3次元トポロジーに基づく静的・動的ネットワークの提案

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 17H06463
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Saitama University
• Principal Investigator: 下川 航也 埼玉大学, 理工学研究科, 教授 (60312633)
• Co-Investigator(Kenkyū-buntansha): 石原 海 山口大学, 教育学部, 准教授 (40634762) ; 出口 哲生 お茶の水女子大学, 基幹研究院, 教授 (70227544) ; 伊藤 克司 東京工業大学, 理学院, 教授 (60221769) ; 手塚 育志 東京工業大学, 物質理工学院, 教授 (80155457)
• Project Period (FY): 2017-06-30 – 2022-03-31
• Project Status: Granted (Fiscal Year 2020)
• Budget Amount: ¥52,130,000 (Direct Cost: ¥40,100,000、Indirect Cost: ¥12,030,000); Fiscal Year 2021: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2020: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2019: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2018: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2017: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
• Keywords: ネットワーク / 3次元トポロジー / 高分子材料 / 共連続構造 / トポロジー / トポロジー高分子 / 結び目 / ３次元トポロジー / ３次元多様体 / ポリマー / 高分子 / 3次元ネットワーク

Outline of Annual Research Achievements

本年度は、これまでこの新学術領域研究として行って来た高分子のトポロジーに関する研究を、著書``Topology of Polymers''として石原氏、手塚氏とともにまとめ、Springer Monographから出版した。ここでは、多環状高分子の合成方法、そのトポロジーの数学的記述と命名法などをまとめている。また、金属とペプチドから構成される環が６つ絡まることで作られるカプセル状の分子のトポロジーを東大の藤田研究室とともに考察し、Nature Communicationsから2019年12月に出版した。この構造は交点数24を持つものであり、交点数が決定できる絡み目状の構造としては、これまでで世界で最も複雑なものとなっている。この絡み目は多面体から構成されるが、その構成方法を数学的に特徴付けた。この研究については、東京大学と埼玉大学からプレスリリースを発表した。また、共連続構造の数学的モデル化に関してもその分類成果を挙げ、論文として発表を準備している。ここでは、２つの共連続構造が与えられた場合に、どのような変形を行うと一方を他方に変形できるかを明らかにしている。
高分子に纏わる数学、化学、物理に関する国際会議を、2019年8月7日～9日に"Polymers and networks via topology and entanglement"として、お茶の水女子大学で開催した。この国際会議のアブストラクトは、小冊子としてまとめている。また、2019年12月に材料科学の大きな国際会議であるMRM2019において、招待講演を行った。

Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

高分子のトポロジーに関して、当初の予定通りのペースで研究が進んでいる。特に今年度は研究成果を著書として出版することが出来たことは、大きな成果であると考えている。また、今年度も国際会議を開催し、大変有意義な情報交換を行うことが出来た。さらに、領域外の方とのコラボレーションとして、東京大学の藤田誠氏との共同研究を行い、その成果を今年度もNature Communicationsから出版することが出来た。これは、交点数24をもつ絡み目のトポロジーをもつ分子があり、これまで観測されたもので最も交点数が多いものとなっている。この成果は、東京大学、埼玉大学からプレスリリースとして発表を行った。またこの論文は、Nature Communicationsの2019年の``Top 50 Chemistry and Materials Sciences Articles''に選出された。この共同研究の成果は、当初の計画には無い部分であり、世界記録としてプレスリリースを発表出来た点でも、当初の計画を上回る成果と言える。

Strategy for Future Research Activity

引き続き、高分子とトポロジーの研究を行う。特に、3相共連続構造に関する成果を２つの論文にまとめ投稿予定である。その中で３相共連続構造のリスト作りを行っており、そのデータをもとに材料設計を行う予定である。現在までの成果を、新学術領域外の研究者へ伝えるためのweb pageを作成している。また、金属とペプチドからなる分子構造の解析も続け、これまでに構成されている構造の特徴付けを行う予定である。

Research Products

• [Int'l Joint Research] University of California, Davis/University of Georgia(米国)
• [Int'l Joint Research] University of Saskatchewan/University of British Colombia(カナダ)
• [Int'l Joint Research] UNAM(メキシコ)
• [Int'l Joint Research] University of Melbourne(オーストリア)
• [Int'l Joint Research] University of California, Davis(アメリカ)
• [Int'l Joint Research] University of Saskatchewan(カナダ)
• [Journal Article] A metal-peptide capsule by multiple ring threading (2019)
  • Author(s): Sawada Tomohisa、Inomata Yuuki、Shimokawa Koya、Fujita Makoto
  • Journal Title: Nature Communications Volume: 10 Pages: 5687-5687
  • DOI: 10.1038/s41467-019-13594-4
  • Peer Reviewed / Open Access
• [Journal Article] Metal-peptide rings form highly entangled topologically inequivalent frameworks with the same ring- and crossing-numbers (2019)
  • Author(s): T. Sawada, A. Saito, K. Tamiya, K. Shimokawa, Y. Hisada, M. Fujita
  • Journal Title: Nature Commun. Volume: 10 Pages: 921-921
  • DOI: 10.1038/s41467-019-08879-7
  • Peer Reviewed / Open Access
• [Journal Article] Neighborhood equivalence for multibranched surfaces in 3-manifolds (2019)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Bimodality in the knotting probability of semiflexible rings suggested by mapping with self-avoiding polygons (2019)
  • Author(s): Uehara Erica、Coronel Lucia、Micheletti Cristian、Deguchi Tetsuo
  • Journal Title: Reactive and Functional Polymers Volume: 134 Pages: 141-149
  • DOI: 10.1016/j.reactfunctpolym.2018.11.008
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Programmed Polymer Folding with Periodically Positioned Tetrafunctional Telechelic Precursors by Cyclic Ammonium Salt Units as Nodal Points (2019)
  • Author(s): Kyoda Kohei、Yamamoto Takuya、Tezuka Yasuyuki
  • Journal Title: J. Am. Chem. Soc. Volume: 141 Pages: 7526-7536
  • DOI: 10.1021/jacs.9b02459
  • Peer Reviewed
• [Journal Article] Characterising knotting properties of polymers in nanochannels (2018)
  • Author(s): N. R. Beaton, J. W. Eng, K. Ishihara, K. Shimokawa, C. E. Soteros
  • Journal Title: Soft Matter Volume: 14 Pages: 5775-5785
  • DOI: 10.1039/c8sm00734a
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Two-point correlation function of ring polymers: Experiments and numerical simulations for the case of circular DNA in 2 dimensions (2018)
  • Author(s): Ropelewski Sophia、Uehara Erica、Lehmann Caroline、Deguchi Tetsuo、Dietler Giovanni
  • Journal Title: Reactive and Functional Polymers Volume: 133 Pages: 66-70
  • DOI: 10.1016/j.reactfunctpolym.2018.10.001
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Mean-square radius of gyration and the hydrodynamic radius for topological polymers expressed with graphs evaluated by the method of quaternions revisited (2018)
  • Author(s): Uehara Erica、Deguchi Tetsuo
  • Journal Title: Reactive and Functional Polymers Volume: 133 Pages: 93-102
  • DOI: 10.1016/j.reactfunctpolym.2018.09.007
  • Peer Reviewed / Open Access
• [Journal Article] Statistical properties of multi-theta polymer chains (2018)
  • Author(s): Uehara Erica、Deguchi Tetsuo
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 51 Pages: 134001-134001
  • DOI: 10.1088/1751-8121/aaae2d
  • Peer Reviewed
• [Journal Article] Macrocyclic poly(p-phenylenevinylene)s by ring expansion metathesis polymerisation and their characterisation by single-molecule spectroscopy (2018)
  • Author(s): Lidster Benjamin John、Hirata Shuzo、Matsuda Shoki、Yamamoto Takuya、Komanduri Venukrishnan、Kumar Dharam Raj、Tezuka Yasuyuki、Vacha Martin、Turner Michael L.
  • Journal Title: Chem. Sci. Volume: 9 Pages: 2934-2941
  • DOI: 10.1039/c7sc03945j
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Recent advances in the construction of cyclic grafted polymers and their potential applications (2018)
  • Author(s): Zhang Shuangshuang、Tezuka Yasuyuki、Zhang Zhengbiao、Li Na、Zhang Wei、Zhu Xiulin
  • Journal Title: Polymer Chemistry Volume: 9 Pages: 677-686
  • DOI: 10.1039/c7py01544e
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Synthesis, Isolation, and Properties of All Head-to-Tail Cyclic Poly(3-hexylthiophene): Fully Delocalized Exciton over the Defect-Free Ring Polymer (2018)
  • Author(s): Yamamoto Takuya、Hosokawa Masaaki、Nakamura Minato、Sato Shin-ichiro、Isono Takuya、Tajima Kenji、Satoh Toshifumi、Sato Masamichi、Tezuka Yasuyuki、Saeki Akinori、Kikkawa Yoshihiro
  • Journal Title: Macromolecules Volume: 51 Pages: 9284-9293
  • DOI: 10.1021/acs.macromol.8b01681
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Enzyme action for topological entanglement in DNA and knot theory (2018)
  • Author(s): K. Ishihara
  • Journal Title: Reactive and Functional Polymers Volume: 132 Pages: 74-80
  • DOI: 10.1016/j.reactfunctpolym.2018.09.006
  • Peer Reviewed / Open Access
• [Journal Article] Bounds for minimum step number of knots confined to tubes in the simple cubic lattice (2017)
  • 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 Pages: 215601-215601
  • DOI: 10.1088/1751-8121/aa6a4f
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Pathways of DNA unlinking: A story of stepwise simplification (2017)
  • 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 Pages: 1-11
  • DOI: 10.1038/s41598-017-12172-2
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A Twisting Ring Polymer: Synthesis and Thermally Induced Chiroptical Responses of a Cyclic Poly(tetrahydrofuran) Having Axially Chiral Units (2017)
  • Author(s): Honda Satoshi、Adachi Kaoru、Yamamoto Takuya、Tezuka Yasuyuki
  • Journal Title: Macromolecules Volume: 50 Pages: 5323-5331
  • DOI: 10.1021/acs.macromol.7b00839
  • Peer Reviewed
• [Journal Article] Load-Induced Frictional Transition at a Well-Defined Alkane Loop Surface (2017)
  • Author(s): A. Shundo, K. Hori, Y. Tezuka, T. Yamamoto, and K. Tanaka
  • Journal Title: Langmuir Volume: 33 Pages: 2396-2401
  • DOI: 10.1021/acs.langmuir.6b04042
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Topological Polymer Chemistry Designing Complex Macromolecular Graph Constructions (2017)
  • Author(s): Tezuka Yasuyuki
  • Journal Title: Accounts of Chemical Research Volume: 50 Pages: 2661-2672
  • DOI: 10.1021/acs.accounts.7b00338
  • Peer Reviewed
• [Journal Article] Knotting probability of self-avoiding polygons under a topological constraint (2017)
  • Author(s): Uehara Erica、Deguchi Tetsuo
  • Journal Title: The Journal of Chemical Physics Volume: 147 Pages: 094901-094901
  • DOI: 10.1063/1.4996645
  • Peer Reviewed
• [Journal Article] Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent (2017)
  • Author(s): Uehara Erica、Deguchi Tetsuo
  • Journal Title: The Journal of Chemical Physics Volume: 147 Pages: 214901-214901
  • DOI: 10.1063/1.4999266
• [Presentation] 3-dimensional topology and polycontinuous pattern (2019)
  • Author(s): Koya Shimokawa
  • Organizer: International Symposium “Polymers and networks via topology and entanglement”
  • Int'l Joint Research / Invited
• [Presentation] 3-dimensional topology and poly-continuous pattern (2019)
  • Author(s): Koya Shimokawa
  • Organizer: MATERIALS RESEARCH MEETING 2019, Mathematical Materials Science -Mathematical Approaches for Materials Designs in the Data Driven Society-
  • Int'l Joint Research / Invited
• [Presentation] Handlebody decomposition of 3-manifolds and their application (2019)
  • Author(s): Koya Shimokawa
  • Organizer: 可微分写像の特異点論とその応用
  • Int'l Joint Research / Invited
• [Presentation] 3-dimensional topology and polycontinuous pattern (2019)
  • Author(s): Koya Shimokawa
  • Organizer: The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
  • 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: 日本数学会 2019年度年会企画特別講演
  • Invited
• [Presentation] Poly-continuous pattern, networks and 3-dimensional topology (2019)
  • Author(s): Koya Shimokawa
  • Organizer: International Symposium "Polymers meet Topology"
  • Int'l Joint Research / Invited
• [Presentation] Rouse Dynamics of Topological Polymers through Gaussian Random Embeddings and Comparison with Experiments (2019)
  • Author(s): Tetsuo Deguchi
  • Organizer: The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
  • Int'l Joint Research / Invited
• [Presentation] Rouse Dynamics of Topological Polymers through Gaussian Random Graph Embeddings (2019)
  • Author(s): Tetsuo Deguchi
  • Organizer: International Symposium "Polymers meet Topology"
  • Int'l Joint Research / Invited
• [Presentation] Knotting probability of self-avoiding polygons under a topological constraint: A sum rule derived from the factorization property (2019)
  • Author(s): T. Deguchi and E. Uehara
  • Organizer: ``Topology of Biopolymers’’, Special Session at the Spring Eastern Sectional Meeting of AMS
  • Int'l Joint Research / Invited
• [Presentation] Topological Polymer Chemistry Designing Macromolecular Graph Constructions, International (2019)
  • Author(s): Y. Tezuka
  • Organizer: International Symposium "Polymers meet Topology"
  • Int'l Joint Research / Invited
• [Presentation] Types of Multicyclic Graphs (2019)
  • Author(s): K. Ishihara
  • Organizer: International Symposium "Polymers meet Topology"
  • Int'l Joint Research / Invited
• [Presentation] First steps of unlinking pathways (2019)
  • Author(s): K. Ishihara
  • Organizer: The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology
  • Int'l Joint Research / Invited
• [Presentation] Knots, links and spatial graphs in the simple cubic lattice (2018)
  • Author(s): Koya Shimokawa
  • Organizer: 2018 Fall AMS Sectional Meeting
  • Int'l Joint Research / Invited
• [Presentation] Lattice knots and links in tube regions (2018)
  • Author(s): Koya Shimokawa
  • Organizer: 33rd Summer Conference on Topology and its Applications
  • Int'l Joint Research / Invited
• [Presentation] Topological Polymer Chemistry with Programmed ESA-CF Polymer Folding Constructions (2018)
  • Author(s): Y. Tezuka
  • Organizer: 14th Japan-Belgium Symposium on Polymer Science
  • Int'l Joint Research / Invited
• [Presentation] Topological Chemistry Designing Novel Macromolecular Constructions (2018)
  • Author(s): Y. Tezuka
  • Organizer: 2018 Taiwan-Japan Bilateral Polymer Symposium
  • Int'l Joint Research / Invited
• [Presentation] On chirality of molecular graphs (2018)
  • Author(s): Koya Shimokawa
  • Organizer: Cyclic & Topologically Complex Polymers, Spring 2018 American Chemical Society Meeting
  • Int'l Joint Research / Invited
• [Presentation] 3-dimensional topology and network analysis in soft materials (2018)
  • Author(s): Koya Shimokawa
  • Organizer: International kick-off workshop "Discrete Geometric Analysis for Materials Design"
  • Int'l Joint Research / Invited
• [Presentation] Statistical and hydrodynamic properties of graph-shaped polymers and quaternions (2018)
  • Author(s): T. Deguchi and E. Uehara
  • Organizer: Cyclic & Topologically Complex Polymers, Spring 2018 American Chemical Society Meeting
  • Int'l Joint Research / Invited
• [Presentation] Topological Chemistry Designing Macromolecular Graph Constructions (2017)
  • Author(s): Yasuyuki Tezuka
  • Organizer: Japan-Taiwan Bilateral Polymer Symposium (JTBPS 2017)
  • Int'l Joint Research / Invited
• [Presentation] Designing Cyclic and Topological Polymer Constructions by Innovative Synthetic Protocols (2017)
  • Author(s): Yasuyuki Tezuka
  • Organizer: International Workshop “Ring Polymers”
  • Int'l Joint Research / Invited
• [Presentation] Statistical and Hydrodynamic Properties of Graph-Shaped Polymers and Quaternions (2017)
  • Author(s): Tetsuo Deguchi
  • Organizer: International workshop``Knots and polymers: aspects of topological enanglement in DNA, proteins and graph-shaped polymers''
  • Int'l Joint Research / Invited
• [Presentation] Statistical Mechanics of Theta-shaped and Ring-shaped Polymer Chains (2017)
  • Author(s): E. Uehara and T. Deguchi
  • Organizer: International workshop``Knots and polymers: aspects of topological enanglement in DNA, proteins and graph-shaped polymers''
  • Int'l Joint Research / Invited
• [Presentation] Additivity of Topological Balance Length and a Slow Growth in the Effective Scaling Exponent of Knotted Random Polygons (2017)
  • Author(s): T. Deguchi and E. Uehara
  • Organizer: CMO-BIRS Workshop: “The Geometry and Topology of Knotting and Entanglement in Proteins
  • Int'l Joint Research / Invited
• [Book] Topology of Polymers (2019)
  • Author(s): Shimokawa, Koya, Ishihara, Kai, Tezuka, Yasuyuki
  • Total Pages: 89
  • Publisher: Springer, SpringerBriefs in the Mathematics of Materials
  • ISBN: 9784431568865
• [Remarks] 下川航也ホームページ
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/KoyaShimokawa.html
• [Remarks] ペプチド鎖が精密に編み込まれたナノカプセルの合成に初成功
  • URL: http://www.saitama-u.ac.jp/topics_archives/2019-1211-1337-18.html
• [Remarks] 国際会議ホームページ
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/kshimoka/polymersandnetworks2019.html
• [Remarks] 下川航也 ホームページ
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/KoyaShimokawa.html
• [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
• [Remarks] 新学術領域「次世代物質探索のための離散幾何学」
  • URL: https://www.math-materials.jp
• [Funded Workshop] 国際シンポジウム "Polymers and networks via topology and entanglement" (2019)
• [Funded Workshop] 国際シンポジウム「Polymers meet Topology」 (2019)
• [Funded Workshop] The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology (2019)
• [Funded Workshop] Knots and Polymers: Aspects of topological entanglement in DNA, proteins and graph-shaped polymers (2017)