A two-length-scale polymer theory for RNA loop free energies and helix stacking

Estimating RNA Secondary Structure Folding Free Energy Changes with efn2

A number of analyses require estimates of the folding free energy changes of specific RNA secondary structures. These predictions are often based on a set of nearest neighbor parameters that models the folding stability of a RNA secondary structure as the sum of folding stabilities of the structural elements that comprise the secondary structure. In the software suite RNAstructure, the free energy change calculation is implemented in the program efn2. The efn2 program estimates the folding free energy change and the experimental uncertainty in the folding free energy change. It can be run through the graphical user interface for RNAstructure, from the command line, or a web server. This chapter provides detailed protocols for using efn2.

Determining parameters for non-linear models of multi-loop free energy change

MOTIVATION

Predicting the secondary structure of RNA is a fundamental task in bioinformatics. Algorithms that predict secondary structure given only the primary sequence, and a model to evaluate the quality of a structure, are an integral part of this. These algorithms have been updated as our model of RNA thermodynamics changed and expanded. An exception to this has been the treatment of multi-loops. Although more advanced models of multi-loop free energy change have been suggested, a simple, linear model has been used since the 1980s. However, recently, new dynamic programing algorithms for secondary structure prediction that could incorporate these models were presented. Unfortunately, these models appear to have lower accuracy for secondary structure prediction.

RESULTS

We apply linear regression and a new parameter optimization algorithm to find better parameters for the existing linear model and advanced non-linear multi-loop models. These include the Jacobson-Stockmayer and Aalberts & Nandagopal models. We find that the current linear model parameters may be near optimal for the linear model, and that no advanced model performs better than the existing linear model parameters even after parameter optimization.

AVAILABILITY AND IMPLEMENTATION

Source code and data is available at https://github.com/maxhwardg/advanced_multiloops.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Making ends meet: New functions of mRNA secondary structure

The 5' cap and 3' poly(A) tail of mRNA are known to synergistically regulate mRNA translation and stability. Recent computational and experimental studies revealed that both protein-coding and non-coding RNAs will fold with extensive intramolecular secondary structure, which will result in close distances between the sequence ends. This proximity of the ends is a sequence-independent, universal property of most RNAs. Only low-complexity sequences without guanosines are without secondary structure and exhibit end-to-end distances expected for RNA random coils. The innate proximity of RNA ends might have important biological implications that remain unexplored. In particular, the inherent compactness of mRNA might regulate translation initiation by facilitating the formation of protein complexes that bridge mRNA 5' and 3' ends. Additionally, the proximity of mRNA ends might mediate coupling of 3' deadenylation to 5' end mRNA decay. This article is categorized under: RNA Structure and Dynamics > RNA Structure, Dynamics, and Chemistry RNA Structure and Dynamics > Influence of RNA Structure in Biological Systems Translation > Translation Regulation.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.

Estimating uncertainty in predicted folding free energy changes of RNA secondary structures

Nearest neighbor parameters for estimating the folding stability of RNA are commonly used in secondary structure prediction, for generating folding ensembles of structures, and for analyzing RNA function. Previously, we demonstrated that we could quantify the uncertainties in each nearest neighbor parameter by perturbing the underlying optical melting data within experimental error and rederiving the parameters, which accounts for the substantial correlations that exist between the parameters. In this contribution, we describe a method to estimate uncertainty in the estimated folding stabilities of RNA structures, accounting for correlations in the nearest neighbor parameters. This method is incorporated in the RNA structure software package.

mRNAs and lncRNAs intrinsically form secondary structures with short end-to-end distances

The 5' and 3' termini of RNA play important roles in many cellular processes. Using Förster resonance energy transfer (FRET), we show that mRNAs and lncRNAs have an intrinsic propensity to fold in the absence of proteins into structures in which the 5' end and 3' end are ≤7 nm apart irrespective of mRNA length. Computational estimates suggest that the inherent proximity of the ends is a universal property of most mRNA and lncRNA sequences. Only guanosine-depleted RNA sequences with low sequence complexity are unstructured and exhibit end-to-end distances expected for the random coil conformation of RNA. While the biological implications remain to be explored, short end-to-end distances could facilitate the binding of protein factors that regulate translation initiation by bridging mRNA 5' and 3' ends. Furthermore, our studies provide the basis for measuring, computing and manipulating end-to-end distances and secondary structure in RNA in research and biotechnology.

Advanced multi-loop algorithms for RNA secondary structure prediction reveal that the simplest model is best

Algorithmic prediction of RNA secondary structure has been an area of active inquiry since the 1970s. Despite many innovations since then, our best techniques are not yet perfect. The workhorses of the RNA secondary structure prediction engine are recursions first described by Zuker and Stiegler in 1981. These have well understood caveats; a notable flaw is the ad-hoc treatment of multi-loops, also called helical-junctions, that persists today. While several advanced models for multi-loops have been proposed, it seems to have been assumed that incorporating them into the recursions would lead to intractability, and so no algorithms for these models exist. Some of these models include the classical model based on Jacobson–Stockmayer polymer theory, and another by Aalberts and Nadagopal that incorporates two-length-scale polymer physics. We have realized practical, tractable algorithms for each of these models. However, after implementing these algorithms, we found that no advanced model was better than the original, ad-hoc model used for multi-loops. While this is unexpected, it supports the praxis of the current model.

CHSalign: A Web Server That Builds upon Junction-Explorer and RNAJAG for Pairwise Alignment of RNA Secondary Structures with Coaxial Helical Stacking

RNA junctions are important structural elements of RNA molecules. They are formed when three or more helices come together in three-dimensional space. Recent studies have focused on the annotation and prediction of coaxial helical stacking (CHS) motifs within junctions. Here we exploit such predictions to develop an efficient alignment tool to handle RNA secondary structures with CHS motifs. Specifically, we build upon our Junction-Explorer software for predicting coaxial stacking and RNAJAG for modelling junction topologies as tree graphs to incorporate constrained tree matching and dynamic programming algorithms into a new method, called CHSalign, for aligning the secondary structures of RNA molecules containing CHS motifs. Thus, CHSalign is intended to be an efficient alignment tool for RNAs containing similar junctions. Experimental results based on thousands of alignments demonstrate that CHSalign can align two RNA secondary structures containing CHS motifs more accurately than other RNA secondary structure alignment tools. CHSalign yields a high score when aligning two RNA secondary structures with similar CHS motifs or helical arrangement patterns, and a low score otherwise. This new method has been implemented in a web server, and the program is also made freely available, at http://bioinformatics.njit.edu/CHSalign/.

Phylogenetic Reconstruction of the Calosphaeriales and Togniniales Using Five Genes and Predicted RNA Secondary Structures of ITS, and Flabellascus tenuirostris gen. et sp. nov

The Calosphaeriales is revisited with new collection data, living cultures, morphological studies of ascoma centrum, secondary structures of the internal transcribed spacer (ITS) rDNA and phylogeny based on novel DNA sequences of five nuclear ribosomal and protein-coding loci. Morphological features, molecular evidence and information from predicted RNA secondary structures of ITS converged upon robust phylogenies of the Calosphaeriales and Togniniales. The current concept of the Calosphaeriales includes the Calosphaeriaceae and Pleurostomataceae encompassing five monophyletic genera, Calosphaeria, Flabellascus gen. nov., Jattaea, Pleurostoma and Togniniella, strongly supported by Bayesian and Maximum Likelihood methods. The structural elements of ITS1 form characteristic patterns that are phylogenetically conserved, corroborate observations based on morphology and have a high predictive value at the generic level. Three major clades containing 44 species of Phaeoacremonium were recovered in the closely related Togniniales based on ITS, actin and β-tubulin sequences. They are newly characterized by sexual and RNA structural characters and ecology. This approach is a first step towards understanding of the molecular systematics of Phaeoacremonium and possibly its new classification. In the Calosphaeriales, Jattaea aphanospora sp. nov. and J. ribicola sp. nov. are introduced, Calosphaeria taediosa is combined in Jattaea and epitypified. The sexual morph of Phaeoacremonium cinereum was encountered for the first time on decaying wood and obtained in vitro. In order to achieve a single nomenclature, the genera of asexual morphs linked with the Calosphaeriales are transferred to synonymy of their sexual morphs following the principle of priority, i.e. Calosphaeriophora to Calosphaeria, Phaeocrella to Togniniella and Pleurostomophora to Pleurostoma. Three new combinations are proposed, i.e. Pleurostoma ochraceum comb. nov., P. repens comb. nov. and P. richardsiae comb. nov. The morphology-based key is provided to facilitate identification of genera accepted in the Calosphaeriales.

Nuclear Magnetic Resonance-Assisted Prediction of Secondary Structure for RNA: Incorporation of Direction-Dependent Chemical Shift Constraints

Knowledge of RNA structure is necessary to determine structure–function relationships and to facilitate design of potential therapeutics. RNA secondary structure prediction can be improved by applying constraints from nuclear magnetic resonance (NMR) experiments to a dynamic programming algorithm. Imino proton walks from NOESY spectra reveal double-stranded regions. Chemical shifts of protons in GH1, UH3, and UH5 of GU pairs, UH3, UH5, and AH2 of AU pairs, and GH1 of GC pairs were analyzed to identify constraints for the 5′ to 3′ directionality of base pairs in helices. The 5′ to 3′ directionality constraints were incorporated into an NMR-assisted prediction of secondary structure (NAPSS-CS) program. When it was tested on 18 structures, including nine pseudoknots, the sensitivity and positive predictive value were improved relative to those of three unrestrained programs. The prediction accuracy for the pseudoknots improved the most. The program also facilitates assignment of chemical shifts to individual nucleotides, a necessary step for determining three-dimensional structure.

Physics-based RNA structure prediction

Despite the success of RNA secondary structure prediction for simple, short RNAs, the problem of predicting RNAs with long-range tertiary folds remains. Furthermore, RNA 3D structure prediction is hampered by the lack of the knowledge about the tertiary contacts and their thermodynamic parameters. Low-resolution structural modeling enables us to estimate the conformational entropies for a number of tertiary folds through rigorous statistical mechanical calculations. The models lead to 3D tertiary folds at coarse-grained level. The coarse-grained structures serve as the initial structures for all-atom molecular dynamics refinement to build the final all-atom 3D structures. In this paper, we present an overview of RNA computational models for secondary and tertiary structures’ predictions and then focus on a recently developed RNA statistical mechanical model—the Vfold model. The main emphasis is placed on the physics behind the models, including the treatment of the non-canonical interactions in secondary and tertiary structure modelings, and the correlations to RNA functions.

Structural analysis of a class III preQ1 riboswitch reveals an aptamer distant from a ribosome-binding site regulated by fast dynamics

PreQ1-III riboswitches are newly identified RNA elements that control bacterial genes in response to preQ1 (7-aminomethyl-7-deazaguanine), a precursor to the essential hypermodified tRNA base queuosine. Although numerous riboswitches fold as H-type or HLout-type pseudoknots that integrate ligand-binding and regulatory sequences within a single folded domain, the preQ1-III riboswitch aptamer forms a HLout-type pseudoknot that does not appear to incorporate its ribosome-binding site (RBS). To understand how this unusual organization confers function, we determined the crystal structure of the class III preQ1 riboswitch from Faecalibacterium prausnitzii at 2.75 Å resolution. PreQ1 binds tightly (KD,app 6.5 ± 0.5 nM) between helices P1 and P2 of a three-way helical junction wherein the third helix, P4, projects orthogonally from the ligand-binding pocket, exposing its stem-loop to base pair with the 3' RBS. Biochemical analysis, computational modeling, and single-molecule FRET imaging demonstrated that preQ1 enhances P4 reorientation toward P1-P2, promoting a partially nested, H-type pseudoknot in which the RBS undergoes rapid docking (kdock ∼ 0.6 s(-1)) and undocking (kundock ∼ 1.1 s(-1)). Discovery of such dynamic conformational switching provides insight into how a riboswitch with bipartite architecture uses dynamics to modulate expression platform accessibility, thus expanding the known repertoire of gene control strategies used by regulatory RNAs.

Accurate SHAPE-directed RNA secondary structure modeling, including pseudoknots

A pseudoknot forms in an RNA when nucleotides in a loop pair with a region outside the helices that close the loop. Pseudoknots occur relatively rarely in RNA but are highly overrepresented in functionally critical motifs in large catalytic RNAs, in riboswitches, and in regulatory elements of viruses. Pseudoknots are usually excluded from RNA structure prediction algorithms. When included, these pairings are difficult to model accurately, especially in large RNAs, because allowing this structure dramatically increases the number of possible incorrect folds and because it is difficult to search the fold space for an optimal structure. We have developed a concise secondary structure modeling approach that combines SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension) experimental chemical probing information and a simple, but robust, energy model for the entropic cost of single pseudoknot formation. Structures are predicted with iterative refinement, using a dynamic programming algorithm. This melded experimental and thermodynamic energy function predicted the secondary structures and the pseudoknots for a set of 21 challenging RNAs of known structure ranging in size from 34 to 530 nt. On average, 93% of known base pairs were predicted, and all pseudoknots in well-folded RNAs were identified.

Free energy cost of stretching mRNA hairpin loops inhibits small RNA binding

Small RNA-mRNA binding is an essential step in RNA interference, an important cellular regulatory process. Calculations of binding free energy have been used in binding site prediction, but the cost of stretching the mRNA loop when the small RNA-mRNA duplex forms requires further exploration. Here, using both polymer physics theory and simulations, we estimate the free energy of a stretched mRNA loop. We find loop stretching significantly increases the free energy of 3' supplementary/compensatory miRNA binding and siRNA binding to mRNA hairpin loops. We also make the observation that sites where 3' supplementary binding is available may bind at the seed only, and that loop stretching often favors seed-only binding over seed plus 3' supplementary binding in mRNA hairpins.

Loop Entropy Assists Tertiary Order: Loopy Stabilization of Stacking Motifs

The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of forming multibranch and other RNA loops is derived with a polymer-physics based theory. We also derive a formula for the free energy of coaxial stacking in the context of a loop. Simulations support the analytic formulas. The effects of stacking of unpaired bases are also studied with simulations.

Predicting coaxial helical stacking in RNA junctions

RNA junctions are important structural elements that form when three or more helices come together in space in the tertiary structures of RNA molecules. Determining their structural configuration is important for predicting RNA 3D structure. We introduce a computational method to predict, at the secondary structure level, the coaxial helical stacking arrangement in junctions, as well as classify the junction topology. Our approach uses a data mining approach known as random forests, which relies on a set of decision trees trained using length, sequence and other variables specified for any given junction. The resulting protocol predicts coaxial stacking within three- and four-way junctions with an accuracy of 81% and 77%, respectively; the accuracy increases to 83% and 87%, respectively, when knowledge from the junction family type is included. Coaxial stacking predictions for the five to ten-way junctions are less accurate (60%) due to sparse data available for training. Additionally, our application predicts the junction family with an accuracy of 85% for three-way junctions and 74% for four-way junctions. Comparisons with other methods, as well applications to unsolved RNAs, are also presented. The web server Junction-Explorer to predict junction topologies is freely available at: http://bioinformatics.njit.edu/junction.

Fluorescence competition and optical melting measurements of RNA three-way multibranch loops provide a revised model for thermodynamic parameters

Three-way multibranch loops (junctions) are common in RNA secondary structures. Computer algorithms such as RNAstructure and MFOLD do not consider the identity of unpaired nucleotides in multibranch loops when predicting secondary structure. There is limited experimental data, however, to parametrize this aspect of these algorithms. In this study, UV optical melting and a fluorescence competition assay are used to measure stabilities of multibranch loops containing up to five unpaired adenosines or uridines or a loop E motif. These results provide a test of our understanding of the factors affecting multibranch loop stability and provide revised parameters for predicting stability. The results should help to improve predictions of RNA secondary structure.