrostatic effects. An ESP‐to‐CD conversion involves multiplication of amplitudes of structure factors as Fourier transforms of these maps in reciprocal space by 1/d², where d is the resolution of reflections. In principle, it should be possible to determine the charges carried by the individual atoms in macromolecules by comparing experimental CD maps with experimental ESP maps.     

2．5分辨率单斜Al－（L－丙氨酸）胰岛素晶体结构研究

空间群为Ｐ２１的Ａ１－（Ｌ－丙氨酸）胰岛素晶胞内,一个不对称单位含有一个六聚体,应用差值Ｆｏｕｒｉｅｒ技术,立体化学制最小二来技术和Ｘ—ＰＬＯＲ程序并辅以电子密度图的人工拟合,解析了分辨率ＡＩ—（Ｌ－丙氨酸）胰岛素（Ａｌ－Ｌ－ＡｌａⅠ）的晶体结构。最终Ｒ因子为２０．６％,与标准键长与键角的均方根偏差分别为和４．１９°,从电子密度图与模型的拟合来看,六聚体中每条Ａ链的Ａｌ位置替换的Ｌ—Ａｌａ清晰可见,每条Ｂ链Ｎ端Ｂ１—Ｂ８伏段都为α螺旋构象,形成了Ｂ１—Ｂ１９的连续α螺旋段。     

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.     

High-Resolution Multipoint Linkage-Disequilibrium Mapping in the Context of a Human Genome Sequence

A new method is presented for fine-scale linkage disequilibrium (LD) mapping of a disease mutation; it uses multiple linked single-nucleotide polymorphisms, restriction-fragment-length polymorphisms, or microsatellite markers and incorporates information from an annotated human genome sequence (HGS) and from a human mutation database. The method takes account of population demographic effects, using Markov chain Monte Carlo methods to integrate over the unknown gene genealogy and gene coalescence times. Information about the relative frequency of disease mutations in exons, introns, and other regions, from mutational databases, as well as assumptions about the completeness of the gene annotation, are used with an annotated HGS, to generate a prior probability that a mutation lies at any particular position in a specified region of the genome. This information is updated with information about mutation location, from LD at a set of linked markers in the region, to generate the posterior probability density of the mutation location. The performance of the method is evaluated by simulation and by analysis of a data set for diastrophic dysplasia (DTD) in Finland. The DTD disease gene has been positionally cloned, so the actual location of the mutation is known and can be compared with the position predicted by our method. For the DTD data, the addition of information from an HGS results in disease-gene localization at a resolution that is much higher than that which would be possible by LD mapping alone. In this case, the gene would be found by sequencing a region < or =7 kb in size.     

Crystal structure of glyceraldehyde-3-phosphate dehydrogenase from Plasmodium falciparum at 2.25 A resolution reveals intriguing extra electron density in the active site

The crystal structure of D-glyceraldehyde-3-phosphate dehydrogenase (PfGAPDH) from the major malaria parasite Plasmodium falciparum is solved at 2.25 A resolution. The structure of PfGAPDH is of interest due to the dependence of the malaria parasite in infected human erythrocytes on the glycolytic pathway for its energy generation. Recent evidence suggests that PfGAPDH may also be required for other critical activities such as apical complex formation. The cofactor NAD(+) is bound to all four subunits of the tetrameric enzyme displaying excellent electron densities. In addition, in all four subunits a completely unexpected large island of extra electron density in the active site is observed, approaching closely the nicotinamide ribose of the NAD(+). This density is most likely the protease inhibitor AEBSF, found in maps from two different crystals. This putative AEBSF molecule is positioned in a crucial location and hence our structure, with expected and unexpected ligands bound, can be of assistance in lead development and design of novel antimalarials.     

三维电子显微学自动化数据采集的进展

生物三维电子显微学在过去几年取得了巨大的突破,一些具有高对称性的病毒颗粒获得了准原子分辨率的结构,非对称性的生物大分子及其复合体的结构分辨率也有快速的提高。而要获得高分辨率的结构,获取足够多的高质量电子显微照片是其中的一个关键因素。近年来,自动化数据采集技术在电子断层成像术和单颗粒方法中都取得了很大的进展。其广泛应用将使结构测定更加快速并使结构分辨率提高到更高的层次。     

Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.     

Determination of chemical identity and occupancy from experimental density maps

Three basic electronic properties of molecules, electron density (ED), charge density (CD), and electrostatic potentials (ESP), are dependent on both atomic mobility and occupancy of components in the molecules. Small protein subunits may bind large macromolecular complexes with a reduced occupancy or an increased atomic mobility or both due to affinity‐based functional regulation, and so may substrates, products, cofactors, ions or solvent molecule to the active sites of enzymes. A quantitative theory is presented in this study that describes the dependence of atomic functions on atomic B‐factor in Fourier transforms of the corresponding maps. An application of this theory is described to an experimental ED map at 1.73‐Å resolution, and to an experimental CD map at 2.2‐Å resolution. All the three density functions are linearly proportional to occupancy when the structure factor F(000) term of Fourier transforms of experimental density maps is included. Upon application of this theory to both experimental CD and ESP maps recently reported for photosystem II‐light harvesting complex II supercomplex at 3.2‐Å resolution, the occupancy of two extrinsic protein subunits PsbQ and PsbP is determined to be 20.4 ± 0.2%, and the negative mean ESP value of vitreous ice displaced by the supercomplex on electron scattering path is estimated to be 3% of the mean ESP value of protein α‐helices.     

Recombination patterns reveal information about centromere location on linkage maps

Linkage mapping is often used to identify genes associated with phenotypic traits and for aiding genome assemblies. Still, many emerging maps do not locate centromeres – an essential component of the genomic landscape. Here, we demonstrate that for genomes with strong chiasma interference, approximate centromere placement is possible by phasing the same data used to generate linkage maps. Assuming one obligate crossover per chromosome arm, information about centromere location can be revealed by tracking the accumulated recombination frequency along linkage groups, similar to half‐tetrad analyses. We validate the method on a linkage map for sockeye salmon (Oncorhynchus nerka) with known centromeric regions. Further tests suggest that the method will work well in other salmonids and other eukaryotes. However, the method performed weakly when applied to a male linkage map (rainbow trout; O. mykiss) characterized by low and unevenly distributed recombination – a general feature of male meiosis in many species. Further, a high frequency of double crossovers along chromosome arms in barley reduced resolution for locating centromeric regions on most linkage groups. Despite these limitations, our method should work well for high‐density maps in species with strong recombination interference and will enrich many existing and future mapping resources.     

Sub-Angstrom resolution enzyme X-ray structures: is seeing believing?

Recent technical advances in crystallographic analysis, particularly highly focused and high brilliance synchrotron beam lines, have significantly improved the resolutions that are attainable for many macromolecular crystal structures. The Protein Data Bank (http://www.rcsb.org/pdb/) contains an increasing number of atomic resolution structures, which are providing a wealth of structural information that was not previously visible in lower resolution electron density maps. Here, we review the importance of visualizing hydrogen atoms and multiple sidechain conformations or anisotropy, as well as substrate strain, at sub-Angstrom resolution. The additional structural features that are visible in the electron density maps as a result of atomic resolution data provide a better understanding of the catalytic mechanisms of cholesterol oxidase, ribonuclease A, beta-lactamase, serine proteases, triosephosphate isomerase and endoglucanase.