In this Letter, we explore how cell electro-deformation and electro-poration are connected. We build a time-domain model of layered concentric shells (a model of biological cells) including their dielectric and elastic properties. We simulate delivery of one trapezoidal voltage pulse to either a single spherical cell or an assembly of three neighboring cells in a specific configuration and calculate cell deformation and pore formation. We describe the qualitative features of the electric field, surface charge density, transmembrane voltage, cell elongation, and pore density distribution at specific times i.e., before, during and after the application of the electric pulse and explore the correlations between them. Our results show that (1) the polarization charge redistribution plays a significant role in the spatial distribution of electrical stresses at μs time scales and (2) the cell deformation and pore density can be correlated with regions of high surface charge density. In future work, our model could be used for understanding basic mechanisms of electro-deformation and electro-poration with high-frequency short bipolar pulses of biological cells in suspension or tissues.
References
1.
D. S.
Dimitrov
, “Electroporation and electrofusion of membranes
,” in Handbook of Biological Physics
, edited by R.
Lipowsky
and E.
Sackmann
(Elsevier, Amsterdam
, 1995
), Vol. 1B, pp. 851
–901
.2.
J. C.
Weaver
and Y. A.
Chizmadzhev
, “Theory of electroporation: A review
,” Bioelectrochem. Bioenergy
41
, 135
–160
(1996
).3.
L.
Rems
and D.
Miklavčič
, “Electroporation of cells in complex materials and tissue
,” J. Appl. Phys.
119
, 201101
(2016
).4.
E.
Goldberg
, C.
Suárez
, M.
Alfonso
, J.
Marchese
, A.
Soba
, and G.
Marshall
, “Cell membrane electroporation modeling: A multiphysics approach
,” Bioelectrochemistry
124
, 28
–39
(2018
).5.
M.
Bier
, W.
Chen
, T. R.
Gowrishankar
, R. D.
Astumian
, and R. C.
Lee
, “Resealing dynamics of a cell membrane after electroporation
,” Phys. Rev. E
66
, 062905
(2002
).6.
C.
Chen
, S. W.
Smye
, and M. P.
Robinson
, “Membrane electroporation theories: A review
,” Med. Biol. Eng. Comput.
44
, 5
–14
(2006
).7.
G.
Pucihar
, D.
Miklavčič
, and T.
Kotnik
, “A time-dependent numerical model of transmembrane voltage inducement and electroporation of irregularly shaped cells
,” IEEE Trans. Biomed. Eng.
56
, 1491
–1501
(2009
).8.
T.
Murovec
, D. C.
Sweeney
, E.
Latouche
, R. V.
Davalos
, and C.
Brosseau
, “Modeling of transmembrane potential in realistic multicellular structures before electroporation
,” Biophys. J.
111
, 2286
–2295
(2016
).9.
M.
Essone Mezeme
, G.
Pucihar
, M.
Pavlin
, C.
Brosseau
, and D.
Miklavčič
, “A numerical analysis of multicellular environment for modeling tissue electroporation
,” Appl. Phys. Lett.
100
, 143701
(2012
);See also
M.
Essone Mezeme
, M.
Kranjc
, F.
Bajd
, I.
Sersa
, C.
Brosseau
, and D.
Miklavčič
, “Assessing how electroporation affects the effective conductivity tensor of biological tissues
,” Appl. Phys. Lett.
101
, 213702
(2012
).10.
H.
Isambert
, “Understanding the electroporation of cells and artificial bilayer membranes
,” Phys. Rev. Lett.
80
, 3404
(1998
).11.
H.
Li
, A.
Denzi
, X.
Ma
, X.
Du
, Y.
Ning
, X.
Cheng
, F.
Apollonio
, M.
Liberti
, and J. C. M.
Hwang
, “Distributed effect in high-frequency electroporation of biological cells
,” IEEE Trans. Microwave Theory Tech.
65
, 3503
–3511
(2017
);S.
Dong
, H.
Wang
, Y.
Zhao
, Y.
Sun
, and C.
Yao
, “First human trial of high-frequency irreversible electroporation therapy for prostate cancer
,” Technol. Cancer Res. Treat.
17
, 1
–9
(2018
);B.
Valič
, M.
Golzio
, M.
Pavlin
, A.
Schatz
, C.
Faurie
, B.
Gabriel
, J.
Teissié
, M.
Rols
, and D.
Miklavčič
, “Effect of electric field induced transmembrane potential on spheroidal cells: Theory and experiment
,” Eur. Biophys. J.
6
, 519
–528
(2003
).12.
C. B.
Arena
, M. B.
Sano
, M. N.
Rylander
, and R. V.
Davalos
, “High-frequency irreversible electroporation (H-FIRE) for non-thermal ablation without muscle contraction
,” IEEE Trans. Biomed. Eng.
58
, 1474
–1481
(2011
);
[PubMed]
D. C.
Sweeney
, M.
Reberšek
, J.
Dermol
, L.
Rems
, D.
Miklavčič
, and R. V.
Davalos
, “Quantification of cell membrane permeability induced by monopolar and high-frequency bipolar bursts of electrical pulses
,” Biochim. Biophys. Acta (BBA)-Biomembr.
11
, 2689
–2698
(2016
);L.
Mescia
, M. A.
Chiapperino
, P.
Bia
, J.
Gielis
, and D.
Caratelli
, “Modeling of electroporation induced by pulsed electric fields in irregularly shaped cells
,” IEEE Trans. Biomed. Eng.
65
, 414
–423
(2018
).
[PubMed]
13.
E. C.
Gianulis
, M.
Casciola
, S.
Xiao
, O. N.
Pakhomova
, and A. G.
Pakhomov
, “Electropermeabilization by uni- or bipolar nanosecond electric pulses: The impact of extracellular conductivity
,” Bioelectrochemistry
119
, 10
–19
(2018
).
[PubMed]
14.
V.
Novickij
, P.
Ruzgys
, A.
Grainys
, and S.
Šatkauskas
, “High frequency electroporation efficiency is under control of membrane capacitive charging and voltage potential relaxation
,” Bioelectrochemistry
119
, 92
–97
(2018
);
[PubMed]
J.
Dermol
and D.
Miklavčič
, “From cell to tissue properties—modeling skin electroporation with pore and local transport region formation
,” IEEE Trans. Biomed. Eng.
65
, 458
–468
(2018
).
[PubMed]
15.
K. A.
DeBruin
and W.
Krassowska
, “Modeling electroporation in a single cell. I. Effects of field strength and rest potential
,” Biophys. J.
77
, 1213
–1224
(1999
);
[PubMed]
K. A.
DeBruin
andW.
Krassowska
, “Modeling electroporation in a single cell. II. Effects of ionic concentrations
,” Biophys. J.
77
, 1225–1233
(1999
);
[PubMed]
J. C.
Neu
and W.
Krassowska
, “Asymptotic model of electroporation
,” Phys. Rev. E
59
, 3471
–3482
(1999
).16.
B.
Varga
, C.
Fazakas
, I.
Wilhelm
, I. A.
Krizbai
, Z.
Szegletes
, G.
Váró
, and A. G.
Végh
, “Elasto-mechanical properties of living cells
,” Biochem. Biophys. Rep.
7
, 303
–308
(2016
).17.
M.-A.
Meyers
, P.-Y.
Chen
, A. Y.-M.
Lin
, and Y.
Seki
, “Biological materials: Structure and mechanical properties
,” Prog. Mater. Sci.
53
, 1
–206
(2008
).18.
J.
Li
and H.
Lin
, “Numerical simulation of molecular uptake via electroporation
,” Bioelectrochemistry
82
, 10
–21
(2011
).
[PubMed]
19.
D.
Voyer
, A.
Silve
, L. M.
Mir
, R.
Scorretti
, and C.
Poignard
, “Dynamical modeling of tissue electroporation
,” Bioelectrochemistry
119
, 98
–110
(2018
);
[PubMed]
G.
Pucihar
, T.
Kotnik
, B.
Valič
, and D.
Miklavčič
, “Numerical determination of transmembrane voltage induced on irregularly shaped cells
,” Ann. Biomed. Eng.
34
, 642
(2006
).
[PubMed]
20.
D.
Shamoon
, S.
Lasquellec
, and C.
Brosseau
, “Perspective: Towards understanding the multiscale description of cells and tissue by electromechanobiology
,” J. Appl. Phys.
123
, 240902
(2018
).21.
R.
Pethig
, Dielectric and Electronic Properties of Biological Materials
(Wiley
, New York
, 1979
).22.
M. R.
Willis
, “Dielectric and Electronic Properties of Biological Materials’ by R Pethig. pp 376. John Wiley & Sons, Chichester and New York. 1979. £15
,” [book review], Biochem. Educ.
8
(1), 31
(1980
).23.
M.
Essone Mezeme
and C.
Brosseau
, “Simulation of a toy model of cylindrical cells submitted to nonionizing electromagnetic field: Effect of membrane cell disruption
,” J. Appl. Phys.
107
, 014701
(2010
).24.
COMSOL Multiphysics version 5.2.
25.
T.
Murovec
and C.
Brosseau
, “Anisotropy of the crossover between electrostatic attraction and repulsion of biological cells
,” Appl. Phys. Lett.
103
, 193702
(2013
).26.
Y.
Zhan
, C.
Sun
, Z.
Cao
, N.
Bao
, J.
Xing
, and C.
Lu
, “Release of intracellular proteins by electroporation with preserved cell viability
,” Anal. Chem.
84
, 8102
(2012
);
[PubMed]
B.
del Rosal
, C.
Sun
, D. N.
Loufakis
, C.
Lu
, and D.
Jaque
, “Thermal loading in flow-through electroporation microfluidic devices
,” Lab Chip
13
, 3119
(2013
);
[PubMed]
T.
Geng
and C.
Lu
, “Microfluidic electroporation for cellular analysis and delivery
,” Lab Chip
13
, 3803
(2013
).
[PubMed]
27.
L.
Mescia
, M. A.
Chiapperino
, P.
Bia
, C. M.
Lamacchia
, J.
Gielis
, and D.
Caratelli
, “Design of electroporation process in irregularly shaped multicellular systems
,” Electronics
8
, 37
(2019
).28.
T.
Kotnik
, L.
Rems L
, M.
Tarek
, and D.
Miklavčič
, “Membrane electroporation and electropermeabilization: Mechanisms and models
,” Annu. Rev. Biophys.
(in press).© 2019 Author(s).
2019
Author(s)
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