Model studies of lipid flip-flop in membranes

  • Giulia Parisio
  • Alberta Ferrarini
  • Maria Maddalena Sperotto


Biomembranes, which are made of a lipid bilayer matrix where proteins are embedded or attached, constitute a physical barrier for cell and its internal organelles. With regard to the distribution of their molecular components, biomembranes are both laterally heterogeneous and transversally asymmetric, and because of this they are sites of vital biochemical activities. Lipids may translocate from one leaflet of the bilayer to the opposite either spontaneously or facilitated by proteins, hence they contribute to the regulation of membrane asymmetry on which cell functioning, differentiation, and growth heavily depend. Such transverse motion—commonly called flip-flop—has been studied both experimentally and computationally. Experimental investigations face difficulties related to time-scales and probe-induced membrane perturbation issues. Molecular dynamics simulations play an important role for the molecular-level understanding of flip-flop. In this review we present a summary of the state of the art of computational studies of spontaneous flip-flop of phospholipids, sterols and fatty acids. Also, we highlight critical issues and strategies that have been developed to solve them, and what remains to be solved.


Flip-flop Molecular dynamics simulations Potential of mean force Sterols Fatty acids Phospholipids 



Coarse grained








1,2-Dierucoyl-sn-glycero-3-phosphocholine (DEPC)












Dissipative particle dynamics










Molecular dynamics


Potential of mean force








Transition path sampling



G.P. acknowledges financial support from University of Padova (Junior Grant 2011).


  1. 1.
    Singer, S.J., Nicolson, G.L.: The fluid mosaic model of the structure of cell membranes. Science 175, 720–731 (1972)CrossRefGoogle Scholar
  2. 2.
    Nicolson, G.L.: Transmembrane control of the receptors on normal and tumor cells. I. Cytoplasmic influence over cell surface components. Biochim. Biophys. Acta 457, 57–108 (1976)CrossRefGoogle Scholar
  3. 3.
    Kornberg, R.D., McConnell, H.M.: Inside-outside transitions of phospholipids in vesicle membranes. Biochemistry 10, 1111–1120 (1971)CrossRefGoogle Scholar
  4. 4.
    Nicolson, G.L.: The fluid-mosaic model of membrane structure: still relevant to understanding the structure, function and dynamics of biological membranes after more than 40 years. Biochim. Biophys. Acta 1838, 1451–1466 (2014)CrossRefGoogle Scholar
  5. 5.
    Simons, K., Ikonen, E.: Functional rafts in cell membranes. Nature 387, 569–572 (1997)CrossRefGoogle Scholar
  6. 6.
    Vigh, L., Escriba, P.V., Sonnleitner, A., Sonnleitner, M., Piotto, S., Maresca, B., Horva’th, I., Harwood, J.L.: The significance of lipid composition for membrane activity: new concepts and ways of assessing function. Prog. Lipid Res. 44, 303–344 (2005)CrossRefGoogle Scholar
  7. 7.
    Hryniewicz-Jankowska, A., Augoff, K., Biernatowska, A., Podkalicka, J., Sikorski, A.F.: Membrane rafts as novel target in cancer therapy. Biochim. Biophys. Acta 1845, 155–165 (2014)Google Scholar
  8. 8.
    Nicolson, G.L., Ash, M.E.: Lipid replacement therapy: a natural medicine approach to replacing damaged lipids in cellular membranes and organelles and restoring function. Biochim. Biophys. Acta 1838, 1657–1679 (2014)CrossRefGoogle Scholar
  9. 9.
    Zachowski, A.: Phospholipids in animal eukaryotic membranes: transverse asymmetry and movement. Biochem. J. 294, 1–14 (1993)CrossRefGoogle Scholar
  10. 10.
    Daleke, D.L.: Regulation of phospholipid asymmetry in the erythrocyte membrane. Curr. Opin. Hematol. 15, 191–195 (2008)CrossRefGoogle Scholar
  11. 11.
    Castegna, A., Lauderback, C.M., Mohammad-Abdul, H., Butterfield, D.H.: Modulation of phospholipid asymmetry in synaptosomal membranes by the lipid peroxidation products, 4-hydroxynonenal and acrolein: implications for Alzheimer’s disease. Brain Res. 1004, 193–197 (2004)CrossRefGoogle Scholar
  12. 12.
    Yamon, Y., Broccardo, C., Chambenoit, O., Luciani, M.-F., Toti, F., Chaslin, S., Freyssinet, J.-M., Devaux, P.F., Niesh, J., Marguet, D., Chimini, G.: ABC1 promotes engulfment of apoptotic cells and transbilayer redistribution of phosphatidylserine. Nat. Cell Biol. 2, 399–406 (2000)CrossRefGoogle Scholar
  13. 13.
    Sathi, A., Viswanad, V., Aneesh, T.P., Kumar, B.A.: Pros and cons of phospholipid asymmetry in erythrocytes. J. Pharm. Bioallied Sci. 6, 81–85 (2014)CrossRefGoogle Scholar
  14. 14.
    Devaux, P.F., Hermann, A. (eds.): Transmembrane Dynamics of Lipids. Wiley, Hoboken, NJ (2011)Google Scholar
  15. 15.
    Tait, J.F., Gibson, D.: Measurements of membrane phospholipid asymmetry in normal and sickle-cell erythrocytes by means of Annexin V binding. J. Lab. Clin. Med. 123, 741–748 (1994)Google Scholar
  16. 16.
    Bevers, E.M., Comfurius, P., Zwaal, R.F.A.: Changes in membrane phospholipid distribution during platelet activation. Biochim. Biophys. Acta 736, 57–66 (1983)CrossRefGoogle Scholar
  17. 17.
    Bevers, E.M., Weidmer, T., Comfurius, P., Shattil, S.J., Weiss, H.J., Zwaal, R.F.A., Sims, P.J.: Defective Ca(2+)-induced micro vesiculation and deficient expression of procoagulant activity in eritrocytes from a patient with a bleeding disorder: a study of the red blood cells of Scott syndrome. Blood 79, 380–388 (1992)Google Scholar
  18. 18.
    Carley, A.N., Kleinfeld, A.M.: Flip-flop is the rate-limiting step for transport of free fatty acids across lipid vesicle membranes. Biochemistry 48, 10437–10445 (2009)CrossRefGoogle Scholar
  19. 19.
    Simard, J.R., Pillai, B.K., Hamilton, J.A.: Fatty acid flip-flop in a model membrane is faster than desorption into the aqueous phase. Biochemistry 47, 9081–9089 (2008)CrossRefGoogle Scholar
  20. 20.
    Bacia, K., Schwille, P., Kurzchalia, T.: Sterol structure determines the separation of phases and the curvature of the liquid-ordered phase in model membranes. Proc. Natl. Acad. Sci. U.S.A. 102, 3272–3277 (2005)CrossRefGoogle Scholar
  21. 21.
    Bruckner, R.J., Mansy, S.S., Ricardo, A., Mahadevan, L., Szostak, J.W.: Flip-flop-induced relaxation of bending energy: implications for membrane remodeling. Biophys. J. 97, 3113–3122 (2009)CrossRefGoogle Scholar
  22. 22.
    Peterlin, P., Arrigler, V., Kogej, K., Svetina, S., Walde, P.: Growth and shape transformations of giant phospholipid vesicles upon interaction with an aqueous oleic acid suspension. Chem. Phys. Lipids 159, 67–76 (2009)CrossRefGoogle Scholar
  23. 23.
    van Meer, G., Voelker, D.R., Feigenson, G.W.: Membrane lipids: where they are and how they behave. Nat. Rev. Mol. Cell Biol. 9, 112–124 (2008)CrossRefGoogle Scholar
  24. 24.
    Rajasekharan, A., Gummadi, S.N.: Inhibition of biogenic membrane flippase activity in reconstituted ER proteoliposomes in the presence of low cholesterol levels. Cell. Mol. Biol. Lett. 17, 136–152 (2012)CrossRefGoogle Scholar
  25. 25.
    Kol, M.A., de Kruijff, B., de Kroon, A.I.P.M.: Semin. Phospholipid flip-flop in biogenic membranes: what is needed to connect opposite sides. Semin. Cell Dev. Biol. 13, 163–170 (2002)CrossRefGoogle Scholar
  26. 26.
    Sanyal, S., Menon, A.K.: Flipping lipids: why an’ what’s the reason for? ACS Chem. Biol. 4, 895–909 (2009)CrossRefGoogle Scholar
  27. 27.
    Contreras, F.-X., Sánchez-Magraner, L., Alonso, A., Goñi, F.M.: Transbilayer (flip-flop) lipid motion and lipid scrambling in membranes. FEBS Lett. 584, 1779–1786 (2010)CrossRefGoogle Scholar
  28. 28.
    Sharom, F.J.: Flipping and flopping—lipids on the move. IUBMB Life 63, 736–746 (2011)Google Scholar
  29. 29.
    de Vries, A.H., Mark, A.E., Marrink, S.J.: Molecular dynamics simulation of the spontaneous formation of a small DPPC vesicle in water in atomistic detail. J. Am. Chem. Soc. 126, 4488–4489 (2004)CrossRefGoogle Scholar
  30. 30.
    Bennett, W.F.D., MacCallum, J.L., Hinner, M.J., Marrink, S.J., Tieleman, D.P.: Molecular view of cholesterol flip-flop and chemical potential in different membrane environments. J. Am. Chem. Soc. 131, 12714–12720 (2009)CrossRefGoogle Scholar
  31. 31.
    Bennett, W.F.D., Tieleman, D.P.: Water defect and pore formation in atomistic and coarse-grained lipid membranes: pushing the limits of coarse graining. J. Chem. Theory Comput. 7, 2981–2988 (2011)CrossRefGoogle Scholar
  32. 32.
    Mouret, L., Da Costa, G., Bondon, A.: Sterols associated with small unilamellar vesicles (SUVs): intrinsic mobility role for 1H NMR detection. Magn. Reson. Chem. 52, 339–344 (2014)CrossRefGoogle Scholar
  33. 33.
    Bretscher, M.S.: Asymmetrical lipid bilayer structure for biological membranes. Nat. New Biol. 236, 11–12 (1972)CrossRefGoogle Scholar
  34. 34.
    Cullis, P.R., de Kruijff, B.: 31P-NMRstudies of unsonicated aqueous dispersions of neutral and acidic phospholipids. Effects of phase transitions, p2H and divalent cations on the motion in the phosphate region of the polar headgroup. Biochim. Biophys. Acta 507, 207–218 (1978)CrossRefGoogle Scholar
  35. 35.
    Pomorski, T.S., Hrafnsdottir, S., Devaux, P.F., van Meer, G.: Lipid distribution and transport across cellular membranes. Semin. Cell Dev. Biol. 12, 139–148 (2001)CrossRefGoogle Scholar
  36. 36.
    Daleke, D.L.: Regulation of transbilayer plasma membrane phospholipid asymmetry. J. Lipid Res. 44, 233–242 (2003)CrossRefGoogle Scholar
  37. 37.
    Gummadi, S.N., Kumar, K.S.: The mystery of phospholipid flip-flop in biogenic membranes. Cell. Mol. Biol. Lett. 10, 101–121 (2005)Google Scholar
  38. 38.
    Homan, R., Pownall, H.J.: Transbilayer diffusion of phospholipids: dependence on headgroup structure and acyl chain length. Biochim. Biophys. Acta 938, 155–166 (1988)CrossRefGoogle Scholar
  39. 39.
    Anglin, T.C., Liu, J., Conboy, J.C.: Facile lipid flip-flop in a phospholipid bilayer induced by gramicidin A measured by sum-frequency vibrational spectroscopy. Biophys. J. 92, L01–L03 (2007)CrossRefGoogle Scholar
  40. 40.
    Anglin, T.C., Brown, K.L., Conboy, J.C.: Phospholipid flip-flop modulated by transmembrane peptides WALP and melittin. J. Struct. Biol. 168, 37–52 (2009)CrossRefGoogle Scholar
  41. 41.
    Pantaler, E., Kamp, D., Haest, C.W.: Acceleration of phospholipid flip-flop in the erythrocyte membrane by detergents differing in polar head group and alkyl chain length. Biochim. Biophys. Acta 1509, 397–408 (2000)CrossRefGoogle Scholar
  42. 42.
    Urbina, P., Alonso, A., Contreras, F.X., Goñi, F.M., López, D.J., Montes, L.R., Sot, J.: Alkanes are not innocuous vehicles for hydrophobic reagents in membrane studies. Chem. Phys. Lipids 139, 107–114 (2006)CrossRefGoogle Scholar
  43. 43.
    Brown, K.L., Conboy, J.C.: Lipid flip-flop in binary membranes composed of phosphatidylserine and phosphatidylcholine. J. Phys. Chem. B 117, 15041–15050 (2013)CrossRefGoogle Scholar
  44. 44.
    Liu, J., Brown, K.L., Conboy, J.C.: The effect of cholesterol on the intrinsic rate of lipid flip–flop as measured by sum-frequency vibrational spectroscopy. Faraday Discuss. 161, 45–61 (2013)CrossRefGoogle Scholar
  45. 45.
    Gerelli, Y., Porcar, L., Fragneto, G.: Lipid rearrangement in DSPC/DMPC bilayers: a neutron reflectometry study. Langmuir 28, 15922–15928 (2012)CrossRefGoogle Scholar
  46. 46.
    Brown, K.L., Conboy, J.C.: Phosphatidylglycerol flip-flop suppression due to headgroup charge repulsion. J. Phys. Chem. B 119, 10252–10260 (2015)CrossRefGoogle Scholar
  47. 47.
    John, K., Schreiber, S., Kubelt, J., Herrmann, A., Müller, P.: Transbilayer movement of phospholipids at the main phase transition of lipid membranes: implications for rapid flip-flop in biological membranes. Biophys. J. 83, 3315–3323 (2002)CrossRefGoogle Scholar
  48. 48.
    Liu, J., Conboy, J.C.: 1,2-Diacyl-phosphatidylcholine flip-flop measured directly by sum-frequency vibrational spectroscopy. Biophys. J. 89, 2522–2532 (2005)CrossRefGoogle Scholar
  49. 49.
    Zachowski, A., Devaux, P.F.: Transmembrane movement of lipids. Experientia 46, 644–656 (1990)CrossRefGoogle Scholar
  50. 50.
    Schaffer, J.E.: Fatty acid transport: the roads taken. Am. J. Physiol. Endocrinol. Metab. 282, E239–E246 (2002)CrossRefGoogle Scholar
  51. 51.
    Hamilton, J.A.: Fast flip-flop of cholesterol and fatty acids in membranes: implications for membrane transport proteins. Curr. Opin. Lipidol. 14, 263–271 (2003)CrossRefGoogle Scholar
  52. 52.
    Steck, T.L., Lange, Y.: How slow is the transbilayer diffusion (flip-flop) of cholesterol? Biophys. J. 102, 945–946 (2012)CrossRefGoogle Scholar
  53. 53.
    Ma, S., Li, H., Tian, K., Ye, S., Luo, Y.: In situ and real-time SFG measurements revealing organization and transport of cholesterol analogue 6-ketocholestanol in a cell membrane. J. Phys. Chem. Lett. 5, 419–424 (2014)CrossRefGoogle Scholar
  54. 54.
    Imparato, A., Shillcock, J.C., Lipowsky, R.: Lateral and transverse diffusion in two-bilayer component membrane. Eur. Phys. J. E 11, 21–28 (2003)CrossRefGoogle Scholar
  55. 55.
    Leontiadou, H., Mark, A.E., Marrink, S.J.: Antimicrobial peptides in action. J. Am. Chem. Soc. 128, 12156–12161 (2006)CrossRefGoogle Scholar
  56. 56.
    Dickey, A.N., Faller, R.: How alcohol chain-length and concentration modulate hydrogen bond formation in a lipid bilayer. Biophys. J. 92, 2366–2376 (2007)CrossRefGoogle Scholar
  57. 57.
    Kandasamy, S., Larson, R.: Cation and anion transport through hydrophilic pores in lipid bilayers. J. Chem. Phys. 125, 074901 (2006)CrossRefGoogle Scholar
  58. 58.
    Gurtovenko, A.A., Onike, O.I., Anwar, J.: Chemically induced phospholipid translocation across biological membranes. Langmuir 24, 9656–9660 (2008)CrossRefGoogle Scholar
  59. 59.
    Gurtovenko, A.A., Vattulainen, I.: Molecular mechanism for lipid flip-flops. J. Phys. Chem. B 111, 13554–13559 (2007)CrossRefGoogle Scholar
  60. 60.
    Róg, T., Stimson, L.M., Pasenkiewicz-Gierula, M., Vattulainen, I., Karttunen, M.: Replacing the cholesterol hydroxyl group with the ketone group facilitates sterol flip-flop and promotes membrane fluidity. J. Phys. Chem. B 112, 1946–1952 (2008)CrossRefGoogle Scholar
  61. 61.
    Arai, N., Akimoto, T., Yamamoto, E., Yasui, M., Yasuoka, K.: Poisson property of the occurrence of flip-flops in a model membrane. J. Chem. Phys. 140, 064901 (2014)CrossRefGoogle Scholar
  62. 62.
    Kucerka, N., Perlmutter, J.D., Pan, J., Tristram-Nagle, S., Katsaras, J., Sachs, J.N.: The effect of cholesterol on short- and long-chain monounsaturated lipid bilayers as determined by molecular dynamics simulations and X-ray scattering. Biophys. J. 95, 2792–2805 (2008)CrossRefGoogle Scholar
  63. 63.
    Choubey, A., Kalia, R.K., Malmstadt, N., Nakano, A., Vashishta, P.: Cholesterol translocation in a phospholipid membrane. Biophys. J. 104, 2429–2436 (2013)CrossRefGoogle Scholar
  64. 64.
    Marrink, S.J., Risselada, H.J., Yefimov, S., Tieleman, D.P., De Vries, A.H.: The MARTINI force field: coarse grained model for biomolecular simulations. J. Phys. Chem. B 111, 7812–7824 (2007)CrossRefGoogle Scholar
  65. 65.
    Marrink, S.J., Tieleman, D.P.: Perspective on the martini model. Chem. Soc. Rev. 42, 6801–6822 (2013)CrossRefGoogle Scholar
  66. 66.
    Marrink, S.J., de Vries, A.H., Harroun, T.A., Katsaras, J., Wassall, S.R.: Cholesterol shows preference for the interior of polyunsaturated lipid membranes. J. Am. Chem. Soc. 130, 10–11 (2008)CrossRefGoogle Scholar
  67. 67.
    Harroun, T.A., Katsaras, J., Wassall, S.R.: Cholesterol hydroxyl group is found to reside in the center of a polyunsaturated lipid membrane. Biochemistry 45, 1227–1233 (2006)CrossRefGoogle Scholar
  68. 68.
    Ogushi, F., Ishitsuka, R., Kobayashi, T., Sugita, Y.: Rapid flip-flop motions of diacylglycerol and ceramide in phospholipid bilayers. Chem. Phys. Lett. 522, 96–102 (2012)CrossRefGoogle Scholar
  69. 69.
    Risselada, H.J., Marrink, S.J.: The molecular face of lipid rafts in model membranes. PNAS 105, 17367–17372 (2008)CrossRefGoogle Scholar
  70. 70.
    Ipsen, J.H., Karlström, G., Mourtisen, O.G., Wennerström, H., Zuckermann, M.: Phase-equilibria in the phosphatidylcholine-cholesterol system. Biochim. Biophys. Acta 905, 162–172 (1987)CrossRefGoogle Scholar
  71. 71.
    Yesylevskyy, S.O., Demchenko, A.P.: How cholesterol is distributed between monolayers in asymmetric lipid membranes. Eur. Biophys. J. 41, 1043–1054 (2012)CrossRefGoogle Scholar
  72. 72.
    Yesylevskyy, S.O., Demchenko, A.P., Kraszewski, S., Ramseyer, C.: Cholesterol induces uneven curvature of asymmetric lipid bilayers. ScientificWorldJournal 2013, 965230 (2013)CrossRefGoogle Scholar
  73. 73.
    Yesylevskyy, S.O., Demchenko, A.P.: Cholesterol behavior in asymmetric lipid bilayers: insights form molecular dynamics simulations. Methods Mol. Biol. 1232, 291–306 (2015)CrossRefGoogle Scholar
  74. 74.
    Ingólfsson, H.I., Melo, M.N., van Eerden, F.J., Arnarez, C., Lopez, C.A., Wassenaar, T.A., Periole, X., de Vries, A.H., Tieleman, D.P., Marrink, S.J.: Lipid organization of the plasma membrane. J. Am. Chem. Soc. 136, 14554–14559 (2014)CrossRefGoogle Scholar
  75. 75.
    Venturoli, M., Sperotto, M.M., Kranenburg, M., Smit, B.: Mesoscopic models of biological membranes. Phys. Rep. 437, 1–54 (2006)CrossRefGoogle Scholar
  76. 76.
    Ramachandran, S., Kumar, P.B.S., Laradji, M.: Lipid flip-flop driven mechanical and morphological changes in model membranes. J. Chem. Phys. 129, 125104 (2008)CrossRefGoogle Scholar
  77. 77.
    Martí, J., Csajka, F.S.: Flip-flop dynamics in a model lipid bilayer membrane. Europhys. Lett. 61, 409–414 (2003)CrossRefGoogle Scholar
  78. 78.
    Martí, J., Csajka, F.S.: Transition path sampling study of flip-flop transitions in model lipid bilayer membranes. Phys. Rev. E 69, 061918 (2004)CrossRefGoogle Scholar
  79. 79.
    Martí, J.: A molecular dynamics transition path sampling study of model lipid bilayer membranes in aqueous environments. J. Phys.: Condens. Matter 16, 5669–5678 (2004)Google Scholar
  80. 80.
    Bolhuis, P.G., Chandler, D., Dellago, C., Geissler, P.L.: Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53, 291–318 (2002)CrossRefGoogle Scholar
  81. 81.
    Bennett, W.F.D., MacCallum, J.L., Tieleman, D.P.: Thermodynamic analysis of the effect of cholesterol on dipalmitoylphosphatidylcholine lipid membranes. J. Am. Chem. Soc. 131, 1972–1978 (2009)CrossRefGoogle Scholar
  82. 82.
    Sapay, N., Bennett, W.F.D., Tieleman, D.P.: Thermodynamics of flip-flop and desorption for a systematic series of phosphatidylcholine lipids. Soft Matter 5, 3295–3302 (2009)CrossRefGoogle Scholar
  83. 83.
    Neale, C., Bennett, W.F.D., Tieleman, D.P., Pomes, R.: Statistical convergence of equilibrium properties in simulations of molecular solutes embedded in lipid bilayers. J. Chem. Theory Comput. 7, 4175–4188 (2011)CrossRefGoogle Scholar
  84. 84.
    Tielemann, D.P., Marrink, S.-J.: Lipids out of equilibrium: energetics of desorption and pore mediated flip-flop. J. Am. Chem. Soc. 128, 12462–12467 (2006)CrossRefGoogle Scholar
  85. 85.
    Bennett, W.F.D., Sapay, N., Tieleman, D.P.: Atomistic simulations of pore formation and closure in lipid bilayers. Biophys. J. 106, 210–219 (2014)CrossRefGoogle Scholar
  86. 86.
    Kol, M.A., de Kroon, A.I.P.M., Rijkers, D.T.S., Killian, J.A., de Kruijff, B.: Membrane-spanning peptides induce phospholipid flop: a model for phospholipid translocation across the inner membrane of E. coli. Biochemistry 40, 10500–10506 (2001)CrossRefGoogle Scholar
  87. 87.
    Bennett, W.F.D., Tieleman, D.P.: Molecular simulation of rapid translocation of cholesterol, diacylglycerol and ceramide in model raft and non-raft membranes. J. Lipid Res. 53, 421–429 (2012)CrossRefGoogle Scholar
  88. 88.
    Neuvonen, M., Manna, M., Mokkila, S., Javanainen, M., Róg, T., Liu, Z., Bittman, R., Vattulainen, I., Ikonen, E.: Enzymatic oxidation of cholesterol: properties and functional effects of cholestenone in cell membranes. PLoS ONE 9, e103743 (2014)CrossRefGoogle Scholar
  89. 89.
    Filipe, H.A.L., Moreno, M.J., Róg, T., Vattulainen, I., Loura, L.M.S.: How to tackle the issues in free energy simulations of long amphiphiles interacting with lipid membranes: convergence and local membrane deformations. J. Phys. Chem. B. 118, 3572–3581 (2014)CrossRefGoogle Scholar
  90. 90.
    Jo, S., Rui, J., Lim, J.B., Klauda, J.B., Im, W.: Cholesterol flip-flop: insights from free energy simulation studies. J. Phys. Chem. B 114, 13342–13348 (2010)CrossRefGoogle Scholar
  91. 91.
    Pan, A.C., Sezer, D., Roux, B.: Finding transition pathways using the string method with swarms of trajectories. J. Phys. Chem. B 112, 3432–3440 (2008)CrossRefGoogle Scholar
  92. 92.
    Wei, C., Pohorille, A.: Flip-flop of oleic acid in a phospholipid membrane: rate and mechanism. J. Phys. Chem. B 118, 12919–12926 (2014)CrossRefGoogle Scholar
  93. 93.
    Parisio, G., Sperotto, M.M., Ferrarini, A.: Flip-flop of steroids in phospholipid bilayers: effects of the chemical structure on transbilayer diffusion. J. Am. Chem. Soc. 134, 12198–12208 (2012)CrossRefGoogle Scholar
  94. 94.
    Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)MathSciNetMATHCrossRefGoogle Scholar
  95. 95.
    van Kampen, N.G.: Stochastic Processes in Physics and Chemistry, 3rd edn. Elsevier, Amsterdam (2007)MATHGoogle Scholar
  96. 96.
    Langer, J.S.: Statistical theory of the decay of metastable states. Ann. Phys. 54, 258–275 (1969)CrossRefGoogle Scholar
  97. 97.
    Parisio, G., Ferrarini, A.: Solute partitioning into lipid bilayers: an implicit model for nonuniform and ordered environment. J. Chem. Theory Comput. 6, 2267–2280 (2010)CrossRefGoogle Scholar
  98. 98.
    Ren, W., Vanden-Eijnden, E.: String method for the study of rare events. Phys. Rev. B 66, 052301 (2002)Google Scholar
  99. 99.
    Jämbeck, J.P.M., Lyubartsev, A.P.: Exploring the free energy landscape of solutes embedded in lipid bilayers. J. Phys. Chem. Lett. 4, 1781–1787 (2013)CrossRefGoogle Scholar
  100. 100.
    Parisio, G., Stocchero, M., Ferrarini, A.: Passive membrane permeability: beyond the standard solubility-diffusion model. J. Chem. Theory Comput. 9, 5236–5246 (2013)CrossRefGoogle Scholar
  101. 101.
    Depa, P., Chen, C., Maranas, J.K.: Why are coarse-grained force fields too fast? A look at dynamics of four coarse-grained polymers. J. Chem. Phys. 134, 014903 (2011)CrossRefGoogle Scholar
  102. 102.
    Huang, K., Garcia, A.E.: Effects of truncating van der Waals interactions in lipid bilayer simulations. J. Chem. Phys. 141, 105101 (2014)CrossRefGoogle Scholar
  103. 103.
    Davis, R.S., Kumar, P.B.S., Sperotto, M.M., Laradji, M.: Prediction of phase separation in three-component lipid membranes by the MARTINI force field. J. Phys. Chem. B 117, 4072–4080 (2013)CrossRefGoogle Scholar
  104. 104.
    Yanagisawa, M., Imai, M., Komura, S., Ohta, T.: Growth dynamics of domains in ternary fluid vesicles. Biophys. J. 92, 115–125 (2007)CrossRefGoogle Scholar
  105. 105.
    Veatch, S.L., Keller, S.L.: Organization in lipid membranes containing cholesterol. Phys. Rev. Lett. 89, 268101 (2002)CrossRefGoogle Scholar
  106. 106.
    Veatch, S.L., Keller, S.L.: Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 85, 3074–3083 (2003)CrossRefGoogle Scholar
  107. 107.
    Li, L., Liang, X., Lin, M., Qiu, F., Yang, Y.: Budding dynamics of multicomponent tubular vesicles. J. Am. Chem. Soc. 127, 17996–17997 (2005)CrossRefGoogle Scholar
  108. 108.
    Moro, G.J., Ferrarini, A., Polimeno, A., Nordio, P.L.: Models of conformational dynamics. In: Dorfmüller, Th. (ed.) Reactive and Flexible Molecules in Liquids, pp. 107–139. Kluwer Academic Publishers, Dordrecht (1989)CrossRefGoogle Scholar

Copyright information

© Indian Institute of Technology Madras 2016

Authors and Affiliations

  • Giulia Parisio
    • 1
  • Alberta Ferrarini
    • 1
  • Maria Maddalena Sperotto
    • 2
  1. 1.Department of Chemical SciencesUniversity of PadovaPadovaItaly
  2. 2.Center for Biological Sequence Analysis, Department of Systems BiologyTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations