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Research on topology using surfaces, and its application

Research Project

Project/Area Number 17K14190
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionYamaguchi University

Principal Investigator

Ishihara Kai  山口大学, 教育学部, 准教授 (40634762)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsDNAトポロジー / 結び目 / 絡み目 / バンド手術 / 交差交換 / ファイバー絡み目 / 結び目解消トンネル / ファイバー結び目 / GOF-knots / 絡み目解消経路 / 低次元トポロジー
Outline of Final Research Achievements

In this project, in order to clarify the action of enzymes that change the topology of DNA, we conducted studies on the topology of 3-manifolds and knots, especially the topology using surfaces, and obtained the following results. We characterized the repeat action of type II topoisomerases and the repeat action of site-specific recombination with respect to the unlinking of replicated DNA. Under weaker assumptions than previous studies, we determined all unlinking pathways from relatively simple substrates. In the general case, all the products obtained from the first action were determined, and it was shown that the action was unique from a topological point of view.

Academic Significance and Societal Importance of the Research Achievements

DNAのトポロジーを変える酵素の作用のモデルとして有理タングル手術を用いて研究した。中でもバンド手術や交差交換といった最も単純な有理タングル手術の決定問題は一般に非常に難しい。この問題の解決が前進したことが本研究の意義と言える。また,応用面では分子生物学的現象の数学的な意味づけやトポロジーによる証明が与えられたことに意義がある。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (16 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (3 results) Journal Article (5 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 5 results,  Open Access: 3 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results) Book (1 results)

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

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Oxford University(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] California State University, Fullerton(米国)

    • Related Report
      2017 Research-status Report
  • [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 Research-status 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 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Enzyme action for topological entanglement in DNA and knot theory2018

    • Author(s)
      K. Ishihara
    • Journal Title

      Reactive and Functional Polymers

      Volume: 132 Pages: 74-80

    • DOI

      10.1016/j.reactfunctpolym.2018.09.006

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [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 Research-status 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 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Topological characterization of unlinking pathways2020

    • Author(s)
      石原 海
    • Organizer
      Friday Seminar on Knot Theory
    • Related Report
      2019 Research-status Report
  • [Presentation] トンネル数1 のファイバー絡み目の構成法について2020

    • Author(s)
      石原 海
    • Organizer
      琉球結び目セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] Types of Multicyclic Graphs2019

    • Author(s)
      Kai Ishihara
    • Organizer
      Polymers meet Topology
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] First steps of unlinking pathways2019

    • Author(s)
      Kai Ishihara
    • Organizer
      The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Complete classification of generalized crossing changes between GOF-knots2017

    • Author(s)
      石原 海
    • Organizer
      広島大学トポロジー幾何セミナー
    • Related Report
      2017 Research-status Report
  • [Presentation] Enzyme action for topological entanglement in DNA and knot theory2017

    • Author(s)
      石原海
    • Organizer
      Knots and Polymers: Aspects of topological entanglement in DNA, proteins and graph-shaped polymers
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Complete classification of generalized crossing changes between GOF-knots2017

    • Author(s)
      石原海
    • Organizer
      東北結び目セミナー2017
    • Related Report
      2017 Research-status Report
  • [Book] Topology of Polymers2019

    • Author(s)
      Koya Shimokawa, Kai Ishihara, Yasuyuki Tezuka
    • Total Pages
      81
    • Publisher
      Springer
    • ISBN
      9784431568889
    • Related Report
      2019 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2022-02-21  

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