Toward Real Real-Space Refinement of Atomic Models.

High-quality atomic models providing structural information are the results of their refinement versus diffraction data (reciprocal-space refinement), or versus experimental or experimentally based maps (real-space refinement). A proper real-space refinement can be achieved by comparing such a map with a map calculated from the atomic model. Similar to density distributions, the maps of a limited and even inhomogeneous resolution can also be calculated as sums of terms, known as atomic images, which are three-dimensional peaky functions surrounded by Fourier ripples. These atomic images and, consequently, the maps for the respective models, can be expressed analytically as functions of coordinates, atomic displacement parameters, and the local resolution. This work discusses the practical feasibility of such calculation for the real-space refinement of macromolecular atomic models.

Aminoglycoside interactions and impacts on the eukaryotic ribosome.

Aminoglycosides are chemically diverse, broad-spectrum antibiotics that target functional centers within the bacterial ribosome to impact all four principle stages (initiation, elongation, termination, and recycling) of the translation mechanism. The propensity of aminoglycosides to induce miscoding errors that suppress the termination of protein synthesis supports their potential as therapeutic interventions in human diseases associated with premature termination codons (PTCs). However, the sites of interaction of aminoglycosides with the eukaryotic ribosome and their modes of action in eukaryotic translation remain largely unexplored. Here, we use the combination of X-ray crystallography and single-molecule FRET analysis to reveal the interactions of distinct classes of aminoglycosides with the 80S eukaryotic ribosome. Crystal structures of the 80S ribosome in complex with paromomycin, geneticin (G418), gentamicin, and TC007, solved at 3.3- to 3.7-Å resolution, reveal multiple aminoglycoside-binding sites within the large and small subunits, wherein the 6'-hydroxyl substituent in ring I serves as a key determinant of binding to the canonical eukaryotic ribosomal decoding center. Multivalent binding interactions with the human ribosome are also evidenced through their capacity to affect large-scale conformational dynamics within the pretranslocation complex that contribute to multiple aspects of the translation mechanism. The distinct impacts of the aminoglycosides examined suggest that their chemical composition and distinct modes of interaction with the ribosome influence PTC read-through efficiency. These findings provide structural and functional insights into aminoglycoside-induced impacts on the eukaryotic ribosome and implicate pleiotropic mechanisms of action beyond decoding.

The integrative role of cryo electron microscopy in molecular and cellular structural biology.

After gradually moving away from preparation methods prone to artefacts such as plastic embedding and negative staining for cell sections and single particles, the field of cryo electron microscopy (cryo-EM) is now heading off at unprecedented speed towards high-resolution analysis of biological objects of various sizes. This 'revolution in resolution' is happening largely thanks to new developments of new-generation cameras used for recording the images in the cryo electron microscope which have much increased sensitivity being based on complementary metal oxide semiconductor devices. Combined with advanced image processing and 3D reconstruction, the cryo-EM analysis of nucleoprotein complexes can provide unprecedented insights at molecular and atomic levels and address regulatory mechanisms in the cell. These advances reinforce the integrative role of cryo-EM in synergy with other methods such as X-ray crystallography, fluorescence imaging or focussed-ion beam milling as exemplified here by some recent studies from our laboratory on ribosomes, viruses, chromatin and nuclear receptors. Such multi-scale and multi-resolution approaches allow integrating molecular and cellular levels when applied to purified or in situ macromolecular complexes, thus illustrating the trend of the field towards cellular structural biology.

From deep TLS validation to ensembles of atomic models built from elemental motions.

The translation-libration-screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because the T, L and S matrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy several conditions. Refining the T, L and S matrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of the PHENIX project.

FEM: feature-enhanced map.

A method is presented that modifies a 2mFobs - DFmodel σA-weighted map such that the resulting map can strengthen a weak signal, if present, and can reduce model bias and noise. The method consists of first randomizing the starting map and filling in missing reflections using multiple methods. This is followed by restricting the map to regions with convincing density and the application of sharpening. The final map is then created by combining a series of histogram-equalized intermediate maps. In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2mFobs - DFmodel σA-weighted map.

Predicting X-ray diffuse scattering from translation-libration-screw structural ensembles.

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier's equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation-libration-screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

Metrics for comparison of crystallographic maps.

Numerical comparison of crystallographic contour maps is used extensively in structure solution and model refinement, analysis and validation. However, traditional metrics such as the map correlation coefficient (map CC, real-space CC or RSCC) sometimes contradict the results of visual assessment of the corresponding maps. This article explains such apparent contradictions and suggests new metrics and tools to compare crystallographic contour maps. The key to the new methods is rank scaling of the Fourier syntheses. The new metrics are complementary to the usual map CC and can be more helpful in map comparison, in particular when only some of their aspects, such as regions of high density, are of interest.

Universal parameters of bulk-solvent masks.

The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Šfor the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox (CCTBX) and in Phenix as the default choice.

Program VUE: analysing distributions of cryo-EM projections using uniform spherical grids.

Three-dimensional cryo electron microscopy reconstructions are obtained by extracting information from a large number of projections of the object. These projections correspond to different 'views' or 'orientations', i.e. directions in which these projections show the reconstructed object. Uneven distribution of these views and the presence of dominating preferred orientations may distort the reconstructed spatial images. This work describes the program VUE (views on uniform grids for cryo electron microscopy), designed to study such distributions. Its algorithms, based on uniform virtual grids on a sphere, allow an easy calculation and accurate quantitative analysis of the frequency distribution of the views. The key computational element is the Lambert azimuthal equal-area projection of a spherical uniform grid onto a disc. This projection keeps the surface area constant and represents the frequency distribution with no visual bias. Since it has multiple tunable parameters, the program is easily adaptable to individual needs, and to the features of a particular project or of the figure to be produced. It can help identify problems related to an uneven distribution of views. Optionally, it can modify the list of projections, distributing the views more uniformly. The program can also be used as a teaching tool.

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.

On effective and optical resolutions of diffraction data sets.

In macromolecular X-ray crystallography, diffraction data sets are traditionally characterized by the highest resolution dhigh of the reflections that they contain. This measure is sensitive to individual reflections and does not refer to the eventual data incompleteness and anisotropy; it therefore does not describe the data well. A physically relevant and robust measure that provides a universal way to define the `actual' effective resolution deff of a data set is introduced. This measure is based on the accurate calculation of the minimum distance between two immobile point scatterers resolved as separate peaks in the Fourier map calculated with a given set of reflections. This measure is applicable to any data set, whether complete or incomplete. It also allows characterizion of the anisotropy of diffraction data sets in which deff strongly depends on the direction. Describing mathematical objects, the effective resolution deff characterizes the `geometry' of the set of measured reflections and is irrelevant to the diffraction intensities. At the same time, the diffraction intensities reflect the composition of the structure from physical entities: the atoms. The minimum distance for the atoms typical of a given structure is a measure that is different from and complementary to deff; it is also a characteristic that is complementary to conventional measures of the data-set quality. Following the previously introduced terms, this value is called the optical resolution, dopt. The optical resolution as defined here describes the separation of the atomic images in the `ideal' crystallographic Fourier map that would be calculated if the exact phases were known. The effective and optical resolution, as formally introduced in this work, are of general interest, giving a common `ruler' for all kinds of crystallographic diffraction data sets.

Structure of the protein core of translation initiation factor 2 in apo, GTP-bound and GDP-bound forms.

Translation initiation factor 2 (IF2) is involved in the early steps of bacterial protein synthesis. It promotes the stabilization of the initiator tRNA on the 30S initiation complex (IC) and triggers GTP hydrolysis upon ribosomal subunit joining. While the structure of an archaeal homologue (a/eIF5B) is known, there are significant sequence and functional differences in eubacterial IF2, while the trimeric eukaryotic IF2 is completely unrelated. Here, the crystal structure of the apo IF2 protein core from Thermus thermophilus has been determined by MAD phasing and the structures of GTP and GDP complexes were also obtained. The IF2-GTP complex was trapped by soaking with GTP in the cryoprotectant. The structures revealed conformational changes of the protein upon nucleotide binding, in particular in the P-loop region, which extend to the functionally relevant switch II region. The latter carries a catalytically important and conserved histidine residue which is observed in different conformations in the GTP and GDP complexes. Overall, this work provides the first crystal structure of a eubacterial IF2 and suggests that activation of GTP hydrolysis may occur by a conformational repositioning of the histidine residue.

TLS from fundamentals to practice.

The Translation-Libration-Screw-rotation (TLS) model of rigid-body harmonic displacements introduced in crystallography by Schomaker & Trueblood (1968) is now a routine tool in macromolecular studies and is a feature of most modern crystallographic structure refinement packages. In this review we consider a number of simple examples that illustrate important features of the TLS model. Based on these examples simplified formulae are given for several special cases that may occur in structure modeling and refinement. The derivation of general TLS formulae from basic principles is also provided. This manuscript describes the principles of TLS modeling, as well as some select algorithmic details for practical application. An extensive list of applications references as examples of TLS in macromolecular crystallography refinement is provided.

Local heterogeneity analysis of crystallographic and cryo-EM maps using shell-approximation.

In X-ray crystallography and cryo-EM, experimental maps can be heterogeneous, showing different level of details in different regions. In this work we interpret heterogeneity in terms of two parameters, assigned individually for each atom, combining the conventional atomic displacement parameter with the resolution of the atomic image in the map. We propose a local real-space procedure to estimate the values of these heterogeneity parameters, assuming that a fragment of the density map and atomic positions are given. The procedure is based on an analytic representation of the atomic image, as a function of the inhomogeneity parameters and atomic coordinates. In this article, we report the results of the tests both with maps simulated and those derived from experimental data. For simulated maps containing regions with different resolutions, the method determines the local map resolution around the atomic centers and the values of the displacement parameter with reasonable accuracy. For experimental maps, obtained as a Fourier synthesis of a given global resolution, estimated values of the local resolution are close to the global one, and the values of the estimated displacement parameters are close to the respective values of the closest atoms in the refined model. Shown successful applications of the proposed method to experimental crystallographic and cryo-EM maps can be seen as a practical proof of method.

Efficient structure-factor modeling for crystals with multiple components.

Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.

Towards automated crystallographic structure refinement with phenix.refine.

phenix.refine is a program within the PHENIX package that supports crystallographic structure refinement against experimental data with a wide range of upper resolution limits using a large repertoire of model parameterizations. It has several automation features and is also highly flexible. Several hundred parameters enable extensive customizations for complex use cases. Multiple user-defined refinement strategies can be applied to specific parts of the model in a single refinement run. An intuitive graphical user interface is available to guide novice users and to assist advanced users in managing refinement projects. X-ray or neutron diffraction data can be used separately or jointly in refinement. phenix.refine is tightly integrated into the PHENIX suite, where it serves as a critical component in automated model building, final structure refinement, structure validation and deposition to the wwPDB. This paper presents an overview of the major phenix.refine features, with extensive literature references for readers interested in more detailed discussions of the methods.

Analytic modeling of inhomogeneous-resolution maps in cryo-electron microscopy and crystallography.

Refinement of macromolecular atomic models versus experimental maps in crystallography and cryo-electron microscopy is a critical step in structure solution. For an appropriate comparison, model maps should mimic the imperfections in the experimental maps, mainly atomic disorder and limited resolution, which are often inhomogeneous over the molecular region. In the suggested method, these model maps are calculated as the sum of atomic contributions expressed through a specifically designed function describing a solitary spherical wave. Thanks to this function, atomic contributions are analytically expressed through their atomic displacement parameter and local resolution, a value now associated with each atom. Such a full analytic dependence of inhomogeneous-resolution map values on model parameters permits the refinement of all of these parameters together.

Direct calculation of cryo-EM and crystallographic model maps for real-space refinement.

This work addresses the problem of the calculation of limited-resolution maps from an atomic model in cryo-electron microscopy and in X-ray and neutron crystallography, including cases where the resolution varies from one molecular region to another. Such maps are necessary in real-space refinement for comparison with the experimental maps. For an appropriate numeric comparison, the calculated maps should reproduce not only the structural features contained in the experimental maps but also the principal map distortions. These model maps can be obtained with no use of Fourier transforms but, similar to density distributions, as a sum of individual atomic contributions. Such contributions, referred to as atomic density images, are atomic densities morphed to reflect distortions of the experimental map, in particular the loss of resolution. They are described by functions composed of a central peak surrounded by Fourier ripples. For practical calculations, atomic images should be cut at some distance. It is shown that to reach a reasonable accuracy such a distance should be significantly larger than the distance customarily applied when calculating density distributions. This is a consequence of the slow rate with which the amplitude of the Fourier ripples decreases. Such a large distance means that at least a few ripples should be included in calculations in order to obtain a map that is sufficiently accurate. Oscillating functions describing these atomic contributions depend, for a given atomic type, on the resolution and on the atomic displacement parameter values. To express both the central peak and the Fourier ripples of the atomic images, these functions are represented by the sums of especially designed terms, each concentrated in a spherical shell and depending analytically on the atomic parameters. In this work, the strength of the dependence of the accuracy of resulting map on the accuracy of the atomic displacement parameters and on the truncation distance, i.e. the number of ripples included in atomic density images, is analyzed. This analysis is completed by practical aspects of the calculation of maps of inhomogeneous resolution. Tests show that the calculation of limited-resolution maps from an atomic model as a sum of atomic contributions requires a large truncation radius extending beyond the central peak of an atomic image and the first Fourier ripples. The article discusses the practical details of such calculations expressing atomic contributions as analytic functions of the atomic coordinates, the atomic displacement parameters and the local resolution.

A regular pattern of Ig super-motifs defines segmental flexibility as the elastic mechanism of the titin chain.

Myofibril elasticity, critical to muscle function, is dictated by the intrasarcomeric filament titin, which acts as a molecular spring. To date, the molecular events underlying the mechanics of the folded titin chain remain largely unknown. We have elucidated the crystal structure of the 6-Ig fragment I65-I70 from the elastic I-band fraction of titin and validated its conformation in solution using small angle x-ray scattering. The long-range properties of the chain have been visualized by electron microscopy on a 19-Ig fragment and modeled for the full skeletal tandem. Results show that conserved Ig-Ig transition motifs generate high-order in the structure of the filament, where conformationally stiff segments interspersed with pliant hinges form a regular pattern of dynamic super-motifs leading to segmental flexibility in the chain. Pliant hinges support molecular shape rearrangements that dominate chain behavior at moderate stretch, whereas stiffer segments predictably oppose high stretch forces upon full chain extension. There, librational entropy can be expected to act as an energy barrier to prevent Ig unfolding while, instead, triggering the unraveling of flanking springs formed by proline, glutamate, valine, and lysine (PEVK) sequences. We propose a mechanistic model based on freely jointed rigid segments that rationalizes the response to stretch of titin Ig-tandems according to molecular features.

Implementation of the riding hydrogen model in CCTBX to support the next generation of X-ray and neutron joint refinement in Phenix.

A fundamental prerequisite for implementing new procedures of atomic model refinement against neutron diffraction data is the efficient handling of hydrogen atoms. The riding hydrogen model, which constrains hydrogen atom parameters to those of the non-hydrogen atoms, is a plausible parameterization for refinements. This work describes the implementation of the riding hydrogen model in the Computational Crystallography Toolbox and in Phenix. Riding hydrogen atoms can be found in several different configurations that are characterized by specific geometries. For each configuration, the hydrogen atom parameterization and the expressions for the gradients of refinement target function with respect to non-hydrogen parameters are described.