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Research on knot theory and its application

Research Project

Project/Area Number 16H03928
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionSaitama University

Principal Investigator

Shimokawa Koya  埼玉大学, 理工学研究科, 教授 (60312633)

Co-Investigator(Kenkyū-buntansha) 河内 明夫  大阪市立大学, 大学院理学研究科, 特任教授 (00112524)
石原 海  山口大学, 教育学部, 准教授 (40634762)
小沢 誠  駒澤大学, 総合教育研究部, 教授 (50308160)
三松 佳彦  中央大学, 理工学部, 教授 (70190725)
門上 晃久  金沢大学, 機械工学系, 教授 (80382026)
山口 祥司  秋田大学, 教育文化学部, 准教授 (30534044)
谷山 公規  早稲田大学, 教育・総合科学学術院, 教授 (10247207)
Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥17,810,000 (Direct Cost: ¥13,700,000、Indirect Cost: ¥4,110,000)
Fiscal Year 2020: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Keywords結び目 / DNA / 高分子 / トポロジー / ポリマー
Outline of Final Research Achievements

In this research project, we have studied the topology of macromolecules and supramolecules using knot theory. In particular, we (1) clarified the three-dimensional structure of chromosomes and analyzed their topology, (2) studied the behavior of DNA in the tubular region of nanochannels using knot theory, and (3) characterized the way recombinases untangle DNA links and applied the results to vortex knot research.

Academic Significance and Societal Importance of the Research Achievements

この研究では、高分子や超分子などのひも状のものが作る形を結び目理論を用いて解析し、これまで知られていなかった新たな性質を明らかにしている。この数学的なモデル化により、強力なトポロジーの解析の手段である結び目理論を様々な分野に応用することが出来、これまで無かった新しい視点をいくつかの研究分野において与えたことは学術的意義が大きいと考えられる。

Report

(6 results)
  • 2021 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (46 results)

All 2021 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (10 results) Journal Article (10 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 10 results,  Open Access: 8 results,  Acknowledgement Compliant: 6 results) Presentation (12 results) (of which Int'l Joint Research: 6 results,  Invited: 12 results) Book (1 results) Remarks (7 results) Funded Workshop (6 results)

  • [Int'l Joint Research] University of California, Davis(米国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] University of California, Davis(米国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] University of California, Davis(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] UC Davis(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Saskatchewan(カナダ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of California, Davis(米国)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] A metal-peptide capsule by multiple ring threading2019

    • Author(s)
      Sawada Tomohisa、Inomata Yuuki、Shimokawa Koya、Fujita Makoto
    • Journal Title

      Nature Communications

      Volume: 10 Issue: 1 Pages: 5687-5687

    • DOI

      10.1038/s41467-019-13594-4

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Neighborhood equivalence for multibranched surfaces in 3-manifolds2019

    • Author(s)
      Ishihara Kai、Koda Yuya、Ozawa Makoto、Shimokawa Koya
    • Journal Title

      Topology and its Applications

      Volume: 257 Pages: 11-21

    • DOI

      10.1016/j.topol.2019.02.005

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterising knotting properties of polymers in nanochannels2018

    • Author(s)
      N. R. Beaton, J. W. Eng, K. Ishihara, K. Shimokawa, C. E. Soteros
    • Journal Title

      Soft Matter

      Volume: 14 Issue: 28 Pages: 5775-5785

    • DOI

      10.1039/c8sm00734a

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Bounds for minimum step number of knots confined to tubes in the simple cubic lattice2017

    • Author(s)
      Ishihara, Kai; Pouokam, Maxime; Suzuki, Atsumi; Scharein, Robert; Vazquez, Mariel; Arsuaga, Javier; Shimokawa, Koya
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 50 Issue: 21 Pages: 1-28

    • DOI

      10.1088/1751-8121/aa6a4f

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Pathways of DNA unlinking: A story of stepwise simplification2017

    • Author(s)
      Stolz Robert、Yoshida Masaaki、Brasher Reuben、Flanner Michelle、Ishihara Kai、Sherratt David J.、Shimokawa Koya、Vazquez Mariel
    • Journal Title

      Scientific Reports

      Volume: 7 Issue: 1 Pages: 12420-12420

    • DOI

      10.1038/s41598-017-12172-2

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Band surgeries and crossing changes between fibered links2016

    • Author(s)
      Dorothy Buck, Kai Ishihara, Matt Rathbun, and Koya Shimokawa
    • Journal Title

      J. London Math. Soc.

      Volume: 94(2) Issue: 2 Pages: 557-582

    • DOI

      10.1112/jlms/jdw049

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Dehn surgery and Seifert surface system2016

    • Author(s)
      Makoto Ozawa and Koya Shimokawa
    • Journal Title

      Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)

      Volume: - Pages: 267-276

    • DOI

      10.2422/2036-2145.201410_008

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A knot with destabilized bridge spheres of arbitrarily high bridge number2016

    • Author(s)
      Yeonhee Jang, Tsuyoshi Kobayashi, Makoto Ozawa, Kazuto Takao
    • Journal Title

      J. London Math.

      Volume: 93 Issue: 2 Pages: 379-396

    • DOI

      10.1112/jlms/jdw004

    • NAID

      120006658032

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] An obstruction to embedding 2-dimensional complexes into the 3-sphere2016

    • Author(s)
      Kazufumi Eto, Shosaku Matsuzaki, Makoto Ozawa
    • Journal Title

      Topology and its Appl.

      Volume: 198 Pages: 117-125

    • DOI

      10.1016/j.topol.2015.11.008

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Knot homotopy in subspaces of the 3-sphere2015

    • Author(s)
      Yuya Koda, Makoto Ozawa
    • Journal Title

      Pacific J. Math.

      Volume: 282 Issue: 2 Pages: 389-414

    • DOI

      10.2140/pjm.2016.282.389

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] DNAと結び目理論2021

    • Author(s)
      下川航也
    • Organizer
      埼玉大学・埼玉医科大学包括協定締結記念キックオフシンポジウム
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] DNA組換え酵素の結び目理論的考察2021

    • Author(s)
      下川航也
    • Organizer
      MIMS/CMMA「第1回トポロジーとその応用融合研究セミナー」
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Untying pathways of vortex knots2021

    • Author(s)
      Koya Shimokawa
    • Organizer
      ヘリシティと時空対称性、古典場から量子場まで
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3-dimensional topology and polycontinuous pattern2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      International Symposium “Polymers and networks via topology and entanglement”
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3-dimensional topology and poly-continuous pattern2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      MATERIALS RESEARCH MEETING 2019, Mathematical Materials Science -Mathematical Approaches for Materials Designs in the Data Driven Society-
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Handlebody decomposition of 3-manifolds and their application2019

    • Author(s)
      Koya Shimokawa
    • Organizer
      可微分写像の特異点論とその応用
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] トポロジーと高分子科学2019

    • Author(s)
      下川航也
    • Organizer
      2019年度年会企画特別講演
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 結び目理論の高分子科学への応用 -- DNA組換え酵素、高分子化学、 材料科学、統計力学的エントロピー--,2018

    • Author(s)
      下川航也
    • Organizer
      名古屋大学多元数理科学研究科談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On chirality of molecular graphs2018

    • Author(s)
      Koya Shimokawa
    • Organizer
      Cyclic & Topologically Complex Polymers, Spring 2018 American Chemical Society Meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Lattice knots and links confined in tube regions2017

    • Author(s)
      Koya Shimokawa
    • Organizer
      Conference on Means, Methods and Results in the Statistical Mechanics of Polymeric Systems II, Fields Institute, University of Toronto, Canada
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] トポロジーの高分子化学への応用2016

    • Author(s)
      下川航也
    • Organizer
      ナノ学会主催 ナノ構造・物性- ナノ機能・応用部会 合同シンポジウム
    • Place of Presentation
      グランドパレス川端(秋田県大仙市)
    • Year and Date
      2016-12-27
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 結び目理論の応用について -DNA 組換え酵素、高分子化学、統計力学的エントロピー-2016

    • Author(s)
      下川航也
    • Organizer
      第63 回トポロジーシンポジウム
    • Place of Presentation
      神戸大学(兵庫県神戸市)
    • Year and Date
      2016-07-07
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Book] Topology of Polymers2019

    • Author(s)
      Shimokawa, Koya, Ishihara, Kai, Tezuka, Yasuyuki
    • Total Pages
      89
    • Publisher
      Springer, SpringerBriefs in the Mathematics of Materials
    • ISBN
      9784431568865
    • Related Report
      2019 Annual Research Report
  • [Remarks] 下川研究室

    • URL

      https://www-p.sci.ocha.ac.jp/shimokawa-lab/

    • Related Report
      2020 Annual Research Report
  • [Remarks] 下川航也ホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/KoyaShimokawa.html

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report 2016 Annual Research Report
  • [Remarks] 国際シンポジウムホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/polymersandnetworks2019.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] 下川航也 ホームページ

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/KoyaShimokawa.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] 国際ワークショップ Knots and Polymers

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/knotsandpolymers2017J.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] Topology and graphs in polymer chemistry

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/polymerchemistryJ.html

    • Related Report
      2016 Annual Research Report
  • [Remarks] International Workshop on Spatial Graphs 2016

    • URL

      http://www.f.waseda.jp/taniyama/SG2016/SG2016.html

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] 国際シンポジウム"Polymers and networks via topology and entanglement"2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] 国際ワークショップ “The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology” (19w5226)2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 国際シンポジウム“Polymers meet Topology”2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 国際ワークショップ Knots and Polymers: Aspects of topological entanglement in DNA, proteins and graph-shaped polymers2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] 国際ワークショップ Topology and graphs in polymer chemistry2016

    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2016-08-06
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] International Workshop on Spatial Graphs 20162016

    • Place of Presentation
      早稲田大学(東京都新宿区)
    • Year and Date
      2016-08-03
    • Related Report
      2016 Annual Research Report

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Published: 2016-04-21   Modified: 2023-01-30  

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