Prediction and statistics of pseudoknots in RNA structures using exactly clustered stochastic simulations

Ab initio RNA secondary structure predictions have long dismissed helices interior to loops, so-called pseudoknots, despite their structural importance. Here, we report that many pseudoknots can be predicted through long time scales RNA folding simulations, which follow the stochastic closing and opening of individual RNA helices. The numerical efficacy of these stochastic simulations relies on an O(n^2) clustering algorithm which computes time averages over a continously updated set of n reference structures. Applying this exact stochastic clustering approach, we typically obtain a 5- to 100-fold simulation speed-up for RNA sequences up to 400 bases, while the effective acceleration can be as high as 100,000-fold for short multistable molecules (<150 bases). We performed extensive folding statistics on random and natural RNA sequences, and found that pseudoknots are unevenly distributed amongst RNAstructures and account for up to 30% of base pairs in G+C rich RNA sequences (Online RNA folding kinetics server including pseudoknots : http://kinefold.u-strasbg.fr/ ).Comment: 6 pages, 5 figure

Prediction of RNA pseudoknots by Monte Carlo simulations

In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the non-planar topologies of RNA structures and propose a classification of RNA pseudoknots according to the minimal genus of the surface on which the RNA structure can be embedded. This classification provides a simple and natural way to tackle the problem of RNA folding prediction in presence of pseudoknots. Based on that approach, we describe a Monte Carlo algorithm for the prediction of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure

McGenus: A Monte Carlo algorithm to predict RNA secondary structures with pseudoknots

We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non trivial pseudoknot topologies. Specifically, McGenus employs a multiple Markov chain scheme for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web-server at http://ipht.cea.fr/rna/mcgenus.php .Comment: 6 pages, 1 figur

Computational identification and analysis of noncoding RNAs - Unearthing the buried treasures in the genome

The central dogma of molecular biology states that the genetic information flows from DNA to RNA to protein. This dogma has exerted a substantial influence on our understanding of the genetic activities in the cells. Under this influence, the prevailing assumption until the recent past was that genes are basically repositories for protein coding information, and proteins are responsible for most of the important biological functions in all cells. In the meanwhile, the importance of RNAs has remained rather obscure, and RNA was mainly viewed as a passive intermediary that bridges the gap between DNA and protein. Except for classic examples such as tRNAs (transfer RNAs) and rRNAs (ribosomal RNAs), functional noncoding RNAs were considered to be rare. However, this view has experienced a dramatic change during the last decade, as systematic screening of various genomes identified myriads of noncoding RNAs (ncRNAs), which are RNA molecules that function without being translated into proteins [11], [40]. It has been realized that many ncRNAs play important roles in various biological processes. As RNAs can interact with other RNAs and DNAs in a sequence-specific manner, they are especially useful in tasks that require highly specific nucleotide recognition [11]. Good examples are the miRNAs (microRNAs) that regulate gene expression by targeting mRNAs (messenger RNAs) [4], [20], and the siRNAs (small interfering RNAs) that take part in the RNAi (RNA interference) pathways for gene silencing [29], [30]. Recent developments show that ncRNAs are extensively involved in many gene regulatory mechanisms [14], [17]. The roles of ncRNAs known to this day are truly diverse. These include transcription and translation control, chromosome replication, RNA processing and modification, and protein degradation and translocation [40], just to name a few. These days, it is even claimed that ncRNAs dominate the genomic output of the higher organisms such as mammals, and it is being suggested that the greater portion of their genome (which does not encode proteins) is dedicated to the control and regulation of cell development [27]. As more and more evidence piles up, greater attention is paid to ncRNAs, which have been neglected for a long time. Researchers began to realize that the vast majority of the genome that was regarded as “junk,” mainly because it was not well understood, may indeed hold the key for the best kept secrets in life, such as the mechanism of alternative splicing, the control of epigenetic variations and so forth [27]. The complete range and extent of the role of ncRNAs are not so obvious at this point, but it is certain that a comprehensive understanding of cellular processes is not possible without understanding the functions of ncRNAs [47]

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

Structural Alignment of RNAs Using Profile-csHMMs and Its Application to RNA Homology Search: Overview and New Results

Systematic research on noncoding RNAs (ncRNAs) has revealed that many ncRNAs are actively involved in various biological networks. Therefore, in order to fully understand the mechanisms of these networks, it is crucial to understand the roles of ncRNAs. Unfortunately, the annotation of ncRNA genes that give rise to functional RNA molecules has begun only recently, and it is far from being complete. Considering the huge amount of genome sequence data, we need efficient computational methods for finding ncRNA genes. One effective way of finding ncRNA genes is to look for regions that are similar to known ncRNA genes. As many ncRNAs have well-conserved secondary structures, we need statistical models that can represent such structures for this purpose. In this paper, we propose a new method for representing RNA sequence profiles and finding structural alignment of RNAs based on profile context-sensitive hidden Markov models (profile-csHMMs). Unlike existing models, the proposed approach can handle any kind of RNA secondary structures, including pseudoknots. We show that profile-csHMMs can provide an effective framework for the computational analysis of RNAs and the identification of ncRNA genes

Pseudoknots in a Homopolymer

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.Comment: submitted to PR

Target prediction and a statistical sampling algorithm for RNA-RNA interaction

It has been proven that the accessibility of the target sites has a critical influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not only the energetically most favorable targets site based on the hybrid-probability, but also a statistical sampling structure to illustrate the statistical characterization and representation of the Boltzmann ensemble of RNA-RNA interaction structures. The outputs are retrieved via backtracing an improved dynamic programming solution for the partition function based on the approach of Huang et al. (Bioinformatics). The $O(N^6)$ time and $O(N^4)$ space algorithm is implemented in C (available from \url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure