Chapter 1 Random Processes in the Appearance and Dynamics of an Electropore in a Lipid Membrane

Advances in Planar Lipid Bilayers and Liposomes

Volumn 7, Issue , 2008, Pages 1-38

  Kotulska, Malgorzata ^a   Kubica, Krystian ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46949112006     PISSN: 15544516     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1554-4516(08)00001-X     Document Type: Review

References (142)

1. In: Chang D.C., Chassy B.M., Saunders J.A., and Sowers A.E. (Eds). Guide to Electroporation and Electrofusion (1992), Academic Press, San Diego
2. Neumann E., Kakorin S., and Toensing K. Fundamentals of electroporative delivery of drugs and genes. Bioelectrochem. Bioenerg. 48 (1999) 3-16
3. Weaver J.C., and Chizmadzhev Yu.A. Theory of electroporation: A review. Bioelectrochem. Bioenerg. 41 (1996) 135-160
4. Kotulska M. Electro-Nanopores in the Lipid Membrane and Their Application in Medicine (2007), IBIB, Warsaw (habilitation thesis)
5. Stämpfli R. Reversible electrical breakdown of the excitable membrane of a Ranvier node. Ann. Acad. Bras. Cienc. 30 (1958) 57-63
6. Neumann E., and Rosenheck K. Permeability changes induced by electric impulses in vesicular membranes. J. Membr. Biol. 10 (1972) 279-290
7. Benz R., Beckers F., and Zimmermann U. Reversible electrical breakdown of lipid bilayer membranes: A charge-pulse relaxation study. J. Membr. Biol. 4 (1979) 181-204
8. el-Mashak E.M., and Tsong T.Y. Ion selectivity of temperature-induced and electric field induced pores in dipalmitoylphosphatidylcholine vesicles. Biochemistry 24 (1985) 2884-2888
9. Movileanu L., Popescu D., Ion S., and Popescu A.I. Transbilayer pores induced by thickness fluctuations. Bull. Math. Biol. 68 (2006) 1231-1255
10. Zhelev D.V., and Needham D. Tension-stabilized pores in giant vesicles: Determination of pore size and pore line tension. Biochim. Biophys. Acta 1147 (1993) 89-104
11. Winterhalter M., and Helfrich W. Effect of voltage on pores in membranes. Phys. Rev. A 36 (1987) 5874-5876
12. Neumann E., Schaefer-Ridder M., Wang Y., and Hofschneider P.H. Gene transfer into mouse lyoma cells by electroporation in high electric fields. EMBO J. 1 (1982) 841-845
13. Mir L.M., and Orlowski S. Mechanisms of electrochemotherapy. Adv. Drug Deliv. Rev. 35 (1999) 107-118
14. Beebe S.J., Fox P.M., Rec L.J., Lauren E., Willis K., and Schoenbach K.H. Nanosecond, high intensity pulsed electric fields induce apoptosis in human cells. FASEB 17 (2003) 1493-1495
15. Roth B.J., and Krassowska W. The induction of reentry in cardiac tissue. The missing link: how electric fields alter transmembrane potential. Chaos 8 (1998) 204-220
16. Frey W., White J.A., Price R.O., Blackmore P.F., Joshi R.P., Nuccitelli R., Beebe S.J., Schoenbach K.H., and Kolb J.F. Plasma membrane voltage changes during nanosecond pulsed electric field exposure. Biophys. J. 90 (2006) 3608-3615
17. Vernier T.P., Sun Y., and Gundersen M.A. Nanoelectropulse driven membrane perturbation and small molecule permeabilization. BMC Cell Biol. 7 (2006) 37-53
18. Kotnik T., Pucihar G., Rebersek M., Miklavcic D., and Mir L.M. Role of pulse shape in cell membrane electropermeabilization. Biochim. Biophys. Acta 1614 (2003) 193-200
19. Kalinowski S., Ibron G., Bryl K., and Figaszewski Z. Chronopotentiometric studies of electroporation of bilayer lipid membranes. Biochim. Biophys. Acta 1369 (1998) 204-212
20. Robello M., and Gliozzi A. Conductance transition induced by an electric field in lipid bilayers. Biochim. Biophys. Acta 982 (1989) 173-176
21. Kotulska M. Natural fluctuations of an electropore show fractional Lévy stable motion. Biophys. J. 92 (2007) 2412-2421
22. Jain K.M., and Wagner R.C. Introduction to Biological Membranes (1980), John Wiley and Sons, New York 1-382
23. Hauser H. Conformation of phospholipids crystal structure of a lyso-phosphatidylcholine analogue. J. Mol. Biol. 137 (1980) 249-264
24. Hauser H., Pascher I., Pearson R.H., and Sundell S. Preferred conformation and molecular packing of phosphatidylethanolamine and phosphatidylcholine. Biochim. Biophys. Acta 650 (1981) 21-51
25. Tieleman D.P., Marrink S.J., and Berendsen H.J.C. A computer perspective of membranes: Molecular dynamics studies of lipid bilayer systems. Biochim. Biophys. Acta 1331 (1997) 235-270
26. Edidin M. Rotational and lateral diffusion of membrane proteins and lipids: Phenomena and function. In: Klausner R.D., Kempf Ch., and van Renswoude J. (Eds). Membrane Structure and Function, Current Topics in Membrane and Transport Vol. 29 (1987), Academic Press
27. Papahadjopoulos D., and Kimelberg H.K. Phospholipid vesicles (liposomes) as models for biological membranes: Their properties and interactions with cholesterol and proteins. In: Davson S.G. (Ed). Progress in Surface Sciences (1973), Pergamon Press, Oxford 141-232
28. Kunitake T. Syntheses aggregate morphologies and applications of membrane-forming amphiphiles. J. Am. Chem. Soc. 99 (1977) 3860-3871
29. Singer S.J., and Nicolson G.L. The fluid mosaic model of the structure of cell membranes. Science 175 (1972) 720-731
30. Seelig J., and Seelig A. Lipid conformation in model membranes and biological membranes. Q. Rev. Biophys. 13 (1980) 19-61
31. Lagaly G. Kink-block and gauche-block structures of bimolecular films. Angew. Chem. Int. Ed. Engl. 15 (1976) 576-586
32. Seelig J., and Niederberg W. Two pictures of a lipid bilayer. A comparison between deuterium label and spin-label experiments. Biochemistry 13 (1974) 1585-1588
33. Nagle J.F. Theory of biomembrane phase transitions. J. Chem. Phys. 58 1 (1973) 252-264
34. Scott H.L. A theoretical model for lipid monolayer transitions. Biochim. Biophys. Acta (BBA) 406 (1975) 329-346
35. McCammon J.A., and Deutch J.M. Semiempirical models for biomembrane phase transitions and phase separations. J. Am. Chem. Sci. 97 (1975) 6675-6681
36. Pechhold W., and Blasenberg S. Molekulbewegung in polymeren. Kolloid Z. Z. Polym. 241 (1970) 955-976
37. Blasenbrey S., and Pechhold W. Theorie der phasenumwandlung in polymeren. Ber. Bunsenges Phys. Chem. 74 (1970) 784-796
38. Baumann M. Early stage shape change of human erythrocytes after application of electric field pulses. Mol. Memb. Biol. 18 (2001) 153-160
39. Hitchcock P.B., Mason R., Thomas K.M., and Shipley G.G. Structural chemistry of 1,2 dilauroyl-dl-phosphatidylethanolamine: Molecular conformation and intermolecular packing of phospholipids. Proc. Natl. Acad. Sci. USA 71 8 (1974) 3036-3040
40. Healy T.W., and Ralston J. Specific cation effects under monolayers of octadecanol. Nature 220 (1968) 1026-1027
41. Kuczera J., Janas T., Przestalski S., Witek S., and Owicimska M. Influence of some amphiphilic derivatives of glycine esters on sulphate ion transport across lecithin liposome membrane. Studia Biophys. 105 (1985) 167-176
42. Sackman E., Fischer A., and Frey W. Polymorphism of monolayers of monomeric and macromolecular lipids: On the defect structure of crystalline phases and the possibility of hexatic order formation in physics of amphiphilic layers. In: Meunier J., Langevin D., and Boccara V. (Eds). Physics of amphiphilic layers (1987), Springer, Berlin
43. Langner M., Pruchnik H., and Kubica K. The effect of the lipid bilayer state on fluorescence intensity of fluorescein-PE in a saturated lipid bilayer. Z. Naturforsch. 55 (2000) 418-424
44. Kubica K. Monte Carlo simulation towards ripple phase modeling. Comput. Chem. 25 (2001) 245-250
45. Kubica K. Computer simulation studies on significance of lipid polar head orientation. Comput. Chem. 26 (2002) 351-356
46. Langner M., and Kubica K. The electrostatics of lipid surfaces. Chem. Phys. Lipids 101 (1999) 3-35
47. Lee G.M., Ishihara A., and Jacobson K.A. Direct observation of Brownian motion of lipids in a membrane. Proc. Natl. Acad. Sci. USA 88 14 (1991) 6274-6278
48. Sugar I.P., and Biltonen R.L. Lateral diffusion of molecules in two-component lipid bilayer: A Monte Carlo simulation study. J. Phys. Chem. B 109 15 (2005) 7373-7386
49. Kornberg R.D., and McConnell A. Inside-outside transitions of phospholipids in vesicle membranes. Biochemistry 10 (1971) 1111-1120
50. Roseman M., Litman B.J., and Thompson T.E. Transbilayer exchange of phosphatidylethanolamine in single-walled bilayer vesicles. Biochemistry 14 (1975) 4826-4830
51. Hamilton J.A. Fatty acid transport: Difficult or easy?. J. Lipid Res. 39 (1998) 467-481
52. Kamp F., Guo W., Souto R., Pilch P.F., Corkey B.E., and Hamilton J.A. Rapid flip-flop of oleic acid across the plasma membrane of adipocytes. J. Biol. Chem. 278 (2003) 7988-7995
53. Armstrong V.T., Brzustowicz M.R., Wassall S.R., Jenski L.J., and Stillwell W. Rapid flip-flop in polyunsaturated (docosahexaenoate) phospholipid membranes. Arch. Biochem. Biophys. 414 (2003) 74-82
54. Dickey A.N., and Faller R. How alcohol chain-length and concentration modulate hydrogen bound formation in a lipid bilayer. Biophys. J. 92 (2007) 2366-2376
55. Kamp F., and Hamilton J.A. How fatty acids of different chain length enter and leave cells by free diffusion. Prostaglandins Leukot. Essent. Fatty Acids 75 (2006) 149-159
56. Leventis R., and Silvius J.R. Use of cyclodextrins to monitor transbilayer movement and differential lipid affinities of cholesterol. Biophys. J. 81 (2001) 2257-2267
57. Kampf J.P., Cupp D., and Kleinfeld A.M. Different mechanisms of free acid flip-flop and dissociation revealed by temperature and molecular species dependence of transport across lipid vesicles. J. Biol. Chem. 281 (2006) 21566-21574
58. Moreno M.J., Estronca L.M.B.B., and Vaz W.L.C. Translocation of phospholipids and dithionite permeability in liquid-ordered and liquid-disordered membranes. Biophys. J. 91 (2006) 873-881
59. John K., Schreiber S., Kubelt J., Herrmann A., and Muller P. Transbilayer movement of phospholipids at the main phase transition of lipid membranes: Implications for rapid flip-flop in biological membranes. Biophys. J. 83 6 (2002) 3315-3323
60. Biavas L., Winterhalter M., Meleard P., and Bothorel P. Elasticity of bilayer containing PEG lipids. Europhys. Lett. 41 (1998) 261-266
61. Ibuki Y., Suzuki A., and Goto R. UVA irradiation induces energy-independent phospholipid-flip in mammalian plasma membrane. Photochem. Photobiol. 73 (2001) 513-517
62. Yaroslavov A.A., Melik-Nubarov N.S., and Menger F.M. Polymer-induced flip-flop in biomembranes. Acc. Chem. Res. 39 (2006) 702-710
63. Meshulam T., Simard J.R., Wharton J., Hamilton J.A., and Pilch P.F. Role of caveolin-1 and cholesterol in transmembrane fatty acid movement. Biochemistry 45 (2006) 2882-2893
64. Bootsveld A., Degenhardt R., Kamp D., and Haest C.W.M. On the mechanism of drug-induced acceleration of phospholipid translocation in the human erythrocyte membrane. Mol. Memb. Biol. 21 (2004) 315-322
65. Fahr A., van Hoogevest P., May S., Bergstrand N., and Leigh M.L.S. Transfer of lipophilic drugs between liposomal membranes and biological interfaces: Consequences for drug delivery. Eur. J. Pharm. Sci. 26 (2005) 251-265
66. Stremmel W., Pohl J., Ring A., and Herrmann T. A new concept of cellular uptake and intercellular trafficking of long-chain fatty acids. Lipids 36 (2001) 981-989
67. Li W.J., Nicol F., and Szoka F.C. GALA: A designed synthetic pH-responsive amphipathic peptide with applications in drug and gene delivery. Adv. Drug Deliv. Rev. 56 (2004) 967-985
68. Reif F. Statistical Physics. Berkeley Physics Course Vol. 5 (1967), McGraw-Hill Book Company, New York
69. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21 (1953) 1087-1092
70. Mouritsen O.G. Computers simulations of cooperative phenomena in lipid membranes. In: Brasseur R. (Ed). Molecular Description of Biological Membranes by Computer Aided Conformational Analysis (1990), CRC Press, Boston
71. Pink D.A., Green T.J., and Chapman D. Raman scattering in bilayers of saturated phosphatidylcholines. Experiment and theory. Biochemistry 19 (1980) 349-356
72. Mouritsen O.G., Boothroyd A., Harris R., Jan N., Lookman T., MacDonald L., Pink D.A., and Zuckermann M.J. Computer simulation of the main gel-fluid phase transition of lipid bilayers. J. Chem. Phys. 79 (1983) 2027-2041
73. Kubica K. Pink's model and lipid membranes. Cell. Mol. Biol. Lett. 2 (1997) 257-263
74. Kubica K. The effect of amphiphilic counterions on the gel-fluid phase transition of the lipid bilayer. Appl. Math. Comp. 87 (1997) 261-270
75. Ipsen J., Jorgensen K., and Mouristen O. Density fluctuations in saturated phospholipid bilayers increase as the acyl-chain decreases. Biophys. J. 58 (1990) 1099-1107
76. Ipsen J., Mouristen O., and Zuckermann M. Theory of thermal anomalies in the specific heat of lipid bilayers containing cholesterol. Biophys. J. 56 (1989) 661-667
77. Ipsen J., Mouristen O., and Bloom M. Relationships between lipid membrane area, hydrophobic thickness, and acyl-chain orientational order. Biophys. J. 57 (1990) 405-412
78. Jorgensen K., Ipsen J., Mouritsen O., Bennett D., and Zuckermann M. The effect of density fluctuations on the partitioning of foreign molecules into lipid bilayers: Application to anaesthetics and insecticides. Biochi. Biophys. Acta 1067 (1991) 241-253
79. Jorgensen K., Ipsen J., Mouritsen O., Bennett D., and Zuckermann M. A general model for the interaction of foreign molecules with lipid membranes: Drugs and anaesthetics. Biochim. Biophys. Acta 1062 (1991) 227-238
80. Mouritsen O., and Jorgensen K. Dynamic lipid-bilayer heterogeneity: A mesoscopic vehicle for membrane function?. BioEssays 14 (1992) 129-136
81. Mouritsen O., and Jorgensen K. Dynamical order and disorder in lipid bilayers. Chem. Phys. Lipids 73 (1994) 3-25
82. Sperotto M.M., and Mouritsen O.G. Monte Carlo simulation studies of lipid order parameter profiles near integral membrane proteins. Biophys. J. 59 (1991) 261-270
83. Sperotto M., and Mouritsen O. Lipid enrichment and selectivity of integral membrane proteins in tow-component lipid bilayers. Eur. Biophys. J. 22 (1993) 323-328
84. Zhang Z., Sperotto M., Zuckermann M., and Mouritsen O. A microscopic model for lipid/protein bilayers with critical mixing. Biochim. Biophys. Acta 1147 (1993) 154-160
85. Mouritsen O., and Jorgensen K. Micro- nano- and meso-scale heterogeneity of lipid bilayers and its influence on macroscopic membrane properties. Mol. Membr. Biol. 12 (1995) 15-20
86. Mouritsen O., and Jorgensen K. A new look at lipid-membrane structure in relation to drug research. Pharm. Res. 15 (1998) 1507-1519
87. Jorgensen K., and Mouritsen O.G. Phase separation dynamics and lateral organization of tow-component lipid membranes. Biophys. J. 95 (1995) 942-954
88. Kubica K. Polar head charge of membrane modifiers and their biological activity: The Monte Carlo simulation studies. Task Quarterly 2 (1998) 601-609
89. Kubica K. Computer simulation studies on the significance of lipid polar head charge. Cell. Mol. Biol. Lett. 7 (2002) 971-982
90. Kubica K., Langner M., and Gabrielska J. The dependence of fluorescein-PE fluorescence intensity on lipid bilayer state. Evaluating the interaction between the probe and lipid molecules. Cell. Mol. Biol. Lett. 8 (2003) 943-954
91. Kotulska M., Kubica K., Koronkiewicz S., and Kalinowski S. Modeling the induction of lipid membrane electropermeabilization. Bioelectrochemistry 70 (2007) 64-70
92. Sugar I.P., Tang D., and Parkson Lee-Gau Chong. Monte Carlo simulation of lateral distribution of molecules in a two-component lipid membrane. Effect of long-range repulsive interactions. J. Phys. Chem. 98 (1994) 7201-7210
93. Teissie J., Golzio M., and Rols M.P. Mechanisms of cell membrane electro-permeabilization: A minireview of our present (lack of ?) knowledge. Biochim. Biophys. Acta 1724 (2005) 270-280
94. Tieleman D.P. The molecular basis of electroporation. BMC Biochem. 19 (2004) 5-10
95. Leontiadou H., Mark A.E., and Marrink S.J. Molecular dynamics simulations of hydrophilic pores in lipid bilayers. Biophys. J. 86 (2004) 2156-2164
96. Loison C., Mareschal M., and Schmid F. Pores in bilayer membranes of amphiphilic molecules: Coarse-grained molecular dynamics simulations compared with simple mesoscopic models. J. Chem. Phys. 121 (2004) 1890-1900
97. Tarek M. Membrane electroporation: A molecular dynamics simulation. Biophys. J. 88 (2005) 4045-4053
98. Sugar I.P. A theory of the electric field-induced phase transition of phospholipid bilayers. Biochim. Biophys. Acta 556 (1979) 72-85
99. Schillcock J.C., and Seifert U. Thermally induced proliferation of pores in a model fluid membrane. Biophys. J. 74 (1998) 1754-1766
100. Muller M., and Schick M. Structure and nucleation of pores in polymeric bilayers: A Monte Carlo simulation. J. Chem. Phys. 105 (1996) 8282-8292
101. Marrink S.J., and Berendsen H.J.C. Simulation of water transport through a lipid membrane. J. Phys. Chem. 98 (1994) 4155-4168
102. Glaser R.W., Leikin S.L., Chernomordik L.V., Pastushenko V.F., and Sokirko A.I. Reversible electrical breakdown of lipid bilayers: Formation and evolution of pores. Biochim. Biophys. Acta 940 (1988) 275-287
103. Kubica K. A pore creation in a triangular network model membrane. Comput. Biol. Chem. (2008) in press
104. Diederich A., Günther B., and Winterhalter M. Influence of surface charges on the rupture of black lipid membranes. Phys. Rev. E 58 (1998) 4883-4889
105. S. Koronkiewicz, Badanie procesu elektroporacji i odtwarzania ciaglej struktury dwuwarstwowych membran lipidowych. Ph.D. thesis, University of Warmia and Mazury, Olsztyn.
106. Kotulska M., Koronkiewicz S., and Kalinowski S. Self-similar processes and flicker noise from a fluctuating nanopore in a lipid membrane. Phys. Rev. E 69 (2004) 031920-031930
107. Carrion F.J., De La Maza A., and Parra J.L. The influence of ionic strength and lipid bilayer charge on the stability of liposomes. J. Coll. Interf. Sci. 164 (1994) 78-87
108. Böckman R.A., Hac A., Heimburg T., and Grubmüller H. Effect of sodium chloride on a lipid bilayer. Biophys. J. 85 (2003) 1-9
109. Tatulian S.A. Ionization and ion binding. In: Cevc G. (Ed). Phospholipids Handbook (1993), Marcel Dekker, New York 511-552
110. Gurtovenko A.A. Asymmetry of lipid bilayers induced by monovalent salt: Atomistic molecular-dynamics study. J. Chem. Phys. 122 (2005) 244902
111. Sachs J.N., Nanda H., Petrache H.I., and Woolf T.B. Changes in phosphatidylcholine headgroup tilt and water order induced by monovalent salts: molecular dynamics simulations. Biophys J. 86 (2004) 3772-3782
112. Kotulska M., and Kubica K. Structural and energetic model of the mechanisms for reduced self-diffusion in a lipid bilayer with increasing ionic strength. Phys. Rev. E 72 (2005) 061903-061909
113. Koronkiewicz S., Kalinowski S., and Bryl K. Changes of structural and dynamic properties of model lipid membranes induced by alpha-tocopherol: Implication to the membrane stabilization under external electric field. Biochim. Biophys. Acta 1510 (2001) 300-306
114. Koronkiewicz S., Kalinowski S., and Bryl K. Programmable chrono-potentiometry as a tool for the study of electroporation and resealing of pores in bilayer lipid membranes. Biochim. Biophys. Acta 1561 (2002) 222-229
115. Koronkiewicz S., and Kalinowski S. Influence of cholesterol on electroporation of bilayer lipid membranes: Chronopotentiometric studies. Biochim. Biophys. Acta 1661 (2004) 196-203
116. Kotulska M. A comparison between deterministic and probabilistic approaches to the phenomenon of anomalous diffusion in tissue. Cell. Mol. Biol. Lett. 4 (1999) 105-116
117. Corry B., Kuyucak S., and Chung S.-H. Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus Brownian dynamics. Biophys. J. 78 (2000) 2364-2381
118. Dyrka W., Augousti A.T., and Kotulska M. Ion flux through membrane channels-an enhanced algorithm for Poisson-Nernst-Planck model. J. Comp. Chem. (2008) in press
119. Mercik S., and Weron K. Stochastic origins of the long-range correlations of ionic current fluctuations in membrane channels. Phys. Rev. E 63 (2001) 051910-051919
120. Brockwell P.J., and Davis R.A. Introduction to Time Series and Forecasting (1987), Springer, Berlin
121. Beran J. Statistics for Long-Memory Processes (1994), Chapman and Hall, New York
122. Eke A., Herman P., Bassingthwaighte J.B., Raymond G.M., Percival D.B., Cannon M., Balla I., and Ikrenyi C. Physiological time series: Distinguishing fractal noises from motions. Pflugers Arch. Eur. J. Physiol. 439 (2000) 403-415
123. Mercik S., Weron K., Burnecki K., and Weron A. Enigma of self-similarity of fractional Levy stable motions. Acta Phys. Pol. B 34 (2003) 1-19
124. Burnecki K., Rosinski J., and Weron A. Spectral representation and structure of self-similar processes. In: Karatzas I., Rajput B., and Taqqu M. (Eds). Stochastic Processes & Related Topics (1998), Birhäuser 1-14
125. Lamperti J.W. Semi-stable stochastic processes. Trans. Am. Math. Soc. 104 (1962) 62-78
126. Maejima M. Self-similar processes and limit theorems. Sugaku Expositions 2 (1989) 102-123
127. Mandelbrot B., and Van Ness J.W. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Rev. 10 (1968) 422-437
128. Weron A., Burnecki K., Mercik S., and Weron K. Complete description of all self-similar models driven by Levy stable noise. Phys. Rev. E 71 (2005) 016113-016123
129. Nolan J.P. Maximum likelihood estimation of stable parameters. In: Barndorff-Nielsen O.E., Mikosch T., and Resnick S.I. (Eds). Lévy Processes: Theory and Applications (2001), Birkhäuser, Boston 379-400
130. Nolan J.P. Fitting data and assessing goodness-of-fit with stable distributions. In: Nolan J.P., and Swami A. (Eds). Proc. ASA-IMS Conf. Heavy Tailed Distributions (1999)
131. Hurst H.E. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116 (1951) 770-808
132. Peng C.K., Buldyrev S.V., Havlin S., Stanley H.E., and Goldberger A.L. Mosaic organization of DNA nucleotides. Phys. Rev. E 49 (1994) 1685-1689
133. Ridi A., Scalas E., and Gliozzi A. Noise measurements in bilayer lipid membranes during electroporation. Eur. Phys. J. E 2 (2000) 161-168
134. Bezrukov S.M., and Winterhalter M. Examining noise sources at the single-molecule level: 1/f noise of an open maltoporin channel. Phys. Rev. Lett. 85 (2000) 202-205
135. α noise in membrane channel currents. Phys. Rev. Lett. 89 (2002) 15810-15814
136. Wohnsland F., and Benz R. 1/f noise of open bacterial porin channel. J. Membr. Biol. 158 (1997) 77-85
137. Fulinski A. Non-Markovian noise. Phys. Rev. E 50 (1994) 2668-2681
138. Dutta P., and Horn P.M. Low-frequency fluctuations in solids: 1/f noise. Rev. Mod. Phys. (1981) 497-515
139. Kaulakys B., Gontis V., and Alaburd M. Point process model of 1/f noise vs a sum of Lorentzians. Phys. Rev. E 71 (2005) 051105
140. Weissman M.B. Models for 1/f noise in nerve membranes. Biophys J. 16 (1976) 1105-1108
141. Bak P., Tang C., and Wiesenfeld K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59 (1987) 381-384
142. Brazhe A.R., and Maksimov G.V. Self-organized critical gating of ion channels: On the origin of long-term memory in dwell time series. Chaos 16 (2006) 033129-033137