A geometric theory on the elasticity of bio-membranes

By Z. C. Tu, Z. Ou-Yang. 2004

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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.

Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/61e45901af8c5b0ab6f55858aaf132af0758f1d6