Sensitivity of transmembrane voltage induced by applied electric fields—A theoretical analysis

A High-Voltage Pulse Generation Instrument for Electrochemotherapy Method

Electrochemotherapy (ECT) is a new method that uses anticancer drugs delivery with intensive electrical pulses. Recently, ECT as the treatment method can be applied for basal cell and spin cell carcinoma and for melanoma metastases. In this paper, a new design of a high voltage pulse generator with variable output pulse magnitude, repetition frequency, and pulse duration is presented. Furthermore, it has presented the basic theory of ECT, the importance/advantages against other cancer treatment methods, the theoretical model of electroporated cell membrane, and the application ways of ECT method. The proposed instrument is suitable for effective drug delivery of ECT in anti-tumor treatment. Also, this instrument can be applied to gene transfer/therapy methods.

Numerical study of the electrical conductivity and polarization in a suspension of spherical cells

The spatial distribution of electrical potential and current in a suspension of spherical cells under an applied electric field was numerically obtained using the equivalent circuit method (ECM). The effect of the proximity of the cells was studied in a set of simulations where the volumetric fraction varied from 0.24 to 0.66. The results show that the transmembrane potential for cells in the suspension is lower than the theoretically predicted value for a single dielectric membrane under a uniform electric field. It was also observed that as the volumetric fraction is increased, the transmembrane potential on the pole of the cells decreases linearly. Furthermore, the conductivity of the suspension was also observed to be a function of the volumetric fraction and this result is in a good agreement with the Maxwell's model for spherical particles suspended in a volume conductor.

Model of a confined spherical cell in uniform and heterogeneous applied electric fields

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).

Numerical Determination of Transmembrane Voltage Induced on Irregularly Shaped Cells

The paper presents an approach that reduces several difficulties related to the determination of induced transmembrane voltage (ITV) on irregularly shaped cells. We first describe a method for constructing realistic models of irregularly shaped cells based on microscopic imaging. This provides a possibility to determine the ITV on the same cells on which an experiment is carried out, and can be of considerable importance in understanding and interpretation of the data. We also show how the finite-thickness, nonzero-conductivity membrane can be replaced by a boundary condition in which a specific surface conductivity is assigned to the interface between the cell interior (the cytoplasm) and the exterior. We verify the results obtained using this method by a comparison with the analytical solution for an isolated spherical cell and a tilted oblate spheroidal cell, obtaining a very good agreement in both cases. In addition, we compare the ITV computed for a model of two irregularly shaped CHO cells with the ITV measured on the same two cells by means of a potentiometric fluorescent dye, and also with the ITV computed for a simplified model of these two cells.

Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields

Several reports have recently been published on effects of very short and intense electric pulses on cellular organelles; in a number of cases, the cell plasma membrane appeared to be affected less than certain organelle membranes, whereas with longer and less intense pulses the opposite is the case. The effects are the consequence of the voltages induced on the membranes, and in this article we investigate the conditions under which the induced voltage on an organelle membrane could exceed its counterpart on the cell membrane. This would provide a possible explanation of the observed effects of very short pulses. Frequency-domain analysis yields an insight into the dependence of the voltage inducement on the electric and geometric parameters characterizing the cell and its vicinity. We show that at sufficiently high field frequencies, for a range of parameter values the voltage induced on the organelle membrane can indeed exceed the voltage induced on the cell membrane. Particularly, this can occur if the organelle interior is electrically more conductive than the cytosol, or if the organelle membrane has a lower dielectric permittivity than the cell membrane, and we discuss the plausibility of these conditions. Time-domain analysis is then used to determine the courses of the voltage induced on the membranes by pulses with risetimes and durations in the nanosecond range. The particularly high resting voltage in mitochondria, to which the induced voltage superimposes, could contribute to the explanation why these organelles are the primary target of many observed effects.

Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.

Cell membrane fluidity related to electroporation and resealing

In this paper, we report the results of a systematic attempt to relate the intrinsic plasma membrane fluidity of three different cell lines to their electroporation behaviour, which consists of reversible and irreversible electroporation. Apart from electroporation behaviour of given cell lines the time course required for membrane resealing was determined in order to distinguish the effect of resealing time from the cell's ability to survive given electric pulse parameters. Reversible, irreversible electroporation and membrane resealing were then related to cell membrane fluidity as determined by electron paramagnetic resonance spectroscopy and computer characterization of membrane domains. We found that cell membrane fluidity does not have significant effect on reversible electroporation although there is a tendency for the voltage required for reversible electroporation to increase with increased membrane fluidity. Cell membrane fluidity, however, may affect irreversible electroporation. Nevertheless, this effect, if present, is masked with different time courses of membrane resealing found for the different cell lines studied. The time course of cell membrane resealing itself could be related to the cell's ability to survive.

Mechanisms of cell membrane electropermeabilization: a minireview of our present (lack of ?) knowledge

Cell electropulsation is routinely used in cell Biology for protein, RNA or DNA transfer. Its clinical applications are under development for targeted drug delivery and gene therapy. Nevertheless, the molecular mechanisms supporting the induction of permeabilizing defects in the membrane assemblies remain poorly understood. This minireview describes the present state of the investigations concerning the different steps in the reversible electropermeabilization process. The different hypotheses, which were proposed to give a molecular description of the membrane events, are critically discussed. Other possibilities are then given. The need for more basic research on the associated loss of cohesion of the membrane appears as a conclusion.

Techniques of signal generation required for electropermeabilization. Survey of electropermeabilization devices

Electropermeabilization is a phenomenon that transiently increases permeability of the cell plasma membrane. In the state of high permeability, the plasma membrane allows ions, small and large molecules to be introduced into the cytoplasm, although the cell plasma membrane represents a considerable barrier for them in its normal state. Besides introduction of various substances to cell cytoplasm, permeabilized cell membrane allows cell fusion or insertion of proteins to the cell membrane. Efficiency of all these applications strongly depends on parameters of electric pulses that are delivered to the treated object using specially developed electrodes and electronic devices--electroporators. In this paper we present and compare most commonly used techniques of signal generation required for electropermeabilization. In addition, we present an overview of commercially available electroporators and electroporation systems that were described in accessible literature.

Electric Fields Within Cells as a Function of Membrane Resistivity—A Model Study

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.

Osmotically induced membrane tension facilitates the triggering of living cell electropermeabilization

Very little is known about the molecular mechanisms supporting living cell membrane electropermeabilization. This concept is based on the local membrane permeability induced by cell exposure to brief and intense external electric field pulses. During the electric field application, an electro-induced membrane electric potential difference is created that is locally associated with the dielectric properties of the plasma membrane. When the new membrane electric potential difference locally reaches a critical value, a local alteration of the membrane structure is induced and leads to reversible permeabilization. In our study, we attempted to determine whether mechanical tension could modulate the triggering of membrane electropermeabilization. Change in lateral tension of Chinese Hamster Ovary cell membrane has been osmotically induced. Cell electropermeabilization was performed in the minute time range after the osmotic stress, i.e., before the regulatory volume decrease being activated by the cell. Living cell electropermeabilization was analyzed on cell population using flow cytometry. We observed that electropermeabilization triggering was significantly facilitated when the lateral membrane tension was increased. The main conclusion is that the critical value of transmembrane potential needed to trigger membrane electropermeabilization, is smaller when the membrane is under lateral mechanical constraint. This supports the hypothesis that both mechanical and electrical constraints play a key role in transient membrane destabilization.

Role of pulse shape in cell membrane electropermeabilization

The role of the amplitude, number, and duration of unipolar rectangular electric pulses in cell membrane electropermeabilization in vitro has been the subject of several studies. With respect to unipolar rectangular pulses, an improved efficiency has been reported for several modifications of the pulse shape: separate bipolar pulses, continuous bipolar waveforms, and sine-modulated pulses. In this paper, we present the results of a systematic study of the role of pulse shape in permeabilization, cell death, and molecular uptake. We have first compared the efficiency of 1-ms unipolar pulses with rise- and falltimes ranging from 2 to 100 micros, observing no statistically significant difference. We then compared the efficiency of triangular, sine, and rectangular bipolar pulses, and finally the efficiency of sine-modulated unipolar pulses with different percentages of modulation. We show that the results of these experiments can be explained on the basis of the time during which the pulse amplitude exceeds a certain critical value.

Effective conductivity of a suspension of permeabilized cells: a theoretical analysis

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.

Quantitative model of small molecules uptake after in vitro cell electropermeabilization

Electropermeabilization of the cell membrane is a phenomenon caused by exposure of the cell to electric pulses. Permeabilization depends on pulse duration, pulse amplitude, the number of pulses delivered, and also on other experimental conditions. With these parameters properly chosen, the process of permeabilization is reversible and cells return to their normal physiological state. This article describes the development of a model of diffusion-driven transmembrane transport of small molecules caused by electropermeabilization. The process of permeabilization is divided into a short permeabilizing phase that takes place during the pulse, and a longer resealing phase that begins after the end of the pulse. Because both phases of permeabilization are important for uptake of molecules into cells, most of the effort is focused on the optimization of parameters that influence the flow between intracellular and extracellular space. The model describes well the transmembrane transport caused by electropermeabilization, allowing to study the uptake of molecules as a function of elapsed time, voltage and pulse duration. In addition, our results show that the shapes of the curves of cell permeabilization and survival as functions of pulse amplitude can to a large extent be explained by cell size distribution.

Electroporation: theory and methods, perspectives for drug delivery, gene therapy and research

Electroporation designates the use of short high-voltage pulses to overcome the barrier of the cell membrane. By applying an external electric field, which just surpasses the capacitance of the cell membrane, transient and reversible breakdown of the membrane can be induced. This transient, permeabilized state can be used to load cells with a variety of different molecules, either through simple diffusion in the case of small molecules, or through electrophoretically driven processes allowing passage through the destabilized membrane--as is the case for DNA transfer. Initially developed for gene transfer, electroporation is now in use for delivery of a large variety of molecules: From ions to drugs, dyes, tracers, antibodies, and oligonucleotides to RNA and DNA. Electroporation has proven useful both in vitro, in vivo and in patients, where drug delivery to malignant tumours has been performed. Whereas initial electroporation procedures caused considerable cell damage, developments over the past decades have led to sophistication of equipment and optimization of protocols. The electroporation procedures used in many laboratories could be optimized with limited effort. This review (i) outlines the theory of electroporation, (ii) discusses factors of importance for optimization of electroporation protocols for mammalian cells, (iii) addresses particular concerns when using electroporation in vivo, e.g. effects on blood flow and considerations regarding choice of electrodes, (iv) describes DNA electrotransfer with emphasis on use in the in vivo setting, and (v) sums up data on safety and efficacy of electroporation used to enhance delivery of chemotherapy to tumours in cancer patients.

Factors controlling electropermeabilisation of cell membranes

Electric field pulses are a new approach for drug and gene delivery for cancer therapy. They induce a localized structural alteration of cell membranes. The associated physical mechanisms are well explained and can be safely controlled. A position dependent modulation of the membrane potential difference is induced when an electric field is applied to a cell. Electric field pulses with an overcritical intensity evoke a local membrane alteration. A free exchange of hydrophilic low molecular weight molecules takes place across the membrane. A leakage of cytosolic metabolites and a loading of polar drugs into the cytoplasm are obtained. The fraction of the cell surface which is competent for exchange is a function of the field intensity. The level of local exchange is strongly controlled by the pulse duration and the number of successive pulses. The permeabilised state is long lived. Its lifetime is under the control of the cumulated pulse duration. Cell viability can be preserved. Gene transfer is obtained but its mechanism is not a free diffusion. Plasmids are electrophoretically accumulated against the permeabilised cell surface and form aggregates due to the field effect. After the pulses, several steps follow: translocation to the cytoplasm, traffic to the nucleus and expression. Molecular structural and metabolic changes in cells remain mostly poorly understood. Nevertheless, while most studies were established on cells in culture (in vitro), recent experiments show that similar effects are obtained on tissue (in vivo). Transfer remains controlled by the physical parameters of the electrical treatment.

Investigating membrane breakdown of neuronal cells exposed to nonuniform electric fields by finite-element modeling and experiments

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.

Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system

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.

Effective conductivity of cell suspensions

Using finite-element method (FEM) effective conductivity of cell suspension was calculated for different cell volume fractions and membrane conductivities. Cells were modeled as spheres having equivalent conductivity and were organized in cubic lattices, layers and clusters. The results were compared to different analytical expressions for effective conductivity and they showed that Maxwell theory is valid also for higher volume fractions.

The influence of medium conductivity on electropermeabilization and survival of cells in vitro

Electropermeabilization and cell death caused by the exposure to high voltage electric pulses depends on the parameters of pulses, as well as the composition of the extracellular medium. We studied the influence of extracellular conductivity on electropermeabilization and survival of cells in vitro. For this purpose, we used a physiological medium with a conductivity of 1.6 S/m and three artificial media with conductivities of 0.14, 0.005, and 0.001 S/m. Measurements of pH, osmolarity, and cell diameter were made to estimate possible side effects of the media on the cells. Our study shows that the percentage of surviving cells increases with the decreasing medium conductivity, while the percentage of electropermeabilized cells remains unaffected. Our results show that cell survival in experiments involving electropermeabilization can be improved by decreasing the medium conductivity. To provide an interpretation of experimental results, we have theoretically estimated the resting transmembrane voltage, the induced transmembrane voltage, the time constant of the voltage inducement, and heating of the cell suspension for each of the media used. These calculations imply that for accurate interpretation of experimental results, both the induced and the resting transmembrane voltage must be considered, taking into account the conductivity and the ionic composition of the extracellular medium.

Cell membrane electropermeabilization by symmetrical bipolar rectangular pulses. Part I. Increased efficiency of permeabilization

The paper presents a comparative study of electropermeabilization of cells in suspension by unipolar and symmetrical bipolar rectangular electric pulses. While the parameters of electropermeabilization by unipolar pulses have been investigated extensively both in cell suspensions and in tissues, studies using bipolar pulses have been rare, partly due to the lack of commercially available bipolar pulse generators with pulse parameters suitable for electropermeabilization. We have developed a high-frequency amplifier and coupled it to a function generator to deliver high-voltage pulses of programmable shapes. With symmetrical bipolar pulses, the pulse amplitude required for the permeabilization of 50% of the cells was found to be approximately 20% lower than with unipolar pulses, while no statistically significant difference was detected between the pulse amplitudes causing the death of 50% of the cells. Bipolar pulses also led to more than 20% increase in the uptake of lucifer yellow. We show that these results have a theoretical background, because bipolar pulses (i) counterbalance the asymmetry of the permeabilized areas at the poles of the cell which is introduced by the resting transmembrane voltage, and (ii) increase the odds of permeabilization of cells having a nonspherical shape or a nonhomogeneous membrane. If similar results are also obtained in tissues, bipolar pulse generators could in due course gain a wide, or even a predominant use in cell membrane electropermeabilization.

A validated model of in vivo electric field distribution in tissues for electrochemotherapy and for DNA electrotransfer for gene therapy

Permeabilising electric pulses can be advantageously used for DNA electrotransfer in vivo for gene therapy, as well as for drug delivery. In both cases, it is essential to know the electric field distribution in the tissues: the targeted tissue must be submitted to electric field intensities above the reversible permeabilisation threshold (to actually permeabilise it) and below the irreversible permeabilisation threshold (to avoid toxic effects of the electric pulses). A three-dimensional finite element model was built. Needle electrodes of different diameters were modelled by applying appropriate boundary conditions in corresponding grid points of the model. The observations resulting from the numerical calculations, like the electric field distribution dependence on the diameter of the electrodes, were confirmed in appropriate experiments in rabbit liver tissue. The agreement between numerical predictions and experimental observations validated our model. Then it was possible to make the first precise determination of the magnitude of the electric field intensity for reversible (362+/-21 V/cm, mean +/- S.D.) and for irreversible (637+/-43 V/cm) permeabilisation thresholds of rabbit liver tissue in vivo. Therefore the maximum of induced transmembrane potential difference in a single cell of the rabbit liver tissue can be estimated to be 394+/-75 and 694+/-136 mV, respectively, for reversible and irreversible electroporation threshold. These results carry important practical implications.

Analytical description of transmembrane voltage induced by electric fields on spheroidal cells

An analytical description of transmembrane voltage induced on spherical cells was determined in the 1950s, and the tools for numerical assessment of transmembrane voltage induced on spheroidal cells were developed in the 1970s. However, it has often been claimed that an analytical description is unattainable for spheroidal cells, while others have asserted that even if attainable, it does not befit the reality due to the nonuniform membrane thickness, which is unrealistic but inevitable in spheroidal geometry. In this paper we show that for all spheroidal cells, membrane thickness is irrelevant to the induced transmembrane voltage under the assumption of a nonconductive membrane, which was also applied in the derivation of Schwan's equation. We then derive the analytical description of transmembrane voltage induced on prolate and oblate spheroidal cells. The final result, which we cast from spheroidal into more familiar spherical coordinates, represents a generalization of Schwan's equation to all spheroidal cells (of which spherical cells are a special case). The obtained expression is easy to apply, and we give a simple example of such application. We conclude the study by analyzing the variation of induced transmembrane voltage as a spheroidal cell is stretched by the field, performing one study at a constant membrane surface area, and another at a constant cell volume.

Second-order model of membrane electric field induced by alternating external electric fields

With biological cells exposed to ac electric fields below 100 kHz, external field is amplified in the cell membrane by a factor of several thousands (low-frequency plateau), while above 100 kHz, this amplification gradually decreases with frequency. Below 10 MHz, this situation is well described by the established first-order theory which treats the cytoplasm and the external medium as pure conductors. At higher frequencies, capacitive properties of the cytoplasm and the external medium become increasingly important and thus must be accounted for. This leads to a broader, second-order model, which is treated in detail in this paper. Unlike the first-order model, this model shows that above 10 MHz, the membrane field amplification stops decreasing and levels off again in the range of tens (high-frequency plateau). Existence of the high-frequency plateau could have an important impact on present theories of high-frequency electric fields effects on cells and their membranes.

In vivo electroporation of skeletal muscle: threshold, efficacy and relation to electric field distribution

In vivo electroporation is increasingly being used to deliver small molecules as well as DNA to tissues. The aim of this study was to quantitatively investigate in vivo electroporation of skeletal muscle, and to determine the threshold for permeabilization. We designed a quantitative method to study in vivo electroporation, by measuring uptake of (51)Cr-EDTA. As electrode configuration influences electric field (E-field) distribution, we developed a method to calculate this. Electroporation of mouse muscle tissue was investigated using either external plate electrodes or internal needle electrodes placed 4 mm apart, and eight pulses of 99 micros duration at a frequency of 1 Hz. The applied voltage to electrode distance ratio was varied from 0 to 2.0 kV/cm. We found that: (1) the threshold for permeabilization of skeletal muscle tissue using short duration pulses was at an applied voltage to electrode distance ratio of 0.53 kV/cm (+/-0.03 kV/cm), corresponding to an E-field of 0.45 kV/cm; (2) there were two phases in the uptake of (51)Cr-EDTA, the first indicating increasing permeabilization and the second indicating beginning irreversible membrane damage; and (3) the calculated E-field distribution was more homogeneous for plate than for needle electrodes, which was reflected in the experimental results.

Elementary [Ca2+]i signals generated by electroporation functionally mimic those evoked by hormonal stimulation

The generation of oscillations and global Ca2+ waves relies on the spatio-temporal recruitment of elementary Ca2+ signals, such as 'Ca2+ puffs'. Each elementary signal contributes a small amount of Ca2+ into the cytoplasm, progressively promoting neighboring Ca2+ release sites into an excitable state. Previous studies have indicated that increases in frequency or amplitude of such hormone-evoked elementary Ca2+ signals are necessary to initiate Ca2+ wave propagation. In the present study, an electroporation device was used to rapidly and reversibly permeabilize the plasma membrane of HeLa cells and to allow a limited influx of Ca2+. With low field intensities (100-500 V/cm), brief (50-100 micros) electroporation triggered localized Ca2+ signals that resembled hormone-evoked Ca2+ puffs, but not global signals. With such low intensity electroporative pulses, the Ca2+ influx component was usually undetectable, confirming that the electroporation-induced local signals represented Ca2+ puffs arising from the opening of intracellular Ca2+ release channels. Increasing either the frequency at which low-intensity electroporative pulses were applied, or the intensity of a single electroporative pulse (>500 V/cm), resulted in caffeine-sensitive regenerative Ca2+ waves. We suggest that Ca2+ puffs caused by electroporation functionally mimic hormone-evoked elementary events and can activate global Ca2+ signals if they provide a sufficient trigger.

Electropermeabilization of cell membranes

A position dependent modulation of the membrane potential difference is induced when an electric field is applied to a cell. When cells are submitted to short lived electric field pulses with an overcritical intensity, a local membrane alteration is induced, which may reseal. Its molecular definition remains unknown. A free exchange of hydrophilic molecules takes place across the membrane. A leakage of cytosolic metabolites is present. However, a loading of polar drugs into the cytoplasm is obtained. A short description of the processes affecting the cell membrane organization is given. Lipids appear as the primary target of the field effect as in the case of liposomes. Nevertheless membrane proteins appear to be affected by a direct or by a back effect. The permeabilized state is long lived. The cell metabolism plays indeed a critical role in the recovery. The cell viability can be nevertheless preserved.

The importance of electric field distribution for effective in vivo electroporation of tissues

Cells exposed to short and intense electric pulses become permeable to a number of various ionic molecules. This phenomenon was termed electroporation or electropermeabilization and is widely used for in vitro drug delivery into the cells and gene transfection. Tissues can also be permeabilized. These new approaches based on electroporation are used for cancer treatment, i.e., electrochemotherapy, and in vivo gene transfection. In vivo electroporation is thus gaining even wider interest. However, electrode geometry and distribution were not yet adequately addressed. Most of the electrodes used so far were determined empirically. In our study we 1) designed two electrode sets that produce notably different distribution of electric field in tumor, 2) qualitatively evaluated current density distribution for both electrode sets by means of magnetic resonance current density imaging, 3) used three-dimensional finite element model to calculate values of electric field for both electrode sets, and 4) demonstrated the difference in electrochemotherapy effectiveness in mouse tumor model between the two electrode sets. The results of our study clearly demonstrate that numerical model is reliable and can be very useful in the additional search for electrodes that would make electrochemotherapy and in vivo electroporation in general more efficient. Our study also shows that better coverage of tumors with sufficiently high electric field is necessary for improved effectiveness of electrochemotherapy.