Statistical Physics of RNA-folding

We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large enough costs the model exhibits a thermal denaturation transition which we analyze in terms of the radius of gyration. We point out an inconsistency in the standard approach to RNA secondary structure prediction for large molecules. Under an external force a second order phase transition between a globular and an extended phase takes place. A Harris-type criterion shows that sequence disorder does not affect the correlation length exponent while the other critical exponents are modified in the glass phase. However, at high temperatures, on a coarse-grained level, disordered RNA is well described by a homogeneous model. The characteristics of force-extension curves are discussed as a function of the energy parameters. We show that the force transition is always second order. A re-entrance phenomenon relevant for real disordered RNA is predicted.Comment: accepted for publication in Phys. Rev.

RNAslider: a faster engine for consecutive windows folding and its application to the analysis of genomic folding asymmetry

<p>Abstract</p> <p>Background</p> <p>Scanning large genomes with a sliding window in search of locally stable RNA structures is a well motivated problem in bioinformatics. Given a predefined window size L and an RNA sequence S of size N (L < N), the consecutive windows folding problem is to compute the minimal free energy (MFE) for the folding of each of the L-sized substrings of S. The consecutive windows folding problem can be naively solved in O(NL³) by applying any of the classical cubic-time RNA folding algorithms to each of the N-L windows of size L. Recently an O(NL²) solution for this problem has been described.</p> <p>Results</p> <p>Here, we describe and implement an O(NLψ(L)) engine for the consecutive windows folding problem, where ψ(L) is shown to converge to O(1) under the assumption of a standard probabilistic polymer folding model, yielding an O(L) speedup which is experimentally confirmed. Using this tool, we note an intriguing directionality (5'-3' vs. 3'-5') folding bias, i.e. that the minimal free energy (MFE) of folding is higher in the native direction of the DNA than in the reverse direction of various genomic regions in several organisms including regions of the genomes that do not encode proteins or ncRNA. This bias largely emerges from the genomic dinucleotide bias which affects the MFE, however we see some variations in the folding bias in the different genomic regions when normalized to the dinucleotide bias. We also present results from calculating the MFE landscape of a mouse chromosome 1, characterizing the MFE of the long ncRNA molecules that reside in this chromosome.</p> <p>Conclusion</p> <p>The efficient consecutive windows folding engine described in this paper allows for genome wide scans for ncRNA molecules as well as large-scale statistics. This is implemented here as a software tool, called RNAslider, and applied to the scanning of long chromosomes, leading to the observation of features that are visible only on a large scale.</p

RNA structure analysis : algorithms and applications

In this doctoral thesis, efficient algorithms for aligning RNA secondary structures and mining unknown RNA motifs are presented. As the major contribution, a structure alignment algorithm, which combines both primary and secondary structure information, can find the optimal alignment between two given structures where one of them could be either a pattern structure of a known motif or a real query structure and the other be a subject structure. Motivated by widely used algorithms for RNA folding, the proposed algorithm decomposes an RNA secondary structure into a set of atomic structural components that can be further organized in a tree model to capture the structural particularities. The novel structure alignment algorithm is implemented using dynamic programming techniques coupled by position-independent scoring matrices. The algorithm can find the optimal global and local alignments between two RNA secondary structures at quadratic time complexity. When applied to searching a structure database, the algorithm can find similar RNA substructures and therefore can be used to identify functional RNA motifs. Extension of the algorithm has also been accomplished to deal with position-dependent scoring matrix in the purpose of aligning multiple structures. All algorithms have been implemented in a package under the name RSmatch and applied to searching mRNA UTR structure database and mining RNA motifs. The experimental results showed high efficiency and effectiveness of the proposed techniques

DNA nano-mechanics: how proteins deform the double helix

It is a standard exercise in mechanical engineering to infer the external forces and torques on a body from its static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with proteins. We extract the local mean forces and torques acting on each base-pair of bound DNA from high-resolution complex structures. Our method relies on known elastic potentials and a careful choice of coordinates of the well-established rigid base-pair model of DNA. The results are robust with respect to parameter and conformation uncertainty. They reveal the complex nano-mechanical patterns of interaction between proteins and DNA. Being non-trivially and non-locally related to observed DNA conformations, base-pair forces and torques provide a new view on DNA-protein binding that complements structural analysis.Comment: accepted for publication in JCP; some minor changes in response to review 18 pages, 5 figure + supplement: 4 pages, 3 figure

Computational Methods for Comparative Non-coding RNA Analysis: from Secondary Structures to Tertiary Structures

Unlike message RNAs (mRNAs) whose information is encoded in the primary sequences, the cellular roles of non-coding RNAs (ncRNAs) originate from the structures. Therefore studying the structural conservation in ncRNAs is important to yield an in-depth understanding of their functionalities. In the past years, many computational methods have been proposed to analyze the common structural patterns in ncRNAs using comparative methods. However, the RNA structural comparison is not a trivial task, and the existing approaches still have numerous issues in efficiency and accuracy. In this dissertation, we will introduce a suite of novel computational tools that extend the classic models for ncRNA secondary and tertiary structure comparisons. For RNA secondary structure analysis, we first developed a computational tool, named PhyloRNAalifold, to integrate the phylogenetic information into the consensus structural folding. The underlying idea of this algorithm is that the importance of a co-varying mutation should be determined by its position on the phylogenetic tree. By assigning high scores to the critical covariances, the prediction of RNA secondary structure can be more accurate. Besides structure prediction, we also developed a computational tool, named ProbeAlign, to improve the efficiency of genome-wide ncRNA screening by using high-throughput RNA structural probing data. It treats the chemical reactivities embedded in the probing information as pairing attributes of the searching targets. This approach can avoid the time-consuming base pair matching in the secondary structure alignment. The application of ProbeAlign to the FragSeq datasets shows its capability of genome-wide ncRNAs analysis. For RNA tertiary structure analysis, we first developed a computational tool, named STAR3D, to find the global conservation in RNA 3D structures. STAR3D aims at finding the consensus of stacks by using 2D topology and 3D geometry together. Then, the loop regions can be ordered and aligned according to their relative positions in the consensus. This stack-guided alignment method adopts the divide-and-conquer strategy into RNA 3D structural alignment, which has improved its efficiency dramatically. Furthermore, we also have clustered all loop regions in non-redundant RNA 3D structures to de novo detect plausible RNA structural motifs. The computational pipeline, named RNAMSC, was extended to handle large-scale PDB datasets, and solid downstream analysis was performed to ensure the clustering results are valid and easily to be applied to further research. The final results contain many interesting variations of known motifs, such as GNAA tetraloop, kink-turn, sarcin-ricin and t-loops. We also discovered novel functional motifs that conserved in a wide range of ncRNAs, including ribosomal RNA, sgRNA, SRP RNA, GlmS riboswitch and twister ribozyme

Identification of clustered microRNAs using an ab initio prediction method

BACKGROUND: MicroRNAs (miRNAs) are endogenous 21 to 23-nucleotide RNA molecules that regulate protein-coding gene expression in plants and animals via the RNA interference pathway. Hundreds of them have been identified in the last five years and very recent works indicate that their total number is still larger. Therefore miRNAs gene discovery remains an important aspect of understanding this new and still widely unknown regulation mechanism. Bioinformatics approaches have proved to be very useful toward this goal by guiding the experimental investigations. RESULTS: In this work we describe our computational method for miRNA prediction and the results of its application to the discovery of novel mammalian miRNAs. We focus on genomic regions around already known miRNAs, in order to exploit the property that miRNAs are occasionally found in clusters. Starting with the known human, mouse and rat miRNAs we analyze 20 kb of flanking genomic regions for the presence of putative precursor miRNAs (pre-miRNAs). Each genome is analyzed separately, allowing us to study the species-specific identity and genome organization of miRNA loci. We only use cross-species comparisons to make conservative estimates of the number of novel miRNAs. Our ab initio method predicts between fifty and hundred novel pre-miRNAs for each of the considered species. Around 30% of these already have experimental support in a large set of cloned mammalian small RNAs. The validation rate among predicted cases that are conserved in at least one other species is higher, about 60%, and many of them have not been detected by prediction methods that used cross-species comparisons. A large fraction of the experimentally confirmed predictions correspond to an imprinted locus residing on chromosome 14 in human, 12 in mouse and 6 in rat. Our computational tool can be accessed on the world-wide-web. CONCLUSION: Our results show that the assumption that many miRNAs occur in clusters is fruitful for the discovery of novel miRNAs. Additionally we show that although the overall miRNA content in the observed clusters is very similar across the three considered species, the internal organization of the clusters changes in evolution

Single DNA conformations and biological function

From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications.Comment: 53 pages, 45 figures. Slightly revised version of a review article, that is going to appear in the J. Comput. Theoret. Nanoscience; some typos correcte

In silico methods for co-transcriptional RNA secondary structure prediction and for investigating alternative RNA structure expression

RNA transcripts are the primary products of active genes in any living organism, including many viruses. Their cellular destiny not only depends on primary sequence signals, but can also be determined by RNA structure. Recent experimental evidence shows that many transcripts can be assigned more than a single functional RNA structure throughout their cellular life and that structure formation happens co-transcriptionally, i.e. as the transcript is synthesised in the cell. Moreover, functional RNA structures are not limited to non-coding transcripts, but can also feature in coding transcripts. The picture that now emerges is that RNA structures constitute an additional layer of information that can be encoded in any RNA transcript (and on top of other layers of information such as protein-context) in order to exert a wide range of functional roles. Moreover, different encoded RNA structures can be expressed at different stages of a transcript's life in order to alter the transcript's behaviour depending on its actual cellular context. Similar to the concept of alternative splicing for protein-coding genes, where a single transcript can yield different proteins depending on cellular context, it is thus appropriate to propose the notion of alternative RNA structure expression for any given transcript. This review introduces several computational strategies that my group developed to detect different aspects of RNA structure expression in vivo. Two aspects are of particular interest to us: (1) RNA secondary structure features that emerge during co-transcriptional folding and (2) functional RNA structure features that are expressed at different times of a transcript's life and potentially mutually exclusive

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