Budding and vesiculation induced by conical membrane inclusions

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

Volumn 80, Issue 3, 2009, Pages

  Auth, Thorsten ^a   Gompper, Gerhard ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL MODEL; BENDING ENERGIES; CURVATURE RADII; DIFFERENT SIZES; INCLUSION DENSITY; LIPID BILAYER MEMBRANES; LIPID DOMAINS; MEDIATED INTERACTION; MEMBRANE BENDING; MEMBRANE PROTEINS; SPONTANEOUS CURVATURE; TRANSLATIONAL ENTROPIES;

BRUSHES; COMPUTER SIMULATION; LIPID BILAYERS; MEMBRANES; PROTEINS;

INCLUSIONS;

EID: 70349500348     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.031901     Document Type: Article

References (70)

1. A. D. Dupuy and D. M. Engelman, Proc. Natl. Acad. Sci. U.S.A. 105, 2848 (2008). 10.1073/pnas.0712379105 (Pubitemid 351723632)
2. P. Sens, L. Johannes, and P. Bassereau, Curr. Opin. Cell Biol. 20, 476 (2008). 10.1016/j.ceb.2008.04.004
3. G. Drin, J. F. Casella, R. Gautier, T. Boehmer, T. U. Schwartz, and B. Antonny, Nat. Struct. Mol. Biol. 14, 138 (2007). 10.1038/nsmb1194 (Pubitemid 46245807)
4. P. D. Blood and G. A. Voth, Proc. Natl. Acad. Sci. U.S.A. 103, 15068 (2006). 10.1073/pnas.0603917103 (Pubitemid 44583165)
5. T. Auth and G. Gompper, Phys. Rev. E 72, 031904 (2005). 10.1103/PhysRevE.72.031904
6. T. Bickel and C. M. Marques, Eur. Phys. J. E 9, 349 (2002). 10.1140/epje/i2001-10113-8 (Pubitemid 36256458)
7. M. G. J. Ford, I. G. Mills, B. J. Peter, Y. Vallis, G. J. K. Praefcke, P. R. Evans, and H. T. McMahon, Nature (London) 419, 361 (2002). 10.1038/nature01020
8. J. L. Harden and F. C. Mackintosh, Europhys. Lett. 28, 495 (1994). 10.1209/0295-5075/28/7/007
9. H. Hagerstrand, L. Mrowczynska, U. Salzer, R. Prohaska, K. A. Michelsen, V. Kralj-Iglic, and A. Iglic, Mol. Membr. Biol. 23, 277 (2006). 10.1080/09687860600682536 (Pubitemid 43922339)
10. M. M. Kozlov, Nature (London) 447, 387 (2007). 10.1038/447387a (Pubitemid 46816725)
11. B. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006). 10.1016/j.ceb.2006.06. 003 (Pubitemid 44016053)
12. R. Shlomovitz and N. S. Gov, Phys. Rev. Lett. 98, 168103 (2007). 10.1103/PhysRevLett.98.168103 (Pubitemid 46633672)
13. W. Römer, Nature (London) 450, 670 (2007). 10.1038/nature05996 (Pubitemid 350207679)
14. H. T. McMahon and J. L. Gallop, Nature (London) 438, 590 (2005). 10.1038/nature04396 (Pubitemid 41740562)
15. H. J. Gao, W. D. Shi, and L. B. Freund, Proc. Natl. Acad. Sci. U.S.A. 102, 9469 (2005). 10.1073/pnas.0503879102 (Pubitemid 40981705)
16. W. T. Góźdź, Langmuir 23, 5665 (2007). 10.1021/la063522m (Pubitemid 46826520)
17. T. Auth and G. Gompper, Phys. Rev. E 68, 051801 (2003). 10.1103/PhysRevE.68.051801
18. I. Tsafrir, Y. Caspi, M. A. Guedeau-Boudeville, T. Arzi, and J. Stavans, Phys. Rev. Lett. 91, 138102 (2003). 10.1103/PhysRevLett.91.138102
19. F. Campelo, J. M. Allain, and M. Ben Amar, Europhys. Lett. 77, 38006 (2007). 10.1209/0295-5075/77/38006
20. T. Baumgart, S. T. Hess, and W. W. Webb, Nature (London) 425, 821 (2003). 10.1038/nature02013 (Pubitemid 37351463)
21. C. K. Haluska, W. T. Gozdz, H. G. Döbereiner, S. Forster, and G. Gompper, Phys. Rev. Lett. 89, 238302 (2002). 10.1103/PhysRevLett.89.238302
22. W. T. Góźdź and G. Gompper, Europhys. Lett. 55, 587 (2001). 10.1209/epl/i2001-00456-2
23. R. Bruinsma and P. Pincus, Curr. Opin. Solid State Mater. Sci. 1, 401 (1996). 10.1016/S1359-0286(96)80032-5 (Pubitemid 126407987)
24. M. Goulian, Curr. Opin. Colloid Interface Sci. 1, 358 (1996).
25. M. Goulian, R. Bruinsma, and P. Pincus, Europhys. Lett. 22, 145 (1993). 10.1209/0295-5075/22/2/012
26. M. Goulian, R. Bruinsma, and P. Pincus, Europhys. Lett. 23, 155 (1993). 10.1209/0295-5075/23/2/014
27. T. R. Weikl, M. M. Kozlov, and W. Helfrich, Phys. Rev. E 57, 6988 (1998). 10.1103/PhysRevE.57.6988
28. T. Chou, K. S. Kim, and G. Oster, Biophys. J. 80, 1075 (2001). 10.1016/S0006-3495(01)76086-9
29. K. S. Kim, J. Neu, and G. Oster, Biophys. J. 75, 2274 (1998). 10.1016/S0006-3495(98)77672-6
30. P. G. Dommersnes, J. B. Fournier, and P. Galatola, Europhys. Lett. 42, 233 (1998). 10.1209/epl/i1998-00235-7
31. K. S. Kim, J. C. Neu, and G. F. Oster, Europhys. Lett. 48, 99 (1999). 10.1209/epl/i1999-00120-y
32. W. Helfrich and T. R. Weikl, Eur. Phys. J. E 5, 423 (2001). 10.1007/s101890170049
33. T. R. Weikl, Europhys. Lett. 54, 547 (2001). 10.1209/epl/i2001-00281-7
34. R. Golestanian, M. Goulian, and M. Kardar, Phys. Rev. E 54, 6725 (1996). 10.1103/PhysRevE.54.6725
35. R. Golestanian, M. Goulian, and M. Kardar, Europhys. Lett. 33, 241 (1996). 10.1209/epl/i1996-00327-4
36. B. J. Reynwar, G. Illya, V. A. Harmandaris, M. M. Müller, K. Kremer, and M. Deserno, Nature (London) 447, 461 (2007). 10.1038/nature05840 (Pubitemid 46816743)
37. E. Atilgan and S. X. Sun, J. Chem. Phys. 121, 10392 (2004). 10.1063/1.1813434 (Pubitemid 40001583)
38. In general, the boundary conditions are given by h (ρb) = h0 (ρb) and h′ (ρb) = h1 (ρb) for the inner and the outer boundaries each or alternatively-if the values of h and h′ are not known at the boundary-by the natural boundary conditions ρ Δh (ρ) ρ= ρb =0 and Δh (ρ) ρ= ρb =0, respectively.
39. Part of a small sphere (the inclusion) is matched to the narrow part of the catenoid such that the slope is continuous, which again is matched to a larger sphere (the vesicle); see Fig. 3.
40. The equations are applicable for large n, but also in the exact relations the inclusion geometry enters only as a single variable, |a| ρi.
41. Budding in this regime of inclusion concentration might be possible for a negative value of κ̄.
42. Equation 7 is valid for large n; for very small vesicles the approximation breaks down and in addition discretization effects become important.
43. J. J. Sieber, K. I. Willing, C. Kutzner, C. Gerding-Reimers, B. Harke, G. Donnert, B. Rammner, C. Eggeling, S. W. Hell, H. Grubmueller, and T. Lang, Science 317, 1072 (2007). 10.1126/science.1141727 (Pubitemid 47330189)
44. We neglect the contribution of the geodesic curvature, the influence of which is characterized by κ̄.
45. In the original method that applies to steep potentials, E (ρu) =0 is used.
46. R. R. Netz and P. Pincus, Phys. Rev. E 52, 4114 (1995). 10.1103/PhysRevE.52.4114
47. J. B. Fournier and P. G. Dommersnes, Europhys. Lett. 39, 681 (1997). 10.1209/epl/i1997-00548-y
48. T. R. Weikl, Phys. Rev. E 66, 061915 (2002). 10.1103/PhysRevE.66.061915
49. J. A. Barker and D. Henderson, J. Chem. Phys. 47, 2856 (1967). 10.1063/1.1712308
50. D. Henderson and J. A. Barker, Phys. Rev. A 1, 1266 (1970). 10.1103/PhysRevA.1.1266
51. R. O. Watts and D. Henderson, J. Chem. Phys. 50, 1651 (1969). 10.1063/1.1671254
52. It is not clear whether for κ1 kB T the thermal undulations of the membrane can still be neglected, i.e., whether our model applies.
53. N. F. Carnahan and K. E. Starling, J. Chem. Phys. 51, 635 (1969). 10.1063/1.1672048
54. M. J. Maeso and J. R. Solana, J. Chem. Phys. 99, 548 (1993). 10.1063/1.465779
55. C. Gögelein, G. Nägele, R. Tuinier, T. Gibaud, A. Stradner, and P. Schurtenberger, J. Chem. Phys. 129, 085102 (2008). 10.1063/1.2951987
56. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic Press, London, 2006).
57. The cell approximation for the free energy of the crystalline phase is not useful, because the effective hard disks overlap already at densities that are slightly higher than the crystallization transition of the inclusions and below densities that are observed in simulations.
58. C. Eisenmann, P. Keim, U. Gasser, and G. Maret, J. Phys.: Condens. Matter 16, S4095 (2004). 10.1088/0953-8984/16/38/024
59. M. Deserno, Macromol. Rapid Commun. 30, 752 (2009). 10.1002/marc. 200900090
60. Y. I. Henis, in Biomembranes: Physical Aspects, edited by, M. Shinitzky, (VCH, Weinheim, 1993), pp. 279-339.
61. N. Gov, A. G. Zilman, and S. Safran, Phys. Rev. Lett. 90, 228101 (2003). 10.1103/PhysRevLett.90.228101
62. B. Alberts, D. Bray, and J. Lewis, Molecular Biology of the Cell, 4th ed. (Garland Science, New York, 2002).
63. J. Pecreaux, H. G. Döbereiner, J. Prost, J. F. Joanny, and P. Bassereau, Eur. Phys. J. E 13, 277 (2004). 10.1140/epje/i2004-10001-9 (Pubitemid 40877406)
64. By this mechanism, the final number of inclusions per bud is already determined in an early stage of bud formation. The area of lipid bilayer per bud can adjust during the budding process and is regulated by the number of inclusions on the bud.
65. A.-S. Smith and U. Seifert, Phys. Rev. E 71, 061902 (2005). 10.1103/PhysRevE.71.061902
66. Many numerical values of the parameters in the figures have been chosen such that they correspond to those in Ref..
67. T. Kohyama, D. M. Kroll, and G. Gompper, Phys. Rev. E 68, 061905 (2003). 10.1103/PhysRevE.68.061905
68. J. Heuser and L. Evans, J. Cell Biol. 84, 560 (1980). 10.1083/jcb.84.3.560
69. N. Dan, A. Berman, P. Pincus, and S. A. Safran, J. Phys. II 4, 1713 (1994). 10.1051/jp2:1994227
70. G. Döge, K. Mecke, J. Moller, D. Stoyan, and R. P. Waagepetersen, Int. J. Mod. Phys. C 15, 129 (2004). 10.1142/S0129183104005565 (Pubitemid 39436242)