Abstract
Cell membrane permeabilization mechanics and the resulting shape of nanopores in response to electrical pulsing are probed based on a continuum approach. This has implications for electropermeabilization and cell membrane transport. It is argued that small pores resulting from high-intensity (~100 kV/cm), nanosecond pulsing would have an initial asymmetric shape. This would lead to asymmetric membrane current–voltage characteristics, at least at early times. The role of the cytoskeleton is ignored here, but can be expected to additionally contribute to such asymmetries. Furthermore, we show that the pore shape and membrane conduction would be dynamic, and evolve toward a symmetric characteristic over time. This duration has been shown to be in the micro-second range.
Similar content being viewed by others
References
Abidor IG, Arakelyan VB, Chernomordik LV, Chizmadzhev YA, Pastuchenko VF, Tarasevich MR (1979) Electric breakdown of bilayer lipid membranes: main experimental facts and their qualitative discussion. Bioelectrochem Bioenerg 6:37–52
Beckstein O, Sansom MSP (2004) The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores. Phys Biol 1:42–52
Beebe SJ, Fox PM, Rec LJ, Willis EL, Schoenbach KH (2003) Nanosecond, high-intensity pulsed electric fields induce apoptosis in human cells. FASEB J 17:1493–1495
Beebe SJ, Blackmore PF, White J, Joshi RP, Schoenbach KH (2004) Nanosecond pulsed electric fields modulate cell function through intracellular signal transduction mechanisms. Physiol Meas 25:1077–1093
Boal D (2002) Mechanics of the cell. Cambridge University Press, Cambridge
Born M (1920) Volumen und hydratationswarme der ionen. Z Phys 1:45–48
Chen C, Smye SW, Robinson MP, Evans JA (2006) Membrane electroporation theories: a review. Med Biol Eng Comput 44:5–14
Denet AR, Preat V (2003) Transdermal delivery of timolol by electroporation through human skin. J Control Release 88:253–262
Deryagin BV, Gutop YV (1962) Theory of the breakdown (rupture) of free films. Kolloidn Zh 24:370–374
Evans E, Heinrich V, Ludwig F, Rawicz W (2003) Dynamic tension spectroscopy and strength of biomembranes. Biophys J 85:2342–2350
Farago O (2003) Water-free computer model for fluid bilayer membranes. J Chem Phys 119:596–605
Farago O, Santangelo CD (2005) Pore formation in fluctuating membranes. J Chem Phys 122:044901-1–044901-9
Giaya A, Thompson RW (2002) Observations on an equation of state for water confined in narrow slit-pores. J Chem Phys 116:2565–2571
Giaya A, Thompson RW (2002) Water confined in cylindrical micropores. J Chem Phys 117:3464–3475
Glaser RW, Leikin SL, Chernomordik LV, Pastushenko VF, Sokirko AI (1988) Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. Biochim Biophys Acta 940:275–287
Helfrich W (1973) Elastic properties of lipid bilayers—theory and possible experiments. Z Naturforsch 28:693–703
Helfrich W (1974) The size of bilayer vesicles generated by sonication. Phys Lett A 50:115–116
Joshi RP, Hu Q, Aly R, Schoenbach KH, Hjalmarson HP (2001) Self-consistent simulations of electroporation dynamics in biological cells subjected to ultrafast electrical pulses. Phys Rev E 64:011913-1–011913-10
Joshi RP, Mishra A, Song J, Pakhomov A, Schoenbach KH (2008) Simulation studies of ultrashort, high-intensity electric pulse induced action potential block in whole-animal nerves. IEEE Trans Biomed Eng 55:1391–1398
Joshi RP, Song J, Sridhara V (2009) Aspects of lipid membrane bio-responses to subnanosecond, ultrahigh voltage pulsing. IEEE Trans Dielectr Electr Insulation 16:1243–1250
Kubo R, Toda M, Hashitsume N (1991) Statistical physics II, 2nd edn. Springer-Verlag, Berlin
Lee RC, Kolodney MS (1987) Electrical injury mechanisms: dynamics of the thermal response. Plast Reconstr Surg 80:663–671
Levitt DG (1978) Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys J 22:209–219
Lin JH, Baumgaertner A (2000) Stability of a melittin pore in a lipid bilayer: a molecular dynamics study. Biophys J 78:1714–1724
Lindahl E, Edholm O (2000) Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys J 79:426–433
Litster JD (1975) Stability of lipid bilayers and red blood cell membranes. Phys Lett A 53:193–194
Mali B, Jarm T, Corovic S, Paulin-Kosir MS, Cemazar M, Sersa G, Miklavcic D (2008) The effect of electroporation pulses on functioning of the heart. Med Biol Eng Comput 46:745–757
Melikov KC, Frolov VA, Shcherbakov A, Samsonov AV, Chizmadzhev YA (2001) Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer. Biophys J 80:1829–1836
Mir LM, Orlowski S, Belehradek J Jr, Teissie J, Rols MP, Sersa G, Miklavcic D, Gilbert R, Heller R (1995) Biomedical applications of electric pulses with special emphasis on antitumour electrochemotherapy. Bioelectrochem Bioenerg 38:203–207
Mir LM, Moller PH, Andre F, Gehl J (2005) Advances in genetics. Academic Press, New York, pp 83–114
Napotnik TB, Reberšek M, Kotnik T, Lebrasseur E, Cabodevila G, Miklavčič D (2010) Electropermeabilization of endocytotic vesicles in B16 F1 mouse melanoma cells. Med Biol Eng Comput 48:407–413
Neu JC, Krassowska W (2003) Modeling postshock evolution of large electropores. Phys Rev E 67:021915-1–021915-12
Neu JC, Krassowska W (2006) Singular perturbation analysis of the pore creation transient. Phys Rev E 74:031917-1–031917-9
Neu JC, Smith KC, Krassowska W (2003) Electrical energy required to form large conducting pores. Bioelectrochemistry 60:107–114
Neumann E, Sowers AE, Jordan CA (1989) Electroporation and electrofusion in cell biology. Plenum Press, New York
Neumann E, Kakorin S, Toensig K (1999) Fundamentals of electroporative delivery of drugs and genes. Bioelectrochem Bioenerg 48:3–16
Nuccitelli R, Pliquett U, Chen X, Ford W, Swanson J, Beebe SJ, Kolb JF, Schoenbach KH (2006) Nanosecond pulsed electric fields cause melanomas to self-destruct. Biochem Biophys Res Commun 343:351–360
Pakhomov AG, Kolb JF, Joshi RP, Schoenbach KH, Dayton T, Comeaux J, Ashmore J, Beason C (2006) Neuromuscular disruption with ultrashort electrical pulses. Proc SPIE Int Soc Opt Eng 6219:621903–621910
Pakhomov AG, Shevin R, White JA, Kolb JF, Pakhomova ON, Joshi RP, Schoenbach KH (2007) Membrane permeabilization and cell damage by ultrashort electric field shocks. Arch Biochem Biophys 465:109–118
Pakhomov AG, Bowman AM, Ibey BL, Andre FM, Pakhomova ON, Schoenbach KH (2009) Lipid nanopores can form a stable, ion channel-like conduction pathway in cell membrane. Biochem Biophys Res Comm 385:181–186
Parsegian A (1969) Energy of an ion crossing of a low dielectric membrane: solutions to four relevant electrostatic problems. Nature (London) 221:844–846
Pastushenko VF, Chhizmadzhev YA (1982) Stabilization of conducting pores in BLM by electric current. Gen Physiol Biophys 1:43–52
Resat H, Mezei M (1994) Grand canonical Monte Carlo simulation of water positions in crystal hydrates. J Am Chem Soc 116:7451–7452
Rols MP, Teissie J (1992) Experimental evidence for the involvement of the cytoskeleton in mammalian cell electropermeabilization. Biochim Biophys Acta 1111:45–50
Rosado JA, Gonzalez A, Salido GM, Pariente JA (2002) Effects of reactive oxygen species on actin filament polymerisation and amylase secretion in mouse pancreatic acinar cells. Cell Signal 14:547–556
Schoenbach KH, Beebe SJ, Buescher ES (2001) Intracellular effect of ultrashort electrical pulses. Bioelectromagnetics 22:440–448
Schoenbach KH, Joshi RP, Kolb J, Chen N, Stacey M, Blackmore P, Buescher ES, Beebe SJ (2004) Ultrashort electrical pulses open a new gateway into biological cells. Proc IEEE 92:1122–1137
Schoenbach KH, Hargrave B, Joshi RP, Kolb JF, Nuccitelli R, Osgood C, Pakhomov A, Stacey M, Swanson RJ, White J, Xiao S, Zhang J, Beebe SJ, Blackmore PF, Buescher ES (2007) Bioelectric effects of intense nanosecond pulses. IEEE Trans Dielectr Electr Insulation 14:1088–1109
Shai Y (1999) Mechanism of the binding, insertion and destabilization of phospholipid bilayer membranes by α-helical antimicrobial and cell non-selective membrane-lytic peptides. Biophys Biochim Acta 1462:55–70
Siwy Z, Kosinska ID, Fulinski A, Martin CR (2005) Asymmetric diffusion through synthetic nanopores. Phys Rev Lett 94:048102-1–048102-4
Smith KC, Neu JC, Krassowska W (2004) Model of creation and evolution of stable macropores for DNA delivery. Biophys J 86:2813–2826
Sung W, Park PJ (1997) Polymer translocation through a pore in a membrane. Biophys J 73:1797–1804
Taupin C, Dvolaitzky M, Sauterey C (1975) Osmotic pressure induced pores in phospholipid vesicles. Biochemistry 14:4771–4775
Teissie J, Eynard N, Gabriel B, Rols MP (1999) Electropermeabilization of cell membranes. Adv Drug Deliv Rev 35:3–19
Tien HT, Ottova-Leitmannova A (2003) Planar lipid bilayers (BLMs) and their applications. Elsevier, Amsterdam, pp 917–961
Truskett TM, Debenedetti PG, Torquato S (2001) Thermodynamic implications of confinement for a waterlike fluid. J Chem Phys 114:2401–2418
Vernier PT, Sun Y, Marcu L, Salemi S, Craft CM, Gundersen MA (2003) Calcium bursts induced by nanosecond electric field. Biochem Biophys Res Commun 310:286–295
Weaver JC (1994) Molecular basis for cell membrane electroporation. Ann N Y Acad Sci 720:141–152
Weaver JC, Chizmadzhev YA (1996) Theory of electroporation: a review. Bioelectrochem Bioenerg 41:135–160
Weaver JC, Mintzer RA (1981) Decreased bilayer stability due to transmembrane potentials. Phys Lett A 86:57–59
Wilhelm C, Winterhalter M, Zimmermann U, Benz R (1993) Kinetics of pore size during irreversible electrical breakdown of lipid bilayer membranes. Biophys J 64:121–128
Winterhalter M, Helfrich W (1987) Effect of voltage on pores in membranes. Phys Rev A 36:5874–5876
Wolf H, Rols MP, Boldt E, Neumann E, Teissie J (1994) Control by pulse parameters of electric field-mediated gene transfer in mammalian cells. Biophys J 66:524–531
Zemel A, Fattal DR, Ben-Shaul A (2003) Energetics and self-assembly of amphipathic peptide pores in lipid membranes. Biophys J 84:2242–2255
Zuckermann MJ, Heimburg T (2001) Insertion and pore formation driven by adsorption of proteins onto lipid bilayer membrane-water interfaces. Biophys J 81:2458–2472
Acknowledgments
We would like to thank A. Pakhomov (ODU) for useful discussions. Partial support from ORSP of Central Michigan University is also gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Joshi, R.P., Hu, Q. Analysis of cell membrane permeabilization mechanics and pore shape due to ultrashort electrical pulsing. Med Biol Eng Comput 48, 837–844 (2010). https://doi.org/10.1007/s11517-010-0659-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11517-010-0659-1