A nucleotide-level coarse-grained model of RNA

Precise and Programmable Detection of Mutations Using Ultraspecific Riboregulators

The ability to identify single-nucleotide mutations is critical for probing cell biology and for precise detection of disease. However, the small differences in hybridization energy provided by single-base changes makes identification of these mutations challenging in living cells and complex reaction environments. Here, we report a class of de novo-designed prokaryotic riboregulators that provide ultraspecific RNA detection capabilities in vivo and in cell-free transcription-translation reactions. These single-nucleotide-specific programmable riboregulators (SNIPRs) provide over 100-fold differences in gene expression in response to target RNAs differing by a single nucleotide in E. coli and resolve single epitranscriptomic marks in vitro. By exploiting the programmable SNIPR design, we implement an automated design algorithm to develop riboregulators for a range of mutations associated with cancer, drug resistance, and genetic disorders. Integrating SNIPRs with portable paper-based cell-free reactions enables convenient isothermal detection of cancer-associated mutations from clinical samples and identification of Zika strains through unambiguous colorimetric reactions.

Atomistic to continuum model for studying mechanical properties of RNA nanotubes

With rapid advancements in the emerging field of RNA nanotechnology, its current and potential applications, new important problems arise in our quest to better understand properties of RNA nanocomplexes. In this paper, our focus is on the modeling of RNA nanotubes which are important for many biological processes. These RNA complexes are also important for human beings, with their theurapeutical and biomedical applications discussed vigorously in the literature over the recent years. Here, we develop a continuum model of RNA nanotubes, originally obtained from self assembly of RNA building blocks in the molecular dynamics simulation. Based on the finite element method, we calculate the elastic properties of these nanostructures and provide a relationship between stress and strain induced in the RNA nanotube. We also analyze the variations in the displacement vector along the assembly axis for RNA nanotubes of different sizes. In particular, we show that oscillations in the amplitudes of strains and displacements significantly differ for such RNA nanotubes. These findings are discussed in the context of atomistic simulations and experimental results in this field.

Small RNA Biosensor Design Strategy To Mitigate Off-Analyte Response

Several bottlenecks in the design of current sensor technologies for small noncoding RNA must be addressed. The small size of the sensors and the large number of other nucleotides that may have sequence similarity makes selectivity a real concern. Many of the current sensors have one strand with an exposed region called a toehold. The toehold serves as a place for the analyte nucleic acid strand to bind and initiate competitive displacement of sensors' secondary strands. Since the toehold region is not protected, any endogenous oligonucleotide sequences that are similar or only different by a few nucleic acids will interact with the toehold and cause false signals. To address sensor selectivity, we investigated how the toehold location in the sensor impacts the sensitivity and selectivity for the analyte of interest. We will discuss the differences in sensitivity and selectivity for a miR-146a-5p biosensor in the presence of different naturally occurring mismatch sequences. We found that altering the toehold location lowered the rate of the false signal from off-analyte microRNA by upward of 20 percentage points. Detection limits as low as 56 pM were observed when the sensor concentration was 5 nM. The findings herein are broadly applicable to other small and large RNAs as well as other types of sensing platforms.

Brief Comparison between Experimental and Computationally Generated Ensembles of RNA Dinucleotides

The computational modeling of RNA and its interactions is of crucial importance for the understanding of the wide variety of biological functions it performs. Among these approaches, several coarse-grained models employ structural databases to derive their energy functions or to define scoring functions for structure prediction purposes. In many cases, the parametrization is done by using as a reference a set of experimentally determined structures or data obtained from Molecular Dynamics simulations. Since the two choices are clearly different, we present here a brief comparison of the essential spaces of a set of conformations of two topologically connected nucleotides generated by these means. We find that when the nucleotides are embedded into a duplex, the essential spaces of both ensembles are quite restricted and do not differ substantially. Nevertheless, when the conformational space of a free dinucleoside monophosphate simulation is compared against a similar set obtained from the structural database, the differences of the essential spaces are considerable. In addition, we show a brief comparison of a specific distance between the nucleotides which correlates with the sugar pucker of the first nucleotide and analyze its distribution under similar conditions.

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.

3D structure stability of the HIV-1 TAR RNA in ion solutions: A coarse-grained model study

As an extremely common structural motif, RNA hairpins with bulge loops [e.g., the human immunodeficiency virus type 1 (HIV-1) transactivation response (TAR) RNA] can play essential roles in normal cellular processes by binding to proteins and small ligands, which could be very dependent on their three-dimensional (3D) structures and stability. Although the structures and conformational dynamics of the HIV-1 TAR RNA have been extensively studied, there are few investigations on the thermodynamic stability of the TAR RNA, especially in ion solutions, and the existing studies also have some divergence on the unfolding process of the RNA. Here, we employed our previously developed coarse-grained model with implicit salt to predict the 3D structure, stability, and unfolding pathway for the HIV-1 TAR RNA over a wide range of ion concentrations. As compared with the extensive experimental/theoretical results, the present model can give reliable predictions on the 3D structure stability of the TAR RNA from the sequence. Based on the predictions, our further comprehensive analyses on the stability of the TAR RNA as well as its variants revealed that the unfolding pathway of an RNA hairpin with a bulge loop is mainly determined by the relative stability between different states (folded state, intermediate state, and unfolded state) and the strength of the coaxial stacking between two stems in folded structures, both of which can be apparently modulated by the ion concentrations as well as the sequences.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami

Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.

RNA structure interactions and ribonucleoprotein processes of the influenza A virus

In one more years, we will ‘celebrate’ an exact centenary of the Spanish flu pandemic. With the rapid evolution of the influenza virus, the possibility of novel pandemic remains ever a concern. This review covers our current knowledge of the influenza A virus: on the role of RNA in translation, replication, what is known of the expressed proteins and the protein products generated from alternative splicing, and on the role of base pairing in RNA structure. We highlight the main events associated with viral entry into the cell, the transcription and replication process, an export of the viral genetic material from the nucleus and the final release of the virus. We discuss the observed potential roles of RNA secondary structure (the RNA base-pairing arrangement) and RNA/RNA interactions in this scheme.

Coarse-grained dynamic RNA titration simulations

Electrostatic interactions play a pivotal role in many biomolecular processes. The molecular organization and function in biological systems are largely determined by these interactions. Owing to the highly negative charge of RNA, the effect is expected to be more pronounced in this system. Moreover, RNA base pairing is dependent on the charge of the base, giving rise to alternative secondary and tertiary structures. The equilibrium between uncharged and charged bases is regulated by the solution pH, which is therefore a key environmental condition influencing the molecule's structure and behaviour. By means of constant-pH Monte Carlo simulations based on a fast proton titration scheme, coupled with the coarse-grained model HiRE-RNA, molecular dynamic simulations of RNA molecules at constant pH enable us to explore the RNA conformational plasticity at different pH values as well as to compute electrostatic properties as local pK _a values for each nucleotide.

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.

RNA3DCNN: Local and global quality assessments of RNA 3D structures using 3D deep convolutional neural networks

Quality assessment is essential for the computational prediction and design of RNA tertiary structures. To date, several knowledge-based statistical potentials have been proposed and proved to be effective in identifying native and near-native RNA structures. All these potentials are based on the inverse Boltzmann formula, while differing in the choice of the geometrical descriptor, reference state, and training dataset. Via an approach that diverges completely from the conventional statistical potentials, our work explored the power of a 3D convolutional neural network (CNN)-based approach as a quality evaluator for RNA 3D structures, which used a 3D grid representation of the structure as input without extracting features manually. The RNA structures were evaluated by examining each nucleotide, so our method can also provide local quality assessment. Two sets of training samples were built. The first one included 1 million samples generated by high-temperature molecular dynamics (MD) simulations and the second one included 1 million samples generated by Monte Carlo (MC) structure prediction. Both MD and MC procedures were performed for a non-redundant set of 414 RNAs. For two training datasets (one including only MD training samples and the other including both MD and MC training samples), we trained two neural networks, named RNA3DCNN_MD and RNA3DCNN_MDMC, respectively. The former is suitable for assessing near-native structures, while the latter is suitable for assessing structures covering large structural space. We tested the performance of our method and made comparisons with four other traditional scoring functions. On two of three test datasets, our method performed similarly to the state-of-the-art traditional scoring function, and on the third test dataset, our method was far superior to other scoring functions. Our method can be downloaded from https://github.com/lijunRNA/RNA3DCNN.

Modeling Structure, Stability, and Flexibility of Double-Stranded RNAs in Salt Solutions

Double-stranded (ds) RNAs play essential roles in many processes of cell metabolism. The knowledge of three-dimensional (3D) structure, stability, and flexibility of dsRNAs in salt solutions is important for understanding their biological functions. In this work, we further developed our previously proposed coarse-grained model to predict 3D structure, stability, and flexibility for dsRNAs in monovalent and divalent ion solutions through involving an implicit structure-based electrostatic potential. The model can make reliable predictions for 3D structures of extensive dsRNAs with/without bulge/internal loops from their sequences, and the involvement of the structure-based electrostatic potential and corresponding ion condition can improve the predictions for 3D structures of dsRNAs in ion solutions. Furthermore, the model can make good predictions for thermal stability for extensive dsRNAs over the wide range of monovalent/divalent ion concentrations, and our analyses show that the thermally unfolding pathway of dsRNA is generally dependent on its length as well as its sequence. In addition, the model was employed to examine the salt-dependent flexibility of a dsRNA helix, and the calculated salt-dependent persistence lengths are in good accordance with experiments.

Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations

A coarse-grained model for simulating structural properties of double-stranded RNA is developed with parameters obtained from quantum-mechanical calculations. This model follows previous parametrization for double-stranded DNA, which is based on mapping the all-atom picture to a coarse-grained four-bead scheme. Chemical and structural differences between RNA and DNA have been taken into account for the model development. The parametrization is based on simulations using density functional theory (DFT) on separate units of the RNA molecule without implementing experimental data. The total energy is decomposed into four terms of physical significance: hydrogen bonding interaction, stacking interactions, backbone interactions, and electrostatic interactions. The first three interactions are treated within DFT, whereas the last one is included within a mean field approximation. Our double-stranded RNA coarse-grained model predicts stable helical structures for RNA. Other characteristics, such as structural or mechanical properties are reproduced with a very good accuracy. The development of the coarse-grained model for RNA allows extending the spatial and temporal length scales accessed by computer simulations and being able to model RNA-related biophysical processes, as well as novel RNA nanostructures.

Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions

RNA pseudoknots are a kind of minimal RNA tertiary structural motifs, and their three-dimensional (3D) structures and stability play essential roles in a variety of biological functions. Therefore, to predict 3D structures and stability of RNA pseudoknots is essential for understanding their functions. In the work, we employed our previously developed coarse-grained model with implicit salt to make extensive predictions and comprehensive analyses on the 3D structures and stability for RNA pseudoknots in monovalent/divalent ion solutions. The comparisons with available experimental data show that our model can successfully predict the 3D structures of RNA pseudoknots from their sequences, and can also make reliable predictions for the stability of RNA pseudoknots with different lengths and sequences over a wide range of monovalent/divalent ion concentrations. Furthermore, we made comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions. Our analyses for extensive pseudokonts and the wide range of monovalent/divalent ion concentrations verify that the unfolding pathway of RNA pseudoknots is mainly dependent on the relative stability of unfolded intermediate states, and show that the unfolding pathway of RNA pseudoknots can be significantly modulated by their sequences and solution ion conditions.

Isothermal folding of a light-up bio-orthogonal RNA origami nanoribbon

RNA presents intringuing roles in many cellular processes and its versatility underpins many different applications in synthetic biology. Nonetheless, RNA origami as a method for nanofabrication is not yet fully explored and the majority of RNA nanostructures are based on natural pre-folded RNA. Here we describe a biologically inert and uniquely addressable RNA origami scaffold that self-assembles into a nanoribbon by seven staple strands. An algorithm is applied to generate a synthetic De Bruijn scaffold sequence that is characterized by the lack of biologically active sites and repetitions larger than a predetermined design parameter. This RNA scaffold and the complementary staples fold in a physiologically compatible isothermal condition. In order to monitor the folding, we designed a new split Broccoli aptamer system. The aptamer is divided into two nonfunctional sequences each of which is integrated into the 5' or 3' end of two staple strands complementary to the RNA scaffold. Using fluorescence measurements and in-gel imaging, we demonstrate that once RNA origami assembly occurs, the split aptamer sequences are brought into close proximity forming the aptamer and turning on the fluorescence. This light-up 'bio-orthogonal' RNA origami provides a prototype that can have potential for in vivo origami applications.

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.

IsRNA: An Iterative Simulated Reference State Approach to Modeling Correlated Interactions in RNA Folding

Coarse-grained RNA folding models promise great potential for RNA structure prediction. A key component in a coarse-grained folding model is the force field. One of the challenges in the coarse-grained force field calculation is how to treat the correlation between the different degrees of freedoms. Here, we describe a new approach (IsRNA) to extract the correlated energy functions from the known structures. Through iterative molecular dynamics simulations, we build the correlation effects into the reference states, from which we extract the energy functions. The validity of IsRNA is supported by the close agreement between the simulated Boltzmann-like probability distributions for all the structure parameters and those observed from the experimentally determined structures. The correlated energy functions derived here may provide a new tool for RNA 3D structure prediction.

A nucleobase-centered coarse-grained representation for structure prediction of RNA motifs

We introduce the SPlit-and-conQueR (SPQR) model, a coarse-grained (CG) representation of RNA designed for structure prediction and refinement. In our approach, the representation of a nucleotide consists of a point particle for the phosphate group and an anisotropic particle for the nucleoside. The interactions are, in principle, knowledge-based potentials inspired by the $\mathcal {E}$SCORE function, a base-centered scoring function. However, a special treatment is given to base-pairing interactions and certain geometrical conformations which are lost in a raw knowledge-based model. This results in a representation able to describe planar canonical and non-canonical base pairs and base-phosphate interactions and to distinguish sugar puckers and glycosidic torsion conformations. The model is applied to the folding of several structures, including duplexes with internal loops of non-canonical base pairs, tetraloops, junctions and a pseudoknot. For the majority of these systems, experimental structures are correctly predicted at the level of individual contacts. We also propose a method for efficiently reintroducing atomistic detail from the CG representation.

Dynamic Histogram Analysis To Determine Free Energies and Rates from Biased Simulations

We present an algorithm to calculate free energies and rates from molecular simulations on biased potential energy surfaces. As input, it uses the accumulated times spent in each state or bin of a histogram and counts of transitions between them. Optimal unbiased equilibrium free energies for each of the states/bins are then obtained by maximizing the likelihood of a master equation (i.e., first-order kinetic rate model). The resulting free energies also determine the optimal rate coefficients for transitions between the states or bins on the biased potentials. Unbiased rates can be estimated, e.g., by imposing a linear free energy condition in the likelihood maximization. The resulting "dynamic histogram analysis method extended to detailed balance" (DHAMed) builds on the DHAM method. It is also closely related to the transition-based reweighting analysis method (TRAM) and the discrete TRAM (dTRAM). However, in the continuous-time formulation of DHAMed, the detailed balance constraints are more easily accounted for, resulting in compact expressions amenable to efficient numerical treatment. DHAMed produces accurate free energies in cases where the common weighted-histogram analysis method (WHAM) for umbrella sampling fails because of slow dynamics within the windows. Even in the limit of completely uncorrelated data, where WHAM is optimal in the maximum-likelihood sense, DHAMed results are nearly indistinguishable. We illustrate DHAMed with applications to ion channel conduction, RNA duplex formation, α-helix folding, and rate calculations from accelerated molecular dynamics. DHAMed can also be used to construct Markov state models from biased or replica-exchange molecular dynamics simulations. By using binless WHAM formulated as a numerical minimization problem, the bias factors for the individual states can be determined efficiently in a preprocessing step and, if needed, optimized globally afterward.

Optimization of RNA 3D structure prediction using evolutionary restraints of nucleotide-nucleotide interactions from direct coupling analysis

Direct coupling analysis of nucleotide coevolution provides a novel approach to identify which nucleotides in an RNA molecule are likely in direct contact, and this information obtained from sequence only can be used to predict RNA 3D structures with much improved accuracy. Here we present an efficient method that incorporates this information into current RNA 3D structure prediction methods, specifically 3dRNA. Our method makes much more accurate RNA 3D structure prediction than the original 3dRNA as well as other existing prediction methods that used the direct coupling analysis. In particular our method demonstrates a significant improvement in predicting multi-branch junction conformations, a major bottleneck for RNA 3D structure prediction. We also show that our method can be used to optimize the predictions by other methods. These results indicate that optimization of RNA 3D structure prediction using evolutionary restraints of nucleotide-nucleotide interactions from direct coupling analysis offers an efficient way for accurate RNA tertiary structure predictions.

An asymmetric mesoscopic model for single bulges in RNA

Simple one-dimensional DNA or RNA mesoscopic models are of interest for their computational efficiency while retaining the key elements of the molecular interactions. However, they only deal with perfectly formed DNA or RNA double helices and consider the intra-strand interactions to be the same on both strands. This makes it difficult to describe highly asymmetric structures such as bulges and loops and, for instance, prevents the application of mesoscopic models to determine RNA secondary structures. Here we derived the conditions for the Peyrard-Bishop mesoscopic model to overcome these limitations and applied it to the calculation of single bulges, the smallest and simplest of these asymmetric structures. We found that these theoretical conditions can indeed be applied to any situation where stacking asymmetry needs to be considered. The full set of parameters for group I RNA bulges was determined from experimental melting temperatures using an optimization procedure, and we also calculated average opening profiles for several RNA sequences. We found that guanosine bulges show the strongest perturbation on their neighboring base pairs, considerably reducing the on-site interactions of their neighboring base pairs.

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.

What Can Human-Guided Simulations Bring to RNA Folding?

Inspired by the recent success of scientific-discovery games for predicting protein tertiary and RNA secondary structures, we have developed an open software for coarse-grained RNA folding simulations, guided by human intuition. To determine the extent to which interactive simulations can accurately predict 3D RNA structures of increasing complexity and lengths (four RNAs with 22-47 nucleotides), an interactive experiment was conducted with 141 participants who had very little knowledge of nucleic acids systems and computer simulations, and had received only a brief description of the important forces stabilizing RNA structures. Their structures and full trajectories have been analyzed statistically and compared to standard replica exchange molecular dynamics simulations. Our analyses show that participants gain easily chemical intelligence to fold simple and nontrivial topologies, with little computer time, and this result opens the door for the use of human-guided simulations to RNA folding. Our experiment shows that interactive simulations have better chances of success when the user widely explores the conformational space. Interestingly, providing on-the-fly feedback of the root mean square deviation with respect to the experimental structure did not improve the quality of the proposed models.

Martini Coarse-Grained Force Field: Extension to RNA

RNA has an important role not only as the messenger of genetic information but also as a regulator of gene expression. Given its central role in cell biology, there is significant interest in studying the structural and dynamic behavior of RNA in relation to other biomolecules. Coarse-grain molecular dynamics simulations are a key tool to that end. Here, we have extended the coarse-grain Martini force field to include RNA after our recent extension to DNA. In the same way DNA was modeled, the tertiary structure of RNA is constrained using an elastic network. This model, therefore, is not designed for applications involving RNA folding but rather offers a stable RNA structure for studying RNA interactions with other (bio)molecules. The RNA model is compatible with all other Martini models and opens the way to large-scale explicit-solvent molecular dynamics simulations of complex systems involving RNA.

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.

Coarse-grained modelling of supercoiled RNA

We study the behaviour of double-stranded RNA under twist and tension using oxRNA, a recently developed coarse-grained model of RNA. Introducing explicit salt-dependence into the model allows us to directly compare our results to data from recent single-molecule experiments. The model reproduces extension curves as a function of twist and stretching force, including the buckling transition and the behaviour of plectoneme structures. For negative supercoiling, we predict denaturation bubble formation in plectoneme end-loops, suggesting preferential plectoneme localisation in weak base sequences. OxRNA exhibits a positive twist-stretch coupling constant, in agreement with recent experimental observations.

Predicting 3D Structure, Flexibility, and Stability of RNA Hairpins in Monovalent and Divalent Ion Solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility, and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we further develop the model by improving the implicit-salt electrostatic potential and including a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. The model presented here can predict 3D structures of RNA hairpins with bulges/internal loops (<77 nucleotides) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy compared to the experimental data; the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different lengths at several divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

Structure Prediction of RNA Loops with a Probabilistic Approach

The knowledge of the tertiary structure of RNA loops is important for understanding their functions. In this work we develop an efficient approach named RNApps, specifically designed for predicting the tertiary structure of RNA loops, including hairpin loops, internal loops, and multi-way junction loops. It includes a probabilistic coarse-grained RNA model, an all-atom statistical energy function, a sequential Monte Carlo growth algorithm, and a simulated annealing procedure. The approach is tested with a dataset including nine RNA loops, a 23S ribosomal RNA, and a large dataset containing 876 RNAs. The performance is evaluated and compared with a homology modeling based predictor and an ab initio predictor. It is found that RNApps has comparable performance with the former one and outdoes the latter in terms of structure predictions. The approach holds great promise for accurate and efficient RNA tertiary structure prediction.

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

Introducing improved structural properties and salt dependence into a coarse-grained model of DNA

We introduce an extended version of oxDNA, a coarse-grained model of deoxyribonucleic acid (DNA) designed to capture the thermodynamic, structural, and mechanical properties of single- and double-stranded DNA. By including explicit major and minor grooves and by slightly modifying the coaxial stacking and backbone-backbone interactions, we improve the ability of the model to treat large (kilobase-pair) structures, such as DNA origami, which are sensitive to these geometric features. Further, we extend the model, which was previously parameterised to just one salt concentration ([Na(+)] = 0.5M), so that it can be used for a range of salt concentrations including those corresponding to physiological conditions. Finally, we use new experimental data to parameterise the oxDNA potential so that consecutive adenine bases stack with a different strength to consecutive thymine bases, a feature which allows a more accurate treatment of systems where the flexibility of single-stranded regions is important. We illustrate the new possibilities opened up by the updated model, oxDNA2, by presenting results from simulations of the structure of large DNA objects and by using the model to investigate some salt-dependent properties of DNA.

Holliday Junction Thermodynamics and Structure: Coarse-Grained Simulations and Experiments

Holliday junctions play a central role in genetic recombination, DNA repair and other cellular processes. We combine simulations and experiments to evaluate the ability of the 3SPN.2 model, a coarse-grained representation designed to mimic B-DNA, to predict the properties of DNA Holliday junctions. The model reproduces many experimentally determined aspects of junction structure and stability, including the temperature dependence of melting on salt concentration, the bias between open and stacked conformations, the relative populations of conformers at high salt concentration, and the inter-duplex angle (IDA) between arms. We also obtain a close correspondence between the junction structure evaluated by all-atom and coarse-grained simulations. We predict that, for salt concentrations at physiological and higher levels, the populations of the stacked conformers are independent of salt concentration, and directly observe proposed tetrahedral intermediate sub-states implicated in conformational transitions. Our findings demonstrate that the 3SPN.2 model captures junction properties that are inaccessible to all-atom studies, opening the possibility to simulate complex aspects of junction behavior.

Modelling toehold-mediated RNA strand displacement

We study the thermodynamics and kinetics of an RNA toehold-mediated strand displacement reaction with a recently developed coarse-grained model of RNA. Strand displacement, during which a single strand displaces a different strand previously bound to a complementary substrate strand, is an essential mechanism in active nucleic acid nanotechnology and has also been hypothesized to occur in vivo. We study the rate of displacement reactions as a function of the length of the toehold and temperature and make two experimentally testable predictions: that the displacement is faster if the toehold is placed at the 5' end of the substrate; and that the displacement slows down with increasing temperature for longer toeholds.

SimRNA: a coarse-grained method for RNA folding simulations and 3D structure prediction

RNA molecules play fundamental roles in cellular processes. Their function and interactions with other biomolecules are dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is laborious and challenging, and therefore, the majority of known RNAs remain structurally uncharacterized. Here, we present SimRNA: a new method for computational RNA 3D structure prediction, which uses a coarse-grained representation, relies on the Monte Carlo method for sampling the conformational space, and employs a statistical potential to approximate the energy and identify conformations that correspond to biologically relevant structures. SimRNA can fold RNA molecules using only sequence information, and, on established test sequences, it recapitulates secondary structure with high accuracy, including correct prediction of pseudoknots. For modeling of complex 3D structures, it can use additional restraints, derived from experimental or computational analyses, including information about secondary structure and/or long-range contacts. SimRNA also can be used to analyze conformational landscapes and identify potential alternative structures.

Computational modeling of RNA 3D structures and interactions

RNA molecules have key functions in cellular processes beyond being carriers of protein-coding information. These functions are often dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is difficult, which has prompted the development of computational methods for structure prediction from sequence. Recent progress in 3D structure modeling of RNA and emerging approaches for predicting RNA interactions with ions, ligands and proteins have been stimulated by successes in protein 3D structure modeling.

Computational Approaches to Nucleic Acid Origami

Recent advances in experimental DNA origami have dramatically expanded the horizon of DNA nanotechnology. Complex 3D suprastructures have been designed and developed using DNA origami with applications in biomaterial science, nanomedicine, nanorobotics, and molecular computation. Ribonucleic acid (RNA) origami has recently been realized as a new approach. Similar to DNA, RNA molecules can be designed to form complex 3D structures through complementary base pairings. RNA origami structures are, however, more compact and more thermodynamically stable due to RNA's non-canonical base pairing and tertiary interactions. With all these advantages, the development of RNA origami lags behind DNA origami by a large gap. Furthermore, although computational methods have proven to be effective in designing DNA and RNA origami structures and in their evaluation, advances in computational nucleic acid origami is even more limited. In this paper, we review major milestones in experimental and computational DNA and RNA origami and present current challenges in these fields. We believe collaboration between experimental nanotechnologists and computer scientists are critical for advancing these new research paradigms.

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

Coarse-Grained HiRE-RNA Model for ab Initio RNA Folding beyond Simple Molecules, Including Noncanonical and Multiple Base Pairings

HiRE-RNA is a coarse-grained model for RNA structure prediction and the dynamical study of RNA folding. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking, we show that noncanonical and multiple base interactions are necessary to capture the full physical behavior of complex RNAs. In this paper, we give a full account of the model and present results on the folding, stability, and free energy surfaces of 16 systems with 12 to 76 nucleotides of increasingly complex architectures, ranging from monomers to dimers, using a total of 850 μs of simulation time.