Accounting for nonuniformity of bulk-solvent: A mosaic model.

A flat mask-based model is almost universally used in macromolecular crystallography to account for disordered (bulk) solvent. This model assumes any voxel of the crystal unit cell that is not occupied by the atomic model is occupied by the solvent. The properties of this solvent are assumed to be exactly the same across the whole volume of the unit cell. While this is a reasonable approximation in practice, there are a number of scenarios where this model becomes suboptimal. In this work, we enumerate several of these scenarios and describe a new generalized approach to modeling the bulk-solvent which we refer to as mosaic bulk-solvent model. The mosaic bulk-solvent model allows nonuniform features of the solvent in the crystal to be accounted for in a computationally efficient way. It is implemented in the computational crystallography toolbox and the Phenix software.

Overall protein structure quality assessment using hydrogen-bonding parameters.

Atomic model refinement at low resolution is often a challenging task. This is mostly because the experimental data are not sufficiently detailed to be described by atomic models. To make refinement practical and ensure that a refined atomic model is geometrically meaningful, additional information needs to be used such as restraints on Ramachandran plot distributions or residue side-chain rotameric states. However, using Ramachandran plots or rotameric states as refinement targets diminishes the validating power of these tools. Therefore, finding additional model-validation criteria that are not used or are difficult to use as refinement goals is desirable. Hydrogen bonds are one of the important noncovalent interactions that shape and maintain protein structure. These interactions can be characterized by a specific geometry of hydrogen donor and acceptor atoms. Systematic analysis of these geometries performed for quality-filtered high-resolution models of proteins from the Protein Data Bank shows that they have a distinct and a conserved distribution. Here, it is demonstrated how this information can be used for atomic model validation.

PDBx/mmCIF Ecosystem: Foundational Semantic Tools for Structural Biology.

PDBx/mmCIF, Protein Data Bank Exchange (PDBx) macromolecular Crystallographic Information Framework (mmCIF), has become the data standard for structural biology. With its early roots in the domain of small-molecule crystallography, PDBx/mmCIF provides an extensible data representation that is used for deposition, archiving, remediation, and public dissemination of experimentally determined three-dimensional (3D) structures of biological macromolecules by the Worldwide Protein Data Bank (wwPDB, wwpdb.org). Extensions of PDBx/mmCIF are similarly used for computed structure models by ModelArchive (modelarchive.org), integrative/hybrid structures by PDB-Dev (pdb-dev.wwpdb.org), small angle scattering data by Small Angle Scattering Biological Data Bank SASBDB (sasbdb.org), and for models computed generated with the AlphaFold 2.0 deep learning software suite (alphafold.ebi.ac.uk). Community-driven development of PDBx/mmCIF spans three decades, involving contributions from researchers, software and methods developers in structural sciences, data repository providers, scientific publishers, and professional societies. Having a semantically rich and extensible data framework for representing a wide range of structural biology experimental and computational results, combined with expertly curated 3D biostructure data sets in public repositories, accelerates the pace of scientific discovery. Herein, we describe the architecture of the PDBx/mmCIF data standard, tools used to maintain representations of the data standard, governance, and processes by which data content standards are extended, plus community tools/software libraries available for processing and checking the integrity of PDBx/mmCIF data. Use cases exemplify how the members of the Worldwide Protein Data Bank have used PDBx/mmCIF as the foundation for its pipeline for delivering Findable, Accessible, Interoperable, and Reusable (FAIR) data to many millions of users worldwide.

Protein identification from electron cryomicroscopy maps by automated model building and side-chain matching.

Using single-particle electron cryo-microscopy (cryo-EM), it is possible to obtain multiple reconstructions showing the 3D structures of proteins imaged as a mixture. Here, it is shown that automatic map interpretation based on such reconstructions can be used to create atomic models of proteins as well as to match the proteins to the correct sequences and thereby to identify them. This procedure was tested using two proteins previously identified from a mixture at resolutions of 3.2 Å, as well as using 91 deposited maps with resolutions between 2 and 4.5 Å. The approach is found to be highly effective for maps obtained at resolutions of 3.5 Šand better, and to have some utility at resolutions as low as 4 Å.

Macromolecular refinement of X-ray and cryoelectron microscopy structures with Phenix/OPLS3e for improved structure and ligand quality.

With the advent of the resolution revolution in cryoelectron microscopy (cryo-EM), low-resolution refinement is common, and likewise increases the need for a reliable force field. Here, we report on the incorporation of the OPLS3e force field with the VSGB2.1 solvation model in the structure determination package Phenix. Our results show significantly improved structure quality and reduced ligand strain at lower resolution for X-ray refinement. For refinement of cryo-EM-based structures, we find comparable quality structures, goodness-of-fit, and reduced ligand strain. We also show how structure quality and ligand strain are related to the map-model cross-correlation as a function of data weight, and how that can detect overfitting. Signs of overfitting are found in over half of our cryo-EM dataset, which can be remedied by a re-refinement at a lower data weight. Finally, a start-to-end script for refining structures with Phenix/OPLS3e is available in the Schrödinger 2020-3 distribution.

Real-space quantum-based refinement for cryo-EM: Q|R#3.

Electron cryo-microscopy (cryo-EM) is rapidly becoming a major competitor to X-ray crystallography, especially for large structures that are difficult or impossible to crystallize. While recent spectacular technological improvements have led to significantly higher resolution three-dimensional reconstructions, the average quality of cryo-EM maps is still at the low-resolution end of the range compared with crystallography. A long-standing challenge for atomic model refinement has been the production of stereochemically meaningful models for this resolution regime. Here, it is demonstrated that including accurate model geometry restraints derived from ab initio quantum-chemical calculations (HF-D3/6-31G) can improve the refinement of an example structure (chain A of PDB entry 3j63). The robustness of the procedure is tested for additional structures with up to 7000 atoms (PDB entry 3a5x and chain C of PDB entry 5fn5) using the less expensive semi-empirical (GFN1-xTB) model. The necessary algorithms enabling real-space quantum refinement have been implemented in the latest version of qr.refine and are described here.

Density modification of cryo-EM maps.

Density modification uses expectations about features of a map such as a flat solvent and expected distributions of density in the region of the macromolecule to improve individual Fourier terms representing the map. This process transfers information from one part of a map to another and can improve the accuracy of a map. Here, the assumptions behind density modification for maps from electron cryomicroscopy are examined and a procedure is presented that allows the incorporation of model-based information. Density modification works best in cases where unfiltered, unmasked maps with clear boundaries between the macromolecule and solvent are visible, and where there is substantial noise in the map, both in the region of the macromolecule and the solvent. It also is most effective if the characteristics of the map are relatively constant within regions of the macromolecule and the solvent. Model-based information can be used to improve density modification, but model bias can in principle occur. Here, model bias is reduced by using ensemble models that allow an estimation of model uncertainty. A test of model bias is presented that suggests that even if the expected density in a region of a map is specified incorrectly by using an incorrect model, the incorrect expectations do not strongly affect the final map.

A Global Ramachandran Score Identifies Protein Structures with Unlikely Stereochemistry.

Ramachandran plots report the distribution of the (ϕ, ψ) torsion angles of the protein backbone and are one of the best quality metrics of experimental structure models. Typically, validation software reports the number of residues belonging to "outlier," "allowed," and "favored" regions. While "zero unexplained outliers" can be considered the current "gold standard," this can be misleading if deviations from expected distributions are not considered. We revisited the Ramachandran Z score (Rama-Z), a quality metric introduced more than two decades ago but underutilized. We describe a reimplementation of the Rama-Z score in the Computational Crystallography Toolbox along with an algorithm to estimate its uncertainty for individual models; final implementations are available in Phenix and PDB-REDO. We discuss the interpretation of the Rama-Z score and advocate including it in the validation reports provided by the Protein Data Bank. We also advocate reporting it alongside the outlier/allowed/favored counts in structural publications.

Cryo-EM map interpretation and protein model-building using iterative map segmentation.

A procedure for building protein chains into maps produced by single-particle electron cryo-microscopy (cryo-EM) is described. The procedure is similar to the way an experienced structural biologist might analyze a map, focusing first on secondary structure elements such as helices and sheets, then varying the contour level to identify connections between these elements. Since the high density in a map typically follows the main-chain of the protein, the main-chain connection between secondary structure elements can often be identified as the unbranched path between them with the highest minimum value along the path. This chain-tracing procedure is then combined with finding side-chain positions based on the presence of density extending away from the main path of the chain, allowing generation of a Cα model. The Cα model is converted to an all-atom model and is refined against the map. We show that this procedure is as effective as other existing methods for interpretation of cryo-EM maps and that it is considerably faster and produces models with fewer chain breaks than our previous methods that were based on approaches developed for crystallographic maps.

Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix.

Diffraction (X-ray, neutron and electron) and electron cryo-microscopy are powerful methods to determine three-dimensional macromolecular structures, which are required to understand biological processes and to develop new therapeutics against diseases. The overall structure-solution workflow is similar for these techniques, but nuances exist because the properties of the reduced experimental data are different. Software tools for structure determination should therefore be tailored for each method. Phenix is a comprehensive software package for macromolecular structure determination that handles data from any of these techniques. Tasks performed with Phenix include data-quality assessment, map improvement, model building, the validation/rebuilding/refinement cycle and deposition. Each tool caters to the type of experimental data. The design of Phenix emphasizes the automation of procedures, where possible, to minimize repetitive and time-consuming manual tasks, while default parameters are chosen to encourage best practice. A graphical user interface provides access to many command-line features of Phenix and streamlines the transition between programs, project tracking and re-running of previous tasks.

Cryo_fit: Democratization of flexible fitting for cryo-EM.

Cryo-electron microscopy (cryo-EM) is becoming a method of choice for describing native conformations of biomolecular complexes at high resolution. The rapid growth of cryo-EM in recent years has created a high demand for automated solutions, both in hardware and software. Flexible fitting of atomic models to three-dimensional (3D) cryo-EM reconstructions by molecular dynamics (MD) simulation is a popular technique but often requires technical expertise in computer simulation. This work introduces cryo_fit, a package for the automatic flexible fitting of atomic models in cryo-EM maps using MD simulation. The package is integrated with the Phenix software suite. The module was designed to automate the multiple steps of MD simulation in a reproducible manner, as well as facilitate refinement and validation through Phenix. Through the use of cryo_fit, scientists with little experience in MD simulation can produce high quality atomic models automatically and better exploit the potential of cryo-EM.

Magnetoelastic hybrid excitations in CeAuAl3.

Nearly a century of research has established the Born-Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born-Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4f electron states, and conduction electrons in the paramagnetic regime of [Formula: see text], an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF-phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS in [Formula: see text] arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra of [Formula: see text] identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities.

A fully automatic method yielding initial models from high-resolution cryo-electron microscopy maps.

We report a fully automated procedure for the optimization and interpretation of reconstructions from cryo-electron microscopy (cryo-EM) data, available in Phenix as phenix.map_to_model. We applied our approach to 476 datasets with resolution of 4.5 Å or better, including reconstructions of 47 ribosomes and 32 other protein-RNA complexes. The median fraction of residues in the deposited structures reproduced automatically was 71% for reconstructions determined at resolutions of 3 Å or better and 47% for those at resolutions worse than 3 Å.

New tools for the analysis and validation of cryo-EM maps and atomic models.

Recent advances in the field of electron cryomicroscopy (cryo-EM) have resulted in a rapidly increasing number of atomic models of biomacromolecules that have been solved using this technique and deposited in the Protein Data Bank and the Electron Microscopy Data Bank. Similar to macromolecular crystallography, validation tools for these models and maps are required. While some of these validation tools may be borrowed from crystallography, new methods specifically designed for cryo-EM validation are required. Here, new computational methods and tools implemented in PHENIX are discussed, including d99 to estimate resolution, phenix.auto_sharpen to improve maps and phenix.mtriage to analyze cryo-EM maps. It is suggested that cryo-EM half-maps and masks should be deposited to facilitate the evaluation and validation of cryo-EM-derived atomic models and maps. The application of these tools to deposited cryo-EM atomic models and maps is also presented.

Map segmentation, automated model-building and their application to the Cryo-EM Model Challenge.

A recently-developed method for identifying a compact, contiguous region representing the unique part of a density map was applied to 218 Cryo-EM maps with resolutions of 4.5 Šor better. The key elements of the segmentation procedure are (1) identification of all regions of density above a threshold and (2) choice of a unique set of these regions, taking symmetry into consideration, that maximize connectivity and compactness. This segmentation approach was then combined with tools for automated map sharpening and model-building to generate models for the 12 maps in the 2016 Cryo-EM Model Challenge in a fully automated manner. The resulting models have completeness from 24% to 82% and RMS distances from reference interpretations of 0.6 Å-2.1 Å.

Real-space refinement in PHENIX for cryo-EM and crystallography.

This article describes the implementation of real-space refinement in the phenix.real_space_refine program from the PHENIX suite. The use of a simplified refinement target function enables very fast calculation, which in turn makes it possible to identify optimal data-restraint weights as part of routine refinements with little runtime cost. Refinement of atomic models against low-resolution data benefits from the inclusion of as much additional information as is available. In addition to standard restraints on covalent geometry, phenix.real_space_refine makes use of extra information such as secondary-structure and rotamer-specific restraints, as well as restraints or constraints on internal molecular symmetry. The re-refinement of 385 cryo-EM-derived models available in the Protein Data Bank at resolutions of 6 Šor better shows significant improvement of the models and of the fit of these models to the target maps.

Automated map sharpening by maximization of detail and connectivity.

An algorithm for automatic map sharpening is presented that is based on optimization of the detail and connectivity of the sharpened map. The detail in the map is reflected in the surface area of an iso-contour surface that contains a fixed fraction of the volume of the map, where a map with high level of detail has a high surface area. The connectivity of the sharpened map is reflected in the number of connected regions defined by the same iso-contour surfaces, where a map with high connectivity has a small number of connected regions. By combining these two measures in a metric termed the `adjusted surface area', map quality can be evaluated in an automated fashion. This metric was used to choose optimal map-sharpening parameters without reference to a model or other interpretations of the map. Map sharpening by optimization of the adjusted surface area can be carried out for a map as a whole or it can be carried out locally, yielding a locally sharpened map. To evaluate the performance of various approaches, a simple metric based on map-model correlation that can reproduce visual choices of optimally sharpened maps was used. The map-model correlation is calculated using a model with B factors (atomic displacement factors; ADPs) set to zero. This model-based metric was used to evaluate map sharpening and to evaluate map-sharpening approaches, and it was found that optimization of the adjusted surface area can be an effective tool for map sharpening.

Polder maps: improving OMIT maps by excluding bulk solvent.

The crystallographic maps that are routinely used during the structure-solution workflow are almost always model-biased because model information is used for their calculation. As these maps are also used to validate the atomic models that result from model building and refinement, this constitutes an immediate problem: anything added to the model will manifest itself in the map and thus hinder the validation. OMIT maps are a common tool to verify the presence of atoms in the model. The simplest way to compute an OMIT map is to exclude the atoms in question from the structure, update the corresponding structure factors and compute a residual map. It is then expected that if these atoms are present in the crystal structure, the electron density for the omitted atoms will be seen as positive features in this map. This, however, is complicated by the flat bulk-solvent model which is almost universally used in modern crystallographic refinement programs. This model postulates constant electron density at any voxel of the unit-cell volume that is not occupied by the atomic model. Consequently, if the density arising from the omitted atoms is weak then the bulk-solvent model may obscure it further. A possible solution to this problem is to prevent bulk solvent from entering the selected OMIT regions, which may improve the interpretative power of residual maps. This approach is called a polder (OMIT) map. Polder OMIT maps can be particularly useful for displaying weak densities of ligands, solvent molecules, side chains, alternative conformations and residues both in terminal regions and in loops. The tools described in this manuscript have been implemented and are available in PHENIX.

De Gennes Narrowing and Hard-Sphere Approach.

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.