Related papers: RNA foldings and Stuck Knots

RNAs self-interact through hydrogen-bond base-pairing between nucleotides and fold into specific, stable structures that substantially govern their biochemical behaviour. Experimental characterization of these structures remains difficult,…

We give a generating set of the generalized Reidemeister moves for oriented singular links. We use it to introduce an algebraic structure arising from the study of oriented singular knots. We give some examples, including some…

Computational prediction of RNA structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence,…

Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using…

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter,…

Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output.…

We use a link invariant defined by Cimasoni-Florens to compute \rho-invariants. This generalizes results of Cochran-Teichner and Friedl on knots to the setting of links. As an application, we prove with only twelve possible exceptions that…

We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting…

This paper introduces new invariants of rigid vertex graph embeddings by using non-local combinatorial information that is available at each graphical node. The new non-local information that we use in this paper involves parity in the…

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly…

The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…

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…

Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a…

We review the construction of Heegaard Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link…

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…

We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs…

Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a…

We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically…

Dual graphs have been applied to model RNA secondary structures. The purpose of the paper is two-fold: we present new graph-theoretic properties of dual graphs to validate the further analysis and classification of RNAs using these…