Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.Comment: 28 pages, 18 figure

Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics

BACKGROUND: The general problem of RNA secondary structure prediction under the widely used thermodynamic model is known to be NP-complete when the structures considered include arbitrary pseudoknots. For restricted classes of pseudoknots, several polynomial time algorithms have been designed, where the O(n(6))time and O(n(4)) space algorithm by Rivas and Eddy is currently the best available program. RESULTS: We introduce the class of canonical simple recursive pseudoknots and present an algorithm that requires O(n(4)) time and O(n(2)) space to predict the energetically optimal structure of an RNA sequence, possible containing such pseudoknots. Evaluation against a large collection of known pseudoknotted structures shows the adequacy of the canonization approach and our algorithm. CONCLUSIONS: RNA pseudoknots of medium size can now be predicted reliably as well as efficiently by the new algorithm

Algorithms for RNA secondary structure analysis : prediction of pseudoknots and the consensus shapes approach

Reeder J. Algorithms for RNA secondary structure analysis : prediction of pseudoknots and the consensus shapes approach. Bielefeld (Germany): Bielefeld University; 2007.Our understanding of the role of RNA has undergone a major change in the last decade. Once believed to be only a mere carrier of information and structural component of the ribosomal machinery in the advent of the genomic age, it is now clear that RNAs play a much more active role. RNAs can act as regulators and can have catalytic activity - roles previously only attributed to proteins. There is still much speculation in the scientific community as to what extent RNAs are responsible for the complexity in higher organisms which can hardly be explained with only proteins as regulators. In order to investigate the roles of RNA, it is therefore necessary to search for new classes of RNA. For those and already known classes, analyses of their presence in different species of the tree of life will provide further insight about the evolution of biomolecules and especially RNAs. Since RNA function often follows its structure, the need for computer programs for RNA structure prediction is an immanent part of this procedure. The secondary structure of RNA - the level of base pairing - strongly determines the tertiary structure. As the latter is computationally intractable and experimentally expensive to obtain, secondary structure analysis has become an accepted substitute. In this thesis, I present two new algorithms (and a few variations thereof) for the prediction of RNA secondary structures. The first algorithm addresses the problem of predicting a secondary structure from a single sequence including RNA pseudoknots. Pseudoknots have been shown to be functionally relevant in many RNA mediated processes. However, pseudoknots are excluded from considerations by state-of-the-art RNA folding programs for reasons of computational complexity. While folding a sequence of length n into unknotted structures requires O(n^3) time and O(n^2) space, finding the best structure including arbitrary pseudoknots has been proven to be NP-complete. Nevertheless, I demonstrate in this work that certain types of pseudoknots can be included in the folding process with only a moderate increase of computational cost. In analogy to protein coding RNA, where a conserved encoded protein hints at a similar metabolic function, structural conservation in RNA may give clues to RNA function and to finding of RNA genes. However, structure conservation is more complex to deal with computationally than sequence conservation. The method considered to be at least conceptually the ideal approach in this situation is the Sankoff algorithm. It simultaneously aligns two sequences and predicts a common secondary structure. Unfortunately, it is computationally rather expensive - O(n^6) time and O(n^4) space for two sequences, and for more than two sequences it becomes exponential in the number of sequences! Therefore, several heuristic implementations emerged in the last decade trying to make the Sankoff approach practical by introducing pragmatic restrictions on the search space. In this thesis, I propose to redefine the consensus structure prediction problem in a way that does not imply a multiple sequence alignment step. For a family of RNA sequences, my method explicitly and independently enumerates the near-optimal abstract shape space and predicts an abstract shape as the consensus for all sequences. For each sequence, it delivers the thermodynamically best structure which has this shape. The technique of abstract shapes analysis is employed here for a synoptic view of the suboptimal folding space. As the shape space is much smaller than the structure space, and identification of common shapes can be done in linear time (in the number of shapes considered), the method is essentially linear in the number of sequences. Evaluations show that the new method compares favorably with available alternatives

Genomics and proteomics: a signal processor's tour

The theory and methods of signal processing are becoming increasingly important in molecular biology. Digital filtering techniques, transform domain methods, and Markov models have played important roles in gene identification, biological sequence analysis, and alignment. This paper contains a brief review of molecular biology, followed by a review of the applications of signal processing theory. This includes the problem of gene finding using digital filtering, and the use of transform domain methods in the study of protein binding spots. The relatively new topic of noncoding genes, and the associated problem of identifying ncRNA buried in DNA sequences are also described. This includes a discussion of hidden Markov models and context free grammars. Several new directions in genomic signal processing are briefly outlined in the end

Torsion and bending of nucleic acids studied by subnanosecond time-resolved fluorescence depolarization of intercalated dyes

Subnanosecond time‐resolved fluorescence depolarization has been used to monitor the reorientation of ethidium bromide intercalated in native DNA, synthetic polynucleotide complexes, and in supercoiled plasmid DNA. The fluorescence polarization anisotropy was successfully analyzed with an elastic model of DNA dynamics, including both torsion and bending, which yielded an accurate value for the torsional rigidity of the different DNA samples. The dependence of the torsional rigidity on the base sequence, helical structure, and tertiary structure was experimentally observed. The magnitude of the polyelectrolyte contribution to the torsional rigidity of DNA was measured over a wide range of ionic strength, and compared with polyelectrolyte theories for the persistence length. We also observed a rapid initial reorientation of the intercalated ethidium which had a much smaller amplitude in RNA than in DNA

Clustering RNA structural motifs in ribosomal RNAs using secondary structural alignment

RNA structural motifs are the building blocks of the complex RNA architecture. Identification of non-coding RNA structural motifs is a critical step towards understanding of their structures and functionalities. In this article, we present a clustering approach for de novo RNA structural motif identification. We applied our approach on a data set containing 5S, 16S and 23S rRNAs and rediscovered many known motifs including GNRA tetraloop, kink-turn, C-loop, sarcin–ricin, reverse kink-turn, hook-turn, E-loop and tandem-sheared motifs, with higher accuracy than the state-of-the-art clustering method. We also identified a number of potential novel instances of GNRA tetraloop, kink-turn, sarcin–ricin and tandem-sheared motifs. More importantly, several novel structural motif families have been revealed by our clustering analysis. We identified a highly asymmetric bulge loop motif that resembles the rope sling. We also found an internal loop motif that can significantly increase the twist of the helix. Finally, we discovered a subfamily of hexaloop motif, which has significantly different geometry comparing to the currently known hexaloop motif. Our discoveries presented in this article have largely increased current knowledge of RNA structural motifs

SimulFold: Simultaneously Inferring RNA Structures Including Pseudoknots, Alignments, and Trees Using a Bayesian MCMC Framework

Computational methods for predicting evolutionarily conserved rather than thermodynamic RNA structures have recently attracted increased interest. These methods are indispensable not only for elucidating the regulatory roles of known RNA transcripts, but also for predicting RNA genes. It has been notoriously difficult to devise them to make the best use of the available data and to predict high-quality RNA structures that may also contain pseudoknots. We introduce a novel theoretical framework for co-estimating an RNA secondary structure including pseudoknots, a multiple sequence alignment, and an evolutionary tree, given several RNA input sequences. We also present an implementation of the framework in a new computer program, called SimulFold, which employs a Bayesian Markov chain Monte Carlo method to sample from the joint posterior distribution of RNA structures, alignments, and trees. We use the new framework to predict RNA structures, and comprehensively evaluate the quality of our predictions by comparing our results to those of several other programs. We also present preliminary data that show SimulFold's potential as an alignment and phylogeny prediction method. SimulFold overcomes many conceptual limitations that current RNA structure prediction methods face, introduces several new theoretical techniques, and generates high-quality predictions of conserved RNA structures that may include pseudoknots. It is thus likely to have a strong impact, both on the field of RNA structure prediction and on a wide range of data analyses