Coarse-grained modeling of RNA 3D structure

gRNAde: Geometric Deep Learning for 3D RNA inverse design

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde , a g eometric RNA de sign pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. Under the hood, gRNAde is a multi-state Graph Neural Network that generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. [2010], gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent RNA polymerase ribozyme structure.

Coarse-grained modeling of DNA-RNA hybrids

We introduce oxNA, a new model for the simulation of DNA-RNA hybrids that is based on two previously developed coarse-grained models-oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes, including their structure, persistence length, and force-extension characteristics. By parameterizing the DNA-RNA hydrogen bonding interaction, we fit the model's thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model's applicability, we provide three examples of its use-calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop, and simulating RNA-scaffolded wireframe origami.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

Modeling the 3D structure and conformational dynamics of very large RNAs using coarse-grained molecular simulations

We describe a computational approach to building and simulating realistic 3D models of very large RNA molecules (>1000 nucleotides) at a resolution of one "bead" per nucleotide. The method starts with a predicted secondary structure and uses several stages of energy minimization and Brownian dynamics (BD) simulation to build 3D models. A key step in the protocol is the temporary addition of a 4 ^th spatial dimension that allows all predicted helical elements to become disentangled from each other in an effectively automated way. We then use the resulting 3D models as input to Brownian dynamics simulations that include hydrodynamic interactions (HIs) that allow the diffusive properties of the RNA to be modelled as well as enabling its conformational dynamics to be simulated. To validate the dynamics part of the method, we first show that when applied to small RNAs with known 3D structures the BD-HI simulation models accurately reproduce their experimental hydrodynamic radii (Rh). We then apply the modelling and simulation protocol to a variety of RNAs for which experimental Rh values have been reported ranging in size from 85 to 3569 nucleotides. We show that the 3D models, when used in BD-HI simulations, produce hydrodynamic radii that are usually in good agreement with experimental estimates for RNAs that do not contain tertiary contacts that persist even under very low salt conditions. Finally, we show that sampling of the conformational dynamics of large RNAs on timescales of 100 µs is computationally feasible with BD-HI simulations.

RNA Folding Based on 5 Beads Model and Multiscale Simulation

RNA folding prediction is very meaningful and challenging. The molecular dynamics simulation (MDS) of all atoms (AA) is limited to the folding of small RNA molecules. At present, most of the practical models are coarse grained (CG) model, and the coarse-grained force field (CGFF) parameters usually depend on known RNA structures. However, the limitation of the CGFF is obvious that it is difficult to study the modified RNA. Based on the 3 beads model (AIMS_RNA_B3), we proposed the AIMS_RNA_B5 model with three beads representing a base and two beads representing the main chain (sugar group and phosphate group). We first run the all atom molecular dynamic simulation (AAMDS), and fit the CGFF parameter with the AA trajectory. Then perform the coarse-grained molecular dynamic simulation (CGMDS). AAMDS is the foundation of CGMDS. CGMDS is mainly to carry out the conformation sampling based on the current AAMDS state and improve the folding speed. We simulated the folding of three RNAs, which belong to hairpin, pseudoknot and tRNA respectively. Compared to the AIMS_RNA_B3 model, the AIMS_RNA_B5 model is more reasonable and performs better.

Ribonucleic Acid Folding Prediction Based on Iterative Multiscale Simulation

RNA folding prediction is a challenge. Currently, many RNA folding models are coarse-grained (CG) with the potential derived from the known RNA structures. However, this potential is not suitable for modified and entirely new RNA. It is also not suitable for the folding simulation of RNA in the real cellular environment, including many kinds of molecular interactions. In contrast, our proposed model has the potential to address these issues, which is a multiscale simulation scheme based on all-atom (AA) force fields. We fit the CG force field using the trajectories generated by the AA force field and then iteratively perform molecular dynamics (MD) simulations of the two scales. The all-atom molecular dynamics (AAMD) simulation is mainly responsible for the correction of RNA structure, and the CGMD simulation is mainly responsible for efficient conformational sampling. On the basis of this scheme, we can successfully fold three RNAs belonging to a hairpin, a pseudoknot, and a four-way junction.

Molecular Modeling in Anion Exchange Membrane Research: A Brief Review of Recent Applications

Anion Exchange Membrane (AEM) fuel cells have attracted growing interest, due to their encouraging advantages, including high power density and relatively low cost. AEM is a polymer matrix, which conducts hydroxide (OH−) ions, prevents physical contact of electrodes, and has positively charged head groups (mainly quaternary ammonium (QA) groups), covalently bound to the polymer backbone. The chemical instability of the quaternary ammonium (QA)-based head groups, at alkaline pH and elevated temperature, is a significant threshold in AEMFC technology. This review work aims to introduce recent studies on the chemical stability of various QA-based head groups and transportation of OH− ions in AEMFC, via modeling and simulation techniques, at different scales. It starts by introducing the fundamental theories behind AEM-based fuel-cell technology. In the main body of this review, we present selected computational studies that deal with the effects of various parameters on AEMs, via a variety of multi-length and multi-time-scale modeling and simulation methods. Such methods include electronic structure calculations via the quantum Density Functional Theory (DFT), ab initio, classical all-atom Molecular Dynamics (MD) simulations, and coarse-grained MD simulations. The explored processing and structural parameters include temperature, hydration levels, several QA-based head groups, various types of QA-based head groups and backbones, etc. Nowadays, many methods and software packages for molecular and materials modeling are available. Applications of such methods may help to understand the transportation mechanisms of OH− ions, the chemical stability of functional head groups, and many other relevant properties, leading to a performance-based molecular and structure design as well as, ultimately, improved AEM-based fuel cell performances. This contribution aims to introduce those molecular modeling methods and their recent applications to the AEM-based fuel cells research community.

Thermodynamics of unfolding mechanisms of mouse mammary tumor virus pseudoknot from a coarse-grained loop-entropy model

Pseudoknotted RNA molecules play important biological roles that depend on their folded structure. To understand the underlying principles that determine their thermodynamics and folding/unfolding mechanisms, we carried out a study on a variant of the mouse mammary tumor virus pseudoknotted RNA (VPK), a widely studied model system for RNA pseudoknots. Our method is based on a coarse-grained discrete-state model and the algorithm of PK3D (pseudoknot structure predictor in three-dimensional space), with RNA loops explicitly constructed and their conformational entropic effects incorporated. Our loop entropy calculations are validated by accurately capturing previously measured melting temperatures of RNA hairpins with varying loop lengths. For each of the hairpins that constitutes the VPK, we identified alternative conformations that are more stable than the hairpin structures at low temperatures and predicted their populations at different temperatures. Our predictions were validated by thermodynamic experiments on these hairpins. We further computed the heat capacity profiles of VPK, which are in excellent agreement with available experimental data. Notably, our model provides detailed information on the unfolding mechanisms of pseudoknotted RNA. Analysis of the distribution of base-pairing probability of VPK reveals a cooperative unfolding mechanism instead of a simple sequential unfolding of first one stem and then the other. Specifically, we find a simultaneous "loosening" of both stems as the temperature is raised, whereby both stems become partially melted and co-exist during the unfolding process.

Modeling Noncanonical RNA Base Pairs by a Coarse-Grained IsRNA2 Model

Noncanonical base pairs contribute crucially to the three-dimensional architecture of large RNA molecules; however, how to accurately model them remains an open challenge in RNA 3D structure prediction. Here, we report a promising coarse-grained (CG) IsRNA2 model to predict noncanonical base pairs in large RNAs through molecular dynamics simulations. By introducing a five-bead per nucleotide CG representation to reserve the three interacting edges of nucleobases, IsRNA2 accurately models various base-pairing interactions, including both canonical and noncanonical base pairs. A benchmark test indicated that IsRNA2 achieves a comparable performance to the atomic model in de novo modeling of noncanonical RNA structures. In addition, IsRNA2 was able to refine the 3D structure predictions for large RNAs in RNA-puzzle challenges. Finally, the graphics processing unit acceleration was introduced to speed up the sampling efficiency in IsRNA2 for very large RNA molecules. Therefore, the CG IsRNA2 model reported here offers a reliable approach to predict the structures and dynamics of large RNAs.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

Salt-Dependent RNA Pseudoknot Stability: Effect of Spatial Confinement

Macromolecules, such as RNAs, reside in crowded cell environments, which could strongly affect the folded structures and stability of RNAs. The emergence of RNA-driven phase separation in biology further stresses the potential functional roles of molecular crowding. In this work, we employed the coarse-grained model that was previously developed by us to predict 3D structures and stability of the mouse mammary tumor virus (MMTV) pseudoknot under different spatial confinements over a wide range of salt concentrations. The results show that spatial confinements can not only enhance the compactness and stability of MMTV pseudoknot structures but also weaken the dependence of the RNA structure compactness and stability on salt concentration. Based on our microscopic analyses, we found that the effect of spatial confinement on the salt-dependent RNA pseudoknot stability mainly comes through the spatial suppression of extended conformations, which are prevalent in the partially/fully unfolded states, especially at low ion concentrations. Furthermore, our comprehensive analyses revealed that the thermally unfolding pathway of the pseudoknot can be significantly modulated by spatial confinements, since the intermediate states with more extended conformations would loss favor when spatial confinements are introduced.

IsRNA1: De Novo Prediction and Blind Screening of RNA 3D Structures

Modeling structures and functions of large ribonucleic acid (RNAs) especially with complicated topologies is highly challenging due to the inefficiency of large conformational sampling and the presence of complicated tertiary interactions. To address this problem, one highly promising approach is coarse-grained modeling. Here, following an iterative simulated reference state approach to decipher the correlations between different structural parameters, we developed a potent coarse-grained RNA model named as IsRNA1 for RNA studies. Molecular dynamics simulations in the IsRNA1 can predict the native structures of small RNAs from a sequence and fold medium-sized RNAs into near-native tertiary structures with the assistance of secondary structure constraints. A large-scale benchmark test on RNA 3D structure prediction shows that IsRNA1 exhibits improved performance for relatively large RNAs of complicated topologies, such as large stem-loop structures and structures containing long-range tertiary interactions. The advantages of IsRNA1 include the consideration of the correlations between the different structural variables, the appropriate characterization of canonical base-pairing and base-stacking interactions, and the better sampling for the backbone conformations. Moreover, a blind screening protocol was developed based on IsRNA1 to identify good structural models from a pool of candidates without prior knowledge of the native structures.

A Fiedler Vector Scoring Approach for Novel RNA Motif Selection

Novel RNA motif design is of great practical importance for technology and medicine. Increasingly, computational design plays an important role in such efforts. Our coarse-grained RAG (RNA-As-Graphs) framework offers strategies for enumerating the universe of RNA 2D folds, selecting "RNA-like" candidates for design, and determining sequences that fold onto these candidates. In RAG, RNA secondary structures are represented as tree or dual graphs. Graphs with known RNA structures are called "existing", and the others are labeled "hypothetical". By using simplified features for RNA graphs, we have clustered the hypothetical graphs into "RNA-like" and "non-RNA-like" groups and proposed RNA-like graphs as candidates for design. Here, we propose a new way of designing graph features by using Fiedler vectors. The new features reflect graph shapes better, and they lead to a more clustered organization of existing graphs. We show significant increases in K-means clustering accuracy by using the new features (e.g., up to 95% and 98% accuracy for tree and dual graphs, respectively). In addition, we propose a scoring model for top graph candidate selection. This scoring model allows users to set a threshold for candidates, and it incorporates weighing of existing graphs based on their corresponding number of known RNAs. We include a list of top scored RNA-like candidates, which we hope will stimulate future novel RNA design.

Intrinsic Regulatory Role of RNA Structural Arrangement in Alternative Splicing Control

Alternative splicing is a highly sophisticated process, playing a significant role in posttranscriptional gene expression and underlying the diversity and complexity of organisms. Its regulation is multilayered, including an intrinsic role of RNA structural arrangement which undergoes time- and tissue-specific alterations. In this review, we describe the principles of RNA structural arrangement and briefly decipher its cis- and trans-acting cellular modulators which serve as crucial determinants of biological functionality of the RNA structure. Subsequently, we engage in a discussion about the RNA structure-mediated mechanisms of alternative splicing regulation. On one hand, the impairment of formation of optimal RNA structures may have critical consequences for the splicing outcome and further contribute to understanding the pathomechanism of severe disorders. On the other hand, the structural aspects of RNA became significant features taken into consideration in the endeavor of finding potential therapeutic treatments. Both aspects have been addressed by us emphasizing the importance of ongoing studies in both fields.

Free energy-based model of CTCF-mediated chromatin looping in the human genome

In recent years, high-throughput techniques have revealed considerable structural organization of the human genome with diverse regions of the chromatin interacting with each other in the form of loops. Some of these loops are quite complex and may encompass regions comprised of many interacting chain segments around a central locus. Popular techniques for extracting this information are chromatin interaction analysis by paired-end tag sequencing (ChIA-PET) and high-throughput chromosome conformation capture (Hi-C). Here, we introduce a physics-based method to predict the three-dimensional structure of chromatin from population-averaged ChIA-PET data. The approach uses experimentally-validated data from human B-lymphoblastoid cells to generate 2D meta-structures of chromatin using a dynamic programming algorithm that explores the chromatin free energy landscape. By generating both optimal and suboptimal meta-structures we can calculate both the free energy and additionally the relative thermodynamic probability. A 3D structure prediction program with applied restraints then can be used to generate the tertiary structures. The main advantage of this approach for population-averaged experimental data is that it provides a way to distinguish between the principal and the spurious contacts. This study also finds that euchromatin appear to have rather precisely regulated 2D meta-structures compared to heterochromatin. The program source-code is available at https://github.com/plewczynski/looper.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library

BACKGROUND

We re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications.

METHODS

Clustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into 'existing' or hypothetical, and the latter into, 'RNA-like' or 'non RNA-like' topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups.

RESULTS

The unsupervised PAM and K-means clustering approaches correctly classify 72-77% of all existing graph topologies and 75-82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%.

CONCLUSIONS

Using linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach.

GENERAL SIGNIFICANCE

Our updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.

Inverse folding with RNA-As-Graphs produces a large pool of candidate sequences with target topologies

We present an RNA-As-Graphs (RAG) based inverse folding algorithm, RAG-IF, to design novel RNA sequences that fold onto target tree graph topologies. The algorithm can be used to enhance our recently reported computational design pipeline (Jain et al., NAR 2018). The RAG approach represents RNA secondary structures as tree and dual graphs, where RNA loops and helices are coarse-grained as vertices and edges, opening the usage of graph theory methods to study, predict, and design RNA structures. Our recently developed computational pipeline for design utilizes graph partitioning (RAG-3D) and atomic fragment assembly (F-RAG) to design sequences to fold onto RNA-like tree graph topologies; the atomic fragments are taken from existing RNA structures that correspond to tree subgraphs. Because F-RAG may not produce the target folds for all designs, automated mutations by RAG-IF algorithm enhance the candidate pool markedly. The crucial residues for mutation are identified by differences between the predicted and the target topology. A genetic algorithm then mutates the selected residues, and the successful sequences are optimized to retain only the minimal or essential mutations. Here we evaluate RAG-IF for 6 RNA-like topologies and generate a large pool of successful candidate sequences with a variety of minimal mutations. We find that RAG-IF adds robustness and efficiency to our RNA design pipeline, making inverse folding motivated by graph topology rather than secondary structure more productive.

Structure folding of RNA kissing complexes in salt solutions: predicting 3D structure, stability, and folding pathway

RNA kissing complexes are essential for genomic RNA dimerization and regulation of gene expression, and their structures and stability are critical to their biological functions. In this work, we used our previously developed coarse-grained model with an implicit structure-based electrostatic potential to predict three-dimensional (3D) structures and stability of RNA kissing complexes in salt solutions. For extensive RNA kissing complexes, our model shows great reliability in predicting 3D structures from their sequences, and our additional predictions indicate that the model can capture the dependence of 3D structures of RNA kissing complexes on monovalent/divalent ion concentrations. Moreover, the comparisons with extensive experimental data show that the model can make reliable predictions on the stability for various RNA kissing complexes over wide ranges of monovalent/divalent ion concentrations. Notably, for RNA kissing complexes, our further analyses show the important contribution of coaxial stacking to the 3D structures and stronger stability than the corresponding kissing-interface duplexes at high salts. Furthermore, our comprehensive analyses for RNA kissing complexes reveal that the thermally folding pathway for a complex sequence is mainly determined by the relative stability of two possible folded states of kissing complex and extended duplex, which can be significantly modulated by its sequence.

QRNAS: software tool for refinement of nucleic acid structures

BACKGROUND

Computational models of RNA 3D structure often present various inaccuracies caused by simplifications used in structure prediction methods, such as template-based modeling or coarse-grained simulations. To obtain a high-quality model, the preliminary RNA structural model needs to be refined, taking into account atomic interactions. The goal of the refinement is not only to improve the local quality of the model but to bring it globally closer to the true structure.

RESULTS

We present QRNAS, a software tool for fine-grained refinement of nucleic acid structures, which is an extension of the AMBER simulation method with additional restraints. QRNAS is capable of handling RNA, DNA, chimeras, and hybrids thereof, and enables modeling of nucleic acids containing modified residues.

CONCLUSIONS

We demonstrate the ability of QRNAS to improve the quality of models generated with different methods. QRNAS was able to improve MolProbity scores of NMR structures, as well as of computational models generated in the course of the RNA-Puzzles experiment. The overall geometry improvement may be associated with increased model accuracy, especially on the level of correctly modeled base-pairs, but the systematic improvement of root mean square deviation to the reference structure should not be expected. The method has been integrated into a computational modeling workflow, enabling improved RNA 3D structure prediction.

3D based on 2D: Calculating helix angles and stacking patterns using forgi 2.0, an RNA Python library centered on secondary structure elements

We present forgi, a Python library to analyze the tertiary structure of RNA secondary structure elements. Our representation of an RNA molecule is centered on secondary structure elements (stems, bulges and loops). By fitting a cylinder to the helix axis, these elements are carried over into a coarse-grained 3D structure representation. Integration with Biopython allows for handling of all-atom 3D information. forgi can deal with a variety of file formats including dotbracket strings, PDB and MMCIF files. We can handle modified residues, missing residues, cofold and multifold structures as well as nucleotide numbers starting at arbitrary positions. We apply this library to the study of stacking helices in junctions and pseudoknots and investigate how far stacking helices in solved experimental structures can divert from coaxial geometries.

3D based on 2D: Calculating helix angles and stacking patterns using forgi 2.0, an RNA Python library centered on secondary structure elements

We present forgi, a Python library to analyze the tertiary structure of RNA secondary structure elements. Our representation of an RNA molecule is centered on secondary structure elements (stems, bulges and loops). By fitting a cylinder to the helix axis, these elements are carried over into a coarse-grained 3D structure representation. Integration with Biopython allows for handling of all-atom 3D information. forgi can deal with a variety of file formats including dotbracket strings, PDB and MMCIF files. We can handle modified residues, missing residues, cofold and multifold structures as well as nucleotide numbers starting at arbitrary positions. We apply this library to the study of stacking helices in junctions and pseudo knots and investigate how far stacking helices in solved experimental structures can divert from coaxial geometries.

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.

Prediction of DNA and RNA structure with the NARES-2P force field and conformational space annealing

A physics-based method for the prediction of the structures of nucleic acids, which is based on the physics-based 2-bead NARES-2P model of polynucleotides and global-optimization Conformational Space Annealing (CSA) algorithm has been proposed. The target structure is sought as the global-energy-minimum structure, which ignores the entropy component of the free energy but spares expensive multicanonical simulations necessary to find the conformational ensemble with the lowest free energy. The CSA algorithm has been modified to optimize its performance when treating both single and multi-chain nucleic acids. It was shown that the method finds the native fold for simple RNA molecules and DNA duplexes and with limited distance restraints, which can easily be obtained from the secondary-structure-prediction servers, complex RNA folds can be treated with using moderate computer resources.

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Predicting ligand binding poses for low-resolution membrane protein models: Perspectives from multiscale simulations

Membrane receptors constitute major targets for pharmaceutical intervention. Drug design efforts rely on the identification of ligand binding poses. However, the limited experimental structural information available may make this extremely challenging, especially when only low-resolution homology models are accessible. In these cases, the predictions may be improved by molecular dynamics simulation approaches. Here we review recent developments of multiscale, hybrid molecular mechanics/coarse-grained (MM/CG) methods applied to membrane proteins. In particular, we focus on our in-house MM/CG approach. It is especially tailored for G-protein coupled receptors, the largest membrane receptor family in humans. We show that our MM/CG approach is able to capture the atomistic details of the receptor/ligand binding interactions, while keeping the computational cost low by representing the protein frame and the membrane environment in a highly simplified manner. We close this review by discussing ongoing improvements and challenges of the current implementation of our MM/CG code.

F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly

Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications.

RNA structure prediction: from 2D to 3D

We summarize different levels of RNA structure prediction, from classical 2D structure to extended secondary structure and motif-based research toward 3D structure prediction of RNA. We outline the importance of classical secondary structure during all those levels of structure prediction.

A coarse-grained model for assisting the investigation of structure and dynamics of large nucleic acids by ion mobility spectrometry-mass spectrometry

Ion Mobility Spectrometry-Mass Spectrometry (IMS-MS) is a rapidly emerging tool for the investigation of nucleic acid structure and dynamics. IMS-MS determinations can provide valuable information regarding alternative topologies, folding intermediates, and conformational heterogeneities, which are not readily accessible to other analytical techniques. The leading strategies for data interpretation rely on computational and experimental approaches to correctly assign experimental observations to putative structures. A very effective strategy involves the application of molecular dynamics (MD) simulations to predict the structure of the analyte molecule, calculate its collision cross section (CCS), and then compare this computational value with the corresponding experimental data. While this approach works well for small nucleic acid species, analyzing larger nucleic acids of biological interest is hampered by the computational cost associated with capturing their extensive structure and dynamics in all-atom detail. In this report, we describe the implementation of a coarse graining (CG) approach to reduce the cost of the computational methods employed in the data interpretation workflow. Our framework employs a five-bead model to accurately represent each nucleotide in the nucleic acid structure. The beads are appropriately parameterized to enable the direct calculation of CCS values from CG models, thus affording the ability to pursue the analysis of larger, highly dynamic constructs. The validity of this approach was successfully confirmed by the excellent correlation between the CCS values obtained in parallel by all-atom and CG workflows.

Capturing RNA Folding Free Energy with Coarse-Grained Molecular Dynamics Simulations

We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3-4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).

Exploring RNA conformational space under sparse distance restraints

We show that the application of a small number of restraints predicted by coevolution analysis can provide a powerful restriction on the conformational freedom of an RNA molecule. The greatest degree of restriction occurs when a contact is predicted between the distal ends of a pair of adjacent stemloops but even with this location additional flexibilities in the molecule can mask the contribution. Multiple cross-links, especially those including a pseudoknot provided the strongest restraint on conformational freedom with the effect being most apparent in topologically simple folds and less so if the fold is more topologically entwined. Little was expected for large structures (over 300 bases) and although a few strong localised restrictions were observed, they contributed little to the restraint of the overall fold. Although contacts predicted using a correlated mutation analysis can provide some powerful restrictions on the conformational freedom of RNA molecules, they are too erratic in their occurrence and distribution to provide a general approach to the problem of RNA 3D structure prediction from sequence.

Electron Transport in a Dioxygenase-Ferredoxin Complex: Long Range Charge Coupling between the Rieske and Non-Heme Iron Center

Dioxygenase (dOx) utilizes stereospecific oxidation on aromatic molecules; consequently, dOx has potential applications in bioremediation and stereospecific oxidation synthesis. The reactive components of dOx comprise a Rieske structure Cys₂[2Fe-2S]His₂ and a non-heme reactive oxygen center (ROC). Between the Rieske structure and the ROC, a universally conserved Asp residue appears to bridge the two structures forming a Rieske-Asp-ROC triad, where the Asp is known to be essential for electron transfer processes. The Rieske and ROC share hydrogen bonds with Asp through their His ligands; suggesting an ideal network for electron transfer via the carboxyl side chain of Asp. Associated with the dOx is an itinerant charge carrying protein Ferredoxin (Fdx). Depending on the specific cognate, Fdx may also possess either the Rieske structure or a related structure known as 4-Cys-[2Fe-2S] (4-Cys). In this study, we extensively explore, at different levels of theory, the behavior of the individual components (Rieske and ROC) and their interaction together via the Asp using a variety of density function methods, basis sets, and a method known as Generalized Ionic Fragment Approach (GIFA) that permits setting up spin configurations manually. We also report results on the 4-Cys structure for comparison. The individual optimized structures are compared with observed spectroscopic data from the Rieske, 4-Cys and ROC structures (where information is available). The separate pieces are then combined together into a large Rieske-Asp-ROC (donor/bridge/acceptor) complex to estimate the overall coupling between individual components, based on changes to the partial charges. The results suggest that the partial charges are significantly altered when Asp bridges the Rieske and the ROC; hence, long range coupling through hydrogen bonding effects via the intercalated Asp bridge can drastically affect the partial charge distributions compared to the individual isolated structures. The results are consistent with a proton coupled electron transfer mechanism.