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Dynamical system approach to the transition structure between asymptotic Turing patterns and the generation of Turing patterns

Research Project

Project/Area Number 16K05231
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionHiroshima University

Principal Investigator

SAKAMOTO KUNIMOCHI  広島大学, 理学研究科, 教授 (40243547)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords安定性 / 細胞極性モデル / Turing不安定化 / 安定性とスペクトルの挙動 / 非一様解の分岐 / 反応拡散系 / 境界上の相互作用 / ロバン型非線形境界条件 / 固有値の変分法的特徴付け / フラックスタイプ境界条件 / Tuirng patternと細胞極性 / スペクトルの変分法的特徴付け / 領域境界と領域内部の相互作用 / 細胞極性 / 拡散 / 相互作用 / 非線形境界条件 / 非一様平衡解 / 安定性解析 / 非線形解析 / 力学系 / 遷移構造
Outline of Final Research Achievements

Two-component system of the bulk diffusion equations are considered under the non-linear Robin type boundary conditions. The coupling between the two components are realized trough the nonlinear interaction on the boundary. Uniform steady states (representing non-polarized states) destabilized as the difference of diffusion rates of the two species increases, and give rise to the emergence of non-uniform stable states. Namely, the generation of Turing pattern has been proven mathematically rigorous manner. All of the three characteristics of polarization such as (i)spontaneity, (ii) stability, (iii) response to the external stimuli have been proven mathematically present in the model equation.

Academic Significance and Societal Importance of the Research Achievements

細胞極性の発現は,細胞の運動,細胞分裂,等の前駆段階として必ず現れるとされていて,細胞の諸機能発現の準備を極性発現段階で行っていると考えられている。従って,極性の発現は.細胞が行う全機能を決定づける重要なイベントとして捉えられている。多くの実験家や分子生物学者によってその分子動力学的な振る舞いを基礎としたタンパク質ダイナミクスの問題としてモデル化されている。本研究では,細胞極性が持つ三つの重要な特性が実験家、分子生物学者によって提示された数学モデルにおいてサポートされることを示した点において、細胞の振る舞いのメカニズムの基本的な仕組みの解明に寄与できた点に意義がある。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (7 results)

All 2018 2016

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results)

  • [Journal Article] A diffusion model for cell polarization with interaction on the membrane2018

    • Author(s)
      Yoshihisa Morita and Kunimochi Sakamoto
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 35 Pages: 261-276

    • NAID

      210000174677

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A diffusion model for cell polarization with interactions on the membrane2018

    • Author(s)
      Yoshihisa Morita and Kunimoch Sakamoto
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 35 Pages: 261-276

    • NAID

      210000174677

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] A Turing mechanism in A Cell Polarization2018

    • Author(s)
      坂元国望
    • Organizer
      岡山大学理学部「パターン形成の数理とその周辺」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 領域境界上反応-領域内部拡散系にたいするTuring 不安定化について2018

    • Author(s)
      坂元国望
    • Organizer
      北海道大学電子科学研究所「反応拡散系の理論と応用ー現状と未来ー」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of non-uniform solutions for diffusive systems with nonlinear boundary flux2016

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      ミクロな振る舞いと集団的パターン形成に係わる 階層的構造の解明
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-09-12
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Bulk Reaction versus Boundary Flux in diffusive systems2016

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      日本数理生物学会
    • Place of Presentation
      九州大学
    • Year and Date
      2016-09-07
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] An elementary analysis of boundary interactions and bulk diffusion systems2016

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      International Conference on Reaction Diffusion Equations and their Applications to the Life, Social and Physical Sciences,
    • Place of Presentation
      中国人民大学(中華人民共和国、北京)
    • Year and Date
      2016-05-26
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2016-04-21   Modified: 2020-03-30  

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