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The real bio-membranes are of multi-component, and they usually carry a certain quantity of charges. Therefore, it is of great biological significance to study charged multicomponent vesicles. However, the charged multi-component vesicles have been not yet systematically studied due mainly to the following two reasons: first, there are too many factors that will influence the behaviors of charged multi-component vesicles; second, theoretically it is difficult to deal with the phase separation of the multiple components from the Coulomb interaction of charged components at the same time. This work shows that the combination of the discrete-spatial variational method and dissipative dynamics can be used to address the above issues. For simplicity, we will consider only the deformation coupled with the phase separation of two-component charged vesicles in a two-dimensional plane rather than in three-dimensional space, which can present us more systematic research results. Besides, we have not considered the screening effects of counter ions or salts in this work, or equivalently we consider only the case where the screening length is relatively big. The charged vesicle is composed of two components A and B, where component A is negatively charged while component B is neutral. In particular, the charges on the vesicle can freely move in the membrane, which may be described by a time-dependent Ginzburg Landau equation. Initially, the two components are uniformly distributed on the vesicle.In this work, we specially focus on the influence of the electrostatic interaction on the compatibility of different components. It is found that introduction of charges will promote the apparent miscibility between different components. This could explain that the electrostatic interactions may contribute to the increase of the compatibility of different biomolecules in biological system. When temperature is relatively high, the electrostatic interaction will completely inhibit the phase separation which actually prevents the same component from being clustered. When temperature is relatively low, the electrostatic interaction will increase the number of phase domains, which actually turns the original macro phase separation into the micro one, thus reducing the cluster size. In this work, we also systematically study the influences of other factors, such as temperature, charge density of charged components, and the averaged concentration of charged component, on the final configuration of charged multicomponent vesicle. In particular, a phase diagram of the temperature and the averaged concentration of the charged component is obtained, and it is found that the number of phase domains will increase with the increase of charge density of component A. These conclusions are also qualitatively applicable to three-dimensional two-component charged vesicles.
[1] Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[2] Lim H W G, Wortis M, Mukhopadhyay R 2002 Proc. Natl. Acad. Sci. USA 99 16766
[3] Mukhopadhyay R, Gerald L H W, Wortis M 2002 Biophys. J. 82 1756
[4] Yang F Y, Halidan J M H, Jiang Z Y 2014 J. Atom. Mol. Phys. 31 677 (in Chinese) [杨方源, 哈丽旦 居马汗, 蒋中英 2014 原子与分子 31 677]
[5] Li J F, Zhang H D, Qiu F 2013 J. Phys. Chem. B 117 843
[6] Liang X Y, Li L, Qiu F, Yang Y L 2010 Physica A 389 3965
[7] Li L, Liang X Y, Lin M Y, Qiu F, Yang Y L 2005 J. Am. Chem. Soc. 127 17996
[8] Lipowsky R 1992 J. de Physique Ⅱ 2 1825
[9] Jlicher F, Lipowsky R 1993 Phys. Rev. Lett. 70 2964
[10] Leibler S 1986 J. Phys. 47 507
[11] Seifert U 1993 Phys. Rev. Lett. 70 1335
[12] Jrgensen K, Klinger A, Raiman M, Biltonen R L 1996 J. Phys. Chem. 100 2766
[13] Jrgensen K, Mouritsen O G 1999 Thermochim. Acta 328 81
[14] Sunil-Kumar P B, Gompper G, Lipowsky R 2001 Phys. Rev. Lett. 86 3911
[15] Yamamoto S, Hyodo S 2003 J. Chem. Phys. 118 7937
[16] Laradji M, Sunil Kumar P B 2004 Phys. Rev. Lett. 93 198105
[17] Taniguchi T 1996 Phys. Rev. Lett. 76 4444
[18] Sinha K P, Thaokar R M 2016 Eur. Phys. J. E 39 73
[19] Li J F, Zhang H D, Qiu F, Yang Y L, Chen J Z Y 2015 Soft Matter 11 1788
[20] Ito H, Higuchi Y J 2016 Phys. Rev. E 94 042611
[21] 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]
[22] Li J F, Zhang H D, Qiu F, Shi A C 2013 Phys. Rev. E 88 012719
[23] Guo K K 2005 Ph. D. Dissertation (Shanghai: Fudan University) (in Chinese) [郭坤琨 2005 博士学位论文 (上海: 复旦大学)]
[24] Li J F, Zhang H D, Tang P, Qiu F, Yang Y L 2006 Macromol. Theory Simul. 15 432
[25] 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]
[26] Helfrich W 1973 Z. Naturforsch. C 28 693
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[1] Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[2] Lim H W G, Wortis M, Mukhopadhyay R 2002 Proc. Natl. Acad. Sci. USA 99 16766
[3] Mukhopadhyay R, Gerald L H W, Wortis M 2002 Biophys. J. 82 1756
[4] Yang F Y, Halidan J M H, Jiang Z Y 2014 J. Atom. Mol. Phys. 31 677 (in Chinese) [杨方源, 哈丽旦 居马汗, 蒋中英 2014 原子与分子 31 677]
[5] Li J F, Zhang H D, Qiu F 2013 J. Phys. Chem. B 117 843
[6] Liang X Y, Li L, Qiu F, Yang Y L 2010 Physica A 389 3965
[7] Li L, Liang X Y, Lin M Y, Qiu F, Yang Y L 2005 J. Am. Chem. Soc. 127 17996
[8] Lipowsky R 1992 J. de Physique Ⅱ 2 1825
[9] Jlicher F, Lipowsky R 1993 Phys. Rev. Lett. 70 2964
[10] Leibler S 1986 J. Phys. 47 507
[11] Seifert U 1993 Phys. Rev. Lett. 70 1335
[12] Jrgensen K, Klinger A, Raiman M, Biltonen R L 1996 J. Phys. Chem. 100 2766
[13] Jrgensen K, Mouritsen O G 1999 Thermochim. Acta 328 81
[14] Sunil-Kumar P B, Gompper G, Lipowsky R 2001 Phys. Rev. Lett. 86 3911
[15] Yamamoto S, Hyodo S 2003 J. Chem. Phys. 118 7937
[16] Laradji M, Sunil Kumar P B 2004 Phys. Rev. Lett. 93 198105
[17] Taniguchi T 1996 Phys. Rev. Lett. 76 4444
[18] Sinha K P, Thaokar R M 2016 Eur. Phys. J. E 39 73
[19] Li J F, Zhang H D, Qiu F, Yang Y L, Chen J Z Y 2015 Soft Matter 11 1788
[20] Ito H, Higuchi Y J 2016 Phys. Rev. E 94 042611
[21] 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]
[22] Li J F, Zhang H D, Qiu F, Shi A C 2013 Phys. Rev. E 88 012719
[23] Guo K K 2005 Ph. D. Dissertation (Shanghai: Fudan University) (in Chinese) [郭坤琨 2005 博士学位论文 (上海: 复旦大学)]
[24] Li J F, Zhang H D, Tang P, Qiu F, Yang Y L 2006 Macromol. Theory Simul. 15 432
[25] 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]
[26] Helfrich W 1973 Z. Naturforsch. C 28 693
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