Related papers: Irreducibility in RNA structures
RNA pseudoknots are a kind of minimal RNA tertiary structural motifs, and their three-dimensional (3D) structures and stability play essential roles in a variety of biological functions. Therefore, to predict 3D structures and stability of…
RNA function is tied to secondary structure, operating through dynamic and heterogeneous structural ensembles. While current analysis tools typically output single static structures or averaged contact maps, chemical probing methods like…
By exerting mechanical force it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a…
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…
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…
We describe an algorithm for comparing two RNA secondary structures coded in the form of trees that introduces two new operations, called node fusion and edge fusion, besides the tree edit operations of deletion, insertion, and relabeling…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed…
The alignment between RNA sequences and structures in foundation models (FMs) has yet to be thoroughly investigated. Existing FMs have struggled to establish sequence-structure alignment, hindering the free flow of genomic information…
Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be…
Integrative biomolecular modeling of RNA relies on structural refined collections and accurate experimental data that reflect binding and folding behavior. However, the prediction of such collections remains challenging due to the rugged…
Many recent exciting discoveries have revealed the versatility of RNAs and their importance in a variety of cellular functions which are strongly coupled to RNA structures. To understand the functions of RNAs, some structure prediction…
We study numerically the behavior of RNA secondary structures under influence of a varying external force. This allows to measure the work $W$ during the resulting fast unfolding and refolding processes. Here, we investigate a medium-size…
We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…
The tertiary structures of functional RNA molecules remain difficult to decipher. A new generation of automated RNA structure prediction methods may help address these challenges but have not yet been experimentally validated. Here we apply…
The structure of an RNA molecule plays a significant role in its biological function. Predicting structure given a one dimensional sequence of RNA nucleotide bases is a difficult and important problem. Many computer programs (known as in…
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's diverse biological functions stem from its structural versatility, yet accurately predicting and designing RNA sequences given a 3D conformation (inverse folding) remains a challenge. Here, I introduce a deep learning framework that…
The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the…
Secondary structure plays an important role in determining the function of non-coding RNAs. Hence, identifying RNA secondary structures is of great value to research. Computational prediction is a mainstream approach for predicting RNA…