| Project/Area Number |
16KT0128
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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 | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Tohoku University |
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Principal Investigator |
Takagi Izumi 東北大学, 理学研究科, 名誉教授 (40154744)
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| Co-Investigator(Kenkyū-buntansha) |
今井 正幸 東北大学, 理学研究科, 教授 (60251485)
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| Project Period (FY) |
2016-07-19 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | ベシクルの形状 / 幾何学的変分問題 / 面積差弾性エネルギー / 反応拡散方程式 / ベシクルの形態変換 / 面積差弾性エネルギーモデル / 非等方非一様場におけるパターン / Willmore汎函数 / 面積差弾性モデル / 幾何学的変分法 / 束縛条件附変分問題 / Willmore 汎函数 / 束縛条件附き変分問題 / ベシクル / 接触と融合 / 出芽 / 分岐図 |
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| Outline of Final Research Achievements |
A vesicle is a lipid bilayer forming a spherical or toroidal shell. Its shape is determined as a closed surface which minimizes the sum of the bending energy and area-difference elastic energy, among surfaces having the prescribed surface area and enclosing volume. We found that the Euler-Lagrange equation is an integro-differential equation, which makes mathematical analysis of this model quite difficult. The rigorous analysis of the shape equation for axially symmetric surfaces remains open due to this difficulty. In addition, we considered reaction-diffusion equations with variable coefficients arising from models of two-phase vesicles as well as mechano-chemical models of biological pattern formation. We proved the existence and stability of steady-state solutions for some of such equations; however, we could not study the interaction between the (visco-)elastic deformation of membrane and the chemical patterning within the research period.
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| Academic Significance and Societal Importance of the Research Achievements |
脂質の二重膜がつくる小胞がベシクルであるが，生体膜で囲まれた細胞の形状を決めるメカニズムは，ベシクルの形状を支配するものと本質的には変わらないことが知られており，ベシクルに関する知見は細胞の構造を理解する上で有益である．特に，多成分ベシクルでは，相分離が弾性エネルギー係数に影響を及ぼし形状を変化させる．これは生物の形態形成の仕組みと共通する部分があると考えられる．
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