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.

Taura syndrome virus IRES initiates translation by binding its tRNA-mRNA-like structural element in the ribosomal decoding center.

In cap-dependent translation initiation, the open reading frame (ORF) of mRNA is established by the placement of the AUG start codon and initiator tRNA in the ribosomal peptidyl (P) site. Internal ribosome entry sites (IRESs) promote translation of mRNAs in a cap-independent manner. We report two structures of the ribosome-bound Taura syndrome virus (TSV) IRES belonging to the family of Dicistroviridae intergenic IRESs. Intersubunit rotational states differ in these structures, suggesting that ribosome dynamics play a role in IRES translocation. Pseudoknot I of the IRES occupies the ribosomal decoding center at the aminoacyl (A) site in a manner resembling that of the tRNA anticodon-mRNA codon. The structures reveal that the TSV IRES initiates translation by a previously unseen mechanism, which is conceptually distinct from initiator tRNA-dependent mechanisms. Specifically, the ORF of the IRES-driven mRNA is established by the placement of the preceding tRNA-mRNA-like structure in the A site, whereas the 40S P site remains unoccupied during this initial step.

Structure of the ribosome with elongation factor G trapped in the pretranslocation state.

During protein synthesis, tRNAs and their associated mRNA codons move sequentially on the ribosome from the A (aminoacyl) site to the P (peptidyl) site to the E (exit) site in a process catalyzed by a universally conserved ribosome-dependent GTPase [elongation factor G (EF-G) in prokaryotes and elongation factor 2 (EF-2) in eukaryotes]. Although the high-resolution structure of EF-G bound to the posttranslocation ribosome has been determined, the pretranslocation conformation of the ribosome bound with EF-G and A-site tRNA has evaded visualization owing to the transient nature of this state. Here we use electron cryomicroscopy to determine the structure of the 70S ribosome with EF-G, which is trapped in the pretranslocation state using antibiotic viomycin. Comparison with the posttranslocation ribosome shows that the small subunit of the pretranslocation ribosome is rotated by ∼12° relative to the large subunit. Domain IV of EF-G is positioned in the cleft between the body and head of the small subunit outwardly of the A site and contacts the A-site tRNA. Our findings suggest a model in which domain IV of EF-G promotes the translocation of tRNA from the A to the P site as the small ribosome subunit spontaneously rotates back from the hybrid, rotated state into the nonrotated posttranslocation state.

Use of Localized Reconstruction to Visualize the Shigella Phage Sf6 Tail Apparatus.

Cryogenic electron microscopy (cryo-EM) single-particle analysis has revolutionized the structural analysis of icosahedral viruses, including tailed bacteriophages. In recent years, localized (or focused) reconstruction has emerged as a powerful data analysis method to capture symmetry mismatches and resolve asymmetric features in icosahedral viruses. Here, we describe the methods used to reconstruct the 2.65-MDa tail apparatus of the Shigella phage Sf6, a representative member of the Podoviridae superfamily.

Elucidating structural variability in p53 conformers using combinatorial refinement strategies and molecular dynamics.

Low molecular weight proteins and protein assemblies can now be investigated using cryo-electron microscopy (EM) as a complement to traditional structural biology techniques. It is important, however, to not lose sight of the dynamic information inherent in macromolecules that give rise to their exquisite functionality. As computational methods continue to advance the field of biomedical imaging, so must strategies to resolve the minute details of disease-related entities. Here, we employed combinatorial modeling approaches to assess flexible properties among low molecular weight proteins (~100 kDa or less). Through a blend of rigid body refinement and simulated annealing, we determined new hidden conformations for wild type p53 monomer and dimer forms. Structures for both states converged to yield new conformers, each revealing good stereochemistry and dynamic information about the protein. Based on these insights, we identified fluid parts of p53 that complement the stable central core of the protein responsible for engaging DNA. Molecular dynamics simulations corroborated the modeling results and helped pinpoint the more flexible residues in wild type p53. Overall, the new computational methods may be used to shed light on other small protein features in a vast ensemble of structural data that cannot be easily delineated by other algorithms.

New model-fitting and model-completion programs for automated iterative nucleic acid refinement.

In the past decade many structures of nucleic acids have been determined, which have contributed to our understanding of their biological functions. However, crystals containing nucleic acids often diffract X-rays poorly. This makes electron-density interpretation difficult and requires a great deal of expertise in crystallography and knowledge of nucleic acid structure. Here, new programs called NAFIT and NABUILD for fitting and extending nucleic acid models are presented. These programs can be used as modules in the automated refinement system LAFIRE, as well as acting as independent programs. NAFIT performs sequential grouped fitting with empirical torsion-angle restraints and antibumping restraints including H atoms. NABUILD extends the model using a skeletonized map in a coarse-grained manner. It has been shown that NAFIT greatly improves electron-density fit and geometric quality and that iterative refinement with NABUILD significantly reduces the Rfree factor.

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.

Delineating Conformational Variability in Small Protein Structures Using Combinatorial Refinement Strategies.

As small protein assemblies and even small proteins are becoming more amenable to cryo-Electron Microscopy (EM) structural studies, it is important to consider the complementary dynamic information present in the data. Current computational strategies are limited in their ability to resolve minute differences among low molecular weight entities. Here, we demonstrate a new combinatorial approach to delineate flexible conformations among small proteins using real-space refinement applications. We performed a meta-analysis of structural data for the SARS CoV-2 Nucleocapsid (N) protein using a combination of rigid-body refinement and simulated annealing methods. For the N protein monomer, we determined three new flexible conformers with good stereochemistry and quantitative comparisons provided new evidence of their dynamic properties. A similar analysis performed for the N protein dimer showed only minor structural differences among the flexible models. These results suggested a more stable view of the N protein dimer than the monomer structure. Taken together, the new computational strategies can delineate conformational changes in low molecular weight proteins that may go unnoticed by conventional assessments. The results also suggest that small proteins may be further stabilized for structural studies through the use of solution components that limit the movement of external flexible regions.

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.

Making ripples in the comparison of calculated and experimental maps for real-space refinement and assessment by analytic modelling of local resolution.

Commentary is given on a paper [Urzhumtsev & Lunin (2022). IUCrJ, 9, 728-734] proposing a new method for the analytic modelling of inhomogeneous resolution in electrostatic potential volumes and electron density maps for improved real-space refinement.

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.

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.

Molecular Dynamics Flexible Fitting: All You Want to Know About Resolution Exchange.

In recent years, owing to the advances in instrumentation, cryo-EM has emerged as the go-to tool for obtaining high-resolution structures of biomolecular systems. However, building three-dimensional atomic structures of biomolecules from these high-resolution maps remains a concern for the traditional map-guided structure-determination schemes. Recently, we developed a computational tool, Resolution Exchange Molecular Dynamics Flexible Fitting (ReMDFF) to address this problem by re-refining a search model against a series of maps of progressively higher resolutions, which ends with the original experimental resolution (Wang et al., J Struct Biol 204(2):319-328, 2018). In this chapter, we present a step-by-step outline for preparing, executing, and analyzing ReMDFF refinements of simple proteins and multimeric complexes. The structure determination of carbon monoxide dehydrogenase and Mg2+-channel CorA are employed as case studies. All scripts are provided via GitHub (Vant, Resolution exchange molecular dynamics flexible fitting (ReMDFF) all you want to know about flexible fitting, 2019, https://github.com/jvant/ReMDFF_Singharoy_Group.git ).

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.

Current developments in Coot for macromolecular model building of Electron Cryo-microscopy and Crystallographic Data.

Coot is a tool widely used for model building, refinement, and validation of macromolecular structures. It has been extensively used for crystallography and, more recently, improvements have been introduced to aid in cryo-EM model building and refinement, as cryo-EM structures with resolution ranging 2.5-4 A are now routinely available. Model building into these maps can be time-consuming and requires experience in both biochemistry and building into low-resolution maps. To simplify and expedite the model building task, and minimize the needed expertise, new tools are being added in Coot. Some examples include morphing, Geman-McClure restraints, full-chain refinement, and Fourier-model based residue-type-specific Ramachandran restraints. Here, we present the current state-of-the-art in Coot usage.

ISOLDE: a physically realistic environment for model building into low-resolution electron-density maps.

This paper introduces ISOLDE, a new software package designed to provide an intuitive environment for high-fidelity interactive remodelling/refinement of macromolecular models into electron-density maps. ISOLDE combines interactive molecular-dynamics flexible fitting with modern molecular-graphics visualization and established structural biology libraries to provide an immersive interface wherein the model constantly acts to maintain physically realistic conformations as the user interacts with it by directly tugging atoms with a mouse or haptic interface or applying/removing restraints. In addition, common validation tasks are accelerated and visualized in real time. Using the recently described 3.8 Šresolution cryo-EM structure of the eukaryotic minichromosome maintenance (MCM) helicase complex as a case study, it is demonstrated how ISOLDE can be used alongside other modern refinement tools to avoid common pitfalls of low-resolution modelling and improve the quality of the final model. A detailed analysis of changes between the initial and final model provides a somewhat sobering insight into the dangers of relying on a small number of validation metrics to judge the quality of a low-resolution model.

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.