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

Comparative 3-D Modeling of tmRNA

BACKGROUND: Trans-translation releases stalled ribosomes from truncated mRNAs and tags defective proteins for proteolytic degradation using transfer-messenger RNA (tmRNA). This small stable RNA represents a hybrid of tRNA- and mRNA-like domains connected by a variable number of pseudoknots. Comparative sequence analysis of tmRNAs found in bacteria, plastids, and mitochondria provides considerable insights into their secondary structures. Progress toward understanding the molecular mechanism of template switching, which constitutes an essential step in trans-translation, is hampered by our limited knowledge about the three-dimensional folding of tmRNA. RESULTS: To facilitate experimental testing of the molecular intricacies of trans-translation, which often require appropriately modified tmRNA derivatives, we developed a procedure for building three-dimensional models of tmRNA. Using comparative sequence analysis, phylogenetically-supported 2-D structures were obtained to serve as input for the program ERNA-3D. Motifs containing loops and turns were extracted from the known structures of other RNAs and used to improve the tmRNA models. Biologically feasible 3-D models for the entire tmRNA molecule could be obtained. The models were characterized by a functionally significant close proximity between the tRNA-like domain and the resume codon. Potential conformational changes which might lead to a more open structure of tmRNA upon binding to the ribosome are discussed. The method, described in detail for the tmRNAs of Escherichia coli, Bacillus anthracis, and Caulobacter crescentus, is applicable to every tmRNA. CONCLUSION: Improved molecular models of biological significance were obtained. These models will guide in the design of experiments and provide a better understanding of trans-translation. The comparative procedure described here for tmRNA is easily adopted for the modeling the members of other RNA families

Accurate classification of RNA structures using topological fingerprints

While RNAs are well known to possess complex structures, functionally similar RNAs often have little sequence similarity. While the exact size and spacing of base-paired regions vary, functionally similar RNAs have pronounced similarity in the arrangement, or topology, of base-paired stems. Furthermore, predicted RNA structures often lack pseudoknots (a crucial aspect of biological activity), and are only partially correct, or incomplete. A topological approach addresses all of these difficulties. In this work we describe each RNA structure as a graph that can be converted to a topological spectrum (RNA fingerprint). The set of subgraphs in an RNA structure, its RNA fingerprint, can be compared with the fingerprints of other RNA structures to identify and correctly classify functionally related RNAs. Topologically similar RNAs can be identified even when a large fraction, up to 30%, of the stems are omitted, indicating that highly accurate structures are not necessary. We investigate the performance of the RNA fingerprint approach on a set of eight highly curated RNA families, with diverse sizes and functions, containing pseudoknots, and with little sequence similarity–an especially difficult test set. In spite of the difficult test set, the RNA fingerprint approach is very successful (ROC AUC \u3e 0.95). Due to the inclusion of pseudoknots, the RNA fingerprint approach both covers a wider range of possible structures than methods based only on secondary structure, and its tolerance for incomplete structures suggests that it can be applied even to predicted structures. Source code is freely available at https://github.rcac.purdue.edu/mgribsko/XIOS_RNA_fingerprint

Graphical methods in RNA structure matching

Eukaryotic genomes are pervasively transcribed; almost every base can be found in an RNA transcript. This is a surprising observation since most of the genome does not encode proteins. This RNA must serve an important regulatory function – important because producing non-coding RNA is an energy intensive process, and in the absence of strong selection one would expect it to disappear. RNA families with common functions have specifically conserved structural motifs, which are directly related to the functional roles of RNA in catalysis and regulation. Because the conserved structures depend on base-pairing, similar RNA structures may have little or no detectable sequence similarity, making the identification of conserved RNAs difficult. This is a particularly serious problem when studying regulatory structures in RNA. In many cases, such as that of cellular internal ribosome entry sites, although we can identify RNAs that have similar regulatory responses, it is difficult to tell whether the RNAs have common structural features using current methods. Available tools for identifying common structures based on RNA sequence suffer from one or more of the following problems: they do not consider pseudoknots, which are important in many catalytic and regulatory structures; they do not consider near minimum free energy structures, which is important as many RNAs exist as an ensemble of structures of nearly equal energy; they require many examples of known structures in order to train a computational model; they require impractical amounts of computational time, precluding their use on long sequences or genomic scale; or they use a similarity function that cannot identify RNAs as having similar structure, even when they are from one of the well characterized known classes. The approach presented here has the potential to address all of these issues, allowing novel RNA structures that are shared between RNAs with little or no sequence similarity to be discovered. This provides a powerful tool to investigate and explain the pervasive transcription observed in eukaryotic genomes

Lynx: A Programmatic SAT Solver for the RNA-folding Problem

15th International Conference, Trento, Italy, June 17-20, 2012. ProceedingsThis paper introduces Lynx, an incremental programmatic SAT solver that allows non-expert users to introduce domain-specific code into modern conflict-driven clause-learning (CDCL) SAT solvers, thus enabling users to guide the behavior of the solver. The key idea of Lynx is a callback interface that enables non-expert users to specialize the SAT solver to a class of Boolean instances. The user writes specialized code for a class of Boolean formulas, which is periodically called by Lynx’s search routine in its inner loop through the callback interface. The user-provided code is allowed to examine partial solutions generated by the solver during its search, and to respond by adding CNF clauses back to the solver dynamically and incrementally. Thus, the user-provided code can specialize and influence the solver’s search in a highly targeted fashion. While the power of incremental SAT solvers has been amply demonstrated in the SAT literature and in the context of DPLL(T), it has not been previously made available as a programmatic API that is easy to use for non-expert users. Lynx’s callback interface is a simple yet very effective strategy that addresses this need. We demonstrate the benefits of Lynx through a case-study from computational biology, namely, the RNA secondary structure prediction problem. The constraints that make up this problem fall into two categories: structural constraints, which describe properties of the biological structure of the solution, and energetic constraints, which encode quantitative requirements that the solution must satisfy. We show that by introducing structural constraints on-demand through user provided code we can achieve, in comparison with standard SAT approaches, upto 30x reduction in memory usage and upto 100x reduction in time

Topology of RNA-RNA interaction structures

The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting RNAs, called interaction structures, there exist for fixed genus only finitely many irreducible shadows. This implies that for fixed genus there are only finitely many classes of interaction structures. In particular the simplest case of genus zero already provides the formalism for certain types of structures that occur in nature and are not covered by other filtrations. This case of genus zero interaction structures is already of practical interest, is studied here in detail and found to be expressed by a multiple context-free grammar extending the usual one for RNA secondary structures. We show that in $O(n^6)$ time and $O(n^4)$ space complexity, this grammar for genus zero interaction structures provides not only minimum free energy solutions but also the complete partition function and base pairing probabilities.Comment: 40 pages 15 figure

Computational identification of new structured cis-regulatory elements in the 3'-untranslated region of human protein coding genes

Messenger ribonucleic acids (RNAs) contain a large number of cis-regulatory RNA elements that function in many types of post-transcriptional regulation. These cis-regulatory elements are often characterized by conserved structures and/or sequences. Although some classes are well known, given the wide range of RNA-interacting proteins in eukaryotes, it is likely that many new classes of cis-regulatory elements are yet to be discovered. An approach to this is to use computational methods that have the advantage of analysing genomic data, particularly comparative data on a large scale. In this study, a set of structural discovery algorithms was applied followed by support vector machine (SVM) classification. We trained a new classification model (CisRNA-SVM) on a set of known structured cis-regulatory elements from 3′-untranslated regions (UTRs) and successfully distinguished these and groups of cis-regulatory elements not been strained on from control genomic and shuffled sequences. The new method outperformed previous methods in classification of cis-regulatory RNA elements. This model was then used to predict new elements from cross-species conserved regions of human 3′-UTRs. Clustering of these elements identified new classes of potential cis-regulatory elements. The model, training and testing sets and novel human predictions are available at: http://mRNA.otago.ac.nz/CisRNA-SVM

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