Research on topology using surfaces, and its application

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K14190
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Yamaguchi 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
• Keywords: DNAトポロジー / 結び目 / 絡み目

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.

Free Research Field

結び目理論、低次元トポロジー

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。