A Combinatorial Framework for Designing (Pseudoknotted) RNA Algorithms

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming

A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics

International audienceIn this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold. We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n 2)-space, O(n 2ρ+2.5)-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n ρ+1)-space, O(n ρ+2)-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [20]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph. We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n ρ+2) for the energy barrier problem, improving upon a partial O(n 2ρ+2.5) algorithm for the problem

RNA folding kinetics including pseudoknots

RNA Moleküle sind ein essenzieller Bestandteil biologischer Zellen. Ihre Vielfalt an Funktionen ist eng verknüpft mit der jeweiligen Sequenz und der daraus gebildeten Struktur. Der Großteil bekannter RNA Moleküle faltet in eine bestimmte energetisch stabile Struktur, bzw. ̈hnliche suboptimale Strukturen mit der gleichen biologischen Funktion. Riboswitches hingegen, eine bestimmte Gruppe von RNA Molekülen können zwischen zwei strukturell sehr verschiedenen Konformationen wechseln, wobei eine funktional ist und die andere nicht. Die Umfaltung solcher RNA-Schalter wird normalerweise durch verschiedenste Metaboliten ausgelöst die mit der RNA interagieren. Zellen nutzen dieses Prinzip um auf Signale aus der Umwelt effizient reagieren zu können. Im Zuge der synthetischen Biologie wurde eine neue Art von RNA-Schaltern entwickelt, die statt einem bestimmten Metaboliten ein anderes RNA Molekül erkennt [1]. Dieses Prinzip ziehlt weniger darauf ab Signale aus der Umgebung wahrzunehmen, sondern ein weiteres Level an Genregulation zu ermöglichen. In dieser Abeit wird das Program RNAscout.pl präsentiert, welches die Umfaltung zwischen verschiedenen RNA Strukturen berechnet und damit die Effizienz RNA-induzierter RNA-Schalter bewerten kann. Der zugrundeliegenede Algorithmus berechnet ein Set an Zwischenzuständen die sowohl energetisch günstig, als auch strukturell ähnlich zu den beiden stabilen Riboswitch-Konformationen sind. Basierend auf diesem Umfaltungsnetzwerk werden kinetische Simulationen gezeigt, bei denen der Umfaltungsweg des RNA-Schalters vorhergesagt wird. Des Weiteren wird das Programm pk findpath vorgestellt. Der zugrundeliegende Algorithmus berechnet den besten direkten Umfaltungspfad zwischen zwei RNA Strukturen mittels einer Breitensuche. Beide Programme, RNAscout.pl und pk findpath, werden verwendet um abzuschätzen ob natürliche RNA Moleküle optimiert sind um in ihre energetisch günstigste Konformation zu falten. Im Zuge dessen werden die Programme mit existierenden Programmen des Vienna RNA package [2] verglichen.RNA molecules are essential components of living cells. Their wide range of different functions depends on the sequence of nucleotides and the corresponding structure. The majority of known RNA molecules fold into their energetically most stable conformation, as well as structurally similar suboptimal conformations that do not alter the specific task of the molecule. However, there are RNA molecules which can switch between two structurally distant conformations one of which is functional, the other is not. The best known examples are riboswitches, which usually sense various kinds of metabolites from their environment that trigger the refolding from one conformation into the other. The rather new field of synthetic biology led to the construction of an example for a new type of riboswitches, which refold upon interaction with other RNA molecules [1]. Such RNA-triggered riboswitches are not aimed at sensing the environment, but expand the repertoire of gene-regulation. Inspired by this example, we present RNAscout.pl, a new program to study refolding between two RNA conformations, which can be used to estimate the performance of RNA-triggered riboswitches. The underlying algorithm heuristically computes a set of intermediate conformations that are energetically favorable and structurally related to both stable conformations of the riboswitch. Based on this refolding network, we show kinetic simulations that support the expected refolding path for our riboswitch example. Moreover, we present pk findpath, a breadth-first search algorithm to estimate direct paths (i. e. a small subset of all possible paths) between two different RNA conformations. Both programs RNAscout.pl and pk findpath will be used to estimate whether natural RNA molecules are optimized to fold into their energetically most stable conformation. Thereby, we compare the new programs against existing programs of the Vienna RNA package [2

Predicting folding pathways between RNA conformational structures guided by RNA stacks

Background: Accurately predicting low energy barrier folding pathways between conformational secondary structures of an RNA molecule can provide valuable information for understanding its catalytic and regulatory functions. Most existing heuristic algorithms guide the construction of folding pathways by free energies of intermediate structures in the next move during the folding. However due to the size and ruggedness of RNA energy landscape, energy-guided search can become trapped in local optima. Results: In this paper, we propose an algorithm that guides the construction of folding pathways through the formation and destruction of RNA stacks. Guiding the construction of folding pathways by coarse grained movements of RNA stacks can help reduce the search space and make it easier to jump out of local optima. RNAEAPath is able to find lower energy barrier folding pathways between secondary structures of conformational switches and outperforms the existing heuristic algorithms in most test cases. Conclusions: RNAEAPath provides an alternate approach for predicting low-barrier folding pathways between RNA conformational secondary structures. The source code of RNAEAPath and the test data sets are available at http://genome.ucf.edu/RNAEAPath

Computing the Partition Function for Kinetically Trapped RNA Secondary Structures

An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in time and space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures – indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/

Computational Methods For Analyzing Rna Folding Landscapes And Its Applications

Non-protein-coding RNAs play critical regulatory roles in cellular life. Many ncRNAs fold into specific structures in order to perform their biological functions. Some of the RNAs, such as riboswitches, can even fold into alternative structural conformations in order to participate in different biological processes. In addition, these RNAs can transit dynamically between different functional structures along folding pathways on their energy landscapes. These alternative functional structures are usually energetically favored and are stable in their local energy landscapes. Moreover, conformational transitions between any pair of alternate structures usually involve high energy barriers, such that RNAs can become kinetically trapped by these stable and local optimal structures. We have proposed a suite of computational approaches for analyzing and discovering regulatory RNAs through studying folding pathways, alternative structures and energy landscapes associated with conformational transitions of regulatory RNAs. First, we developed an approach, RNAEAPath, which can predict low-barrier folding pathways between two conformational structures of a single RNA molecule. Using RNAEAPath, we can analyze folding iii pathways between two functional RNA structures, and therefore study the mechanism behind RNA functional transitions from a thermodynamic perspective. Second, we introduced an approach, RNASLOpt, for finding all the stable and local optimal structures on the energy landscape of a single RNA molecule. We can use the generated stable and local optimal structures to represent the RNA energy landscape in a compact manner. In addition, we applied RNASLOpt to several known riboswitches and predicted their alternate functional structures accurately. Third, we integrated a comparative approach with RNASLOpt, and developed RNAConSLOpt, which can find all the consensus stable and local optimal structures that are conserved among a set of homologous regulatory RNAs. We can use RNAConSLOpt to predict alternate functional structures for regulatory RNA families. Finally, we have proposed a pipeline making use of RNAConSLOpt to computationally discover novel riboswitches in bacterial genomes. An application of the proposed pipeline to a set of bacteria in Bacillus genus results in the re-discovery of many known riboswitches, and the detection of several novel putative riboswitch elements