Interacting RNA Molecules Research Articles

RNAscape: geometric mapping and customizable visualization of RNA structure.

Analyzing and visualizing the tertiary structure and complex interactions of RNA is essential for being able to mechanistically decipher their molecular functions in vivo. Secondary structure visualization software can portray many aspects of RNA; however, these layouts are often unable to preserve topological correspondence since they do not consider tertiary interactions between different regions of an RNA molecule. Likewise, quaternary interactions between two or more interacting RNA molecules are not considered in secondary structure visualization tools. The RNAscape webserver produces visualizations that can preserve topological correspondence while remaining both visually intuitive and structurally insightful. RNAscape achieves this by designing a mathematical structural mapping algorithm which prioritizes the helical segments, reflecting their tertiary organization. Non-helical segments are mapped in a way that minimizes structural clutter. RNAscape runs a plotting script that is designed to generate publication-quality images. RNAscape natively supports non-standard nucleotides, multiple base-pairing annotation stylesand requires no programming experience. RNAscape can also be used to analyze RNA/DNA hybrid structures and DNA topologies, including G-quadruplexes. Users can upload their own three-dimensional structures or enter a Protein Data Bank (PDB) ID of an existing structure. The RNAscape webserver allows users to customize visualizations through various settings as desired. URL: https://rnascape.usc.edu/.

LinearCoFold and LinearCoPartition: linear-time algorithms for secondary structure prediction of interacting RNA molecules.

Many RNAs function through RNA-RNA interactions. Fast and reliable RNA structure prediction with consideration of RNA-RNA interaction is useful, however, existing tools are either too simplistic or too slow. To address this issue, we present LinearCoFold, which approximates the complete minimum free energy structure of two strands in linear time, and LinearCoPartition, which approximates the cofolding partition function and base pairing probabilities in linear time. LinearCoFold and LinearCoPartition are orders of magnitude faster than RNAcofold. For example, on a sequence pair with combined length of 26,190nt, LinearCoFold is 86.8× faster than RNAcofold MFE mode, and LinearCoPartition is 642.3× faster than RNAcofold partition function mode. Surprisingly, LinearCoFold and LinearCoPartition's predictions have higher PPV and sensitivity of intermolecular base pairs. Furthermore, we apply LinearCoFold to predict the RNA-RNA interaction between SARS-CoV-2 genomic RNA (gRNA) and human U4 small nuclear RNA (snRNA), which has been experimentally studied, and observe that LinearCoFold's prediction correlates better with the wet lab results than RNAcofold's.

Moduli spaces and macromolecules

Techniques from moduli spaces are applied to biological macromolecules. The first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally. The second main result identifies up to homotopy the natural moduli space of several interacting RNA molecules with the Riemann moduli space of a surface with several boundary components in each fixed genus. Applications to RNA folding prediction are discussed. The mathematical and biological frameworks are surveyed and presented from first principles.

Identification of miRNA-Target RNA Interactions Using CLASH.

We present a detailed protocol for the experimental identification of miRNA-target RNA interaction sites using cross-linking, ligation, and sequencing of hybrids (CLASH). The basis of the technique is the purification of UV-stabilized Argonaute (AGO)-RNA complexes assembled in living cells, with subsequent ligation of AGO-associated RNA-RNA duplexes to form chimeric RNAs. Following cDNA synthesis, DNA library preparation and high-throughput sequencing, interacting RNA molecules are unambiguously identified as chimeric reads in bioinformatic analysis of sequencing data. CLASH potentially recovers any RNA duplex that is bound by RNA-binding protein, so modified approaches would be suitable for the identification of many other inter- and intramolecular RNA-RNA interactions. Since CLASH analysis is independent of bioinformatic predictions it allows the identification and analysis of RNA targeting rules in an unbiased way.

Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.

Combinatorial analysis of interacting RNA molecules

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no “zigzag” configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA–RNA interactions.

A new Motzkin class for joint RNA secondary structures.

In general RNA prediction problem includes genetic mapping, physical mapping and structure prediction. The ultimate goal of structure prediction is to obtain the three dimensional structure of bimolecules through computation. The key concept for solving the above mentioned problem is the appropriate representation of the biological structures. Even though, the problems that concern representations of certain biological structures like secondary structures either are characterized as NP-complete or with high complexity, few approximation algorithms and techniques had been constructed, mainly with polynomial complexity, concerning the prediction of RNA secondary structures. In this paper, a new class of Motzkin paths is introduced, the so-called semi-elevated inverse Motzkin peakless paths for the representation of two interacting RNA molecules. The basic combinatorial interpretations on single RNA secondary structures are extended via these new Motzkin paths on two RNA molecules and can be applied to the prediction methods of joint structures formed by interacting RNAs.

Combinatorics of RNA–RNA interaction

RNA-RNA binding is an important phenomenon observed for many classes of non-coding RNAs and plays a crucial role in a number of regulatory processes. Recently several MFE folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Here joint structure means that in a diagram representation the intramolecular bonds of each partner are pseudoknot-free, that the intermolecular binding pairs are noncrossing, and that there is no so-called "zigzag" configuration. This paper presents the combinatorics of RNA interaction structures including their generating function, singularity analysis as well as explicit recurrence relations. In particular, our results imply simple asymptotic formulas for the number of joint structures.

RNA–RNA Interaction Prediction and Antisense RNA Target Search

Recent studies demonstrating the existence of special noncoding "antisense" RNAs used in post transcriptional gene regulation have received considerable attention. These RNAs are synthesized naturally to control gene expression in C. elegans, Drosophila, and other organisms; they are known to regulate plasmid copy numbers in E. coli as well. Small RNAs have also been artificially constructed to knock out genes of interest in humans and other organisms for the purpose of finding out more about their functions. Although there are a number of algorithms for predicting the secondary structure of a single RNA molecule, no such algorithm exists for reliably predicting the joint secondary structure of two interacting RNA molecules or measuring the stability of such a joint structure. In this paper, we describe the RNA-RNA interaction prediction (RIP) problem between an antisense RNA and its target mRNA and develop efficient algorithms to solve it. Our algorithms minimize the joint free energy between the two RNA molecules under a number of energy models with growing complexity. Because the computational resources needed by our most accurate approach is prohibitive for long RNA molecules, we also describe how to speed up our techniques through a number of heuristic approaches while experimentally maintaining the original accuracy. Equipped with this fast approach, we apply our method to discover targets for any given antisense RNA in the associated genome sequence.

Partition function and base pairing probabilities of RNA heterodimers.

BackgroundRNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms.MethodsThe standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs.ResultsWe present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures.AvailabilityRNAcofold is distributed as part of the Vienna RNA Package, .ContactStephan H. Bernhart – berni@tbi.univie.ac.at

Secondary Structure Prediction of Interacting RNA Molecules

Computational tools for prediction of the secondary structure of two or more interacting nucleic acid molecules are useful for understanding mechanisms for ribozyme function, determining the affinity of an oligonucleotide primer to its target, and designing good antisense oligonucleotides, novel ribozymes, DNA code words, or nanostructures. Here, we introduce new algorithms for prediction of the minimum free energy pseudoknot-free secondary structure of two or more nucleic acid molecules, and for prediction of alternative low-energy (sub-optimal) secondary structures for two nucleic acid molecules. We provide a comprehensive analysis of our predictions against secondary structures of interacting RNA molecules drawn from the literature. Analysis of our tools on 17 sequences of up to 200 nucleotides that do not form pseudoknots shows that they have 79% accuracy, on average, for the minimum free energy predictions. When the best of 100 sub-optimal foldings is taken, the average accuracy increases to 91%. The accuracy decreases as the sequences increase in length and as the number of pseudoknots and tertiary interactions increases. Our algorithms extend the free energy minimization algorithm of Zuker and Stiegler for secondary structure prediction, and the sub-optimal folding algorithm by Wuchty et al. Implementations of our algorithms are freely available in the package MultiRNAFold.

Functionally interacting telomerase RNAs in the yeast telomerase complex.

The ribonucleoprotein (RNP) enzyme telomerase from Saccharomyces cerevisiae adds telomeric DNA to chromosomal ends in short increments both in vivo and in vitro. Whether or not telomerase functions as a multimer has not been addressed previously. Here we show, first, that following polymerization, the telomerase RNP remains stably bound to its telomeric oligonucleotide reaction product. We then exploit this finding and a previously reported mutant telomerase RNA to demonstrate that, unexpectedly, the S. cerevisiae telomerase complex contains at least two functionally interacting RNA molecules that both act as templates for DNA polymerization. Here, functional telomerase contains at least two active sites.

A theory of evolution that includes prebiotic self-organization and episodic species formation

A theory has been proposed that encompasses pre-replication changes in RNA synthesis and non-gradual variant formation, in addition to competitive replication. Using a fundamental theorem of natural selection and maximum principle scaled to nucleotide condensation, evolution in vitro was demonstrated to maximally damp both kinetic and thermodynamic forces driving this reaction, from its pre-replication stage. This led to the finding that evolution follows a path of least action. These principles form the framework for a general theory of evolution, whose scope extends beyond evolution modeled by synthesis of non interacting RNA molecules. It applies, in particular, to standard processes, such as competitive crystallization. In calculations simulating de novo formation of self-replicating RNA molecules in the Qβ replicase system, spontaneous changes in strand secondary structure promoted the transition from random copolymerization to template-directed polymerization. This finding indicates selection preceded genome self-propagation. Non-gradual species formation was attributed to the presence of heterogeneous thermodynamic forces. Growth unconstrained by competition follows mutation to a variant able to utilize a free energy source alien to its progenitors. Evolution in a heterogeneous system can, therefore, exhibit discontinuous rates of species formation and spawn new species populations. Natural selection among competing self-propagators thus gives way to a principle of wider scope stating that evolution optimally damps the physicochemical forces causing change within an evolving system.