2022 Fiscal Year Final Research Report
Mass-conserving reaction-diffusion systems and their perturbation
| Project/Area Number |
16K05273
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kobe University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2023-03-31
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| Keywords | 反応拡散方程式系 / 保存量 / 細胞極性 |
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| 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).
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| Free Research Field |
応用数学
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| 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。
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