Rational tangle surgery and Xer recombination on catenanes

The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a 2-bridge knot N((4mn-1)/(2m)) yielding a (2,2k)-torus link are characterized. We apply this and other rational tangle surgery results to analyze Xer recombination on DNA catenanes using the tangle model for protein-bound DNA.Comment: 20 pages, 23 figure

Tangle analysis of DNA unlinking by the Xer/FtsK system(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

この論文は国立情報学研究所の電子図書館事業により電子化されました。DNAに作用する部位特異的組み換え酵素の働きは、タングルを用いてモデル化され、得られるタングル方程式を数学の結果を用いて解くことにより、部位特異的酵素の働きのトポロジーの特徴付けが出来る。ここでは、Grainge等(2007)によって示された部位特異的Xer/FtsKシステムによるDNA絡み目解消操作の解析を行い、その特徴付けを述べる。特にその作用を特徴付ける主要なタングルが有理タングルとなることを示す。The action of site-specific recombinases can be analyzed using the tangle method, where the reaction is characterized topologically by solving the corresponding tangle equations. We here analyze unlinking of DNA catenanes by the site-specific recombination system Xer/FtsK (Grainge et al., 2007). In particular we show that the key tangle involved in this reaction is rational. Therefore all solutions to the tangle equations can be computed using tangle calculus

A mathematical approach to mechanical properties of networks in thermoplastic elastomers

We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial extensions using networks of spherical domains connected by bridges. We advance previous research and discuss permanent strain and other aspects of the network. It explores the dependency of permanent strain on the extension direction, using the average of tension tensors to represent isotropic material behavior. The concept of deviation angle is introduced to measure network anisotropy and is shown to play an essential role in predicting permanent strain when a network is extended in a specific direction. The paper also discusses methods to create a new network structure using various polymers.Comment: 24 pages, 35 figure

Non-integral boundary slopes of alternating knots

We show, for every positive integer $n$, there is an alternating knot having a boundary slope with denominator $n$. We make use of Kabaya's method for boundary slopes and the layered solid torus construction introduced by Jaco and Rubinstein and further developed by Howie et al.Comment: 18 pages, 5 figures, 12 table