Combinatorial RNA Design Designability and Structure-Approximating Algorithm in Watson-Crick and Nussinov-Jacobson Energy Models

We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where the contributions of base pairs are additive and independent: the purely combinatorial Watson-Crick model, which only allows equally-contributing A -- U and C -- G base pairs, and the real-valued Nussinov-Jacobson model, which associates arbitrary energies to A -- U, C -- G and G -- U base pairs. We first provide a complete characterization of designable structures using restricted alphabets and, in the four-letter alphabet, provide a complete characterization for designable structures without unpaired bases. When unpaired bases are allowed, we characterize extensive classes of (non-)designable structures, and prove the closure of the set of designable structures under the stutter operation. Membership of a given structure to any of the classes can be tested in $\Theta$(n) time, including the generation of a solution sequence for positive instances. Finally, we consider a structure-approximating relaxation of the design, and provide a $\Theta$(n) algorithm which, given a structure S that avoids two trivially non-designable motifs, transforms S into a designable structure constructively by adding at most one base-pair to each of its stems.Comment: To appea

Combinatorial RNA Design: Designability and Structure-Approximating Algorithm

In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete characterizations for the structures that can be designed using restricted alphabets. Under a classic four-letter alphabet, we provide a complete characterization of designable structures without unpaired bases. When unpaired bases are allowed, we provide partial characterizations for classes of designable/undesignable structures, and show that the class of designable structures is closed under the stutter operation. Membership of a given structure to any of the classes can be tested in linear time and, for positive instances, a solution can be found in linear time. Finally, we consider a structure-approximating version of the problem that allows to extend bands (helices) and, assuming that the input structure avoids two motifs, we provide a linear-time algorithm that produces a designable structure with at most twice more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun 2015, Ischia Island, Italy. LNCS, 201

Molecular diversity of arbuscular mycorrhizal fungi colonising Hyacinthoides non-scripta (bluebell) in a seminatural woodland

Arbuscular mycorrhizal (AM) fungi form symbiotic associations with plant roots. Around 150 species have been described and it is becoming clear that many of these species have different functional properties. The species diversity of AM fungi actively growing in roots is therefore an important component of ecosystem diversity. However, it is difficult to identify AM fungi below the genus level from morphology in planta, as they possess few informative characters. We present here a molecular method for identifying infrageneric sequence types that estimate the taxonomic diversity of AM fungi present in actively growing roots. Bluebell roots were sampled from beneath two different canopy types, oak and sycamore, and DNA sequences were amplified from roots by the polymerase chain reaction with fungal-specific primers for part of the small subunit ribosomal RNA gene. Restriction fragment length polymorphism among 141 clones was assessed and 62 clones were sequenced. When aligned, discrete sequence groups emerged that cluster into the three families of AM fungi: Acaulosporaceae, Gigasporaceae and Glomaceae. The sequence variation is consistent with rRNA secondary structure. The same sequence types were found at both sampling times. Frequencies of Scutellospora increased in December, and Acaulospora increased in abundance in July. Sites with a sycamore canopy show a reduced abundance of Acaulospora, and those with oak showed a reduced abundance of Glomus. These distribution patterns are consistent with previous morphological studies carried out in this woodland. The molecular method provides an alternative method of estimating the distribution and abundance of AM fungi, and has the potential to provide greater resolution at the infrageneric level

TT2NE: A novel algorithm to predict RNA secondary structures with pseudoknots

We present TT2NE, a new algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. TT2NE guarantees to find the minimum free energy structure irrespectively of pseudoknot topology. This unique proficiency is obtained at the expense of the maximum length of sequence that can be treated but comparison with state-of-the-art algorithms shows that TT2NE is a very powerful tool within its limits. Analysis of TT2NE's wrong predictions sheds light on the need to study how sterical constraints limit the range of pseudoknotted structures that can be formed from a given sequence. An implementation of TT2NE on a public server can be found at http://ipht.cea.fr/rna/tt2ne.php

Asymptotics of Canonical and Saturated RNA Secondary Structures

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 n^{-3/2} 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures were introduced by Bompf\"unewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up. Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we compute the asymptotic number of saturated structures, we show that the asymptotic expected number of base pairs is $0.337361 n$, and the asymptotic number of saturated stem-loop structures is $0.323954 1.69562^n$, in contrast to the number $2^{n-2}$ of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs of is $0.340633 n$.Comment: accepted: Journal of Bioinformatics and Computational Biology (2009) 22 page

Design, synthesis, conformational analysis and nucleic acid hybridisation properties of thymidyl pyrrolidine-amide oligonucleotide mimics (POM)

Pyrrolidine-amide oligonucleotide mimics (POM) 1 were designed to be stereochemically and conformationally similar to natural nucleic acids, but with an oppositely charged, cationic backbone. Molecular modelling reveals that the lowest energy conformation of a thymidyl-POM monomer is similar to the conformation adopted by ribonucleosides. An e cient solution phase synthesis of the thymidyl POM oligomers has been developed, using both N-alkylation and acylation coupling strategies. 1H NMR spectroscopy con rmed that the highly water soluble thymidyl-dimer, T2-POM, preferentially adopts both a con guration about the pyrrolidine N-atom and an overall conformation in D2O that are very similar to a typical C3 -endo nucleotide in RNA. In addition the nucleic acid hybridisation properties of a thymidyl-pentamer, T5-POM, with an N-terminal phthalimide group were evaluated using both UV spectroscopy and surface plasmon resonance (SPR). It was found that T5-POM exhibits very high a nity for complementary ssDNA and RNA, similar to that of a T5-PNA oligomer. SPR experiments also showed that T5-POM binds with high sequence delity to ssDNA under near physiological conditions. In addition, it was found possible to attenuate the binding a nity of T5-POM to ssDNA and RNA by varying both the ionic strength and pH. However, the most striking feature exhibited by T5-POM is an unprecedented kinetic binding selectivity for ssRNA over DNA

The subnuclear localization of tRNA ligase in yeast

Yeast tRNA ligase is an enzyme required for tRNA splicing. A study by indirect immune fluorescence shows that this enzyme is localized in the cell nucleus. At higher resolution, studies using indirect immune electron microscopy show this nuclear location to be primarily at the inner membrane of the nuclear envelope, most likely at the nuclear pore. There is a more diffuse, secondary location of ligase in a region of the nucleoplasm within 300 nm of the nuclear envelope. When the amount of ligase in the cell is increased, nuclear staining increases but staining of the nuclear envelope remains constant. This experiment indicates that there are a limited number of ligase sites at the nuclear envelope. Since the other tRNA splicing component, the endonuclease, has the characteristics of an integral membrane protein, we hypothesize that it constitutes the site for the interaction of ligase with the nuclear envelope

Controlled non uniform random generation of decomposable structures

Consider a class of decomposable combinatorial structures, using different types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the random generation of such structures with respect to a size $n$ and a targeted distribution in $k$ of its \emph{distinguished} atoms. We consider two variations on this problem. In the first alternative, the targeted distribution is given by $k$ real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 < \TargFreq_i < 1 for all $i$ and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We aim to generate random structures among the whole set of structures of a given size $n$, in such a way that the {\em expected} frequency of any distinguished atom \At_i equals \TargFreq_i. We address this problem by weighting the atoms with a $k$-tuple \Weights of real-valued weights, inducing a weighted distribution over the set of structures of size $n$. We first adapt the classical recursive random generation scheme into an algorithm taking \bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw $m$ structures from the \Weights-weighted distribution. Secondly, we address the analytical computation of weights such that the targeted frequencies are achieved asymptotically, i. e. for large values of $n$. We derive systems of functional equations whose resolution gives an explicit relationship between \Weights and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in \bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies associated with a given $k$-tuple \Weights of weights, and an optimized version in \bigO{k n^2} in the case of context-free languages. This allows for a heuristic resolution of the weights/frequencies relationship suitable for complex specifications. In the second alternative, the targeted distribution is given by a $k$ natural numbers $n_1, \ldots, n_k$ such that $n_1+\cdots+n_k+r=n$ where $r \geq 0$ is the number of undistinguished atoms. The structures must be generated uniformly among the set of structures of size $n$ that contain {\em exactly} $n_i$ atoms \At_i ($1 \leq i \leq k$). We give a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating $m$ structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for regular specifications