A geometric theory on the elasticity of bio-membranes
A geometric theory on the elasticity of bio-membranes
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DOI：
10.1088/0305-4470/37/47/010
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发表时间：
2004-03
期刊：
影响因子：
--
通讯作者：
Z. C. Tu;Z. Ou-Yang
中科院分区：
文献类型：
--
作者：
Z. C. Tu;Z. Ou-Yang
本文的目的是在外微分形式的框架下研究生物膜的形状和稳定性。在简要回顾了生物膜形状的理论和实验研究现状后，提出了一种几何方案，讨论了封闭脂双层的形状方程、开放脂双层和双组分膜的形状方程和边界条件、具有交联结构的细胞膜的形状方程和面内应变方程，以及封闭脂双层和细胞膜的稳定性。该方案的核心是利用外微分形式处理三维欧氏空间中曲面的变分问题。
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status of theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and two-component membranes, the shape equation and in-plane strain equations of cell membranes with cross-linking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on surfaces embedded in three-dimensional Euclidean space by using exterior differential forms.