Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 3, 2009, Pages

  Lowengrub, John S ^a   Rätz, Andreas ^b   Voigt, Axel ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE FINITE ELEMENTS; BENDING RIGIDITIES; BENDING STIFFNESS; COUPLED SYSTEMS; DYNAMIC EVOLUTIONS; FOURTH ORDERS; LINE TENSIONS; LOWER ENERGIES; MULTI COMPONENTS; NONLOCAL EQUATIONS; PHASE SEPARATION DYNAMICS; PHASE-FIELD MODELING; PHASE-FIELD MODELS; SPONTANEOUS CURVATURES; SURFACE MASS; SURFACE PHASIS; THREE DIMENSIONS; TWO DIMENSIONS;

COARSENING; DYNAMICS; NONLINEAR EQUATIONS; PHASE MODULATION; PHASE SEPARATION;

SPINODAL DECOMPOSITION;

EID: 65449146384     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.031926     Document Type: Article

References (99)

1. H. McMahon and J. Gallop, Nature (London) 438, 590 (2005). 10.1038/nature04396
2. U. Seifert, Adv. Phys. 46, 13 (1997). 10.1080/00018739700101488
3. R. Lipowsky, Nature (London) 349, 475 (1991). 10.1038/349475a0
4. S. Hess, M. Kumar, A. Verma, J. Farrington, A. Kenworthy, and J. Zimmerberg, J. Cell Biol. 169, 965 (2005). 10.1083/jcb.200412058
5. K. Simons and E. Ikonen, Nature (London) 387, 569 (1997). 10.1038/42408
6. G. van Meer and H. Sprong, Curr. Opin. Cell Biol. 16, 373 (2004). 10.1016/j.ceb.2004.06.004
7. C. Rauch and E. Farge, Biophys. J. 78, 3036 (2000). 10.1016/S0006- 3495(00)76842-1
8. M. Takeda, G. Leser, C. Russell, and R. Lamb, Proc. Natl. Acad. Sci. U.S.A. 100, 14610 (2003). 10.1073/pnas.2235620100
9. I. Tsafrir, D. Sagi, T. Arzi, M. A. Guedeau-Boudeville, V. Frette, D. Kandel, and J. Stavans, Phys. Rev. Lett. 86, 1138 (2001). 10.1103/PhysRevLett. 86.1138
10. S. Veatch and S. Keller, Biophys. J. 85, 3074 (2003). 10.1016/S0006-3495(03)74726-2
11. T. Baumgart, S. Hess, and W. Webb, Nature (London) 425, 821 (2003). 10.1038/nature02013
12. T. G. D'Onofrio, A. Hatzor, A. Counterman, J. Heetderks, M. Sandel, and P. Weiss, Langmuir 19, 1618 (2003). 10.1021/la026133a
13. M. Beattie, S. Veatch, B. Stottrip, and S. Keller, Biophys. J. 89, 1760 (2005). 10.1529/biophysj.104.049635
14. A. Tian, C. Johnson, W. Wang, and T. Baumgart, Phys. Rev. Lett. 98, 208102 (2007). 10.1103/PhysRevLett.98.208102
15. S. Dutta and D. S. Ray, Phys. Rev. E 75, 016205 (2007). 10.1103/PhysRevE.75.016205
16. A. Garcia-Saz, S. Chiantia, and P. Schwille, J. Biol. Chem. 282, 33537 (2007). 10.1074/jbc.M706162200
17. J. Yuan, S. Hira, G. Strouse, and L. Hirst, J. Am. Chem. Soc. 130, 2067 (2008). 10.1021/ja710305c
18. S. Semrau, T. Idema, L. Holtzer, T. Schmidt, and C. Storm, Phys. Rev. Lett. 100, 088101 (2008). 10.1103/PhysRevLett.100.088101
19. A. Ayuyan and F. Cohen, Biophys. J. 94, 2654 (2008). 10.1529/biophysj. 107.118596
20. W. Helfrich, Z. Naturforsch. C 28, 693 (1973).
21. Statistical Mechanics of Membranes and Surfaces, edited by, D. Nelson, T. Piran, and, S. Weinberg, (World Scientific, Singapore, 2004).
22. Structure and Dynamics of Membranes-From Cells to Vesicles, edited by, R. Lipowsky, and, E. Sackman, (Elsevier, Amsterdam, 1995), Vols. 1A/B.
23. C. Pozrikidis, J. Comput. Phys. 169, 250 (2001). 10.1006/jcph.2000.6582
24. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992).
25. Q. Du, C. Liu, and X. Wang, J. Comput. Phys. 198, 450 (2004). 10.1016/j.jcp.2004.01.029
26. Q. Du, C. Liu, and X. Wang, J. Comput. Phys. 212, 757 (2006). 10.1016/j.jcp.2005.07.020
27. Q. Du, M. Li, and C. Liu, Discrete Contin. Dyn. Syst., Ser. B 8, 539 (2007).
28. F. Campelo and A. Hernandez-Machado, Eur. Phys. J. E 20, 37 (2006). 10.1140/epje/i2005-10079-5
29. T. Biben and C. Misbah, Phys. Rev. E 67, 031908 (2003). 10.1103/PhysRevE.67.031908
30. T. Biben, K. Kassner, and C. Misbah, Phys. Rev. E 72, 041921 (2005). 10.1103/PhysRevE.72.041921
31. D. Jamet and C. Misbah, Phys. Rev. E 76, 051907 (2007). 10.1103/PhysRevE.76.051907
32. D. Jamet and C. Misbah, Phys. Rev. E 78, 031902 (2008). 10.1103/PhysRevE.78.031902
33. B. Kaoui, G. H. Ristow, I. Cantat, C. Misbah, and W. Zimmermann, Phys. Rev. E 77, 021903 (2008). 10.1103/PhysRevE.77.021903
34. J. Barrett, H. Garcke, and R. Nürnberg, SIAM J. Sci. Comput. (USA) 31, 225 (2008). 10.1137/070700231
35. S. Veerapaneni, D. Gueyffier, D. Zorin, and G. Biros, J. Comput. Phys. 228, 2334 (2009). 10.1016/j.jcp.2008.11.036
36. P. Song, D. Hu, and P. Zhang, Comm. Comp. Phys. 3, 794 (2008).
37. P. Kumar, G. Gompper, and R. Lipowsky, Phys. Rev. Lett. 86, 3911 (2001). 10.1103/PhysRevLett.86.3911
38. M. Laradji and P. B. Sunil Kumar, Phys. Rev. Lett. 93, 198105 (2004). 10.1103/PhysRevLett.93.198105
39. J. Shillcock and R. Lipowsky, Nature Mater. 4, 225 (2005). 10.1038/nmat1333
40. E. J. Wallace, N. M. Hooper, and P. D. Olmsted, Biophys. J. 88, 4072 (2005). 10.1529/biophysj.104.054288
41. H. Noguchi and G. Gompper, Phys. Rev. E 73, 021903 (2006). 10.1103/PhysRevE.73.021903
42. K. Huang, R. Mukhopadhyay, and N. Wingreen, PLOS Comput. Biol. 2, e151 (2006). 10.1371/journal.pcbi.0020151
43. M. Laraddji and P. Kumar, J. Chem. Phys. 123, 224902 (2006). 10.1063/1.2102894
44. L. Gau, J. Shillcock, and R. Lipowsky, J. Chem. Phys. 126, 015101 (2007). 10.1063/1.2424698
45. A. Markvoort, A. Smeijers, K. Pieterse, R. van Santen, and P. Hilbers, J. Phys. Chem. B 111, 5719 (2007). 10.1021/jp068277u
46. A. Grafmuller, J. Shillcock, and R. Lipowsky, Phys. Rev. Lett. 98, 218101 (2007). 10.1103/PhysRevLett.98.218101
47. K. Smith and W. Upsal, J. Chem. Phys. 126, 075102 (2007). 10.1063/1.2435355
48. L. Gao, R. Lipowsky, and J. Shillcock, Soft Matter 4, 1208 (2008). 10.1039/b801407h
49. R. Lipowsky, J. Phys. II 2, 1825 (1992). 10.1051/jp2:1992238
50. U. Seifert, Phys. Rev. Lett. 70, 1335 (1993). 10.1103/PhysRevLett.70.1335
51. F. Jülicher and R. Lipowsky, Phys. Rev. Lett. 70, 2964 (1993). 10.1103/PhysRevLett.70.2964
52. F. Jülicher and R. Lipowsky, Phys. Rev. E 53, 2670 (1996). 10.1103/PhysRevE.53.2670
53. D. Andelman, T. Kawakatsu, and K. Kawasaki, Europhys. Lett. 19, 57 (1992). 10.1209/0295-5075/19/1/010
54. T. Kawakatsu, K. Kawasaki, D. Andelman, and T. Taniguchi, J. Phys. II 3, 971 (1993). 10.1051/jp2:1993177
55. T. Taniguchi, K. Kawasaki, D. Andelman, and T. Kawakatsu, J. Phys. II 4, 1333 (1994). 10.1051/jp2:1994203
56. J. Harden and F. MacKintosh, Europhys. Lett. 28, 495 (1994). 10.1209/0295-5075/28/7/007
57. W. T. Gozdz and G. Gompper, Phys. Rev. E 59, 4305 (1999). 10.1103/PhysRevE.59.4305
58. W. T. Gozdz and G. Gompper, Europhys. Lett. 55, 587 (2001). 10.1209/epl/i2001-00456-2
59. J. L. Harden, F. C. MacKintosh, and P. D. Olmsted, Phys. Rev. E 72, 011903 (2005). 10.1103/PhysRevE.72.011903
60. T. Baumgart, S. Das, W. Webb, and J. Jenkins, Biophys. J. 89, 1067 (2005). 10.1529/biophysj.104.049692
61. F. Solis, C. Funkhouser, and K. Thornton, Europhys. Lett. 82, 38001 (2008). 10.1209/0295-5075/82/38001
62. T. Taniguchi, Phys. Rev. Lett. 76, 4444 (1996). 10.1103/PhysRevLett.76. 4444
63. Y. Jiang, T. Lookman, and A. Saxena, Phys. Rev. E 61, R57 (2000). 10.1103/PhysRevE.61.R57
64. J. McWhirter, G. Ayton, and G. Voth, Biophys. J. 87, 3242 (2004). 10.1529/biophysj.104.045716
65. J. Lowengrub, J.-J. Xu, and A. Voigt, Fluid Dyn. Mater. Process. 3, 1 (2007).
66. C. M. Funkhouser, F. J. Solis, and K. Thornton, Phys. Rev. E 76, 011912 (2007). 10.1103/PhysRevE.76.011912
67. F. Campelo and A. Hernandez-Machado, Phys. Rev. Lett. 99, 088101 (2007). 10.1103/PhysRevLett.99.088101
68. X. Wang and Q. Du, J. Math. Biol. 56, 347 (2008). 10.1007/s00285-007- 0118-2
69. F. Campelo and A. Hernandez-Machado, Phys. Rev. Lett. 100, 158103 (2008). 10.1103/PhysRevLett.100.158103
70. L. Landau, Statistical Physics (Butterworth-Heinemann, Oxford, 1984).
71. S. Vey and A. Voigt, Comput. Visualization Sci. 10, 57 (2007). 10.1007/s00791-006-0048-3
72. G. Ayton, J. McWhirter, P. McMurtry, and G. Voth, Biophys. J. 88, 3855 (2005). 10.1529/biophysj.105.059436
73. F. Haußer, J. Lowengrub, A. Rätz, and A. Voigt (unpublished).
74. S. Mukherjee and S. Maxfield, Annu. Rev. Cell Dev. Biol. 20, 839 (2004). 10.1146/annurev.cellbio.20.010403.095451
75. V. Guillemin and A. Pollack, Differential Topology (Prentice-Hall, Englewood Cliffs, NJ, 1974).
76. S. Das and J. Jenkins, J. Fluid Mech. 597, 429 (2008). 10.1017/S0022112007009846
77. E. de Giorgi, Progress in Nonlinear Differential Equations and their Applications: Composite Media and Homogenization Theory (Springer, New York, 1991), Vol. 5, p. 135.
78. J. Lowengrub and L. Truskinovsky, Proc. R. Soc. London, Ser. A 454, 2617 (1998). 10.1098/rspa.1998.0273
79. A. Rätz and A. Voigt, Commun. Math. Sci. 4, 575 (2006).
80. A. Rätz and A. Voigt, Nonlinearity 20, 177 (2007). 10.1088/0951-7715/20/1/011
81. P. Loreti and R. March, Eur. J. Appl. Math. 11, 203 (2000). 10.1017/S0956792599004131
82. Q. Du, C. Liu, R. Ryham, and X. Wang, Nonlinearity 18, 1249 (2005). 10.1088/0951-7715/18/3/016
83. M. Röger and R. Schätzle, Math. Z. 254, 675 (2006). 10.1007/s00209-006-0002-6
84. J. Cahn and J. Hilliard, J. Chem. Phys. 28, 258 (1958). 10.1063/1.1744102
85. S. Allen and J. Cahn, Acta Metall. 27, 1085 (1979). 10.1016/0001-6160(79) 90196-2
86. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner Series Advances in Numerical Mathematics (Wiley-Teubner, Stuttgart, 1996), p. 127.
87. N. Kahya, D. Scherfeld, K. Bacia, B. Poolman, and P. Schwille, J. Biol. Chem. 278, 28109 (2003). 10.1074/jbc.M302969200
88. A. Rätz, A. Ribalta, and A. Voigt, J. Comput. Phys. 214, 187 (2006). 10.1016/j.jcp.2005.09.013
89. Q. Du, C. Liu, and X. Wang, SIAM J. Appl. Math. 65, 1913 (2005). 10.1137/040606417
90. Q. Du, C. Liu, R. Ryham, and X. Wang, Commun. Math. Sci. 5, 23 (2007).
91. M. Ruiz-Arguello, F. Goni, and A. Alonso, J. Biol. Chem. 273, 22977 (1998). 10.1074/jbc.273.36.22977
92. B. Stottrip, D. Stevens, and S. Keller, Biophys. J. 88, 269 (2005). 10.1529/biophysj.104.048439
93. M. Long, A.-S. Cans, and K. Keating, J. Am. Chem. Soc. 130, 756 (2008). 10.1021/ja077439c
94. S. Leibler, J. Phys. (France) 47, 507 (1986). 10.1051/jphys: 01986004703050700
95. J.-M. Allain and M. Ben Amar, Physica A 337, 531 (2004). 10.1016/j.physa.2003.12.058
96. J.-M. Allain and M. Ben Amar, Eur. Phys. J. E 20, 409 (2006). 10.1140/epje/i2006-10030-4
97. W. Shi, X.-Q. Feng, and H. Gao, Acta Mech. Sin. 22, 529 (2006). 10.1007/s10409-006-0036-3
98. S. Das and Q. Du, Phys. Rev. E 77, 011907 (2008). 10.1103/PhysRevE.77. 011907
99. Q. Du and J. Zhang, SIAM J. Sci. Comput. (USA) 30, 1634 (2008). 10.1137/060656449