Related papers: Combinatorial Analysis for Pseudoknot RNA with Com…
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…
RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum stack-length. We show that the numbers of $k$-noncrossing structures without isolated base pairs are significantly smaller than the number of all…
In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the…
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…
Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…
In this paper we derive polynomial time algorithms that generate random $k$-noncrossing matchings and $k$-noncrossing RNA structures with uniform probability. Our approach employs the bijection between $k$-noncrossing matchings and…
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 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…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge \sigma$ and in which there…
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU-base pairings (secondary structure) and additional cross-serial base pairs. These…
We propose a new topological characterization of RNA secondary structures with pseudoknots based on two topological invariants. Starting from the classic arc-representation of RNA secondary structures, we consider a model that couples both…
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…
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\sf T}_{k,\sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the…
We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number,…
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU-base pairings (secondary structure) and additional cross-serial base pairs. These…
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…
Ab initio RNA secondary structure predictions have long dismissed helices interior to loops, so-called pseudoknots, despite their structural importance. Here, we report that many pseudoknots can be predicted through long time scales RNA…
Predicting the secondary structure of RNA is a core challenge in computational biology, essential for understanding molecular function and designing novel therapeutics. The field has evolved from foundational but accuracy-limited…
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…