Abstract
The Smoluchowski equation with an energy profile of a special type and an assumed hydrophobic (“half”) pore source term is used to describe the process of hydrophilic pore formation in a lipid bilayer at the gel-liquid phase transition. The source term reflects the occurrence of molecule packing defects in a lipid bilayer at phase transition. The time sequences of the pore formation and closure events are treated as non-stationary, second-order Erlang flows whose characteristics depend on the equation solution. The computed distributions of the time intervals between hydrophilic pores, and pore lifetimes agree with the previously published experimental interpulse interval and pulse duration histograms for the current fluctuations through planar bilayer membranes of DPPC immersed in a LiCl aqueous solution containing polyethylene glycol. Thus, the statistical analysis of pore formation and closure times leads us to conclude that firstly, the increased permeability of a lipid bilayer during the gel-liquid phase transition is accounted for by the emergence of additional hydrophobic defects in the heterogeneous structure of the bilayer and secondly, that the non-exponential distributions of the lipid channel closed and open times observed in experiments are evidence that the process of hydrophilic pore formation is not a one-step process but involves at least two dependent events.
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Andersen T, Kyrsting A, Bendix PM (2014) Local and transient permeation events are associated with local melting of giant liposomes. Soft Matter 10:4268–4274
Anosov AA, Kuprijanova MS, Nemchenko OYu, Norik VP, Sergeenko EV, Smirnova EYu (2015) States of lipid pores in bilayer lipid membranes at a phase transition in a LiCl solution with addition of molecules of polyethylene glycol. Biophysics 60:73–78
Anosov AA, Sharakshane AA, Smirnova EYu, Nemchenko OYu (2016) Application of the Smoluchowski equation with a source term to the model of lipid pore formation during a phase transition. Biophysics 61:936–941
Anosov AA, Sharakshane AA, Smirnova EY, Nemchenko OYu (2017) Bilayer permeability during phase transition as an Erlang flow of hydrophilic pores resulting from diffusion in the radius space. Biochemistry (Moscow) Suppl Ser A Membr Cell Biol 11:8–16
Antonov VF, Petrov VV, Molnar AA, Predvoditelev DA, Ivanov AS (1980) The appearance of single-ion channels in unmodified lipid bilayer membranes at the phase transition temperature. Nature 283(5747):585–586
Antonov VF, Anosov AA, Norik VP, Smirnova EYu (2005) Soft perforation of planar bilayer lipid membranes of dipalmitoylphosphatidylcholine at the temperature of the phase transition from the liquid crystalline to the gel state. Eur Biophys J 34:155–162
Antonov VF, Smirnova EYu, Anosov AA, Norik VP, Nemchenko OYu (2008) PEG blocking of single pores arising on phase transitions in unmodified lipid bilayers. Biophysics 53:390–395
Böckmann R, de Groot R, Kakorin S, Neumann E, Grubmüller H (2008) Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. Biophys J 95:1837–1850
Cruseiro-Hansso L, Mouritsen OG, Singer MA, Zuckermann M (1988) Passive ion permeability of lipid membranes modeled via lipid-domain interfacial area. BBA 944:63–72
Evans E, Heinrich V, Ludwig F, Rawicz W (2003) Dynamic tension spectroscopy and strength of biomembranes. Biophys J 85:2342–2350
Feller SE, Pastor RW (1996) On simulating lipid bilayers with an applied surface tension: periodic boundary conditions and undulations. Biophys J 71(1996):1350–1355
Freeman SA, Wang MA, Weaver JC (1994) Theory of electroporation of planar bilayer membranes: predictions of the aqueous area, change in capacitance, and pore-pore separation. Biophys J 67:42–56
Gallaher J, Wodzinska K, Heimburg T, Bier M (2010) Ion-channel-like behavior in lipid bilayer membranes at the melting transition. Phys Rev E 81:061925
Glaser RW, Leikin SL, Chernomordik LV, Pastushenko VF, Sokirko AV (1988) Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. Biochim Biophys Acta 940:275–287
Haverstick DM, Glaser M (1988) Visualization of domain formation in inner and outer leaflets of a phospholipid bilayer. J Cell Biol 106:1885–1892
Heimburg T (2010) Lipid ion channels. Biophys Chem 150:2–22
John K, Schreiber S, Kubelt J, Herrmann A, Muller P (2002) 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
Karlin S, Taylor HM (1975) A first course in stochastic processes, 2nd edn. Academic Press, New York, p. 155
Little JD (1961) A proof for the queuing formula: L = λ W. Oper Res 9:383–387
Melikov KC, Frolov VA, Shcherbakov A, Samsonov AV, Chizmadzhev YuA, Chernomordik LV (2001) Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer. Biophys J 80:1829–1836
Nagle JF, Tristram-Nagle S (2000) Structure of lipid bilayers. Biochim Biophys Acta 1469:159–195
Powell KT, Weaver JC (1986) Transient aqueous pores in bilayer membranes: a statistical theory. Bioelectrochem Bioelectroenerg 15:211–227
Saulis G (1997) Pore disappearance in a cell after electroporation: theoretical simulation and comparison with experiments. Biophys J 73:1299–1309
Sillerud LO, Barnett RE (1982) Lack of transbilayer coupling in phase transitions of phosphatidylcholine vesicles. Biochemistry 21:1756–1760
Smith K, Neu J, Krassowska W (2003) Model of creation and evolution of stable electropores for DNA delivery. Biophys J 86:2813–2826
Stewart DA, Gowrishankar TR, Weaver JC (2004) Transport lattice approach to describing cell electroporation: use of a local asymptotic model. IEEE Trans Plasma Sci 32:1696–1708
Teleman DP, Bentz J (2008) Molecular dynamic simulation of the evolution of hydrophobic defects in one monolayer of PC bilayers. Relevance for membrane fusion mechanisms. Biophys J 83:1501–1510
Tieleman DP, Leontiadou H, Marrink SJ (2003) Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. J Am Chem Soc 125:6382–6383
Tien HT (1989) Interfacial chemistry of bilayer lipid membranes (BLM). Surfactants Solut 8:133–178
Tolpekina TV, den Otter WK, Briels WJ (2004) Nucleation free energy of pore formation in an amphiphilic bilayer studied by molecular dynamics simulations. J Chem Phys 121:12060–12066
Weaver JC, Chizmadzhev YuA (1996) Theory of electroporation: a review. Bioelectrochem Bioenerg 41:135–160
Wohlert J, den Otter WK, Edholm O, Briels WJ (2006) Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations. J Chem Phys 124:154905
Wunderlich B, Leirer C, Idzko A-L, Keyser UF, Wixforth A, Myles VM, Heimburg T, Schneider MF (2009) Phase state dependent current fluctuations in pure lipid membranes. Biophys J 96:4592–4597
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The authors thank Prof. V. F. Antonov for his interest in the work and useful discussion.
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Anosov, A.A., Sharakshane, A.A., Smirnova, E.Y. et al. Erlang flow of hydrophilic pore formation and closure events in a lipid bilayer during phase transition resulting from diffusion in the radius space. Eur Biophys J 47, 297–307 (2018). https://doi.org/10.1007/s00249-017-1261-3
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DOI: https://doi.org/10.1007/s00249-017-1261-3