Related papers: Exact enumeration of RNA secondary structures by h…
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 compute the loop homology of bi-secondary structures. Bi-secondary structures were introduced by Haslinger and Stadler and are pairs of RNA secondary structures, i.e. diagrams having non-crossing arcs in the upper…
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,…
We compute explicitly several abstract metrics for RNA secondary structures defined by Reidys and Stadler.
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…
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…
The contact map of a protein fold is a graph that represents the patterns of contacts in the fold. It is known that the contact map can be decomposed into stacks and queues. RNA secondary structures are special stacks in which the degree of…
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 --…
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…
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…
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…
It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2} \cdot 2.618034^n$. Motivated by the kinetics of RNA secondary structure formation, we are interested in…
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-…
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 give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…
We resolve two conjectures of Black-Drellich-Tymoczko about the numbers of valid plane trees for given primary sequences.
We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane…
The combinatorics of RNA plays a central role in biology. Mathematical biologists have several commonly-used models for RNA: words in a fixed alphabet (representing the primary sequence of nucleotides) and plane trees (representing the…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Understanding the base pairing of an RNA sequence provides insight into its molecular structure.By mining suboptimal sampling data, RNAprofiling 1.0 identifies the dominant helices in low-energy secondary structures as features, organizes…