Related papers: RNA Folding and Large N Matrix Theory
The RNA Inverse Folding problem comes from computational biology. The goal is to find a molecule that has a given folding. It is important for scientific fields such as bioengineering, pharmaceutical research, biochemistry, synthetic…
We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
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…
An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence,…
The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA…
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…
We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number,…
An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Hale\v{s} et al. in 2016, is to…
The combinatorics of RNA plays a central role in biology. Mathematical biologists have several commonly-used models for RNA: words in a fixed alphabet (representing the primary sequence of nucleotides) and plane trees (representing the…
Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze…
Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base…
RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite of…
The prevalent method for RNA secondary structure prediction for a single sequence is free energy minimization based on the nearest neighbor thermodynamic model (NNTM). One of the least well-developed parts of the model is the energy…
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…
We extend recent methods for parametric sequence alignment to the parameter space for scoring RNA folds. This involves the construction of an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common…
Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…