Partition function and base pairing probabilities of RNA heterodimers

Background  

RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms.     

Adenine-guanine base pairing ribosomal RNA.

Analyses of secondary structures proposed for ribosomal RNA's show that, of the different kinds of base pairs directly adjoining the ends of postulated double-helical regions, only A-G with A at the 5' end significantly exceeds the number expected for a random base distribution. An A(syn)-G(trans) hydrogen-bonded basepair is proposed. This could fit at the end of an undistorted double helix, but would prevent further base stacking, thus favoring a break in the double helix to produce a non-linear tertiary structure.     

G.U base pairing motifs in ribosomal RNA.

An increasing number of recognition mechanisms in RNA are found to involve G.U base pairs. In order to detect new functional sites of this type, we exhaustively analyzed the sequence alignments and secondary structures of eubacterial and chloroplast 16S and 23S rRNA, seeking positions with high levels of G.U pairs. Approximately 120 such sites were identified and classified according to their secondary structure and sequence environment. Overall biases in the distribution of G.U pairs are consistent with previously proposed structural rules: the side of the wobble pair that is subject to a loss of stacking is preferentially exposed to a secondary structure loop, where stacking is not as essential as in helical regions. However, multiple sites violate these rules and display highly conserved G.U pairs in orientations that could cause severe stacking problems. In addition, three motifs displaying a conserved G.U pair in a specific sequence/structure environment occur at an unusually high frequency. These motifs, of which two had not been reported before, involve sequences 5''UG3'' 3''GA5'' and 5''UG3'' 3''GU5'', as well as G.U pairs flanked by a bulge loop 3'' of U. The possible structures and functions of these recurrent motifs are discussed.     

Alignment of RNA base pairing probability matrices

MOTIVATION: Many classes of functional RNA molecules are characterized by highly conserved secondary structures but little detectable sequence similarity. Reliable multiple alignments can therefore be constructed only when the shared structural features are taken into account. Since multiple alignments are used as input for many subsequent methods of data analysis, structure-based alignments are an indispensable necessity in RNA bioinformatics. RESULTS: We present here a method to compute pairwise and progressive multiple alignments from the direct comparison of base pairing probability matrices. Instead of attempting to solve the folding and the alignment problem simultaneously as in the classical Sankoff's algorithm, we use McCaskill's approach to compute base pairing probability matrices which effectively incorporate the information on the energetics of each sequences. A novel, simplified variant of Sankoff's algorithms can then be employed to extract the maximum-weight common secondary structure and an associated alignment. AVAILABILITY: The programs pmcomp and pmmulti described in this contribution are implemented in Perl and can be downloaded together with the example datasets from http://www.tbi.univie.ac.at/RNA/PMcomp/. A web server is available at http://rna.tbi.univie.ac.at/cgi-bin/pmcgi.pl     

Rfold: an exact algorithm for computing local base pairing probabilities

MOTIVATION: Base pairing probability matrices have been frequently used for the analyses of structural RNA sequences. Recently, there has been a growing need for computing these probabilities for long DNA sequences by constraining the maximal span of base pairs to a limited value. However, none of the existing programs can exactly compute the base pairing probabilities associated with the energy model of secondary structures under such a constraint. RESULTS: We present an algorithm that exactly computes the base pairing probabilities associated with the energy model under the constraint on the maximal span W of base pairs. The complexity of our algorithm is given by O(NW2) in time and O(N+W2) in memory, where N is the sequence length. We show that our algorithm has a higher sensitivity to the true base pairs as compared to that of RNAplfold. We also present an algorithm that predicts a mutually consistent set of local secondary structures by maximizing the expected accuracy function. The comparison of the local secondary structure predictions with those of RNALfold indicates that our algorithm is more accurate. Our algorithms are implemented in the software named 'Rfold.' AVAILABILITY: The C++ source code of the Rfold software and the test dataset used in this study are available at http://www.ncrna.org/software/Rfold/.     

Optical properties and base pairing of E. coli 5S RNA

The ultraviolet absorption, optical rotatory dispersion, circular dichroism, and infrared absorption spectra of renatured 5S RNA have been measured at pH 7.0 in 0.1M NaCl at 25° and used to obtain four independent estimates of the number of base pairs. These four estimations are in reaonable agreement and average values of 28 ± 4 G.C and 13 ± 4 A.U. base pairs.     

RNA structure and dynamics: A base pairing perspective

RNA is now known to possess various structural, regulatory and enzymatic functions for survival of cellular organisms. Functional RNA structures are generally created by three-dimensional organization of small structural motifs, formed by base pairing between self-complementary sequences from different parts of the RNA chain. In addition to the canonical Watson–Crick or wobble base pairs, several non-canonical base pairs are found to be crucial to the structural organization of RNA molecules. They appear within different structural motifs and are found to stabilize the molecule through long-range intra-molecular interactions between basic structural motifs like double helices and loops. These base pairs also impart functional variation to the minor groove of A-form RNA helices, thus forming anchoring site for metabolites and ligands. Non-canonical base pairs are formed by edge-to-edge hydrogen bonding interactions between the bases. A large number of theoretical studies have been done to detect and analyze these non-canonical base pairs within crystal or NMR derived structures of different functional RNA. Theoretical studies of these isolated base pairs using ab initio quantum chemical methods as well as molecular dynamics simulations of larger fragments have also established that many of these non-canonical base pairs are as stable as the canonical Watson–Crick base pairs. This review focuses on the various structural aspects of non-canonical base pairs in the organization of RNA molecules and the possible applications of these base pairs in predicting RNA structures with more accuracy.     

Theoretical analysis of noncanonical base pairing interactions in RNA molecules

Noncanonical base pairs in RNA have strong structural and functional implications but are currently not considered for secondary structure predictions. We present results of comparative ab initio studies of stabilities and interaction energies for the three standard and 24 selected unusual RNA base pairs reported in the literature. Hydrogen added models of isolated base pairs, with heavy atoms frozen in their 'away from equilibrium' geometries, built from coordinates extracted from NDB, were geometry optimized using HF/6-31G** basis set, both before and after unfreezing the heavy atoms. Interaction energies, including BSSE and deformation energy corrections, were calculated, compared with respective single point MP2 energies, and correlated with occurrence frequencies and with types and geometries of hydrogen bonding interactions. Systems having two or more N-H...O/N hydrogen bonds had reasonable interaction energies which correlated well with respective occurrence frequencies and highlighted the possibility of some of them playing important roles in improved secondary structure prediction methods. Several of the remaining base pairs with one N-H...O/N and/or one C-H...O/N interactions respectively, had poor interaction energies and negligible occurrences. High geometry variations on optimization of some of these were suggestive of their conformational switch like characteristics.     

Theoretical analysis of noncanonical base pairing interactions in RNA molecules

Noncanonical base pairs in RNA have strong structural and functional implications but are currently not considered for secondary structure predictions. We present results of comparative ab initio studies of stabilities and interaction energies for the three standard and 24 selected unusual RNA base pairs reported in the literature. Hydrogen added models of isolated base pairs, with heavy atoms frozen in their ‘away from equilibrium’ geometries, built from coordinates extracted from NDB, were geometry optimized using HF/6-31G** basis set, both before and after unfreezing the heavy atoms. Interaction energies, including BSSE and deformation energy corrections, were calculated, compared with respective single point MP2 energies, and correlated with occurrence frequencies and with types and geometries of hydrogen bonding interactions. Systems having two or more N-H...O/N hydrogen bonds had reasonable interaction energies which correlated well with respective occurrence frequencies and highlighted the possibility of some of them playing important roles in improved secondary structure prediction methods. Several of the remaining base pairs with one N-H...O/N and/or one C-H...O/N interactions respectively, had poor interaction energies and negligible occurrences. High geometry variations on optimization of some of these were suggestive of their conformational switch like characteristics.     

Equilibrium conformational dynamics in an RNA tetraloop from massively parallel molecular dynamics

Conformational equilibrium within the ubiquitous GNRA tetraloop motif was simulated at the ensemble level, including 10 000 independent all-atom molecular dynamics trajectories totaling over 110 µs of simulation time. This robust sampling reveals a highly dynamic structure comprised of 15 conformational microstates. We assemble a Markov model that includes transitions ranging from the nanosecond to microsecond timescales and is dominated by six key loop conformations that contribute to fluctuations around the native state. Mining of the Protein Data Bank provides an abundance of structures in which GNRA tetraloops participate in tertiary contact formation. Most predominantly observed in the experimental data are interactions of the native loop structure within the minor groove of adjacent helical regions. Additionally, a second trend is observed in which the tetraloop assumes non-native conformations while participating in multiple tertiary contacts, in some cases involving multiple possible loop conformations. This tetraloop flexibility can act to counterbalance the energetic penalty associated with assuming non-native loop structures in forming tertiary contacts. The GNRA motif has thus evolved not only to readily participate in simple tertiary interactions involving native loop structure, but also to easily adapt tetraloop secondary conformation in order to participate in larger, more complex tertiary interactions.     

Secondary structure of the 3'-noncoding region of flavivirus genomes: comparative analysis of base pairing probabilities.

The prediction of the complete matrix of base pairing probabilities was applied to the 3'' noncoding region (NCR) of flavivirus genomes. This approach identifies not only well-defined secondary structure elements, but also regions of high structural flexibility. Flaviviruses, many of which are important human pathogens, have a common genomic organization, but exhibit a significant degree of RNA sequence diversity in the functionally important 3''-NCR. We demonstrate the presence of secondary structures shared by all flaviviruses, as well as structural features that are characteristic for groups of viruses within the genus reflecting the established classification scheme. The significance of most of the predicted structures is corroborated by compensatory mutations. The availability of infectious clones for several flaviviruses will allow the assessment of these structural elements in processes of the viral life cycle, such as replication and assembly.     

RNA sequence and base pairing effects on insertion editing in Trypanosoma brucei

RNA editing inserts and deletes uridylates (U's) in kinetoplastid mitochondrial pre-mRNAs by a series of enzymatic steps. Small guide RNAs (gRNAs) specify the edited sequence. Editing, though sometimes extensive, is precise. The effects of mutating pre-mRNA and gRNA sequences in, around, and upstream of the editing site on the specificity and efficiency of in vitro insertion editing were examined. U's could be added opposite guiding pyrimidines, but guiding purines, particularly A's, were required for efficient ligation. A base pair between mRNA and gRNA immediately upstream of the editing site was not required for insertion editing, although it greatly enhanced its efficiency and accuracy. In addition, a gRNA/mRNA duplex upstream of the editing site enhanced insertion editing when it was close to the editing site, but prevented cleavage, and hence editing, when immediately adjacent to the editing site. Thus, several aspects of mRNA-gRNA interaction, as well as gRNA base pairing with added U's, optimize editing efficiency, although they are not required for insertion editing.     

The equilibrium partition function and base pair binding probabilities for RNA secondary structure.

A novel application of dynamic programming to the folding problem for RNA enables one to calculate the full equilibrium partition function for secondary structure and the probabilities of various substructures. In particular, both the partition function and the probabilities of all base pairs are computed by a recursive scheme of polynomial order N3 in the sequence length N. The temperature dependence of the partition function gives information about melting behavior for the secondary structure. The pair binding probabilities, the computation of which depends on the partition function, are visually summarized in a "box matrix" display and this provides a useful tool for examining the full ensemble of probable alternative equilibrium structures. The calculation of this ensemble representation allows a proper application and assessment of the predictive power of the secondary structure method, and yields important information on alternatives and intermediates in addition to local information about base pair opening and slippage. The results are illustrated for representative tRNA, 5S RNA, and self-replicating and self-splicing RNA molecules, and allow a direct comparison with enzymatic structure probes. The effect of changes in the thermodynamic parameters on the equilibrium ensemble provides a further sensitivity check to the predictions.     

Prediction of strand pairing in antiparallel and parallel beta-sheets using information theory

An information theory approach was developed to predict the alignment of interacting antiparallel and parallel beta-strands. Information scores were derived for the preference of a residue on a beta-strand to be opposite a sequence of residues on an adjacent beta-strand. These scores were used to predict the interstrand register of interacting beta-strands from 10 alternative offset positions either side of the experimentally observed beta-sheet register. The amino acid sequence of an internal beta-strand can be correctly aligned with two beta-strands in a fixed position either side of the strand in 45% of antiparallel and 48% of parallel arrangements. For comparison, when another beta-strand from a nonhomologous protein substitutes the internal beta-strand, the same register is predicted for only 24 and 36% of antiparallel and parallel arrangements. As expected, alignment of a single fixed strand with just a second beta-strand sequence was more difficult, and gave a correct register in 31 and 37% of antiparallel and parallel beta-pairs, respectively. These scores are 10% higher than for two randomly selected beta-strand sequences. In general, prediction accuracy was not improved by information tables that distinguished hydrogen-bonding patterns or beta-strand order. These results will contribute to predicting the arrangement of beta-strands in beta-pleated sheets and protein topology.