双凹盘形解开口膜泡形状的解析法研究

李树玲; 张劭光

doi:10.7498/aps.59.5202

摘要

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=－2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.

关键词:

开口膜泡 /
边界条件 /
解析法

Abstract

The numerical and the analytical studies of the opening-up vesicles have become hot topics since the experimental observation by A. Saitoh et al. This paper deals with how to obtain the analytical solution of an opening-up shape from the Ouyang biconcave analytical solution. We find only two of the three boundary conditions for the vesicle rims to be independent. The second boundary condition can be satisfied by the Gaussian bending modulus kg=-2, then we obtain the geometric equation for the rims of an opening-up vesicle from the first boundary condition. By analyzing the Ouyang analytic solutions for a closed circular biconcave vesicle and periodic noduloidlike vesicle, we obtain three kinds of shapes with tube topology, which are the convex tube, the toruslike tube, and the catenoidlike tube.

Keywords:

作者及机构信息

1.
陕西师范大学物理学与信息技术学院,西安 710062

基金项目: 国家自然科学基金(批准号:10374063)资助的课题.

Authors and contacts

1.
College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

参考文献

[1]	Bassis M 1973 Living Blood Cells and Their Ultrastructure (Berlin: Springer) p10
[2]	Saitoh A, Takiguchi K, Tanaka Y, Hotani H 1998 Proc. Natl. Acad. Sci. USA 95 1026
[3]	Lieber M R, Steck T L 1982 J. Biol. Chem. 257 11651
[4]	Lieber M R, Steck T L 1982 J. Biol. Chem. 257 11660
[5]	Capovilla R, Guven J, Santiago J A 2002 Phys. Rev. E 66 021607
[6]	Tu Z C, Ouyang Z C 2003 Phys. Rev. E 68 061915
[7]	Helfrich W 1973 Z. Naturforsch. C 28 693
[8]	Umeda T, Suezaki Y 2005 Phys. Rev. E 71 011913
[9]	Naito H, Okuda M, Ouyang Z C 1993 Phys. Rev. E 48 2304
[10]	Naito H, Okuda M, Ouyang Z C 1995 Phys. Rev. Lett. 74 4345
[11]	Liu Q H, Zhou H J, Liu J X, Ouyang Z C 1999 Phys. Rev. E 60 3227
[12]	Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[13]	Ouyang Z C, Helfrich W 1988 Phys. Rev. A 39 5280
[14]	Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[15]	Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[16]	Miao L, Seifert U, Wortis M, Dbereiner H G 1994 Phys. Rev. E 49 5389
[17]	Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华、张劭光 2006 物理学报 55 5568]
[18]	Zhou X H, Zhang S G, Yang J Q, Qu X M, Liu Y S, Wang S G 2007 Acta Phys. Sin. 56 6137 (in Chinese) [周晓华、张劭光、杨继庆、屈学民、刘渊声、王斯刚 2007 物理学报 56 6137]
[19]	Helfrich W 1974 Phys. Lett. A 50 115
[20]	Lipowsky R 1993 Biophys. J. 64 1133

施引文献

[1]	Bassis M 1973 Living Blood Cells and Their Ultrastructure (Berlin: Springer) p10
[2]	Saitoh A, Takiguchi K, Tanaka Y, Hotani H 1998 Proc. Natl. Acad. Sci. USA 95 1026
[3]	Lieber M R, Steck T L 1982 J. Biol. Chem. 257 11651
[4]	Lieber M R, Steck T L 1982 J. Biol. Chem. 257 11660
[5]	Capovilla R, Guven J, Santiago J A 2002 Phys. Rev. E 66 021607
[6]	Tu Z C, Ouyang Z C 2003 Phys. Rev. E 68 061915
[7]	Helfrich W 1973 Z. Naturforsch. C 28 693
[8]	Umeda T, Suezaki Y 2005 Phys. Rev. E 71 011913
[9]	Naito H, Okuda M, Ouyang Z C 1993 Phys. Rev. E 48 2304
[10]	Naito H, Okuda M, Ouyang Z C 1995 Phys. Rev. Lett. 74 4345
[11]	Liu Q H, Zhou H J, Liu J X, Ouyang Z C 1999 Phys. Rev. E 60 3227
[12]	Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[13]	Ouyang Z C, Helfrich W 1988 Phys. Rev. A 39 5280
[14]	Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[15]	Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[16]	Miao L, Seifert U, Wortis M, Dbereiner H G 1994 Phys. Rev. E 49 5389
[17]	Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华、张劭光 2006 物理学报 55 5568]
[18]	Zhou X H, Zhang S G, Yang J Q, Qu X M, Liu Y S, Wang S G 2007 Acta Phys. Sin. 56 6137 (in Chinese) [周晓华、张劭光、杨继庆、屈学民、刘渊声、王斯刚 2007 物理学报 56 6137]
[19]	Helfrich W 1974 Phys. Lett. A 50 115
[20]	Lipowsky R 1993 Biophys. J. 64 1133

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