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Theoretical Evaluation of Voltage Inducement on Internal Membranes of Biological Cells Exposed to Electric Fields
Open accessAbstract
Several reports have recently been published on effects of very short and intense electric pulses on cellular organelles; in a number of cases, the cell plasma membrane appeared to be affected less than certain organelle membranes, whereas with longer and less intense pulses the opposite is the case. The effects are the consequence of the voltages induced on the membranes, and in this article we investigate the conditions under which the induced voltage on an organelle membrane could exceed its counterpart on the cell membrane. This would provide a possible explanation of the observed effects of very short pulses. Frequency-domain analysis yields an insight into the dependence of the voltage inducement on the electric and geometric parameters characterizing the cell and its vicinity. We show that at sufficiently high field frequencies, for a range of parameter values the voltage induced on the organelle membrane can indeed exceed the voltage induced on the cell membrane. Particularly, this can occur if the organelle interior is electrically more conductive than the cytosol, or if the organelle membrane has a lower dielectric permittivity than the cell membrane, and we discuss the plausibility of these conditions. Time-domain analysis is then used to determine the courses of the voltage induced on the membranes by pulses with risetimes and durations in the nanosecond range. The particularly high resting voltage in mitochondria, to which the induced voltage superimposes, could contribute to the explanation why these organelles are the primary target of many observed effects.
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“as the frequency of the field increases, the high membrane field gain diminishes, allowing for higher field intensities to penetrate into the cell.”
From An Overview of Sub-Cellular Mechanisms Involved in the Action of TTFields (2016) · cites this paper as [31]
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MethodThe application of PEF technology in food processing and human nutrition
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Induced Transmembrane Voltage and Its Correlation with Electroporation-Mediated Molecular Transport
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MethodAdvanced Electroporation Techniques in Biology and Medicine
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Membrane permeabilization and cell damage by ultrashort electric field shocks
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“…based on the Laplace equation (see, e.g., Pauly and Schwan 1959 for the first-order analysis on a spherical vesicle; Kotnik et al. 1998 for the second-order analysis; and Kotnik and Miklavcic 2006 for the second-order analysis for two concentric spherical vesicles, i.e., modeling an organelle).”
MethodTutorial: Electroporation of cells in complex materials and tissue
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Kinetics of Transmembrane Transport of Small Molecules into Electropermeabilized Cells
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Pucihar, G., Damijan Miklavčič, A., & Kotnik, T. (2009) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2009.2014244 · Cited by 176
“where a, fS1 , fS2 , τ1, and τ2 are given in [27] and [36].”
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Napotnik, T. B., Wu, Y., Gundersen, M. A., Damijan Miklavčič, A., & Vernier, P. T. (2011) · Bioelectromagnetics · doi:10.1002/bem.20707 · Cited by 171
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BackgroundInfluentialInvestigating ROS sources in male infertility: A common end for numerous pathways
Lavranos, G. M., Balla, M., Tzortzopoulou, A., Syriou, V., & Angelopoulou, R. (2012) · Reproductive Toxicology · doi:10.1016/j.reprotox.2012.06.007 · Cited by 166
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“These channels are activated by membrane depolarization by 30–50 mV, whereas the transmembrane potential required for electroporation is about an order of magnitude greater [1,2,8].”
A review of sublethal effects of pulsed electric field on cells in food processing
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“Kotnik T, Miklavcic D. Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields.”
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Modulation of cell function by electric field: a high-resolution analysis
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Reberšek, M., Damijan Miklavčič, A., Bertacchini, C., & Sack, M. (2014) · IEEE Electrical Insulation Magazine · doi:10.1109/mei.2014.6804737 · Cited by 102
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Subnanosecond Electric Pulses Cause Membrane Permeabilization and Cell Death
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“For subnanosecond pulses, the probability of penetrating into the interior of the cell is even higher than for nanosecond pulses [19].”
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Perspective on Pulsed Electric Field Treatment in the Bio-based Industry
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Nanosecond Pulsed Electric Field (nsPEF): Opening the Biotechnological Pandora’s Box
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Electroporation of Intracellular Liposomes Using Nanosecond Electric Pulses—A Theoretical Study
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“Although the nsEP have strong effects on cell interior, theoretical models and simulations [21, 32, 55] point out that generally, the plasma membrane is also affected.”
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Effect of nanosecond pulsed electric field treatment on cell proliferation of microalgae
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“Based on mathematical models an increased electropermeabilization effect on intracellular structures compared to the cell membrane was observed for angular frequencies ω (rad s−1) above 107 (Kotnik and Miklavčič, 2006; Vernier et al., 2006).”
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Pulse Electric Field Technology for Wastewater and Biomass Residues’ Improved Valorization
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“In conventional PEF processing the electric field is applied in intervals in the range of micro- to milliseconds; in nanosecond PEF (nsPEF) processing, much higher electric fields (10–100 kV/cm) are applied for intervals of 1–300 ns, inducing distinct intracellular effects from those of conventional PEF [8].”
BackgroundVariability of the Minimal Transmembrane Voltage Resulting in Detectable Membrane Electroporation
Towhidi, L., Kotnik, T., Pucihar, G., Firoozabadi, M., Mozdarani, H., & Damijan Miklavčič, A. (2008) · Electromagnetic Biology and Medicine · doi:10.1080/15368370802394644 · Cited by 58
“The conductivities of the cytoplasm and the (non porated) membrane were set at 3 10 1 S/m and 5 10 7 Sm 1, respectively, and the membrane thickness at 5 nm (Kotnik et al., 1997; Kotnik and Miklavčič, 2006).”
BackgroundMechanisms and immunogenicity of nsPEF-induced cell death in B16F10 melanoma tumors
Rossi, A., Pakhomova, O. N., Pakhomov, A. G., Weygandt, S., Bulysheva, A. A., Murray, L., Mollica, P. A., & Muratori, C. (2019) · Scientific Reports · doi:10.1038/s41598-018-36527-5 · Cited by 58
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Advantages and Disadvantages of Different Concepts of Electroporation Pulse Generation
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Assessment of Cytoplasm Conductivity by Nanosecond Pulsed Electric Fields
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“result, three-layer microdosimetry models often resorted to the conductivity of simple phosphate buffer saline solution (PBS) [15], [19], [30], or water with a certain fraction of dissolved”
BackgroundEffects of Oscillatory Electric Fields on Internal Membranes: An Analytical Model
Vajrala, V., Claycomb, J. R., Sanabria, H., & Miller, J. H. (2007) · Biophysical Journal · doi:10.1529/biophysj.107.114611 · Cited by 51
“More recently, Kotnik and Miklavčič calculated the ac transmembrane voltage induced on spheroidal cells (26) and across internal membranes, using a double-shell model for application to cells exposed to nanosecond-duration pulsed electric fields (27).”
MethodHuang, K., Yu, L., Wang, W., Gai, L., & Wang, J. (2013) · Food Control · doi:10.1016/j.foodcont.2013.07.011 · Cited by 48
Controlling properties of human neural progenitor cells using 2D and 3D conductive polymer scaffolds
Song, S., Amores, D., Chen, C., McConnell, K. W., Oh, B., Poon, A. S. Y., & George, P. M. (2019) · Scientific Reports · doi:10.1038/s41598-019-56021-w · Cited by 49
Ye, H., Cotic, M., Kang, E. E., Fehlings, M. G., & Carlen, P. L. (2010) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/1743-0003-7-12 · Cited by 47
“Another study [41] has modeled the internal membrane response to the time-varying electric field, and has investigated the condition under which ψorg can temporarily exceed ψcell under nanosecond duration pulsed electric fields.”
InfluentialSong, J., Joshi, R. P., & Schoenbach, K. H. (2011) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-011-0745-z · Cited by 48
Histopathology of normal skin and melanomas after nanosecond pulsed electric field treatment
Chen, X., Swanson, R. J., Kolb, J. F., Nuccitelli, R., & Schoenbach, K. H. (2009) · Melanoma Research · doi:10.1097/cmr.0b013e32832f1558 · Cited by 46
From the basic science of biological effects of ultrashort electrical pulses to medical therapies
Schoenbach, K. H. (2018) · Bioelectromagnetics · doi:10.1002/bem.22117 · Cited by 44
“This simple, analytical model, which served as the basis for the understanding of intracellular effects caused by ultrashort pulses, has been refined and expanded [Foster, 2000; Kotnik and Miklavcic, 2006].”
MethodMicrodosimetric Study for Nanosecond Pulsed Electric Fields on a Cell Circuit Model with Nucleus
Denzi, A., Merla, C., Camilleri, P., Paffi, A., d'Inzeo, G., Apollonio, F., & Liberti, M. (2013) · The Journal of Membrane Biology · doi:10.1007/s00232-013-9546-7 · Cited by 44
“The analytical models rely on the solution of the quasi-static Laplace equation on a spherical cell (Kotnik and Miklavcic 2006; Kotnik et al. 2010; Merla et al. 2011); the numerical ones are based on a distributed circuit representation (Joshi et al.”
BackgroundMethodInfluentialYe, H., Hendee, J., Ruan, J., Zhirova, A., Ye, J., & Dima, M. (2022) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/s12984-022-01094-4 · Cited by 46
“Computational work revealed that larger cell bodies are associated with greater transmembrane potentials under electrical [56] and magnetic [13] stimulation.”
BackgroundŽgalin, M. K., Hodžić, D., Reberšek, M., & Kandušer, M. (2012) · The Journal of Membrane Biology · doi:10.1007/s00232-012-9481-z · Cited by 43
Nanosecond Electric Pulse Effects on Gene Expression
Chopinet, L., Napotnik, T. B., Montigny, A., Reberšek, M., Teissié, J., Rols, M., & Damijan Miklavčič, A. (2013) · The Journal of Membrane Biology · doi:10.1007/s00232-013-9579-y · Cited by 43
“Numerical simulations (Joshi et al. 2004; Kotnik and Miklavcic 2006; Retelj et al. 2013) predict that the electric parameters of cells Fig.”
BackgroundWindow effect of pulsed electric field on biological cells
Yao, C., Hu, X., Mi, Y., Li, C., & Sun, C. (2009) · IEEE Transactions on Dielectrics and Electrical Insulation · doi:10.1109/tdei.2009.5293936 · Cited by 40
“Kontik and Damijan [17-19] extended the Schwan theory, introducing a general analytical method.”
BackgroundKranjc, M., Kranjc, S., Bajd, F., Serša, G., Serša, I., & Miklavčič, D. (2017) · Scientific Reports · doi:10.1038/s41598-017-10846-5 · Cited by 42
Cell membrane thermal gradients induced by electromagnetic fields
Garner, A. L., Deminsky, M., Neculaes, V. B., Chashihin, V., Knizhnik, A. A., & Potapkin, B. V. (2013) · Journal of Applied Physics · doi:10.1063/1.4809642 · Cited by 39
Membrane dielectric dispersion in nanosecond pulsed electroporation of biological cells
Salimi, E., Thomson, D. J., & Bridges, G. E. (2013) · IEEE Transactions on Dielectrics and Electrical Insulation · doi:10.1109/tdei.2013.6571442 · Cited by 39
“There is evidence that by applying megavolt-per-meter, nanosecond duration electric pulses, such that the pulse duration is less than the charging time of the cell membrane, the electric field can penetrate inside the cell and electroporate internal membranes [9-11].”
BackgroundHaberkorn, I., Buchmann, L., Hiestand, M., & Mathys, A. (2019) · Bioresource Technology · doi:10.1016/j.biortech.2019.122029 · Cited by 40
Mercadal, B., Vernier, P. T., & Ivorra, A. (2016) · The Journal of Membrane Biology · doi:10.1007/s00232-016-9907-0 · Cited by 38
“, 1988) εe 70 Relative permittivity of the extracellular medium (Kotnik and Miklavčič, 2006) εi 70 Relative permittivity of the intracellular medium (Kotnik and Miklavčič, 2006) εm 5 Relative permittivity of the membrane (Kotnik and Miklavčič, 2006) w 10 × R Dimensions of the simulated space (10 times cell radius) σp…”
BackgroundTemperature Dependence of High Frequency Irreversible Electroporation Evaluated in a 3D Tumor Model
Fesmire, C. C., Petrella, R. A., FOGLE, C. A., Gerber, D. A., Xing, L., & Sano, M. B. (2020) · Annals of Biomedical Engineering · doi:10.1007/s10439-019-02423-w · Cited by 38
Evaluation of the Electroporation Efficiency of a Grid Electrode for Electrochemotherapy
Ongaro, A., Campana, L. G., Mattei, M. D., Dughiero, F., Forzan, M., Pellati, A., Rossi, C. R., & Sieni, E. (2015) · Technology in Cancer Research & Treatment · doi:10.1177/1533034615582350 · Cited by 37
“A simple model of needles inserted in homogeneous tissue was proposed previously.(2,18,27-29,31-35) Figure 2 shows the model geometry, a parallelepiped (eg, sizes 5 3.”
MethodField Distribution and DNA Transport in Solid Tumors During Electric Field-Mediated Gene Delivery
Henshaw, J. W., & Yuan, F. (2007) · Journal of Pharmaceutical Sciences · doi:10.1002/jps.21000 · Cited by 37
Assessing how electroporation affects the effective conductivity tensor of biological tissues
Mezeme, M. E., Kranjc, M., Bajd, F., Serša, I., Brosseau, C., & Damijan Miklavčič, A. (2012) · Applied Physics Letters · doi:10.1063/1.4767450 · Cited by 37
Transmembrane potential induced in a spherical cell model under low-frequency magnetic stimulation
Ye, H., Cotic, M., & Carlen, P. L. (2007) · Journal of Neural Engineering · doi:10.1088/1741-2560/4/3/014 · Cited by 36
Ye, H., Cotic, M., Fehlings, M. G., & Carlen, P. L. (2010) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-010-0704-0 · Cited by 36
“The choice of values and their ranges for the electric parameters was based on reports in the literature [23, 24].”
MethodSteuer, A., Schmidt, A., Labohá, P., Babica, P., & Kolb, J. F. (2016) · Bioelectrochemistry · doi:10.1016/j.bioelechem.2016.07.003 · Cited by 36
Huang, K., Jiang, T., Wang, W., Gai, L., & Wang, J. (2014) · Food and Bioprocess Technology · doi:10.1007/s11947-014-1272-3 · Cited by 35
The Phenomenon of Electroporation
Mahnič-Kalamiza, S., & Damijan Miklavčič, A. (2022) · Food engineering series · doi:10.1007/978-3-030-70586-2_3 · Cited by 33
“This is followed, within a microsecond, by the transmembrane field being amplified by polarization (positive and negative charge carriers accumulating either side of the membrane), resulting in the buildup of an induced transmembrane voltage (Kotnik and Miklavčič 2006).”
BackgroundGarcía-Sánchez, T., Merla, C., Fontaine, J., Muscat, A., & Mir, L. M. (2018) · Biochimica et Biophysica Acta (BBA) - Biomembranes · doi:10.1016/j.bbamem.2018.01.018 · Cited by 32
“Considering our results as a reflect of electropermeabilization of the internal membranes, the observed low pass filter frequency response is not in agreement with the theoretical predictions where a band pass filter behavior is usually assigned for the intracellular membranes [23,24].”
BackgroundMethodResultInfluentialNatural Fluctuations of an Electropore Show Fractional Lévy Stable Motion
Kotulska, M. (2006) · Biophysical Journal · doi:10.1529/biophysj.106.091363 · Cited by 32
Merla, C., Pakhomov, A. G., Semenov, I., & Vernier, P. T. (2017) · Biochimica et Biophysica Acta (BBA) - Biomembranes · doi:10.1016/j.bbamem.2017.04.014 · Cited by 31
Buchmann, L., Böcker, L., Frey, W., Haberkorn, I., Nyffeler, M., & Mathys, A. (2018) · Innovative Food Science & Emerging Technologies · doi:10.1016/j.ifset.2018.04.013 · Cited by 31
Electrolytic ablation enables cancer cell targeting through pH modulation
Perkons, N. R., Stein, E. J., Nwaezeapu, C., Wildenberg, J. C., Saleh, K. S., Itkin-Ofer, R., Ackerman, D., Soulen, M. C., Hunt, S. J., Nadolski, G., et al. (2018) · Communications Biology · doi:10.1038/s42003-018-0047-1 · Cited by 31
Metadata
- Authors
- Kotnik, T., & Miklavčič, D.
- Affiliations
- University of Ljubljana (SI)
- Corresponding author
- Kotnik, Tadej
- ORCID
- Kotnik, Tadej
- Venue
- Biophysical Journal
- Publisher
- Elsevier BV
- Published
- 2006-01
- Volume
- 90
- Issue
- 2
- Pages
- 480-491
- ISSN
- 0006-3495 (ISSN-L)
- PMC
- PMC1367054
- OpenAlex
- W2106955112
- Cited by
- 318
- References
- 68
- Citations by year
- 2026: 13 · 2025: 11 · 2024: 15 · 2023: 22 · 2022: 12 · 2021: 12 · 2020: 17 · 2019: 20 · 2018: 19 · 2017: 26 · 2016: 19 · 2015: 12 · 2014: 19 · 2013: 17 · 2012: 17
- FWCI
- 4.26
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Biophysical Journal (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Biophysics › Electromagnetic Fields and Biological Effects
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Biotechnology › Microbial Inactivation Methods
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Electrical and Electromagnetic Research
- Keywords
- electric field effects on cells, organelle membranes, nanosecond pulses, frequency domain analysis, time-domain analysis, membrane conductivity
- MeSH terms
- Animals, Biological Transport, Active, Biophysics, Cell Membrane, Cell Membrane Permeability, Cytosol, Electric Conductivity, Electromagnetic Fields, Intracellular Membranes, Membrane Fluidity, Membrane Lipids, Membrane Potentials, Models, Theoretical, Time Factors
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