Bioelectrochemistry. 2010 Oct;79(2):257-60. Epub 2010 Mar 10.
Electroporation and alternating current cause membrane permeation of photodynamic cytotoxins yielding necrosis and apoptosis of cancer cells.
Traitcheva N, Berg H.
Institute of Plant Physiology “M. Popov,” Bulgarian Acad. of Sciences, Sofia, Bulgaria.
In order to increase the permeability of cell membranes for low doses of cytostatic drugs, two bioelectrochemical methods have been compared: (a) electric pore formation in the plasma membranes by single electric impulses (electroporation), and (b) reordering of membrane structure by alternating currents (capacitively coupled). These treatments were applied to human leukemic K-562 cells and human lymphoma U-937 cells, yielding apoptotic and necrotic effects, determined by flow cytometry. Additional cell death occurs after exposure to light irradiation at wavelengths lambda > 600 nm, of cells which were electroporated and had incorporated actinomycin-C or daunomycin (daunorubicin). It is observed that drug uptake after an exponentially decaying electroporation pulse of the initial field strength Eo=1.4 kV/cm and pulse time constants in the time range 0.5-3 ms is faster than during PEMF-treatment, i.e., application of an alternating current of 16 kHz, voltage U<100 V, I=55 mA, and exposure time 20 min. However, at the low a.c. voltage of this treatment, more apoptotic and necrotic cells are produced as compared to the electroporation treatment with one exponentially decaying voltage pulse. Thus, additional photodynamic action appears to be more effective than solely drugs and electroporation as applied in clinical electrochemotherapy, and more effective than the noninvasive pulsed electromagnetic fields (PEMFs), for cancer cells in general and animals bearing tumors in particular.
Pol Merkur Lekarski. 2010 Jun;28(168):501-4.
Electroporation and its application.
[Article in Polish]
Sko?ucka N, Saczko J, Kotulska M, Kulbacka J, Choroma?ska A.
Akademia Medyczna we Wroclawiu, Katedra i Zak?ad Biochemii Lekarskiej. email@example.com
Electroporation (EP) is a modern and versatile method that allows the penetration of macromolecules from the intercellular space into cells by forming the channels, under the influence of electromagnetic field. In addition to natural channels and pumps, building cell membranes, resulting electropores an additional way for the transport of macromolecules. The use of this phenomenon has brought good results as a complement to traditional therapeutic methods of treatment during application of cytostatics. EP combination with chemotherapy has reduced the need for surgical intervention (rescue authority). Electroporation is particularly useful for cancer with multidrug resistance, where the dose that enters the interior of cancer cells is limited. Electroporation was also used in transfection of nucleic acids, in photodynamic therapy, cosmetology, as well as the consolidation of the food.
EEE Trans Biomed Eng. 2009 May;56(5):1491-501. Epub 2009 Feb 6.
A time-dependent numerical model of transmembrane voltage inducement and electroporation of irregularly shaped cells.
Pucihar G, Miklavcic D, Kotnik T.
Faculty of Electrical Engineering, University of Ljubljana, Ljubljana SI-1000, Slovenia. firstname.lastname@example.org
We describe a finite-element model of a realistic irregularly shaped biological cell in an external electric field that allows the calculation of time-dependent changes of the induced transmembrane voltage (Delta Psi) and simulation of cell membrane electroporation. The model was first tested by comparing its results to the time-dependent analytical solution for Delta Psi on a nonporated spherical cell, and a good agreement was obtained. To simulate electroporation, the model was extended by introducing a variable membrane conductivity. In the regions exposed to a sufficiently high Delta Psi, the membrane conductivity rapidly increased with time, leading to a modified spatial distribution of Delta Psi. We show that steady-state models are insufficient for accurate description of Delta Psi, as well as determination of electroporated regions of the membrane, and time-dependent models should be used instead. Our modeling approach also allows direct comparison of calculations and experiments. As an example, we show that calculated regions of electroporation correspond to the regions of molecular transport observed experimentally on the same cell from which the model was constructed. Both the time-dependent model of Delta Psi and the model of electroporation can be exploited further to study the behavior of more complicated cell systems, including those with cell-to-cell interactions.
Sheng Wu Yi Xue Gong Cheng Xue Za Zhi. 2008 Oct;25(5):1206-9.
Research progress of nanosecond pulsed electric field applied to intracellular electromanipulation.
[Article in Chinese]
Yao C, Mo D, Sun C, Chen X, Xiong Z.
Key Lab of High Voltage Engineering and Electrical New Technology, Ministry of Education, Chongqing University, Chongqing 400044, China. email@example.com
In recent years, many experts have done some researches on experiment and mechanism of intracellular electromanipulation (IEM) under nanosecond pulsed electric field (nsPEF). The experiment results have shown that nsPEF could not induce electroporation of cell membrane, but could induce intracellular effects such as apoptosis, calcium release, enhancement of gene expression, and fragmentation of DNA and chromosome. In order to account for the phenomenon, researchers believe that when the pulse width of the pulsed electric field is larger than the charging time of plasma membrane, the pulsed electric field mainly targets on the outer membrane of cell; and that the effect of the pulsed electric field on nucleus and nuclear membrane increases with the decrease of the pulse width. It is also believed that the effect of electroporation changes from the outer membrane to intracellular electromanipulation when the pulse width decreases to a value being smaller than the charging time of plasma membrane.
Biomech Model Mechanobiol. 2008 Oct;7(5):379-86. Epub 2007 Jul 27.
Finite element analysis of microelectrotension of cell membranes.
Bae C, Butler PJ.
Department of Bioengineering, The Pennsylvania State University, 205 Hallowell Building, University Park, PA 16802, USA. firstname.lastname@example.org
Electric fields can be focused by micropipette-based electrodes to induce stresses on cell membranes leading to tension and poration. To date, however, these membrane stress distributions have not been quantified. In this study, we determine membrane tension, stress, and strain distributions in the vicinity of a microelectrode using finite element analysis of a multiscale electro-mechanical model of pipette, media, membrane, actin cortex, and cytoplasm. Electric field forces are coupled to membranes using the Maxwell stress tensor and membrane electrocompression theory. Results suggest that micropipette electrodes provide a new non-contact method to deliver physiological stresses directly to membranes in a focused and controlled manner, thus providing the quantitative foundation for micreoelectrotension, a new technique for membrane mechanobiology.
Ann Biomed Eng. 2007 Jul;35(7):1264-75. Epub 2007 Mar 6.
Electric fields around and within single cells during electroporation-a model study.
Mossop BJ, Barr RC, Henshaw JW, Yuan F.
Department of Biomedical Engineering, Duke University, 136 Hudson Hall, Box 90281, Durham, NC 27708, USA.
One of the key issues in electric field-mediated molecular delivery into cells is how the intracellular field is altered by electroporation. Therefore, we simulated the electric field in both the extracellular and intracellular domains of spherical cells during electroporation. The electroporated membrane was modeled macroscopically by assuming that its electric resistivity was smaller than that of the intact membrane. The size of the electroporated region on the membrane varied from zero to the entire surface of the cell. We observed that for a range of values of model constants, the intracellular current could vary several orders of magnitude whereas the maximum variations in the extracellular and total currents were less than 8% and 4%, respectively. A similar difference in the variations was observed when comparing the electric fields near the center of the cell and across the permeabilized membrane, respectively. Electroporation also caused redirection of the extracellular field that was significant only within a small volume in the vicinity of the permeabilized regions, suggesting that the electric field can only facilitate passive cellular uptake of charged molecules near the pores. Within the cell, the field was directed radially from the permeabilized regions, which may be important for improving intracellular distribution of charged molecules.
Biophys J. 2008 Jun;94(12):5018-27. Epub 2008 Mar 13.
Quantification of electroporative uptake kinetics and electric field heterogeneity effects in cells.
Kennedy SM, Ji Z, Hedstrom JC, Booske JH, Hagness SC.
Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA. email@example.com
We have conducted experiments quantitatively investigating electroporative uptake kinetics of a fluorescent plasma membrane integrity indicator, propidium iodide (PI), in HL60 human leukemia cells resulting from exposure to 40 mus pulsed electric fields (PEFs). These experiments were possible through the use of calibrated, real-time fluorescence microscopy and the development of a microcuvette: a specialized device designed for exposing cell cultures to intense PEFs while carrying out real-time microscopy. A finite-element electrostatic simulation was carried out to assess the degree of electric field heterogeneity between the microcuvette’s electrodes allowing us to correlate trends in electroporative response to electric field distribution. Analysis of experimental data identified two distinctive electroporative uptake signatures: one characterized by low-level, decelerating uptake beginning immediately after PEF exposure and the other by high-level, accelerating fluorescence that is manifested sometimes hundreds of seconds after PEF exposure. The qualitative nature of these fluorescence signatures was used to isolate the conditions required to induce exclusively transient electroporation and to discuss electropore stability and persistence. A range of electric field strengths resulting in transient electroporation was identified for HL60s under our experimental conditions existing between 1.6 and 2 kV/cm. Quantitative analysis was used to determine that HL60s experiencing transient electroporation internalized between 50 and 125 million nucleic acid-bound PI molecules per cell. Finally, we show that electric field heterogeneity may be used to elicit asymmetric electroporative PI uptake within cell cultures and within individual cells.
Bioelectrochemistry. 2007 May;70(2):275-82. Epub 2006 Oct 18.
High electrical field effects on cell membranes.
Pliquett U, Joshi RP, Sridhara V, Schoenbach KH.
Frank Reidy Research Center for Bioelectrics 830 Southampton Ave., Suite 5100, Norfolk, VA 23510, United States.
Electrical charging of lipid membranes causes electroporation with sharp membrane conductance increases. Several recent observations, especially at very high field strength, are not compatible with the simple electroporation picture. Here we present several relevant experiments on cell electrical responses to very high external voltages. We hypothesize that, not only are aqueous pores created within the lipid membranes, but that nanoscale membrane fragmentation occurs, possibly with micelle formation. This effect would produce conductivity increases beyond simple electroporation and display a relatively fast turn-off with external voltage. In addition, material loss can be expected at the anode side of cells, in agreement with published experimental reports at high fields. Our hypothesis is qualitatively supported by molecular dynamics simulations. Finally, such cellular responses might temporarily inactivate voltage-gated and ion-pump activity, while not necessarily causing cell death. This hypothesis also supports observations on electrofusion.
J Biomol Struct Dyn. 2007 Apr;24(5):495-503.
Self-electroporation as a model for fusion pore formation.
Luitel P, Schroeter DF, Powell JW.
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA.
The creation of a small opening called the fusion pore is a necessary prerequisite for neurotransmitter release from synaptic vesicles. It is known that high intensity electric fields can create pores in vesicles by a process called electroporation. Due to the presence of charged phosphatidylserine (PS) molecules on the inner leaflet of the cell membrane, an electric field that is strong enough to cause electroporation of a synaptic vesicle might be present. It was shown by K. Rosenheck [K. Rosenheck. Biophys J 75, 1237-1243 (1998)] that in a planar geometry, fields sufficient to cause electroporation can occur at intermembrane separations of less than approximately 3 nm. It is frequently found, however, that the cell membrane is not planar but caves inward at the locations where a vesicle is close to it. Indentation of the cell membrane in the fusion region was modelled as a hemisphere and a theoretical study of the electric field in the vicinity of the cell membrane taking into account the screening effect of dissolved ions in the cytoplasm was performed. It was discovered that fields crossing the electroporation threshold occurred at a distance of 2 nm or less, supporting the claim that electroporation could be a possible mechanism for fusion pore formation.
IEEE Trans Biomed Eng. 2007 Apr;54(4):611-20.
Hybrid finite element method for describing the electrical response of biological cells to applied fields.
Ying W, Henriquez CS.
Department of Biomedical Engineering, Duke University, Durham, NC 27708-0281, USA. firstname.lastname@example.org
A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.
Electromagn Biol Med. 2007;26(3):239-50.
Modeling environment for numerical simulation of applied electric fields on biological cells.
Suzuki DO, Ramos A, Marques JL.
Department of Electrical Engineering, Institute of Biomedical Engineering, Federal University of Santa Catarina (UFSC), Santa Catarina, Brazil.
The application of electric pulses in cells increases membrane permeability. This phenomenon is called electroporation. Current electroporation models do not explain all experimental findings: part of this problem is due to the limitations of numerical methods. The Equivalent Circuit Method (ECM) was developed in an attempt to solve electromagnetic problems in inhomogeneous and anisotropic media. ECM is based on modeling of the electrical transport properties of the medium by lumped circuit elements as capacitance, conductance, and current sources, representing the displacement, drift, and diffusion current, respectively. The purpose of the present study was to implement a 2-D cell Model Development Environment (MDE) of ionic transport process, local anisotropy around cell membranes, biological interfaces, and the dispersive behaviour of tissues. We present simulations of a single cell, skeletal muscle, and polygonal cell arrangement. Simulation of polygonal form indicates that the potential distribution depends on the geometrical form of cell. The results demonstrate the importance of the potential distributions in biological cells to provide strong evidences for the understanding of electroporation.
Biophys J. 2007 Jan 15;92(2):404-17. Epub 2006 Oct 20.
Modeling electroporation in a single cell.
Krassowska W, Filev PD.
Department of Biomedical Engineering, Duke University, Durham, North Carolina, USA. email@example.com
Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.
Phys Biol. 2006 Nov 2;3(4):233-47.
Nanopore-facilitated, voltage-driven phosphatidylserine translocation in lipid bilayers–in cells and in silico.
Vernier PT, Ziegler MJ, Sun Y, Gundersen MA, Tieleman DP.
Department of Electrical Engineering-Electrophysics, Viterbi School of Engineering, University of Southern California, Los Angeles CA, 90089-0271, USA. firstname.lastname@example.org
Nanosecond, megavolt-per-meter pulses–higher power but lower total energy than the electroporative pulses used to introduce normally excluded material into biological cells–produce large intracellular electric fields without destructively charging the plasma membrane. Nanoelectropulse perturbation of mammalian cells causes translocation of phosphatidylserine (PS) to the outer face of the cell, intracellular calcium release, and in some cell types a subsequent progression to apoptosis. Experimental observations and molecular dynamics (MD) simulations of membranes in pulsed electric fields presented here support the hypothesis that nanoelectropulse-induced PS externalization is driven by the electric potential that appears across the lipid bilayer during a pulse and is facilitated by the poration of the membrane that occurs even during pulses as brief as 3 ns. MD simulations of phospholipid bilayers in supraphysiological electric fields show a tight association between PS externalization and membrane pore formation on a nanosecond time scale that is consistent with experimental evidence for electropermeabilization and anode-directed PS translocation after nanosecond electric pulse exposure, suggesting a molecular mechanism for nanoelectroporation and nanosecond PS externalization: electrophoretic migration of the negatively charged PS head group along the surface of nanometer-diameter electropores initiated by field-driven alignment of water dipoles at the membrane interface.
BMC Cell Biol. 2006 Oct 19;7:37.
Nanoelectropulse-driven membrane perturbation and small molecule permeabilization.
Vernier PT, Sun Y, Gundersen MA.
Department of Electrical Engineering-Electrophysics, Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-0271, USA. email@example.com
BACKGROUND: Nanosecond, megavolt-per-meter pulsed electric fields scramble membrane phospholipids, release intracellular calcium, and induce apoptosis. Flow cytometric and fluorescence microscopy evidence has associated phospholipid rearrangement directly with nanoelectropulse exposure and supports the hypothesis that the potential that develops across the lipid bilayer during an electric pulse drives phosphatidylserine (PS) externalization.
RESULTS: In this work we extend observations of cells exposed to electric pulses with 30 ns and 7 ns durations to still narrower pulse widths, and we find that even 3 ns pulses are sufficient to produce responses similar to those reported previously. We show here that in contrast to unipolar pulses, which perturb membrane phospholipid order, tracked with FM1-43 fluorescence, only at the anode side of the cell, bipolar pulses redistribute phospholipids at both the anode and cathode poles, consistent with migration of the anionic PS head group in the transmembrane field. In addition, we demonstrate that, as predicted by the membrane charging hypothesis, a train of shorter pulses requires higher fields to produce phospholipid scrambling comparable to that produced by a time-equivalent train of longer pulses (for a given applied field, 30, 4 ns pulses produce a weaker response than 4, 30 ns pulses). Finally, we show that influx of YO-PRO-1, a fluorescent dye used to detect early apoptosis and activation of the purinergic P2X7 receptor channels, is observed after exposure of Jurkat T lymphoblasts to sufficiently large numbers of pulses, suggesting that membrane poration occurs even with nanosecond pulses when the electric field is high enough. Propidium iodide entry, a traditional indicator of electroporation, occurs with even higher pulse counts.
CONCLUSION: Megavolt-per-meter electric pulses as short as 3 ns alter the structure of the plasma membrane and permeabilize the cell to small molecules. The dose responses of cells to unipolar and bipolar pulses ranging from 3 ns to 30 ns duration support the hypothesis that a field-driven charging of the membrane dielectric causes the formation of pores on a nanosecond time scale, and that the anionic phospholipid PS migrates electrophoretically along the wall of these pores to the external face of the membrane.
IEEE Trans Nanobioscience. 2006 Sep;5(3):157-63.
Effect of pore size on the calculated pressure at biological cells pore wall.
El-Hag AH, Zheng Z, Boggs SA, Jayaram SH.
Electrical Engineering Department, American University of Sharjah, Sharjah, United Arab Emirate. firstname.lastname@example.org
A transient nonlinear finite-element program has been used to calculate the electric field distribution as a function of time for a spherical cell with a pore in a conducting medium during application of a subnanosecond rise time “step” wave, including the effects of dipolar saturation in the water-based cytoplasm and cell medium. The time-dependent pressure on the pore wall has been computed as a function of time as the system polarizes from the change of the energy in the electric field to the left (inside the pore) and to the right (inside the membrane) of the pore wall. The computations suggest that dipolar saturation, while significant, has little effect on the time-dependent electric field distribution but a substantial effect on the field-induced pore wall pressure. Also, the effect of pore size on both the computed electric field and field-induced pressure was studied. As the pore size increases, a collapse in both the electric field and field-induced pressure has been noticed. This suggests that as the pore size increases, the driving force for further opening the pore is not electrical.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 1):021904. Epub 2006 Aug 3.
Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation.
Vasilkoski Z, Esser AT, Gowrishankar TR, Weaver JC.
Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a 10 ns trapezoidal pulse with 1.5 ns rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska’s asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.
J Biomech Eng. 2006 Feb;128(1):76-84.
Numerical modeling of in vivo plate electroporation thermal dose assessment.
Becker SM, Kuznetsov AV.
Mechanical and Aerospace Engineering, North Carolina State University, Box 7910, Raleigh, NC 27695, USA. email@example.com
Electroporation is an approach used to enhance the transport of large molecules to the cell cytosol in which a targeted tissue region is exposed to a series of electric pulses. The cell membrane, which normally acts as a barrier to large molecule transport into the cell interior, is temporarily destabilized due to the development of pores in the cell membrane. Consequently, agents that are ordinarily unable enter the cell are able to pass through the cell membrane. Of possible concern when exposing biological tissue to an electric field is thermal tissue damage associated with joule heating. This paper explores the thermal effects of various geometric, biological, and electroporation pulse parameters including the blood vessel presence and size, plate electrode configuration, and pulse duration and frequency. A three-dimensional transient finite volume model of in vivo parallel plate electroporation of liver tissue is used to develop a better understanding of the underlying relationships between the physical parameters involved with tissue electroporation and resulting thermal damage potential.
Conf Proc IEEE Eng Med Biol Soc. 2006;1:2276-9.
Field stimulation of cells in suspension: use of a hybrid finite element method.
Ying W, Pourtaheri N, Henriquez CS.
Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA. firstname.lastname@example.org
Electric fields are used in a range of applications, including gene transfection, electrochemotherapy of tumors and cardiac defibrillation. Despite the widespread use of electric fields, most of the theoretical and computational studies on discrete cellular tissue have focused on a single cell. In this work, we propose a hybrid finite element method to simulate the effects of external electric fields on clusters of excitable cells. The method can be used to model cells of arbitrary cell geometries and non-linear membrane dynamics. The results show that the response of multiple cell, like a single cell, is a two-stage process consisting of the initial polarization that proceeds with cellular time constant (less than one microsecond) and the actual excitation of the cell membrane that proceeds with the membrane time constant (on the order of milliseconds). The results also show that the stimulation of a given cell depends in part on the arrangement of cells within the field and not simply the location within the field, suggesting that classical approaches that ignores the effect of the cells on the field do not adequately predict the cellular response.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 1):031902. Epub 2005 Sep 8.
Simulations of nanopore formation and phosphatidylserine externalization in lipid membranes subjected to a high-intensity, ultrashort electric pulse.
Hu Q, Joshi RP, Schoenbach KH.
Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529-0246, USA.
A combined MD simulator and time dependent Laplace solver are used to analyze the electrically driven phosphatidylserine externalization process in cells. Time dependent details of nanopore formation at cell membranes in response to a high-intensity (100 kV/cm), ultrashort (10 ns) electric pulse are also probed. Our results show that nanosized pores could typically be formed within about 5 ns. These predictions are in very good agreement with recent experimental data. It is also demonstrated that defect formation and PS externalization in membranes should begin on the anode side. Finally, the simulations confirm that PS externalization is a nanopore facilitated event, rather than the result of molecular translocation across the trans-membrane energy barrier.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Mar;71(3 Pt 1):031914. Epub 2005 Mar 29.
Simulations of transient membrane behavior in cells subjected to a high-intensity ultrashort electric pulse.
Hu Q, Viswanadham S, Joshi RP, Schoenbach KH, Beebe SJ, Blackmore PF.
Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529-0246, USA.
A molecular dynamics (MD) scheme is combined with a distributed circuit model for a self-consistent analysis of the transient membrane response for cells subjected to an ultrashort (nanosecond) high-intensity (approximately 0.01-V/nm spatially averaged field) voltage pulse. The dynamical, stochastic, many-body aspects are treated at the molecular level by resorting to a course-grained representation of the membrane lipid molecules. Coupling the Smoluchowski equation to the distributed electrical model for current flow provides the time-dependent transmembrane fields for the MD simulations. A good match between the simulation results and available experimental data is obtained. Predictions include pore formation times of about 5-6 ns. It is also shown that the pore formation process would tend to begin from the anodic side of an electrically stressed membrane. Furthermore, the present simulations demonstrate that ions could facilitate pore formation. This could be of practical importance and have direct relevance to the recent observations of calcium release from the endoplasmic reticulum in cells subjected to such ultrashort, high-intensity pulses.
Bioelectromagnetics. 2004 Dec;25(8):634-7.
Electroporation of a lipid bilayer as a chemical reaction.
Bier M, Gowrishankar TR, Chen W, Lee RC.
Department of Physics, East Carolina University, Greenville, North Carolina 27858, USA. email@example.com
When a cell’s transmembrane potential is increased from a physiological one to more than 370 mV, the transmembrane current increases more than hundredfold within a millisecond. This is due to the formation of conductive pores in the membrane. We construct a model in which we conceive of pore formation as a voltage sensitive chemical reaction. The model predicts the logarithm of the pore formation rate to increase proportionally to the square of the voltage. We measure currents through frog muscle cell membranes under 8 ms pulses of up to 440 mV. The experimental data appear consistent with the model.
IEEE Trans Nanobioscience. 2004 Sep;3(3):225-31.
Electric fields within cells as a function of membrane resistivity–a model study.
Mossop BJ, Barr RC, Zaharoff DA, Yuan F.
Department of Biomedical Engineering, Duke University, Durham, NC 27708-0281, USA.
Externally applied electric fields play an important role in many therapeutic modalities, but the fields they produce inside cells remain largely unknown. This study makes use of a three-dimensional model to determine the electric field that exists in the intracellular domain of a 10-microm spherical cell exposed to an applied field of 100 V/cm. The transmembrane potential resulting from the applied field was also determined and its change was compared to those of the intracellular field. The intracellular field increased as the membrane resistance decreased over a wide range of values. The results showed that the intracellular electric field was about 1.1 mV/cm for Rm of 10,000 omega x cm2, increasing to about 111 mV/cm as Rm decreased to 100 omega x cm2. Over this range of Rm the transmembrane potential was nearly constant. The transmembrane potential declined only as Rm decreased below 1 omega x cm2. The simulation results suggest that intracellular electric field depends on Rm in its physiologic range, and may not be negligible in understanding some mechanisms of electric field-mediated therapies.
FEBS Lett. 2004 Aug 13;572(1-3):103-8.
Nanosecond pulsed electric fields perturb membrane phospholipids in T lymphoblasts.
Vernier PT, Sun Y, Marcu L, Craft CM, Gundersen MA.
Department of Materials Science, School of Engineering, University of Southern California, Los Angeles, CA 90089-0271, USA. firstname.lastname@example.org
Nanosecond, megavolt-per-meter pulsed electric fields scramble the asymmetric arrangement of phospholipids in cell membranes without the permeabilization associated with longer, lower-field pulses. A single 30 ns, 2.5 MV/m pulse produces perturbations consistent with phosphatidylserine (PS) externalization in Jurkat T lymphoblasts within milliseconds, polarized in the direction of the applied field, indicating an immediate interaction between membrane components and the electric field. This disturbance occurs only at the anode pole of the cell, supporting the hypothesis that the pulsed field drives the negatively charged PS head group toward the positive electrode, directly providing the energy for crossing the membrane dielectric barrier.
Bioelectrochemistry. 2004 Jun;63(1-2):311-5.
The effect of resting transmembrane voltage on cell electropermeabilization: a numerical analysis.
Valic B, Pavlin M, Miklavcic D.
Faculty of Electrical Engineering, University of Ljubljana, Trzaska 25, SI-1000 Ljubljana, Slovenia.
The transmembrane voltage induced due to applied electric field superimposes to the resting transmembrane voltage of the cell. On the part of the cell membrane, where the transmembrane voltage exceeds the threshold transmembrane voltage, changes in the membrane occur, leading to increase in membrane permeability known as electropermeabilization. This part of the cell membrane represents the permeabilized area through which the transport of molecules occurs. In this paper we calculated numerically the permeabilized area for different electric field strength, resting transmembrane voltage, cell shape and cell orientation with respect to the applied electric field. Results show that when the transmembrane voltage is near the threshold transmembrane voltage, the permeabilized area of the cell is increased on the anodic side and decreased on the cathodic side due to the resting transmembrane voltage. In some cases, only anodic side of the cell is permeabilized. Therefore, by using bipolar pulses, the permeabilized area can be significantly increased and consequentially also the efficiency of electropermeabilization. However, when the induced transmembrane voltage is far above the threshold, the effect of the resting transmembrane voltage is negligible. These observations are valid for different cell shapes and orientations.
Biophys J. 2004 Jun;86(6):4040-8.
Nanoelectropulse-induced phosphatidylserine translocation.
Vernier PT, Sun Y, Marcu L, Craft CM, Gundersen MA.
Department of Electrical Engineering-Electrophysics, School of Engineering, MOSIS, University of Southern California, Los Angeles, California, USA. email@example.com
Nanosecond, megavolt-per-meter, pulsed electric fields induce phosphatidylserine (PS) externalization, intracellular calcium redistribution, and apoptosis in Jurkat T-lymphoblasts, without causing immediately apparent physical damage to the cells. Intracellular calcium mobilization occurs within milliseconds of pulse exposure, and membrane phospholipid translocation is observed within minutes. Pulsed cells maintain cytoplasmic membrane integrity, blocking propidium iodide and Trypan blue. Indicators of apoptosis-caspase activation and loss of mitochondrial membrane potential-appear in nanoelectropulsed cells at later times. Although a theoretical framework has been established, specific mechanisms through which external nanosecond pulsed electric fields trigger intracellular responses in actively growing cells have not yet been experimentally characterized. This report focuses on the membrane phospholipid rearrangement that appears after ultrashort pulse exposure. We present evidence that the minimum field strength required for PS externalization in actively metabolizing Jurkat cells with 7-ns pulses produces transmembrane potentials associated with increased membrane conductance when pulse widths are microseconds rather than nanoseconds. We also show that nanoelectropulse trains delivered at repetition rates from 2 to 2000 Hz have similar effects, that nanoelectropulse-induced PS externalization does not require calcium in the external medium, and that the pulse regimens used in these experiments do not cause significant intra- or extracellular Joule heating.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Apr;69(4 Pt 1):041901. Epub 2004 Apr 14.
Fields and forces acting on a planar membrane with a conducting channel.
Bivas I, Danelon C.
Laboratory of Liquid Crystals, Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee Boulevard, Sofia 1784, Bulgaria. firstname.lastname@example.org
Modeling electric fields and forces around a channel in a planar membrane is still an open problem. Until now, most of the existing theories have oversimplified the electric field distribution by placing the electrode directly at the entry of the channel. However, in any relevant experimental setup the electrodes are placed far away in the electrolyte solution. We demonstrate that long-range deformation of the electric field distribution appears around the membrane, spanning on distances of the order of the distance between the membrane and the electrode. The forces acting due to this distribution are in most of the cases negligible. They can be important for channels with radii of the order of the thickness of the layer of structured water at the oil-water interface.
Bioelectrochemistry. 2003 Oct;61(1-2):65-72.
Sub-microsecond, intense pulsed electric field applications to cells show specificity of effects.
Hair PS, Schoenbach KH, Buescher ES.
Center for Pediatric Research, Eastern Virginia Medical School, Norfolk, VA 23510, USA.
Application of sub-microsecond duration (60-300 ns), intense (15-60 kV/cm) pulsed electric fields (sm/i-PEF) to six types of human cells was examined for its effects on individual cell surface membrane permeability and membrane potential. With short (60 ns) pulses, increasing percentages of Jurkat cells showed propidium iodide (PI) uptake at progressively shorter post-pulse times as the pulse train increased from 1 to 10 sequential pulses, while human blood polymorphonuclear leukocytes (PMN) were unresponsive to these short pulses regardless of train size. With 300 ns pulses, a similar pattern (increasing percentages of cells taking up PI, and progressively shorter times of onset after pulse applications as pulse train size increased) was seen with both Jurkat cells and PMN, but the patterns for both effects were different. Jurkat cell size did not appear to influence the responsiveness of this cell type. Comparisons of sm/i-PEF-induced PI uptake by human monocyte-derived macrophages vs. aged human mononuclear cells, human trunk skin (HTS) cells vs. fresh human mononuclear cells and human macrophages vs. HTS cells showed similar overall effects, but with differences between the patterns for each cell type compared (except the macrophages vs. HTS cells comparison). Application of sm/i-PEFs also caused different patterns of membrane potential loss in Jurkat cells vs. PMN. Jurkat cells developed significant decreases in t heir membrane potential only following the highest intensity pulse applications examined, i.e., 300 ns, 60 kV/cm x5, while PMN showed this effect over the entire range of pulse intensities (300 ns, 15-60 kV/cm, x5) applied. These data indicate that sm/i-PEF applications can have “specificity” (i.e., achieve different levels of effect in different cell types), that cell size does not appear to be the major factor determining sm/i-PEF effects in either Jurkat cells or PMN, that heterogeneous sm/i-PEF effects on cells tend to become homogeneous with increasing pulse train size, and that specificity of sm/i-PEF applications effects can occur at either end of the sm/i-PEF intensity spectrum examined.
Eur Biophys J. 2003 Sep;32(6):519-28. Epub 2003 Apr 24.
Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment.
Valic B, Golzio M, Pavlin M, Schatz A, Faurie C, Gabriel B, Teissié J, Rols MP, Miklavcic D.
Faculty of Electrical Engineering, University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia.
The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.
Biophys J. 2003 Aug;85(2):719-29.
Effective conductivity of a suspension of permeabilized cells: a theoretical analysis.
Pavlin M, Miklavcic D.
University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia. email@example.com
During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be <10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.
Adv Anat Embryol Cell Biol. 2003;173:III-IX, 1-77.
Electric field-induced effects on neuronal cell biology accompanying dielectrophoretic trapping.
University of Twente, Faculty of Electrical Engineering, Mathematics and Computer Science, Laboratory of Measurement and Instrumentation, Laboratory of Biomedical Engineering, P.O. Box 217, 7500 AE Enschede, The Netherlands. firstname.lastname@example.org
Trapping neuronal cells may aid in the creation of the cultured neuron probe. The aim of the development of this probe is the creation of the interface between neuronal cells or tissue in a (human) body and electrodes that can be used to stimulate nerves in the body by an external electrical signal in a very selective way. In this way, functions that were (partially) lost due to nervous system injury or disease may be restored. First, a direct contact between cultured neurons and electrodes is created. This is realized using a microelectrode array (MEA) which can be fabricated using standard photolithographic and etching methods. Section 1 gives an overview of the human nervous system, methods for functional recovery focused on the cultured neuron probe, and the prerequisites for culturing neurons on a microelectrode array. An important aspect in the selective stimulation of neuronal cells is the positioning of cells or a small group of cells on top of each of the electrode sites of the MEA. One of the most efficient methods for trapping neuronal cells is to make use of di-electrophoresis (DEP). Dielectrophoretic forces are created when (polarizable) cells are located in nonuniform electric fields. Depending on the electrical properties of the cells and the suspending medium, the DEP force directs the cells towards the regions of high field strength (positive dielectrophoresis; PDEP) or towards regions of minimal field intensities (negative dielectrophoresis; NDEP). Since neurons require a physiological medium with a sufficient concentration of Na+, the medium conductivity is rather high (~ 1.6 S/m). The result is that negative dielectrophoretic forces are created over the entire frequency range. With the use of a planar quadrupole electrode sturcture negative forces are directed so that in the center of this structure cell can be collected. The process of trapping cortical rat neurons is described in Sect. 2 theoretically and experimentally. Medium and cell properties are frequency-dependent due to relaxation processes, which have a direct influence on the strength of the dielectrophorectic force. On the other hand, the nonideal material properties of the gold electrodes and glass substrate largely determine the electric field strength created inside the medium. Especially, the electrode-medium interface results in a significant loss of the imput signal at lower frequencies (< 1 MHz), and thus a reduction of the electric field strength inside the medium. Furthermore, due to the high medium conductivity, the electric field causes Joule heating. Local temperature rises result in local gradients in fluid density, which induces fluid flow. The electrode-medium interface and induced fluid flow are theoretically investigated with the use of modeling techniques such as finite elements modeling. Experimental and theoretical results agreed with each other on the occurrence of the effects described in this section. For the creation of the cultured neuron probe, preservation of cell viability during the trapping process is a prerequisite. Cell viability of dielectrophoretically trapped neurons has to be investigated. The membrane potential induced by the external field plays a crucial role in preservation of cell viability. The membrane can effectively be represented by a capaticance in parallel woth a low conductance; with increasing frequency and /or decreasing field strength the induced membrane potential decreases. At high induced membrane potentials ths representation for the membrane is no longer valid. At this point membrane breakdown occurs and the normally insulating membrane becomes conductive and permeable. The creation of electropores has been proposed in literature to be the cause of this high permeability state. Pores may grow or many small pores may be created which eventually may lead to membrane rupture, and thus cell death. Membrane breakdown may be reversible, but a chemical imbalance created during the high permeability state may still exist after the resealing of the membrane. This may cause cell death after several hours or even days after field application. Section 3 gives a detailed description of membrane breakdown. Since many investigations on electroporation of lipid bilayers and cell membranes are based on uniform electric fields, a finite element model is used to investigate induced membrane potentials in the nonuniform field created by the quadropole electrode structure. Modeling results are presented in cmbination with the results of breakdown experiments using four frequencies in the range from 100 kHz to 1MHz. Radomly positioned neuronals cells were exposed to stepwise increasing electric field strengths. The field strength at which membrane rupture occurred gives an indication of the maximum induced membrane potential. Due to the nonuniformity of the electric field, cell collapse was expected to be position-dependent. However, at 100 kHz cells collapsed at a break down level of about 0.4 V, in contradistinction to findings at higher frequencies where more variation in breakdown levels were found. Model simulations were able to explain the experimental results. For examining whether the neuronal cells trapped by dielectrophoresis were still viable after the trapping process, the frequency range was divided into two ranges. First, a high frequency (14 MHz) and a rather low signal amplitude (3 Vpp) were used to trap cells. At this high frequency the field-induced membrane potential is small according to the theoretical model, and therefore no real damage is expected. The experimental analysis included the investigation of the growth of the neurons, number and length of the processes (dendrites and axons), and the number of outgrowing (~ viable) versus nonoutgrowing (~ nonviable) neural cells. The experimental results agreed with the expectation. The effect of the use of driving signals with lower frequencies and/or higher amplitudes on cell viability was investigated using a staining method as described in the second part of Sect. 4. Survival chances are not directly linked to the estimated maximum induced membrane potential. The frequency of the dield plays an important role, decreasing frequency lowering the chance of survival. A lower frequency limit of 100 kHz is preferable at field strengths less than 80 k V/m, while with increasing field strength this limit shifts towards higher frequencies. The theoretical and experimental results presented in this review form the inception of the development of new electrode structures for trapping neuronal cells on top of each of the electrodes of the MEA. New ways to investigate cell properties and the phenomenon of electroporation using electrokinetic methods were developed that can be exploited in future research linking cell biology to technology.
IEEE Trans Biomed Eng. 2002 Oct;49(10):1195-203.
Investigating membrane breakdown of neuronal cells exposed to nonuniform electric fields by finite-element modeling and experiments.
Heida T, Wagenaar JB, Rutten WL, Marani E.
Institute of BioMedical Technology, Department of Biomedical Engineering, Faculty of Electrical Engineering, University of Twente, Enschede, The Netherlands.
High electric field strengths may induce high cell membrane potentials. At a certain breakdown level the membrane potential becomes constant due to the transition from an insulating state into a high conductivity and high permeability state. Pores are thought to be created through which molecules may be transported into and out of the cell interior. Membrane rupture may follow due to the expansion of pores or the creation of many small pores across a certain part of the membrane surface. In nonuniform electric fields, it is difficult to predict the electroporated membrane area. Therefore, in this study the induced membrane potential and the membrane area where this potential exceeds the breakdown level is investigated by finite-element modeling. Results from experiments in which the collapse of neuronal cells was detected were combined with the computed field strengths in order to investigate membrane breakdown and membrane rupture. It was found that in nonuniform fields membrane rupture is position dependent, especially at higher breakdown levels. This indicates that the size of the membrane site that is affected by electroporation determines rupture.
Phys Med Biol. 2000 Jul;45(7):1965-88.
Nonlinear cell response to strong electric fields.
Bardos DC, Thompson CJ, Yang YS, Joyner KH.
Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria , Australia.
The response of living cells to externally applied electric fields is of widespread interest. In particular, the intensification of electric fields across cell membranes is believed to be responsible, through membrane rupture and reversible membrane breakdown processes, for certain types of tissue damage in electrical trauma cases which cannot be attributed to Joule heating. Large elongated cells such as skeletal muscle fibres are particularly vulnerable to such damage. Previous theoretical studies of field intensification across cell membranes in such cells have assumed the membrane current to be linear in the applied field (Ohmic membrane conductivity) and were limited to sinusoidal applied fields. In this paper, we investigate a simple model of a long cylindrical cell, corresponding to nerve or skeletal muscle cells. Employing the electroquasistatic approximation, a system of coupled first-order differential equations for the membrane electric field is derived which incorporates arbitrary time dependence in the external field and nonlinear membrane response (non-Ohmic conductivity). The behaviour of this model is investigated for a variety of applied fields in both the linear and highly nonlinear regimes. We find that peak membrane fields predicted by the nonlinear model are approximately twice as intense, for low-frequency electrical trauma conditions, as those of the linear theory.
IEEE Trans Biomed Eng. 2002 Jun;49(6):605-12.
Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system.
Pavlin M, Pavselj N, Miklavcic D.
University of Ljubljana, Faculty of Electrical Engineering, Slovenia.
A nonuniform transmembrane potential (TMP) is induced on a cell membrane exposed to external electric field. If the induced TMP is above the threshold value, cell membrane becomes permeabilized in a reversible process called electropermeabilization. Studying electric potential distribution on the cell membrane gives us an insight into the effects of the electric field on cells and tissues. Since cells are always surrounded by other cells, we studied how their interactions influence the induced TMP. In the first part of our study, we studied dependence of potential distribution on cell arrangement and density in infinite cell suspensions where cells were organized into simple-cubic, body-centered cubic, and face-centered cubic lattice. In the second part of the study, we examined how induced TMP on a cell membrane is dependent on its position inside a three-dimensional cell cluster. Finally, the results for cells inside the cluster were compared to those in infinite lattice. We used numerical analysis for the study, specifically the finite-element method (FEM). The results for infinite cell suspensions show that the induced TMP depends on both: cell volume fraction and cell arrangement. We established from the results for finite volume cell clusters and layers, that there is no radial dependence of induced TMP for cells inside the cluster.
Laryngoscope. 2001 Jan;111(1):52-6.
Electroporation therapy for head and neck cancer including carotid artery involvement.
Allegretti JP, Panje WR.
Department of Otolaryngology, Rush-Presbyterian-St Luke’s Medical Center, Rush Medical College, Chicago, Illinois 60612, USA.
OBJECTIVES: Electroporation therapy with intralesional bleomycin (EPT) is a novel, technically simple outpatient technique in which high-voltage electric impulses delivered into a neoplasm transiently increase cell membrane permeability to large molecules, including cytotoxic agents, causing localized progressive necrosis. Unlike many laser ablation methods, EPT can treat bulky tumors (>2 cm) with complete penetration. Our recent publication confirms an excellent response rate in the use of EPT in a clinical trial. STUDY
DESIGN, PATIENTS, AND METHODS: Following our initial prospective study report in 1998, we have followed our entire initial cohort (10 patients) of patients with head and neck cancer beyond 24-months follow-up. Additionally, we have used this approach to treat four additional patients (total: 9 males/5 females) with upper aerodigestive tract squamous cell carcinoma, including three with internal carotid artery (ICA) involvement up to or within the skull base. Two patients underwent preoperative balloon test occlusion with cerebral perfusion studies followed by carotid embolization. EPT was then done safely at least 2 weeks later to avoid the temporary hypercoagulable state.
RESULTS: Within the overall cohort (14 patients) 6 patients had a complete response, 6 had a partial response, and 2 did not respond (overall 85.7% response rate). Both patients with ICA involvement had a partial or complete response to treatment; neither patient had a hemorrhagic or neurologic complication. Overall, 13 of the 14 patients were treated for persistent or recurrent head and neck cancer. Two of the four patients with early recurrent stage tumors had no evidence of recurrence after EPT with an average follow-up of 31.5 months. The overall early stage tumor group had four complete responders out of five (80%). On the contrary, only 2 of 9 patients with advanced recurrent stage tumors were disease-free at 18 months. Morbidity was low for early stage tumors, but higher for advanced tumors with complications, including poor wound healing, dysphagia, and osteomyelitis. There were no treatment-related deaths.
CONCLUSION: We found EPT to be safe and efficacious in patients with head and neck cancer, even with internal carotid artery involvement. Patients with early stage recurrences have the potential for prolonged survival beyond 2 years without the morbidity of surgery and radiation or toxicity of systemic chemotherapy. Because of its superb access qualities even for bulky tumors, EPT is a potential method of delivery for other tumoricidal agents such as in genetic-altering schemes.
J Membr Biol. 1984;78(1):53-60.
Electric field-induced breakdown of lipid bilayers and cell membranes: a thin viscoelastic film model.
A simple viscoelastic film model is presented, which predicts a breakdown electric potential having a dependence on the electric pulse length which approximates the available experimental data for the electric breakdown of lipid bilayers and cell membranes (summarized in the reviews of U. Zimmermann and J. Vienken, 1982, J. Membrane Biol. 67:165 and U. Zimmermann, 1982, Biochim. Biophys. Acta 694:227). The basic result is a formula for the time tau of membrane breakdown (up to the formation of pores): tau = alpha (mu/G)/(epsilon 2m epsilon 2oU4/24 sigma Gh3 + T2/sigma Gh-1), where alpha is a proportionality coefficient approximately equal to ln(h/2 zeta o), h being the membrane thickness and zeta o the amplitude of the initial membrane surface shape fluctuation (alpha is usually of the order of unity), mu represents the membrane shear viscosity, G the membranes shear elasticity modules, epsilon m the membrane relative permittivity, epsilon o = 8.85 X 10(-12) F/m, U the electric potential across the membrane, sigma the membrane surface tension and T the membrane tension. This formula predicts a critical potential Uc; Uc = (24 sigma Gh3/epsilon 2m epsilon 2o)1/4 (for tau = infinity and T = 0). It is proposed that the time course of the electric field-induced membrane breakdown can be divided into three stages: (i) growth of the membrane surface fluctuations, (ii) molecular rearrangements leading to membrane discontinuities, and (iii) expansion of the pores, resulting in the mechanical breakdown of the membrane.
Biophys Chem. 1984 May;19(3):211-25.
Stochastic model for electric field-induced membrane pores. Electroporation.
Sugar IP, Neumann E.
Electric impulses (1-20 kV cm-1, 1-5 microseconds) cause transient structural changes in biological membranes and lipid bilayers, leading to apparently reversible pore formation ( electroporation ) with cross-membrane material flow and, if two membranes are in contact, to irreversible membrane fusion ( electrofusion ). The fundamental process operative in electroporation and electrofusion is treated in terms of a periodic lipid block model, a block being a nearest-neighbour pair of lipid molecules in either of two states: (i) the polar head group in the bilayer plane or (ii) facing the centre of a pore (or defect site). The number of blocks in the pore wall is the stochastic variable of the model describing pore size and stability. The Helmholtz free energy function characterizing the transition probabilities of the various pore states contains the surface energies of the pore wall and the planar bilayer and, if an electric field is present, also a dielectric polarization term (dominated by the polarization of the water layer adjacent to the pore wall). Assuming a Poisson process the average number of blocks in a pore wall is given by the solution of a non-linear differential equation. At subcritical electric fields the average pore size is stationary and very small. At supercritical field strengths the pore radius increases and, reaching a critical pore size, the membrane ruptures (dielectric breakdown). If, however, the electric field is switched off, before the critical pore radius is reached, the pore apparently completely reseals to the closed bilayer configuration (reversible electroporation ).