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

Modulation of cell function by electric field: a high-resolution analysis

Regulation of cell function by a non-thermal, physiological-level electromagnetic field has potential for vascular tissue healing therapies and advancing hybrid bioelectronic technology. We have recently demonstrated that a physiological electric field (EF) applied wirelessly can regulate intracellular signalling and cell function in a frequency-dependent manner. However, the mechanism for such regulation is not well understood. Here, we present a systematic numerical study of a cell-field interaction following cell exposure to the external EF. We use a realistic experimental environment that also recapitulates the absence of a direct electric contact between the field-sourcing electrodes and the cells or the culture medium. We identify characteristic regimes and present their classification with respect to frequency, location, and the electrical properties of the model components. The results show a striking difference in the frequency dependence of EF penetration and cell response between cells suspended in an electrolyte and cells attached to a substrate. The EF structure in the cell is strongly inhomogeneous and is sensitive to the physical properties of the cell and its environment. These findings provide insight into the mechanisms for frequency-dependent cell responses to EF that regulate cell function, which may have important implications for EF-based therapies and biotechnology development.

3D nanochannel electroporation for high-throughput cell transfection with high uniformity and dosage control

Of great interest to modern medicine and biomedical research is the ability to inject individual target cells with the desired genes or drug molecules. Some advances in cell electroporation allow for high throughput, high cell viability, or excellent dosage control, yet no platform is available for the combination of all three. In an effort to solve this problem, here we show a "3D nano-channel electroporation (NEP) chip" on a silicon platform designed to meet these three criteria. This NEP chip can simultaneously deliver the desired molecules into 40,000 cells per cm(2) on the top surface of the device. Each 650 nm pore aligns to a cell and can be used to deliver extremely small biological elements to very large plasmids (>10 kbp). When compared to conventional bulk electroporation (BEP), the NEP chip shows a 20 fold improvement in dosage control and uniformity, while still maintaining high cell viability (>90%) even in cells such as cardiac cells which are characteristically difficult to transfect. This high-throughput 3D NEP system provides an innovative and medically valuable platform with uniform and reliable cellular transfection, allowing for a steady supply of healthy, engineered cells.

Response of single cell with acute angle exposed to an external electric field

It is known that the electric field incurs effects on the living cells. Predicting the response of single cell or multilayer cells to induced alternative or static eclectic field has permanently been a challenge. In the present study a first order single cell with acute angle under the influence of external electric field is considered. The cell division stage or the special condition of reshaping is modelled with a cone being connected. In the case of cell divisions, anaphase, it can be considered with two cones that connected nose-to-nose. Each cone consists of two regions. The first is the membrane modelled with a superficial layer, and the second is cytoplasm at the core. A Laplace equation is written for this model and the distribution of its electric field is a sharp point in the single cell for which an acute angle model is calculated.

Neuron matters: electric activation of neuronal tissue is dependent on the interaction between the neuron and the electric field

In laboratory research and clinical practice, externally-applied electric fields have been widely used to control neuronal activity. It is generally accepted that neuronal excitability is controlled by electric current that depolarizes or hyperpolarizes the excitable cell membrane. What determines the amount of polarization? Research on the mechanisms of electric stimulation focus on the optimal control of the field properties (frequency, amplitude, and direction of the electric currents) to improve stimulation outcomes. Emerging evidence from modeling and experimental studies support the existence of interactions between the targeted neurons and the externally-applied electric fields. With cell-field interaction, we suggest a two-way process. When a neuron is positioned inside an electric field, the electric field will induce a change in the resting membrane potential by superimposing an electrically-induced transmembrane potential (ITP). At the same time, the electric field can be perturbed and re-distributed by the cell. This cell-field interaction may play a significant role in the overall effects of stimulation. The redistributed field can cause secondary effects to neighboring cells by altering their geometrical pattern and amount of membrane polarization. Neurons excited by the externally-applied electric field can also affect neighboring cells by ephaptic interaction. Both aspects of the cell-field interaction depend on the biophysical properties of the neuronal tissue, including geometric (i.e., size, shape, orientation to the field) and electric (i.e., conductivity and dielectricity) attributes of the cells. The biophysical basis of the cell-field interaction can be explained by the electromagnetism theory. Further experimental and simulation studies on electric stimulation of neuronal tissue should consider the prospect of a cell-field interaction, and a better understanding of tissue inhomogeneity and anisotropy is needed to fully appreciate the neural basis of cell-field interaction as well as the biological effects of electric stimulation.

Vesicle biomechanics in a time-varying magnetic field

Background

Cells exhibit distortion when exposed to a strong electric field, suggesting that the field imposes control over cellular biomechanics. Closed pure lipid bilayer membranes (vesicles) have been widely used for the experimental and theoretical studies of cellular biomechanics under this electrodeformation. An alternative method used to generate an electric field is by electromagnetic induction with a time-varying magnetic field. References reporting the magnetic control of cellular mechanics have recently emerged. However, theoretical analysis of the cellular mechanics under a time-varying magnetic field is inadequate.

We developed an analytical theory to investigate the biomechanics of a modeled vesicle under a time-varying magnetic field. Following previous publications and to simplify the calculation, this model treated the inner and suspending media as lossy dielectrics, the membrane thickness set at zero, and the electric resistance of the membrane assumed to be negligible. This work provided the first analytical solutions for the surface charges, electric field, radial pressure, overall translational forces, and rotational torques introduced on a vesicle by the time-varying magnetic field. Frequency responses of these measures were analyzed, particularly the frequency used clinically by transcranial magnetic stimulation (TMS).

Results

The induced surface charges interacted with the electric field to produce a biomechanical impact upon the vesicle. The distribution of the induced surface charges depended on the orientation of the coil and field frequency. The densities of these charges were trivial at low frequency ranges, but significant at high frequency ranges. The direction of the radial force on the vesicle was dependent on the conductivity ratio between the vesicle and the medium. At relatively low frequencies (<200 KHz), including the frequency used in TMS, the computed radial pressure and translational forces on the vesicle were both negligible.

Conclusions

This work provides an analytical framework and insight into factors affecting cellular biomechanics under a time-varying magnetic field. Biological effects of clinical TMS are not likely to occur via alteration of the biomechanics of brain cells.

Theoretical analyses of cellular transmembrane voltage in suspensions induced by high-frequency fields

A change of the transmembrane voltage is considered to cause biophysical and biochemical responses in cells. The present study focuses on the cellular transmembrane voltage (Δφ) induced by external fields. We detail analytical equations for the transmembrane voltage induced by external high-frequency (above the relaxation frequency of the cell membrane) fields on cells of a spherical shape in suspensions and layers. At direct current (DC) and low frequencies, the cell membrane was assumed to be non-conductive under physiologic conditions. However, with increasing frequency, the permittivity of the cytoplasm/extracellular medium and conductivity of the membrane must be accounted for. Our main work is to extend application of the analytical solution of Δφ to the high-frequency range. We first introduce the transmembrane voltage generated by DC and low-frequency exposures on a single cell. Then, we focus on cell suspensions exposed to high-frequency fields. Using the effective medium theory and the reasonable assumption, the approximate analytical solution of Δφ on cells in suspensions and layers can be derived. Phenomenological effective medium theory equations cannot be used to calculate the local electric field of cell suspensions, so we raised a possible solution based on the Bergman theory.

Direct drug cocktail analyses using microscale vortex-assisted electroporation

Combination therapy has become one of the leading approaches for treating complex diseases because it coadministers clinically proven drugs to concurrently target multiple signaling pathways of diseased cells. Identification of synergic drug combinations at their respective effective doses without unwanted accumulative side effects is the key to success for such therapy. In this work, we demonstrate the feasibility of the vortex-assisted microfluidic electroporation system for direct drug cocktail analyses where drug substances were individually delivered into cytosols in a sequential and dosage-controlled manner. Through quantitative analyses, the synergic combinational dosage ratios of the chemotherapeutic drug and the anticancer flavonoid were identified. When integrated with high-throughput label-free rare cell purification techniques, the presented system has the potential for development of personalized medicines as the system would be capable of comprehensively assessing drug combinations directly on patients' cellular samples.

Cell-cell proximity effects in multi-cell electroporation

We report a fundamental study of how the electropermeabilization of a cell is affected by nearby cells. Previous researchers studying electroporation of dense suspensions of cells have observed, both theoretically and experimentally, that such samples cannot be treated simply as collections of independent cells. However, the complexity of those systems makes quantitative modeling difficult. We studied the change in the minimum applied electric field, the threshold field, required to affect electropermeabilization of a cell due to the presence of a second cell. Experimentally, we used optical tweezers to accurately position two cells in a custom fluidic electroporation device and measured the threshold field for electropermeabilization. We also captured video of the process. In parallel, finite element simulations of the electrostatic potential distributions in our systems were generated using the 3-layer model and the contact resistance methods. Reasonably good agreement with measurements was found assuming a model in which changes in a cell's threshold field were predicted from the calculated changes in the maximum voltage across the cell's membrane induced by the presence of a second cell. The threshold field required to electroporate a cell is changed ∼5%-10% by a nearby, nearly touching second cell. Cells aligned parallel to the porating field shield one another. Those oriented perpendicular to the field enhance the applied field's effect. In addition, we found that the dynamics of the electropermeabilization process are important in explaining observations for even our simple two-cell system.

Sequential multi-molecule delivery using vortex-assisted electroporation

We developed an on-chip microscale electroporation system that enables sequential delivery of multiple molecules with precise and independent dosage controllability into pre-selected identical populations of target cells. The ability to trap cells with uniform size distribution contributed to enhanced molecular delivery efficiency and cell viability. Additionally, the system provides real-time monitoring ability of the entire delivery process, allowing timely and independent modification of cell- and molecule-specific electroporation parameters. The precisely controlled amount of inherently membrane-impermeant molecules was transferred into human cancer cells by varying electric field strengths and molecule injection durations. The proposed microfluidic electroporation system's improved viability and comparable gene transfection efficiency to that of commercial systems suggest that the current system has great potential to expand the research fields that on-chip electroporation techniques can be used in.

Planning of electroporation-based treatments using Web-based treatment-planning software

Electroporation-based treatment combining high-voltage electric pulses and poorly permanent cytotoxic drugs, i.e., electrochemotherapy (ECT), is currently used for treating superficial tumor nodules by following standard operating procedures. Besides ECT, another electroporation-based treatment, nonthermal irreversible electroporation (N-TIRE), is also efficient at ablating deep-seated tumors. To perform ECT or N-TIRE of deep-seated tumors, following standard operating procedures is not sufficient and patient-specific treatment planning is required for successful treatment. Treatment planning is required because of the use of individual long-needle electrodes and the diverse shape, size and location of deep-seated tumors. Many institutions that already perform ECT of superficial metastases could benefit from treatment-planning software that would enable the preparation of patient-specific treatment plans. To this end, we have developed a Web-based treatment-planning software for planning electroporation-based treatments that does not require prior engineering knowledge from the user (e.g., the clinician). The software includes algorithms for automatic tissue segmentation and, after segmentation, generation of a 3D model of the tissue. The procedure allows the user to define how the electrodes will be inserted. Finally, electric field distribution is computed, the position of electrodes and the voltage to be applied are optimized using the 3D model and a downloadable treatment plan is made available to the user.

Nanofountain probe electroporation (NFP-E) of single cells

The ability to precisely deliver molecules into single cells is of great interest to biotechnology researchers for advancing applications in therapeutics, diagnostics, and drug delivery toward the promise of personalized medicine. The use of bulk electroporation techniques for cell transfection has increased significantly in the past decade, but the technique is nonspecific and requires high voltage, resulting in variable efficiency and low cell viability. We have developed a new tool for electroporation using nanofountain probe (NFP) technology, which can deliver molecules into cells in a manner that is highly efficient and gentler to cells than bulk electroporation or microinjection. Here we demonstrate NFP electroporation (NFP-E) of single HeLa cells within a population by transfecting them with fluorescently labeled dextran and imaging the cells to evaluate the transfection efficiency and cell viability. Our theoretical analysis of the mechanism of NFP-E reveals that application of the voltage creates a localized electric field between the NFP cantilever tip and the region of the cell membrane in contact with the tip. Therefore, NFP-E can deliver molecules to a target cell with minimal effect of the electric potential on the cell. Our experiments on HeLa cells confirm that NFP-E offers single cell selectivity, high transfection efficiency (>95%), qualitative dosage control, and very high viability (92%) of transfected cells.

Modeling of electric field distribution in tissues during electroporation

BACKGROUND

Electroporation based therapies and treatments (e.g. electrochemotherapy, gene electrotransfer for gene therapy and DNA vaccination, tissue ablation with irreversible electroporation and transdermal drug delivery) require a precise prediction of the therapy or treatment outcome by a personalized treatment planning procedure. Numerical modeling of local electric field distribution within electroporated tissues has become an important tool in treatment planning procedure in both clinical and experimental settings. Recent studies have reported that the uncertainties in electrical properties (i.e. electric conductivity of the treated tissues and the rate of increase in electric conductivity due to electroporation) predefined in numerical models have large effect on electroporation based therapy and treatment effectiveness. The aim of our study was to investigate whether the increase in electric conductivity of tissues needs to be taken into account when modeling tissue response to the electroporation pulses and how it affects the local electric distribution within electroporated tissues.

METHODS

We built 3D numerical models for single tissue (one type of tissue, e.g. liver) and composite tissue (several types of tissues, e.g. subcutaneous tumor). Our computer simulations were performed by using three different modeling approaches that are based on finite element method: inverse analysis, nonlinear parametric and sequential analysis. We compared linear (i.e. tissue conductivity is constant) model and non-linear (i.e. tissue conductivity is electric field dependent) model. By calculating goodness of fit measure we compared the results of our numerical simulations to the results of in vivo measurements.

RESULTS

The results of our study show that the nonlinear models (i.e. tissue conductivity is electric field dependent: σ(E)) fit experimental data better than linear models (i.e. tissue conductivity is constant). This was found for both single tissue and composite tissue. Our results of electric field distribution modeling in linear model of composite tissue (i.e. in the subcutaneous tumor model that do not take into account the relationship σ(E)) showed that a very high electric field (above irreversible threshold value) was concentrated only in the stratum corneum while the target tumor tissue was not successfully treated. Furthermore, the calculated volume of the target tumor tissue exposed to the electric field above reversible threshold in the subcutaneous model was zero assuming constant conductivities of each tissue.Our results also show that the inverse analysis allows for identification of both baseline tissue conductivity (i.e. conductivity of non-electroporated tissue) and tissue conductivity vs. electric field (σ(E)) of electroporated tissue.

CONCLUSION

Our results of modeling of electric field distribution in tissues during electroporation show that the changes in electrical conductivity due to electroporation need to be taken into account when an electroporation based treatment is planned or investigated. We concluded that the model of electric field distribution that takes into account the increase in electric conductivity due to electroporation yields more precise prediction of successfully electroporated target tissue volume. The findings of our study can significantly contribute to the current development of individualized patient-specific electroporation based treatment planning.

Micro-/nanofluidics based cell electroporation

Non-viral gene delivery has been extensively explored as the replacement for viral systems. Among various non-viral approaches, electroporation has gained increasing attention because of its easy operation and no restrictions on probe or cell type. Several effective systems are now available on the market with reasonably good gene delivery performance. To facilitate broader biological and medical applications, micro-/nanofluidics based technologies were introduced in cell electroporation during the past two decades and their advances are summarized in this perspective. Compared to the commercially available bulk electroporation systems, they offer several advantages, namely, (1) sufficiently high pulse strength generated by a very low potential difference, (2) conveniently concentrating, trapping, and regulating the position and concentration of cells and probes, (3) real-time monitoring the intracellular trafficking at single cell level, and (4) flexibility on cells to be transfected (from single cell to large scale cell population). Some of the micro-devices focus on cell lysis or fusion as well as the analysis of cellular properties or intracellular contents, while others are designed for gene transfection. The uptake of small molecules (e.g., dyes), DNA plasmids, interfering RNAs, and nanoparticles has been broadly examined on different types of mammalian cells, yeast, and bacteria. A great deal of progress has been made with a variety of new micro-/nanofluidic designs to address challenges such as electrochemical reactions including water electrolysis, gas bubble formation, waste of expensive reagents, poor cell viability, low transfection efficacy, higher throughput, and control of transfection dosage and uniformity. Future research needs required to advance micro-/nanofluidics based cell electroporation for broad life science and medical applications are discussed.

Synchronization of neuron population subject to steady DC electric field induced by magnetic stimulation

Electric fields, which are ubiquitous in the context of neurons, are induced either by external electromagnetic fields or by endogenous electric activities. Clinical evidences point out that magnetic stimulation can induce an electric field that modulates rhythmic activity of special brain tissue, which are associated with most brain functions, including normal and pathological physiological mechanisms. Recently, the studies about the relationship between clinical treatment for psychiatric disorders and magnetic stimulation have been investigated extensively. However, further development of these techniques is limited due to the lack of understanding of the underlying mechanisms supporting the interaction between the electric field induced by magnetic stimulus and brain tissue. In this paper, the effects of steady DC electric field induced by magnetic stimulation on the coherence of an interneuronal network are investigated. Different behaviors have been observed in the network with different topologies (i.e., random and small-world network, modular network). It is found that the coherence displays a peak or a plateau when the induced electric field varies between the parameter range we defined. The coherence of the neuronal systems depends extensively on the network structure and parameters. All these parameters play a key role in determining the range for the induced electric field to synchronize network activities. The presented results could have important implications for the scientific theoretical studies regarding the effects of magnetic stimulation on human brain.

Microcapillary-assisted dielectrophoresis for single-particle positioning

Here, we demonstrate microcapillary-assisted dielectrophoresis (μC-DEP), a new capability for precise positioning of particles or biological cells in applications such as dynamic assays. The method largely derives from a need to evade the challenges faced with hydrodynamic trapping of particles or cells at microcapillaries typically realized through brief application of suction. Microcapillaries here serve a dual purpose by firstly squeezing field lines to define localized positive DEP traps and then establishing an exclusive access to the trapped cell for probing. Strength of the traps is presented through numerical results at various excitation frequencies. Their effectiveness is shown experimentally against relevant solution conductivities using 10 μm polystyrene microspheres. Usefulness of the method for positioning individual cells is demonstrated via experimental results on cell viability and single-cell impedance spectroscopy.

Molecular-level characterization of lipid membrane electroporation using linearly rising current

We present experimental and theoretical results of electroporation of small patches of planar lipid bilayers by means of linearly rising current. The experiments were conducted on ~120-μm-diameter patches of planar phospholipid bilayers. The steadily increasing voltage across the bilayer imposed by linearly increasing current led to electroporation of the membrane for voltages above a few hundred millivolts. This method shows new molecular mechanisms of electroporation. We recorded small voltage drops preceding the breakdown of the bilayer due to irreversible electroporation. These voltage drops were often followed by a voltage re-rise within a fraction of a second. Modeling the observed phenomenon by equivalent electric circuits showed that these events relate to opening and closing of conducting pores through the bilayer. Molecular dynamics simulations performed under similar conditions indicate that each event is likely to correspond to the opening and closing of a single pore of about 5 nm in diameter, the conductance of which ranges in the 100-nS scale. This combined experimental and theoretical investigation provides a better quantitative characterization of the size, conductance and lifetime of pores created during lipid bilayer electroporation. Such a molecular insight should enable better control and tuning of electroporation parameters for a wide range of biomedical and biotechnological applications.

Treatment planning of electroporation-based medical interventions: electrochemotherapy, gene electrotransfer and irreversible electroporation

In recent years, cancer electrochemotherapy (ECT), gene electrotransfer for gene therapy and DNA vaccination (GET) and tissue ablation with irreversible electroporation (IRE) have all entered clinical practice. We present a method for a personalized treatment planning procedure for ECT, GET and IRE, based on medical image analysis, numerical modelling of electroporation and optimization with the genetic algorithm, and several visualization tools for treatment plan assessment. Each treatment plan provides the attending physician with optimal positions of electrodes in the body and electric pulse parameters for optimal electroporation of the target tissues. For the studied case of a deep-seated tumour, the optimal treatment plans for ECT and IRE require at least two electrodes to be inserted into the target tissue, thus lowering the necessary voltage for electroporation and limiting damage to the surrounding healthy tissue. In GET, it is necessary to place the electrodes outside the target tissue to prevent damage to target cells intended to express the transfected genes. The presented treatment planning procedure is a valuable tool for clinical and experimental use and evaluation of electroporation-based treatments.

System for measuring planar lipid bilayer properties

We present a system for measuring planar lipid bilayer properties. The system is composed of a control unit, an output stage, an LCR meter, pumps for filling reservoirs, a bath with temperature regulation and a measurement chamber with four electrodes. The planar lipid bilayer is automatically formed using a folding method on apertures of different sizes. The automatization is assured by two syringes, which are clamped in actuators. Actuators are driven and controlled by a control unit via RS-232 communication. The temperature of the planar lipid bilayer can be regulated between 15 and 55 °C. The regulation is assured by insertion of the measurement chamber into the temperature-regulated bath. Different shapes of voltage- or current-clamp signals can be applied to the planar lipid bilayer. By measuring the response of the planar lipid bilayer to the applied signal, the capacitance and breakdown voltage of the planar lipid bilayer can be determined. The cutoff frequencies of the system output stage for voltage- and current-clamp methods are 11 and 17 kHz, respectively.

Nanochannel electroporation delivers precise amounts of biomolecules into living cells

Many transfection techniques can deliver biomolecules into cells, but the dose cannot be controlled precisely. Delivering well-defined amounts of materials into cells is important for various biological studies and therapeutic applications. Here, we show that nanochannel electroporation can deliver precise amounts of a variety of transfection agents into living cells. The device consists of two microchannels connected by a nanochannel. The cell to be transfected is positioned in one microchannel using optical tweezers, and the transfection agent is located in the second microchannel. Delivering a voltage pulse between the microchannels produces an intense electric field over a very small area on the cell membrane, allowing a precise amount of transfection agent to be electrophoretically driven through the nanochannel, the cell membrane and into the cell cytoplasm, without affecting cell viability. Dose control is achieved by adjusting the duration and number of pulses. The nanochannel electroporation device is expected to have high-throughput delivery applications.

Identification of In Vitro Electropermeabilization Equivalent Pulse Protocols

Exposure of cells to an external sufficiently strong electric field results in the formation of pores across the membrane. This phenomenon, termed electropermeabilization, permits the transport of poorly permeant molecules into cytosol. In clinical practice, cell membrane permeabilization for drug electrotransfer is achieved using the ESOPE pulse protocol (1000 V/cm, 8 pulses, 100 μs, 5 kHz). The aim of this study was to investigate several combinations of electric field amplitude and pulse number able to induce electropermeabilization as the one observed when the ESOPE protocol was applied. Decreasing electric field amplitudes (1000 to 300 V/cm) in combination with increasing number of pulses (8 to 320) were applied to in vitro MG63 cells. Propidium iodide and Calcein blue AM uptake were used to evaluate cell electropermeabilization and viability. Results showed that the threshold of local electric field needed to obtain electropermeabilization decreased exponentially with increasing the number of pulses delivered (r2 50.92, p < 0.0001). The absorbed dose threshold was dependent on the number of pulses for each voltage applied (r2 50.96, p < 0.0001). In conclusion, the possibility of applying an increased number of pulses rather than increasing the electric field amplitude to perform electropermeabilization, may become an important tool for electropermeabilization - related clinical applications.

Equivalent pulse parameters for electroporation

Electroporation-based applications require the use of specific pulse parameters for a successful outcome. When recommended values of pulse parameters cannot be set, similar outcomes can be obtained by using equivalent pulse parameters. We determined the relations between the amplitude and duration/number of pulses resulting in the same fraction of electroporated cells. Pulse duration was varied from 150 ns to 100 ms, and the number of pulses from 1 to 128. Fura 2-AM was used to determine electroporation of cells to Ca(2+). With longer pulses or higher number of pulses, lower amplitudes are needed for the same fraction of electroporated cells. The expression derived from the model of electroporation could describe the measured data on the whole interval of pulse durations. In a narrower range (0.1-100 ms), less complex, logarithmic or power functions could be used instead. The relation between amplitude and number of pulses could best be described with a power function or an exponential function. We show that relatively simple two-parameter power or logarithmic functions are useful when equivalent pulse parameters for electroporation are sought. Such mathematical relations between pulse parameters can be important in planning of electroporation-based treatments, such as electrochemotherapy and nonthermal irreversible electroporation.

Theoretical and experimental analysis of electroporated membrane conductance in cell suspension

An intense electric field can be applied to increase the membrane conductance G(m) and consequently, the conductivity of cell suspension. This phenomenon is called electroporation. This mechanism is used in a wide range of medical applications, genetic engineering, and therapies. Conductivity measurements of cell suspensions were carried out during application of electric fields from 40 to 165 kV/m. Experimental results were analyzed with two electroporation models: the asymptotic electroporation model was used to estimate G(m) at the beginning and at the end of electric field pulse, and the extended Kinosita electroporation model to increase G(m) linearly in time. The maximum G(m) was 1-7 × 10(4) S/m(2), and the critical angle (when the G(m) is insignificant) was 50°-65°. In addition, the sensitivity of electroporated membrane conductance to extracellular and cytoplasmatic conductivity and cell radius has been studied. This study showed that external conductivity and cell radius are important parameters affecting the pore-opening phenomenon. However, if the cell radius is larger than 7 μm in low conductivity medium, the cell dimensions are not so important.

Influence of uncertain electrical properties on the conditions for the onset of electroporation in an eukaryotic cell

A detailed numerical investigation concerning the influence on the electrical response of an eukaryotic cell model due to the variations of the conductivity and permittivity of the plasma and nuclear membranes is carried out by means of a vertex analysis. The dynamics of three cell performances, the voltages across the external and the nuclear membrane, and the pores density are analyzed by adopting a novel FEM-based model coupled with the nonlinear equation describing the electroporation (EP) phenomenon. The variations of the electrical and morphological performances, when the cell is stressed by a nonideal step input, are studied in three interesting regimes, i.e., at the nominal threshold for the onset of EP, and when the applied stress is over or under the EP threshold. The performed numerical analysis puts in evidence that, around the nominal EP threshold, uncertainties may lead to an indeterminate state of the plasma membrane, whereas the other two regimes remain well definite.

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.

Frequency-dependent interaction of ultrashort E-fields with nociceptor membranes and proteins

We examined the influence of ultrashort pulses (USP) on sensory neurons. Single and high frequency bursts of 12 ns E-fields were presented to rat skin nociceptors that expressed distinct combinations of voltage-sensitive proteins. A single E-field pulse produced action potentials in all nociceptor subtypes at a critical threshold (E(c) ) of 403 V/cm. When configured into high frequency bursts, USP charge integrated to reduce the action potential threshold in a frequency and burst duration-dependent manner with E(c) as low as 16 V/cm (4000 Hz, 25 ms burst). There was no evidence of electroporation at field intensities near the E(c) for nociceptor activation. USP bursts activated a late, persistent Ca(++) flux that was identified as a dantrolene-sensitive Ca(++) -induced Ca(++) release (CICR). Influx of Ca(++) into the cell was required for the CICR and resulted in a reduction of the single pulse E(c) by about 50%.

Induced transmembrane voltage and its correlation with electroporation-mediated molecular transport

Exposure of a cell to an electric field results in inducement of a voltage across its membrane (induced transmembrane voltage, DeltaPsi (m)) and, for sufficiently strong fields, in a transient increase of membrane permeability (electroporation). We review the analytical, numerical and experimental methods for determination of DeltaPsi (m) and a method for monitoring of transmembrane transport. We then combine these methods to investigate the correlation between DeltaPsi (m) and molecular transport through an electroporated membrane for isolated cells of regular and irregular shapes, for cells in dense suspensions as well as for cells in monolayer clusters. Our experiments on isolated cells of both regular and irregular shapes confirm the theoretical prediction that the highest absolute values of DeltaPsi (m) are found in the membrane regions facing the electrodes and that electroporation-mediated transport is confined to these same regions. For cells in clusters, the location of transport regions implies that, at the field strengths sufficient for electroporation, the cells behave as electrically insulated (i.e., as individual) cells. In contrast, with substantially weaker, nonelectroporating fields, potentiometric measurements show that the cells in these same clusters behave as electrically interconnected cells (i.e., as one large cell). These results suggest that sufficiently high electric fields affect the intercellular pathways and thus alter the electric behavior of the cells with respect to their normal physiological state.

Micronozzle array enhanced sandwich electroporation of embryonic stem cells

Electroporation is one of the most popular nonviral gene transfer methods for embryonic stem cell transfection. Bulk electroporation techniques, however, require a high electrical field and provide a nonuniform electrical field distribution among randomly distributed cells, leading to limited transfection efficiency and cell viability, especially for a low number of cells. We present here a membrane sandwich electroporation system using a well-defined micronozzle array. This device is capable of transfecting hundred to millions of cells with good performance. The ability to treat a small number of cells (i.e., a hundred) offers great potential to work with hard-to-harvest patient cells for pharmaceutical kinetic studies. Numerical simulation of the initial transmembrane potential distribution and propidium iodide (PI) dye diffusion experiments demonstrated the advantage of highly focused and localized electric field strength provided by the micronozzle array over conventional bulk electroporation.

The current-voltage relation for electropores with conductivity gradients

In electroporation, an electric field transiently permeabilizes the cell membrane to gain access to the cytoplasm, and to deliver active agents such as DNA, proteins, and drug molecules. Past work suggests that the permeabilization is caused by the formation of aqueous, conducting pores on the lipid membrane, which are also known as electropores. The current-voltage relation across the membrane-bound pores is critical for understanding and predicting electroporation. In this work, we solve the Nernst-Planck equations in a geometry encompassing an isolated electropore to investigate this relation. In particular, we study cases where the intra- and extracellular electrical conductivities differ. We first derive an analytical solution, which is subsequently validated with a direct numerical simulation using a finite volume method. The main result of the current work is a formula for the effective pore resistance as a function of the pore radius, the membrane thickness, and the intra- and extracellular conductivities. This formula can be incorporated into whole-cell or planar-membrane electroporation models for system-level prediction and understanding.

Transmembrane potential induced on the internal organelle by a time-varying magnetic field: a model study

BACKGROUND

When a cell is exposed to a time-varying magnetic field, this leads to an induced voltage on the cytoplasmic membrane, as well as on the membranes of the internal organelles, such as mitochondria. These potential changes in the organelles could have a significant impact on their functionality. However, a quantitative analysis on the magnetically-induced membrane potential on the internal organelles has not been performed.

METHODS

Using a two-shell model, we provided the first analytical solution for the transmembrane potential in the organelle membrane induced by a time-varying magnetic field. We then analyzed factors that impact on the polarization of the organelle, including the frequency of the magnetic field, the presence of the outer cytoplasmic membrane, and electrical and geometrical parameters of the cytoplasmic membrane and the organelle membrane.

RESULTS

The amount of polarization in the organelle was less than its counterpart in the cytoplasmic membrane. This was largely due to the presence of the cell membrane, which "shielded" the internal organelle from excessive polarization by the field. Organelle polarization was largely dependent on the frequency of the magnetic field, and its polarization was not significant under the low frequency band used for transcranial magnetic stimulation (TMS). Both the properties of the cytoplasmic and the organelle membranes affect the polarization of the internal organelle in a frequency-dependent manner.

CONCLUSIONS

The work provided a theoretical framework and insights into factors affecting mitochondrial function under time-varying magnetic stimulation, and provided evidence that TMS does not affect normal mitochondrial functionality by altering its membrane potential.

Variability of the minimal transmembrane voltage resulting in detectable membrane electroporation

We present a study of the variability of the minimal transmembrane voltage resulting in detectable electroporation of the plasma membrane of spherical and irregularly shaped CHO cells (we denote this voltage by ITVc). Electroporation was detected by monitoring the influx of Ca(2+), and the transmembrane voltage was computed on a 3D finite-elements model of each cell constructed from its cross-section images. We found that ITVc was highly variable, particularly in irregularly shaped cells, where it ranged from 512-1028 mV. We show that this range is much too large to be an artifact due to numerical errors and experimental inaccuracies, implying that for cells of the same type and exposed to the same number of pulses with the same duration, the value of ITVc can differ considerably from one cell to another. We also observed that larger cells are in many cases characterized by a higher ITVc than a smaller one. This is in qualitative agreement with the reports that higher membrane curvature facilitates electroporation, but quantitative considerations suggest that the observed variability of ITVc cannot be attributed entirely to the differences in membrane curvature.

A time-dependent numerical model of transmembrane voltage inducement and electroporation of irregularly shaped cells

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.

Vascular disrupting action of electroporation and electrochemotherapy with bleomycin in murine sarcoma

Electrochemotherapy has a direct cytotoxic effect on tumour cells, and presumably, a vascular disrupting effect. In this study, on the basis of the prediction of the mathematical model, histological evaluation and physiological measurements of the tumours were carried out to confirm that electroporation and electrochemotherapy of tumours have a vascular disrupting action. In the study, SA-1 solid subcutaneous sarcoma tumours in A/J mice were treated by bleomycin (BLM) given intravenously (1 mg kg(-1)), application of electric pulses (8 pulses, 1040 V, 100 micros, 1 Hz) or a combination of both - electrochemotherapy. The vascular effect was determined by laser Doppler flowmetry, power Doppler ultrasonographic imaging and Patent blue staining. The extent of tumour hypoxia was determined immunohistochemically by hypoxia marker pimonidazole and partial pressure of oxygen (pO(2)) in tumours by electron paramagnetic resonance oximetry. Electrochemotherapy with BLM induced good antitumour effect with 22 days, tumour growth delay and 38% tumour cures. The application of electric pulses to the tumours induced instant but transient tumour blood flow reduction (for 70%) that was recovered in 24 h. During this tumour blood flow reduction, we determined an increase in hypoxic tumour area for up to 30%, which was also reflected in reduced tumour oxygenation (for 70%). According to the described mathematical model, endothelial cells lining in tumour blood vessels are exposed to a approximately 40% higher electric field than the surrounding tumour cells, and therefore easily electroporated, allowing access of high BLM concentration to the cytosol. Consequently, electrochemotherapy has, besides the immediate vascular disrupting action, also a delayed one (after 24 h), as a consequence of endothelial cell swelling and apoptosis demonstrated by extensive tumour necrosis, tumour hypoxia, prolonged reduction of tumour blood flow and significant tumour growth delay, and tumour cures. Our results demonstrate that in addition to the well-established direct cytotoxic effect on tumour cells, electrochemotherapy also has an indirect vascular disrupting action resulting altogether in extensive tumour cell necrosis leading to complete regression of tumours.

Effects of oscillatory electric fields on internal membranes: an analytical model

We derive an analytical model of the potential differences induced across plasma and internal organelle membranes in suspended cells exposed to oscillatory electric fields. Multiple shells are modeled using iterative applications of the single-shell calculation with mobile charges. This work is motivated, in part, by recent results suggesting the ability to use alternating current (ac) fields to noninvasively monitor enzyme activity within internal membranes, particularly the mitochondrial electron transport chain. Previous work, on induced transmembrane voltages in cells subjected to ac fields, has mainly been limited to oscillatory potentials across the plasma membrane. Here we first develop a three-membrane model, consisting of a plasma membrane surrounding inner and outer membranes representing an internal organelle, such as a mitochondrion. Frequency-dependent transmembrane potentials are modeled for spherical, weakly conducting membrane shells enclosing a conductive cytoplasm surrounding an idealized internal organelle. We then use a two-shell model to simulate induced ac membrane potentials of a suspended isolated mitochondrion in which the outer membrane is usually much more permeable than the inner membrane.

Feasibility study for cell electroporation detection and separation by means of dielectrophoresis

Electroporation is a phenomenon during which exposure of a cell to high voltage electric pulses results in a significant increase in its membrane permeability. Aside from the fact that after the electroporation the cell membrane becomes more permeable, the cells' geometrical and electrical properties change considerably. These changes enable use of the force on dielectric particles exposed to non-uniform electric field (dielectrophoresis) for separation of non-electroporated and electroporated cells. This paper reports the results of an attempt to separate non-electroporated and electroporated cells by means of dielectrophoresis. In several experiments we managed to separate the non-electroporated and electroporated cells suspended in a medium with conductivity 0.174 S/m by exposing them to a non-uniform electric field at a frequency of 2 MHz. The behaviour of electroporated cells exposed to dielectrophoresis raises the presumption that in addition to conductivity, considerable changes in membrane permittivity occur after the electroporation.

Transmembrane potential induced in a spherical cell model under low-frequency magnetic stimulation

Time-varying magnetic fields can induce electric fields in the neuronal tissue, a phenomenon that has been recently explored in clinical applications such as peripheral nerve stimulation and transcranial magnetic stimulation. Although the transmembrane potential induced during direct electric stimulation has already been the subject of a number of theoretical studies, an analytical solution for the magnetically induced transmembrane potential change is still unavailable. In addition, although several studies have analyzed the impact of stimulation parameters, including stimulation intensity and frequency, as well as coil design and position, on the amount of tissue polarization, the effects of tissue non-homogeneity on cell polarization have not been fully elucidated. In this study, we have derived an analytical expression for the transmembrane potential induced by a low-frequency magnetic field in a spherical neuronal structure. This model is representative of a spherical cell body or any neuronal structure of a similar shape. The model cell is located in an extracellular medium and possesses a low-conductive membrane and an internal cytoplasm. These three regions represent the basic tissue non-homogeneity of a neuron at a microscopic level. The sensitivity of the induced transmembrane potential to the coil position and to the geometrical and electrical parameters of the model structure was studied in a broad physiologically relevant range. Our results demonstrate that the structure is regionally polarized, with the pattern of polarization depending on the relative positioning between the model cell and the stimulation coil. In addition, both the geometrical and electrical parameters of the structure affect the amount of polarization. These results may be generalized to other neuronal tissues that possess similar non-homogenous properties, but different shapes, such as an axon. Our results support the idea that aside from coil design and position, tissue non-homogeneity could play an important role in determining the effects of magnetic stimulation.

Numerical calculations of single-cell electroporation with an electrolyte-filled capillary

An electric field is focused on one cell in single-cell electroporation. This enables selective electroporation treatment of the targeted cell without affecting its neighbors. While factors that lead to membrane permeation are the same as in bulk electroporation, quantitative description of the single-cell experiments is more complicated. This is due to the fact that the potential distribution cannot be solved analytically. We present single-cell electroporation with an electrolyte-filled capillary modeled with a finite element method. Potential is calculated in the capillary, the solution surrounding the cell, and the cell. The model enables calculation of the transmembrane potential and the fraction of the cell membrane that is above the critical electroporation potential. Electroporation at several cell-to-tip distances of human lung carcinoma cells (A549) stained with ThioGlo-1 demonstrated membrane permeation at distances shorter than approximately 7.0 microm. This agrees well with the model's prediction that a critical transmembrane potential of 250 mV is achieved when the capillary is approximately 6.5 microm or closer to the cell. Simulations predict that at short cell-to-tip distances, the transmembrane potential increases significantly while the total area of the cell above the critical potential increases only moderately.

Electropermeabilization of dense cell suspensions

This paper investigates the influence of cell density on cell membrane electropermeabilization. The experiments were performed on dense cell suspensions (up to 400 x 10(6) cells/ml), which represent a simple model for studying electropermeabilization of tissues. Permeabilization was assayed with a fluorescence test using Propidium iodide to obtain the mean number of permeabilized cells (i.e. fluorescence positive) and the mean fluorescence per cell (amount of loaded dye). In our study, as the cell density increased from 10 x 10(6) to 400 x 10(6) cells/ml, the fraction of permeabilized cells decreased by approximately 50%. We attributed this to the changes in the local electric field, which led to a decrease in the amplitude of the induced transmembrane voltage. To obtain the same fraction of cell permeabilization in suspensions with 10 x 10(6) and 400 x 10(6) cells/ml, the latter suspension had to be permeabilized with higher pulse amplitude, which is in qualitative agreement with numerical computations. The electroloading of the cells also decreased with cell density. The decrease was considerably larger than expected from the differences in the permeabilized cell fractions alone. The additional decrease in fluorescence was mainly due to cell swelling after permeabilization, which reduced extracellular dye availability to the permeabilized membrane and hindered the dye diffusion into the cells. We also observed that resealing of cells appeared to be slower in dense suspensions, which can be attributed to cell swelling resulting from electropermeabilization.