Reversible Electrical Breakdown Research Articles

Linear resistance limiting the current of intergranular barriers in varistor ceramics

Method for measuring the linear resistivity ρlin, which affects the volt-ampere characteristic (VAC) nonlinearity of varistor materials in a high current region is proposed. For ZnO based varistor ceramics the dependence of ρlin on amplitude density Jmax of current pulse is studied in the range 5 A cm-2 – 4600 A cm-2. At Jmax < 200 A cm-2 a sharp decrease of ρlin with increasing Jmax takes place. This behavior indicates a non-uniform distribution of high current over the cross section of ceramics sample. At Jmax > 1000 A cm-2 ρlin does not depend on Jmax and has a value of 0.49 – 0.50 Ohm cm corresponding to the volume resistivity ρg of ZnO grains. The decrease in nonlinearity of VAC at high currents is due to the formation of conductive paths of electric current between the electrodes of a sample. Along such paths, all intergranular double Schottky barriers are in a reversible electrical breakdown mode, probably due to impact ionization. The current in these paths is limited by small linear volume resistance of the grains. A spread of grain sizes is the reason for existence of current paths with different numbers of contacts between grains and therefore with different breakdown voltages. At voltage increases, the sequential formation of parallel-connected conductive paths occurs. This explains the inhomogeneous distribution of high current over the cross section of a sample at Jmax < 200 A cm-2. At Jmax > 1000 A cm-2 almost all current paths in a sample are switched on and the value of ρlin limiting the barriers current is close to the volume resistivity ρg of grains.

Multiple relaxation, reversible electrical breakdown and bipolar conductivity of pyrochlore–type Bi2Cu0.5Zn0.5Ta2O9 ceramics

Cu-doped bismuth zinc tantalate pyrochlore was synthesized for the first time using standard ceramic technology. Electrical properties were investigated by impedance spectroscopy in a wide frequency range of 10 Hz – 1 MHz and a temperature range of 25–450 °C. As a result of modeling the Nyquist curves, the structure of the equivalent circuit of the ceramic is determined. Two mechanisms of ion-migration polarization caused by ionic transfer of copper and oxygen have been discovered. The activation energy of conduction at temperatures above 200 °C was 0.796 ± 0.009 eV. Current-voltage characteristics were investigated in the potential range 0.1–2 V and temperature 150–450 °C. The calculation of the potential barrier on the electrodes showed that at temperatures above ~250 °C, the potential barrier changes sign and magnitude by an order of magnitude from - 150 mV to +10 mV, which is associated with a change in the nature of charge carriers and activation of oxygen conductivity. In ceramics at 400–450 °C, a reversible effect is observed, which is characteristic of electrochromic materials. When measuring the current in the sample at a fixed potential, a transition from a direct current to an increasing current was detected, and then its sharp drop almost to zero. The instant of the onset of the growing current and electrical breakdown, as well as the recovery time of the electrical characteristics of the sample, depend on the applied potential and the temperature of the sample.

MODELLING AND ANALYSIS OF ELECTROPORATION PARAMETERS OF THE MEMBRANE OF A BIOLOGICAL CELL IN A VARIED INTENSITY PULSED ELECTRIC FIELD

Context. The problem of constructing electroporation models for membranes of biological cells by the methods of nonlinear approximation using the experimental dependences of their specific electric conductivity on intensity pulsed electric field was solved in the paper.Objective is a construction of models, which adequately describe the experimentally obtained nonlinear effects of the conductivity of the cell, including reversible electroporation, irreversible electrical breakdown or local reversible electrical breakdown of membranes at the fusion of two contacting cells.Method. Polynomials of 8–10 degrees are chosen as the functions that modelling the experimental ones and the criteria for estimating the parameters of electroporation are the coordinates of the local extrema of their curvature and inflexion points that characterize the specified state of the cell membrane at current field intensity. The approximation problem was solved by the least squares method. The calculation of the estimate of the polynomials coefficients was carried out by the Gaussian elimination – the forward and reverse moves were realized. It is possible to search for extrema of the obtained polynomials of high degrees by specifying a calculation error. The root-mean-square error of the approximation is used for finding the degree of the polynomial. The current curvature of the polynomial is counted by calculating the first and second order derivatives of conductivity. The values of the curvature, which obtained via these methods, make possible to determine the inflexion points of the curve for purpose to determine breakdown of a cell membrane.Results. Applied software was developed, polynomial models of the conductivity of a biological cell in a varied intensity pulsed electric field were constructed and their quantitative mathematical analysis was carried out by using this software. All these calculations are proved by graphs, some of which can be viewed on an enlarged scale.Conclusions. The parameters of electroporation of a biological cell membrane obtained by analysing the curvature function of polynomial models are calculated. The developed analytical methods and software for determining the parameters of electroporation allow us to recommend them for use in practice in calculating the numerical values of the field intensity and conductivity at which specific electroporation regimes of the biological cell membrane are provided.

Cascade Model of Conduction Instability and Giant Fluctuations in Polymer Materials and Nanocomposites

A new cascade model of polymer composite materials giant current fluctuations is developed on the basis of published representable set of experimental data. This qualitative model describes the anomalous features of the conduction of polymer nanocomposites, in particular, conduction many orders of magnitude self-switching to the conducting state in polymer films including relatively thick up to tens of microns or more. The development is achieved by combining well known model of hopping conduction mechanism with experimental data of soft reversible electric breakdown. With much simplification the can be explained as follows: dividing the distance between electrodes on conducting islands (with constant potential with zero electric field) and insulating gaps (where electric field is higher than average level). In such a system we obtain instability - type correlation of electric field in the adjacent insulating gaps: one gap microbreakdown increases the field strength in the adjacent gaps.

Controlling Reversible Dielectric Breakdown in Metal/Polymer Nanocomposites

Composites comprising metal nanorods encased in a polymer matrix exhibit reversible electric breakdown and can be cycled between low- and high-conductance states multiple times without permanent damage to the material. The voltage at which the breakdown occurs can be adjusted by engineering the properties of the polymeric matrix, in particular by doping the polymer with dipole-possessing additives whose role is to screen the applied electric fields.

Discovery of “punch-through” or membrane electrical breakdown and electroporation

As part of a detailed study in Alex Hope's laboratory of the V-I characteristics of the membrane of the giant cells of Chara corallina, it was discovered that at a well defined potential difference of around 500 mV (depending on the temperature), the cell membrane undergoes a reversible electrical breakdown. The author coined the word "punchthrough" to describe this electrical breakdown phenomenon. Detailed studies followed on the nature of this electrical breakdown phenomenon, in various cells, aimed at elucidating the physical mechanism(s) involved. The applications and the significance of the phenomenon that were subsequently developed in later years were not foreseen at that time. Electrical breakdown/electroporation is now a commonplace procedure and has entered into the mainstream biological vocabulary. Here we trace its humble beginnings to experiments carried out in Alex Hope's laboratory and review briefly some of the aspects of this phenomenon and its applications that were developed much later by others as well as the author. The discovery of membrane electrical breakdown described below took whilst the author was his student of Alex Hope but whilst Alex was away on sabbatical leave in the UK. Because this occurred in his absence, Alex Hope elected to not put his name on the paper that described the discovery in 1965.

Experimental Studies on Killing and Inhibiting Effects of Steep Pulsed Electric Field (SPEF) to Target Cancer Cell and Solid Tumor

Electroporation (i.e., reversible electrical breakdown) has been used for biomedicine such as electroporation therapy, transdermal drug delivery, cellular drug carrier systems, and gene transfer therapy. However, little research on the biological effect of irreversible electrical breakdown has been published. In this paper, the killing and inhibiting effects of pulsed electric field, whose rising edge is 100 ns level (we call it steep pulsed electric field, SPEF), to target cancer cell and solid tumor were successfully observed. The SPEF consists of two parts: the rising process containing ample high-frequency components, and the falling process containing lots of low-frequency components. Cell exposed to the pulse presented multiple changes: destructed membrane, swollen nucleus, disintegrated karyotheca, and cavitated, swollen mitochondria in histological and ultrastructure observations. SPEF blocked cell transition from G0/G1 phase to S+G2/M phase in flow cytometry analysis, and tumor growth retardation was observed in tumor-bearing mice. These experimental results show SPEF have a certain function to generate irreversible electrical breakdown in tumor cells, and might provide a new promising therapeutic approach for tumor treatment.

Electromanipulation of mammalian cells: fundamentals and application

Electroinjection of membrane-impermeable xenomolecules into freely suspended mammalian cells (so-called electroporation) and cell-to-cell electrofusion are powerful tools for manipulation of the genom and the cytosol of cells. Both field pulse techniques are based on the temporary increase of the membrane permeability due to reversible electrical breakdown of the plasma membrane upon application of external high-intensity field pulses of very short duration. Membrane charging and permabilization caused by high-intensity field pulses are preceded and accompanied by transient electrodeformation forces, which lead to an elongation of the cells in low-conductivity media, thus affecting the membrane area of electropermabilization in response to a breakdown pulse. Transient stretching force assumes a maximum value in low-conductivities pulse media. This facilitates incorporation of membrane-impermeable xenomolecules and field-mediated hybridization as well. Therefore, high and reproducible fields of (genetically) manipulated cells can be expected provided that: 1) the duration of the high-intensity field pulses does not exceed shout 100 /spl mu/s and 2) that the (pulse or fusion) media are hypo-osmolar and exhibit a relatively low conductivities. Such media are also beneficial because field-inducted apoptosis does not occur under these conditions (in contrast to highly conductive media). Indeed, electroporation and electrofusion protocols that fulfill these requirements lead: 1) to high incorporation rates of plasmids (DNA) or artificial chromesomes into living cells without deterioration and 2) to the production of hybridoma cells (by fusion of tumor-infiltrating lymphocytes with heteromyeloma cells), which secrete functional human monoclonal antibodies. Human monoclonal antibodies that bind to and induce apoptosis in autologous tumor cells are promising gents for cancer treatment, as shown by first clinical trials.

Electric field pulses can induce apoptosis.

Injection of electric field pulses of high intensity (kV/cm) and short duration (microsecond range) into a cell suspension results in a temporary increase of the membrane permeability due to a reversible electric breakdown of the cell membrane. Here we demonstrate that application of supercritical field pulses between 4. 5 and 8.1 kV/cm strength and 40 microsec duration induce typical features of apoptosis in Jurkat T-lymphoblasts and in HL-60 cells including DNA fragmentation and cleavage of the poly(ADP ribose) polymerase. Apoptosis induction did not depend on the presence of any particular electrolyte in the extracellular medium. However, no apoptosis was observed in solutions without a minimum amount of salt. Apoptotic DNA fragmentation was prevented by the caspase inhibitor zVAD.

Effects of electroporation on transmembrane potential induced by defibrillation shocks.

This study uses a one-dimensional model of cardiac strand to investigate the effects of electroporation on transmembrane potential (Vm) induced by defibrillation shocks. The strand is stimulated at the ends by extracellular electrodes. Its membrane, when exposed to large Vm, increases its conductance in a manner consistent with reversible electrical breakdown. Numerical simulations indicate that Vm increases proportionally to the shock strength only until the ends of the strand electroporate. Beyond this point, further increases in shock strength result in only a minor change in Vm. This arrest in the growth of Vm is caused by pores that develop in the cells immediately adjacent to the electrodes and that shunt part of the stimulating current directly into intracellular space. Consequently, only a fraction of the delivered current, Icr, gives rise to Vm; the current in excess of Icr divides itself proportionally between intra- and extracellular space and does not contribute to macroscopic Vm. Thus, electroporation has a beneficial effect: the formation of pores prevents the development of an excessively high Vm and limits the damage to the tissue. In contrast, electroporation does not affect the "sawtooth" component of Vm that reflects polarization of individual cells by electric field. These results indicate that electroporation does not impair the ability of the shock to reach the distant myocardium and may actually aid defibrillation by reducing nonuniformity of electrical conditions between regions close to the electrodes and in the bulk of tissue.

Electroporation theory. Concepts and mechanisms.

The basic features of electrical and mechanical behavior of electroporated cell membranes are reasonably well established experimentally. Overall, the electrical and mechanical features of electroporation are consistent with a transient aqueous pore hypothesis, and several features, such as membrane rupture and reversible electrical breakdown, are reasonably well described quantitatively. This gives confidence that "electroporation" is an attractive hypothesis, and that the appearance of temporary pores owing to the simultaneous contributions of thermal fluctuations ("kT energy") and an elevated transmembrane voltage ("electric field energy") is the microscopic basis of electroporation.

Theory of electroporation of planar bilayer membranes: predictions of the aqueous area, change in capacitance, and pore-pore separation

A large increase in the transmembrane voltage, U(t), of a fluid bilayer membrane is believed to result in the occurrence of temporary aqueous pathways ("pores") across the membrane. The number, size, and evolution dynamics of these pores are expected to be crucial to the transport of water-soluble species ranging from small ions to macromolecules such as proteins and nucleic acids. In this paper we use a transient aqueous pore theory to estimate the fraction of the membrane area, Fw(t), which is temporarily occupied by water-filled pores for short square, exponential, and bipolar square pulses. For short pulses, "reversible electrical breakdown" occurs when the transmembrane voltage reaches about 1 V, and Fw(t) is predicted to rise rapidly, but always to be less than 10(-3). The conductance of a large number of pores causes reversible electrical breakdown and prevents a significantly larger U from being reached. Despite the large dielectric constant of water, for reversible electroporation the associated change in membrane capacitance, delta C, due to the pores is predicted to be small. Moreover, for a flat membrane the minimum value of the mean pore-pore separation is large, about 60 times the minimum pore radius. In flat membranes, pores are predicted to repel, but the opposite is expected for curved cell membranes, allowing the possibility of coalescence in cell membranes. For some moderate values of U, rupture (irreversible electrical breakdown) occurs, as one or more supracritical pores expand to the membrane boundary and the entire membrane area becomes aqueous. In all cases it is found that a quantitative description of electroporation requires that a pore size distribution, rather than a single size pore.

Electroporation: a general phenomenon for manipulating cells and tissues.

Electroporation is a fascinating cell membrane phenomenon with several existing biological applications and others likely. Although DNA introduction is the most common use, electroporation of isolated cells has also been used for: (1) introduction of enzymes, antibodies, and other biochemical reagents for intracellular assays; (2) selective biochemical loading of one size cell in the presence of many smaller cells; (3) introduction of virus and other particles; (4) cell killing under nontoxic conditions; and (5) insertion of membrane macromolecules into the cell membrane. More recently, tissue electroporation has begun to be explored, with potential applications including: (1) enhanced cancer tumor chemotherapy, (2) gene therapy, (3) transdermal drug delivery, and (4) noninvasive sampling for biochemical measurement. As presently understood, electroporation is an essentially universal membrane phenomenon that occurs in cell and artificial planar bilayer membranes. For short pulses (microsecond to ms), electroporation occurs if the transmembrane voltage, U(t), reaches 0.5-1.5 V. In the case of isolated cells, the pulse magnitude is 10(3)-10(4) V/cm. These pulses cause reversible electrical breakdown (REB), accompanied by a tremendous increase molecular transport across the membrane. REB results in a rapid membrane discharge, with the elevated U(t) returning to low values within a few microseconds of the pulse. However, membrane recovery can be orders of magnitude slower. An associated cell stress commonly occurs, probably because of chemical influxes and effluxes leading to chemical imbalances, which also contribute to eventual survival or death. Basic phenomena, present understanding of mechanism, and the existing and potential applications are briefly reviewed.

Kinetics and mechanism of cell membrane electrofusion

A new quantitative approach to study cell membrane electrofusion has been developed. Erythrocyte ghosts were brought into close contact using dielectrophoresis and then treated with one square or even exponentially decaying fusogenic pulse. Individual fusion events were followed by lateral diffusion of the fluorescent lipid analogue 1,1'-dihexadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (Dil) from originally labeled to unlabeled adjacent ghosts. It was found that ghost fusion can be described as a first-order rate process with corresponding rate constants; a true fusion rate constant, k(f), for the square waveform pulse and an effective fusion rate constant, k(ef), for the exponential pulse. Compared with the fusion yield, the fusion rate constants are more fundamental characteristics of the fusion process and have implications for its mechanisms. Values of k(f) for rabbit and human erythrocyte ghosts were obtained at different electric field strength and temperatures. Arrhenius k(f) plots revealed that the activation energy of ghost electrofusion is in the range of 6-10 kT. Measurements were also made with the rabbit erythrocyte ghosts exposed to 42 degrees C for 10 min (to disrupt the spectrin network) or 0.1-1.0 mM uranyl acetate (to stabilize the bilayer lipid matrix of membranes). A correlation between the dependence of the fusion and previously published pore-formation rate constants for all experimental conditions suggests that the cell membrane electrofusion process involve pores formed during reversible electrical breakdown. A statistical analysis of fusion products (a) further supports the idea that electrofusion is a stochastic process and (b) shows that the probability of ghost electrofusion is independent of the presence of Dil as a label as well as the number of fused ghosts.

Electroporation: A unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes

We present a quantitative theory of electroporation of artificial planar lipid bilayer membranes. Assuming that aqueous pores are involved in electroporation, we describe the pore population of the membrane by the density function n ( r, t), where n ( r, t) d r is the number of pores with radius between r and r + d r at time t. We further assume that there is a minimum pore size r min, that pores of radius r min are created and destroyed by thermal fluctuations, and that the pore creation rate is proportional to exp( aΔφ m 2/ kT, where a is a constant, Δφ m is the membrane voltage, k is Boltzmann's constant, and T is the absolute temperature. We use a simple formula for the conductance of a pore as a function of radius, the expression for the pore energy previously derived by Pastushenko and Chizmadzhev, and a simple model of the external circuit. We solve the equations numerically and compare the solutions to the results of charge pulse experiments. In a charge-pulse experiment a membrane suffers one of four possible fates: (1) a slight increase in electrical conductance, (2) mechanical rupture, (3) incomplete reversible electrical breakdown, resulting in incomplete discharge of the membrane, or (4) reversible electrical breakdown (REB), resulting in complete discharge of the membrane. In agreement with experiment, this theory describes these four fates and predicts that the fate in any particular experiment is determined by the properties of the membrane and the duration and amplitude of the charging pulse.

Electroporation: a unified, quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes

We present a quantitative theory of electroporation of artificial planar lipid bilayer membranes. Assuming that aqueous pores are involved in electroporation, we describe the pore population of the membrane by the density function n ( r, t), where n ( r, t) d r is the number of pores with radius between r and r + d r at time t. We further assume that there is a minimum pore size r min, that pores of radius r min are created and destroyed by thermal fluctuations, and that the pore creation rate is proportional to exp( aΔφ 2 m/ kT), where a is a constant, Δφ m is the membrane voltage, k is Boltzmann's constant, and T is the absolute temperature. We use a simple formula for the conductance of a pore as a function of radius, the expression for the pore energy previously derived by Pastushenko and Chizmadzhev, and a simple model of the external circuit. We solve the equations numerically and compare the solutions to the results of charge pulse experiments. In a charge-pulse experiment a membrane suffers one of four possible fates: (1) a slight increase in electrical conductance, (2) mechanical rupture, (3) incomplete reversible electrical breakdown, resulting in incomplete discharge of the membrane, or (4) reversible electrical breakdown (REB), resulting in complete discharge of the membrane. In agreement with experiment, this theory describes these four fates and predicts that the fate in any particular experiment is determined by the properties of the membrane and the duration and amplitude of the charging pulse.

Tissue electroporation. Observation of reversible electrical breakdown in viable frog skin

Experiments by others have used isolated cell or bilayer membrane preparations to study the dramatic phenomena associated with electroporation. The present study observes electroporation behavior in an intact tissue. Viable samples of frog skin (Rana pipiens) were exposed to short electrical pulses of varying width and magnitude under "charge injection" conditions. After a pulse, the transtissue potential decayed with two distinct time constants, one short (tau approximately 0.3 ms) and the other longer (tau L approximately 2 ms). Above thresholds for the pulse magnitude and for the pulse width tau L decreased significantly, with progressively smaller tau L as the pulse magnitude and width increased. The postpulse potential, delta Utissue (t), and resistance, Rtissue, also decreased progressively. The tissue subsequently recovered to its original resistance and open circuit potential, delta U tissue,oc, within 2-3 min after a pulse. At that time another pulse experiment could be carried out, demonstrating repeatability and reversibility. No significant permanent changes in Rtissue and delta Utissue,oc were found. This is interpreted as avoidance of significant tissue damage. Taken together, these dramatic phenomena are characteristic of the reversible electrical breakdown previously observed in charge injection experiments with artificial planar bilayer membranes and with isolated cell membranes by similar very short pulses. The present experiments therefore demonstrate that electroporation can be repeatedly caused and observed in a viable tissue without apparent damage.

Electroporation: The population distribution of macromolecular uptake and shape changes in red blood cells following a single 50 μs square wave pulse

We describe a method of using flow cytometry for determining the distribution of electroporation effects within a statistically significant cell population. Here we illustrate basic aspects of the method by investigating the electroporation of red blood cells, which have been widely used by others in previous investigations of electroporation, including studies of reversible electrical breakdown, and molecular uptake or release associated with a transient high permeability state. We make two measurements on each cell in a population of 10,000 or more cells: (1) light scatter to indicate changes in cell morphology, and (2) fluorescence to determine the uptake of a fluorescence-labeled macromolecule (FITC-dextran; 70,000 dalton). Computer processing of the single cell data allows construction of statistical distributions which reveal how electroporation occurs within a large cell population. Using this method we find that after a single 50 μs square pulse of optimal magnitude about 30% have formed spherical ghosts because of electroporation, and that two distinct ghost subpopulations occur. One subpopulation (about 10% of analyzed cells) has negligible uptake, while the second subpopulation (about 20%) consists of ghosts which have taken up significant amounts of the test macromolecule. Two interesting findings are the high frequency-of-occurrence of electroporation due to a single, optimal pulse, and the implication, because of the two distinct ghost subpopulations, that there is a significant variation in pore sizes.

Electroporation: the population distribution of macromolecular uptake and shape changes in red blood cells following a single 50 μs square wave pulse

We describe a method of using flow cytometry for determining the distribution of electroporation effects within a statistically significant cell population. Here we illustrate basic aspects of the method by investigating the electroporation of red blood cells, which have been widely used by others in previous investigations of electroporation, including studies of reversible electrical breakdown, and molecular uptake or release associated with a transient high permeability state. We make two measurements on each cell in a population of 10,000 or more cells: (1) light scatter to indicate changes in cell morphology, and (2) fluorescence to determine the uptake of a fluorescence-labeled macromolecule (FITC-dextran; 70,000 dalton). Computer processing of the single cell data allows construction of statistical distributions which reveal how electroporation occurs within a large cell population. Using this method we find that after a single 50 μs square pulse of optimal magnitude about 30% have formed spherical ghosts because of electroporation, and that two distinct ghost subpopulations occur. One subpopulation (about 10% of analyzed cells) has negligible uptake, while the second subpopulation (about 20%) consists of ghosts which have taken up significant amounts of the test macromolecule. Two interesting findings are the high frequency-of-occurrence of electroporation due to a single, optimal pulse, and the implication, because of the two distinct ghost subpopulations, that there is a significant variation in pore sizes.

Reversible electrical breakdown of lipid bilayers: formation and evolution of pores

The mechanism of reversible electric breakdown of lipid membranes is studied. The following stages of the process of pore development are substantiated. Hydrophobic pores are formed in the lipid bilayer by spontaneous fluctuations. If these water-filled defects extend to a radius of 0.3 to 0.5 nm, a hydrophilic pore is formed by reorientation of the lipid molecules. This process is favoured by a potential difference across the membrane. The conductivity of the pores depends on membrane voltage, and the type of this dependence changes with the radius of the pore. Hydrophilic pores of an effective radius of 0.6 up to more than 1 nm are formed, which account for the membrane conductivity increase observed. The characteristic times of changes in average radius and number of pores during the voltage pulse and after it are investigated.