相关论文: Combinatorics Of RNA Structures With Pseudoknots

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,…

Riordan arrays, denoted by pairs of generating functions (g(z), f(z)), are infinite lower-triangular matrices that are used as combinatorial tools. In this paper, we present Riordan and stochastic Riordan arrays that have connections to the…

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 dominant paradigm in origin of life research is that of an RNA world. However, despite experimental progress towards the spontaneous formation of RNA, the RNA world hypothesis still has its problems. Here, we introduce a novel…

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…

The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…

RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by…

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…

We have the generating function which determines the number of $2$-bridge knot groups admitting epimorphisms onto the knot group of a given $2$-bridge knot, in terms of crossing number. In this paper, we will refine this formula by taking…

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 --…

In this paper we study $k$-noncrossing matchings. A $k$-noncrossing matching is a labeled graph with vertex set $\{1,...,2n\}$ arranged in increasing order in a horizontal line and vertex-degree 1. The $n$ arcs are drawn in the upper…

Long non-coding RNA, microRNA, and messenger RNA enable key regulations of various biological processes through a variety of diverse interaction mechanisms. Identifying the interactions and cross-talk between these heterogeneous RNA classes…

The Human Genome Project has led to an exponential increase in data related to the sequence, structure, and function of biomolecules. Bioinformatics is an interdisciplinary research field that primarily uses computational methods to analyze…

The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced…

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant,…

We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where…

RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main…

An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Hale\v{s} et al. in 2016, is to…

In this paper, we consider the problem of designing DNA sequences (codewords) for DNA storage systems and DNA computing that are unlikely to fold back onto themselves to form undesirable secondary structures. The paper addresses both the…

An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that any two of the curves are either disjoint or intersect in exactly two crossing points. We call an arrangement intersecting if…