Related papers: Zigzag Stacks and m-Regular Linear Stacks
Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and…
In this study, we tackle the challenging task of predicting secondary structures from protein primary sequences, a pivotal initial stride towards predicting tertiary structures, while yielding crucial insights into protein activity,…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
In a statistical approach to protein structure analysis, Miyazawa and Jernigan (MJ) derived a $20\times 20$ matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we…
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…
Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a…
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…
Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA m-diagrams of degree k, combinatorial objects which can be…
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\sf T}_{k,\sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the…
Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. To tackle…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the…
We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the…
In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be…
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…
Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides a set of birth and death pairs for the topological features…
Arc-annotated sequences are useful for representing structural information of RNAs and have been extensively used for comparing RNA structures in both terms of sequence and structural similarities. Among the many paradigms referring to…
Accurate prediction of RNA secondary structure underpins transcriptome annotation, mechanistic analysis of non-coding RNAs, and RNA therapeutic design. Recent gains from deep learning and RNA foundation models are difficult to interpret…
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…