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Mass-conserving reaction-diffusion systems and their perturbation

Research Project

Project/Area Number 16K05273
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKobe University

Principal Investigator

Kuwamura Masataka  神戸大学, 人間発達環境学研究科, 教授 (30270333)

Project Period (FY) 2016-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords反応拡散方程式系 / 保存量 / 細胞極性 / 周期倍分岐 / 細胞の極性化 / 極性の周期的振動 / 反応拡散方程式 / 特異摂動法 / 細胞の極性化現象 / limit cycle / 拡散不安定化 / 応用数学 / 解析学
Outline of Final Research Achievements

In this research, I studied mass-conserving reaction-diffusion systems which are mathematical models for the polarity formation of cells. First, I investigated the dynamics of a localized unimodal pattern in mass-conserving reaction-diffusion systems, and provided mathematical characterizations of the motion of the localized unimodal pattern. Next, I investigated the oscillatory dynamics and bifurcation structure of a mass-conserving reaction-diffusion system with bistable nonlinearity, and showed that it exhibits four different spatiotemporal patterns including two types of oscillatory patterns, My research was based on a joint work with Professors Hirofumi Izuhara (Miyazaki),Sungrim Seirin-Lee (Kyoto) and Shin-Ichiro Ei (Hokkaido), and my results were published in Chaos, vol.27 (2017), SIAM Journal on Applied Mathematics, vol.78 (2018) and Journal of Mathematical Biology, vol.84 (2022).

Academic Significance and Societal Importance of the Research Achievements

保存量をもつ反応拡散方程式系は細胞の極性化現象を理解する上で役に立つものであると考えられている。本研究により、細胞極性が外部シグナルによって誘導されて移動する現象や周期的に生成と消失を繰り返す現象(cell polarity oscillations)を数学的に理解する手掛かりが得られると思われる。これは、分子生物学的な研究によって得られた static な化学反応ネットワークにもとづく大規模な常微分方程式モデルでは理解できないような細胞極性の動的な現象が保存量をもつ反応拡散方程式系によって理解できることを示している。

Report

(8 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (8 results)

All 2022 2020 2018 2017 2016

All Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (6 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results)

  • [Journal Article] Oscillations and bifurcation structure of reaction?diffusion model for cell polarity formation2022

    • Author(s)
      Kuwamura Masataka、Izuhara Hirofumi、Ei Shin-ichiro
    • Journal Title

      Journal of Mathematical Biology

      Volume: 84 Issue: 4 Pages: 1-26

    • DOI

      10.1007/s00285-022-01723-5

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Diffusion-driven destabilization of spatially homogeneous limit cycles in reaction-diffusion systems2017

    • Author(s)
      Masataka Kuwamura, Hirofumi Izuhara
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 27 Issue: 3 Pages: 033112-033112

    • DOI

      10.1063/1.4978924

    • NAID

      120006318793

    • Related Report
      2018 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 細胞の極性化における polarity oscillations と wave-pinning について2022

    • Author(s)
      桑村雅隆
    • Organizer
      日本数学会2022年度秋季総合分科会(北海道大学)
    • Related Report
      2022 Annual Research Report
  • [Presentation] 細胞極性化に関連する微分方程式の解の性質について2020

    • Author(s)
      桑村雅隆
    • Organizer
      明治大学MIMS共同研究集会「幾何学・連続体力学・情報科学の交差領域の探索」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 保存量をもつ反応拡散系における特異摂動の例について2020

    • Author(s)
      桑村雅隆
    • Organizer
      反応拡散方程式と非線形分散型方程式の解の挙動(OCAMI共同研究事業(B))
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Dynamics of localized patterns in reaction-diffusion systems for cell polarization by extracellular signaling2018

    • Author(s)
      Masataka Kuwamura
    • Organizer
      The 43rd Sapporo Symposium on Partial Differential Equations
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 保存量をもつ反応拡散方程式におけるパルス状局在解の挙動について2017

    • Author(s)
      桑村雅隆、李聖林、栄伸一郎
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] Diffusion-driven destabilization of a spatially homogeneous limit cycle in reaction-diffusion systems2016

    • Author(s)
      Masataka Kuwamura, Hirofumi Izuhara
    • Organizer
      JSMB2016
    • Place of Presentation
      Kyushu Univerisity, Fukuoka
    • Year and Date
      2016-09-07
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research

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Published: 2016-04-21   Modified: 2024-01-30  

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