BRaliBase is a widely used benchmark for assessing the accuracy of RNA secondary structure alignment methods. In most case studies based on the BRaliBase benchmark, one can observe a puzzling drop in accuracy in the 40-60% sequence identity range, the so-called 'BRaliBase Dent'. In this article, we show this dent is owing to a bias in the composition of the BRaliBase benchmark, namely the inclusion of a disproportionate number of transfer RNAs, which exhibit a conserved secondary structure. Our analysis, aside of its interest regarding the specific case of the BRaliBase benchmark, also raises important questions regarding the design and use of benchmarks in computational biology.

ter. Statistics of landscapes based on free energies, replication and degradation rate constants of RNA secondary structures.tion of a strange attractor. chaotic dynamics in low dimensional replicator systems. Mutation in autocatalytic networks — an analysis based on perturbation theory. Correlation structure of the landscape of the graph-bipartitioning-problem.structure landscapes. a study based on temperature dependent partition functions. Eur.

Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1) We introduce the operation of a “Pareto algebra product” in the dynamic programming framework of Bellman’s GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman’s GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2) We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman’s GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch.

The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller computational complexity is highly desirable. However, our comparison of the Levenshtein with a generic dictionary-based distance indicates their statistical independence. This suggests that a simplification along this line might not be possible without restricting the class of sequences. Several other probabilistic properties are briefly discussed, emphasizing various questions that deserve further investigation.

MOTIVATION:Abstract shape analysis, first proposed in 2004, allows one to extract several relevant structures from the folding space of an RNA sequence, preferable to focusing in a single structure of minimal free energy. We report recent extensions to this approach.RESULTS:We have rebuilt the original RNAshapes as a repository of components that allows us to integrate several established tools for RNA structure analysis: RNAshapes, RNAalishapes and pknotsRG, including its recent extension pKiss. As a spin-off, we obtain heretofore unavailable functionality: e. g. with pKiss, we can now perform abstract shape analysis for structures holding pseudoknots up to the complexity of kissing hairpin motifs. The new tool pAliKiss can predict kissing hairpin motifs from aligned sequences. Along with the integration, the functionality of the tools was also extended in manifold ways.AVAILABILITY AND IMPLEMENTATION:As before, the tool is available on the Bielefeld Bioinformatics server at http://bibiserv.cebitec.uni-bielefeld.de/rnashapesstudio.CONTACT:bibi-help@cebitec.uni-bielefeld.de.

RNA family models describe classes of functionally related, non-coding RNAs based on sequence and structure conservation. The most important method for modeling RNA families is the use of covariance models, which are stochastic models that serve in the discovery of yet unknown, homologous RNAs. However, the performance of covariance models in finding remote homologs is poor for RNA families with high sequence conservation, while for families with high structure but low sequence conservation, these models are difficult to built in the first place. A complementary approach to RNA family modeling involves the use of thermodynamic matchers. Thermodynamic matchers are RNA folding programs, based on the established thermodynamic model, but tailored to a specific structural motif. As thermodynamic matchers focus on structure and folding energy, they unfold their potential in discovering homologs, when high structure conservation is paired with low sequence conservation. In contrast to covariance models, construction of thermodynamic matchers does not require an input alignment, but requires human design decisions and experimentation, and hence, model construction is more laborious. Here we report a case study on an RNA family that was constructed by means of thermodynamic matchers. It starts from a set of known but structurally different members of the same RNA family. The consensus secondary structure of this family consists of 2 to 4 adjacent hairpins. Each hairpin loop carries the same motif, CCUCCUCCC, while the stems show high variability in their nucleotide content. The present study describes (1) a novel approach for the integration of the structurally varying family into a single RNA family model by means of the thermodynamic matcher methodology, and (2) provides the results of homology searches that were conducted with this model in a wide spectrum of bacterial species.

Pareto optimization combines independent objectives by computing the Pareto front of its search space, defined as the set of all solutions for which no other candidate solution scores better under all objectives. This gives, in a precise sense, better information than an artificial amalgamation of different scores into a single objective, but is more costly to compute. Pareto optimization naturally occurs with genetic algorithms, albeit in a heuristic fashion. Non-heuristic Pareto optimization so far has been used only with a few applications in bioinformatics. We study exact Pareto optimization for two objectives in a dynamic programming framework. We define a binary Pareto product operator [Formula: see text] on arbitrary scoring schemes. Independent of a particular algorithm, we prove that for two scoring schemes A and B used in dynamic programming, the scoring scheme [Formula: see text] correctly performs Pareto optimization over the same search space. We study different implementations of the Pareto operator with respect to their asymptotic and empirical efficiency. Without artificial amalgamation of objectives, and with no heuristics involved, Pareto optimization is faster than computing the same number of answers separately for each objective. For RNA structure prediction under the minimum free energy versus the maximum expected accuracy model, we show that the empirical size of the Pareto front remains within reasonable bounds. Pareto optimization lends itself to the comparative investigation of the behavior of two alternative scoring schemes for the same purpose. For the above scoring schemes, we observe that the Pareto front can be seen as a composition of a few macrostates, each consisting of several microstates that differ in the same limited way. We also study the relationship between abstract shape analysis and the Pareto front, and find that they extract information of a different nature from the folding space and can be meaningfully combined.

BACKGROUND:Evolutionary variations let us define a set of similar nucleic acid sequences as a family if these different molecules execute a common function. Capturing their sequence variation by using e. g. position specific scoring matrices significantly improves sensitivity of detection tools. Members of a functional (non-coding) RNA family are affected by these variations not only on the sequence, but also on the structural level. For example, some transfer-RNAs exhibit a fifth helix in addition to the typical cloverleaf structure. Current covariance models - the unrivaled homology search approach for structured RNA - do not benefit from structural variation within a family, but rather penalize it. This leads to artificial subdivision of families and loss of information in the RFAM database.RESULTS:We propose an extension to the fundamental architecture of covariance models to allow for several, compatible consensus structures. The resulting models are called ambivalent covariance models. Evaluation on several RFAM families shows that coalescence of structural variation within a family by using ambivalent consensus models is superior to subdividing the family into multiple classical covariance models.CONCLUSION:A prototype and source code is available at http://bibiserv.cebitec.uni-bielefeld.de/acms.

The symbiotic α-rhizobia Sinorhizobium meliloti, Bradyrhizobium japonicum, Rhizobium etli and the related plant pathogen Agrobacterium tumefaciens are important model organisms for studying plant-microbe interactions. These metabolically versatile soil bacteria are characterized by complex lifestyles and large genomes. Here we summarize the recent knowledge on their small non-coding RNAs (sRNAs) including conservation, function, and interaction of the sRNAs with the RNA chaperone Hfq. In each of these organisms, an inventory of hundreds of cis- and trans-encoded sRNAs with regulatory potential was uncovered by high-throughput approaches and used for the construction of 39 sRNA family models. Genome-wide analyses of hfq mutants and co-immunoprecipitation with tagged Hfq revealed a major impact of the RNA chaperone on the physiology of plant-associated α-proteobacteria including symbiosis and virulence. Highly conserved members of the SmelC411 family are the AbcR sRNAs, which predominantly regulate ABC transport systems. AbcR1 of A. tumefaciens controls the uptake of the plant-generated signaling molecule GABA and is a central regulator of nutrient uptake systems. It has similar functions in S. meliloti and the human pathogen Brucella abortus. As RNA degradation is an important process in RNA-based gene regulation, a short overview on ribonucleases in plant-associated α-proteobacteria concludes this review.

Dynamic programming algorithms are traditionally expressed by a set of matrix recurrences-a low level of abstraction, which renders the design of novel dynamic programming algorithms difficult and makes debugging cumbersome.Bellman's GAP is a declarative, domain-specific language, which supports dynamic programming over sequence data. It implements the algebraic style of dynamic programming and allows one to specify algorithms by combining so-called yield grammars with evaluation algebras. Products on algebras allow to create novel types of analyses from already given ones, without modifying tested components. Bellman's GAP extends the previous concepts of algebraic dynamic programming in several respects, such as an "interleaved" product operation and the analysis of multi-track input.Extensive analysis of the yield grammar and the evaluation algebras is required for generating efficient imperative code from the algebraic specification. This article gives an overview of the analyses required and presents several of them in detail. Measurements with "real-world" applications demonstrate the quality of the code produced. (C) 2013 Elsevier B.V. All rights reserved.

Many methods have been proposed for RNA secondary structure comparison, and new ones are still being developed. In this chapter, we first consider structure representations and discuss their suitability for structure comparison. Then, we take a look at the more commonly used methods, restricting ourselves to structures without pseudo-knots. For comparing structures of the same sequence, we study base pair distances. For structures of different sequences (and of different length), we study variants of the tree edit model. We name some of the available tools and give pointers to the literature. We end with a short review on comparing structures with pseudo-knots as an unsolved problem and topic of active research.

Dynamic programming is a classical algorithmic paradigm, which often allows the evaluation of a search space of exponential size in polynomial time. Recursive problem decomposition, tabulation of intermediate results for re-use, and Bellman's Principle of Optimality are its well-understood ingredients. However, algorithms often lack abstraction and are difficult to implement, tedious to debug, and delicate to modify. The present article proposes a generic framework for specifying dynamic programming problems. This framework can handle all kinds of sequential inputs, as well as tree-structured data. Biosequence analysis, document processing, molecular structure analysis, comparison of objects assembled in a hierarchic fashion, and generally, all domains come under consideration where strings and ordered, rooted trees serve as natural data representations. The new approach introduces inverse coupled rewrite systems. They describe the solutions of combinatorial optimization problems as the inverse image of a term rewrite relation that reduces problem solutions to problem inputs. This specification leads to concise yet translucent specifications of dynamic programming algorithms. Their actual implementation may be challenging, but eventually, as we hope, it can be produced automatically. The present article demonstrates the scope of this new approach by describing a diverse set of dynamic programming problems which arise in the domain of computational biology, with examples in biosequence and molecular structure analysis.

shape analysis abstract shape analysis is a method to learn more about the complete Boltzmann ensemble of the secondary structures of a single RNA molecule. Abstract shapes classify competing secondary structures into classes that are defined by their arrangement of helices. It allows us to compute, in addition to the structure of minimal free energy, a set of structures that represents relevant and interesting structural alternatives. Furthermore, it allows to compute probabilities of all structures within a shape class. This allows to ensure that our representative subset covers the complete Boltzmann ensemble, except for a portion of negligible probability. This chapter explains the main functions of abstract shape analysis, as implemented in the tool RNA shapes. RNA shapes It reports on some other types of analysis that are based on the abstract shapes idea and shows how you can solve novel problems by creating your own shape abstractions.

Pareto optimization combines independent objectives by computing the Pareto front of its search space, defined as the set of all candidates whose scores are not dominated by others in at least one objective. This gives, in a precise sense, better information that an artificial amalgamation of different scores into a single objective, but is more costly to compute. We define a general Pareto product operator *Par on scoring schemes. Independent of a particular algorithm, we prove that for two scoring schemes A and B used in dynamic programming, the scoring scheme A *Par B correctly performs Pareto optimization over the same search space. We show that a Pareto-eager implementation of dynamic programming can achieve the same asymptotics as a single-objective optimization which computes the same number of results. For a concrete application in RNA structure prediction, we show that the empirical size of the Pareto front remains within reasonable bounds. Without artificial amalgamation of objectives, and with no heuristics involved, Pareto optimization is faster than computing the same number of answers separately for each objective.

The RNA chaperone Hfq is a global post-transcriptional regulator in bacteria. Here, we used RNAseq to analyze RNA populations from the legume symbiont Sinorhizobium meliloti that were co-immunoprecipitated (CoIP-RNA) with a FLAG-tagged Hfq in five growth/stress conditions. Hfq-bound transcripts (1315) were largely identified in stressed bacteria and derived from small RNAs (sRNAs), both trans-encoded (6.4%) and antisense (asRNAs; 6.3%), and mRNAs (86%). Pull-down with Hfq recovered a small proportion of annotated S. meliloti sRNAs (14% of trans-sRNAs and 2% of asRNAs) suggesting a discrete impact of this protein in sRNA pathways. Nonetheless, Hfq selectively stabilized CoIP-enriched sRNAs, anticipating that these interactions are functionally significant. Transcription of 26 Hfq-bound sRNAs was predicted to occur from promoters recognized by the major stress σ factors σE2 or σH1/2. Recovery rates of sRNAs in each of the CoIP–RNA libraries suggest a large impact of Hfq-assisted riboregulation in S. meliloti osmoadaptation. Hfq directly targeted 18% of the predicted S. meliloti mRNAs, which encode functionally diverse proteins involved in transport and metabolism, σE2-dependent stress responses, quorum sensing, flagella biosynthesis, ribosome, and membrane assembly or symbiotic nitrogen fixation. Canonical targeting of the 5′ regions of two of the ABC transporter mRNAs by the homologous Hfq-binding AbcR1 and AbcR2 sRNAs leading to inhibition of protein synthesis was confirmed in vivo. We therefore provide a comprehensive resource for the systems-level deciphering of hitherto unexplored S. meliloti stress and symbiotic post-transcriptional regulons and the identification of Hfq-dependent sRNA–mRNA regulatory pairs.

Sinorhizobium meliloti is a soil-dwelling α-proteobacterium that possesses a large, tripartite genome and engages in a nitrogen fixing symbiosis with its plant hosts. Although much is known about this important model organism, global characterization of genetic regulatory circuits has been hampered by a lack of information about transcription and promoters.

We present a--yet unpublished-- generalization of the Algebraic Dynamic Programming framework which also accomodates problems on trees. The new framework is not an add-on extension, but suggests a reformulation of classical ADP. ADP 2.0 is not only more general, but (arguably) more elegant - and more difficult to implement. In fact, no general implementation technique is known at present. An ensemble of about 30 problems - most classical, some new - from biosequence and structure analysis has been described in the new framework.