Related papers: Enumeration of RNA structures by Matrix Models
Predicting the secondary structure of RNA is a core challenge in computational biology, essential for understanding molecular function and designing novel therapeutics. The field has evolved from foundational but accuracy-limited…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge \sigma$ and in which there…
Lattice-model simulations and experiments of some small proteins suggest that folding is essentially controlled by a few conserved contacts. Residues of these conserved contacts form the minimum set of native contacts needed to ensure…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
An essential quantity to ensure evolvability of populations is the navigability of the genotype space. Navigability relies on the existence of sufficiently large genotype networks, that is ensembles of sequences with the same phenotype that…
We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane…
Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and linear time uniform sampling algorithm for RNA complexes of…
In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus $g$, for arbitrary $g>0$. Furthermore…
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
Given the importance of non-coding RNAs to cellular regulatory functions and rapid growth of RNA transcripts, computational prediction of RNA tertiary structure remains highly demanded yet significantly challenging. Even for a short RNA…
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…
The increasing importance of RNA as a prime player in biology can hardly be overstated. Problems in RNA, such as folding and RNA-RNA interactions that drive phase separation, require cations. Because experiments alone cannot reveal the…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very…
Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it…
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…
RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main…
We present a thermodynamically robust coarse-grained model to simulate folding of RNA in monovalent salt solutions. The model includes stacking, hydrogen bond and electrostatic interactions as fundamental components in describing the…
In this paper we study the distribution of stacks in $k$-noncrossing, $\tau$-canonical RNA pseudoknot structures ($<k,\tau> $-structures). An RNA structure is called $k$-noncrossing if it has no more than $k-1$ mutually crossing arcs and…
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…