RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g., as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactorily in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots i...

In this article, we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse-grained RNA structures allowing for cross-serial interactions, subject to the constraint that there are at most k - 1 mutually crossing arcs in the diagram representation of the molecule. We prove central limit theorems by means of...

In this article, we present the novel ab initio folding algorithm cross, which generates minimum free energy (mfe), 3-noncrossing, canonical RNA structures. Here an RNA structure is 3-noncrossing if it does not contain three or more mutually crossing arcs and canonical, if each of its stacks has size greater or equal than two. Our notion of mfe-structure is based on a specific concept of pseudo...

The tmRNA pseudoknot PK1 is essential for bacterial trans-translation, a ribosomal rescue mechanism. We report the solution structure of PK1 from Aquifex aeolicus which, despite an unprecedented small number of nulcleotides and thus an unprecented compact size, displays a very high thermal stability. Several unusual structural features account for these properties and indicate that PK1 belongs ...

We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind, which turns out to be the hypergeometric function. To match the experimental findings of the statistical behavior, we regard the substructure as a grand canonical ensemble and find its fugacity value. We also suggest a hierarchical picture based on t...

Several grammars have been proposed for modeling RNA pseudoknotted structure. In this paper, we focus on multiple context-free grammars (MCFGs), which are natural extension of context-free grammars and can represent pseudoknots, and extend a specific subclass of MCFGs to a probabilistic model called SMCFG. We present a polynomial time parsing algorithm for finding the most probable derivation t...

The transfer-messenger RNA (tmRNA) pseudoknot PK1 is essential for bacterial trans-translation, a ribosomal rescue mechanism. We report the solution structure of PK1 from Aquifex aeolicus, which despite an unprecedented small number of nucleotides and thus an unprecented compact size, displays a very high thermal stability. Several unusual structural features account for these properties and in...