A new procedure to analyze RNA non-branching structures

RNA structure prediction and structural motifs analysis are challenging tasks in the investigation of RNA function. We propose a novel procedure to detect structural motifs shared between two RNAs (a reference and a target). In particular, we developed two core modules: (i) nbRSSP_extractor, to assign a unique structure to the reference RNA encoded by a set of non-branching structures; (ii) SSD_finder, to detect structural motifs that the target RNA shares with the reference, by means of a new score function that rewards the relative distance of the target non-branching structures compared to the reference ones. We integrated these algorithms with already existing software to reach a coherent pipeline able to perform the following two main tasks: prediction of RNA structures (integration of RNALfold and nbRSSP_extractor) and search for chains of matches (integration of Structator and SSD_finder)

Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

Tree decomposition and parameterized algorithms for RNA structure-sequence alignment including tertiary interactions and pseudoknots

We present a general setting for structure-sequence comparison in a large class of RNA structures that unifies and generalizes a number of recent works on specific families on structures. Our approach is based on tree decomposition of structures and gives rises to a general parameterized algorithm, where the exponential part of the complexity depends on the family of structures. For each of the previously studied families, our algorithm has the same complexity as the specific algorithm that had been given before.Comment: (2012

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

Prediction of secondary structures for large RNA molecules

The prediction of correct secondary structures of large RNAs is one of the unsolved challenges of computational molecular biology. Among the major obstacles is the fact that accurate calculations scale as O(n⁴), so the computational requirements become prohibitive as the length increases. We present a new parallel multicore and scalable program called GTfold, which is one to two orders of magnitude faster than the de facto standard programs mfold and RNAfold for folding large RNA viral sequences and achieves comparable accuracy of prediction. We analyze the algorithm's concurrency and describe the parallelism for a shared memory environment such as a symmetric multiprocessor or multicore chip. We are seeing a paradigm shift to multicore chips and parallelism must be explicitly addressed to continue gaining performance with each new generation of systems. We provide a rigorous proof of correctness of an optimized algorithm for internal loop calculations called internal loop speedup algorithm (ILSA), which reduces the time complexity of internal loop computations from O(n⁴) to O(n³) and show that the exact algorithms such as ILSA are executed with our method in affordable amount of time. The proof gives insight into solving these kinds of combinatorial problems. We have documented detailed pseudocode of the algorithm for predicting minimum free energy secondary structures which provides a base to implement future algorithmic improvements and improved thermodynamic model in GTfold. GTfold is written in C/C++ and freely available as open source from our website.M.S.Committee Chair: Bader, David; Committee Co-Chair: Heitsch, Christine; Committee Member: Harvey, Stephen; Committee Member: Vuduc, Richar