相关论文: Rational tangle surgery and Xer recombination on c…

Integrase proteins acting on circular double-stranded DNA often change its topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations--corresponding to the two initial DNA sequences--arise when…

This paper is an introduction to rational tangles, rational knots and links and their applications to DNA. The paper can be read as an introduction to our more technical papers on rational tangles (math.GT/0311499) and on rational knots…

Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products and they can act as substrates for further rounds of…

Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces…

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. We develop a model of this process, and give extensive experimental evidence that the assumptions of our model are reasonable. We…

We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small…

A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai,…

How a nano-searcher finds its nano-target is a general problem in non-equilibrium statistical physics. It becomes vital when the searcher is a damaged DNA fragment trying to find its counterpart on the intact homologous chromosome. If the…

We study the elastic response of a worm-like polymer chain with reversible kink-like structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of…

Gene assembly in ciliates is an extremely involved DNA transformation process, which transforms a nucleus, the micronucleus, to another functionally different nucleus, the macronucleus. In this paper we characterize which loop recombination…

It is a standard exercise in mechanical engineering to infer the external forces and torques on a body from its static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with…

This paper gives infinitely many examples of unknot diagrams that are hard, in the sense that the diagrams need to be made more complicated by Reidemeister moves before they can be simplified. In order to construct these diagrams, we prove…

We study two systems of tangle equations that arise when modeling the action of the Integrase family of proteins on DNA. These two systems--direct and inverted repeats--correspond to two different possibilities for the initial DNA sequence.…

We determine the Dehn surgeries on 2-bridge links, which yield reducible 3-manifolds. Further, we show the conditions that we obtain a torus or cable knot from one component of a 2-bridge link by a surgery on another component.

We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.

We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA…

This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…

We calculate the electronic structure for a modulation doped and gated T-shaped quantum wire using density functional theory. We calculate the bandgap renormalization as a function of the density of conduction band electrons, induced by the…

We show that all large enough positive integral surgeries on algebraic knots bound a 4-manifold with a negative definite plumbing tree, which we describe explicitly. Then we apply the lattice embedding obstruction coming from Donaldson's…

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…