Related papers: RNA secondary structures having a compatible seque…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…
RNA secondary structure is an important computational model to understand how genetic variation maps into phenotypic (structural) variation. Evolutionary innovation in RNA structures is facilitated by neutral networks, large connected sets…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…
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…
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
Formation of base pairs between the nucleotides of an RNA sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching --…
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…
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…
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…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
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…
In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete…
Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as…
It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
Recently Yoffe {\it et al.} observed that the average distances between $5'-3'$ ends of RNA molecules are very small and largely independent of sequence length. This observation is based on numerical computations as well as theoretical…
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…
In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all $k$-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate…