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Fundamentals of Electroporation, Theory and Mathematical Models for Simulation of PEE Processing

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Processing of Foods and Biomass Feedstocks by Pulsed Electric Energy

Abstract

Cell membrane electroporation phenomena depend on the size of cells, their spatial orientation, electro-physical parameters of cells, pH of surrounding media and presence of osmotic agents. This chapter discusses fundamentals of membrane electroporation, various non-pore and pore models (condenser and conductor approximations), stages of electroporation development and simulations of electroporation in planar lipid membranes. Electroporation of single cell, Schwan’s equation for spherical and non-spherical cells are presented. Electroporation of cell ensembles, mixtures of intact and electroporated cells, and biological tissues are also discussed.

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References

  • Apollonio F, Liberti M, Marracino P, Mir L (2012) Electroporation mechanism: Review of molecular models based on computer simulation. In: 2012 6th European conference on antennas and propagation (EUCAP). Prague, Czech Republic, pp 356–358

    Google Scholar 

  • Ben Ammar J, Lanoisellé J-L, Lebovka NI et al (2011) Impact of a pulsed electric field on damage of plant tissues: effects of cell size and tissue electrical conductivity. J Food Sci 76:E90–E97

    Article  CAS  PubMed  Google Scholar 

  • Bernhardt J, Pauly H (1973) On the generation of potential differences across the membranes of ellipsoidal cells in an alternating electrical field. Biophysik 10:89–98

    Article  CAS  PubMed  Google Scholar 

  • Böckmann RA, De Groot BL, Kakorin S et al (2008) Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. Biophys J 95:1837–1850

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Bryant G, Wolfe J (1987) Electromechanical stresses produced in the plasma membranes of suspended cells by applied electric fields. J Membr Biol 96:129–139

    Article  CAS  PubMed  Google Scholar 

  • Casciola M, Tarek M (2016) A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields. Biochim Biophys Acta Biomembr 1858:2278–2289

    Article  CAS  Google Scholar 

  • Casciola M, Kasimova MA, Rems L et al (2016) Properties of lipid electropores I: molecular dynamics simulations of stabilized pores by constant charge imbalance. Bioelectrochemistry 109:108–116

    Article  CAS  PubMed  Google Scholar 

  • Castellvi Q, Banús J, Ivorra A (2016) 3d assessment of irreversible electroporation treatments in vegetal models. In: Jarm T, Kramar P (eds) 1st world congress on electroporation and pulsed electric fields in biology, medicine and food & environmental technologies. IFMBE Proceedings. Springer, Singapore, pp 294–297

    Google Scholar 

  • Chen C, Smye SW, Robinson MP, Evans JA (2006) Membrane electroporation theories: a review. Med Biol Eng Comput 44:5–14

    Article  CAS  PubMed  Google Scholar 

  • Crowley JM (1973) Electrical breakdown of bimolecular lipid membranes as an electromechanical instability. Biophys J 13:711–724

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Delemotte L, Tarek M (2012) Molecular dynamics simulations of lipid membrane electroporation. J Membr Biol 245:531–543

    Article  CAS  PubMed  Google Scholar 

  • Fernández ML, Marshall G, Sagués F, Reigada R (2010) Structural and kinetic molecular dynamics study of electroporation in cholesterol-containing bilayers. J Phys Chem B 114:6855–6865

    Article  PubMed  CAS  Google Scholar 

  • Fošnarič M, Kralj-Iglič V, Bohinc K et al (2003) Stabilization of pores in lipid bilayers by anisotropic inclusions. J Phys Chem B 107:12519–12526

    Article  CAS  Google Scholar 

  • Frank DJ, Lobb CJ (1988) Highly efficient algorithm for percolative transport studies in two dimensions. Phys Rev B 37:302

    Article  CAS  Google Scholar 

  • Fricke H (1953) The electric permittivity of a dilute suspension of membrane-covered ellipsoids. J Appl Phys 24:644–646

    Article  CAS  Google Scholar 

  • Gerlach D, Alleborn N, Baars A et al (2008) Numerical simulations of pulsed electric fields for food preservation: a review. Innov Food Sci Emerg Technol 9:408–417

    Article  Google Scholar 

  • Gimsa J, Wachner D (1999) A polarization model overcoming the geometric restrictions of the Laplace solution for spheroidal cells: obtaining new equations for field-induced forces and transmembrane potential. Biophys J 77:1316–1326

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Gimsa J, Wachner D (2001) Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells. Biophys J 81:1888–1896

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Gowrishankar TR, Weaver JC (2003) An approach to electrical modeling of single and multiple cells. Proc Natl Acad Sci 100:3203–3208

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Grosse C, Schwan HP (1992) Cellular membrane potentials induced by alternating fields. Biophys J 63:1632–1642

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Henslee BE, Morss A, Hu X et al (2014) Cell-cell proximity effects in multi-cell electroporation. Biomicrofluidics 8:52002

    Article  Google Scholar 

  • Ho M-C, Levine ZA, Vernier PT (2013) Nanoscale, electric field-driven water bridges in vacuum gaps and lipid bilayers. J Membr Biol 246:793–801

    Article  CAS  PubMed  Google Scholar 

  • Holl MMB (2008) Cell plasma membranes and phase transitions. In: Pollack GH, Chin W-C (eds) Phase transitions in cell biology. Springer, Netherlands, pp 171–181

    Google Scholar 

  • Hu Q, Joshi RP (2009) Transmembrane voltage analyses in spheroidal cells in response to an intense ultrashort electrical pulse. Phys Rev E 79:11901

    Article  CAS  Google Scholar 

  • Hu Q, Joshi RP, Schoenbach KH (2005) Simulations of nanopore formation and phosphatidylserine externalization in lipid membranes subjected to a high-intensity, ultrashort electric pulse. Phys Rev E 72:31902

    Article  CAS  Google Scholar 

  • Hu Q, Zhang Z, Qiu H et al (2013) Physics of nanoporation and water entry driven by a high-intensity, ultrashort electrical pulse in the presence of membrane hydrophobic interactions. Phys Rev E 87:32704

    Article  CAS  Google Scholar 

  • Huang K, Tian H, Gai L, Wang J (2012) A review of kinetic models for inactivating microorganisms and enzymes by pulsed electric field processing. J Food Eng 111:191–207

    Article  CAS  Google Scholar 

  • Jerry RA, Popel AS, Brownell WE (1996) Potential distribution for a spheroidal cell having a conductive membrane in an electric field. IEEE Trans Biomed Eng 43:970–972

    Article  CAS  PubMed  Google Scholar 

  • Kinosita K Jr, Tsong TY (1977) Voltage-induced pore formation and hemolysis of human erythrocytes. Biochim Biophys Acta Biomembr 471:227–242

    Article  CAS  Google Scholar 

  • Klee M, Plonsey R (1976) Stimulation of spheroidal cells – the role of cell shape. IEEE Trans Biomed Eng 4:347–354

    Article  Google Scholar 

  • Kotnik T, Miklavčič D (2000) Analytical description of transmembrane voltage induced by electric fields on spheroidal cells. Biophys J 79:670–679

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kotnik T, Pucihar G (2010) Induced transmembrane voltage-theory, modeling, and experiments. In: Pakhomov AG, Miklavčič D, Markov MS (eds) Advanced electroporation techniques in biology and medicine. CRC Press, Taylor/Francis Group, Boca Raton, pp 51–70

    Google Scholar 

  • Kotnik T, Bobanovic F, Miklavčič D (1997) Sensitivity of transmembrane voltage induced by applied electric fields: a theoretical analysis. Bioelectrochem Bioenerg 43:285–291

    Article  CAS  Google Scholar 

  • Kotnik T, Miklavčič D, Slivnik T (1998) Time course of transmembrane voltage induced by time-varying electric fields: a method for theoretical analysis and its application. Bioelectrochem Bioenerg 45:3–16

    Article  CAS  Google Scholar 

  • Kranjc M, Bajd F, Serša I et al (2016) Electric field distribution in relation to cell membrane electroporation in potato tuber tissue studied by magnetic resonance techniques. Innov Food Sci Emerg Technol 37C:384–390

    Article  CAS  Google Scholar 

  • Langus J, Kranjc M, Kos B et al (2016) Dynamic finite-element model for efficient modelling of electric currents in electroporated tissue. Sci Rep 6:26409

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lebedeva NE (1987) Electric breakdown of bilayer lipid membranes at short times of voltage action. Biol Membr (Biochem Moscow Ser A Membr Cell Biol) 4:994–998. (in Russian)

    CAS  Google Scholar 

  • Lebovka NI, Vorobiev EI (2004) On the origin of the deviation from the first-order kinetics in inactivation of microbial cells by pulsed electric fields. Int J Food Microbiol 91:83–89

    Article  CAS  PubMed  Google Scholar 

  • Lebovka N, Vorobiev E (2007) The kinetics of inactivation of spheroidal microbial cells by pulsed electric fields. ArXiv Prepr arXiv 0704(2750):1–18

    Google Scholar 

  • Lebovka NI, Bazhal MI, Vorobiev E (2001) Pulsed electric field breakage of cellular tissues: visualisation of percolative properties. Innov Food Sci Emerg Technol 2:113–125

    Article  Google Scholar 

  • Lebovka NI, Bazhal MI, Vorobiev E (2002) Estimation of characteristic damage time of food materials in pulsed-electric fields. J Food Eng 54:337–346

    Article  Google Scholar 

  • Lebovka NI, Mhemdi H, Grimi N et al (2014) Treatment of potato tissue by pulsed electric fields with time-variable strength: theoretical and experimental analysis. J Food Eng 137:23–31

    Article  Google Scholar 

  • McLachlan DS, Cai K, Chiteme C, Heiss WD (2000) An analysis of dispersion measurements in percolative metal--insulator systems using analytic scaling functions. Phys B Condens Matter 279:66–68

    Article  CAS  Google Scholar 

  • Mercadal B, Vernier PT, Ivorra A (2016) Dependence of electroporation detection threshold on cell radius: an explanation to observations non compatible with Schwan’s equation model. J Membr Biol 249:663–676

    Article  CAS  PubMed  Google Scholar 

  • Michael DH, O’Neill ME (1970) Electrohydrodynamic instability in plane layers of fluid. J Fluid Mech 41:571–580

    Article  Google Scholar 

  • Muehsam DJ, Pilla AA (1999) The sensitivity of cells and tissues to exogenous fields: effects of target system initial state. Bioelectrochem Bioenerg 48:35–42

    Article  CAS  PubMed  Google Scholar 

  • Neu JC, Krassowska W (1999) Asymptotic model of electroporation. Phys Rev E 59:3471

    Article  CAS  Google Scholar 

  • Pakhomov AG, Bowman AM, Ibey BL et al (2009) Lipid nanopores can form a stable, ion channel-like conduction pathway in cell membrane. Biochem Biophys Res Commun 385:181–186

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Pavlin M, Pavselj N, Miklavčič D (2002) Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system. Biomed Eng IEEE Trans 49:605–612

    Article  Google Scholar 

  • Pucihar G, Kotnik T, Teissié J, Miklavčič D (2007) Electropermeabilization of dense cell suspensions. Eur Biophys J 36:173–185

    Article  PubMed  Google Scholar 

  • Qin Y, Lai S, Jiang Y et al (2005) Transmembrane voltage induced on a cell membrane in suspensions exposed to an alternating field: a theoretical analysis. Bioelectrochemistry 67:57–65

    Article  CAS  PubMed  Google Scholar 

  • Ramos A, Suzuki DOH, Marques JLB (2006) Numerical study of the electrical conductivity and polarization in a suspension of spherical cells. Bioelectrochemistry 68:213–217

    Article  CAS  PubMed  Google Scholar 

  • Reigada R (2014) Electroporation of heterogeneous lipid membranes. Biochim Biophys Acta Biomembr 1838:814–821

    Article  CAS  Google Scholar 

  • Rems L, Miklavčič D (2016) Tutorial: electroporation of cells in complex materials and tissue. J Appl Phys 119:201101

    Article  Google Scholar 

  • Rems L, Viano M, Kasimova MA et al (2019) The contribution of lipid peroxidation to membrane permeability in electropermeabilization: a molecular dynamics study. Bioelectrochemistry 125:46–57

    Article  CAS  PubMed  Google Scholar 

  • Rols M-P (2006) Electropermeabilization, a physical method for the delivery of therapeutic molecules into cells. Biochim Biophys Acta Biomembr 1758:423–428

    Article  CAS  Google Scholar 

  • Rols M-P, Teissie J (1990) Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon. Biophys J 58:1089–1098

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Sachs JN, Crozier PS, Woolf TB (2004) Atomistic simulations of biologically realistic transmembrane potential gradients. J Chem Phys 121:10847–10851

    Article  CAS  PubMed  Google Scholar 

  • Saulis G (1997) Pore disappearance in a cell after electroporation: theoretical simulation and comparison with experiments. Biophys J 73:1299–1309

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Stämpfli R (1958) Reversible electrical breakdown of the excitable membrane of a Ranvier node. An da Acad Bras Ciências (Annals Brazilian Acad Sci) 30:57–63

    Google Scholar 

  • Stämpfli R, Willi M (1957) Membrane potential of a Ranvier node measured after electrical destruction of its membrane. Experientia 13:297–298

    Article  PubMed  Google Scholar 

  • Stauffer D, Aharony A (1991) Introduction to percolation theory. Taylor & Francis, London

    Google Scholar 

  • Sugar IP, Förster W, Neumann E (1987) Model of cell electrofusion: membrane electroporation, pore coalescence and percolation. Biophys Chem 26:321–335

    Article  CAS  PubMed  Google Scholar 

  • Sun S, Yin G, Lee Y-K et al (2011) Effects of deformability and thermal motion of lipid membrane on electroporation: by molecular dynamics simulations. Biochem Biophys Res Commun 404:684–688

    Article  CAS  PubMed  Google Scholar 

  • Susil R, Semrov D, Miklavčič D (1998) Electric field-induced transmembrane potential depends on cell density and organization. Electro Magnetobio 17:391–399

    Article  Google Scholar 

  • Tang J, Yin H, Ma J et al (2018) Terahertz electric field-induced membrane electroporation by molecular dynamics simulations. J Membr Biol 251:681–693

    Article  CAS  PubMed  Google Scholar 

  • Tarek M (2005) Membrane electroporation: a molecular dynamics simulation. Biophys J 88:4045–4053

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Tieleman DP (2004) The molecular basis of electroporation. BMC Biochem 5:10

    Article  PubMed  PubMed Central  Google Scholar 

  • Tieleman DP, Leontiadou H, Mark AE, Marrink S-J (2003) Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. J Am Chem Soc 125:6382–6383

    Article  CAS  PubMed  Google Scholar 

  • Tien HT, Ottova A (2003) The bilayer lipid membrane (BLM) under electrical fields. IEEE Trans Dielectr Electr Insul 10:717–727

    Article  CAS  Google Scholar 

  • Valič B, Golzio M, Pavlin M et al (2003) Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment. Eur Biophys J 32:519–528

    Article  PubMed  Google Scholar 

  • Vernier PT, Levine ZA, Gundersen MA (2013) Water bridges in electropermeabilized phospholipid bilayers. Proc IEEE 101:494–504

    Article  CAS  Google Scholar 

  • Washizu M, Techaumnat B (2008) Polarisation and membrane voltage of ellipsoidal particle with a constant membrane thickness: a series expansion approach. IET Nanobiotechnol 2:62–71

    Article  CAS  PubMed  Google Scholar 

  • Weaver JC, Chizmadzhev YA (1996) Theory of electroporation: a review. Bioelectrochem Bioenerg 41:135–160

    Article  CAS  Google Scholar 

  • Winterhalter M, Helfrich W (1987) Effect of voltage on pores in membranes. Phys Rev A 36:5874

    Article  CAS  Google Scholar 

  • Yildiz H, Icier F, Eroglu S, Dagci G (2016) Effects of electrical pretreatment conditions on osmotic dehydration of apple slices: experimental investigation and simulation. Innov Food Sci Emerg Technol 35:149–159

    Article  Google Scholar 

  • Ziegler MJ, Vernier PT (2008) Interface water dynamics and porating electric fields for phospholipid bilayers. J Phys Chem B 112:13588–13596

    Article  CAS  PubMed  Google Scholar 

  • Zimmermann U, Pilwat G, Riemann F (1974) Dielectric breakdown of cell membranes. Biophys J 14:881–899

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Zudans I, Agarwal A, Orwar O, Weber SG (2007) Numerical calculations of single-cell electroporation with an electrolyte-filled capillary. Biophys J 92:3696–3705

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Authors and Affiliations

  1. Université de Technologie de Compiègne, Sorbonne Universités, Compiègne Cedex, France

    Eugene Vorobiev

  2. F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv, Ukraine

    Nikolai Lebovka

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  1. Eugene Vorobiev
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  2. Nikolai Lebovka
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Vorobiev, E., Lebovka, N. (2020). Fundamentals of Electroporation, Theory and Mathematical Models for Simulation of PEE Processing. In: Processing of Foods and Biomass Feedstocks by Pulsed Electric Energy. Springer, Cham. https://doi.org/10.1007/978-3-030-40917-3_2

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