Related papers: Irreducibility in RNA structures
In this paper we study the effect of energy parameters on minimum free energy (mfe) RNA secondary structures. Employing a simplified combinatorial energy model, that is only dependent on the diagram representation and that is not sequence…
RNA design is the search for a sequence or set of sequences that will fold into predefined structures, also known as the inverse problem of RNA folding. While numerous RNA design methods have been invented to find sequences capable of…
Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…
Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with…
In this paper we present a selfcontained analysis and description of the novel {\it ab initio} folding algorithm {\sf cross}, which generates the minimum free energy (mfe), 3-noncrossing, $\sigma$-canonical RNA structure. Here an RNA…
We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure find a sequence that has that structure as its ground state. If such a sequence exists, the structure is called…
RNA design aims to identify RNA sequences that fold into a target secondary structure. This task is challenging in terms of computational efficiency. Most existing methods focus on either minimum free energy (MFE)-based or ensemble-based…
Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
RNA design aims to find a sequence that folds with highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA…
We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for…
The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
A k-noncrossing RNA pseudoknot structure is a graph over $\{1,...,n\}$ without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
In this paper we analyze the length-spectrum of blocks in $\gamma$-structures. $\gamma$-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time RNA folding. A $\gamma$-structure is…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
RNA-RNA binding is an important phenomenon observed for many classes of non-coding RNAs and plays a crucial role in a number of regulatory processes. Recently several MFE folding algorithms for predicting the joint structure of two…
The information-encoding molecules RNA and DNA form a combinatorially large set of secondary structures through nucleic acid base pairing. Thermodynamic prediction algorithms predict favoured, or minimum free energy (MFE), secondary…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…