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2022 Fiscal Year Final Research Report

New modeling and mathematical analysis for pattern formations in life sciences

Research Project

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Project/Area Number 18H01139
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionRyukoku University

Principal Investigator

Morita Yoshihisa  龍谷大学, 先端理工学部, 教授 (10192783)

Co-Investigator(Kenkyū-buntansha) 宮路 智行  京都大学, 理学研究科, 准教授 (20613342)
村川 秀樹  龍谷大学, 先端理工学部, 准教授 (40432116)
李 聖林  京都大学, 高等研究院, 教授 (50620069)
神保 秀一  北海道大学, 理学研究院, 特任教授 (80201565)
岩見 真吾  名古屋大学, 理学研究科, 教授 (90518119)
Project Period (FY) 2018-04-01 – 2022-03-31
Keywordsパターン形成 / 反応拡散方程式 / 保存則 / 非線形偏微分方程式 / 生物モデル / 非局所効果 / 細胞極性 / 安定性
Outline of Final Research Achievements

In this project we obtained new results for developments of mathematical theory for cell polarization models and adhesion models. Specifically, we proved the existence of spatially nonuniform steady states of reaction-diffusion systems describing segregation pattern arising in an asymmetric cell division and reveled the new mechanism that a mass conservation works in the occurrence of the segregation pattern. On the other hand, by studying a reaction-diffusion model in a metric graph which is reduced from cylindrical and dendritical domain, we revealed that junctions in the graph play a crucial role for the existence of stable standing waves. Besides these results we provided new mathematical models and developed mathematical methods for some model equations in research fields in relevance to life science.

Free Research Field

応用解析

Academic Significance and Societal Importance of the Research Achievements

複雑な生命現象において数理モデルの果たす役割を数学的な観点からも明らかにでき,反応拡散方程式系や関連した数理モデルの今後の研究の発展においてモデル化と解析の両面で貢献できる成果として位置付けることができる.このような具体的な数理モデルの研究から得られる知見は,数理的に考察することの重要性について理解を深めることにも貢献できると期待できる.

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Published: 2024-01-30  

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