Combining efficient conformational sampling with a deformable elastic network model facilitates structure refinement at low resolution

Influence of lipid bilayer on the structure of the muscle-type nicotinic acetylcholine receptor

The muscle-type nicotinic acetylcholine receptor is a transmitter-gated ion channel residing in the plasma membrane of electrocytes and striated muscle cells. It is present predominantly at synaptic junctions, where it effects rapid depolarization of the postsynaptic membrane in response to acetylcholine released into the synaptic cleft. Previously, cryo-EM of intact membrane from Torpedo revealed that the lipid bilayer surrounding the junctional receptor has a uniquely asymmetric and ordered structure, due to a high concentration of cholesterol. It is now shown that this special lipid environment influences the transmembrane (TM) folding of the protein. All five submembrane MX helices of the membrane-intact junctional receptor align parallel to the surface of the cholesterol-ordered lipids in the inner leaflet of the bilayer; also, the TM helices in the outer leaflet are splayed apart. However in the structure obtained from the same protein after extraction and incorporation in nanodiscs, the MX helices do not align to a planar surface, and the TM helices arrange compactly in the outer leaflet. Realignment of the MX helices of the nanodisc-solved structure to a planar surface converts their adjoining TM helices into an obligatory splayed configuration, characteristic of the junctional receptor. Thus, the form of the receptor sustained by the special lipid environment of the synaptic junction is the one that mediates fast synaptic transmission; whereas, the nanodisc-embedded protein may be like the extrajunctional form, existing in a disordered lipid environment.

Advancing cryo-electron microscopy data analysis through accelerated simulation-based flexible fitting approaches

Flexible fitting based on molecular dynamics simulation is a technique for structure modeling from cryo-EM data. It has been utilized for nearly two decades, and while cryo-EM resolution has improved significantly, it remains a powerful approach that can provide structural and dynamical insights that are not directly accessible from experimental data alone. Molecular dynamics simulations provide a means to extract atomistic details of conformational changes that are encoded in cryo-EM data and can also assist in improving the quality of structural models. Additionally, molecular dynamics simulations enable the characterization of conformational heterogeneity in cryo-EM data. We will summarize the advancements made in these techniques and highlight recent developments in this field.

Explicit versus implicit consideration of binding partners in protein-protein complex to elucidate intrinsic dynamics

The binding of many proteins to their protein partners is tightly regulated via control of their relative intrinsic dynamics during the binding process, a phenomenon which can in turn be modulated. Therefore, investigating the intrinsic dynamics of proteins is necessary to understand function in a comprehensive way. By intrinsic dynamics herein, we principally refer to the vibrational signature of a protein molecule popularly obtained from normal modes or essential modes. For normal modes, one often considers that the molecule under investigation is a collection of springs in a solvent-free or implicit-solvent medium. In the context of a protein-binding partner, the analysis of vibration of the target protein is often complicated due to molecular interaction within the complex. Generally, it is assumed that the isolated bound conformation of the target protein captures the implicit effect of the binding partner on the intrinsic dynamics, therefore suggesting that any influence of the partner molecule is also already integrated. Such an assumption allows large-scale studies of the conservation of protein flexibility. However, in cases where a partner protein directly influences the vibration of the target via critical contacts at the protein-protein interface, the above assumption falls short of providing a detailed view. In this review article, we discuss the implications of considering the dynamics of a protein in a protein-protein complex, as modelled implicitly and explicitly with methods dependent on elastic network models. We further propose how such an explicit consideration can be applied to understand critical protein-protein contacts that can be targeted in future studies.

Structure of a cholinergic cell membrane

While it has long been established that cell membranes are complex assemblies of proteins and bilayer-forming lipids, the inherent mobility and wide-ranging heterogeneity of the lipids have limited our ability to understand cell-membrane structure at a molecular level. Consequently, little is yet known about the protein-lipid and lipid-lipid interplay that exists in situ. The present study exploits the regular architecture of a cholinergic cell membrane to determine how the phospholipid and cholesterol organization is influenced by the protein surfaces and by differences in cholesterol concentration between the two leaflets. Lipids in the leaflet containing the most cholesterol form an ordered sterol-hydrocarbon “skin.” This hitherto unobserved hydrophobic-core structure has far-reaching implications in terms of how cholesterol-rich membranes are constructed and function.

Cell membranes are complex assemblies of proteins and lipids making transient or long-term associations that have yet to be characterized at a molecular level. Here, cryo-electron microscopy is applied to determine how phospholipids and cholesterol arrange between neighboring proteins (nicotinic acetylcholine receptors) of Torpedo cholinergic membrane. The lipids exhibit distinct properties in the two leaflets of the bilayer, influenced by the protein surfaces and by differences in cholesterol concentration. In the outer leaflet, the lipids show no consistent motif away from the protein surfaces, in keeping with their assumed fluidity. In the inner leaflet, where the cholesterol concentration is higher, the lipids organize into extensive close-packed linear arrays. These arrays are built from the sterol groups of cholesterol and the initial saturated portions of the phospholipid hydrocarbon chains. Together, they create an ordered ∼7 Å-thick “skin” within the hydrophobic core of the bilayer. The packing of lipids in the arrays appears to bear a close relationship to the linear cholesterol arrays that form crystalline monolayers at the air-water interface.

Accurate flexible refinement for atomic-level protein structure using cryo-EM density maps and deep learning

With the rapid progress of deep learning in cryo-electron microscopy and protein structure prediction, improving the accuracy of the protein structure model by using a density map and predicted contact/distance map through deep learning has become an urgent need for robust methods. Thus, designing an effective protein structure optimization strategy based on the density map and predicted contact/distance map is critical to improving the accuracy of structure refinement. In this article, a protein structure optimization method based on the density map and predicted contact/distance map by deep-learning technology was proposed in accordance with the result of matching between the density map and the initial model. Physics- and knowledge-based energy functions, integrated with Cryo-EM density map data and deep-learning data, were used to optimize the protein structure in the simulation. The dynamic confidence score was introduced to the iterative process for choosing whether it is a density map or a contact/distance map to dominate the movement in the simulation to improve the accuracy of refinement. The protocol was tested on a large set of 224 non-homologous membrane proteins and generated 214 structural models with correct folds, where 4.5% of structural models were generated from structural models with incorrect folds. Compared with other state-of-the-art methods, the major advantage of the proposed methods lies in the skills for using density map and contact/distance map in the simulation, as well as the new energy function in the re-assembly simulations. Overall, the results demonstrated that this strategy is a valuable approach and ready to use for atomic-level structure refinement using cryo-EM density map and predicted contact/distance map.

NMMD: Efficient cryo-EM flexible fitting based on simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.

GLIMPS: A Machine Learning Approach to Resolution Transformation for Multiscale Modeling

We describe a general approach to transforming molecular models between different levels of resolution, based on machine learning methods. The approach uses a matched set of models at both levels of resolution for training, but requires only the coordinates of their particles and no side information (e.g., templates for substructures, defined mappings, or molecular mechanics force fields). Once trained, the approach can transform further molecular models of the system between the two levels of resolution in either direction with equal facility.

Combining Cryo-EM Density Map and Residue Contact for Protein Secondary Structure Topologies

Although atomic structures have been determined directly from cryo-EM density maps with high resolutions, current structure determination methods for medium resolution (5 to 10 Å) cryo-EM maps are limited by the availability of structure templates. Secondary structure traces are lines detected from a cryo-EM density map for α-helices and β-strands of a protein. A topology of secondary structures defines the mapping between a set of sequence segments and a set of traces of secondary structures in three-dimensional space. In order to enhance accuracy in ranking secondary structure topologies, we explored a method that combines three sources of information: a set of sequence segments in 1D, a set of amino acid contact pairs in 2D, and a set of traces in 3D at the secondary structure level. A test of fourteen cases shows that the accuracy of predicted secondary structures is critical for deriving topologies. The use of significant long-range contact pairs is most effective at enriching the rank of the maximum-match topology for proteins with a large number of secondary structures, if the secondary structure prediction is fairly accurate. It was observed that the enrichment depends on the quality of initial topology candidates in this approach. We provide detailed analysis in various cases to show the potential and challenge when combining three sources of information.

Validation, analysis and annotation of cryo-EM structures

The process of turning 2D micrographs into 3D atomic models of the imaged macromolecules has been under rapid development and scrutiny in the field of cryo-EM. Here, some important methods for validation at several stages in this process are described. Firstly, how Fourier shell correlation of two independent maps and phase randomization beyond a certain frequency address the assessment of map resolution is reviewed. Techniques for local resolution estimation and map sharpening are also touched upon. The topic of validating models which are either built de novo or based on a known atomic structure fitted into a cryo-EM map is then approached. Map-model comparison using Q-scores and Fourier shell correlation plots is used to assure the agreement of the model with the observed map density. The importance of annotating the model with B factors to account for the resolvability of individual atoms in the map is illustrated. Finally, the timely topic of detecting and validating water molecules and metal ions in maps that have surpassed ∼2 Å resolution is described.

Endo-lysosomal Aβ concentration and pH trigger formation of Aβ oligomers that potently induce Tau missorting

Amyloid-β peptide (Aβ) forms metastable oligomers >50 kDa, termed AβOs, that are more effective than Aβ amyloid fibrils at triggering Alzheimer’s disease-related processes such as synaptic dysfunction and Tau pathology, including Tau mislocalization. In neurons, Aβ accumulates in endo-lysosomal vesicles at low pH. Here, we show that the rate of AβO assembly is accelerated 8,000-fold upon pH reduction from extracellular to endo-lysosomal pH, at the expense of amyloid fibril formation. The pH-induced promotion of AβO formation and the high endo-lysosomal Aβ concentration together enable extensive AβO formation of Aβ42 under physiological conditions. Exploiting the enhanced AβO formation of the dimeric Aβ variant dimAβ we furthermore demonstrate targeting of AβOs to dendritic spines, potent induction of Tau missorting, a key factor in tauopathies, and impaired neuronal activity. The results suggest that the endosomal/lysosomal system is a major site for the assembly of pathomechanistically relevant AβOs.

Aβ oligomers (AβO) are thought to represent the main toxic species in Alzheimer’s disease but very high Aβ concentrations are required to study them in vitro and it remains unknown what role these off-pathway oligomers play in vivo. Here, the authors use a dimeric variant of Aβ termed dimAβ, where two Aβ40 units are linked, which facilitates to study AβO formation kinetics and they observe that Aβ off-pathway oligomer formation is strongly accelerated at endo-lysosomal pH, while amyloid fibril formation is delayed. Furthermore, the authors demonstrate that dimAβ is a disease-relevant model construct for pathogenic AβO formation by showing that dimAβ AβOs target dendritic spines and induce AD-like somatodendritic Tau missorting.

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways Using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.

Adaptive Cartesian and torsional restraints for interactive model rebuilding

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows beyond that range. In each current implementation the rate at which the potential flattens at large deviations follows a fixed form, although the form chosen varies among implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here, two new such potentials are described: a Cartesian distance restraint derived from a recent generalization of common loss functions and a periodic torsion restraint based on a renormalization of the von Mises distribution. Further, their implementation as user-adjustable/switchable restraints in ISOLDE is described and their use in some real-world examples is demonstrated.

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

High-Resolution Cryo-EM Structure of the Cardiac Actomyosin Complex

Heart contraction depends on a complicated array of interactions between sarcomeric proteins required to convert chemical energy into mechanical force. Cyclic interactions between actin and myosin molecules, controlled by troponin and tropomyosin, generate the sliding force between the actin-based thin and myosin-based thick filaments. Alterations in this sophisticated system due to missense mutations can lead to cardiovascular diseases. Numerous structural studies proposed pathological mechanisms of missense mutations at the myosin-myosin, actin-tropomyosin, and tropomyosin-troponin interfaces. However, despite the central role of actomyosin interactions a detailed structural description of the cardiac actomyosin interface remained unknown. Here, we report a cryo-EM structure of a cardiac actomyosin complex at 3.8 Å resolution. The structure reveals the molecular basis of cardiac diseases caused by missense mutations in myosin and actin proteins.

Retrieving functional pathways of biomolecules from single-particle snapshots

A primary reason for the intense interest in structural biology is the fact that knowledge of structure can elucidate macromolecular functions in living organisms. Sustained effort has resulted in an impressive arsenal of tools for determining the static structures. But under physiological conditions, macromolecules undergo continuous conformational changes, a subset of which are functionally important. Techniques for capturing the continuous conformational changes underlying function are essential for further progress. Here, we present chemically-detailed conformational movies of biological function, extracted data-analytically from experimental single-particle cryo-electron microscopy (cryo-EM) snapshots of ryanodine receptor type 1 (RyR1), a calcium-activated calcium channel engaged in the binding of ligands. The functional motions differ substantially from those inferred from static structures in the nature of conformationally active structural domains, the sequence and extent of conformational motions, and the way allosteric signals are transduced within and between domains. Our approach highlights the importance of combining experiment, advanced data analysis, and molecular simulations.

Combine Cryo-EM Density Map and Residue Contact for Protein Structure Prediction - A Case Study

Cryo-electron microscopy is a major structure determination technique for large molecular machines and membrane-associated complexes. Although atomic structures have been determined directly from cryo-EM density maps with high resolutions, current structure determination methods for medium resolution (5 to 10 Å) cryo-EM maps are limited by the availability of structure templates. Secondary structure traces are lines detected from a cryo-EM density map for α-helices and β-strands of a protein. When combined with secondary structure sequence segments predicted from a protein sequence, it is possible to generate a set of likely topologies of α-traces and β-sheet traces. A topology describes the overall folding relationship among secondary structures; it is a critical piece of information for deriving the corresponding atomic structure. We propose a method for protein structure prediction that combines three sources of information: the secondary structure traces detected from the cryo-EM density map, predicted secondary structure sequence segments, and amino acid contact pairs predicted using MULTICOM. A case study shows that using amino acid contact prediction from MULTICOM improves the ranking of the true topology. Our observations convey that using a small set of highly voted secondary structure contact pairs enhances the ranking in all experiments conducted for this case.

Predicting Protein Functional Motions: an Old Recipe with a New Twist

Large macromolecules, including proteins and their complexes, very often adopt multiple conformations. Some of them can be seen experimentally, for example with x-ray crystallography or cryo-electron microscopy. This structural heterogeneity is not occasional and is frequently linked with specific biological function. Thus, the accurate description of macromolecular conformational transitions is crucial for understanding fundamental mechanisms of life's machinery. We report on a real-time method to predict such transitions by extrapolating from instantaneous eigen motions, computed using the normal mode analysis, to a series of twists. We demonstrate the applicability of our approach to the prediction of a wide range of motions, including large collective opening-closing transitions and conformational changes induced by partner binding. We also highlight particularly difficult cases of very small transitions between crystal and solution structures. Our method guarantees preservation of the protein structure during the transition and allows accessing conformations that are unreachable with classical normal mode analysis. We provide practical solutions to describe localized motions with a few low-frequency modes and to relax some geometrical constraints along the predicted transitions. This work opens the way to the systematic description of protein motions, whatever their degree of collectivity. Our method is freely available as a part of the NOn-Linear rigid Block (NOLB) package.

Cryo-EM reveals an asymmetry in a novel single-ring viral chaperonin

Chaperonins are ubiquitously present protein complexes, which assist the proper folding of newly synthesized proteins and prevent aggregation of denatured proteins in an ATP-dependent manner. They are classified into group I (bacterial, mitochondrial, chloroplast chaperonins) and group II (archaeal and eukaryotic cytosolic variants). However, both of these groups do not include recently discovered viral chaperonins. Here, we solved the symmetry-free cryo-EM structures of a single-ring chaperonin encoded by the gene 246 of bacteriophage OBP Pseudomonas fluorescens, in the nucleotide-free, ATPγS-, and ADP-bound states, with resolutions of 4.3 Å, 5.0 Å, and 6 Å, respectively. The structure of OBP chaperonin reveals a unique subunit arrangement, with three pairs of subunits and one unpaired subunit. Each pair combines subunits in two possible conformations, differing in nucleotide-binding affinity. The binding of nucleotides results in the increase of subunits' conformational variability. Due to its unique structural and functional features, OBP chaperonin can represent a new group.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Interpretation of medium resolution cryoEM maps of multi-protein complexes

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CryoEM maps at medium (3.5–6 Å) resolution can be challenging to interpret.

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Integration of multiple methods can inform cryoEM studies.

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Mass spectrometry and biochemistry facilitate map interpretation and model building.

Electron cryo-microscopy (cryoEM) is used to determine structures of biological molecules, including multi-protein complexes. Maps at better than 3.0 Å resolution are relatively straightforward to interpret since atomic models of proteins and nucleic acids can be built directly. Still, these resolutions are often difficult to achieve, and map quality frequently varies within a structure. This results in data that are challenging to interpret, especially when crystal structures or suitable homology models are not available. Recent advances in mass spectrometry techniques, computational methods and model building tools facilitate subunit/domain fitting into maps, elucidation of protein contacts, and de novo generation of atomic models. Here, we review techniques for map interpretation and provide examples from recent studies of multi-protein complexes.

Backmapping from Multiresolution Coarse-Grained Models to Atomic Structures of Large Biomolecules by Restrained Molecular Dynamics Simulations Using Bayesian Inference

Coarse-grained (CG) simulations have allowed access to larger length scales and longer time scales in the study of the dynamic processes of large biomolecules than all-atom (AA) molecular dynamics (MD) simulations. Backmapping from CG models to AA structures has long been studied because it enables us to gain detailed structure insights from CG simulations. Many methods first construct an AA structure from the CG model by fragments, random placement, or geometrical rules and subsequently optimize the solution via energy minimization, simulated annealing or position-restrained simulations. However, such methods may only work well on residue-level CG models and cannot consider the deviations of CG models. In this work, we describe, to the best of our knowledge, a new backmapping method based on Bayesian inference and restrained MD simulations. Restraints with log harmonic energy terms are defined according to the target CG model using the Bayesian inference in which the CG deviations can be estimated. From an initial AA structure obtained from either high-resolution experiments or homology modeling, a MD simulation with the aforementioned restraints is performed to obtain a final AA structure that is a backmapping of the target CG model. The method was validated using multiresolution CG models of the soluble extracellular region of the human epidermal growth factor receptor and was further applied to construct AA structures from CG simulations of the nucleosome core particle. The results demonstrate that our method can generate accurate AA structures of different types of biomolecules from multiple CG models with either residue-level resolution or much lower resolution than one-site-per-residue.

How low-resolution structural data predict the conformational changes of a protein: a study on data-driven molecular dynamics simulations

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways between a given reactant and a product. PaCS-MD repeats the following two steps: (1) selections of initial structures relevant to transitions and (2) their conformational resampling. When selecting the initial structures, several measures are utilized to identify their potential to undergo transitions. In the present study, low-resolution structural data obtained from small angle scattering (SAXS) and cryo-electron microscopy (EM) are adopted as the measures in PaCS-MD to promote the conformational transitions of proteins, which is defined as SAXS-/EM-driven targeted PaCS-MD. By selecting the essential structures that have high correlations with the low-resolution structural data, the SAXS-/EM-driven targeted PaCS-MD identifies a set of transition pathways between the reactant and the product. As a demonstration, the present method successfully predicted the open-closed transition pathway of the lysine-, arginine-, ornithine-binding protein with a ns-order simulation time, indicating that the data-driven PaCS-MD simulation might work to promote the conformational transitions of proteins efficiently.

Automated cryo-EM structure refinement using correlation-driven molecular dynamics

We present a correlation-driven molecular dynamics (CDMD) method for automated refinement of atomistic models into cryo-electron microscopy (cryo-EM) maps at resolutions ranging from near-atomic to subnanometer. It utilizes a chemically accurate force field and thermodynamic sampling to improve the real-space correlation between the modeled structure and the cryo-EM map. Our framework employs a gradual increase in resolution and map-model agreement as well as simulated annealing, and allows fully automated refinement without manual intervention or any additional rotamer- and backbone-specific restraints. Using multiple challenging systems covering a wide range of map resolutions, system sizes, starting model geometries and distances from the target state, we assess the quality of generated models in terms of both model accuracy and potential of overfitting. To provide an objective comparison, we apply several well-established methods across all examples and demonstrate that CDMD performs best in most cases.

Computational modeling of RNA 3D structure based on experimental data

RNA molecules are master regulators of cells. They are involved in a variety of molecular processes: they transmit genetic information, sense cellular signals and communicate responses, and even catalyze chemical reactions. As in the case of proteins, RNA function is dictated by its structure and by its ability to adopt different conformations, which in turn is encoded in the sequence. Experimental determination of high-resolution RNA structures is both laborious and difficult, and therefore the majority of known RNAs remain structurally uncharacterized. To address this problem, predictive computational methods were developed based on the accumulated knowledge of RNA structures determined so far, the physical basis of the RNA folding, and taking into account evolutionary considerations, such as conservation of functionally important motifs. However, all theoretical methods suffer from various limitations, and they are generally unable to accurately predict structures for RNA sequences longer than 100-nt residues unless aided by additional experimental data. In this article, we review experimental methods that can generate data usable by computational methods, as well as computational approaches for RNA structure prediction that can utilize data from experimental analyses. We outline methods and data types that can be potentially useful for RNA 3D structure modeling but are not commonly used by the existing software, suggesting directions for future development.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

N-Terminal Domains of Cardiac Myosin Binding Protein C Cooperatively Activate the Thin Filament

Muscle contraction relies on interaction between myosin-based thick filaments and actin-based thin filaments. Myosin binding protein C (MyBP-C) is a key regulator of actomyosin interactions. Recent studies established that the N'-terminal domains (NTDs) of MyBP-C can either activate or inhibit thin filaments, but the mechanism of their collective action is poorly understood. Cardiac MyBP-C (cMyBP-C) harbors an extra NTD, which is absent in skeletal isoforms of MyBP-C, and its role in regulation of cardiac contraction is unknown. Here we show that the first two domains of human cMyPB-C (i.e., C0 and C1) cooperate to activate the thin filament. We demonstrate that C1 interacts with tropomyosin via a positively charged loop and that this interaction, stabilized by the C0 domain, is required for thin filament activation by cMyBP-C. Our data reveal a mechanism by which cMyBP-C can modulate cardiac contraction and demonstrate a function of the C0 domain.

Constructing atomic structural models into cryo-EM densities using molecular dynamics - Pros and cons

Accurate structure determination from electron density maps at 3-5 Å resolution necessitates a balance between extensive global and local sampling of atomistic models, yet with the stereochemical correctness of backbone and sidechain geometries. Molecular Dynamics Flexible Fitting (MDFF), particularly through a resolution-exchange scheme, ReMDFF, provides a robust way of achieving this balance for hybrid structure determination. Employing two high-resolution density maps, namely that of β-galactosidase at 3.2 Å and TRPV1 at 3.4 Å, we showcase the quality of ReMDFF-generated models, comparing them against ones submitted by independent research groups for the 2015-2016 Cryo-EM Model Challenge. This comparison offers a clear evaluation of ReMDFF's strengths and shortcomings, and those of data-guided real-space refinements in general. ReMDFF results scored highly on the various metric for judging the quality-of-fit and quality-of-model. However, some systematic discrepancies are also noted employing a Molprobity analysis, that are reproducible across multiple competition entries. A space of key refinement parameters is explored within ReMDFF to observe their impact within the final model. Choice of force field parameters and initial model seem to have the most significant impact on ReMDFF model-quality. To this end, very recently developed CHARMM36m force field parameters provide now more refined ReMDFF models than the ones originally submitted to the Cryo-EM challenge. Finally, a set of good-practices is prescribed for the community to benefit from the MDFF developments.

Role of Computational Methods in Going beyond X-ray Crystallography to Explore Protein Structure and Dynamics

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

Acceleration of cryo-EM Flexible Fitting for Large Biomolecular Systems by Efficient Space Partitioning

Flexible fitting is a powerful technique to build the 3D structures of biomolecules from cryoelectron microscopy (cryo-EM) density maps. One popular method is a cross-correlation coefficient-based approach, where the molecular dynamics (MD) simulation is carried out with the biasing potential that includes the cross-correlation coefficient between the experimental and simulated density maps. Here, we propose efficient parallelization schemes for the calculation of the cross-correlation coefficient to accelerate flexible fitting. Our schemes are tested for small, medium, and large biomolecules using CPU and hybrid CPU + GPU architectures. The scheme for the atomic decomposition MD is suitable for small proteins such as Ca²⁺-ATPase with the all-atom Go model, while that for the domain decomposition MD is better for larger systems such as ribosome with the all-atom Go or the all-atom explicit solvent models. Our methods allow flexible fitting for various biomolecules with reasonable computational cost. This approach also connects high-resolution structure refinements with investigation of protein structure-function relationship.

Accurate flexible refinement of atomic models against medium-resolution cryo-EM maps using damped dynamics

BACKGROUND

Dramatic progress has recently been made in cryo-electron microscopy technologies, which now make possible the reconstruction of a growing number of biomolecular structures to near-atomic resolution. However, the need persists for fitting and refinement approaches that address those cases that require modeling assistance.

METHODS

In this paper, we describe algorithms to optimize the performance of such medium-resolution refinement methods. These algorithms aim to automatically optimize the parameters that define the density shape of the flexibly fitted model, as well as the time-dependent damper cutoff distance. Atomic distance constraints can be prescribed for cases where extra containment of parts of the structure is helpful, such as in regions where the density map is poorly defined. Also, we propose a simple stopping criterion that estimates the probable onset of overfitting during the simulation.

RESULTS

The new set of algorithms produce more accurate fitting and refinement results, and yield a faster rate of convergence of the trajectory toward the fitted conformation. The latter is also more reliable due to the overfitting warning provided to the user.

CONCLUSIONS

The algorithms described here were implemented in the new Damped-Dynamics Flexible Fitting simulation tool "DDforge" in the Situs package.

Searching for 3D structural models from a library of biological shapes using a few 2D experimental images

Background

Advancements in biophysical experimental techniques have pushed the limits in terms of the types of phenomena that can be characterized, the amount of data that can be produced and the resolution at which we can visualize them. Single particle techniques such as Electron Microscopy (EM) and X-ray free electron laser (XFEL) scattering require a large number of 2D images collected to resolve three-dimensional (3D) structures. In this study, we propose a quick strategy to retrieve potential 3D shapes, as low-resolution models, from a few 2D experimental images by searching a library of 2D projection images generated from existing 3D structures.

Results

We developed the protocol to assemble a non-redundant set of 3D shapes for generating the 2D image library, and to retrieve potential match 3D shapes for query images, using EM data as a test. In our strategy, we disregard differences in volume size, giving previously unknown structures and conformations a greater number of 3D biological shapes as possible matches. We tested the strategy using images from three EM models as query images for searches against a library of 22750 2D projection images generated from 250 random EM models. We found that our ability to identify 3D shapes that match the query images depends on how complex the outline of the 2D shapes are and whether they are represented in the search image library.

Conclusions

Through our computational method, we are able to quickly retrieve a 3D shape from a few 2D projection images. Our approach has the potential for exploring other types of 2D single particle structural data such as from XFEL scattering experiments, for providing a tool to interpret low-resolution data that may be insufficient for 3D reconstruction, and for estimating the mixing of states or conformations that could exist in such experimental data.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2358-0) contains supplementary material, which is available to authorized users.

Structures reveal opening of the store-operated calcium channel Orai

The store-operated calcium (Ca²⁺) channel Orai governs Ca²⁺ influx through the plasma membrane of many non-excitable cells in metazoans. The channel opens in response to the depletion of Ca²⁺ stored in the endoplasmic reticulum (ER). Loss- and gain-of-function mutants of Orai cause disease. Our previous work revealed the structure of Orai with a closed pore. Here, using a gain-of-function mutation that constitutively activates the channel, we present an X-ray structure of Drosophila melanogaster Orai in an open conformation. Well-defined electron density maps reveal that the pore is dramatically dilated on its cytosolic side in comparison to the slender closed pore. Cations and anions bind in different regions of the open pore, informing mechanisms for ion permeation and Ca²⁺ selectivity. Opening of the pore requires the release of cytosolic latches. Together with additional X-ray structures of an unlatched-but-closed conformation, we propose a sequence for store-operated activation.

Exploratory Studies Detecting Secondary Structures in Medium Resolution 3D Cryo-EM Images Using Deep Convolutional Neural Networks

Cryo-electron microscopy (cryo-EM) is an emerging biophysical technique for structural determination of protein complexes. However, accurate detection of secondary structures is still challenging when cryo-EM density maps are at medium resolutions (5-10 Å). Most of existing methods are image processing methods that do not fully utilize available images in the cryo-EM database. In this paper, we present a deep learning approach to segment secondary structure elements as helices and β-sheets from medium-resolution density maps. The proposed 3D convolutional neural network is shown to detect secondary structure locations with an F1 score between 0.79 and 0.88 for six simulated test cases. The architecture was also applied to an experimentally-derived cryo-EM density map with good accuracy.

Using Spectral Representation to Classify Proteins' Conformational States

Numerous proteins are molecular targets for drug action and hence are important in drug discovery. Structure-based computational drug discovery relies on detailed information regarding protein conformations for subsequent drug screening in silico. There are two key issues in analyzing protein conformations in virtual screening. The first considers the protein’s conformational change in response to physical and chemical conditions. The second is the protein’s atomic resolution reconstruction from X-ray crystallography or nuclear magnetic resonance (NMR) data. In this latter problem, information is needed regarding the sample’s position relative to the source of X-rays. Here, we introduce a new measure for classifying protein conformational states using spectral representation and Wigner’s D-functions. Predictions based on the new measure are in good agreement with conformational states of proteins. These results could also be applied to improve conformational alignment of the snapshots given by protein crystallography.

CryoEM-based hybrid modeling approaches for structure determination

Recent advances in cryo-electron microscopy (cryoEM) have dramatically improved the resolutions at which vitrified biological specimens can be studied, revealing new structural and mechanistic insights over a broad range of spatial scales. Bolstered by these advances, much effort has been directed toward the development of hybrid modeling methodologies for the construction and refinement of high-fidelity atomistic models from cryoEM data. In this brief review, we will survey the key elements of cryoEM-based hybrid modeling, providing an overview of available computational tools and strategies as well as several recent applications.

Current approaches for the fitting and refinement of atomic models into cryo-EM maps using CCP-EM

Recent advances in instrumentation and software have resulted in cryo-EM rapidly becoming the method of choice for structural biologists, especially for those studying the three-dimensional structures of very large macromolecular complexes. In this contribution, the tools available for macromolecular structure refinement into cryo-EM reconstructions that are available via CCP-EM are reviewed, specifically focusing on REFMAC5 and related tools. Whilst originally designed with a view to refinement against X-ray diffraction data, some of these tools have been able to be repurposed for cryo-EM owing to the same principles being applicable to refinement against cryo-EM maps. Since both techniques are used to elucidate macromolecular structures, tools encapsulating prior knowledge about macromolecules can easily be transferred. However, there are some significant qualitative differences that must be acknowledged and accounted for; relevant differences between these techniques are highlighted. The importance of phases is considered and the potential utility of replacing inaccurate amplitudes with their expectations is justified. More pragmatically, an upper bound on the correlation between observed and calculated Fourier coefficients, expressed in terms of the Fourier shell correlation between half-maps, is demonstrated. The importance of selecting appropriate levels of map blurring/sharpening is emphasized, which may be facilitated by considering the behaviour of the average map amplitude at different resolutions, as well as the utility of simultaneously viewing multiple blurred/sharpened maps. Features that are important for the purposes of computational efficiency are discussed, notably the Divide and Conquer pipeline for the parallel refinement of large macromolecular complexes. Techniques that have recently been developed or improved in Coot to facilitate and expedite the building, fitting and refinement of atomic models into cryo-EM maps are summarized. Finally, a tool for symmetry identification from a given map or coordinate set, ProSHADE, which can identify the point group of a map and thus may be used during deposition as well as during molecular visualization, is introduced.

A probabilistic network model for structural transitions in biomolecules

Biological macromolecules often undergo large conformational rearrangements during a functional cycle. To simulate these structural transitions with full atomic detail typically demands extensive computational resources. Moreover, it is unclear how to incorporate, in a principled way, additional experimental information that could guide the structural transition. This article develops a probabilistic model for conformational transitions in biomolecules. The model can be viewed as a network of anharmonic springs that break, if the experimental data support the rupture of bonds. Hamiltonian Monte Carlo in internal coordinates is used to infer structural transitions from experimental data, thereby sampling large conformational transitions without distorting the structure. The model is benchmarked on a large set of conformational transitions. Moreover, we demonstrate the use of the probabilistic network model for integrative modeling of macromolecular complexes based on data from crosslinking followed by mass spectrometry.

Overview of refinement procedures within REFMAC5: utilizing data from different sources

Refinement is a process that involves bringing into agreement the structural model, available prior knowledge and experimental data. To achieve this, the refinement procedure optimizes a posterior conditional probability distribution of model parameters, including atomic coordinates, atomic displacement parameters (B factors), scale factors, parameters of the solvent model and twin fractions in the case of twinned crystals, given observed data such as observed amplitudes or intensities of structure factors. A library of chemical restraints is typically used to ensure consistency between the model and the prior knowledge of stereochemistry. If the observation-to-parameter ratio is small, for example when diffraction data only extend to low resolution, the Bayesian framework implemented in REFMAC5 uses external restraints to inject additional information extracted from structures of homologous proteins, prior knowledge about secondary-structure formation and even data obtained using different experimental methods, for example NMR. The refinement procedure also generates the `best' weighted electron-density maps, which are useful for further model (re)building. Here, the refinement of macromolecular structures using REFMAC5 and related tools distributed as part of the CCP4 suite is discussed.

Analytical Approaches to Improve Accuracy in Solving the Protein Topology Problem

To take advantage of recent advances in genomics and proteomics it is critical that the three-dimensional physical structure of biological macromolecules be determined. Cryo-Electron Microscopy (cryo-EM) is a promising and improving method for obtaining this data, however resolution is often not sufficient to directly determine the atomic scale structure. Despite this, information for secondary structure locations is detectable. De novo modeling is a computational approach to modeling these macromolecular structures based on cryo-EM derived data. During de novo modeling a mapping between detected secondary structures and the underlying amino acid sequence must be identified. DP-TOSS (Dynamic Programming for determining the Topology Of Secondary Structures) is one tool that attempts to automate the creation of this mapping. By treating the correspondence between the detected structures and the structures predicted from sequence data as a constraint graph problem DP-TOSS achieved good accuracy in its original iteration. In this paper, we propose modifications to the scoring methodology of DP-TOSS to improve its accuracy. Three scoring schemes were applied to DP-TOSS and tested: (i) a skeleton-based scoring function; (ii) a geometry-based analytical function; and (iii) a multi-well potential energy-based function. A test of 25 proteins shows that a combination of these schemes can improve the performance of DP-TOSS to solve the topology determination problem for macromolecule proteins.

Hybrid Methods for Macromolecular Modeling by Molecular Mechanics Simulations with Experimental Data

Hybrid approaches for the modeling of macromolecular complexes that combine computational molecular mechanics simulations with experimental data are discussed. Experimental data for biological molecular structures are often low-resolution, and thus, do not contain enough information to determine the atomic positions of molecules. This is especially true when the dynamics of large macromolecules are the focus of the study. However, computational modeling can complement missing information. Significant increase in computational power, as well as the development of new modeling algorithms allow us to model structures of biological macromolecules reliably, using experimental data as references. We review the basics of molecular mechanics approaches, such as atomic model force field, and coarse-grained models, molecular dynamics simulation and normal mode analysis and describe how they could be used for flexible fitting hybrid modeling with experimental data, especially from cryo-EM and SAXS.

Tools for the cryo-EM gold rush: going from the cryo-EM map to the atomistic model

As cryo-electron microscopy (cryo-EM) enters mainstream structural biology, the demand for fitting methods is high. Here, we review existing flexible fitting methods for cryo-EM. We discuss their importance, potential concerns and assessment strategies. We aim to give readers concrete descriptions of cryo-EM flexible fitting methods with corresponding examples.

Detecting intermediate protein conformations using algebraic topology

Background

Understanding protein structure and dynamics is essential for understanding their function. This is a challenging task due to the high complexity of the conformational landscapes of proteins and their rugged energy levels. In particular, it is important to detect highly populated regions which could correspond to intermediate structures or local minima.

Results

We present a hierarchical clustering and algebraic topology based method that detects regions of interest in protein conformational space. The method is based on several techniques. We use coarse grained protein conformational search, efficient robust dimensionality reduction and topological analysis via persistent homology as the main tools. We use two dimensionality reduction methods as well, robust Principal Component Analysis (PCA) and Isomap, to generate a reduced representation of the data while preserving most of the variance in the data.

Conclusions

Our hierarchical clustering method was able to produce compact, well separated clusters for all the tested examples.

PEM-fitter: A Coarse-Grained Method to Validate Protein Candidate Models

The volumetric images produced by Cryo-Electron Microscopy (cryo-EM) technique are used to model macromolecular assemblies and machines. De novo protein modeling uses these images to computationally model the structure of the molecules. Many candidate conformations are usually generated during the intermediate step. Conventionally, each of these candidates is evaluated by time-consuming approaches such as potential energy. We introduce an initial version of a geometrical screening method that uses the skeleton of the cryo-EM images to evaluate candidate structures. The aim of this method is to reduce the number of native-like candidate conformations and, therefore, reduce the time required for structural evaluation by energy calculations. A test of two datasets was performed. The first dataset contains 10 proteins and shows that our method can successfully detect the correct native structure for the given skeleton among a set of different protein structures. The second dataset contains 12 proteins and shows that our method can filter slightly modified decoy conformations of the same protein. The efficiency of the method is also reported.

Interactive comparison and remediation of collections of macromolecular structures

Often similar structures need to be compared to reveal local differences throughout the entire model or between related copies within the model. Therefore, a program to compare multiple structures and enable correction any differences not supported by the density map was written within the Phenix framework (Adams et al., Acta Cryst 2010; D66:213-221). This program, called Structure Comparison, can also be used for structures with multiple copies of the same protein chain in the asymmetric unit, that is, as a result of non-crystallographic symmetry (NCS). Structure Comparison was designed to interface with Coot(Emsley et al., Acta Cryst 2010; D66:486-501) and PyMOL(DeLano, PyMOL 0.99; 2002) to facilitate comparison of large numbers of related structures. Structure Comparison analyzes collections of protein structures using several metrics, such as the rotamer conformation of equivalent residues, displays the results in tabular form and allows superimposed protein chains and density maps to be quickly inspected and edited (via the tools in Coot) for consistency, completeness and correctness.

Conformational Heterogeneity in a Fully Complementary DNA Three-Way Junction with a GC-Rich Branchpoint

DNA three-way junctions (3WJs) are branched structures that serve as important biological intermediates and as components in DNA nanostructures. We recently derived the global structure of a fully complementary 3WJ and found that it contained unpaired bases at the branchpoint, which is consistent with previous observations of branch flexibility and branchpoint reactivity. By combining high-resolution single-molecule Förster resonance energy transfer, molecular modeling, time-resolved ensemble fluorescence spectroscopy, and the first ¹⁹F nuclear magnetic resonance observations of fully complementary 3WJs, we now show that the 3WJ structure can adopt multiple distinct conformations depending upon the sequence at the branchpoint. A 3WJ with a GC-rich branchpoint adopts an open conformation with unpaired bases at the branch and at least one additional conformation with an increased number of base interactions at the branchpoint. This structural diversity has implications for branch interactions and processing in vivo and for technological applications.