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In this article, the dissipative dynamical evolution method based on the discrete variational principle is applied to a three-dimensional (3D) vesicle system. The stationary shapes of vesicles are obtained through the minimization of membrane bending energy without any symmetric assumption, which is an outstanding merit of our method. Aiming at a 3D vesicle system with certain parameter settings, a series of axisymmetric shapes are achieved by our method. The simulation results are in good agreement with those obtained with axisymmetric assumption, which indicates that our method can describe the deformation of 3D vesicle with extremely high precision. In addition, a shape transition between two stable states with great difference is studied, which further implies the capability of our proposed method in simulating large deformations regarding the 3D membrane. We believe that we have provided a very powerful simulation method for the future studies of bio-membrane deformations.
[1] Lipowsky R 1991 Nature 349 475
[2] Seifert U 1997 Adv. Phys. 46 13
[3] Helfrich W 1973 Z. Naturforschung C 28 693
[4] Svetina S, Zeks B 1983 Biomed. Biochim. Acta 42 S86
[5] Ouyang Z C, Helfrich W 1989 Phys. Rev. A 39 5280
[6] Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[7] Julicher F, Seifert U 1994 Phys. Rev. E 49 4728
[8] Deuling H J, Helfrich W 1976 J. Phys. 37 1335
[9] Naito H, Okuda M, Ouyang Z C 1995 Phys. Rev. Lett. 74 4345
[10] Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[11] Heinrich V, Svetina S, Zeks B 1993 Phys. Rev. E 48 3112
[12] Li S L, Zhang S G 2010 Acta Phys. Sin. 59 5202 (in Chinese) [李树玲, 张劭光 2010 59 5202]
[13] Bloor M I G, Wilson M J 2000 Phys. Rev. E 61 4218
[14] Feng F, Klug W S 2006 J. Comput. Phys. 220 394
[15] Brakke K A 1992 Exp. Math. 1 141
[16] Yan J, Liu Q H, Liu J X, Ouyang Z C 1998 Phys. Rev. E 58 4730
[17] 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]
[18] Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华, 张劭光2006 55 5568]
[19] Jaric M, Seifert U, Wintz W, Wortis M 1995 Phys. Rev. E 52 6623
[20] Li J F, Zhang H D, Qiu F, Yang Y L 2005 Acta Phys. Sin. 54 4000 (in Chinese) [李剑锋, 张红东, 邱枫, 杨玉良 2005 54 4000]
[21] Guo K, Li J F 2011 J. Phys. Condens. Matter 23 285103
[22] Li J F, Zhang H D, Tang P, Qiu F, Yang Y L 2006 Macromol. Theory Simul. 15 432
[23] Devenyi G A, Li J F, Hughes R A, Shi A C, Mascher P, Preston J S 2009 Nano Lett. 9 4258
[24] Li T, Li J F, Zhang H D, Yang Y L 2011 Acta Chim. Sin. 69 466 (in Chinese) [李婷, 李剑锋, 张红东, 杨玉良2011 化学学报 69 466]
[25] Li J F, Zhang H D, Qiu F 2013 J. Phys. Chem. B 117 843
[26] Li J F, Zhang H D, Qiu F, Shi A C 2013 Phys. Rev. E 88 012719
[27] Marsden J E, West M 2001 Acta Numerica 10 357
[28] Taniguchi T 1996 Phys. Rev. Lett. 76 4444
[29] Julicher F 1996 J. Phys. II 6 1797
[30] Li J F 2009 Ph. D. Dissertation (Shanghai: Fudan University) (in Chinese) [李剑锋 2009 博士学位论文 (上海: 复旦大学)]
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[1] Lipowsky R 1991 Nature 349 475
[2] Seifert U 1997 Adv. Phys. 46 13
[3] Helfrich W 1973 Z. Naturforschung C 28 693
[4] Svetina S, Zeks B 1983 Biomed. Biochim. Acta 42 S86
[5] Ouyang Z C, Helfrich W 1989 Phys. Rev. A 39 5280
[6] Hu J G, Ouyang Z C 1993 Phys. Rev. E 47 461
[7] Julicher F, Seifert U 1994 Phys. Rev. E 49 4728
[8] Deuling H J, Helfrich W 1976 J. Phys. 37 1335
[9] Naito H, Okuda M, Ouyang Z C 1995 Phys. Rev. Lett. 74 4345
[10] Seifert U, Berndl K, Lipowsky R 1991 Phys. Rev. A 44 1182
[11] Heinrich V, Svetina S, Zeks B 1993 Phys. Rev. E 48 3112
[12] Li S L, Zhang S G 2010 Acta Phys. Sin. 59 5202 (in Chinese) [李树玲, 张劭光 2010 59 5202]
[13] Bloor M I G, Wilson M J 2000 Phys. Rev. E 61 4218
[14] Feng F, Klug W S 2006 J. Comput. Phys. 220 394
[15] Brakke K A 1992 Exp. Math. 1 141
[16] Yan J, Liu Q H, Liu J X, Ouyang Z C 1998 Phys. Rev. E 58 4730
[17] 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]
[18] Zhou X H, Zhang S G 2006 Acta Phys. Sin. 55 5568 (in Chinese) [周晓华, 张劭光2006 55 5568]
[19] Jaric M, Seifert U, Wintz W, Wortis M 1995 Phys. Rev. E 52 6623
[20] Li J F, Zhang H D, Qiu F, Yang Y L 2005 Acta Phys. Sin. 54 4000 (in Chinese) [李剑锋, 张红东, 邱枫, 杨玉良 2005 54 4000]
[21] Guo K, Li J F 2011 J. Phys. Condens. Matter 23 285103
[22] Li J F, Zhang H D, Tang P, Qiu F, Yang Y L 2006 Macromol. Theory Simul. 15 432
[23] Devenyi G A, Li J F, Hughes R A, Shi A C, Mascher P, Preston J S 2009 Nano Lett. 9 4258
[24] Li T, Li J F, Zhang H D, Yang Y L 2011 Acta Chim. Sin. 69 466 (in Chinese) [李婷, 李剑锋, 张红东, 杨玉良2011 化学学报 69 466]
[25] Li J F, Zhang H D, Qiu F 2013 J. Phys. Chem. B 117 843
[26] Li J F, Zhang H D, Qiu F, Shi A C 2013 Phys. Rev. E 88 012719
[27] Marsden J E, West M 2001 Acta Numerica 10 357
[28] Taniguchi T 1996 Phys. Rev. Lett. 76 4444
[29] Julicher F 1996 J. Phys. II 6 1797
[30] Li J F 2009 Ph. D. Dissertation (Shanghai: Fudan University) (in Chinese) [李剑锋 2009 博士学位论文 (上海: 复旦大学)]
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