Theory of Electroporation

  • Wanda Krassowska Neu
  • John C. Neu

Experiments conducted on artificial bilayers, suspensions of vesicles or cells, and tissues have demonstrated that a large, externally induced transmembrane potential (V m) causes an increase in the conductivity of the membrane by five to six orders of magnitude.13 This effect is generally attributed to the creation of pores, which are the aqueous pathways in the lipid bilayer of the membrane, and whose creation and subsequent growth are facilitated by large V m. This process, called electroporation, can be irreversible, leading to a mechanical rupture of the membrane,2,4 or reversible, in which case pores reseal and the same membrane can experience multiple episodes of the high conductivity state.1,3 Electroporation occurs as an undesirable side effect following the delivery of defibrillation shocks to the heart510 and may be responsible for the late necrosis after accidental exposure to high voltage.11 On the other hand, the transient state of high membrane permeability has important practical applications, allowing the fusion of cells and the introduction of biologically active substances (drugs or genetic material) into cells.1217

Because of great interest in this method, studies use a variety of experimental techniques to provide insight into the processes taking place during electroporation. These techniques include measuring the time course of transmembrane voltage1 or current though the membrane,3,18 monitoring uptake or leakage of fluorescent molecules,19–21 imaging the transmembrane potential,8,10,22 measuring the tissue impedance,23,24 and observing pores with rapid-freezing electron microscopy.25 However, electroporation is difficult to observe directly because pores are very small (nanometers) and their creation and growth is very fast (microseconds), and many questions cannot be answered with available experimental techniques. Thus, there is a need to supplement experimental knowledge with a theoretical model.


Drift Velocity Pore Radius Lipid Bilayer Membrane Membrane Tension Asymptotic Model 
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  1. 1.
    Benz R, Beckers F, Zimmermann U. Reversible electrical breakdown of lipid bilayer membranes: a charge-pulse relaxation study. Memb Biol 1979;48:181–204CrossRefGoogle Scholar
  2. 2.
    Abidor IG, Arakelyan VB, Chernomordik LV, Chizmadzhev YA, Pastushenko VF,Tarasevich MR. Electric breakdown of bilayer lipid membranes: I. Main experimental facts and their qualitative discussion. Bioelectrochem Bioenerg 1979;6:37–52CrossRefGoogle Scholar
  3. 3.
    Chernomordik LV, Sukharev SI, Abidor IG, Chizmadzhev YA. Breakdown of lipid bilayer membranes in an electric field. Biochim Biophys Acta 1983;736:203–213CrossRefGoogle Scholar
  4. 4.
    Diederich A, Bahr G, Winterhalter M. Influence of surface charges on the rupture of black lipid membranes. Phys Rev E 1998;58:4883–4889CrossRefGoogle Scholar
  5. 5.
    Jones JL, Jones RE, Balasky G. Microlesion formation in myocardial cells by high-intensity electric field stimulation. Am J Physiol 1987;253:H480–H486PubMedGoogle Scholar
  6. 6.
    Tung L, Tovar O, Neunlist M, Jain SK, O'Neil RJ. Effects of strong electric shock on cardiac muscle tissue. Ann N Y Acad Sci 1994;720:160–175PubMedCrossRefGoogle Scholar
  7. 7.
    Kodama I, Sakuma I, Mitsui K, Iida M, Suzuki R, Fukui Y, Hosoda S, Toyama J.Aftereffects of high-intensity DC stimulation on the electromechanical performance of ventricular muscle. Am J Physiol 1994;267:H248–H258PubMedGoogle Scholar
  8. 8.
    Knisley SB, Grant AO. Asymmetrical electrically induced injury of rabbit ventricular myocytes. J Mol Cell Cardiol 1995;27:1111–1122PubMedCrossRefGoogle Scholar
  9. 9.
    Fast VG, Cheek ER. Nonlinear changes of transmembrane potential during electricalshocks: role of membrane electroporation. Circ Res 2004;94:208–214PubMedCrossRefGoogle Scholar
  10. 10.
    Nikolski VP, Efimov IR. Electroporation of the heart. Europace 2005;7[Suppl 2]:S146–S154CrossRefGoogle Scholar
  11. 11.
    Lee RC, Kolodney MS. Electrical injury mechanisms: electrical breakdown of cell membranes. Plast Reconst Surg 1987;80:672–679PubMedCrossRefGoogle Scholar
  12. 12.
    Potter H. Electroporation in biology: methods, applications, and instrumentation. Anal Biochem 1988;174:361–373PubMedCrossRefGoogle Scholar
  13. 13.
    Hofmann GA, Dev SB, Nanda GS. Electrochemotherapy: transition from laboratory to the clinic. IEEE Eng Med Biol Mag 1996;15:124–132CrossRefGoogle Scholar
  14. 14.
    Sukharev SI, Klenchin VA, Serov SM, Chernomordik LV, Chizmadzhev YA. Electropo-ration and electrophoretic DNA transfer into cells. The effect of DNA interaction with electropores. Biophys J 1992;63:1320–1327PubMedGoogle Scholar
  15. 15.
    Dev SB, Rabussay DP, Widera G, Hofmann GA. Medical applications of electroporation.IEEE Trans Plasma Sci 2000;28:206–223CrossRefGoogle Scholar
  16. 16.
    Gehl J. Electroporation: theory and methods, perspectives for drug delivery, gene therapy and research. Acta Physiol Scand 2003;117:437–447CrossRefGoogle Scholar
  17. 17.
    Andrè F, Mir LM. DNA electrotransfer: its principles and an updated review to its therapeutic applications. Gene Ther 2004;11:S33–S42PubMedCrossRefGoogle Scholar
  18. 18.
    Melikov KC, Frolov VA, Ahcherbakov A, Samsonov AV, Chizmadzhev YA. Voltage-induced nonconductive and metastable pores in unmodified lipid bilayers. Biophys J 2001;80:1829–1836PubMedCrossRefGoogle Scholar
  19. 19.
    Teissié J, Tsong TY. Electric field induced transient pores in phospholipid bilayer vesicles. Biochemistry 1981;20:1548–1554PubMedCrossRefGoogle Scholar
  20. 20.
    Tekle E, Astumian RD, Chock PB. Selective and asymmetric molecular transport across electroporated cell membranes. Proc Natl Acad Sci 1994;91:11512–11516PubMedCrossRefGoogle Scholar
  21. 21.
    Gabriel B, Teissié J. Direct observation in the millisecond time range of fluorescent molecule asymmetrical interaction with the electropermeabilized cell membrane. Biophys J 1997;73:2630–2637PubMedGoogle Scholar
  22. 22.
    Hibino M, Shigemori M, Itoh H, Nagayama K, Kinosita K Jr. Membrane conductance of an electroporated cell analyzed by submicrosecond imaging of transmembrane potential.Biophys J 1991;59:209–220PubMedGoogle Scholar
  23. 23.
    Ghosh PM, Keese CR, Giaver I. Monitoring electropermeabilization in the plasma membrane of adherent mammalian cells. Biophys J 1993;64:1602–1609PubMedGoogle Scholar
  24. 24.
    Huang Y, Sekhon NS, Borninski J, Chen N, Rubinsky B. Instantaneous, quantitative single-cell viability assessment by electrical evaluation of cell membrane integrity with microfabricated devices. Sens Actuators A 2003;105:31–39Google Scholar
  25. 25.
    Chang DC, Reese TS. Changes in membrane structure induced by electroporation as revealed by rapid-freezing electron microscopy. Biophys J 1990;58:1–12PubMedGoogle Scholar
  26. 26.
    Barnett A, Weaver JC. Electroporation: a unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes.Bioelectrochem Bioenerg 1991;25:163–182CrossRefGoogle Scholar
  27. 27.
    Weaver JC, Chizmadzhev YA. Theory of electroporation: a review. Bioelectrochem Bioenerg1996;41:135–160CrossRefGoogle Scholar
  28. 28.
    Weaver JC. Electroporation of biological membranes from multicellular to nano scales.IEEE Trans Dielectr Electr Insul 2003;10:754–768CrossRefGoogle Scholar
  29. 29.
    Chen C, Smye SW, Robinson MP, Evans JA. Membrane electroporation theories: a review. Med Biol Eng Comput 2006;44:5–14PubMedCrossRefGoogle Scholar
  30. 30.
    Weaver JC. Molecular basis for cell membrane electroporation. Ann N Y Acad Sci 1994;720:141–152PubMedCrossRefGoogle Scholar
  31. 31.
    Glaser RW, Leikin SL, Chernomordik LV, Pastushenko VF, Sokirko AI. Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. Biochim Biophys Acta 1988;940:275–287PubMedCrossRefGoogle Scholar
  32. 32.
    Neu JC, Krassowska W. Asymptotic model of electroporation. Phys Rev E 1999;59:3471–3482CrossRefGoogle Scholar
  33. 33.
    Pastushenko VF, Chizmadzhev YA, Arakelyan VB. Electric breakdown of bilayer lipid membranes: II. Calculations of the membrane lifetime in the steady-state diffusion approximation. Bioelectrochem Bioenerg 1979;6:53–62CrossRefGoogle Scholar
  34. 34.
    Weaver JC, Mintzer RA. Decreased bilayer stability due to transmembrane potential.Phys Lett A 1981;86A:57–59CrossRefGoogle Scholar
  35. 35.
    Powell KT, Weaver JC. Transient aqueous pores in bilayer membranes: a statistical theory. Bioelectrochem Bioenerg 1986;15:211–227CrossRefGoogle Scholar
  36. 36.
    Feynman RP, Leighton RB, Sands M. The Feynman Lectures on Physics, Vol. II.Reading, MA: Addison-Wesley; 1963Google Scholar
  37. 37.
    Plonsey R, Collin RE. Principles and Applications of Electromagnetic Fields. New York:McGraw-Hill; 1961Google Scholar
  38. 38.
    Krassowska W, Neu JC. Post-shock evolution of pores. Ann Biomed Eng 2001;29:S101Google Scholar
  39. 39.
    Neu JC, Smith KC, Krassowska W. Electrical energy required to form large conducting pores. Bioelectrochem Bioenerg 2003;60:107–114Google Scholar
  40. 40.
    Glaser RW. Appearance of a “critical voltage” in reversible electric breakdown. Studia Biophysica 1986;16:77–86Google Scholar
  41. 41.
    Vasilkoski Z, Esser AT, Gowrishankar TR, Weaver JC. Membrane electroporation:the absolute rate equation and nanosecond time scale pore creation. Phys Rev E 2006;74(021904):1–12Google Scholar
  42. 42.
    Plonsey R, Barr RC. Bioelectricity. A Quantitative Approach. New York: Plenum; 1988Google Scholar
  43. 43.
    Neu JC, Krassowska W. Modeling postshock evolution of large electropores. Phys Rev E 2003;67(021915):1–12Google Scholar
  44. 44.
    Saulis G, Venslauskas MS, Naktinis J. Kinetics of pore resealing in cell membranes after electroporation. Bioelectrochem Bioenerg 1991;26:1–13CrossRefGoogle Scholar
  45. 45.
    Bier M, Hammer SM, Canaday DJ, Lee RC. Kinetics of sealing for transient electropores in isolated mammalian skeletal muscle cells. Bioelectromagnetics 1999;20:194–201PubMedCrossRefGoogle Scholar
  46. 46.
    Freeman SA, Wang MA, Weaver JC. Theory of electroporation of planar bilayer membranes: predictions of the aqueous area, change in capacitance, and pore—pore separation. Biophys J 1994;67:42–56PubMedGoogle Scholar
  47. 47.
    Powell KT, Derrick EG, Weaver JC. A quantitative theory of reversible electrical breakdown of bilayer membranes. Bioelectrochem Bioenerg 1986;15:243–255CrossRefGoogle Scholar
  48. 48.
    Joshi RP, Schoenbach KH. Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: a numerical simulation study. Phys Rev E 2000;62:1025–1033CrossRefGoogle Scholar
  49. 49.
    Joshi RP, Hu Q, Schoenbach KH, Bebe SJ. Simulations of electroporation dynamics and shape deformations in biological cells subjected to high voltage pulses. IEEE Trans Plasma Sci 2002;30:1536–1546CrossRefGoogle Scholar
  50. 50.
    Joshi RP, Hu Q, Schoenbach KH. Modeling studies of cell response to ultrashort, high-intensity electric fields — implications for intracellular manipulation. IEEE Trans Plasma Sci 2004;32:1677–1686CrossRefGoogle Scholar
  51. 51.
    Hu Q, Viswanadham S, Joshi RP, Schoenbach KH, Beebe SJ, Blackmore PF. Simulations of transient membrane behavior in cells subjected to a high-intensity ultrashort electric pulse. Phys Rev E 2005;71:031914CrossRefGoogle Scholar
  52. 52.
    Sandre O, Moreaux L, Brochard-Wyart F. Dynamics of transient pores in stretched vesicles. Proc Natl Acad Sci 1999;96:10591–10596PubMedCrossRefGoogle Scholar
  53. 53.
    McNeil PL, Steinhardt RA. Loss, restoration and maintenance of plasma membrane integrity. J Cell Biol 1997;137:1–4PubMedCrossRefGoogle Scholar
  54. 54.
    Zauderer E. Partial Differential Equations of Applied Mathematics. New York: Wiley;1983Google Scholar
  55. 55.
    DeBruin KA, Krassowska W. Modeling electroporation in a single cell. I: effects of field strength and rest potential. Biophys J 1999;77:1213–1224PubMedGoogle Scholar
  56. 56.
    Newman J. Resistance for flow of current to a disk. J Electrochem Soc 1966;113:501–502CrossRefGoogle Scholar
  57. 57.
    Barnett A. The current-voltage relation of an aqueous pore in a lipid bilayer membrane.Biochim Biophys Acta 1990;1025:10–14PubMedCrossRefGoogle Scholar
  58. 58.
    DeBruin KA, Krassowska W. Modeling electroporation in a single cell. II: effects of ionic concentrations. Biophys J 1999;77:1225–1233PubMedGoogle Scholar
  59. 59.
    Sakuma I, Haraguchi T, Ohuchi K, Fukui Y, Kodama I, Toyama J, Shibata N, Hosoda S. A model analysis of aftereffects of high-intensity DC stimulation on action potential of ventricular muscle. IEEE Trans Biomed Eng 1998;45:258–267PubMedCrossRefGoogle Scholar
  60. 60.
    DeBruin KA, Krassowska W. Electroporation and shock-induced transmembrane potential in a cardiac fiber during defibrillation strength shocks. Ann Biomed Eng1998;26:584–596PubMedCrossRefGoogle Scholar
  61. 61.
    Ashihara T, Trayanova NA. Asymmetry in membrane responses to electric shocks:insights from bidomain simulations. Biophys J 2004;87:2271–2282PubMedCrossRefGoogle Scholar
  62. 62.
    Sambelashvili AT, Nikolski VP, Efimov IR. Virtual electrode theory explains pacing threshold increase caused by cardiac tissue damage. Am J Physiol 2004;286:H2183–H2194Google Scholar
  63. 63.
    Bier M, Chen W, Gowrishankar TR, Astumian RD, Lee RC. Resealing dynamics of a cell after electroporation. Phys Rev E 2002;66(062905):1–4Google Scholar
  64. 64.
    Wolf H, Rols M-P, Boldt E, Neumann E, Teissié J. Control by pulse parameters of electric field-mediated gene transfer in mammalian cells. Biophys J 1994;66:524–531PubMedGoogle Scholar
  65. 65.
    Rols M-P, Teissié J. Electropermeabilization of mammalian cells to macro-molecules:control by pulse duration. Biophys J 1998;74:1415–1423Google Scholar
  66. 66.
    Satkauskas S, Bureau MF, Puc M, Mahfoudi A, Scherman D, Miklavčič D, Mir LM.Mechanisms of in vivo DNA electrotransfer: respective contributions of cell electroper-meabilization and DNA electrophoresis. Mol Ther 2002;5:133–140PubMedCrossRefGoogle Scholar
  67. 67.
    Kakorin S, Neumann E. Ionic conductivity of electroporated lipid bilayer membranes.Bioelectrochem 2002;56:163–166CrossRefGoogle Scholar
  68. 68.
    Schwister K, Deuticke B. Formation and properties of aqueous leaks induced in human erythrocytes by electrical breakdown. Biochim Biophys Acta 1985;816:332–348PubMedCrossRefGoogle Scholar
  69. 69.
    Tekle E, Astumian RD, Chock PB. Electroporation by using bipolar oscillating electric field: an improved method for DNA transfection of NIH 3T3 cells. Proc Natl Acad Sci 1991;88:4230–4234PubMedCrossRefGoogle Scholar
  70. 70.
    Tieleman DP, Leontiadou H, Mark AE, Marrink S-J. Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. J Am Chem Soc 2003;125:6382–6383PubMedCrossRefGoogle Scholar
  71. 71.
    Tarek M. Membrane electroporation: a molecular dynamics simulation. Biophys J 2005;88:4045–4053PubMedCrossRefGoogle Scholar
  72. 72.
    Kotulska M, Koronkiewicz S, Kalinowski S. Self-similar process and flicker noise from a fluctuating nanopore in a lipid membrane. Phys Rev E 2004;69(031920):1–10Google Scholar
  73. 73.
    Cranford J, Krassowska W. Effects of ionic concentrations on density and size of pores created by electric pulses. In: Proceedings of the 2006 Annual Fall Meeting of the BMES,vol. 418, 2006Google Scholar
  74. 74.
    Brochard-Wyart F, de Gennes PG, Sandre O. Transient pores in stretched vesicles: role of leak-out. Physica A 2000;278:32–51CrossRefGoogle Scholar
  75. 75.
    Teissié J, Rols M-P. An experimental evaluation of the critical potential difference inducing cell membrane electropermeabilization. Biophys J 1993;65:409–413PubMedGoogle Scholar
  76. 76.
    Hama-Inaba H, Takahashi M, Kasai M, Shiomi T, Ito A, Hanaoka F, Sato K. Optimum conditions for electric pulse mediated gene transfer to mammalian cells in suspension.Cell Struct Funct 1987;12:173–180PubMedCrossRefGoogle Scholar
  77. 77.
    Golzio M, Mora M-P, Raynaud C, Delteil C, Teissié J, Rols M-P. Control by osmotic pressure of voltage-induced permeabilization and gene transfer in mammalian cells.Biophys J 1998;74:3015–3022PubMedGoogle Scholar
  78. 78.
    Chernomordik LV, Sukharev SI, Popov SV, Pastushenko VF, Sokirko AV, Abidor IG,Chizmadzhev YA. The electrical breakdown of cells and lipid membranes: the similarity of phenomenologies. Biochim Biophys Acta 1987;902:360–373PubMedCrossRefGoogle Scholar
  79. 79.
    Genco I, Gliozzi A, Relini A, Robello M, Scalas E. Electroporation in symmetric and asymmetric membranes. Biochim Biophys Acta 1993;1149:10–18PubMedCrossRefGoogle Scholar
  80. 80.
    Kotulska M, Koronkiewicz S, Kalinowski S. Cholesterol induced changes in the characteristics of the time series from planar lipid bilayer membrane during electroporation.Acta Physica Polonica B 2002;1115–1129Google Scholar
  81. 81.
    Stewart DA, Gowrishankar TR, Weaver JC. Transport lattice approach to describing cell electroporation: use of a local asymptotic model. IEEE Trans Plasma Sci 2004;32:1696–1708CrossRefGoogle Scholar
  82. 82.
    Hibino M, Itoh H, Kinosita K Jr. Time courses of cell electroporation as revealed by submicroscopic imaging of transmembrane potential. Biophys J 1993;64:1789–1800PubMedGoogle Scholar
  83. 83.
    Tovar OH, Tung L. Electroporation of cardiac cell membranes with monophasic or biphasic rectangular pulses. PAC E1991;14:1887–1892Google Scholar
  84. 84.
    Neu JC, Krassowska W. Singular perturbation analysis of the pore creation transient.Phys Rev E 2006;74(031917):1–9Google Scholar
  85. 85.
    Teissié J, Golzio M, Rols M-P. Mechanisms of cell membrane electropermeabilization: a minireview of our present (lack of?) knowledge. Biochim Biophys Acta 2005;1724:270–280PubMedGoogle Scholar
  86. 86.
    Haest CWM, Kamp D, Deuticke B. Transbilayer reorientation of phospholopid probes in the human erythrocyte membrane. Lessons from studies on electroporated and resealed cells. Biochim Biophys Acta 1997;1325:17–33PubMedCrossRefGoogle Scholar
  87. 87.
    Vernier PT, Sun Y, Marcu L, Craft CM, Gundersen MA. Nanopulse-induced phos-phatidylserine translocation. Biophys J 2004;86:4040–4048PubMedCrossRefGoogle Scholar
  88. 88.
    Ohuchi K, Fukui Y, Sakuma I, Shibata N, Honjo H, Kodama I. A dynamic action potential model analysis of shock-induced aftereffects in ventricular muscle by reversible breakdown of cell membrane. IEEE Trans Biomed Eng 2002;49:18–30PubMedCrossRefGoogle Scholar
  89. 89.
    Krassowska W. Effects of electroporation on transmembrane potential induced by defibrillation shocks. PAC E 1995;18:1644–1660Google Scholar
  90. 90.
    Aguel F, DeBruin KA, Krassowska W, Trayanova N. Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue. J Cardiovasc Electrophysiol 1999;10:701–714PubMedCrossRefGoogle Scholar
  91. 91.
    Hénon S, Lenormand G, Richert A, Gallet F. A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys J 1999;76:1145–1151PubMedGoogle Scholar
  92. 92.
    Israelachvili J. Intermolecular and Surface Forces, 2nd ed. London: Academic; 1992Google Scholar
  93. 93.
    Smith KC, Neu JC, Krassowska W. Model of creation and evolution of stable macropores for DNA delivery. Biophys J 2004;86:2813–2826PubMedGoogle Scholar
  94. 94.
    Chambers EL, de Armendi J. Membrane potential, action potential and activation potential of eggs of the sea urchin, Lytechinus variegates. Exp Cell Res 1979;122:203–218PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Wanda Krassowska Neu
    • 1
  • John C. Neu
    • 2
  1. 1.Department of Biomedical EngineeringDuke UniversityDurhamUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyUSA

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