Related papers: A steepest descent calculation of RNA pseudoknots
In this paper we analyze the length-spectrum of blocks in $\gamma$-structures. $\gamma$-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time RNA folding. A $\gamma$-structure is…
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…
Computational prediction of RNA structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence,…
A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous…
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…
Shapes of interacting RNA complexes are studied using a filtration via their topological genus. A shape of an RNA complex is obtained by (iteratively) collapsing stacks and eliminating hairpin loops. This shape-projection preserves the…
RNA folding prediction remains challenging, but can be also studied using a topological mathematical approach. In the present paper, the mathematical method to compute the topological classification of RNA structures and based on matrix…
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological…
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…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Our work is concerned with the generation and targeted design of RNA, a type of genetic macromolecule that can adopt complex structures which influence their cellular activities and functions. The design of large scale and complex…
We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating…
We review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), where s and t are respective generating…
RNA molecules are single-stranded analogues of DNA that can fold into various structures which influence their biological function within the cell. RNA structures can be modelled combinatorially in terms of a certain type of graph called an…
We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…
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 --…
Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes…
The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial…
In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly…