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In this paper we introduce a novel, context-free grammar, {it RNAFeatures$^*$}, capable of generating any RNA structure including pseudoknot structures (pk-structure). We represent pk-structures as orientable fatgraphs, which naturally leads to a filtration by their topological genus. Within this framework, RNA secondary structures correspond to pk-structures of genus zero. {it RNAFeatures$^*$} acts on formal, arc-labeled RNA secondary structures, called $lambda$-structures. $lambda$-structures correspond one-to-one to pk-structures together with some additional information. This information consists of the specific rearrangement of the backbone, by which a pk-structure can be made cross-free. {it RNAFeatures$^*$} is an extension of the grammar for secondary structures and employs an enhancement by labelings of the symbols as well as the production rules. We discuss how to use {it RNAFeatures$^*$} to obtain a stochastic context-free grammar for pk-structures, using data of RNA sequences and structures. The induced grammar facilitates fast Boltzmann sampling and statistical analysis. As a first application, we present an $O(n log(n))$ runtime algorithm which samples pk-structures based on ninety tRNA sequences and structures from the Nucleic Acid Database (NDB).
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A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having genus zero. We derive a new bivariate generating function whose singular expansion allows us to analyze the distributions of arcs, stacks, hairpin- , interior- and multi-loops. We then extend this analysis to H-type pseudoknots, kissing hairpins as well as $3$-knots and compute their respective expectation values. Finally we discuss our results and put them into context with data obtained by uniform sampling structures of fixed genus.
Global coronavirus disease pandemic (COVID-19) caused by newly identified SARS- CoV-2 coronavirus continues to claim the lives of thousands of people worldwide. The unavailability of specific medications to treat COVID-19 has led to drug repositioning efforts using various approaches, including computational analyses. Such analyses mostly rely on molecular docking and require the 3D structure of the target protein to be available. In this study, we utilized a set of machine learning algorithms and trained them on a dataset of RNA-dependent RNA polymerase (RdRp) inhibitors to run inference analyses on antiviral and anti-inflammatory drugs solely based on the ligand information. We also performed virtual screening analysis of the drug candidates predicted by machine learning models and docked them against the active site of SARS- CoV-2 RdRp, a key component of the virus replication machinery. Based on the ligand information of RdRp inhibitors, the machine learning models were able to identify candidates such as remdesivir and baloxavir marboxil, molecules with documented activity against RdRp of the novel coronavirus. Among the other identified drug candidates were beclabuvir, a non-nucleoside inhibitor of the hepatitis C virus (HCV) RdRp enzyme, and HCV protease inhibitors paritaprevir and faldaprevir. Further analysis of these candidates using molecular docking against the SARS-CoV-2 RdRp revealed low binding energies against the enzyme active site. Our approach also identified anti-inflammatory drugs lupeol, lifitegrast, antrafenine, betulinic acid, and ursolic acid to have potential activity against SARS-CoV-2 RdRp. We propose that the results of this study are considered for further validation as potential therapeutic options against COVID-19.
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 zig-zag 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.
The effect of polyvalent molecular cations, such as spermine, on the condensation of DNA into very well-defined toroidal shapes have been well studied and understood. However, a great effort has been made trying to obtain similar condensed structures from either ssRNA or dsRNA, which the latter carries similar negative charge density as dsDNA, although it adopts a different helical form. But the analogous condensation of RNA molecules into well-defined structures has so far been elusive. In this work, we show that ssRNA molecules can easily be condensed into nanoring structures on a mice surface, where each nanoring structure is formed mostly by a single RNA molecule. The condensation occurs in a concentration range of different atomic cations, from monovalent to trivalent. The structures of the RNA nanorings on mica surfaces were oberved by atomic force microscopy (AFM). The samples were observed in tapping mode and were prepared by drop evaporation of a solution of RNA in the presence of one type of the different cations used. As far as we know, this is the first time that nanorings or any other well-defined condensed RNA structures have been reported. The RNA nanorings formation can be understood by an energy competition between the hydrogen bonding forming hairpin stems, weakened by the salts, and hairpin loops. This results may have an important biological relevance, since it has been proposed that RNA is the oldest genome coding molecule and the formation of these structures could have given it stability against degradation in primeval times. Even more, the nanoring structures could have the potential to be used as biosensors and functionalized nanodevices.
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