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Different Approaches Used in Modeling of Cell Membrane Electroporation

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Handbook of Electroporation

Abstract

Cell electroporation is a complex phenomenon, which consists in the emergence of defects in cell membranes subjected to electric pulses. Since the end of the 1990s, biophysical models have been developed to explain and predict the conditions for cell electroporation. However the recent biological data, in particular those dealing with the influence of the repetition rate of the pulses, challenge these biophysical models. In this chapter, different approaches to model electropore formation are presented. The simplest equivalent circuit model is first presented. Biophysical approaches are rapidly overviewed. For each approach, advantages and disadvantages are also discussed, in terms of physical meaning and validation with the experimental data. Then phenomenological approach is introduced. Such approaches consist in designing the model on an empirical basis thanks to the experience. Even though the physical bases of such models are still lacking, they provide new interesting views on the electroporation processes, as described by the experiments. The aim of the chapter is to introduce the reader to different ways of modeling cell membrane electroporation and to provide some possible directions to obtain a more reliable theory of electroporation in accordance with the experiments and with a justified theoretical basis.

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References

  • Bray A (2002) Theory of phase-ordering kinetics. Adv Phys 51:481–587

    Article  Google Scholar 

  • Dermol J, Pakhomova O, Pakhomov A, Miklavčič D (2016) Cell electrosensitization exists only in certain electroporation buffers. PLoS ONE 11:e0159434

    Article  Google Scholar 

  • Escoffre J, Portet T, Wasungu L, Teissié J, Dean D, Rols M (2009) What is (still not) known of the mechanism by which electroporation mediates gene transfer and expression in cells and tissues. Mol Biotechnol 41:286–295

    Article  Google Scholar 

  • Fahey PF, Webb WW (1978) Lateral diffusion in phospholipid bilayer membranes and multilamellar liquid crystals. Biochemistry 17(15):3046–3053

    Article  Google Scholar 

  • Foster K, Schwan H (1989) Dielectric properties of tissues and biological materials: a critical review. CRC Biomed Eng 17(1):25–104

    Google Scholar 

  • Harakawa S, Inoue N, Hori T, Tochio K, Kariya T, Takahashi K, Doge F, Suzuki H, Nagasawa H (2005) Effects of a 50 Hz electric field on plasma lipid peroxide level and antioxidant activity in rats. Bioelectromagnetics 26(7):589–594

    Article  Google Scholar 

  • Kotnik T, Pucihar G, Miklavčič D (2010) Induced transmembrane voltage and its correlation with electroporation-mediated molecular transport. J Membr Biol 236:3–13

    Article  Google Scholar 

  • Kotnik T, Kramar P, Pucihar G, Miklavčič D, Tarek M (2012) Cell membrane electroporation? Part 1: the phenomenon. IEEE Electr Insul M 28:14–23

    Article  Google Scholar 

  • Krassowska W, Filev PD (2007) Modelling electroporation in a single cell. Biophys J 92(2):404–4017

    Article  Google Scholar 

  • Kroeger JH, Vernon D, Grant M (2009) Curvature-driven pore growth in charged membranes during charge-pulse and voltage-clamp experiments. Biophys J 96(3):907–916

    Article  Google Scholar 

  • Leguébe M, Silve A, Mir L, Poignard C (2014) Conducting and permeable states of cell membrane submitted to high voltage pulses. mathematical and numerical studies validated by the experiments. J Theor Biol 360:83–94

    Article  MATH  Google Scholar 

  • Li J, Lin H (2011) Numerical simulation of molecular uptake via electroporation. Bioelectrochemistry 82(1):10–21

    Article  Google Scholar 

  • Neu J, Krassowska W (1999) Asymptotic model of electroporation. Phys Rev E 53(3):3471–3482

    Article  Google Scholar 

  • Pakhomova O, Gregory B, Khorokhorina V, Bowman A, Xiao S, Pakhomov A (2011) Electroporation-induced electrosen-sitization. Plos One 6:e17100

    Article  Google Scholar 

  • Perrussel R, Poignard C (2013) Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer. Appl Math Comput 221:48–65

    MathSciNet  MATH  Google Scholar 

  • Poignard C (2009) About the transmembrane voltage potential of a biological cell in time-harmonic regime. ESAIM Proc 26:162–179

    Article  MathSciNet  MATH  Google Scholar 

  • Poignard C, Silve A (2014) Différence de potentiel induite par un champ electrique sur la membrane d’une cellule biologique. La Rev 3EI 75:11–20

    Google Scholar 

  • Portet T, Dimova R (2010) A new method for measuring edge tensions and stability of lipid bilayers: effect of membrane composition. Biophys J 84:3263–3273

    Google Scholar 

  • Pucihar G, Mir L, Miklavčič D (2002) The effect of pulse repetition frequency on the uptake into electropermeabilized cells in vitro with possible applications in electrochemotherapy. Bioelectrochemistry 57:167–172

    Article  Google Scholar 

  • Pucihar G, Kotnik T, Valič B, Miklavčič D (2006) Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann Biomed Eng 34(4):642–652

    Article  Google Scholar 

  • Rols M, Delteil C, Golzio M, Teissié J (1998) Control by ATP and ADP of voltage-induced mammalian-cell-membrane permeabilization, gene transfer and resulting expression. Eur J Biochem 254:382–388

    Article  Google Scholar 

  • Ryham R, Berezovik I, Cohen F (2011) Aqueous viscosity is the primary source of friction in lipidic pore dynamics. Biophys J 101:2929–2938

    Article  Google Scholar 

  • Sandre O, Moreaux L, Brochard-Wyart F (1999) Dynamics of transient pores in stretched vesicles. Proc Natl Acad Sci 96:10591–10596

    Article  Google Scholar 

  • Šatkauskas S, André F, Bureau M, Scherman D, Miklavčič D, Mir L (2005) Electrophoretic component of electric pulses determines the efficacy of in vivo DNA electrotransfer. Hum Gene Ther 16(10):1194–1201

    Article  Google Scholar 

  • Sengel J, Wallace MI (2016) Imaging the dynamics of individual pores. PNAS 113:5281–5286

    Article  Google Scholar 

  • Silve A, Giumerá Brunet A, Ivorra A, Mir L (2014) Comparison of the effects of the repetition rate between microsecond and nanosecond pulses: electropermeabilisation-induced electro-desensitization? Biochim Biophys Acta Gen Subj 1840:2139–2151

    Article  Google Scholar 

  • Smith K, Neu J, Krassowska W (2004) Model of creation and evolution of stable electropores for DNA delivery. Biophys J 86(5):2813–2826

    Article  Google Scholar 

  • Smith K, Son R, Gowrishankar T, Weaver J (2014) Emergence of a large pore subpopulation during electroporating pulses. Bioelectrochemistry 100:3–10

    Article  Google Scholar 

  • Son R, Gowrishankar T, Weaver J (2016) Modeling a conventional electroporation pulse train: decreased pore number, cumulative calcium transport and an example of electrosensitization. IEEE Trans Biomed Eng 63:571–580

    Article  Google Scholar 

  • Vernier T, Sun Y, Marcu L, Salemi S, Craft C, Gundersen M (2003) Calcium bursts induced by nanosecond electric pulses. Biochem Biophys Res Commun 310(2):286–295

    Article  Google Scholar 

  • Weaver J, Chimazdzhev Y (1996) Theory of electroporation: a review. Bioelectrochem Bioenerg 41:135–160

    Article  Google Scholar 

  • Wegner L, Frey W, Silve A (2015) Electroporation of dc–3f cells is a dual process. Biophys J 108:1660–1671

    Article  Google Scholar 

Download references

Acknowledgments

This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the “Investments for the future,” Programme IdEx Bordeaux, CPU (ANR-10-IDEX-03-02).

Numerical simulations presented in this paper were carried out using the PLAFRIM experimental testbed, being developed under the Inria PlaFRIM development action with support from LABRI and IMB and other entities: Conseil Régional d’Aquitaine, FeDER, Université de Bordeaux, and CNRS (see https://plafrim.bordeaux.inria.fr/).

C.P. is partly granted by the Plan Cancer project DYNAMO (9749 Inserm), and the Plan Cancer project NUMEP (11099 Inserm). C.P. is also member of the European lab of CNRS, LEA EBAM, on electroporation.

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Correspondence to Clair Poignard .

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Poignard, C., Silve, A., Wegner, L.H. (2017). Different Approaches Used in Modeling of Cell Membrane Electroporation. In: Miklavčič, D. (eds) Handbook of Electroporation. Springer, Cham. https://doi.org/10.1007/978-3-319-32886-7_3

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