HiRE-RNA: a high resolution coarse-grained energy model for RNA

An Intermediate Resolution Model of RNA Dynamics and Phase Separation with Explicit Mg 2 +

RNAs are major drivers of phase separation in the formation of biomolecular condensates. Recent studies suggest that RNAs can also undergo protein-free phase separation in the presence of divalent ions or crowding agents. Much remains to be understood regarding how the complex interplay of base stacking, base pairing, electrostatics, ion interactions, and structural propensities governs the phase behaviour of RNAs. Here we develop an intermediate resolution model for condensates of RNAs (iConRNA) that can capture key local and long-range structure features of dynamic RNAs and simulate their spontaneous phase transitions in the presence ofMg 2 + . Representing each nucleotide using 6 or 7 beads, iConRNA considers specific RNA base stacking and pairing interactions and includes explicitMg 2 + ions to studyMg 2 + -induced phase separation. Parametrized using theoretical and experimental data, the model can correctly reproduce the chain properties of A-form helical poly(rA) and coil poly(rU), and essential structures of several RNA hairpins. With an effectiveMg 2 + ion model, iConRNA simulations successfully recapitulate the experimentally observed lower critical solution temperature (LCST)-type phase separation of poly(rA) and the dissolution of poly(rU). Furthermore, the phase diagrams of CAG/CUG/CUU-repeat RNAs correctly reproduce the experimentally observed sequence- and length-dependence of phase separation propensity. These results suggest that iConRNA can be a viable tool for studying homotypic RNA and potentially heterotypic RNA-protein phase separations.

Machine learning in RNA structure prediction: Advances and challenges

RNA molecules play a crucial role in various biological processes, with their functionality closely tied to their structures. The remarkable advancements in machine learning techniques for protein structure prediction have shown promise in the field of RNA structure prediction. In this perspective, we discuss the advances and challenges encountered in constructing machine learning-based models for RNA structure prediction. We explore topics including model building strategies, specific challenges involved in predicting RNA secondary (2D) and tertiary (3D) structures, and approaches to these challenges. In addition, we highlight the advantages and challenges of constructing RNA language models. Given the rapid advances of machine learning techniques, we anticipate that machine learning-based models will serve as important tools for predicting RNA structures, thereby enriching our understanding of RNA structures and their corresponding functions.

Comparative analysis of RNA 3D structure prediction methods: towards enhanced modeling of RNA-ligand interactions

Accurate RNA structure models are crucial for designing small molecule ligands that modulate their functions. This study assesses six standalone RNA 3D structure prediction methods-DeepFoldRNA, RhoFold, BRiQ, FARFAR2, SimRNA and Vfold2, excluding web-based tools due to intellectual property concerns. We focus on reproducing the RNA structure existing in RNA-small molecule complexes, particularly on the ability to model ligand binding sites. Using a comprehensive set of RNA structures from the PDB, which includes diverse structural elements, we found that machine learning (ML)-based methods effectively predict global RNA folds but are less accurate with local interactions. Conversely, non-ML-based methods demonstrate higher precision in modeling intramolecular interactions, particularly with secondary structure restraints. Importantly, ligand-binding site accuracy can remain sufficiently high for practical use, even if the overall model quality is not optimal. With the recent release of AlphaFold 3, we included this advanced method in our tests. Benchmark subsets containing new structures, not used in the training of the tested ML methods, show that AlphaFold 3's performance was comparable to other ML-based methods, albeit with some challenges in accurately modeling ligand binding sites. This study underscores the importance of enhancing binding site prediction accuracy and the challenges in modeling RNA-ligand interactions accurately.

ANNaMo: Coarse-grained modeling for folding and assembly of RNA and DNA systems

The folding of RNA and DNA strands plays crucial roles in biological systems and bionanotechnology. However, studying these processes with high-resolution numerical models is beyond current computational capabilities due to the timescales and system sizes involved. In this article, we present a new coarse-grained model for investigating the folding dynamics of nucleic acids. Our model represents three nucleotides with a patchy particle and is parameterized using well-established nearest-neighbor models. Thanks to the reduction of degrees of freedom and to a bond-swapping mechanism, our model allows for simulations at timescales and length scales that are currently inaccessible to more detailed models. To validate the performance of our model, we conducted extensive simulations of various systems: We examined the thermodynamics of DNA hairpins, capturing their stability and structural transitions, the folding of an MMTV pseudoknot, which is a complex RNA structure involved in viral replication, and also explored the folding of an RNA tile containing a k-type pseudoknot. Finally, we evaluated the performance of the new model in reproducing the melting temperatures of oligomers and the dependence on the toehold length of the displacement rate in toehold-mediated displacement processes, a key reaction used in molecular computing. All in all, the successful reproduction of experimental data and favorable comparisons with existing coarse-grained models validate the effectiveness of the new model.

Frontiers and Challenges of Computing ncRNAs Biogenesis, Function and Modulation

Non-coding RNAs (ncRNAs), generated from nonprotein coding DNA sequences, constitute 98-99% of the human genome. Non-coding RNAs encompass diverse functional classes, including microRNAs, small interfering RNAs, PIWI-interacting RNAs, small nuclear RNAs, small nucleolar RNAs, and long non-coding RNAs. With critical involvement in gene expression and regulation across various biological and physiopathological contexts, such as neuronal disorders, immune responses, cardiovascular diseases, and cancer, non-coding RNAs are emerging as disease biomarkers and therapeutic targets. In this review, after providing an overview of non-coding RNAs' role in cell homeostasis, we illustrate the potential and the challenges of state-of-the-art computational methods exploited to study non-coding RNAs biogenesis, function, and modulation. This can be done by directly targeting them with small molecules or by altering their expression by targeting the cellular engines underlying their biosynthesis. Drawing from applications, also taken from our work, we showcase the significance and role of computer simulations in uncovering fundamental facets of ncRNA mechanisms and modulation. This information may set the basis to advance gene modulation tools and therapeutic strategies to address unmet medical needs.

RNA G-quadruplex folding is a multi-pathway process driven by conformational entropy

The kinetics of folding is crucial for the function of many regulatory RNAs including RNA G-quadruplexes (rG4s). Here, we characterize the folding pathways of a G-quadruplex from the telomeric repeat-containing RNA by combining all-atom molecular dynamics and coarse-grained simulations with circular dichroism experiments. The quadruplex fold is stabilized by cations and thus, the ion atmosphere forming a double layer surrounding the highly charged quadruplex guides the folding process. To capture the ionic double layer in implicit solvent coarse-grained simulations correctly, we develop a matching procedure based on all-atom simulations in explicit water. The procedure yields quantitative agreement between simulations and experiments as judged by the populations of folded and unfolded states at different salt concentrations and temperatures. Subsequently, we show that coarse-grained simulations with a resolution of three interaction sites per nucleotide are well suited to resolve the folding pathways and their intermediate states. The results reveal that the folding progresses from unpaired chain via hairpin, triplex and double-hairpin constellations to the final folded structure. The two- and three-strand intermediates are stabilized by transient Hoogsteen interactions. Each pathway passes through two on-pathway intermediates. We hypothesize that conformational entropy is a hallmark of rG4 folding. Conformational entropy leads to the observed branched multi-pathway folding process for TERRA25. We corroborate this hypothesis by presenting the free energy landscapes and folding pathways of four rG4 systems with varying loop length.

RNA regulates cohesiveness and porosity of a biological condensate

Biological condensates have emerged as key elements of a biological cell function, concentrating disparate biomolecules to accomplish specific biological tasks. RNA was identified as a key ingredient of such condensates, however, its effect on the physical properties of the condensate was found to depend on the condensate's composition while its effect on the microstructure has remained elusive. Here, we characterize the physical properties and the microstructure of a protein-RNA condensate by means of large-scale coarse-grained (CG) molecular dynamics simulations. By developing a custom CG model of RNA compatible with a popular CG model of proteins, we systematically investigate the structural, thermodynamic, and kinetic properties of condensate droplets containing thousands of individual protein and RNA molecules over a range of temperatures. While we find RNA to increase the condensate's cohesiveness, its effect on the condensate's fluidity is more nuanced with longer molecules compacting the condensate and making it less fluid. We show that a biological condensate has a sponge-like morphology of interconnected channels of size that increases with temperature and decreases in the presence of RNA. Our results suggest that longer RNA form a dynamic scaffold within a condensate, regulating not only its fluidity but also permeability to intruder molecules.

Quantifying RNA structures and interactions with a unified reduced chain representation model

RNA is a pivotal molecule that plays critical roles in various cellular processes. Quantifying RNA structures and interactions is essential to understanding RNA function and developing RNA-based therapeutics. Using a unified five-bead model and a non-redundant database, this paper investigates the structural features and interactions of five commonly occurring RNA motifs, i.e., double-stranded helices, hairpin loops, internal/bulge loops, multi-branched junctions, and single-stranded terminal tails. Analyzing detailed distributions of RNA local structural features and base-base interactions reveals a preference for helical structures in both local backbone structures and base orientations. The interactions between adjacent bases exhibit motif-specific and sequence-dependent characteristics, reflecting the distinct topological constraints imposed by different loop-helix connection modes and the varying pairing and stacking interactions among different sequences. These findings shed light on the stability of RNA helices, emphasizing their significance in providing dominant base pairing and stacking interactions for RNA structures and stability. The four non-helix motifs encompass unpaired nucleotide loops and exhibit diverse base-base interactions, contributing to the structural diversity observed in RNA. Overall, the complexity of RNA structure arises from the intricate interplay of base-base interactions.

Computational Modeling of DNA 3D Structures: From Dynamics and Mechanics to Folding

DNA carries the genetic information required for the synthesis of RNA and proteins and plays an important role in many processes of biological development. Understanding the three-dimensional (3D) structures and dynamics of DNA is crucial for understanding their biological functions and guiding the development of novel materials. In this review, we discuss the recent advancements in computer methods for studying DNA 3D structures. This includes molecular dynamics simulations to analyze DNA dynamics, flexibility, and ion binding. We also explore various coarse-grained models used for DNA structure prediction or folding, along with fragment assembly methods for constructing DNA 3D structures. Furthermore, we also discuss the advantages and disadvantages of these methods and highlight their differences.

Molecular Complementarity of Proteomimetic Materials for Target-Specific Recognition and Recognition-Mediated Complex Functions

As biomolecules essential for sustaining life, proteins are generated from long chains of 20 different α-amino acids that are folded into unique 3D structures. In particular, many proteins have molecular recognition functions owing to their binding pockets, which have complementary shapes, charges, and polarities for specific targets, making these biopolymers unique and highly valuable for biomedical and biocatalytic applications. Based on the understanding of protein structures and microenvironments, molecular complementarity can be exhibited by synthesizable and modifiable materials. This has prompted researchers to explore the proteomimetic potentials of a diverse range of materials, including biologically available peptides and oligonucleotides, synthetic supramolecules, inorganic molecules, and related coordination networks. To fully resemble a protein, proteomimetic materials perform the molecular recognition to mediate complex molecular functions, such as allosteric regulation, signal transduction, enzymatic reactions, and stimuli-responsive motions; this can also expand the landscape of their potential bio-applications. This review focuses on the recognitive aspects of proteomimetic designs derived for individual materials and their conformations. Recent progress provides insights to help guide the development of advanced protein mimicry with material heterogeneity, design modularity, and tailored functionality. The perspectives and challenges of current proteomimetic designs and tools are also discussed in relation to future applications.

RNAJP: enhanced RNA 3D structure predictions with non-canonical interactions and global topology sampling

RNA 3D structures are critical for understanding their functions. However, only a limited number of RNA structures have been experimentally solved, so computational prediction methods are highly desirable. Nevertheless, accurate prediction of RNA 3D structures, especially those containing multiway junctions, remains a significant challenge, mainly due to the complicated non-canonical base pairing and stacking interactions in the junction loops and the possible long-range interactions between loop structures. Here we present RNAJP ('RNA Junction Prediction'), a nucleotide- and helix-level coarse-grained model for the prediction of RNA 3D structures, particularly junction structures, from a given 2D structure. Through global sampling of the 3D arrangements of the helices in junctions using molecular dynamics simulations and in explicit consideration of non-canonical base pairing and base stacking interactions as well as long-range loop-loop interactions, the model can provide significantly improved predictions for multibranched junction structures than existing methods. Moreover, integrated with additional restraints from experiments, such as junction topology and long-range interactions, the model may serve as a useful structure generator for various applications.

Internal Normal Mode Analysis Applied to RNA Flexibility and Conformational Changes

We investigated the capability of internal normal modes to reproduce RNA flexibility and predict observed RNA conformational changes and, notably, those induced by the formation of RNA-protein and RNA-ligand complexes. Here, we extended our iNMA approach developed for proteins to study RNA molecules using a simplified representation of the RNA structure and its potential energy. Three data sets were also created to investigate different aspects. Despite all the approximations, our study shows that iNMA is a suitable method to take into account RNA flexibility and describe its conformational changes opening the route to its applicability in any integrative approach where these properties are crucial.

RNA origami: design, simulation and application

Design strategies for DNA and RNA nanostructures have developed along parallel lines for the past 30 years, from small structural motifs derived from biology to large 'origami' structures with thousands to tens of thousands of bases. With the recent publication of numerous RNA origami structures and improved design methods-even permitting co-transcriptional folding of kilobase-sized structures - the RNA nanotechnolgy field is at an inflection point. Here, we review the key achievements which inspired and enabled RNA origami design and draw comparisons with the development and applications of DNA origami structures. We further present the available computational tools for the design and the simulation, which will be key to the growth of the RNA origami community. Finally, we portray the transition from RNA origami structure to function. Several functional RNA origami structures exist already, their expression in cells has been demonstrated and first applications in cell biology have already been realized. Overall, we foresee that the fast-paced RNA origami field will provide new molecular hardware for biophysics, synthetic biology and biomedicine, complementing the DNA origami toolbox.

Advances in RNA 3D Structure Prediction

RNA molecules carry out various cellular functions, and understanding the mechanisms behind their functions requires the knowledge of their 3D structures. Different types of computational methods have been developed to model RNA 3D structures over the past decade. These methods were widely used by researchers although their performance needs to be further improved. Recently, along with these traditional methods, machine-learning techniques have been increasingly applied to RNA 3D structure prediction and show significant improvement in performance. Here we shall give a brief review of the traditional methods and recent related advances in machine-learning approaches for RNA 3D structure prediction.

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

The three-dimensional (3D) structure and stability of DNA are essential to understand/control their biological functions and aid the development of novel materials. In this work, we present a coarse-grained (CG) model for DNA based on the RNA CG model proposed by us, to predict 3D structures and stability for both dsDNA and ssDNA from the sequence. Combined with a Monte Carlo simulated annealing algorithm and CG force fields involving the sequence-dependent base-pairing/stacking interactions and an implicit electrostatic potential, the present model successfully folds 20 dsDNAs (≤52nt) and 20 ssDNAs (≤74nt) into the corresponding native-like structures just from their sequences, with an overall mean RMSD of 3.4Å from the experimental structures. For DNAs with various lengths and sequences, the present model can make reliable predictions on stability, e.g., for 27 dsDNAs with/without bulge/internal loops and 24 ssDNAs including pseudoknot, the mean deviation of predicted melting temperatures from the corresponding experimental data is only ~2.0°C. Furthermore, the model also quantificationally predicts the effects of monovalent or divalent ions on the structure stability of ssDNAs/dsDNAs.

To determine 3D structures and quantify stability of single- (ss) and double-stranded (ds) DNAs is essential to unveil the mechanisms of their functions and to further guide the production and development of novel materials. Although many DNA models have been proposed to reproduce the basic structural, mechanical, or thermodynamic properties of dsDNAs based on the secondary structure information or preset constraints, there are very few models can be used to investigate the ssDNA folding or dsDNA assembly from the sequence. Furthermore, due to the polyanionic nature of DNAs, metal ions (e.g., Na⁺ and Mg²⁺) in solutions can play an essential role in DNA folding and dynamics. Nevertheless, ab initio predictions for DNA folding in ion solutions are still an unresolved problem. In this work, we developed a novel coarse-grained model to predict 3D structures and thermodynamic stabilities for both ssDNAs and dsDNAs in monovalent/divalent ion solutions from their sequences. As compared with the extensive experimental data and available existing models, we showed that the present model can successfully fold simple DNAs into their native-like structures, and can also accurately reproduce the effects of sequence and monovalent/divalent ions on structure stability for ssDNAs including pseudoknot and dsDNAs with/without bulge/internal loops.

Computational tools to study RNA-protein complexes

RNA is the key player in many cellular processes such as signal transduction, replication, transport, cell division, transcription, and translation. These diverse functions are accomplished through interactions of RNA with proteins. However, protein–RNA interactions are still poorly derstood in contrast to protein–protein and protein–DNA interactions. This knowledge gap can be attributed to the limited availability of protein-RNA structures along with the experimental difficulties in studying these complexes. Recent progress in computational resources has expanded the number of tools available for studying protein-RNA interactions at various molecular levels. These include tools for predicting interacting residues from primary sequences, modelling of protein-RNA complexes, predicting hotspots in these complexes and insights into derstanding in the dynamics of their interactions. Each of these tools has its strengths and limitations, which makes it significant to select an optimal approach for the question of interest. Here we present a mini review of computational tools to study different aspects of protein-RNA interactions, with focus on overall application, development of the field and the future perspectives.

A Generalized Attraction-Repulsion Potential and Revisited Fragment Library Improves PEP-FOLD Peptide Structure Prediction

Fast and accurate structure prediction is essential to the study of peptide function, molecular targets, and interactions and has been the subject of considerable efforts in the past decade. In this work, we present improvements to the popular simplified PEP-FOLD technique for small peptide structure prediction. PEP-FOLD originality is threefold: (i) it uses a predetermined structural alphabet, (ii) it uses a sequential algorithm to reconstruct the tridimensional structures of these peptides in a discrete space using a fragment library, and (iii) it assesses the energy of these structures using a coarse-grained representation in which all of the backbone atoms but the α-hydrogen are present, and the side chain corresponds to a unique bead. In former versions of PEP-FOLD, a van der Waals formulation was used for non-bonded interactions, with each side chain being associated with a fixed radius. Here, we explore the relevance of using instead a generalized formulation in which not only the optimal distance of interaction and the energy at this distance are parameters but also the distance at which the potential is zero. This allows each side chain to be associated with a different radius and potential energy shape, depending on its interaction partner, and in principle to make more effective the coarse-grained representation. In addition, the new PEP-FOLD version is associated with an updated library of fragments. We show that these modifications lead to important improvements for many of the problematic targets identified with the former PEP-FOLD version while maintaining already correct predictions. The improvement is in terms of both model ranking and model accuracy. We also compare the PEP-FOLD enhanced version to state-of-the-art techniques for both peptide and structure predictions: APPTest, RaptorX, and AlphaFold2. We find that the new predictions are superior, in particular with respect to the prediction of small β-targets, to those of APPTest and RaptorX and bring, with its original approach, additional understanding on folded structures, even when less precise than AlphaFold2. With their strong physical influence, the revised structural library and coarse-grained potential offer, however, the means for a deeper understanding of the nature of folding and open a solid basis for studying flexibility and other dynamical properties not accessible to IA structure prediction approaches.

RNAStat: An Integrated Tool for Statistical Analysis of RNA 3D Structures

The 3D architectures of RNAs are essential for understanding their cellular functions. While an accurate scoring function based on the statistics of known RNA structures is a key component for successful RNA structure prediction or evaluation, there are few tools or web servers that can be directly used to make comprehensive statistical analysis for RNA 3D structures. In this work, we developed RNAStat, an integrated tool for making statistics on RNA 3D structures. For given RNA structures, RNAStat automatically calculates RNA structural properties such as size and shape, and shows their distributions. Based on the RNA structure annotation from DSSR, RNAStat provides statistical information of RNA secondary structure motifs including canonical/non-canonical base pairs, stems, and various loops. In particular, the geometry of base-pairing/stacking can be calculated in RNAStat by constructing a local coordinate system for each base. In addition, RNAStat also supplies the distribution of distance between any atoms to the users to help build distance-based RNA statistical potentials. To test the usability of the tool, we established a non-redundant RNA 3D structure dataset, and based on the dataset, we made a comprehensive statistical analysis on RNA structures, which could have the guiding significance for RNA structure modeling. The python code of RNAStat, the dataset used in this work, and corresponding statistical data files are freely available at GitHub (https://github.com/RNA-folding-lab/RNAStat).

Computer-aided comprehensive explorations of RNA structural polymorphism through complementary simulation methods

While RNA folding was originally seen as a simple problem to solve, it has been shown that the promiscuous interactions of the nucleobases result in structural polymorphism, with several competing structures generally observed for non-coding RNA. This inherent complexity limits our understanding of these molecules from experiments alone, and computational methods are commonly used to study RNA. Here, we discuss three advanced sampling schemes, namely Hamiltonian-replica exchange molecular dynamics (MD), ratchet-and-pawl MD and discrete path sampling, as well as the HiRE-RNA coarse-graining scheme, and highlight how these approaches are complementary with reference to recent case studies. While all computational methods have their shortcomings, the plurality of simulation methods leads to a better understanding of experimental findings and can inform and guide experimental work on RNA polymorphism.

RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.

Biasing RNA Coarse-Grained Folding Simulations with Small-Angle X-ray Scattering Data

RNA molecules can easily adopt alternative structures in response to different environmental conditions. As a result, a molecule's energy landscape is rough and can exhibit a multitude of deep basins. In the absence of a high-resolution structure, small-angle X-ray scattering data (SAXS) can narrow down the conformational space available to the molecule and be used in conjunction with physical modeling to obtain high-resolution putative structures to be further tested by experiments. Because of the low resolution of these data, it is natural to implement the integration of SAXS data into simulations using a coarse-grained representation of the molecule, allowing for much wider searches and faster evaluation of SAXS theoretical intensity curves than with atomistic models. We present here the theoretical framework and the implementation of a simulation approach based on our coarse-grained model HiRE-RNA combined with SAXS evaluations "on-the-fly" leading the simulation toward conformations agreeing with the scattering data, starting from partially folded structures as the ones that can easily be obtained from secondary structure prediction-based tools. We show on three benchmark systems how our approach can successfully achieve high-resolution structures with remarkable similarity with the native structure recovering not only the overall shape, as imposed by SAXS data, but also the details of initially missing base pairs.

Structural 3D Domain Reconstruction of the RNA Genome from Viruses with Secondary Structure Models

Three-dimensional RNA domain reconstruction is important for the assembly, disassembly and delivery functionalities of a packed proteinaceus capsid. However, to date, the self-association of RNA molecules is still an open problem. Recent chemical probing reports provide, with high reliability, the secondary structure of diverse RNA ensembles, such as those of viral genomes. Here, we present a method for reconstructing the complete 3D structure of RNA genomes, which combines a coarse-grained model with a subdomain composition scheme to obtain the entire genome inside proteinaceus capsids based on secondary structures from experimental techniques. Despite the amount of sampling involved in the folded and also unfolded RNA molecules, advanced microscope techniques can provide points of anchoring, which enhance our model to include interactions between capsid pentamers and RNA subdomains. To test our method, we tackle the satellite tobacco mosaic virus (STMV) genome, which has been widely studied by both experimental and computational communities. We provide not only a methodology to structurally analyze the tertiary conformations of the RNA genome inside capsids, but a flexible platform that allows the easy implementation of features/descriptors coming from both theoretical and experimental approaches.

RNA 3D Structure Prediction Using Coarse-Grained Models

The three-dimensional (3D) structures of Ribonucleic acid (RNA) molecules are essential to understanding their various and important biological functions. However, experimental determination of the atomic structures is laborious and technically difficult. The large gap between the number of sequences and the experimentally determined structures enables the thriving development of computational approaches to modeling RNAs. However, computational methods based on all-atom simulations are intractable for large RNA systems, which demand long time simulations. Facing such a challenge, many coarse-grained (CG) models have been developed. Here, we provide a review of CG models for modeling RNA 3D structures, compare the performance of the different models, and offer insights into potential future developments.

Coarse-grained nucleic acid-protein model for hybrid nanotechnology

The emerging field of hybrid DNA-protein nanotechnology brings with it the potential for many novel materials which combine the addressability of DNA nanotechnology with the versatility of protein interactions. However, the design and computational study of these hybrid structures is difficult due to the system sizes involved. To aid in the design and in silico analysis process, we introduce here a coarse-grained DNA/RNA-protein model that extends the oxDNA/oxRNA models of DNA/RNA with a coarse-grained model of proteins based on an anisotropic network model representation. Fully equipped with analysis scripts and visualization, our model aims to facilitate hybrid nanomaterial design towards eventual experimental realization, as well as enabling study of biological complexes. We further demonstrate its usage by simulating DNA-protein nanocage, DNA wrapped around histones, and a nascent RNA in polymerase.

Sequence dependent phase separation of protein-polynucleotide mixtures elucidated using molecular simulations

Ribonucleoprotein (RNP) granules are membraneless organelles (MLOs), which majorly consist of RNA and RNA-binding proteins and are formed via liquid-liquid phase separation (LLPS). Experimental studies investigating the drivers of LLPS have shown that intrinsically disordered proteins (IDPs) and nucleic acids like RNA and other polynucleotides play a key role in modulating protein phase separation. There is currently a dearth of modelling techniques which allow one to delve deeper into how polynucleotides play the role of a modulator/promoter of LLPS in cells using computational methods. Here, we present a coarse-grained polynucleotide model developed to fill this gap, which together with our recently developed HPS model for protein LLPS, allows us to capture the factors driving protein-polynucleotide phase separation. We explore the capabilities of the modelling framework with the LAF-1 RGG system which has been well studied in experiments and also with the HPS model previously. Further taking advantage of the fact that the HPS model maintains sequence specificity we explore the role of charge patterning on controlling polynucleotide incorporation into condensates. With increased charge patterning we observe formation of structured or patterned condensates which suggests the possible roles of polynucleotides in not only shifting the phase boundaries but also introducing microscopic organization in MLOs.

Topological constraints of RNA pseudoknotted and loop-kissing motifs: applications to three-dimensional structure prediction

An RNA global fold can be described at the level of helix orientations and relatively flexible loop conformations that connect the helices. The linkage between the helices plays an essential role in determining the structural topology, which restricts RNA local and global folds, especially for RNA tertiary structures involving cross-linked base pairs. We quantitatively analyze the topological constraints on RNA 3D conformational space, in particular, on the distribution of helix orientations, for pseudoknots and loop-loop kissing structures. The result shows that a viable conformational space is predominantly determined by the motif type, helix size, and loop size, indicating a strong topological coupling between helices and loops in RNA tertiary motifs. Moreover, the analysis indicates that (cross-linked) tertiary contacts can cause much stronger topological constraints on RNA global fold than non-cross-linked base pairs. Furthermore, based on the topological constraints encoded in the 2D structure and the 3D templates, we develop a 3D structure prediction approach. This approach can be further combined with structure probing methods to expand the capability of computational prediction for large RNA folds.

Insights into the Kinetic Partitioning Folding Dynamics of the Human Telomeric G-Quadruplex from Molecular Simulations and Machine Learning

The human telomeric DNA G-quadruplex follows a kinetic partitioning folding mechanism. The underlying folding landscape potentially has many minima separated by high free-energy barriers. However, using current theoretical models to characterize this complex folding landscape has remained a challenging problem. In this study, by developing a hybrid atomistic structure-based model that merges structural information on the hybrid-1, hybrid-2, and chair-type G-quadruplex topologies, we investigated a kinetic partitioning folding process of human telomeric DNA involving three native folds. The model was validated as it reproduced the experimental observation that the hybrid-1 conformation is the major fold and the hybrid-2 conformation is kinetically more accessible. A three-step mechanism was revealed for the formation of the hybrid-1 conformation, while a two-step mechanism was demonstrated for the formation of hybrid-2 and chair-type conformations. Likewise, a class of state in which structures adopted inappropriate combinations of syn/anti guanine nucleotides was found to greatly slow down the folding process. In addition, by employing the XGBoost machine learning algorithm, three interatom distances and six dihedral angles were identified as essential internal coordinates to represent the low-dimensional folding landscape. The strategy of coupling the multibasin model and the machine learning algorithm may be useful to investigate the conformational dynamics of other multistate biomolecules.

Coarse-grained (hybrid) integrative modeling of biomolecular interactions

The computational modeling field has vastly evolved over the past decades. The early developments of simplified protein systems represented a stepping stone towards establishing more efficient approaches to sample intricated conformational landscapes. Downscaling the level of resolution of biomolecules to coarser representations allows for studying protein structure, dynamics and interactions that are not accessible by classical atomistic approaches. The combination of different resolutions, namely hybrid modeling, has also been proved as an alternative when mixed levels of details are required. In this review, we provide an overview of coarse-grained/hybrid models focusing on their applicability in the modeling of biomolecular interactions. We give a detailed list of ready-to-use modeling software for studying biomolecular interactions allowing various levels of coarse-graining and provide examples of complexes determined by integrative coarse-grained/hybrid approaches in combination with experimental information.

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.

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.

VfoldLA: A web server for loop assembly-based prediction of putative 3D RNA structures

RNA three-dimensional (3D) structures are critical for RNA cellular functions. However, structure prediction for large and complex RNAs remains a challenge, which hampers our understanding of RNA structure-function relationship. We here report a new web server, the VfoldLA server (http://rna.physics.missouri.edu/vfoldLA), for the prediction of RNA 3D structures from nucleotide sequences and base-pair information (2D structure). This server is based on the recently developed VfoldLA, a model that classifies the single-stranded loops (junctions) into four different types and according to the loop-helix connections, assembles RNA 3D structures from the loop/junction templates. The VfoldLA web server provides a user-friendly online interface for a fully automated prediction of putative 3D RNA structures using VfoldLA. With a single-RNA or RNA-RNA complex sequence and 2D structure as input, the server generates structure(s) with the JSmol visualization along with a downloadable PDB file. The output result may serve as useful scaffolds for future structure refinement studies.

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.

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.

Quantitative Understanding of SHAPE Mechanism from RNA Structure and Dynamics Analysis

The selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) method probes RNA local structural and dynamic information at single nucleotide resolution. To gain quantitative insights into the relationship between nucleotide flexibility, RNA 3D structure, and SHAPE reactivity, we develop a 3D Structure-SHAPE Relationship model (3DSSR) to rebuild SHAPE profiles from 3D structures. The model starts from RNA structures and combines nucleotide interaction strength and conformational propensity, ligand (SHAPE reagent) accessibility, and base-pairing pattern through a composite function to quantify the correlation between SHAPE reactivity and nucleotide conformational stability. The 3DSSR model shows the relationship between SHAPE reactivity and RNA structure and energetics. Comparisons between the 3DSSR-predicted SHAPE profile and the experimental SHAPE data show correlation, suggesting that the extracted analytical function may have captured the key factors that determine the SHAPE reactivity profile. Furthermore, the theory offers an effective method to sieve RNA 3D models and exclude models that are incompatible with experimental SHAPE data.

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.

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.

Hierarchical Assembly of RNA Three-Dimensional Structures Based on Loop Templates

The current RNA structure prediction methods cannot keep up the pace of the rapidly increasing number of sequences and the emerging new functions of RNAs. Template-based RNA three-dimensional structure prediction methods are restricted by the limited number of known RNA structures, and traditional motif-based search for the templates does not always lead to successful results. Here we report a new template search and assembly algorithm, the hierarchical loop template-assembly method (VfoldLA). The method searches for templates for single strand loop/junctions instead of the whole motifs, which often renders no available templates, or short fragments (several nucleotides), which requires a long computational time to assemble and refine. The VfoldLA method has the advantage of accounting for local and nonlocal interloop interactions. Benchmark tests indicate that this new method can provide low-resolution predictions for RNA conformations at different levels of structural complexities. Furthermore, the VfoldLA-predicted conformations may also serve as reliable putative models for further structure prediction and refinements. VfoldLA is accessible at http://rna.physics.missouri.edu/vfoldLA .

Multi-scale simulations of biological systems using the OPEP coarse-grained model

Biomolecules are complex machines that are optimized by evolution to properly fulfill or contribute to a variety of biochemical tasks in the cellular environment. Computer simulations based on quantum mechanics and atomistic force fields have been proven to be a powerful microscope for obtaining valuable insights into many biological, physical, and chemical processes. Many interesting phenomena involve, however, a time scale and a number of degrees of freedom, notably if crowding is considered, that cannot be explored at an atomistic resolution. To bridge the gap between reality and simulation, many different advanced computational techniques and coarse-grained (CG) models have been developed. Here, we report some applications of the CG OPEP protein model to amyloid fibril formation, the response of catch-bond proteins to two types of fluid flow, and interactive simulations to fold peptides with well-defined 3D structures or with intrinsic disorder.

Fast coarse-grained model for RNA titration

A new numerical scheme for RNA (ribonucleic acid) titration based on the Debye-Hückel framework for the salt description is proposed in an effort to reduce the computational costs for further applications to study protein-RNA systems. By means of different sets of Monte Carlo simulations, we demonstrated that this new scheme is able to correctly reproduce the experimental titration behavior and salt pK_a shifts. In comparison with other theoretical approaches, similar or even better outcomes are achieved at much lower computational costs. The model was tested on the lead-dependent ribozyme, the branch-point helix, and the domain 5 from Azotobacter vinelandii Intron 5.

Protein-RNA complexation driven by the charge regulation mechanism

Electrostatic interactions play a pivotal role in many (bio)molecular association processes. The molecular organization and function in biological systems are largely determined by these interactions from pure Coulombic contributions to more peculiar mesoscopic forces due to ion-ion correlation and proton fluctuations. The latter is a general electrostatic mechanism that gives attraction particularly at low electrolyte concentrations. This charge regulation mechanism due to titrating amino acid and nucleotides residues is discussed here in a purely electrostatic framework. By means of constant-pH Monte Carlo simulations based on a fast coarse-grained titration proton scheme, a new computer molecular model was devised to study protein-RNA interactions. The complexation between the RNA silencing suppressor p19 viral protein and the 19-bp small interfering RNA was investigated at different solution pH and salt conditions. The outcomes illustrate the importance of the charge regulation mechanism that enhances the association between these macromolecules in a similar way as observed for other protein-polyelectrolyte systems typically found in colloidal science. Due to the highly negative charge of RNA, the effect is more pronounced in this system as predicted by the Kirkwood-Shumaker theory. Our results contribute to the general physico-chemical understanding of macromolecular complexation and shed light on the extensive role of RNA in the cell's life.

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.

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).