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.     

Ab initio protein modeling into CryoEM density maps using EM-Fold

EM-Fold was used to build models for nine proteins in the maps of GroEL (7.7 ? resolution) and ribosome (6.4 ? resolution) in the ab initio modeling category of the 2010 cryo-electron microscopy modeling challenge. EM-Fold assembles predicted secondary structure elements (SSEs) into regions of the density map that were identified to correspond to either α-helices or β-strands. The assembly uses a Monte Carlo algorithm where loop closure, density-SSE length agreement, and strength of connecting density between SSEs are evaluated. Top-scoring models are refined by translating, rotating, and bending SSEs to yield better agreement with the density map. EM-Fold produces models that contain backbone atoms within SSEs only. The RMSD values of the models with respect to native range from 2.4 to 3.5 ? for six of the nine proteins. EM-Fold failed to predict the correct topology in three cases. Subsequently, Rosetta was used to build loops and side chains for the very best scoring models after EM-Fold refinement. The refinement within Rosetta's force field is driven by a density agreement score that calculates a cross-correlation between a density map simulated from the model and the experimental density map. All-atom RMSDs as low as 3.4 ? are achieved in favorable cases. Values above 10.0 ? are observed for two proteins with low overall content of secondary structure and hence particularly complex loop modeling problems. RMSDs over residues in secondary structure elements range from 2.5 to 4.8 ?.     

Rules for connectivity of secondary structure elements in protein: Two–layer αβ sandwiches

In protein structures, the fold is described according to the spatial arrangement of secondary structure elements (SSEs: α‐helices and β‐strands) and their connectivity. The connectivity or the pattern of links among SSEs is one of the most important factors for understanding the variety of protein folds. In this study, we introduced the connectivity strings that encode the connectivities by using the types, positions, and connections of SSEs, and computationally enumerated all the connectivities of two‐layer αβ sandwiches. The calculated connectivities were compared with those in natural proteins determined using MICAN, a nonsequential structure comparison method. For 2α‐4β, among 23,000 of all connectivities, only 48 were free from irregular connectivities such as loop crossing. Of these, only 20 were found in natural proteins and the superfamilies were biased toward certain types of connectivities. A similar disproportional distribution was confirmed for most of other spatial arrangements of SSEs in the two‐layer αβ sandwiches. We found two connectivity rules that explain the bias well: the abundances of interlayer connecting loops that bridge SSEs in the distinct layers; and nonlocal β‐strand pairs, two spatially adjacent β‐strands located at discontinuous positions in the amino acid sequence. A two‐dimensional plot of these two properties indicated that the two connectivity rules are not independent, which may be interpreted as a rule for the cooperativity of proteins.     

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.     

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.     

YUP.SCX: coaxing atomic models into medium resolution electron density maps

The structures of large macromolecular complexes in different functional states can be determined by cryo-electron microscopy, which yields electron density maps of low to intermediate resolutions. The maps can be combined with high-resolution atomic structures of components of the complex, to produce a model for the complex that is more accurate than the formal resolution of the map. To this end, methods have been developed to dock atomic models into density maps rigidly or flexibly, and to refine a docked model so as to optimize the fit of the atomic model into the map. We have developed a new refinement method called YUP.SCX. The electron density map is converted into a component of the potential energy function to which terms for stereochemical restraints and volume exclusion are added. The potential energy function is then minimized (using simulated annealing) to yield a stereochemically-restrained atomic structure that fits into the electron density map optimally. We used this procedure to construct an atomic model of the 70S ribosome in the pre-accommodation state. Although some atoms are displaced by as much as 33 Å, they divide themselves into nearly rigid fragments along natural boundaries with smooth transitions between the fragments.     

Molecular modelling of the mass density of single proteins

Using molecular dynamics (MD) simulations, the density of single proteins and its temperature dependence was modelled starting from the experimentally determined protein structure and a generic, transferable force field, without the need of prior parameterization. Although all proteins consist of the same 20 amino acids, their density in aqueous solution varies up to 10% and the thermal expansion coefficient up to twofold. To model the protein density, systematic MD simulations were carried out for 10 proteins with a broad range of densities (1.32-1.43 g/cm(3)) and molecular weights (7-97 kDa). The simulated densities deviated by less than 1.4% from their experimental values that were available for four proteins. Further analyses of protein density showed that it can be essentially described as a consequence of amino acid composition. For five proteins, the density was simulated at different temperatures. The simulated thermal expansion coefficients ranged between 4.3 and 7.1 × 10(-4) K(-1) and were similar to the experimentally determined values of ribonuclease-A and lysozyme (deviations of 2.4 and 14.6%, respectively). Further analyses indicated that the thermal expansion coefficient is linked to the temperature dependence of atomic fluctuations: proteins with a high thermal expansion coefficient show a low increase in flexibility at increasing temperature. A low increase in atomic fluctuations with temperature has been previously described as a possible mechanism of thermostability. Thus, a high thermal expansion coefficient might contribute to protein thermostability.     

Combined approaches to flexible fitting and assessment in virus capsids undergoing conformational change

Fitting of atomic components into electron cryo-microscopy (cryoEM) density maps is routinely used to understand the structure and function of macromolecular machines. Many fitting methods have been developed, but a standard protocol for successful fitting and assessment of fitted models has yet to be agreed upon among the experts in the field. Here, we created and tested a protocol that highlights important issues related to homology modelling, density map segmentation, rigid and flexible fitting, as well as the assessment of fits. As part of it, we use two different flexible fitting methods (Flex-EM and iMODfit) and demonstrate how combining the analysis of multiple fits and model assessment could result in an improved model. The protocol is applied to the case of the mature and empty capsids of Coxsackievirus A7 (CAV7) by flexibly fitting homology models into the corresponding cryoEM density maps at 8.2 and 6.1 Å resolution. As a result, and due to the improved homology models (derived from recently solved crystal structures of a close homolog – EV71 capsid – in mature and empty forms), the final models present an improvement over previously published models. In close agreement with the capsid expansion observed in the EV71 structures, the new CAV7 models reveal that the expansion is accompanied by ∼5° counterclockwise rotation of the asymmetric unit, predominantly contributed by the capsid protein VP1. The protocol could be applied not only to viral capsids but also to many other complexes characterised by a combination of atomic structure modelling and cryoEM density fitting.     

Spare parts for helix-helix interaction.

About 6000 contact regions (patches) of helix-to-helix packing from 300 well-resolved non-homologous protein structures were considered. The patches were defined by the spatial helical neighbors and were estimated in atomic detail using a variable distance criterion. The following questions are addressed. (1) Are the amino acid preferences and atomic composition of distinct types of helical patches indicative for the type of their neighbor? Distributions of size, atomic composition and packing density are compared for different types of helical interfaces. Thereby contact preferences are derived for parts of secondary structures adjoining each other or pointing towards the solvent. (2) Is it possible to cluster helical patches according to their structural similarity? For these purposes the patches were classified with an automatic sequence-independent superposition procedure which yields a distinctively reduced set of representative interfaces. On this basis, the methodology for finding exchangeable patches in different proteins is demonstrated.     

Molecular modelling of the mass density of single proteins

Using molecular dynamics (MD) simulations, the density of single proteins and its temperature dependence was modelled starting from the experimentally determined protein structure and a generic, transferable force field, without the need of prior parameterization. Although all proteins consist of the same 20 amino acids, their density in aqueous solution varies up to 10% and the thermal expansion coefficient up to twofold. To model the protein density, systematic MD simulations were carried out for 10 proteins with a broad range of densities (1.32–1.43?g/cm³) and molecular weights (7–97?kDa). The simulated densities deviated by less than 1.4% from their experimental values that were available for four proteins. Further analyses of protein density showed that it can be essentially described as a consequence of amino acid composition. For five proteins, the density was simulated at different temperatures. The simulated thermal expansion coefficients ranged between 4.3 and 7.1?×?10^?4?K^?1 and were similar to the experimentally determined values of ribonuclease-A and lysozyme (deviations of 2.4 and 14.6%, respectively). Further analyses indicated that the thermal expansion coefficient is linked to the temperature dependence of atomic fluctuations: proteins with a high thermal expansion coefficient show a low increase in flexibility at increasing temperature. A low increase in atomic fluctuations with temperature has been previously described as a possible mechanism of thermostability. Thus, a high thermal expansion coefficient might contribute to protein thermostability.     

Cryo-EM of macromolecular assemblies at near-atomic resolution

With single-particle electron cryomicroscopy (cryo-EM), it is possible to visualize large, macromolecular assemblies in near-native states. Although subnanometer resolutions have been routinely achieved for many specimens, state of the art cryo-EM has pushed to near-atomic (3.3-4.6 ?) resolutions. At these resolutions, it is now possible to construct reliable atomic models directly from the cryo-EM density map. In this study, we describe our recently developed protocols for performing the three-dimensional reconstruction and modeling of Mm-cpn, a group II chaperonin, determined to 4.3 ? resolution. This protocol, utilizing the software tools EMAN, Gorgon and Coot, can be adapted for use with nearly all specimens imaged with cryo-EM that target beyond 5 ? resolution. Additionally, the feature recognition and computational modeling tools can be applied to any near-atomic resolution density maps, including those from X-ray crystallography.     

Structural refinement of protein segments containing secondary structure elements: Local sampling, knowledge-based potentials, and clustering

In this article, we present an iterative, modular optimization (IMO) protocol for the local structure refinement of protein segments containing secondary structure elements (SSEs). The protocol is based on three modules: a torsion-space local sampling algorithm, a knowledge-based potential, and a conformational clustering algorithm. Alternative methods are tested for each module in the protocol. For each segment, random initial conformations were constructed by perturbing the native dihedral angles of loops (and SSEs) of the segment to be refined while keeping the protein body fixed. Two refinement procedures based on molecular mechanics force fields - using either energy minimization or molecular dynamics - were also tested but were found to be less successful than the IMO protocol. We found that DFIRE is a particularly effective knowledge-based potential and that clustering algorithms that are biased by the DFIRE energies improve the overall results. Results were further improved by adding an energy minimization step to the conformations generated with the IMO procedure, suggesting that hybrid strategies that combine both knowledge-based and physical effective energy functions may prove to be particularly effective in future applications.     

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.     

Electron microscopy holdings of the Protein Data Bank: the impact of the resolution revolution,new validation tools,and implications for the future

As a discipline, structural biology has been transformed by the three-dimensional electron microscopy (3DEM) “Resolution Revolution” made possible by convergence of robust cryo-preservation of vitrified biological materials, sample handling systems, and measurement stages operating a liquid nitrogen temperature, improvements in electron optics that preserve phase information at the atomic level, direct electron detectors (DEDs), high-speed computing with graphics processing units, and rapid advances in data acquisition and processing software. 3DEM structure information (atomic coordinates and related metadata) are archived in the open-access Protein Data Bank (PDB), which currently holds more than 11,000 3DEM structures of proteins and nucleic acids, and their complexes with one another and small-molecule ligands (~ 6% of the archive). Underlying experimental data (3DEM density maps and related metadata) are stored in the Electron Microscopy Data Bank (EMDB), which currently holds more than 21,000 3DEM density maps. After describing the history of the PDB and the Worldwide Protein Data Bank (wwPDB) partnership, which jointly manages both the PDB and EMDB archives, this review examines the origins of the resolution revolution and analyzes its impact on structural biology viewed through the lens of PDB holdings. Six areas of focus exemplifying the impact of 3DEM across the biosciences are discussed in detail (icosahedral viruses, ribosomes, integral membrane proteins, SARS-CoV-2 spike proteins, cryogenic electron tomography, and integrative structure determination combining 3DEM with complementary biophysical measurement techniques), followed by a review of 3DEM structure validation by the wwPDB that underscores the importance of community engagement.     

Angle-distance image matching techniques for protein structure comparison

Proteins that contain similar structural elements often have analogous functions regardless of the degree of sequence similarity or structure connectivity in space. In general, protein structure comparison (PSC) provides a straightforward methodology for biologists to determine critical aspects of structure and function. Here, we developed a novel PSC technique based on angle-distance image (A-D image) transformation and matching, which is independent of sequence similarity and connectivity of secondary structure elements (SSEs). An A-D image is constructed by utilizing protein secondary structure information. According to various types of SSEs, the mutual SSE pairs of the query protein are classified into three different types of sub-images. Subsequently, corresponding sub-images between query and target protein structures are compared using modified cross-correlation approaches to identify the similarity of various patterns. Structural relationships among proteins are displayed by hierarchical clustering trees, which facilitate the establishment of the evolutionary relationships between structure and function of various proteins.Four standard testing datasets and one newly created dataset were used to evaluate the proposed method. The results demonstrate that proteins from these five datasets can be categorized in conformity with their spatial distribution of SSEs. Moreover, for proteins with low sequence identity that share high structure similarity, the proposed algorithms are an efficient and effective method for structural comparison.     

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.     

GROmaρs: A GROMACS-Based Toolset to Analyze Density Maps Derived from Molecular Dynamics Simulations

We introduce a computational toolset, named GROmaρs, to obtain and compare time-averaged density maps from molecular dynamics simulations. GROmaρs efficiently computes density maps by fast multi-Gaussian spreading of atomic densities onto a three-dimensional grid. It complements existing map-based tools by enabling spatial inspection of atomic average localization during the simulations. Most importantly, it allows the comparison between computed and reference maps (e.g., experimental) through calculation of difference maps and local and time-resolved global correlation. These comparison operations proved useful to quantitatively contrast perturbed and control simulation data sets and to examine how much biomolecular systems resemble both synthetic and experimental density maps. This was especially advantageous for multimolecule systems in which standard comparisons like RMSDs are difficult to compute. In addition, GROmaρs incorporates absolute and relative spatial free-energy estimates to provide an energetic picture of atomistic localization. This is an open-source GROMACS-based toolset, thus allowing for static or dynamic selection of atoms or even coarse-grained beads for the density calculation. Furthermore, masking of regions was implemented to speed up calculations and to facilitate the comparison with experimental maps. Beyond map comparison, GROmaρs provides a straightforward method to detect solvent cavities and average charge distribution in biomolecular systems. We employed all these functionalities to inspect the localization of lipid and water molecules in aquaporin systems, the binding of cholesterol to the G protein coupled chemokine receptor type 4, and the identification of permeation pathways through the dermicidin antimicrobial channel. Based on these examples, we anticipate a high applicability of GROmaρs for the analysis of molecular dynamics simulations and their comparison with experimentally determined densities.     

Cyclic secondary somatic embryogenesis and efficient plant regeneration in mountain ash (Sorbus pohuashanensis)

An efficient protocol for secondary somatic embryogenesis in mountain ash is reported. Secondary somatic embryos (SSEs), initially obtained from primary embryos, were proliferated and maintained for more than 2?years via cyclic secondary somatic embryogenesis. SSEs were produced on the surfaces of cotyledons and radicles of maternal somatic embryos. Histological observations of the various stages of SSE development revealed four typical stages: globular, heart-shaped, torpedo, and cotyledon. Addition of a low concentration of naphthaleneacetic acid (NAA) to Murashige and Skoog (MS) medium resulted in the induction of SSEs, but addition of 2,4-dichlorophenoxyacetic acid (2,4-d) to MS medium decreased SSE formation. Addition of casein hydrolysate (CH) to MS medium promoted induction of SSEs. Cotyledonary SSEs were cultured on MS medium with 20?C60?g?L^?1 sucrose under light for 1?month until maturation. After transferred to MS medium containing either 0.06???M NAA or 0.15???M indole-3-butyric acid in the light, over 50?% of the mature SSEs developed into plantlets. Addition of 1.0?g?L^?1 activated charcoal was beneficial for SSE germination (over 60?%). At 18?°C, over 90?% of the germinated SSEs converted to plantlets on ? MS (half-strength of MS macroelements) with 1.8???M NAA under light. Plantlets acclimatized successfully to ex vitro conditions and field plants developed with normal phenotypes.     

Novel method for the rapid evaluation of packing in protein structures

There has been considerable effort to predict the structure of proteins from their amino acid sequences. A major problem in all prediction efforts has been that, short of a direct comparison with crystallographic co-ordinates, it is often difficult to evaluate the merit of a model, or "proposed" protein structure. Here, we present a method for evaluating proposed protein structures that does not require a structural model of complete atomic detail. Our method evaluates residue-residue packing density using a simplified model of the polypeptide chain where amino acids are represented as one, two (histidine, tyrosine and phenylalanine), or three (tryptophan) spheres. This method also gives a measure of the appropriateness of residue-residue contacts, thus giving a measure of the amino acid distribution throughout the protein. Amino acid packing and amino acid distribution, as evaluated by this technique, are consistent with the accuracy of model-built structures. We have been able to select the best structures from a set of combinatorially generated models using this method, and we anticipate that it will be useful as a general tool for model-building.     

PSI: indexing protein structures for fast similarity search

MOTIVATION: We consider the problem of finding similarities in protein structure databases. Current techniques sequentially compare the given query protein to all of the proteins in the database to find similarities. Therefore, the cost of similarity queries increases linearly as the volume of the protein databases increase. As the sizes of experimentally determined and theoretically estimated protein structure databases grow, there is a need for scalable searching techniques. RESULTS: Our techniques extract feature vectors on triplets of SSEs (Secondary Structure Elements). Later, these feature vectors are indexed using a multidimensional index structure. For a given query protein, this index structure is used to quickly prune away unpromising proteins in the database. The remaining proteins are then aligned using a popular alignment tool such as VAST. We also develop a novel statistical model to estimate the goodness of a match using the SSEs. Experimental results show that our techniques improve the pruning time of VAST 3 to 3.5 times while maintaining similar sensitivity.