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.     

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.     

Effects of aligned α‐helix peptide dipoles on experimental electrostatic potentials

Aligned protein α‐helix dipoles have been implicated in protein function and structure. The recent breakthroughs in high‐resolution electron microscopy (EM) of macromolecules makes it possible to explore fundamental aspects of structural biology at the detailed molecular level. The electrostatic potential (ESP) generated by aligned protein α‐helix dipole should be observable in high‐resolution EM maps despite the fact that the effect may be partially screened by induced electric fields. Here, we show that aligned backbone dipoles in protein α‐helices account for long‐range features in the protein ESP functions. Our results are consistent with experimental EM maps and density functional theory calculations, including direct Fourier summation for proper calculation of the ESP due to the nonlocal nature of the ESP function from aligned dipoles and other partial atomic charges.     

Cryo-electron microscopy targets in CASP13: Overview and evaluation of results

Structures of seven CASP13 targets were determined using cryo-electron microscopy (cryo-EM) technique with resolution between 3.0 and 4.0 Å. We provide an overview of the experimentally derived structures and describe results of the numerical evaluation of the submitted models. The evaluation is carried out by comparing coordinates of models to those of reference structures (CASP-style evaluation), as well as checking goodness-of-fit of modeled structures to the cryo-EM density maps. The performance of contributing research groups in the CASP-style evaluation is measured in terms of backbone accuracy, all-atom local geometry and similarity of inter-subunit interfaces. The results on the cryo-EM targets are compared with those on the whole set of eighty CASP13 targets. A posteriori refinement of the best models in their corresponding cryo-EM density maps resulted in structures that are very close to the reference structure, including some regions with better fit to the density.     

Detection of secondary and supersecondary structures of proteins from cryo-electron microscopy

Recent advances in three-dimensional electron microscopy (3D EM) have enabled the quantitative visualization of the structural building blocks of proteins at improved resolutions. We provide algorithms to detect the secondary structures (α-helices and β-sheets) from proteins for which the volumetric maps are reconstructed at 6–10 Å resolution. Additionally, we show that when the resolution is coarser than 10 Å, some of the supersecondary structures can be detected from 3D EM maps. For both these algorithms, we employ tools from computational geometry and differential topology, specifically the computation of stable/unstable manifolds of certain critical points of the distance function induced by the molecular surface. Our results connect mathematically well-defined constructions with bio-chemically induced structures observed in proteins.     

On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

Projection Structure of Full Length Connexin 43 by Electron Cryo-Crystallography

We previously used electron cryo-crystallography to determine the three-dimensional structure of recombinant gap junction channels formed by a C-terminal truncation mutant of Cx43 (11). The dodecameric channel is formed by the end-to-end docking of two hexameric connexons, each comprised of 24 transmembrane α-helices. We have now generated two-dimensional crystals of the recombinant, full-length channel, as well as crystals in which the C-tail has been completely removed by trypsin digestion. Projection density maps at 7.5 Å resolution closely resemble our previous analysis of the C-terminal truncation mutant (9). A difference map between the full length and trypsin-treated channels suggests that there are small but significant shifts in protein density upon removal of the C-tail.     

Sequence of rubredoxin by x-ray diffraction

A tentative amino acid sequence has been determined for rubredoxin from Clostridium pasteurianum by examining the shapes of the side chains in an electron density map at 2 Å resolution. Superpositions of the appropiate portions of this map and “ball and stick” representations of the amino acids assigned are presented as evidence in support of our identifications. Discrepancies exist between the sequence shown here and that determined by chemical methods. The sequence deduced from the 2Å resolution map, however, represents our best estimate in the absence of chemical data and before refinement of the structure. We emphasize the results at 2 Å resolution because, until recently, the 2 Å resolution map was usually the final result of an X-ray structure determination. It is instructive to show the level of reliability that can be expected at that stage and to illustrate the kinds of mistakes that are likely to occur when making identifications from electrondensity maps.     

The three-dimensional structure of mitochondrial aspartate aminotransferase at 4.5 A resolution

An X-ray crystallographic study at 4.5 Å resolution has been carried out with triclinic crystals of chicken mitochondrial aspartate aminotransferase.In the electron density map, the enzyme is clearly visible as an isologous α₂-dimer (105 Å × 60 Å × 50 Å) in which the subunits are associated about a molecular 2-fold axis. Each subunit of dimensions 70 Å × 50 Å × 40 Å contains at least seven helices, one of which is about 50 Å long.Difference maps have revealed the positions of the pyridoxyl and the phosphate moieties of the coenzyme as well as the general substrate binding area. The active sites are on opposite sides of the dimer, about 30 Å apart and close to the intersubunit boundary, so that probably both subunits contribute to each active site. An isolated chain segment, passing in front of the active site and ending in contact with the neighbouring subunit is interpreted as one of the chain termini.     

The structure of a centrosymmetric protein crystal

Crystals of racemic rubredoxin, prepared by independent chemical synthesis of the two enantiomers, have been grown and characterized. The unit cell contains two molecules, one of each enantiomer. Examination of the intensity distribution in the diffraction pattern revealed that the crystals are centrosymmetric. This was confirmed by solution of thestructure to 2 Å resolution via molecular replacement methods. The electron density maps are of very high quality due to the fact that the phaseof each reflection must be exactly 0° or exactly 180°. These results demonstrate the feasibility of using synthetic racemic proteins to yield centrosymmetric protein crystals with electron density maps that have very low phase error and model bias. © 1993 Wiley-Liss, Inc.     

Preliminary crystallographic analysis of an enzyme involved in erythromycin biosynthesis: Cytochrome P450eryF

Cytochrome P450eryF was overexpressed in Escherichia coli and purified in high yield. Crystals of the protein in the presence of the substrate, 6-deoxyerythronolide B, have been obtained by the hanging drop vapor diffusion method, using polyethylene glycol 4000 as a precipitant. The crystals belong to the orthorhombic space group P2₁2₁2₁ with unit cell dimensions of a = 54.16 Å, b = 79.67 Å, and c = 99.48 Å and one molecule per asymmetric unit. A complete native data set has been collected to a resolution of 2.1 Å, and anomalous dispersion difference Patterson maps have revealed the location of the single heme iron atom. © 1994 Wiley-Liss, Inc.     

Non-crystallographic symmetry in the crystal dimer of wheat germ agglutinin

Three isomorphous heavy atom derivatives of wheat germ agglutinin crystals, KAu(CN)₂, K₂Pt(NH₃)₂(NO)₂ and mersalyl, have been examined at high resolution. Heavy atom sites were located from difference Patterson maps in three dimensions at 2.15 Å resolution for the gold and platinum derivatives and with less certainty in the centrosymmetric [010] projection for the mersalyl derivative. These sites are distributed in the crystallographic asymmetric unit such that one half of them can be related to the other half by a 180 ° rotation about an axis parallel to a, and an additional translation of about 6.35 Å along that axis. It is suggested that the two subunits of the wheat germ agglutinin dimer, which represent the asymmetric unit of the C2 unit cell, are related by the same symmetry axis, causing heterologous subunit contacts due to the 6.35 Å translation of one relative to the other subunit.     

Finding rigid bodies in protein structures: Application to flexible fitting into cryoEM maps

We present RIBFIND, a method for detecting flexibility in protein structures via the clustering of secondary structural elements (SSEs) into rigid bodies. To test the usefulness of the method in refining atomic structures within cryoEM density we incorporated it into our flexible fitting protocol (Flex-EM). Our benchmark includes 13 pairs of protein structures in two conformations each, one of which is represented by a corresponding cryoEM map. Refining the structures in simulated and experimental maps at the 5–15 Å resolution range using rigid bodies identified by RIBFIND shows a significant improvement over using individual SSEs as rigid bodies. For the 15 Å resolution simulated maps, using RIBFIND-based rigid bodies improves the initial fits by 40.64% on average, as compared to 26.52% when using individual SSEs. Furthermore, for some test cases we show that at the sub-nanometer resolution range the fits can be further improved by applying a two-stage refinement protocol (using RIBFIND-based refinement followed by an SSE-based refinement). The method is stand-alone and could serve as a general interactive tool for guiding flexible fitting into EM maps.     

Crystallization and preliminary X-ray diffraction studies of a bacterial flavohemoglobin protein

A flavohemoglobin protein (FHP) was isolated from Alcaligenes eutrophus and has been crystallized by vapor diffusion methods using PEG 3350 as precipitant. The crystals of the FAD- and heme-containing protein belong to the monoclinic space group P2₁ with unit cell parameters of 52.2 Å, 85.8 Å, 103.9 Å, and 81.8° corresponding to two molecules per asymmetric unit. The crystals diffract at least to a resolution of 2.0 Å and are suitable for an X-ray structure analysis. © 1995 Wiley-Liss, Inc.     

Lamellar dispersion and phase separation of chloroplast membrane lipids by negative staining electron microscopy

Aqueous dispersions of lipids isolated from spinach chloroplast membranes were studied by electron microscopy after negative staining with phosphotungstic acid. Influence of low temperature (5°C for 24 h) was also investigated. It was observed that when contacted with water, these lipids, as such, formed multilamellar structures. Upon sonication, these multilamellar structures gave rise to a clear suspension of unilamellar vesicles varying in size (diameter) between 250 and 750 Å. When samples of sonicated unilamellar vesicles were stored at 5°C for 24 h or more, they revealed a variety of lipid aggregates including liposomes, cylindrical rods (about 100 Å wide and up to 3600 Å long), and spherical micellar structures (100–200 Å in diameter)—thus indicating phase separation of lipids.     

On the reliability of peptide nonplanarity seen in ultra‐high resolution crystal structures

Ultra‐high resolution protein crystal structures have been considered as relatively reliable sources for defining details of protein geometry, such as the extent to which the peptide unit deviates from planarity. Chellapa and Rose (Proteins 2015; 83:1687) recently called this into question, reporting that for a dozen representative protein structures determined at ～1 Å resolution, the diffraction data could be equally well fit with models restrained to have highly planar peptides, i.e. having a standard deviation of the ω torsion angles of only ～1° instead of the typically observed value of ～6°. Here, we document both conceptual and practical shortcomings of that study and show that the more tightly restrained models are demonstrably incorrect and do not fit the diffraction data equally well. We emphasize the importance of inspecting electron density maps when investigating the agreement between a model and its experimental data. Overall, this report reinforces that modern standard refinement protocols have been well‐conceived and that ultra‐high resolution protein crystal structures, when evaluated carefully and used with an awareness of their levels of coordinate uncertainty, are powerful sources of information for providing reliable information about the details of protein geometry.     

Predictions of protein backbone bond distances and angles from first principles

A procedure is described, based on a spline-function representation of ab initio peptide conformational geometry maps, that allows one to predict backbone bond distances and angles of proteins as functions of the peptide ?(N-C^α)/Ψ(C^α-C′) torsions with an accuracy comparable to that of high-resolution protein crystallography. For example, for the more than 40 residues of crambin, the rms deviation between predicted and crystallographic values of N-C^α-C′ is 1.9° for the 1.5 Å resolution structure and 1.9° for the 0.83 Å resolution structure, compared with angle variations of < 10°. Accurate information on protein backbone geometries is important for establishing dictionaries of flexible geometry functions for use in empirical peptide and protein modeling. © 1995 John Wiley & Sons, Inc.     

Crystallographic studies of azide, thiocyanate and perchlorate complexes of methemerythrin.

Difference Fourier maps of azide, thiocyanate and perchlorate complexes of methemerythrin from Themiste dyscritum have been calculated at 4 Å, 3.5 Å and 3.5 Å resolution, respectively, with phases from a refined model. N^?₃ and SCN^? bind to the Fe complex in each subunit, indicating the mode of oxygen binding and suggesting a possible route followed by the anions in reaching the complex. ClO^?₄ binds in two different locations on the non-crystallographic 2-fold axes near cysteine 9 and cysteine 50, apparently being held to the protein by peptide amides and lysine side-chains. Binding of ClO^?₄ at these locations away from the Fe complex is observed to have some effect on the active site structure.     

Characterization of crystals of a cytochrome oxidase (nitrite reductase) from Pseudomonas aeruginosa by x-ray diffraction and electron microscopy

Cytochrome oxidase from Pseudomonas aeruginosa has been crystallized from 2 m-ammonium sulfate. The crystals occur principally as thin diamond-shaped plates of space group P2₁2₁2 with unit cell dimensions of 92 Å × 115 Å × 76 Å. Determination of the density of glutaraldehyde-fixed, water-equilibrated crystals (1.167 g/cm³), coupled with the unit cell volume (804,000 ų), indicates that there is one subunit (~63,000 Mr) per asymmetric unit. X-ray diffraction data which were limited to 12 Å resolution due to small crystal size were obtained for the hk0 and 0kl zones using precession photography. Amplitude and phase data for the hk0, 0kl, and h0l zones were obtained from computer-based Fourier analysis of appropriate micrographs recorded from negatively stained microplates and thin sections of larger crystals using minimal beam electron microscopy. For crystals embedded in the presence of tannic acid it was possible to achieve 20 Å resolution which is comparable to the resolution achieved with negative staining of thin crystalline arrays. In addition, unstained electron diffraction on glutaraldehyde-fixed, glucose-stabilized plates was recorded to a resolution of 9 Å. The three-dimensional packing of the cytochrome oxidase dimer in the unit cell has been deduced from computer reconstructed images of the three principal projections along the crystallographic axes. The cytochrome oxidase dimer is located in the unit cell with the dimer axis coincident with a crystallographic 2-fold axis; thus within the resolution of the present data in projection (9 Å) the two subunits are identical, in agreement with biochemical evidence. The crystals have been prepared with the enzyme in the fully oxidized state and upon reduction a progressive cracking of the crystals is observed, possibly due to a conformational change dependent on the oxidation state of the heme iron.     

Idealized atomic coordinates of yeast phenylalanine transfer RNA.

The atomic coordinates are given for yeast phenylalanine transfer RNA in the orthorhombic crystal form. The structure has been refined by fitting to successively improved electron density maps at 2.7 Å resolution. The model fitting has been accomplished by using an interactive computer graphics system to minimize the errors inherent in manual model building and coordinate measurements, using an optical comparator. The atomic coordinates have then been “idealized” to make bond distances, bond angles, steric conformation and non-bonded contacts close to standard values, while constraining the model to fit the electron density maps.