Alignment of RNA base pairing probability matrices

Motivation: Many classes of functional RNA molecules are characterized by highly conserved secondary structures but little detectable sequence similarity. Reliable multiple alignments can therefore be constructed only when the shared structural features are taken into account. Since multiple alignments are used as input for many subsequent methods of data analysis, structure-based alignments are an indispensable necessity in RNA bioinformatics. Results: We present here a method to compute pairwise and progressive multiple alignments from the direct comparison of base pairing probability matrices. Instead of attempting to solve the folding and the alignment problem simultaneously as in the classical Sankoff's algorithm, we use McCaskill's approach to compute base pairing probability matrices which effectively incorporate the information on the energetics of each sequences. A novel, simplified variant of Sankoff's algorithms can then be employed to extract the maximum-weight common secondary structure and an associated alignment

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Mixed Linear Layouts of Planar Graphs

A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed $1$-stack $1$-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering. We disprove this conjecture by providing a planar graph that does not have such a mixed layout. In addition, we study mixed layouts of graph subdivisions, and show that every planar graph has a mixed subdivision with one division vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Translational Control by RNA-RNA Interaction: Improved Computation of RNA-RNA Binding Thermodynamics

The thermodynamics of RNA-RNA interaction consists of two components: the energy necessary to make a potential binding region accessible, i.e., unpaired, and the energy gained from the base pairing of the two interaction partners. We show here that both components can be efficiently computed using an improved variant of RNAup. The method is then applied to a set of bacterial small RNAs involved in translational control. In all cases of biologically active sRNA target interactions, the target sites predicted by RNAup is in perfect agreement with literature. In addition to prediction of target site location, RNAup can be also be used to determine the mode of sRNA action. Using information about target site location and the accessibility change resulting form sRNA binding we can discriminate between positive and negative regulators of translation

How to compare arc-annotated sequences: The alignment hierarchy

International audienceWe describe a new unifying framework to express comparison of arc-annotated sequences, which we call alignment of arc-annotated sequences. We first prove that this framework encompasses main existing models, which allows us to deduce complexity results for several cases from the literature. We also show that this framework gives rise to new relevant problems that have not been studied yet. We provide a thorough analysis of these novel cases by proposing two polynomial time algorithms and an NP-completeness proof. This leads to an almost exhaustive study of alignment of arc-annotated sequences

Target prediction and a statistical sampling algorithm for RNA-RNA interaction

It has been proven that the accessibility of the target sites has a critical influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not only the energetically most favorable targets site based on the hybrid-probability, but also a statistical sampling structure to illustrate the statistical characterization and representation of the Boltzmann ensemble of RNA-RNA interaction structures. The outputs are retrieved via backtracing an improved dynamic programming solution for the partition function based on the approach of Huang et al. (Bioinformatics). The $O(N^6)$ time and $O(N^4)$ space algorithm is implemented in C (available from \url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure

Pericardial effusion unrelated to surgery is a predictor of mortality in heart transplant patients

Background: Hemodynamically irrelevant pericardial effusion (PeEf) is a predictor of adverse outcome in heart failure patients. The clinical relevance of a PeEf unrelated to surgery in heart transplant patients remains unknown. This study assesses the prognostic value of PeEf occurring later than 1 year after transplantation. Methods: All patients undergoing heart transplantation in Zurich between 1989 and 2012 were screened. Cox proportional hazard models were used to analyze mortality (primary) and hospitalization (secondary endpoint). PeEf time points were compared to baseline for rejection, immunosuppressants, tumors, inflam­mation, heart failure, kidney function, hemodynamic, and echocardiographic parameters. Results: Of 152 patients (mean age 48.3 ± 11.9), 25 developed PeEf. Median follow-up period was 11.9 (IQR 5.8–17) years. The number of deaths was 6 in the PeEf group and 46 in the non-PeEf group. The occurrence of PeEf was associated with a 2.5-fold increased risk of death (HR 2.49, 95% CI 1.02–6.13, p = 0.046) and hospitalization (HR 2.53, 95% CI 1.57–4.1, p = 0.0002). Conclusions: This study reveals that the finding of hemodynamically irrelevant PeEf in heart trans­plant patients is a predictor of adverse outcome, suggesting that a careful clinical assessment is war­ranted in heart transplant patients exhibiting small PeEf

Changes of bivalent chromatin coincide with increased expression of developmental genes in cancer

Bivalent (poised or paused) chromatin comprises activating and repressing histone modifications at the same location. This combination of epigenetic marks at promoter or enhancer regions keeps genes expressed at low levels but poised for rapid activation. Typically, DNA at bivalent promoters is only lowly methylated in normal cells, but frequently shows elevated methylation levels in cancer samples. Here, we developed a universal classifier built from chromatin data that can identify cancer samples solely from hypermethylation of bivalent chromatin. Tested on over 7,000 DNA methylation data sets from several cancer types, it reaches an AUC of 0.92. Although higher levels of DNA methylation are often associated with transcriptional silencing, counter-intuitive positive statistical dependencies between DNA methylation and expression levels have been recently reported for two cancer types. Here, we re-analyze combined expression and DNA methylation data sets, comprising over 5,000 samples, and demonstrate that the conjunction of hypermethylation of bivalent chromatin and up-regulation of the corresponding genes is a general phenomenon in cancer. This up-regulation affects many developmental genes and transcription factors, including dozens of homeobox genes and other genes implicated in cancer. Thus, we reason that the disturbance of bivalent chromatin may be intimately linked to tumorigenesis

Thermodynamics of RNA-RNA binding

Background: Reliable prediction of RNA–RNA binding energies is crucial, e.g. for the understanding on RNAi, microRNA–mRNA binding and antisense interactions. The thermodynamics of such RNA–RNA interactions can be understood as the sum of two energy contributions: (1) the energy necessary to ‘open’ the binding site and (2) the energy gained from hybridization. Methods: We present an extension of the standard partition function approach to RNA secondary structures that computes the probabilities Pu[i, j] that a sequence interval [i, j] is unpaired. Results: Comparison with experimental data shows that Pu[i, j] can be applied as a significant determinant of local target site accessibility for RNA interference (RNAi). Furthermore, these quantities can be used to rigorously determine binding free energies of short oligomers to large mRNA targets. The resource consumption is comparable with a single partition function computation for the large target molecule. We can show that RNAi efficiency correlates well with the binding energies of siRNAs to their respective mRNA target