Related papers: RNA Folding and Large N Matrix Theory
RNA design aims to find a sequence that folds with highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA…
We show how to make a topological string theory starting from an $N=4$ superconformal theory. The critical dimension for this theory is $\hat c= 2$ ($c=6$). It is shown that superstrings (in both the RNS and GS formulations) and critical…
The secondary structure of ribonucleic acid (RNA) is more stable and accessible in the cell than its tertiary structure, making it essential for functional prediction. Although deep learning has shown promising results in this field,…
In this paper we present a novel framework for sequence to shape maps. These combinatorial maps realize exponentially many shapes, and have preimages which contain extended connected subgraphs of diameter n (neutral networks). We prove that…
In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all $k$-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate…
Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in…
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…
RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary…
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…
We construct and study an extended random matrix model of RNA (polymer) folding. A perturbation which acts on all the nucleotides in the chain is added to the action of the RNA partition function. The effect of this perturbation on the…
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's…
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…
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…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
Motivation: Predicting the secondary structure of an RNA sequence is useful in many applications. Existing algorithms (based on dynamic programming) suffer from a major limitation: their runtimes scale cubically with the RNA length, and…
RNA design is the search for a sequence or set of sequences that will fold into predefined structures, also known as the inverse problem of RNA folding. While numerous RNA design methods have been invented to find sequences capable of…
Predicting protein secondary structure using lattice model is one of the most studied computational problem in bioinformatics. Here secondary structure or three dimensional structure of protein is predicted from its amino acid sequence.…
We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization,…
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…
The computer-aided folding of biomolecules, particularly RNAs, is one of the most difficult challenges in computational structural biology. RNA tetraloops are fundamental RNA motifs playing key roles in RNA folding and RNA-RNA and…