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Thermodynamics and dynamics of the formation of spherical lipid vesicles

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Abstract

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipid membranes and derive a Fokker–Planck equation for the probability distribution describing the dynamics of vesicle formation. We find that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.

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References

  1. Lei, G., MacDonald, R.C.J.: Effects on interactions of oppositely charged phospholipid vesicles of covalent attachment of polyethylene glycol oligomers to their surfaces: Adhesion, Hemifusion, Full Fusion and “Endocytosis”. J. Membr. Biol. 221, 97–106 (2008)

    Article  Google Scholar 

  2. Cans, A.-S., Wittenberg, N., Karlsson, R., Sombers, L., Karlsson, M., Orwar, O., Ewing, A.: Artificial cells: unique insights into exocytosis using liposomes and lipid nanotubes. PNAS 100(2), 400–404 (2003)

    Article  ADS  Google Scholar 

  3. Pantazatos, D.P., MacDonald, R.C.: Directly observed membrane fusion between oppositely charged phospholipid bilayers. J. Membrane Biol. 170, 27–38 (1999)

    Article  Google Scholar 

  4. Lei, G., MacDonald, R.C.: Lipid bilayer vesicle fusion: intermediate captured by high-speed microfluorescence spectroscopy. J. Biophys. 85, 1585–1599 (2003)

    Article  Google Scholar 

  5. Lapinski, M.M., Castro-Forero, A., Greiner, A.J., Ofoli, R.Y., Blanchard, G.J.: Comparison of liposomes formed by sonication and extrusion: rotational and translational diffusion of an embedded chromophore. Langmuir 23, 11677–11683 (2007)

    Article  Google Scholar 

  6. Svetina, S., Žekš, B.: Shape behavior of lipid vesicles as the basis of some cellular processes. Anat. Rec. 268, 215–225 (2002)

    Article  Google Scholar 

  7. Leonetti, J.P., Machy, P., Degols, G., Lebleu, B., Leserman, L.: Antibody-targeted liposomes containing oligodeoxyribonucleotides complementary to viral-RNA selectively inhibit viral replication. PNAS USA 87, 2448–2451 (1990)

    Article  ADS  Google Scholar 

  8. Renneisen, K., Leserman, L., Matthes, E., Schroder, H.C., Müller, W.E.G.: Inhibition of expression of human immunodeficiency virus-1 in vitro by antibody-targeted liposomes containing antisense RNA to the ENV region. J. Biol. Chem. 265(27), 16337–16342 (1990)

    Google Scholar 

  9. Dominak, L.M., Keating, C.D.: Polymer encapsulation within giant lipid vesicles. Langmuir 23, 7148–7154 (2007)

    Article  Google Scholar 

  10. Evans, E., Needham, D.: Physical properties of surfactant bilayer membranes – thermal transitions, elasticity, rigidity, cohesion, and colloidal interactions. J. Phys. Chem. 91, 4219–4228 (1987)

    Article  Google Scholar 

  11. Henriksen, J.R., Ipsen, J.H.: Measurements of membrane elasticity by micro-pipette aspiration. Eur. Phys. J. E. 14, 149–167 (2004)

    Article  Google Scholar 

  12. Evans E., Rawicz W.: Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Let. 64(17), 2094–2097 (1990)

    Article  ADS  Google Scholar 

  13. Ly, H.V., Longo, M.L.: The influence of short-chain alcohols on interfacial tension, mechanical properties, area/molecule, and permeability of fluid lipid bilayers. Biophys. J. 87, 1013–1033 (2004)

    Article  ADS  Google Scholar 

  14. Karlsson, A., Scott, K., Markström, M., Davidson, M., Konkoli, Z., Orwar, O.: Controlled initiation of enzymatic reactions in micrometer-sized biomimetic compartments. J. Phys. Chem. B 109, 1609–1617 (2005)

    Article  Google Scholar 

  15. Bolinger, P.Y., Stamou, D., Vogel, H.: Integrated nanoreactor systems: triggering the release and mixing of compounds inside single vesicles. J. Am. Chem. Soc. 126, 8594–8595 (2004)

    Article  Google Scholar 

  16. Lasic, D.D.: The mechanism of vesicle formation. Biochem. J. 256(1), 1–11 (1988)

    Google Scholar 

  17. López-Oyama, A., Paredes-Quijada, G., Acuna-Campa, H., Maldonado, A.: Effect of phospholipid composition and of different salts on the shape and size of giant SOPC: SOPS vesicles. Biophys. J. 88(1 Part 2 Suppl. S), 234A (2005)

    Google Scholar 

  18. Paredes-Quijada, G., Aranda-Espinoza, H., Maldonado, A.: Shapes of mixed phospholipid vesicles. J. Biol. Phys. 32(2), 177–181 (2006)

    Article  Google Scholar 

  19. Angelova, M.I., Dimitrov, D.S.: Liposome electroformation. Faraday Discuss. 81, 303-311 (1986)

    Article  Google Scholar 

  20. Dimitrov, D.S., Angelova, M.I.: Lipid swelling and liposome formation mediated by electric fields. Bioelectrochemistry and Bioenergetics 19(2), 323–336 (1988)

    Article  Google Scholar 

  21. Krzywicki, T.G., Tardieu, A., Luzzati, V.: The smectic phase of lipid-water systems: properties related to the nature of the lipid and to the presence of net electrical charges. Mol. Cryst. Liq. Cryst. 8, 285–291 (1969)

    Article  Google Scholar 

  22. Srividya, N., Muralidharan, S.: Determination of the line tension of giant vesicles from pore-closing dynamics. J. Phys. Chem. B 112(24), 7147–7152 (2008)

    Article  Google Scholar 

  23. Gadomski, A., Rubí J.M.: On the two principal curvatures as potential barriers in a model of complex matter agglomeration. Chem. Phys. 293, 169–177 (2003)

    Article  Google Scholar 

  24. Gadomski, A.: Curvature effects in clusters grown in a 2D discrete space: an algebraic approach. Intern. J. Mod. Phys. C 13(9), 1285–1299 (2002)

    Article  ADS  Google Scholar 

  25. Helfrich, W.: Elastic properties of liquid bilayers: theory and possible experiments. Naturforsch Z. C 28, 693–703 (1973)

    Google Scholar 

  26. Safran, S.A.: Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Addison-Wesley, New York (1994)

    Google Scholar 

  27. Boal, D.: Mechanics of the Cell. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  28. Antonietti, M., Forster, S.: Vesicles and liposomes: a self-assembly principle beyond lipids. Adv. Mater. 15, 1323–1333 (2003)

    Article  Google Scholar 

  29. Le, T.D., Olsson, U., Mortensen, K.: Topological transformation of a surfactant bilayer. Physica B 276–278, 379–380 (2000)

    Article  Google Scholar 

  30. Siegel, D.P., Kozlov, M.M.: The Gaussian curvature elastic modulus of N-monomethylated dioleoyilphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior. Biophys J. 87, 366–374 (2004)

    Article  ADS  Google Scholar 

  31. de Groot, S.R., Mazur, P.: Non-equilibrium Thermodynamics. Dover, New York (1984)

    Google Scholar 

  32. Reguera, D., Vilar, J.M.G., Rubi, J.M.: The mesoscopic dynamics of thermodynamic systems. J. Phys. Chem. B 109, 21502–21515 (2005)

    Article  Google Scholar 

  33. Gadomski, A., Kruszewska, N., Santamaría-Holek, I., Uher, J.J., Pawlak, Z., Oloyede, A., Pechkova, E., Nicolini, C.: Can modern statistical mechanics unravel some practical problems encountered in model biomatter aggregations emerging in internal—& external—friction conditions? In: Kim, B.-S. (ed.) Statistical Mechanics Research, pp. 44–91. Nova, New York (2008)

    Google Scholar 

  34. Landau, L., Lifshitz, E.M.: Course of Theoretical Physics, Statistical Physics Part 1. Pergamon, New York (1980)

    Google Scholar 

  35. Miao, L., Lomholt, N.A., Kleis, J.: Dynamics of shape fluctuations of quasi-spherical vesicles revisited. Eur. Phys. J. E. 9, 143–160 (2002)

    Article  Google Scholar 

  36. Risken, H.: The Fokker–Planck Equation. Springer, Berlin (1989)

    MATH  Google Scholar 

  37. Pérez-Madrid, A.: A model for nonexponential relaxation and aging in dissipative systems. J. Chem. Phys. 122, 214914-1–214914-6 (2005)

    Article  ADS  Google Scholar 

  38. Pérez-Madrid, A., Santamaría-Holek, I.: Fluctuation theorems for systems under Fokker-Planck dynamics. Phys. Rev. E 79, 011101-1–011101-5 (2009)

    Article  ADS  Google Scholar 

  39. Zwanzig, R.: Nonequilibrium Statistical Mechanics. Oxford University Press, New York (2001)

    Google Scholar 

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Acknowledgements

We acknowledge useful discussions with Dr. A. Maldonado and with G. Paredes and C. Luna. This work has been done under the framework of the Programa de Intercambio Académico UNAM-UNISON. We also acknowledge financial support by Grant No. DGAPA-IN102609.

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Correspondence to Ernesto Hernández-Zapata.

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Hernández-Zapata, E., Martínez-Balbuena, L. & Santamaría-Holek, I. Thermodynamics and dynamics of the formation of spherical lipid vesicles. J Biol Phys 35, 297–308 (2009). https://doi.org/10.1007/s10867-009-9169-5

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  • DOI: https://doi.org/10.1007/s10867-009-9169-5

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