Related papers: Irreducibility in RNA structures
We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The…
In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…
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…
In this article, we study the hierarchical structure of metastability in the reversible inclusion process. We fully characterize the third time scale of metastability subject to any underlying geometry of the system and prove that this is…
Many computerized methods for RNA-RNA interaction structure prediction have been developed. Recently, $O(N^6)$ time and $O(N^4)$ space dynamic programming algorithms have become available that compute the partition function of RNA-RNA…
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on the…
Let $\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\Sigma=\{0,1\}^{\mathbb{N}}$ associated with a H\"older potential. The thermodynamic and multifractal properties of $\mu$ are well known to be linked via the…
Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…
In this paper we study $k$-noncrossing RNA structures with minimum arc-length 4 and at most $k-1$ mutually crossing bonds. Let ${\sf T}_{k}^{[4]}(n)$ denote the number of $k$-noncrossing RNA structures with arc-length $\ge 4$ over $n$…
Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction…
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…
Ribonucleic Acid (RNA) can fold into shapes that perform functions in the cell. These foldings are governed by Watson-Crick base pairing, namely Adenine to Uracil and Cytosine to Guanine (A-U and G-C). The properties of the H-P…
RNA secondary structure prediction and classification are two important problems in the field of RNA biology. Here, we propose a new permutation based approach to create logical non-disjoint clusters of different secondary structures of a…
RNA forms elaborate secondary structures through intramolecular base pairing. These structures perform critical biological functions within each cell. Due to the availability of a polynomial algorithm to calculate the partition function…
Co-optimizing mRNA sequences for both codon optimality and secondary structure is crucial for producing stable and efficacious mRNA therapeutics. Codon optimization, which adjusts nucleotide sequences to enhance translational efficiency,…
As a consequence of the rugged landscape of RNA molecules their folding is described by the kinetic partitioning mechanism according to which only a small fraction ($\phi_F$) reaches the folded state while the remaining fraction of…
We derived simple polynomial equations to determine the entire resonance spectra of split ring structures. For double stacking split rings made with flat wires, we showed that the resonance frequency depends linearly on the ring-ring…
We enumerate possible topologies of pseudoknots in single-stranded RNA molecules. We use a steepest-descent approximation in the large N matrix field theory, and a Feynman diagram formalism to describe the resulting pseudoknot structure.
The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical…
In this paper we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse grained RNA structures allowing for cross-serial interactions, subject to the…