Related papers: RNA substructure as a random matrix ensemble
We propose a new deterministic methodology to predict RNA sequence and protein folding. Is stem enough for structure prediction? The main idea is to consider all possible stem formation in the given sequence. With the stem loop energy and…
There exists many complicated $k$-noncrossing pseudoknot RNA structures in nature based on some special conditions. The special characteristic of RNA structures gives us great challenges in researching the enumeration, prediction and the…
In this paper we experiment with using neural network structures to predict a protein's secondary structure ({\alpha} helix positions) from only its primary structure (amino acid sequence). We implement a fully connected neural network…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
Generative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain…
Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…
Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with…
The intricate network of interactions observed in RNA three-dimensional structures is often described in terms of a multitude of geometrical properties, including helical parameters, base pairing/stacking, hydrogen bonding and backbone…
RNA secondary structure is an important computational model to understand how genetic variation maps into phenotypic (structural) variation. Evolutionary innovation in RNA structures is facilitated by neutral networks, large connected sets…
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
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…
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…
We introduce RNA-FrameFlow, the first generative model for 3D RNA backbone design. We build upon SE(3) flow matching for protein backbone generation and establish protocols for data preparation and evaluation to address unique challenges…
We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We enumerate possible topologies of pseudoknots in single-stranded RNA molecules. We use a steepest-descent approximation in the large N matrix field theory, and a Feynman diagram formalism to describe the resulting pseudoknot structure.