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

High sensitivity RNA pseudoknot prediction

Most ab initio pseudoknot predicting methods provide very few folding scenarios for a given RNA sequence and have low sensitivities. RNA researchers, in many cases, would rather sacrifice the specificity for a much higher sensitivity for pseudoknot detection. In this study, we introduce the Pseudoknot Local Motif Model and Dynamic Partner Sequence Stacking (PLMM_DPSS) algorithm which predicts all PLM model pseudoknots within an RNA sequence in a neighboring-region-interference-free fashion. The PLM model is derived from the existing Pseudobase entries. The innovative DPSS approach calculates the optimally lowest stacking energy between two partner sequences. Combined with the Mfold, PLMM_DPSS can also be used in predicting complicated pseudoknots. The test results of PLMM_DPSS, PKNOTS, iterated loop matching, pknotsRG and HotKnots with Pseudobase sequences have shown that PLMM_DPSS is the most sensitive among the five methods. PLMM_DPSS also provides manageable pseudoknot folding scenarios for further structure determination

Thermodynamics of RNA structures by Wang–Landau sampling

Motivation: Thermodynamics-based dynamic programming RNA secondary structure algorithms have been of immense importance in molecular biology, where applications range from the detection of novel selenoproteins using expressed sequence tag (EST) data, to the determination of microRNA genes and their targets. Dynamic programming algorithms have been developed to compute the minimum free energy secondary structure and partition function of a given RNA sequence, the minimum free-energy and partition function for the hybridization of two RNA molecules, etc. However, the applicability of dynamic programming methods depends on disallowing certain types of interactions (pseudoknots, zig-zags, etc.), as their inclusion renders structure prediction an nondeterministic polynomial time (NP)-complete problem. Nevertheless, such interactions have been observed in X-ray structures

RNA pseudoknots: folding and finding

RNA pseudoknots are important for function. Three-dimensional structural information is available, insights into factors affecting pseudoknot stability are being reported, and computer programs are available for predicting pseudoknots

On the combinatorics of sparsification

Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze the sparsification of a particular decomposition rule, $\Lambda^*$, that splits an interval for RNA secondary and pseudoknot structures of fixed topological genus. Essential for quantifying the sparsification is the size of its so called candidate set. We present a combinatorial framework which allows by means of probabilities of irreducible substructures to obtain the expected size of the set of $\Lambda^*$-candidates. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) for RNA secondary structures as well as RNA pseudoknot structures. For RNA secondary structures we also consider a simplified loop-energy model. This combinatorial analysis is then compared to the expected number of $\Lambda^*$-candidates obtained from folding mfe-structures. In case of the mfe-folding of RNA secondary structures with a simplified loop energy model our results imply that sparsification provides a reduction of time complexity by a constant factor of 91% (theory) versus a 96% reduction (experiment). For the "full" loop-energy model there is a reduction of 98% (experiment).Comment: 27 pages, 12 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

ConStruct: Improved construction of RNA consensus structures

<p>Abstract</p> <p>Background</p> <p>Aligning homologous non-coding RNAs (ncRNAs) correctly in terms of sequence and structure is an unresolved problem, due to both mathematical complexity and imperfect scoring functions. High quality alignments, however, are a prerequisite for most consensus structure prediction approaches, homology searches, and tools for phylogeny inference. Automatically created ncRNA alignments often need manual corrections, yet this manual refinement is tedious and error-prone.</p> <p>Results</p> <p>We present an extended version of CONSTRUCT, a semi-automatic, graphical tool suitable for creating RNA alignments correct in terms of both consensus sequence and consensus structure. To this purpose CONSTRUCT combines sequence alignment, thermodynamic data and various measures of covariation.</p> <p>One important feature is that the user is guided during the alignment correction step by a consensus dotplot, which displays all thermodynamically optimal base pairs and the corresponding covariation. Once the initial alignment is corrected, optimal and suboptimal secondary structures as well as tertiary interaction can be predicted. We demonstrate CONSTRUCT's ability to guide the user in correcting an initial alignment, and show an example for optimal secondary consensus structure prediction on very hard to align SECIS elements. Moreover we use CONSTRUCT to predict tertiary interactions from sequences of the internal ribosome entry site of CrP-like viruses. In addition we show that alignments specifically designed for benchmarking can be easily be optimized using CONSTRUCT, although they share very little sequence identity.</p> <p>Conclusion</p> <p>CONSTRUCT's graphical interface allows for an easy alignment correction based on and guided by predicted and known structural constraints. It combines several algorithms for prediction of secondary consensus structure and even tertiary interactions. The CONSTRUCT package can be downloaded from the URL listed in the Availability and requirements section of this article.</p

The Rna Newton Polytope And Learnability Of Energy Parameters

Computational RNA secondary structure prediction has been a topic of much research interest for several decades now. Despite all the progress made in the field, even the state-of-the-art algorithms do not provide satisfying results, and the accuracy of output is limited for all the existent tools. Very complex energy models, different parameter estimation methods, and recent machine learning approaches had not been the answer for this problem. We believe that the first step to achieve results with high quality is to use the energy model with the potential for predicting accurate output. Hence, it is necessary to have a systematic way to analyze the suitability of an energy model. We introduced the notion of learnability to measure this suitability. A learnable energy model has at least one subset of parameters that can render every known RNA to date the minimum free energy structure, which means 100% accuracy. We also found the necessary condition for a model to be learnable and implemented the dynamic programming based algorithm to asses this condition for a set of RNAs. This algorithm computes the convex hull of all possible feature vectors for a sequence. With the partition function as a polynomial, this convex hull is also the Newton polytope of the partition function. To the best of our knowledge, this is the first systematic approach for evaluating the inherent capability of an energy model