Clustering to identify RNA conformations constrained by secondary structure

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.

Exploring the multiple conformational states of RNA genome through interhelical dynamics and network analysis

The structural variation of RNA is often very transient and can be easily missed in experiments. Molecular dynamics simulation studies along with network analysis can be an effective tool to identify prominent conformations of such dynamic biomolecular systems. Here we describe a method to effectively sample different RNA conformations at six different temperatures based on the changes in the interhelical orientations. This method gives the information about prominent states of the RNA as well as the probability of the existence of different conformations and their interconnections during the process of evolution. In the case of the SARS-CoV-2 genome, the change of prominent structures was found to be faster at 333 K as compared to higher temperatures due to the formation of the non-native base pairs. ΔΔG calculated between 288 K and 363 K are found to be 10.31 kcal/mol (88 nt) considering the contribution from the multiple states of the RNA which agrees well with the experimentally reported denaturation energy for E. coli α mRNA pseudoknot (∼16 kcal/mol, 112 nt) determined by calorimetry/UV hyperchromicity and human telomerase RNA telomerase (4.5-6.6 kcal/mol, 54 nt) determined by FRET analysis.

Predicting RNA Scaffolds with a Hybrid Method of Vfold3D and VfoldLA

The ever-increasing discoveries of noncoding RNA functions draw a strong demand for RNA structure determination from the sequence. In recently years, computational studies for RNA structures, at both the two-dimensional and the three-dimensional levels, led to several highly promising new developments. In this chapter, we describe a hybrid method, which combines the motif template-based Vfold3D model and the loop template-based VfoldLA model, to predict RNA 3D structures. The main emphasis is placed on the definition of motifs and loops, the treatment of no-template motifs, and the 3D structure assembly from templates of motifs and loops. For illustration, we use the ZIKV xrRNA1 as an example to show the template-based prediction of RNA 3D structures from the 2D structure. The web server for the hybrid model is freely accessible at http://rna.physics.missouri.edu/vfold3D2 .

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.

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.

Nucleotide Dependent Switching in Rho GTPase: Conformational Heterogeneity and Competing Molecular Interactions

Ras superfamily of GTPases regulate myriad cellular processes through a conserved nucleotide (GTP/GDP) dependent switching mechanism. Unlike Ras family of GTPases, for the Rho GTPases, there is no clear evidence for the existence of “sub-states” such as state 1 & state 2 in the GTP bound form. To explore the nucleotide dependent conformational space of the Switch I loop and also to look for existence of state 1 like conformations in Rho GTPases, atomistic molecular dynamics and metadynamics simulations on RhoA were performed. These studies demonstrate that both the nucleotide-free state and the GDP bound “OFF” state have very similar conformations, whereas the GTP bound “ON” state has unique conformations with signatures of two intermediate states. The conformational free energy landscape for these systems suggests the presence of multiple intermediate states. Interestingly, the energetic penalty of exposing the non-polar residues in the GTP bound form is counter balanced by the favourable hydrogen bonded interactions between the γ-phosphate group of GTP with the highly conserved Tyr34 and Thr37 residues. These competing molecular interactions lead to a tuneable energy landscape of the Switch I conformation, which can undergo significant changes based on the local environment including changes upon binding to effectors.

Structure Prediction: New Insights into Decrypting Long Noncoding RNAs

Long noncoding RNAs (lncRNAs), which form a diverse class of RNAs, remain the least understood type of noncoding RNAs in terms of their nature and identification. Emerging evidence has revealed that a small number of newly discovered lncRNAs perform important and complex biological functions such as dosage compensation, chromatin regulation, genomic imprinting, and nuclear organization. However, understanding the wide range of functions of lncRNAs related to various processes of cellular networks remains a great experimental challenge. Structural versatility is critical for RNAs to perform various functions and provides new insights into probing the functions of lncRNAs. In recent years, the computational method of RNA structure prediction has been developed to analyze the structure of lncRNAs. This novel methodology has provided basic but indispensable information for the rapid, large-scale and in-depth research of lncRNAs. This review focuses on mainstream RNA structure prediction methods at the secondary and tertiary levels to offer an additional approach to investigating the functions of lncRNAs.

Predicting RNA 3D structure using a coarse-grain helix-centered model

A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a fine-grain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.

Noncanonical secondary structure stabilizes mitochondrial tRNA(Ser(UCN)) by reducing the entropic cost of tertiary folding

Mammalian mitochondrial tRNA(Ser(UCN)) (mt-tRNA(Ser)) and pyrrolysine tRNA (tRNA(Pyl)) fold to near-canonical three-dimensional structures despite having noncanonical secondary structures with shortened interhelical loops that disrupt the conserved tRNA tertiary interaction network. How these noncanonical tRNAs compensate for their loss of tertiary interactions remains unclear. Furthermore, in human mt-tRNA(Ser), lengthening the variable loop by the 7472insC mutation reduces mt-tRNA(Ser) concentration in vivo through poorly understood mechanisms and is strongly associated with diseases such as deafness and epilepsy. Using simulations of the TOPRNA coarse-grained model, we show that increased topological constraints encoded by the unique secondary structure of wild-type mt-tRNA(Ser) decrease the entropic cost of folding by ∼2.5 kcal/mol compared to canonical tRNA, offsetting its loss of tertiary interactions. Further simulations show that the pathogenic 7472insC mutation disrupts topological constraints and hence destabilizes the mutant mt-tRNA(Ser) by ∼0.6 kcal/mol relative to wild-type. UV melting experiments confirm that insertion mutations lower mt-tRNA(Ser) melting temperature by 6-9 °C and increase the folding free energy by 0.8-1.7 kcal/mol in a largely sequence- and salt-independent manner, in quantitative agreement with our simulation predictions. Our results show that topological constraints provide a quantitative framework for describing key aspects of RNA folding behavior and also provide the first evidence of a pathogenic mutation that is due to disruption of topological constraints.

Efficient in silico exploration of RNA interhelical conformations using Euler angles and WExplore

HIV-1 TAR RNA is a two-helix bulge motif that plays a critical role in HIV viral replication and is an important drug target. However, efforts at designing TAR inhibitors have been challenged by its high degree of structural flexibility, which includes slow large-amplitude reorientations of its helices with respect to one another. Here, we use the recently introduced algorithm WExplore in combination with Euler angles to achieve unprecedented sampling of the TAR conformational ensemble. Our ensemble achieves similar agreement with experimental NMR data when compared with previous TAR computational studies, and is generated at a fraction of the computational cost. It clearly emerges from configuration space network analysis that the intermittent formation of the A22-U40 base pair acts as a reversible switch that enables sampling of interhelical conformations that would otherwise be topologically disallowed. We find that most previously determined ligand-bound structures are found in similar location in the network, and we use a sample-and-select approach to guide the construction of a set of novel conformations which can serve as the basis for future drug development efforts. Collectively, our findings demonstrate the utility of WExplore in combination with suitable order parameters as a method for exploring RNA conformational space.

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA's allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA's helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA's different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.

Hierarchy of RNA functional dynamics

RNA dynamics play a fundamental role in many cellular functions. However, there is no general framework to describe these complex processes, which typically consist of many structural maneuvers that occur over timescales ranging from picoseconds to seconds. Here, we classify RNA dynamics into distinct modes representing transitions between basins on a hierarchical free-energy landscape. These transitions include large-scale secondary-structural transitions at >0.1-s timescales, base-pair/tertiary dynamics at microsecond-to-millisecond timescales, stacking dynamics at timescales ranging from nanoseconds to microseconds, and other "jittering" motions at timescales ranging from picoseconds to nanoseconds. We review various modes within these three different tiers, the different mechanisms by which they are used to regulate function, and how they can be coupled together to achieve greater functional complexity.

Graph-based sampling for approximating global helical topologies of RNA

A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.

Secondary structures of rRNAs from all three domains of life

Accurate secondary structures are important for understanding ribosomes, which are extremely large and highly complex. Using 3D structures of ribosomes as input, we have revised and corrected traditional secondary (2°) structures of rRNAs. We identify helices by specific geometric and molecular interaction criteria, not by co-variation. The structural approach allows us to incorporate non-canonical base pairs on parity with Watson-Crick base pairs. The resulting rRNA 2° structures are up-to-date and consistent with three-dimensional structures, and are information-rich. These 2° structures are relatively simple to understand and are amenable to reproduction and modification by end-users. The 2° structures made available here broadly sample the phylogenetic tree and are mapped with a variety of data related to molecular interactions and geometry, phylogeny and evolution. We have generated 2° structures for both large subunit (LSU) 23S/28S and small subunit (SSU) 16S/18S rRNAs of Escherichia coli, Thermus thermophilus, Haloarcula marismortui (LSU rRNA only), Saccharomyces cerevisiae, Drosophila melanogaster, and Homo sapiens. We provide high-resolution editable versions of the 2° structures in several file formats. For the SSU rRNA, the 2° structures use an intuitive representation of the central pseudoknot where base triples are presented as pairs of base pairs. Both LSU and SSU secondary maps are available (http://apollo.chemistry.gatech.edu/RibosomeGallery). Mapping of data onto 2° structures was performed on the RiboVision server (http://apollo.chemistry.gatech.edu/RiboVision).

The impact of a ligand binding on strand migration in the SAM-I riboswitch

Riboswitches sense cellular concentrations of small molecules and use this information to adjust synthesis rates of related metabolites. Riboswitches include an aptamer domain to detect the ligand and an expression platform to control gene expression. Previous structural studies of riboswitches largely focused on aptamers, truncating the expression domain to suppress conformational switching. To link ligand/aptamer binding to conformational switching, we constructed models of an S-adenosyl methionine (SAM)-I riboswitch RNA segment incorporating elements of the expression platform, allowing formation of an antiterminator (AT) helix. Using Anton, a computer specially developed for long timescale Molecular Dynamics (MD), we simulated an extended (three microseconds) MD trajectory with SAM bound to a modeled riboswitch RNA segment. Remarkably, we observed a strand migration, converting three base pairs from an antiterminator (AT) helix, characteristic of the transcription ON state, to a P1 helix, characteristic of the OFF state. This conformational switching towards the OFF state is observed only in the presence of SAM. Among seven extended trajectories with three starting structures, the presence of SAM enhances the trend towards the OFF state for two out of three starting structures tested. Our simulation provides a visual demonstration of how a small molecule (<500 MW) binding to a limited surface can trigger a large scale conformational rearrangement in a 40 kDa RNA by perturbing the Free Energy Landscape. Such a mechanism can explain minimal requirements for SAM binding and transcription termination for SAM-I riboswitches previously reported experimentally.

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU-powered parallel k-centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370-residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k-centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.

De novo automated design of small RNA circuits for engineering synthetic riboregulation in living cells

A grand challenge in synthetic biology is to use our current knowledge of RNA science to perform the automatic engineering of completely synthetic sequences encoding functional RNAs in living cells. We report here a fully automated design methodology and experimental validation of synthetic RNA interaction circuits working in a cellular environment. The computational algorithm, based on a physicochemical model, produces novel RNA sequences by exploring the space of possible sequences compatible with predefined structures. We tested our methodology in Escherichia coli by designing several positive riboregulators with diverse structures and interaction models, suggesting that only the energy of formation and the activation energy (free energy barrier to overcome for initiating the hybridization reaction) are sufficient criteria to engineer RNA interaction and regulation in bacteria. The designed sequences exhibit nonsignificant similarity to any known noncoding RNA sequence. Our riboregulatory devices work independently and in combination with transcription regulation to create complex logic circuits. Our results demonstrate that a computational methodology based on first-principles can be used to engineer interacting RNAs with allosteric behavior in living cells.

Structure and mechanical properties of the ribosomal L1 stalk three-way junction

The L1 stalk is a key mobile element of the large ribosomal subunit which interacts with tRNA during translocation. Here, we investigate the structure and mechanical properties of the rRNA H76/H75/H79 three-way junction at the base of the L1 stalk from four different prokaryotic organisms. We propose a coarse-grained elastic model and parameterize it using large-scale atomistic molecular dynamics simulations. Global properties of the junction are well described by a model in which the H76 helix is represented by a straight, isotropically flexible elastic rod, while the junction core is represented by an isotropically flexible spherical hinge. Both the core and the helix contribute substantially to the overall H76 bending fluctuations. The presence of wobble pairs in H76 does not induce any increased flexibility or anisotropy to the helix. The half-closed conformation of the L1 stalk seems to be accessible by thermal fluctuations of the junction itself, without any long-range allosteric effects. Bending fluctuations of H76 with a bulge introduced in it suggest a rationale for the precise position of the bulge in eukaryotes. Our elastic model can be generalized to other RNA junctions found in biological systems or in nanotechnology.

Determining RNA three-dimensional structures using low-resolution data

Knowing the 3-D structure of an RNA is fundamental to understand its biological function. Nowadays X-ray crystallography and NMR spectroscopy are systematically applied to newly discovered RNAs. However, the application of these high-resolution techniques is not always possible, and thus scientists must turn to lower resolution alternatives. Here, we introduce a pipeline to systematically generate atomic resolution 3-D structures that are consistent with low-resolution data sets. We compare and evaluate the discriminative power of a number of low-resolution experimental techniques to reproduce the structure of the Escherichia coli tRNA(VAL) and P4-P6 domain of the Tetrahymena thermophila group I intron. We test single and combinations of the most accessible low-resolution techniques, i.e. hydroxyl radical footprinting (OH), methidiumpropyl-EDTA (MPE), multiplexed hydroxyl radical cleavage (MOHCA), and small-angle X-ray scattering (SAXS). We show that OH-derived constraints are accurate to discriminate structures at the atomic level, whereas EDTA-based constraints apply to global shape determination. We provide a guide for choosing which experimental techniques or combination of thereof is best in which context. The pipeline represents an important step towards high-throughput low-resolution RNA structure determination.

Simultaneous prediction of RNA secondary structure and helix coaxial stacking

Background

RNA secondary structure plays a scaffolding role for RNA tertiary conformation. Accurate secondary structure prediction can not only identify double-stranded helices and single stranded-loops but also help provide information for potential tertiary interaction motifs critical to the 3D conformation. The average accuracy in ab initio prediction remains 70%; performance improvement has only been limited to short RNA sequences. The prediction of tertiary interaction motifs is difficult without multiple, related sequences that are usually not available. This paper presents research that aims to improve the secondary structure prediction performance and to develop a capability to predict coaxial stacking between helices. Coaxial stacking positions two helices on the same axis, a tertiary motif present in almost all junctions that account for a high percentage of RNA tertiary structures.

Results

This research identified energetic rules for coaxial stacks and geometric constraints on stack combinations, which were applied to developing an efficient dynamic programming application for simultaneous prediction of secondary structure and coaxial stacking. Results on a number of non-coding RNA data sets, of short and moderately long lengths, show a performance improvement (specially on tRNAs) for secondary structure prediction when compared with existing methods. The program also demonstrates a capability for prediction of coaxial stacking.

Conclusions

The significant leap of performance on tRNAs demonstrated in this work suggests that a breakthrough to a higher performance in RNA secondary structure prediction may lie in understanding contributions from tertiary motifs critical to the structure, as such information can be used to constrain geometrically as well as energetically the space of RNA secondary structure.