Recent advances of theoretical researches in morphologies of lipid vesicles

Yang Pan; Tu Zhan-Chun

doi:10.7498/aps.65.188701

Abstract

Lipid membrane is a continuous barrier between cell and organelle, providing relatively separate room for the vital biological reaction to take place and guarantee substance, energy and information exchange between cells and organelles. Helfrich proposed a spontaneous curvature model to describe the free energy of lipid bilayer. This article reviews the equations describing the equilibrium morphologies of closed lipid membranes and lipid membranes with free edge based on the spontaneous model, and some analytic solutions are provided as well. The practicality of proving linking condition for splitting vesicle is also discussed.

Keywords:

Authors and contacts

1.
Department of Physics, Beijing Normal University, Beijing 100875, China

Corresponding author: Tu Zhan-Chun, tuzc@bnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274046).

References

[1]	Singer S J, Nicolson G L 1972 Science 175 720
[2]	Fung Y C, Tong P 1968 Biophys. J. 8 175
[3]	Pinder D N 1972 J. Theor. Biol. 34 407
[4]	Lopez L, Duck I M, Hunt W A 1968 Biophys. J. 8 1228
[5]	Greer M A, Baker R F 1970 Proceedings of the 7th International Congress of Electron Microscopy Grenoble, France
[6]	Murphy J R 1965 J. Lab. Clin. Med. 65 756
[7]	Seeman P, Cheng D, Lies G H 1973 J. Cell Biol. 56 519
[8]	Canham P B 1970 J. Theor. Biol. 26 61
[9]	Helfrich W 1973 Z. Naturforsch. C 28 693
[10]	Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[11]	Ouyang Z C, Helfrich W 1989 Phys. Rev. A 39 5280
[12]	Ouyang Z C 1990 Phys. Rev. A 41 4517
[13]	Mutz M, Bensimon D 1991 Phys. Rev. A 43 4525
[14]	Rudolph A S, Ratna B R, Kahn B 1991 Nature 3 52
[15]	Lin Z 1994 Langmuir 10 1008
[16]	Willmore T J, 1965 Al. I. Cuza Iasi Sect. I a Mat. An. Sti. Univ. 11B 493
[17]	Marques F C, Neves A 2012 Annals of Mathematics 179 83
[18]	Ouyang Z C, Liu J X, Xie Y Z 1999 Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (Singapore: World Scientific)
[19]	Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[20]	Zheng W M, Liu J X 1993 Phys. Rev. E 48 2856
[21]	Naito H, Okuda M, Ouyang Z C 1993 Phys. Rev. E 48 2304
[22]	Saitoh A, Takiguchi K, Tanaka Y, Hotani H 1998 Proc. Nat. Acad. Sci. 95 1026
[23]	Capovilla R, Guven J, Santiago J 2002 Phys. Rev. E 66 021607
[24]	Tu Z C, Ouyang Z C 2003 Phys. Rev. E 68 061915
[25]	Tu Z C, Ouyang Z C 2004 J. Phys. A: Math. Gen. 37 11407
[26]	Tu Z C, Ouyang Z C 2008 J. Comput. Theor. Nanosci. 5 422
[27]	Tu Z C 2010 J. Chem. Phys. 132 084111
[28]	Tu Z C 2011 J. Geom. Symmetry Phys. 24 45
[29]	Tu Z C, Ouyang Z C 2014 Adv. Colloid Interface Sci. 208 66
[30]	Tu Z C 2013 Chin. Phys. B 22 028701
[31]	Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[32]	Fourcade B, Miao L, Rao M, Mortis M, Zia R K P 1994 Phys. Rev. E 49 5276
[33]	Jlicher F, Lipowsky R 1996 Phys. Rev. E 53 2670
[34]	Seifert U 1997 Adv. Phys. 46 13
[35]	Xie Y Z, Liu J X, Ouyang Z C 2003 Elastic Theory of Surfaces of Biomembrane-Vesicle (Shanghai: Shanghai Scientific Technical Publishers) (in Chinese) [谢毓章, 刘寄星, 欧阳钟灿 2003 生物膜泡曲面弹性理论 (上海: 上海科学技术出版社)]
[36]	Du Q, Liu C, Wang X 2006 J. Comput. Phys. 212 757
[37]	Du Q, Liu C, Ryham R, Wang X 2005 Commun. Pure Appl. Anal. 4 537
[38]	Yan J, Liu Q H, Liu J X, Ouyang Z C 1998 Phys. Rev. E 58 4730
[39]	Su Y C, Chen J Z 2015 Soft Matter 11 4054
[40]	Zhang P W, Shi A C 2015 Chin. Phys. B 24 128707
[41]	Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华, 张劭光 2006 55 5568]
[42]	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 56 6137]
[43]	Xia B K, Li J F, Li W H, Zhang H D, Qiu F 2013 Acta Phys. Sin. 62 248701 (in Chinese) [夏彬凯, 李剑锋, 李卫华, 张红东, 邱枫 2013 62 248701]
[44]	Yang K, Ma Y Q 2010 Nat. Nanotechnol. 5 579
[45]	Ding H M, Ma Y Q 2012 Biomaterials 33 5798
[46]	Ding H M, Ma Y Q 2015 Small 11 1055

Cited By

[1]	Singer S J, Nicolson G L 1972 Science 175 720
[2]	Fung Y C, Tong P 1968 Biophys. J. 8 175
[3]	Pinder D N 1972 J. Theor. Biol. 34 407
[4]	Lopez L, Duck I M, Hunt W A 1968 Biophys. J. 8 1228
[5]	Greer M A, Baker R F 1970 Proceedings of the 7th International Congress of Electron Microscopy Grenoble, France
[6]	Murphy J R 1965 J. Lab. Clin. Med. 65 756
[7]	Seeman P, Cheng D, Lies G H 1973 J. Cell Biol. 56 519
[8]	Canham P B 1970 J. Theor. Biol. 26 61
[9]	Helfrich W 1973 Z. Naturforsch. C 28 693
[10]	Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[11]	Ouyang Z C, Helfrich W 1989 Phys. Rev. A 39 5280
[12]	Ouyang Z C 1990 Phys. Rev. A 41 4517
[13]	Mutz M, Bensimon D 1991 Phys. Rev. A 43 4525
[14]	Rudolph A S, Ratna B R, Kahn B 1991 Nature 3 52
[15]	Lin Z 1994 Langmuir 10 1008
[16]	Willmore T J, 1965 Al. I. Cuza Iasi Sect. I a Mat. An. Sti. Univ. 11B 493
[17]	Marques F C, Neves A 2012 Annals of Mathematics 179 83
[18]	Ouyang Z C, Liu J X, Xie Y Z 1999 Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (Singapore: World Scientific)
[19]	Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[20]	Zheng W M, Liu J X 1993 Phys. Rev. E 48 2856
[21]	Naito H, Okuda M, Ouyang Z C 1993 Phys. Rev. E 48 2304
[22]	Saitoh A, Takiguchi K, Tanaka Y, Hotani H 1998 Proc. Nat. Acad. Sci. 95 1026
[23]	Capovilla R, Guven J, Santiago J 2002 Phys. Rev. E 66 021607
[24]	Tu Z C, Ouyang Z C 2003 Phys. Rev. E 68 061915
[25]	Tu Z C, Ouyang Z C 2004 J. Phys. A: Math. Gen. 37 11407
[26]	Tu Z C, Ouyang Z C 2008 J. Comput. Theor. Nanosci. 5 422
[27]	Tu Z C 2010 J. Chem. Phys. 132 084111
[28]	Tu Z C 2011 J. Geom. Symmetry Phys. 24 45
[29]	Tu Z C, Ouyang Z C 2014 Adv. Colloid Interface Sci. 208 66
[30]	Tu Z C 2013 Chin. Phys. B 22 028701
[31]	Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[32]	Fourcade B, Miao L, Rao M, Mortis M, Zia R K P 1994 Phys. Rev. E 49 5276
[33]	Jlicher F, Lipowsky R 1996 Phys. Rev. E 53 2670
[34]	Seifert U 1997 Adv. Phys. 46 13
[35]	Xie Y Z, Liu J X, Ouyang Z C 2003 Elastic Theory of Surfaces of Biomembrane-Vesicle (Shanghai: Shanghai Scientific Technical Publishers) (in Chinese) [谢毓章, 刘寄星, 欧阳钟灿 2003 生物膜泡曲面弹性理论 (上海: 上海科学技术出版社)]
[36]	Du Q, Liu C, Wang X 2006 J. Comput. Phys. 212 757
[37]	Du Q, Liu C, Ryham R, Wang X 2005 Commun. Pure Appl. Anal. 4 537
[38]	Yan J, Liu Q H, Liu J X, Ouyang Z C 1998 Phys. Rev. E 58 4730
[39]	Su Y C, Chen J Z 2015 Soft Matter 11 4054
[40]	Zhang P W, Shi A C 2015 Chin. Phys. B 24 128707
[41]	Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华, 张劭光 2006 55 5568]
[42]	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 56 6137]
[43]	Xia B K, Li J F, Li W H, Zhang H D, Qiu F 2013 Acta Phys. Sin. 62 248701 (in Chinese) [夏彬凯, 李剑锋, 李卫华, 张红东, 邱枫 2013 62 248701]
[44]	Yang K, Ma Y Q 2010 Nat. Nanotechnol. 5 579
[45]	Ding H M, Ma Y Q 2012 Biomaterials 33 5798
[46]	Ding H M, Ma Y Q 2015 Small 11 1055

[1]	Lin Shu, Tian Jia-Yuan. Medium correction to gravitational form factors. Acta Physica Sinica, 2023, 72(7): 071201. doi: 10.7498/aps.72.20222473
[2]	Liang Yi-Ran, Liang Qing. Molecular simulation of interaction between charged nanoparticles and phase-separated biomembranes containning charged lipids. Acta Physica Sinica, 2019, 68(2): 028701. doi: 10.7498/aps.68.20181891
[3]	Liang Yue-Feng, Zhang Shao-Guang. Shape transformations of opening-up vesicles with one hole. Acta Physica Sinica, 2017, 66(15): 158701. doi: 10.7498/aps.66.158701
[4]	Zhou Xian-Chun, Wang Mei-Ling, Shi Lan-Fang, Zhou Lin-Feng, Wu Qin. Image smoothing model based on the combination of the gradient and curvature. Acta Physica Sinica, 2015, 64(4): 044201. doi: 10.7498/aps.64.044201
[5]	Zhang Jin-Bi, Ding Lei, Wang Ying-Ping, Zheng Hai-Yang, Fang Li. Shape classification of single aerosol particle using near-forward optical scattering patterns calculation. Acta Physica Sinica, 2015, 64(5): 054202. doi: 10.7498/aps.64.054202
[6]	Ren Dian-Bo, Zhang Jing-Ming, Wang Cong. Virtual trajectory model for lane changing of a vehicle on curved road with variable curvature. Acta Physica Sinica, 2014, 63(7): 078902. doi: 10.7498/aps.63.078902
[7]	Niu Yu-Quan, Zheng Bin, Cui Chun-Hong, Wei Wei, Zhang Cai-Xia, Meng Qing-Tian. The adhesion of two cylindrical colloids to a tubular membrane. Acta Physica Sinica, 2014, 63(3): 038701. doi: 10.7498/aps.63.038701
[8]	Xia Bin-Kai, Li Jian-Feng, Li Wei-Hua, Zhang Hong-Dong, Qiu Feng. A dissipative dynamical method based on discrete variational principle：stationary shapes of three-dimensional vesicle. Acta Physica Sinica, 2013, 62(24): 248701. doi: 10.7498/aps.62.248701
[9]	Zhang Chun-Lai, Liu Chun-Ming, Xiang Xia, Wang Zhi-Guo, Li Li, Yuan Xiao-Dong, He Shao-Bo, Zu Xiao-Tao. The effects of shape and position on field distribution of discontinuous crack. Acta Physica Sinica, 2012, 61(16): 164207. doi: 10.7498/aps.61.164207
[10]	Zhi Qi-Jun. The study of shape and shape-coexistence of neutron rich nuclei around N=28. Acta Physica Sinica, 2011, 60(5): 052101. doi: 10.7498/aps.60.052101
[11]	Peng Yong-Gang, Zheng Yu-Jun. Dynamic properties of bilayer membrane. Acta Physica Sinica, 2011, 60(8): 088701. doi: 10.7498/aps.60.088701
[12]	Li Shu-Ling, Zhang Shao-Guang. An analytical solution for opening-up vesicle based on the circular biconcave shape. Acta Physica Sinica, 2010, 59(8): 5202-5208. doi: 10.7498/aps.59.5202
[13]	Zhang Jun-Bing, Lin Yue-Ming, Bo Lin, Zeng Xiang-Hua. Optimization of the electrode shape of AlGaInP LED. Acta Physica Sinica, 2008, 57(9): 5881-5886. doi: 10.7498/aps.57.5881
[14]	Zhou Xiao-Hua, Zhang Shao-Guang, Yang Ji-Qing, Qu Xue-Min, Liu Yuan-Sheng, Wang Si-Gang. Some new limiting vesicles and typical phase transforms and abruptions processes studied using the spontaneous-curvature model. Acta Physica Sinica, 2007, 56(10): 6137-6142. doi: 10.7498/aps.56.6137
[15]	Wei Xiang-Jun, Xu Qing, Wang Tian-Min, Jia Quan-Jie, Wang Huan-Hua, Feng Song-Lin. Microstructure of TiNi shape memory alloy films made of sputter-deposited Ni/Ti multilayers. Acta Physica Sinica, 2006, 55(3): 1508-1511. doi: 10.7498/aps.55.1508
[16]	Zhou Xiao-Hua, Zhang Shao-Guang. Obtaining and stability analysis of spherical topological vesicles with complex configurations. Acta Physica Sinica, 2006, 55(10): 5568-5574. doi: 10.7498/aps.55.5568
[17]	ZHANG JING, SUN RUN-GUANG. A STUDY OF THE PHYSICOCHEMICAL CHARACTER OF THE INTERACTION OF THE LIPOSOME CONTAINING OLEIC ACID OF THE LIQUID-CRYSTAL STATE AND BIOMEMBRANE. Acta Physica Sinica, 1994, 43(9): 1495-1501. doi: 10.7498/aps.43.1495
[18]	WU ZI-YU, WANG KE-LIN, LAN HUI-BIN, ZHANG ZHENG-GANG, XIAN DING-CHANG. A PHENOMENOLOGICAL MODEL FOR 0- MESON (Ⅱ)——THE ELECTROMAGNETIC FORM FACTOR. Acta Physica Sinica, 1987, 36(12): 1618-1623. doi: 10.7498/aps.36.1618
[19]	. . Acta Physica Sinica, 1966, 22(5): 607-610. doi: 10.7498/aps.22.607
[20]	. . Acta Physica Sinica, 1965, 21(7): 1464-1468. doi: 10.7498/aps.21.1464

Catalog

Vol. 65, Issue 18 - 2016-09-20

Metrics

Abstract views: 7744
PDF Downloads: 378
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板