Universality in the diffusion of knots

We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot $K$ and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The ratio is found to be constant with respect to the number of monomers, $N$, and hence the estimate at some $N$ should be valid practically over a wide range of $N$ for various polymer models. Interestingly, the ratio is determined by the average crossing number ($N_{AC}$) of an ideal conformation of knotted curve $K$, i.e. that of the ideal knot. The $N_{AC}$ of ideal knots should therefore be fundamental in the dynamics of knots.Comment: 8 pages, 14 figure

Diffusion of a ring polymer in good solution via the Brownian dynamics

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.Comment: 11 pages, 4 figure

2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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2017 HRS/EHRA/ECAS/APHRS/SOLAECE expert consensus statement on catheter and surgical ablation of atrial fibrillation: executive summary.

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withdrawn 2017 hrs ehra ecas aphrs solaece expert consensus statement on catheter and surgical ablation of atrial fibrillation

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Intrinsic viscosity of knots in solution evaluated through the Brownian Dynamics(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。我々は溶液中における結び目高分子の固有粘度を、Brownian dynamicsにより排除体積効果および流体力学的相互作用を考慮して計算した。近年の実験技術の進展により、結び目高分子の合成が予見される中で、溶液の固有粘度を表す公式を導入することは重要である。また結び目高分子は溶液中に混在しているため、それらの分離にも役立つことが期待される。その結果、結び目高分子の三葉結び目に対する固有粘度の比が、Nに依存しないことが分かった。またその固有粘度の比は、理想結び目の平均交点数(ACN)の二次関数であることも分かった。We have evaluated the intrinsic viscosity of the solution of ring polymers of a knot type K by the Brownian dynamics with both hydrodynamic and excluded volume effects. Due to recent development of experiments, we expect that knotted ring polymers will be synthesized near future. It is thus important to formulate empirical equations for describing the intrinsic viscosity in terms of K. They should be useful for separating knot species in solution. We found that the ratio of the intrinsic viscosity of a knot to that of the trefoil knot is independent of the number of segments N in the investigated range. We also found that it is expressed by a quadratic function of the average crossing number of the ideal knot of K (ACN(K))

Diffusion of circular DNA in solution by Brownian Dynamics(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。我々は環状鎖と線形鎖の拡散定数の比(C因子)を、Brownian dynamicsにより排除体積効果および流体力学的相互作用を考慮して計算した。その目的は環状鎖のモデルの妥当性を、実験と比較することにより検討することである。FENEバネでつながれたバネビーズ模型では、C因子は1.1であった。これは合成環状高分子の実験結果と一致する。その一方この結果は、環状DNAによる実験結果C～1.3と合わない。しかし強い角度ポテンシャルを与えた場合、C因子はおよそ1.3になることが分かった。この強い角度ポテンシャルは、kinkと呼ばれるDNA分子内部の鋭く曲がった構造を表しているのかもしれない。We have evaluated the ratio of diffusion constant of a ring to that of a linear polymer in solution by the Brownian dynamics with both hydrodynamic and excluded-volume effects. The ratio is called the C-factor. It is given by about 1.1 when we use the bead-spring model where beads are connected by the finite extensible non-linear elongational (FENE) potential. The value 1.1 is consistent with the experiments of synthesized ring polymers. However, it is different from the C-factor ～1.3 for the experiments of circular DNA. However, we found that the C-factor becomes about 1.3 when we employ the strong angle potential. It agrees well with the experimental results of circular DNA. We also suggest the strong angle potential should describe the effect of a kink, which is a sharp-bending part in a DNA

Diffusion of supercoiled DNA and the effect of base-flipping by Brownian dynamics(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。Supercoiled DNAは、2本の環状鎖が絡み合っているlinkとみなせる。その絡み目数(linking number L_k)は、熱揺らぎのもとで保存する。我々ははしご型のモデルを作り、絡み目数と拡散の関係を調べた。はしごを何度かねじった後に右端と左端のビーズをFENEバネでつなぐことにより、絡み目数を保存する。その結果、拡散定数は絡み目数の線形関数であることが分かった。さらに我々はbase-flippingの拡散に与える影響を調べるため、FENEバネでつながれたペアの1つを切り離した。その結果拡散は、base-flippingを考慮しないモデルに比較して遅くなることが分かった。この傾向は角度ポテンシャルを考慮する時、より顕著となった。We have evaluated the diffusion constant of a ladder-like model of supercoiled DNA (see figure) in solution through Brownian dynamics with both hydrodynamic and excluded volume effects. After twisting the ladder we connect the ends so that its linking number L_k is conserved. We found that the diffusion constant is a linear function of L_k. In order to study the effect of base-flipping we disconnect the FENE spring potential that connects one of the pairs. The diffusion constant of the model with base-flipping becomes smaller especially when we take into account the angle potential