Predicting RNA secondary structure by free energy minimization

RNA structure is hierarchical. Secondary structure contacts, i.e. the canonical base pair contacts, are generally stronger and form faster than the tertiary structure. Therefore, RNA secondary structures can be predicted independently of tertiary structure prediction. Furthermore, the stability of a given RNA secondary structure can be quantified using nearest neighbor free energy parameters. These parameters are the basis of a number of free energy minimization algorithms that predict RNA secondary structure for either a single sequence or multiple sequences. This article reviews the progress of RNA secondary structure prediction by free energy minimization and describes many of the algorithms that have been developed.     

Automated RNA tertiary structure prediction from secondary structure and low‐resolution restraints

A novel protocol for all‐atom RNA tertiary structure prediction is presented that uses restrained molecular mechanics and simulated annealing. The restraints are from secondary structure, covariation analysis, coaxial stacking predictions for helices in junctions, and, when available, cross‐linking data. Results are demonstrated on the Alu domain of the mammalian signal recognition particle RNA, the Saccharomyces cerevisiae phenylalanine tRNA, the hammerhead ribozyme, the hepatitis C virus internal ribosomal entry site, and the P4–P6 domain of the Tetrahymena thermophila group I intron. The predicted structure is selected from a pool of decoy structures with a score that maximizes radius of gyration and base–base contacts, which was empirically found to select higher quality decoys. This simple ab initio approach is sufficient to make good predictions of the structure of RNAs compared to current crystal structures using both root mean square deviation and the accuracy of base–base contacts. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Tertiary DNA structure in the single-stranded hTERT promoter fragment unfolds and refolds by parallel pathways via cooperative or sequential events

The discovery of G-quadruplexes and other DNA secondary elements has increased the structural diversity of DNA well beyond the ubiquitous double helix. However, it remains to be determined whether tertiary interactions can take place in a DNA complex that contains more than one secondary structure. Using a new data analysis strategy that exploits the hysteresis region between the mechanical unfolding and refolding traces obtained by a laser-tweezers instrument, we now provide the first convincing kinetic and thermodynamic evidence that a higher order interaction takes place between a hairpin and a G-quadruplex in a single-stranded DNA fragment that is found in the promoter region of human telomerase. During the hierarchical unfolding or refolding of the DNA complex, a 15-nucleotide hairpin serves as a common species among three intermediates. Moreover, either a mutant that prevents this hairpin formation or the addition of a DNA fragment complementary to the hairpin destroys the cooperative kinetic events by removing the tertiary interaction mediated by the hairpin. The coexistence of the sequential and the cooperative refolding events provides direct evidence for a unifying kinetic partition mechanism previously observed only in large proteins and complex RNA structures. Not only does this result rationalize the current controversial observations for the long-range interaction in complex single-stranded DNA structures, but also this unexpected complexity in a promoter element provides additional justification for the biological function of these structures in cells.     

A visual representation for RNA secondary structure and its application

The graphical representation of biological sequences is an important subject in the area of genome studies. We propose a novel visual representation for RNA secondary structures. Some symmetric properties and information on the base distribution and compositions can be intuitively reflected by the projection graphs of the points corresponding to the RNA secondary structures. Then our method is applied to compute the similarity of 12 classical samples and 11 real RNA secondary structures. The results indicate that our method can not only effectively analyze the similarity between RNA secondary structures but also show a high consistency with other literatures. Moreover, our method only needs the geometrical center of the characteristic curve of the RNA secondary structure to compute the similarity matrix, which means a low computational complexity. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Tertiary Motifs in RNA Structure and Folding

Specific tertiary structural motifs determine the complete architecture of RNA molecules (see picture for examples). Within the last few years a number of high-resolution crystal structures of complex RNAs have led to new insights into the mechanisms by which these complex folds are attained. In this review the structures of these tertiary motifs and how they influence the folding pathway of biological RNAs are discussed, as well as new developments in modeling RNA structure based upon these findings.     

Toward beta-amino acid proteins: a cooperatively folded beta-peptide quaternary structure

Folded polymers in nature are assembled from simple monomers and adopt complex folded structures through networks of stabilizing noncovalent interactions. These interactions define secondary and tertiary structure and in most cases specify a unique three-dimensional architecture. Individual secondary or tertiary structures can also associate with one another to form multi-subunit quaternary structures. Nonnatural folded polymers have potential for similar structural versatility. Here we describe a pair of beta3-peptides whose sequences were designed to promote a 14-helix structure in water, favor hetero-oligomer formation, and disfavor nonspecific aggregation. These beta3-peptides assemble noncovalently into a well-defined hetero-oligomer characterized by a defined stoichiometry, a highly stabilized secondary structure, and a cooperative melting transition (TM > 55 degrees C). This work demonstrates that beta3-peptides can assemble into defined, cooperatively folded quaternary structures and constitutes an important step toward designing protein-like assemblies from nonnatural polymers.     

A semi-supervised learning approach for RNA secondary structure prediction

RNA secondary structure prediction is a key technology in RNA bioinformatics. Most algorithms for RNA secondary structure prediction use probabilistic models, in which the model parameters are trained with reliable RNA secondary structures. Because of the difficulty of determining RNA secondary structures by experimental procedures, such as NMR or X-ray crystal structural analyses, there are still many RNA sequences that could be useful for training whose secondary structures have not been experimentally determined. In this paper, we introduce a novel semi-supervised learning approach for training parameters in a probabilistic model of RNA secondary structures in which we employ not only RNA sequences with annotated secondary structures but also ones with unknown secondary structures. Our model is based on a hybrid of generative (stochastic context-free grammars) and discriminative models (conditional random fields) that has been successfully applied to natural language processing. Computational experiments indicate that the accuracy of secondary structure prediction is improved by incorporating RNA sequences with unknown secondary structures into training. To our knowledge, this is the first study of a semi-supervised learning approach for RNA secondary structure prediction. This technique will be useful when the number of reliable structures is limited.     

A powerful approach for the selection of 2-aminopurine substitution sites to investigate RNA folding

A precise tertiary structure must be adopted to allow the function of many RNAs in cells. Accordingly, increasing resources have been devoted to the elucidation of RNA structures and the folding of RNAs. 2-Aminopurine (2AP), a fluorescent nucleobase analogue, can be substituted in strategic positions of DNA or RNA molecules to act as site-specific probe to monitor folding and folding dynamics of nucleic acids. Recent studies further demonstrated the potential of 2AP modifications in the assessment of folding kinetics during ligand-induced secondary and tertiary RNA structure rearrangements. However, an efficient way to unambiguously identify reliable positions for 2AP sensors is as yet unavailable and would represent a major asset, especially in the absence of crystallographic or NMR structural data for a target molecule. We report evidence of a novel and direct correlation between the 2'-OH flexibility of nucleotides, observed by selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) probing and the fluorescence response following nucleotide substitutions by 2AP. This correlation leads to a straightforward method, using SHAPE probing with benzoyl cyanide, to select appropriate nucleotide sites for 2AP substitution. This clear correlation is presented for three model RNAs of biological significance: the SAM-II, adenine (addA), and preQ(1) class II (preQ(1)cII) riboswitches.     

Development of carbohydrate-based scaffolds for restricted presentation of recognition groups. Extension to divalent ligands and implications for the structure of dimerized receptors

The solution structure of glycosyl amides has been studied by using NMR. A strong preference is displayed by tertiary aromatic glycosyl amides for E-anti structures in contrast with secondary aromatic glycosyl amides where Z-anti structures predominate. The structural diversity displayed by these classes of molecules would seem to be important as the directional properties of the aromatic ring, or groups attached to the aromatic ring, would be determined by choosing to have either a secondary or tertiary amide at the anomeric center and could be considered when designing bioactive molecules with carbohydrate scaffolds. The structural analysis was also carried out for related divalent secondary and tertiary glycosyl amides and these compounds display preferences similar to that of the monovalent compounds. The constrained divalent compounds have potential for promoting formation of clusters that will have restricted structure and thus have potential for novel studies of mechanisms of action of multivalent ligands. Possible applications of such compounds would be as scaffolds for the design and synthesis of ligands that will facilitate protein-protein or other receptor-receptor interactions. The affinity of restricted divalent (or higher order) ligands, designed to bind to proteins that recognize carbohydrates which would facilitate clustering and concomitantly promote protein-protein interactions, may be significantly higher than monovalent counterparts or multivalent ligands without these properties. This may be useful as a new approach in the development of therapeutics based on carbohydrates.     

Intrinsic contribution of the 2'-hydroxyl to RNA conformational heterogeneity

Canonical duplex RNA assumes only the A-form conformation at the secondary structure level while, in contrast, a wide range of noncanonical, tertiary conformations of RNA occur. Here, we show how the 2'-hydroxyl controls RNA conformational properties. Quantum mechanical calculations reveal that the orientation of the 2'-hydroxyl significantly alters the intrinsic flexibility of the phosphodiester backbone, favoring the A-form in duplex RNA when it is in the base orientation and facilitating sampling of a wide range of noncanonical, tertiary structures when it is in the O3' orientation. Influencing the orientation of the 2'-hydroxyl are interactions with the environment, as evidenced by crystallographic survey data, indicating the 2'-hydroxyl to sample more of the O3' orientation in noncanonical RNA structures. These results indicate that the 2'-hydroxyl acts as a "switch", both limiting the conformation of RNA to the A-form at the secondary structure level and allowing RNA to sample a wide range of noncanonical tertiary conformations.     

RNACluster: An integrated tool for RNA secondary structure comparison and clustering

RNA structure comparison is a fundamental problem in structural biology, structural chemistry, and bioinformatics. It can be used for analysis of RNA energy landscapes, conformational switches, and facilitating RNA structure prediction. The purpose of our integrated tool RNACluster is twofold: to provide a platform for computing and comparison of different distances between RNA secondary structures, and to perform cluster identification to derive useful information of RNA structure ensembles, using a minimum spanning tree (MST) based clustering algorithm. RNACluster employs a cluster identification approach based on a MST representation of the RNA ensemble data and currently supports six distance measures between RNA secondary structures. RNACluster provides a user-friendly graphical interface to allow a user to compare different structural distances, analyze the structure ensembles, and visualize predicted structural clusters.     

Time-resolved RNA SHAPE chemistry

Selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) chemistry yields quantitative RNA secondary and tertiary structure information at single nucleotide resolution. SHAPE takes advantage of the discovery that the nucleophilic reactivity of the ribose 2'-hydroxyl group is modulated by local nucleotide flexibility in the RNA backbone. Flexible nucleotides are reactive toward hydroxyl-selective electrophiles, whereas constrained nucleotides are unreactive. Initial versions of SHAPE chemistry, which employ isatoic anhydride derivatives that react on the minute time scale, are emerging as the ideal technology for monitoring equilibrium structures of RNA in a wide variety of biological environments. Here, we extend SHAPE chemistry to a benzoyl cyanide scaffold to make possible facile time-resolved kinetic studies of RNA in approximately 1 s snapshots. We then use SHAPE chemistry to follow the time-dependent folding of an RNase P specificity domain RNA. Tertiary interactions form in two distinct steps with local tertiary contacts forming an order of magnitude faster than long-range interactions. Rate-determining tertiary folding requires minutes despite that no non-native interactions must be disrupted to form the native structure. Instead, overall folding is limited by simultaneous formation of interactions approximately 55 A distant in the RNA. Time-resolved SHAPE holds broad potential for understanding structural biogenesis and the conformational interconversions essential to the functions of complex RNA molecules at single nucleotide resolution.     

Discrete state model and accurate estimation of loop entropy of RNA secondary structures

Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.     

Learning the Fastest RNA Folding Path Based on Reinforcement Learning and Monte Carlo Tree Search

RNA molecules participate in many important biological processes, and they need to fold into well-defined secondary and tertiary structures to realize their functions. Like the well-known protein folding problem, there is also an RNA folding problem. The folding problem includes two aspects: structure prediction and folding mechanism. Although the former has been widely studied, the latter is still not well understood. Here we present a deep reinforcement learning algorithms 2dRNA-Fold to study the fastest folding paths of RNA secondary structure. 2dRNA-Fold uses a neural network combined with Monte Carlo tree search to select residue pairing step by step according to a given RNA sequence until the final secondary structure is formed. We apply 2dRNA-Fold to several short RNA molecules and one longer RNA 1Y26 and find that their fastest folding paths show some interesting features. 2dRNA-Fold is further trained using a set of RNA molecules from the dataset bpRNA and is used to predict RNA secondary structure. Since in 2dRNA-Fold the scoring to determine next step is based on possible base pairings, the learned or predicted fastest folding path may not agree with the actual folding paths determined by free energy according to physical laws.     

A binary coding method of RNA secondary structure and its application

According to the three classifications of nucleotides, we introduce a sort of binary coding method of RNA secondary structures. On the basis of this representation, we can reduce a RNA secondary structure into three binary digit sequences. We also propose coding rules based on the exclusive‐OR operation. Associating with the proposed coding rules, we can judge the mutation between bases or between base and base pair, and make sequence alignment easily. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

RNA secondary structure 2D graphical representation without degeneracy

A two‐dimensional graphical representation (2DGRR) of RNA secondary structures using a two Cartesian coordinates system has been derived for mathematical denotation of RNA structure. The 2DGRR resolves structure degeneracy and avoids loss of information and the limitation that different structures correspond to the same curve. The RNA pseudo‐knots also can be represented as 2D graphical representations. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Studying the mechanism of RNA separations using RNA chromatography and its application in the analysis of ribosomal RNA and RNA:RNA interactions

DNA/RNA chromatography presents a versatile platform for the analysis of nucleic acids. Although the mechanism of separation of double stranded (ds) DNA fragments is largely understood, the mechanism by which RNA is separated appears more complicated. To further understand the separation mechanisms of RNA using ion pair reverse phase liquid chromatography, we have analysed a number of dsRNA and single stranded (ss) RNA fragments. The high-resolution separation of dsRNA was observed, in a similar manner to dsDNA under non-denaturing conditions. Moreover, the high-resolution separation of ssRNA was observed at high temperatures (75 °C) in contrast to ssDNA. It is proposed that the presence of duplex regions/secondary structures within the RNA remain at such temperatures, resulting in high-resolution RNA separations. The retention time of the nucleic acids reflects the relative hydrophobicity, through contributions of the nucleic sequence and the degree of secondary structure present. In addition, the analysis of RNA using such approaches was extended to enable the discrimination of bacterial 16S rRNA fragments and as an aid to conformational analysis of RNA. RNA:RNA interactions of the human telomerase RNA component (hTR) were analysed in conjunction with the incorporation of Mg²⁺ during chromatography. This novel chromatographic procedure permits analysis of the temperature dependent formation of dimeric RNA species.     

CSSP2: an improved method for predicting contact-dependent secondary structure propensity

The calculation of contact-dependent secondary structure propensity (CSSP) has been reported to sensitively detect non-native β-strand propensities in the core sequences of amyloidogenic proteins. Here we describe a noble energy-based CSSP method implemented on dual artificial neural networks that rapidly and accurately estimate the potential for the non-native secondary structure formation in local regions of protein sequences. In this method, we attempted to quantify long-range interaction patterns in diverse secondary structures by potential energy calculations and decomposition on a pairwise per-residue basis. The calculated energy parameters and seven-residue sequence information were used as inputs for artificial neural networks (ANNs) to predict sequence potential for secondary structure conversion. The trained single ANN using the >(i, i ± 4) interaction energy parameter exhibited 74% accuracy in predicting the secondary structure of test sequences in their native energy state, while the dual ANN-based predictor using (i, i ± 4) and >(i, i ± 4) interaction energies showed 83% prediction accuracy. The present method provides a simple and accurate tool for predicting sequence potential for secondary structure conversions without using 3D structural information.