A continuous analog for RNA folding

A linear segment in which a number of pairs of intervals of equal length are identified as potential stems is the subject of a folding problem analogous to inference of RNA secondary structure. A quantity of free energy (or equivalently, energy per unit length) is associated with each stem, and the various types of loops are assigned energy costs as a function of their lengths. Inference of stable structures can then be carried out in the same way as in RNA folding. More important, perturbation of stem lengths and energy densities (modelling various mutational processes affecting nucleotide sequences) allows the delineation of domains of stability of various foldings, through the explicit calculation of their boundaries, in a low-dimensional parameter space.     

Predicting Secondary Structural Folding Kinetics for Nucleic Acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.     

A Boltzmann filter improves the prediction of RNA folding pathways in a massively parallel genetic algorithm

RNA folding using the massively parallel genetic algorithm (GA) has been enhanced by the addition of a Boltzmann filter. The filter uses the Boltzmann probability distribution in conjunction with Metropolis' relaxation algorithm. The combination of these two concepts within the GA's massively parallel computational environment helps guide the genetic algorithm to more accurately reflect RNA folding pathways and thus final solution structures. Helical regions (base-paired stems) now form in the structures based upon the stochastic properties of the thermodynamic parameters that have been determined from experiments. Thus, structural changes occur based upon the relative energetic impact that the change causes rather than just geometric conflicts alone. As a result, when comparing the predictions to phylogenetically determined structures, over multiple runs, fewer false-positive stems (predicted incorrectly) and more true-positive stems (predicted correctly) are generated, and the total number of predicted stems representing a solution is diminished. In addition, the significance (rate of occurrence) of the true-positive stems is increased. Thus, the predicted results more accurately reflect phylogenetically determined structures.     

No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies indistinguishable from randomized sequences. This suggests that the predicted free energy is not always a good determinant for RNA folding.     

Identifying complete RNA structural ensembles including pseudoknots

The close relationship between RNA structure and function underlines the significance of accurately predicting RNA structures from sequence information. Structural topologies such as pseudoknots are of particular interest due to their ubiquity and direct involvement in RNA function, but identifying pseudoknots is a computationally challenging problem and existing heuristic approaches usually perform poorly for RNA sequences of even a few hundred bases. We survey the performance of pseudoknot prediction methods on a data set of full-length RNA sequences representing varied sequence lengths, and biological RNA classes such as RNase P RNA, Group I Intron, tmRNA and tRNA. Pseudoknot prediction methods are compared with minimum free energy and suboptimal secondary structure prediction methods in terms of correct base-pairs, stems and pseudoknots and we find that the ensemble of suboptimal structure predictions succeeds in identifying correct structural elements in RNA that are usually missed in MFE and pseudoknot predictions. We propose a strategy to identify a comprehensive set of non-redundant stems in the suboptimal structure space of a RNA molecule by applying heuristics that reduce the structural redundancy of the predicted suboptimal structures by merging slightly varying stems that are predicted to form in local sequence regions. This reduced-redundancy set of structural elements consistently outperforms more specialized approaches.in data sets. Thus, the suboptimal folding space can be used to represent the structural diversity of an RNA molecule more comprehensively than optimal structure prediction approaches alone.     

RGRNA: prediction of RNA secondary structure based on replacement and growth of stems

Owing to their structural diversity, RNAs perform many diverse biological functions in the cell. RNA secondary structure is thus important for predicting RNA function. Here, we propose a new combinatorial optimization algorithm, named RGRNA, to improve the accuracy of predicting RNA secondary structure. Following the establishment of a stempool, the stems are sorted by length, and chosen from largest to smallest. If the stem selected is the true stem, the secondary structure of this stem when combined with another stem selected at random will have low free energy, and the free energy will tend to gradually diminish. The free energy is considered as a parameter and the structure is converted into binary numbers to determine stem compatibility, for step-by-step prediction of the secondary structure for all combinations of stems. The RNA secondary structure can be predicted by the RGRNA method. Our experimental results show that the proposed algorithm outperforms RNAfold in terms of sensitivity, specificity, and Matthews correlation coefficient value.     

Computer simulation of tRNA secondary structure folding

Computer simulation results of folding linear RNA moleculesinto secondaty structures are presented. The structure is formedby two interacting processes: the RNA molecular chain growth(beginning from an initial length, L_o), and the structuring(secondary structure sequential growth in the region of theexisting molecular chain, based on the local free energy minimizationby sequential addition of elementary substruc tures-stems).It was found that the final secondary structure formation isgreatly influenced by the ‘structuring period’ T(the ratio of the molecular chain growth rate to the structuringrate), and the direction of RNA synthesis. The computer simulationhas been performed for 219 and 906 tRNA genes from two publishedcatalogues, on the whale two-dimensional domain (T,L₀) parameters,by using four known free-energy models. Minimwn stem lengthand molecular chain growth direction have been also varied Thecalculated secondary structures have been compared to the naturaltRNA structures given in the catalogues, and the region of bestcoincidence for the model parameters has been determined. Ithas been proved that, on average, >86% of the paired basesof natural tRNA structures appear in the folding simulation.     

RNA2D3D: a program for generating, viewing, and comparing 3-dimensional models of RNA

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

Predicting the secondary structures and tertiary interactions of 211 group I introns in IE subgroup

The large number of currently available group I intron sequences in the public databases provides opportunity for studying this large family of structurally complex catalytic RNA by large-scale comparative sequence analysis. In this study, the detailed secondary structures of 211 group I introns in the IE subgroup were manually predicted. The secondary structure-favored alignments showed that IE introns contain 14 conserved stems. The P13 stem formed by long-range base-pairing between P2.1 and P9.1 is conserved among IE introns. Sequence variations in the conserved core divide IE introns into three distinct minor subgroups, namely IE1, IE2 and IE3. Co-variation of the peripheral structural motifs with core sequences supports that the peripheral elements function in assisting the core structure folding. Interestingly, host-specific structural motifs were found in IE2 introns inserted at S516 position. Competitive base-pairing is found to be conserved at the junctions of all long-range paired regions, suggesting a possible mechanism of establishing long-range base-pairing during large RNA folding. These findings extend our knowledge of IE introns, indicating that comparative analysis can be a very good complement for deepening our understanding of RNA structure and function in the genomic era.     

RNA2D3D: A program for Generating,Viewing, and Comparing 3-Dimensional Models of RNA

Abstract

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

Mutational patterns in RNA secondary structure evolution examined in three RNA families

The goal of this work was to study mutational patterns in the evolution of RNA secondary structure. We analyzed bacterial tmRNA, RNaseP and eukaryotic telomerase RNA secondary structures, mapping structural variability onto phylogenetic trees constructed primarily from rRNA sequences. We found that secondary structures evolve both by whole stem insertion/deletion, and by mutations that create or disrupt stem base pairing. We analyzed the evolution of stem lengths and constructed substitution matrices describing the changes responsible for the variation in the RNA stem length. In addition, we used principal component analysis of the stem length data to determine the most variable stems in different families of RNA. This data provides new insights into the evolution of RNA secondary structures and patterns of variation in the lengths of double helical regions of RNA molecules. Our findings will facilitate design of improved mutational models for RNA structure evolution.     

RNA STRAND: The RNA Secondary Structure and Statistical Analysis Database

Background  

The ability to access, search and analyse secondary structures of a large set of known RNA molecules is very important for deriving improved RNA energy models, for evaluating computational predictions of RNA secondary structures and for a better understanding of RNA folding. Currently there is no database that can easily provide these capabilities for almost all RNA molecules with known secondary structures.     

Secondary structure models of D2-D3 expansion segments of 28S rRNA for Hoplolaiminae species

The D2-D3 expansion segments of the 28S ribosomal RNA (rRNA) were sequenced and compared to predict secondary structures for Hoplolaiminae species based on free energy minimization and comparative sequence analysis. The free energy based prediction method provides putative stem regions within primary structure and these base pairings in stems were confirmed manually by compensatory base changes among closely and distantly related species. Sequence differences ranged from identical between Hoplolaimus columbus and H. seinhorsti to 20.8% between Scutellonema brachyurum and H. concaudajuvencus. The comparative sequence analysis and energy minimization method yielded 9 stems in the D2 and 6 stems in the D3 which showed complete or partial compensatory base changes. At least 75% of nucleotides in the D2 and 68% of nucleotides in the D3 were related with formation of base pairings to maintain secondary structure. GC contents in stems ranged from 61 to 73% for the D2 and from 64 to 71% for the D3 region. These ranges are higher than G-C contents in loops which ranged from 37 to 48% in the D2 and 33-45% in the D3. In stems, G-C/C-G base pairings were the most common in the D2 and the D3 and also non-canonical base pairs including A•A and U•U, C•U/U•C, and G•A/A•G occurred in stems. The predicted secondary model and new sequence alignment based on predicted secondary structures for the D2 and D3 expansion segments provide useful information to assign positional nucleotide homology and reconstruction of more reliable phylogenetic trees.     

Folding path of P5abc RNA involves direct coupling of secondary and tertiary structures

Folding mechanisms in which secondary structures are stabilized through the formation of tertiary interactions are well documented in protein folding but challenge the folding hierarchy normally assumed for RNA. However, it is increasingly clear that RNA could fold by a similar mechanism. P5abc, a small independently folding tertiary domain of the Tetrahymena thermophila group I ribozyme, is known to fold by a secondary structure rearrangement involving helix P5c. However, the extent of this rearrangement and the precise stage of folding that triggers it are unknown. We use experiments and simulations to show that the P5c helix switches to the native secondary structure late in the folding pathway and is directly coupled to the formation of tertiary interactions in the A-rich bulge. P5c mutations show that the switch in P5c is not rate-determining and suggest that non-native interactions in P5c aid folding rather than impede it. Our study illustrates that despite significant differences in the building blocks of proteins and RNA, there may be common ways in which they self-assemble.