The 5′-3′ Distance of RNA Secondary Structures

Han, Hillary S. W.; Reidys, Christian M.

doi:10.1089/cmb.2011.0301

Cited by 14 publications

(10 citation statements)

References 15 publications

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“…We propose that range 2 is the correct one for the comparison and that the persistence length of the exterior loop should be much higher than 2.1 nm to get results consistent with the width of the histograms (Supplementary Figure S2c–e). Under these assumptions, all the measured RNA molecules give an ℒ between 9 and 16 nt, which is consistent with theoretical predictions ( 14 – 17 ). It is known that magnesium ions are important for the structural stability of RNA molecules ( 32 ).…”

Section: Discussionsupporting

confidence: 90%

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The separation between the 5′-3′ ends in long RNA molecules is short and nearly constant

Leija-Martínez

Casas-Flores

Cadena-Nava³

et al. 2014

Nucleic Acids Research

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RNA molecules play different roles in coding, decoding and gene expression regulation. Such roles are often associated to the RNA secondary or tertiary structures. The folding dynamics lead to multiple secondary structures of long RNA molecules, since an RNA molecule might fold into multiple distinct native states. Despite an ensemble of different structures, it has been theoretically proposed that the separation between the 5′ and 3′ ends of long single-stranded RNA molecules (ssRNA) remains constant, independent of their base content and length. Here, we present the first experimental measurements of the end-to-end separation in long ssRNA molecules. To determine this separation, we use single molecule Fluorescence Resonance Energy Transfer of fluorescently end-labeled ssRNA molecules ranging from 500 to 5500 nucleotides in length, obtained from two viruses and a fungus. We found that the end-to-end separation is indeed short, within 5–9 nm. It is remarkable that the separation of the ends of all RNA molecules studied remains small and similar, despite the origin, length and differences in their secondary structure. This implies that the ssRNA molecules are ‘effectively circularized’ something that might be a general feature of RNAs, and could result in fine-tuning for translation and gene expression regulation.

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Section: Discussionsupporting

confidence: 90%

“…In addition, Han et al. ( 17 ) found a probability distribution for the 5′-3′ end distance from which the end-to-end separation of random RNA sequences ‘were distinctively lower than those reported by Yoffe et al. ’.…”

Section: Introductionmentioning

confidence: 90%

The separation between the 5′-3′ ends in long RNA molecules is short and nearly constant

Leija-Martínez

Casas-Flores

Cadena-Nava³

et al. 2014

Nucleic Acids Research

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“…That the polymer-zeta property does not hold for RNA has also been observed in the context of the limit distribution of the 5'-3' distances of RNA secondary structures [42]. Here it is observed that long arcs, to be precise arcs of lengths O(n) always exist.…”

Section: Resultsmentioning

confidence: 56%

On the combinatorics of sparsification

Huang

Reidys

2012

Algorithms Mol Biol

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BackgroundWe study the sparsification of dynamic programming based on folding algorithms of RNA structures. Sparsification is a method that improves significantly the computation of minimum free energy (mfe) RNA structures.ResultsWe provide a quantitative analysis of the sparsification of a particular decomposition rule, Λ∗. This rule splits an interval of RNA secondary and pseudoknot structures of fixed topological genus. Key for quantifying sparsifications is the size of the so called candidate sets. Here we assume mfe-structures to be specifically distributed (see Assumption 1) within arbitrary and irreducible RNA secondary and pseudoknot structures of fixed topological genus. We then present a combinatorial framework which allows by means of probabilities of irreducible sub-structures to obtain the expectation of the Λ∗-candidate set w.r.t. a uniformly random input sequence. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) in case of RNA secondary structures as well as RNA pseudoknot structures. Furthermore, for RNA secondary structures we also analyze a simplified loop-based energy model. Our combinatorial analysis is then compared to the expected number of Λ∗-candidates obtained from the folding mfe-structures. In case of the mfe-folding of RNA secondary structures with a simplified loop-based energy model our results imply that sparsification provides a significant, constant improvement of 91% (theory) to be compared to an 96% (experimental, simplified arc-based model) reduction. However, we do not observe a linear factor improvement. Finally, in case of the “full” loop-energy model we can report a reduction of 98% (experiment).ConclusionsSparsification was initially attributed a linear factor improvement. This conclusion was based on the so called polymer-zeta property, which stems from interpreting polymer chains as self-avoiding walks. Subsequent findings however reveal that the O(n) improvement is not correct. The combinatorial analysis presented here shows that, assuming a specific distribution (see Assumption 1), of mfe-structures within irreducible and arbitrary structures, the expected number of Λ∗-candidates is Θ(n2). However, the constant reduction is quite significant, being in the range of 96%. We furthermore show an analogous result for the sparsification of the Λ∗-decomposition rule for RNA pseudoknotted structures of genus one. Finally we observe that the effect of sparsification is sensitive to the employed energy model.

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“…These recursions have been derived in several different contexts, e.g. force induced RNA denaturations [ 6 ], the investigate of loop entropy dependence [ 9 ], the analysis of FRET signals in the presence of single-stranded binding proteins [ 5 ], as well as in mathematical studies of RNA panhandle-like structures [ 3 , 4 ].…”

Section: Theorymentioning

confidence: 99%

“…Panhandles have been reported in particular for many RNA virus genomes. Several studies [ 1 - 4 ] agree based on different models that the two ends of single-stranded RNA molecules are typically not far apart. On a more technical level, the problem to compute the partition function over RNA secondary structures with given end-to-end distance d , usually measured as the number of external bases (plus possibly the number of structural domains) arises for instance when predicting nucleic acid secondary structure in the presence of single-stranded binding proteins [ 5 ] or in models of RNA subjected to pulling forces (e.g.…”

Section: Introductionmentioning

confidence: 99%

Graph-distance distribution of the Boltzmann ensemble of RNA secondary structures

Qin

Fricke

Marz

et al. 2014

Algorithms Mol Biol

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BackgroundLarge RNA molecules are often composed of multiple functional domains whose spatial arrangement strongly influences their function. Pre-mRNA splicing, for instance, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium harbors useful information on the shape of the molecule that in turn can give insights into the interplay of its functional domains.ResultSpatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between a fixed pair of nucleotides can be computed in polynomial time by means of dynamic programming. While a naïve implementation would yield recursions with a very high time complexity of O(n6D5) for sequence length n and D distinct distance values, it is possible to reduce this to O(n4) for practical applications in which predominantly small distances are of of interest. Further reductions, however, seem to be difficult. Therefore, we introduced sampling approaches that are much easier to implement. They are also theoretically favorable for several real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.ConclusionsThe graph-distance distribution can be computed using a dynamic programming approach. Although a crude approximation of reality, our initial results indicate that the graph-distance can be related to the smFRET data. The additional file and the software of our paper are available from http://www.rna.uni-jena.de/RNAgraphdist.html.

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The 5′-3′ Distance of RNA Secondary Structures

Cited by 14 publications

References 15 publications

The separation between the 5′-3′ ends in long RNA molecules is short and nearly constant

The separation between the 5′-3′ ends in long RNA molecules is short and nearly constant

On the combinatorics of sparsification

Graph-distance distribution of the Boltzmann ensemble of RNA secondary structures

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