Related papers: Irreducibility in RNA structures
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…
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…
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…
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…
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…
An $k$-noncrossing RNA structure can be identified with an $k$-noncrossing diagram over $[n]$, which in turn corresponds to a vacillating tableaux having at most $(k-1)$ rows. In this paper we derive the limit distribution of irreducible…
We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is…
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…
Researchers have repeatedly found that the ends of an RNA sequence are significantly closer than expected for a random linear chain. However, we prove that the ends of a branched structure are almost certainly close. Our results are…
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc-…
A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…
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…
The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost,…
Due to the hierarchical organization of RNA structures and their pivotal roles in fulfilling RNA functions, the formation of RNA secondary structure critically influences many biological processes and has thus been a crucial research topic.…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite of…
We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two…
Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of…
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…
In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set,…